ABSTRACT Title of Document: NUCLEATE POOL BOILING CHARACTERISTICS FROM A HORIZONTAL MICROHEATER ARRAY Christopher Henry, Ph.D., 2005 Directed By: Associate Professor, Jungho Kim, Department of Mechanical Engineering Pool boiling heat transfer measurements from different heater sizes and shapes were obtained in low-g (0.01 g) and high-g (1.7 g) aboard the NASA operated KC-135 aircraft. Boiling on 4 square heater arrays of different size (0.65 mm 2 , 2.62 mm 2 , 7.29 mm 2 , 49 mm 2 ) was investigated. The heater arrays consist of 96 independent square heaters that were maintained at an isothermal boundary condition using control circuitry. A fractional factorial experimental method was designed to investigate the effects of bulk liquid subcooling, wall superheat, gravitational level, heater size and aspect ratio, and dissolved gas concentration on pool boiling behavior. In high-g, pool boiling behavior was found to be consistent with classical models for nucleate pool boiling in 1-g. For heater sizes larger than the isolated bubble departure diameter predicted from the Fritz correlation, the transport process was dominated by the ebullition cycle and the primary mechanisms for heat transfer were transient conduction and microconvection to the rewetting liquid in addition to latent heat transfer. For heater sizes smaller than this value, the boiling process is dominated by surface tension effects which can cause the formation of a single primary bubble that does not depart the heater surface and a strong reduction in heat transfer. In low-g, pool boiling performance is always dominated by surface tension effects and two mechanisms were identified to dominate heat and mass transport: 1) satellite bubble coalescence with the primary bubble which tends to occur at lower wall superheats and 2) thermocapillary convection at higher wall superheats and higher bulk subcoolings. Satellite bubble coalescence was identified to be the CHF mechanism under certain conditions. Thermocapillary convection caused a dramatic enhancement in heat transfer at higher subcoolings and is modeled analytically. Lastly, lower dissolved gas concentrations were found to enhance the heat transfer in low-g. At higher dissolved gas concentrations, bubbles grow larger and dryout a larger portion of the heater surface. NUCLEATE POOL BOILING CHARACTERISTICS FROM A HORIZONTAL MICROHEATER ARRAY By Christopher Douglas Henry Thesis or Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2005 Advisory Committee: Associate Professor Jungho Kim, Chair Professor Marino Di Marzo Professor James Duncan Associate Professor Greg Jackson Associate Professor Gary Pertmer ? Copyright by Christopher Douglas Henry 2005 ii Dedication Dedicated to my grandfather Dr. Victor Charles Dawson Urbanus et Instructus iii Acknowledgements I am forever grateful to my parents, Richard and Joan Henry, for their unfading support and encouragement throughout my academic career. Their strength, hard work, determination, courage, and love is a constant reminder of the triumph of the human spirit and is a testament to their character and integrity. They have provided me with tremendous opportunity without which this work would not have been possible. This effort is built on the solid foundation created by previous researchers including John Benton, Toby Rule, and Dr. Kim. I would like to sincerely thank my advisor, Dr. Jungho Kim, for his insight into the physical process, and guidance. His constant motivation enabled me to see this effort through to fruition. The personal and professional growth that I experienced while working for him were the result of opportunity and scholarly discourse and I am grateful for his generosity. I would like to thank my colleagues, Johnathan Coursey, Fatih Demiray, Dr. Sakamoto, and all of my peers in the Phase Change Heat Transfer Lab for their friendship and encouragement. The countless inquiries and arguments in which we engaged were enlightening and invaluable to the progress and quality of this endeavor. This project was supported by the Office of Biological and Physical Research at NASA Headquarters. I would like to personally thank John McQuillen, Jerry Myers, John Yaniec, and the entire team at the microgravity office for their assistance and guidance during flight weeks aboard the KC-135. iv Table of Contents DEDICATION ................................................................................................................. II ACKNOWLEDGEMENTS ...........................................................................................III TABLE OF CONTENTS ...............................................................................................IV TABLE OF FIGURES....................................................................................................IX NOMENCLATURE.......................................................................................................XX CHAPTER 1: STATE OF THE ART IN POOL BOILING........................................ 1 1.1 INTRODUCTION / MOTIVATION ........................................................................... 1 1.2 CLASSICAL BOILING LITERATURE REVIEW ..................................................... 4 1.2.1 Terrestrial Boiling .......................................................................................................................4 1.2.2 Terrestrial Pool Boiling Enhancement ......................................................................................15 1.2.3 High-g Boiling ...........................................................................................................................17 1.2.4 Summary of Classical Boiling....................................................................................................20 1.3 MICROGRAVITY BOILING.................................................................................... 21 1.3.1 Thermocapillary Convection .....................................................................................................28 1.3.2 Summary ....................................................................................................................................32 1.4 PROBLEM STATEMENT / RESEARCH OBJECTIVE........................................... 36 CHAPTER 2: EXPERIMENTAL METHOD............................................................. 38 2.1 INTRODUCTION...................................................................................................... 38 2.2 EXPERIMENTAL METHODOLOGY ..................................................................... 39 2.3 PARAMETRICALLY INVESTIGATED FACTORS............................................... 41 2.3.1 Gravitational Environment ........................................................................................................41 2.3.2 Fluid...........................................................................................................................................46 2.3.3 Wall Temperature / Heat Flux Measurement.............................................................................54 2.3.4 Heater Geometry........................................................................................................................66 2.3.5 Bulk Liquid Subcooling..............................................................................................................69 2.4 DATA ACQUISITION .............................................................................................. 70 2.5 IMAGING & PIV SYSTEM ...................................................................................... 70 2.6 SYSTEM INTEGRATION ........................................................................................ 73 2.7 EXPERIMENTAL TEST MATRIX .......................................................................... 76 2.8 EXPERIMENTAL SUMMARY................................................................................ 77 CHAPTER 3: DATA REDUCTION AND UNCERTAINTY ANALYSIS .............. 79 3.1 PURPOSE .................................................................................................................. 79 3.2 VOLTAGE / POWER MEASUREMENT ................................................................. 79 3.3 SUBSTRATE CONDUCTION.................................................................................. 82 3.3.1 Analytical Model........................................................................................................................82 3.3.2 Numerical Model .......................................................................................................................86 v 3.3.3 Experimental Results .................................................................................................................95 3.4 BOILING HEAT FLUX........................................................................................... 101 3.5 ADDITIONAL PARAMETERS.............................................................................. 103 CHAPTER 4: EXPERIMENTAL HIGH-G BOILING RESULTS........................ 106 4.1 INTRO...................................................................................................................... 106 4.2 BOILING FROM SQUARE HEATERS.................................................................. 106 4.2.1 7 x 7 mm 2 , 96 Heater Array .....................................................................................................106 4.2.2 2.7 x 2.7 mm 2 , 96 Heater Array ...............................................................................................111 4.2.3 1.62 x 1.62 mm 2 , 36 Heater Array ...........................................................................................120 4.2.4 0.8 x 0.8 mm 2 , 9 Heater Array .................................................................................................129 4.3 COMPARISON OF BOILING CURVE AND HEATER SIZE RESULTS............. 135 4.4 TRANSITION FROM HIGH TO LOW-G............................................................... 139 4.4.1 Gravitational Effects on the Bubble Departure Diameter .......................................................139 4.5 HIGH-G CONCLUSIONS....................................................................................... 144 CHAPTER 5: LOW-G BOILING RESULTS........................................................... 145 5.1 INTRO...................................................................................................................... 145 5.2 HEATER SIZE EFFECTS ....................................................................................... 146 5.2.1 7 x 7 mm 2 , 96 Heater Array .....................................................................................................146 5.2.2 1.62 x 1.62 mm 2 , 36 Heater Array and 2.7 x 2.7 mm 2 , 96 Heater Array..................................153 5.2.3 0.8 x 0.8 mm 2 (9 heater array).................................................................................................174 5.3 LOW-G HEATER SIZE EFFECTS SUMMARY.................................................... 178 5.4 HEATER ASPECT RATIO EFFECTS .................................................................... 186 5.4.1 Comparison of 2 x 2, 1.4 x 1.4 mm 2 array and Baseline Heater (1.62 x 1.62 mm 2 ) ................186 5.4.2 Aspect Ratio Effects .................................................................................................................188 5.4.3 Summary of Heater Aspect Ratio Effects .................................................................................192 5.5 DISSOLVED GAS EFFECTS ................................................................................. 194 CHAPTER 6: SUMMARY OF GRAVITATIONAL EFFECTS ON POOL BOILING....................................................................................................................... 198 CHAPTER 7: CONTRIBUTIONS AND FUTURE SCOPE ................................... 201 7.1 CONTRIBUTION TO THE STATE OF THE ART................................................. 201 7.2 FUTURE WORK ..................................................................................................... 201 BIBLIOGRAPHY......................................................................................................... 204 APPENDIX A: TEDP REPORT ................................................................................ 209 A.1 CHANGE PAGE ..................................................................................................... 210 A.2 QUICK REFERENCE DATA SHEET.................................................................... 210 A.3 FLIGHT MANIFEST .............................................................................................. 211 A.4 EXPERIMENT BACKGROUND........................................................................... 211 A.5 EXPERIMENT DESCRIPTION............................................................................. 213 A.6 EQUIPMENT DESCRIPTION ............................................................................... 215 A.7 STRUCTURAL VERIFICATION .......................................................................... 218 A.8 ELECTRICAL LOAD ANALYSIS ........................................................................ 225 A.9 LOAD ANALYSIS ................................................................................................. 227 vi A.10 PRESSURE VESSEL CERTIFICATION............................................................. 228 A.11 LASER CERTIFICATION ................................................................................... 230 A.12 PARABOLA DETAILS AN D CREW ASSISTANCE ........................................ 231 A.13 HAZARDS ANALYSIS REPORT GUIDELINES............................................... 232 APPENDIX B: OPTIMIZATION OF A CONSTANT TEMPERATURE MICROHEATER ARRAY FEEDBACK CONTROL CIRCUIT ........................... 233 B.1 PROBLEM DEFINITION....................................................................................... 234 B.2 FORMULATION .................................................................................................... 237 B.2.1 Objective Function 1: Maximize Temperature Resolution .....................................................237 B.2.2 Objective Function 2: Maximize Temperature Range (Single Objective Constr. 4) ..............239 B.2.3 Inequality Constraint 1: Low Temperature Control...............................................................240 B.2.4 Inequality Constraint 2: Minimize Power Dissipation Across Right Side of Bridge..............240 B.2.5 Inequality Constraint 3: Maximum Voltage Drop Across R 1 ..................................................241 B.2.6 Inequality Constraint 5: Op-amp Sensitivity (R 1 Bound) .......................................................242 B.2.7 Inequality Constraints 6-11: Additional Design Variable Bounds.........................................242 B.2.8 Equality Constraint 1: Define Optimized Temperature..........................................................243 B.2.9 Optimization Formulation Summary.......................................................................................244 B.3 ASSUMPTIONS ..................................................................................................... 247 B.4 METHODS, RESULTS, AND DISCUSSION........................................................ 248 B.5 SINGLE OBJECTIVE RESULTS USING ?FMINCON?........................................... 251 B.5.1 Initial Point Sensitivity ............................................................................................................251 B.5.2 Pareto Frontier........................................................................................................................254 B.5.3 Parametric Study.....................................................................................................................258 B.6 EXTERIOR PENALTY METHOD......................................................................... 260 APPENDIX C................................................................................................................ 262 C.1 FINAL HEATER RESISTANCE VALUES ........................................................... 262 C.2 COMPRESSIBLE FLOW THEORY ...................................................................... 264 APPENDIX D: DATA REDUCTION AND OPTIMIZATION PROGRAMS...... 266 D.1 DATA REDUCTION PROGRAMS ....................................................................... 266 D.1.1 Program name: qfluxdet.m ....................................................................................................266 D.2 OPTIMIZATION PROGRAMS.............................................................................. 297 D.2.1 Program name: Fmincon Solution Algorithm........................................................................297 D.2.2 Program name: Exterior Penalty Algorithm..........................................................................301 vii LIST OF TABLES Table 1.1: Capillary length of different fluids (NIST, 2003; 3M)..................................... 7 Table 1.2: Critical wavelength for different fluids. ......................................................... 13 Table 2.1: Experimental factors....................................................................................... 40 Table 2.2: Microgravity platform characteristics (Thomas et al, 2000). ......................... 43 Table 2.3: Gravity level parameter range ......................................................................... 46 Table 2.4: FC-72 saturated fluid properties. .................................................................... 47 Table 2.5: Mass spectrometry results for FC-72 (Hartman, 2004).................................. 52 Table 2.6: Parametrically investigated fluids................................................................... 53 Table 2.7: Heater wall temperature range parametrically investigated. .......................... 66 Table 2.8: Heater sizes parametrically investigated. ....................................................... 67 Table 2.9: Summary of heater aspect ratios investigated. ............................................... 68 Table 2.10: Bulk fluid temperatures investigated............................................................ 69 Table 2.11: Summary of factors parametrically investigated. .......................................... 77 Table 3.1: Numerical substrate conduction results, q sc,i (W/cm 2 ) (3648 nodes).............. 92 Table 3.2: Summary of experimental uncertainties ....................................................... 105 Table 4.1: Condensation heat transfer at two different subcoolings.............................. 129 Table A.1: Description of components in VER............................................................. 215 Table A.2: Maximum Flight Loads ............................................................................... 219 Table A.3: Component weights & moment arms about base ........................................ 219 Table A.4: VER Rack capabilities................................................................................. 219 Table A.5: Wire Gauges ................................................................................................ 226 Table A.6: Components and their power requirements. ................................................ 227 viii Table A.7: Pressure System ............................................................................................ 230 Table B.1: Design parameter values .............................................................................. 251 Table B.2: Current vs. optimal design comparison (single-objective formulation). ..... 256 Table B.3: Pareto results................................................................................................ 257 Table B.4. Exterior penalty and ?fmincon? comparison................................................ 261 ix Table of Figures Figure 1.1: Projected microchip cooling requirements (iNEMI Technology Roadmaps, Dec 2004).................................................................................................................... 2 Figure 1.2: Cooling potential for various processes (iNEMI Technology Roadmaps, Dec 2004). ..........................................................................................................................2 Figure 1.3: Classical nucleate pool boiling curve.............................................................. 5 Figure 1.4: Discrete bubble region (left), vapor mushroom (right), (Courtesy of Gaertner, 1965). ..........................................................................................................................6 Figure 1.5: Microlayer formation beneath bubble ............................................................. 8 Figure 1.6: Forces acting on a bubble.............................................................................. 10 Figure 1.7: Vapor columns formation and the Taylor wavelength, ? d (Courtesy of Van Carey, 1992).............................................................................................................. 11 Figure 1.8: Helmholtz instability mechanisms (Courtesy of Van Carey, 1992).............. 15 Figure 1.9: Single phase thermal boundary layer development at various times. ........... 22 Figure 1.10: Pool boiling from wires (Courtesy of DiMarco and Grassi, 1999).............. 24 Figure 1.11: Comparison between low-g boiling and 1-g boiling predictions (Courtesy of Herman Merte).......................................................................................................... 25 Figure 1.12: Pictures of the Boiling Process in Low Gravity at Various Superheats and Subcoolings (Courtesy of J. Kim)............................................................................. 26 Figure 1.13: Gravitational dependence on CHF (Courtesy of J. Kim). ........................... 27 Figure 1.14: Suspended particle tracing during Marangoni convection, heat flux 6.0x10 5 W/m 2 , 379 K, bulk temp 325K (Courtesy of Wang et al, 2005)............................... 29 Figure 1.15: Thermocapillary flow transport mechanisms.............................................. 31 x Figure 2.1: Block diagram of research process................................................................ 39 Figure 2.2: KC-135 flight profile (left); KC-135 in flight (right) (Courtesy of NASA). 44 Figure 2.3: Gravitational profile for a typical parabola (Courtesy of J. Kim). ................ 44 Figure 2.4: Pictures of the Test Environment .................................................................. 45 Figure 2.5: Theoretically predicted gas concentration during degassing procedure. ...... 50 Figure 2.6: Chamber pressure and gas concentration during degassing procedure......... 51 Figure 2.7: Representative platinum resistance heater array, each heater element = 0.27 mm x 0.27 mm (Courtesy of J. Kim)........................................................................ 55 Figure 2.8: Heater array connected to PCB board (Courtesy of J. Kim)......................... 55 Figure 2.9: Cross-sectional view of heater array (drawing not to scale). ........................ 56 Figure 2.10: Feedback control circuit (Courtesy of J. Kim)............................................ 57 Figure 2.11: Model of lateral conduction between heaters.............................................. 58 Figure 2.12: Comparison between optimized heater temperature resolution and older heater temperature resolution (current design). ........................................................ 62 Figure 2.13: Non-dimensional optimization results......................................................... 63 Figure 2.14: Calibration chamber (left), top view of PCB board inside oven (right)...... 64 Figure 2.15: Comparison between measured and predicted DQ values for a representative heater data set. ................................................................................... 65 Figure 2.16: Relative heater sizes parametrically investigated........................................ 67 Figure 2.17: Heater aspect ratios investigated. ................................................................ 68 Figure 2.18: PIV conceptual drawing. .............................................................................. 72 Figure 2.19: Laser mounting apparatus and CAD rendering........................................... 72 Figure 2.20: Test chamber schematic (Courtesy of J. Kim). ........................................... 73 xi Figure 2.21: 3-D boiling chamber renderings (Courtesy of J. Benton). ........................... 74 Figure 2.22: Photograph of modified test package (the VER) and its components......... 75 Figure 2.23: Assembled test apparatus, high speed camera mounting (left), front view (middle), side view and laser mounting (right)......................................................... 75 Figure 2.24: Fractional factorial experimental test matrix............................................... 76 Figure 3.1: Representative heater resistance temperature dependence (7 x 7 mm 2 heater array, ? = 0.003 o C -1 )................................................................................................ 80 Figure 3.2: Measured ? i values for a representative set of 2.7 x 2.7 mm 2 heater array heaters (? t = 0.002, Kim et al. 2002). ....................................................................... 81 Figure 3.3: Time resolved voltage and heat flux for heater #15, ?T sat = 43?C, T bulk = 28?C, 96 heater array. ............................................................................................... 82 Figure 3.4: 2-D schematic of heat transfer around the 2.7 mm micro-heater array (not to scale). ........................................................................................................................ 83 Figure 3.5: 1-D analytical conduction model for a middle heater (heater 1, Fig. 3.5). ... 85 Figure 3.6: Heater numbers modeled using a numerical 3-D conduction routine........... 86 Figure 3.7: 2-D numerical model of substrate conduction (not to scale)......................... 87 Figure 3.8: 2-D (x-y) non-dimensional temperature distribution within quartz substrate (heater numbers shown in white).............................................................................. 88 Figure 3.9: 3-D non-dimensional temperature distribution within quartz substrate (h b = 10 W/m 2 K, T bulk = 55?C, heater numbers shown in white). ..................................... 89 Figure 3.10: Temperature distribution on the top (y = 0) and bottom (y = 0.5 mm) of the wafer (z = 0, h b = 10 W/m 2 K, T bulk = 55?C). ............................................................ 90 xii Figure 3.11: Heater temperature effects on substrate conduction (h b = 10 W/m 2 K, T bulk = 55?C)......................................................................................................................... 91 Figure 3.12: 2-D grid size effect on numerically calculated substrate conduction heat flux (h b = 10 W/m 2 K, T bulk = 55?C). ................................................................................ 92 Figure 3.13: Effect of h b and T bulk on q sc,i for middle (h-1), edge (h-5) and corner (h-6) heaters (96 heater array, 29 x 31 x 29 grid array)..................................................... 94 Figure 3.14: Comparison of numerical and experimental (method 1)q sc,i for a 96 heater array (T bulk = 55?C, h b = 10 W/m 2 K). ....................................................................... 96 Figure 3.15: Comparison of numerical and experimental (method 1) q sc,i for middle (h-1), edge (h-5), and corner (h-6) heaters (T bulk = 55?C, h b = 10 W/m 2 K). ...................... 97 Figure 3.16: Comparison between analytical, numerical, and experimental q sc,i values. Emphasis should be placed on the large deviations between the experimental and numerical values for higher bulk subcoolings. ......................................................... 98 Figure 3.17: Low-g boiling for extreme subcoolings tested (96 heater array, T h = 100?C). ................................................................................................................................... 99 Figure 3.18: Time resolved gravitational environment for 1 parabola aboard the KC-135, (Courtesy of J. Kim). .............................................................................................. 102 Figure 3.19: Spatially averaged, time resolved heat transfer, 96 heater array, T bulk = 28?C, ?T sat = 32 ?C................................................................................................. 103 Figure 4.1: High-g boiling curves for a 7 x 7 mm 2 heater array.................................... 107 Figure 4.2: 7 x 7 mm 2 array, high-g time averaged spatially resolved heat flux (wall superheat directly below each image and each row corresponds to the bulk subcooling level defined at the far left). ................................................................. 109 xiii Figure 4.3: Predicted vapor column size and spacing from Taylor instability. ............. 110 Figure 4.4: High-g boiling curves for a 2.7 x 2.7 mm 2 heater array.............................. 111 Figure 4.6: bottom and side view images of the boiling process in high-g showing vapor column formation at high wall superheats, ?T sub = 9?C......................................... 114 Figure 4.7: bottom and side view images of the boiling process in high-g showing the formation of 4 primary bubbles at high wall superheats, ?T sub = 31?C. ................ 114 Figure 4.8: Time averaged, spatially resolved heat flux (W/cm 2 ) from a 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 37?C, ?T sub = 9?C. ................................................. 115 Figure 4.9: Time resolved heat transfer from two heaters in the 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 37?C, ?T sub = 9?C. ............................................................ 116 Figure 4.10: Time resolved heat transfer from two heaters in the 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 27?C, ?T sub = 9?C. ............................................................ 117 Figure 4.11: High-g surface averaged heat transfer from interior heaters (1-64) and exterior heaters (65-96), ?T sub = 9?C...................................................................... 119 Figure 4.12: High-g boiling curves for a 1.62 x 1.62 mm 2 heater array........................ 120 Figure 4.14: Primary bubble departure frequency in high-g for a 36 heater array (1.62 x 1.62 mm 2 )................................................................................................................ 123 Figure 4.15: High-g time resolved heat flux from interior heaters in the 1.62 x 1.62 mm 2 array. T wall = 100?C................................................................................................. 124 Figure 4.16: Bottom and side view images of a 36 heater array at low subcoolings, ?T sub = 9?C....................................................................................................................... 126 Figure 4.17: Bottom and side view images of a 36 heater array at high subcoolings, ?Tsub = 30?C.......................................................................................................... 126 xiv Figure 4.18: High-g time averaged boiling heat transfer at high bulk subcooling, ?T sub = 30?C and high wall superheat, ?T sat = 41?C........................................................... 127 Figure 4.19: Boiling heat transfer modes in high-g. ...................................................... 128 Figure 4.20: High-g boiling curves for a 0.81 x 0.81 mm 2 heater array........................ 129 Figure 4.22: High-g boiling images from a 0.81 x 0.81 mm 2 heater array, ?T sub = 9?C. ................................................................................................................................. 131 Figure 4.23: High-g boiling from a 0.81 x 0.81 mm 2 heater array. T bulk = 28?C, ?T sat = 34?C. Colored area represents powered heaters. ................................................... 132 Figure 4.24: High-g surfaced averaged boiling heat flux from representative heaters in the 0.81 x 0.81 mm 2 heater array. ?T sub = 9?C...................................................... 134 Figure 4.25: High-g boiling curves for various square heater arrays. ........................... 136 Figure 4.26: Boiling regime map................................................................................... 138 Figure 4.27: Effect of Heater Size on primary bubble departure frequency (T bulk = 54 o C, T wall = 100 o C).......................................................................................................... 140 Figure 4.28: Effect of the ratio of the Taylor wavelength to heater length on primary bubble departure frequency (T bulk = 54 o C, T wall = 100 o C). ..................................... 140 Figure 5.1: Boiling curves for a 7 x 7 mm 2 heater array in low and high-g. ................. 147 Figure 5.2: Surface resolved time averaged boiling heat transfer in low-g from a 7 x 7 mm 2 heater array..................................................................................................... 148 Figure 5.3: Boiling in high and low-g at low wall superheats, ?T sat = 21?C................. 149 Figure 5.4: Wetted area heat transfer calculation. ......................................................... 152 Figure 5.5: Boiling in low and high-g, ?T sub = 29?C. Top row corresponds to boiling in high-g and bottom row corresponds to boiling in low-g......................................... 152 xv Figure 5.6: Bulk liquid subcooling effect in low-g pool boiling from a 7 x 7 mm 2 array, ?T sat = 32 - 33?C..................................................................................................... 153 Figure 5.7: Low-g boiling curves for a 1.62 x 1.62 mm 2 & 2.7 x 2.7 mm 2 heater arrays. ................................................................................................................................. 154 Figure 5.8: Bottom and side view time averaged low-g boiling images of a 2.7 x 2.7 mm 2 heater array at low subcooling, ?T sub = 6?C........................................................... 154 Figure 5.9: Bottom and side view time averaged low-g boiling images of a 1.62 x 1.62 mm 2 heater array at low subcooling, ?T sub = 6?C. ................................................. 155 Figure 5.10: edge (black,#65-96) and center (gray, #1-64) boiling from a 2.7 x 2.7 mm 2 heater array at low subcooling, ?T sub = 6?C .......................................................... 155 Figure 5.11: Bottom and side view time averaged low-g boiling images of a 1.62 x 1.62 mm 2 , 36 heater array (a) and a 96(b) heater array at high subcooling, ?T sub = 29?C. ................................................................................................................................. 157 Figure 5.12: Time resolved low-g boiling images at CHF, ?T sat =23?C, ?T sub = 29?C for a 2.7 x 2.7 mm 2 heater array. Colored heater corresponds to heater # 8 in the array. ................................................................................................................................. 158 Figure 5.13: Time resolved boiling heat flux from Heater #8 (Fig. 5.10) at CHF, ?T sat = 23?C, ?T sub = 29?C. Fig. 5.10 does not correspond to the time scale in this graph. ................................................................................................................................. 159 Figure 5.14: Time resolved heat transfer for heater #96, 2.7 mm array, at low-g CHF, ?T sat = 23?C, ?T sub = 29?C. .................................................................................... 160 Figure 5.17: Boiling Curves for a 1.62 mm and 2.7 mm heater arrays. ........................ 166 xvi Figure 5.18: Boiling behavior on a 6 x 6 array, 1.62 x 1.62 mm 2 powered array for high- g (top row) and low-g (bottom row). Heat flux is in W/cm 2 . ................................ 166 Figure 5.19: time and surface averaged heat flux from the wetted area in high and low-g T bulk = 28?C, ?T sub ranges from 29-30?C. Wetted heaters are highlighted in black. ................................................................................................................................. 167 Figure 5.20: 2.7 x 2.7 mm 2 heater, T wall =100?C, T bulk = 28?C heater #96 (corner heater). ................................................................................................................................. 168 Figure 5.21: Time resolved boiling images in high-g (b) and low-g (a)........................ 169 Figure 5.22: Wetted area heat flux at various subcoolings for T wall = 90?C.................. 170 Figure 5.23: Low-g time and surface averaged heat transfer from the wetted area for various heater arrays and different wall superheats and subcoolings..................... 171 Figure 5.24: Low-g time and surface averaged heat transfer coefficient from the wetted area.......................................................................................................................... 172 Figure 5.25: Thermocapillary convection velocity analytical model example for following condition, 2.7 x 2.7 mm 2 heater array, ?T sat = 43?C, ?T sub = 29?C....... 173 Figure 5.26: Sensible analytical model for the liquid velocity above the vapor bubble. Example for following condition, 2.7 x 2.7 mm 2 heater array, ?T sat = 43?C, ?T sub = 29?C. ....................................................................................................................... 174 Figure 5.27: Low-g time averaged boiling images from a 0.81 x 0.81 mm 2 heater array. ................................................................................................................................. 175 Figure 5.28: Low-g boiling curves for a 0.81 x 0.81 mm 2 heater array......................... 175 Figure 5.30: Low-g boiling curves for various heater sizes and subcoolings................ 178 xvii Figure 5.31: 2-D axisymmetric model of the thermal boundary layer near the heater surface in low-g....................................................................................................... 180 Figure 5.32: Axisymmetric transient conduction results for a 7 mm heater at t = 1000 s. The x and y axis represent the distance in meters, and the colors represent the temperature, T wall = 100?C. T bulk = 28?C. .............................................................. 181 Figure 5.33: Time resolved boundary layer development. Colors represent temperatures and the vertical axis represents various times......................................................... 182 Figure 5.34: Development of the superheated boundary layer for various heaters (numerical results obtained using FEMLAB)......................................................... 183 Figure 5.35: Primary bubble geometric characteristics for different heaters................. 184 Figure 5.36: Boiling curves for various aspect ratio heaters at various bulk subcoolings. ................................................................................................................................. 187 Figure 5.37: Images of boiling on heaters of various aspect ratio. The superheat at which the images were obtained are listed below each image. Each heater in the array has been shaded according to the time average wall heat transfer................................ 189 Figure 5.38: Time averaged heat transfer from heaters of various aspect ratio, ?T sub = 9?C, ?T sat = 32?C.................................................................................................... 190 Figure 5.39: Time lapse images for the (a) 2x4 and (b) 2x8 arrays at ?T sat = 29.7?C... 191 Figure 5.40: Heater aspect ratio effects on boiling heat transfer in low-g at relatively high wall superheats........................................................................................................ 193 Figure 5.41: Time resolved boiling images from a 7 x 7 mm2 heater array at low and high gas concentrations in the fluid a,b, ?T sub = 28?C. .......................................... 195 xviii Figure 5.42: Boiling curves for a 7 x 7 mm 2 heater array for various dissolved gas concentrations. ........................................................................................................ 196 Figure 5.43: Time resolved boiling in high and low-g for a degassed fluid, C g = 3 ppm. ?T sat = 50 ? 52?C, ?T sub = 28?C. ............................................................................ 197 Figure A.1: Photograph of modified test package (the VER) and its components........ 217 Figure A.2-3: Model of test rig used for stress testing & model of test rig mounted in the frame. ...................................................................................................................... 221 Figure A.4: Testing of model/frame in forward (9 g) direction..................................... 222 Figure A.5: Stress testing in various directions: (a) lateral, and (b) upward. ............... 222 Figure A.6: Laser mounting system: laser mounted block (orange square), micro- positioner (red square), cantilever support (maroon square). ................................. 225 Figure A.7: Electrical schematic.................................................................................... 226 Figure A.8: Low-pressure air cooling jet schematic (Courtesy of J. Benton). ............... 228 Figure A.9: Low-pressure air cooling jet schematic....................................................... 229 Figure A.10: In-flight operational procedure (left), pre-flight routine (right). I have some updated sheets of this to put in the Appendix......................................................... 231 Figure B.1: Feedback Circuit Schematic ....................................................................... 235 Figure B.2. Example objective function distribution for different initial points ........... 253 Figure B.3: Pareto frontier ............................................................................................. 255 Figure B.4: User specified optimal design (?baseline? design parameter values)......... 256 Figure B.5. Parametric effect of T low on optimum solution........................................... 259 Figure B.6. Parametric effect of T opt on optimum solution. .......................................... 259 xix Figure B.7. Non-dimensional results (Par. g4, Par. g1, and Par. h 1 represent the results obtained from Tables 3, 5, and 6 respectively in non-dimensional form). ............. 260 Figure B.8. Affect of the penalty term on the unconstrained optimization results........ 261 xx Nomenclature A i area of individual heater element [m 2 ] A h total heater area [m 2 ] ? i temperature coefficient of resistance (TCOR) for i th heater [? /? ?C] ? t theoretical TCOR for heater element ? thermal diffusivity [m 2 s] ? v cross-sectional area of vapor stems [m 2 ] ? w area of heated surface [m 2 ] Bo Bond number Bo B Bond number (with bubble diameter as length scale) c concentration c p specific heat of liquid [J/kgK] C sf Rohsenhow constant D d bubble departure diameter [m] f bubble departure frequency [Hz] f  Mean area fraction f obj possible objective function f i objective function g gravitational constant [m/s 2 ] ? 1.4 for air h heat transfer coefficient [W/m 2 K] h b bulk heat transfer coefficient [W/m 2 K] h fg heat of vaporization [J/kg] H n Distance between nozzle and heater [mm] k thermal conductivity [W/mK] k v vapor thermal conductivity [W/mK] L b capillary length [m] ? c critical wavelength [m] ? d most dangerous wavelength [m] L h heater length [m] xxi M molecular weight [kg/mol] M a Mach number m 0.12 ? 0.2 log 10 R p n number of powered heaters ? dynamic viscosity of liquid [Ns/m 2 ] ? v dynamic viscosity of vapor [Ns/m 2 ] ?a Marangoni number Nu Nusselt number P pressure [N/m 2 ] P c critical pressure [N/m 2 ] Pr Prandtl number P r reduced pressure q CHF, sub critical heat flux, subcooled bulk conditions [W/m 2 ] q CHF, sat critical heat flux, saturated bulk conditions [W/m 2 ] q? heat flux [W/m 2 ] q? b boiling heat flux [W/m 2 ] q? nc natural convection heat flux [W/cm 2 ] q raw,i heat flux from heater element I [W/cm 2 ] q sc,i substrate conduction from heater element i [W/cm 2 ] q sc,vert,i y-direction vertical substrate conduction from heater element i [W/cm 2 ] q sc,lat,i x-direction substrate conduction from heater element i [W/cm 2 ] q vap heat flux from heater to vapor FC-72 [W/cm 2 ] q i boiling heat transfer from heater element I [W/cm 2 ] q total (t) spatially averaged heat flux [W/cm 2 ] q w,i heat transfer from heater i [W] time and spatially averaged heat flux [W/cm 2 ] ? l liquid density [kg/m 3 ] Ra L Rayleigh number Re Reynolds number total q xxii R c conduction resistance [m 2 K/W] R conv convection resistance [m 2 K/W] R h heater resistance [? ] R DP digital potentiometer resistance [? ] R 1-5 feedback circuit resistors [? ] R p rms roughness of surface [m] R ref reference heater res. at T ref [? ] ? e nozzle exit density [kg/m 3 ] ? v vapor density [kg/m 3 ] s 1.7 for most liquids [1.0 for water] ? surface tension [N/m] ?t 0.004 [s] T temperature [C] T e nozzle exit temperature [C] T t total heat transfer averaging time [s] T bulk bulk liquid temperature [C] T h heater temperature [C] ? contact angle [radians] ? ref reference temperature [C] ?T sub bulk liquid subcooling = T sat ?T bulk [C] ?T sat wall superheat = T w ? T bulk [C] T sat saturated temperature [C] T w wall temperature [C] U Ai area uncertainty [cm] u Vi voltage uncertainty [volts] u qraw,i uncertainty in raw heat flux [W/cm 2 ] u Ri resistance uncertainty [? ] V i i th heater voltage [volts] v e Nozzle exit velocity [m/s] xxiii v n normal velocity [m/s] v t Tangential velocity [m/s] ? kinematic viscosity [m 2 /s] x quality ? electrical potential [V] 1 Chapter 1: State of the Art in Pool Boiling 1.1 INTRODUCTION / MOTIVATION Studies pertaining to the influence of gravity on boiling processes have been stimulated by two motivations. Firstly, higher accuracy predictive modeling is desired for the design of robust, efficient, economical, and reliable space applications that utilize the efficiency of latent heat transport. This type of modeling requires a firm understanding of boiling mechanisms in a host of operational environments. Secondly, a comprehensive physical understanding of the complicated boiling mechanisms is sought. An important industrial application of heat transfer science and engineering in recent years has been electronics thermal control. The relentless emphasis on miniaturization is the primary driving force behind systems with dramatically higher spatial densities. Power dissipating devices, such as computer processors, are being designed to achieve higher computing performance while dissipating larger amounts of power per unit area, Fig. 1.1. These trends pose significant challenges for future thermal design that are not easily solved using contemporary thermal solutions. Boiling heat transfer has gained considerable attention over the years due to the relatively large heat fluxes that can be achieved at relatively small temperature differences, Fig 1.2. Two- phase cooling systems have the ability to provide efficient, application specific, temperature control, and these benefits have led to research efforts aimed at quantifying boiling efficiency at the small scale and in variable gravitational environments. One of the goals of research in this area is to determine the feasibility of applying boiling technology in a space environment. Such efforts will provide a predictive design aid to 2 scientists and engineers tasked with the design, analysis, fabrication, and testing of space based hardware that utilize two-phase transport. Figure 1.1: Projected microchip cooling requirements (iNEMI Technology Roadmaps, Dec 2004). Figure 1.2: Cooling potential for various processes (iNEMI Technology Roadmaps, Dec 2004). 3 The second motivation for work in this area is centered on the desire to understand natural physical processes in space. Many natural two phase processes occur in space systems such as liquid droplet formation in humid environments and vapor generation during distillation and purification. These processes and others require a basic understanding of two-phase transport processes in order to affect reliable and robust operation. For such processes, the design and research objectives are to understand and predict the behavior of the system as opposed to maximizing the efficiency of the transport process as in electronics thermal control. Other multiphase applications where a basic understanding of the physical process is desired are: cryogenic fuel storage and transportation, wastewater recovery, distillation systems, air revitalization, water purification, and material processing. The third motivation for such work focuses on the space environment itself which creates an intriguing setting whereby complex processes on earth can be studied in a more simplistic manner. The pool boiling process is an excellent example of this in which the complex interaction between various boiling mechanisms can be de-coupled and studied at a fundamental level. The various mechanisms referred to and their relative effect on the pool boiling process will be discussed in detail throughout this thesis. Lastly, the human desire to understand their physical environment cannot be overlooked as a primary motivation for research in a general sense. Such work is an intellectually stimulating endeavor providing its own benefits to those who enjoy studying fascinating complex problems. Scientific idealism rooted in inquisitive minds has led to a greater understanding of our relationship with our environment, technological innovation, and provides tremendous insight into our prospects for the future. 4 A logical place to begin the discussion of boiling heat transfer in space is to briefly review the extensive data that has been collected regarding the phenomenon in higher gravitational environments. Under such conditions, the pool boiling process is fairly well understood and the available data provides an excellent introduction into the complexities of a low-gravity boiling environment. Along with introducing the relevant background information, this chapter provides the context in which to begin analysis of the microgravity boiling environment. 1.2 CLASSICAL BOILING LITERATURE REVIEW Boiling in space is poorly understood. The costs associated with experimentation, challenges of creating a suitable space environment, and logistical issues associated with space transportation have hindered progress to date. The lack of progress requires one to look elsewhere to gain insight into the particular process under investigation. In the case of pool boiling, extensive knowledge exists regarding the 1-g condition. A review of the state of the art in 1-g pool boiling therefore provides a number of benefits to the researcher including; a foundation with which to begin further analysis, insight into some of the physical mechanisms of the process, and a plethora of models with which to begin an investigation and comparison. 1.2.1 Terrestrial Boiling The pool boiling process is an extremely complicated one that extends into many disciplines. The physical manifestations of the boiling process can be observed daily from boiling of water for cooking applications to natural processes such as hot spring evaporation. It involves the physics of heterogeneous bubble nucleation, the chemistry of 5 two-phase and triple phase interfaces, the thermodynamics of local heat transport, and the hydrodynamics of two-phase flow. Boiling heat transfer has traditionally been thought of as a combination of free convection, vapor liquid exchange, microconvection, transient conduction, and latent heat transport. Vapor bubble dynamics associated with nucleation, bubble growth, departure, collapse, and subsequent rewetting of the heater surface characterize the classical ebullition cycle which constitutes the primary mechanisms of heat transfer from a superheated wall during nucleate pool boiling in earth gravity. Some of the early work mentioned above has laid the foundation for the classical boiling curve and its constituent boiling regimes, Fig 1.3. At low superheats, natural convection dominates the transport process (a-b, Fig 1.3). As the wall superheat is increased, the process progresses through the isolated bubble regime and regime of vapor Figure 1.3: Classical nucleate pool boiling curve. 6 slugs and columns (d-f, Fig 1.3). Eventually critical heat flux (CHF) is reached and the measured heat flux begins to decrease as transition boiling occurs (f-g, Fig 1.3). Eventually, the boiling process is completed dominated by film boiling (g-h, Fig 1.3). Early studies in the field focused on the qualitative aspects of the nucleate pool boiling process. Photographic results identified the four heat transfer regimes mentioned above which were characterized based on the mode of vapor generation. Consider first a heated flat surface. As the surface temperature increases, vapor structures progress through a sequence of discrete bubbles, vapor columns, vapor mushrooms, and vapor patches, Fig. 1.4 (Gaertner, 1965). The individual vapor structures and their various combinations determine the mechanism of transport. Many researchers have studied these mechanisms in isolation and collectively. A large portion of their results are from heater sizes much larger than the capillary length scale (Eq. 1.1). The capillary length, L b , as shown for various fluids in Table 1, is derived from a balance between surface tension and buoyant forces acting on a vapor bubble. This length scale is relatively small Figure 1.4: Discrete bubble region (left), vapor mushroom (right), (Courtesy of Gaertner, 1965). (1.1) () vl b g L ?? ? ? = 7 and many of the traditional sensors have been unable to accurately resolve heat transfer data at the capillary length scale or smaller. In space, as the g-level goes to zero, the capillary length scale goes toward infinity which indicates that all finite sized heaters appear small compared to this length in space. Boiling from heaters much smaller than the capillary length scale is less well known and is a large motivation for low-gravity pool boiling research. Capillary Length, L b (mm) Fluid Low-g (0.01g) 1-g high-g (1.7g) FC-87 7.48 0.75 0.57 FC-72 7.81 0.78 0.60 R113 12.00 1.20 0.92 R22 12.08 1.21 0.93 Water 27.13 2.71 2.08 Table 1.1: Capillary length of different fluids (NIST, 2003; 3M). 1.2.1.1 Nucleate Boiling Regime. Consider the nucleate pool boiling curve in greater detail, Fig 1.3. At low wall superheats natural convection is the dominant transport mechanism. Natural convection is characterized by single-phase buoyancy effects with no active nucleation sites on the heated surface. Increasing the wall superheat eventually causes boiling incipience to occur with a resulting increase in heat transfer (labeled d in Fig. 1.3). Many researchers have aimed to model the transport process in the nucleate boiling regime using single bubble models. Latent heat transport as well as microconvection is thought to contribute to a relatively high heat transfer between the heater and working fluid. Some researchers have proposed that latent heat transfer due to evaporation of a liquid microlayer near the three-phase contact line is the dominant energy removal mechanism (Straub et al. 1997, Moore and Mesler 1961, Fig 1.5). In contrast, experiments conducted by Gunther and Kreith showed that the majority of heat 8 Figure 1.5: Microlayer formation beneath bubble (Courtesy of Van Carey, 1992). transfer during subcooled nucleate pool boiling could be attributed to microconvection during liquid rewetting of the heated surface (Gunther and Kreith, 1956). Yaddanapuddi and Kim later confirmed these experimental findings while studying nucleate boiling under saturated bulk conditions (Yaddanapuddi and Kim, 2001). Their results showed that during one ebullition cycle, the majority of heat transfer occurred after the bubble departed through transient conduction and microconvection to the rewetting liquid. Additional studies by Zhang et. al. measured a very small amount of heat transfer through the microlayer during the isolated bubble regime lending further support to the microconvection theory (Zhang et. al. 2000). Considerable debate still exists regarding the primary mechanism for heat transfer during isolated bubble growth and departure and is the primary motivation for current work in the area. The various isolated bubble models mentioned above provide some insight into the parameters which tend to enhance the heat transfer during isolated bubble growth and departure. Microconvection theory predicts an increase in time averaged heat transfer from the heated surface if the bubble departure frequency increases. Methods aimed at 9 increasing the bubble departure frequency, such as electrohydrodynamic (EHD) pool boiling, have clearly shown an increase in the attainable heat flux (DiMarco & Grassi, 1992). This technique involves applying an electric field body force which can produce forces that induce localized fluid motions enhancing the two-phase transport process in thermal systems. The EHD mechanisms include a Coulomb force, dielectrophoretic force, and electrostriction force. Baboi et al., while studying boiling from a platinum wire, observed an increase in nucleate boiling heat transfer and CHF in the presence of a strong electric field force collinear with buoyancy (Baboi et al. 1968). They attributed the large increase in heat transfer primarily to an increase in bubble departure frequency. In addition, bubble growth times were diminished and departure diameter was reduced in the presence of an electric field. Such work characterizes the importance of two critical physical parameters of the ebullition cycle on heat transfer: the frequency of bubble departure or surface rewetting, f, and the bubble departure diameter, D d . The bubble departure diameter depends directly on the forces acting on the bubble during dynamic vapor bubble growth while attached to the heater surface. Many forces have been shown to influence departure dynamics including: surface tension (F ?,s ), buoyancy (F B ), inertia of induced liquid motion (F LM ), Marangoni or thermocapillary forces (F ?,v ), and vapor bubble coalescence (F C,E ), Fig. 1.6. The magnitude and influence of these forces have in turn been shown to be a function of many system parameters including: bulk liquid subcooling (?T sub ), gravity (g), wall superheat (?T sat ), the thermophysical properties of the fluid, heater geometry, surface characteristics, and pressure. The frequency of bubble departure depends on the time needed for the bubble to 10 Figure 1.6: Forces acting on a bubble. grow to the departure size (growth time) and the amount of time it takes after a bubble departs for nucleation to occur (waiting time). The departure frequency in the isolated bubble regime tends to increase with wall superheat due to the increased rate of vapor generation producing a smaller growth time. In addition, higher wall superheats tend to reduce the waiting time by decreasing the time needed for the rewetting liquid to reach the superheat limit required for nucleation. It is clear from the research cited previously that bubble departure is critical to the enhancement of heat and mass transport during the pool boiling process. Very little work has been conducted on systems where bubble departure is less frequent or non-existent. As the wall superheat is increased beyond the isolated bubble regime, bubble coalescence becomes a dominant physical occurrence characterized by the formation of vapor columns and slugs. In this regime, metrics such as bubble departure frequency and F B F LM F ?,v F Cond + F therm F C,E F ?,s Heater 11 departure diameter tend to be much less useful due to turbulent vapor and liquid interaction where isolated bubbles are no longer present. For large heaters, vapor is generated at a high rate and at multiple locations enabling lateral and vertical bubble coalescence to occur. This causes vapor columns to form due to Taylor instability and the spacing between columns has been shown to be related to the capillary length scale, Fig. 1.7. Figure 1.7: Vapor columns formation and the Taylor wavelength, ? d (Courtesy of Van Carey, 1992). Many analytical models have been developed that predict nucleate boiling behavior throughout the isolated bubble regime and into the regime of vapor slugs and columns in earth gravity from horizontal heaters significantly larger than L b . An early model developed by Fritz (1935), based on a quasistatic analytical force balance between surface tension and buoyancy, assumes the non-dimensional Bond number to be the governing parameter for bubble departure diameter, Eq. 1.2. This equation predicts (1.2) () ? ?? ? 2 2 1 0208.0 dvl B Dg Bo ? == 12 departure occurs at a constant Bond number for a given fluid/surface combination. A major deficiency in this model is that it only accounts for the effects of wall superheat and bulk subcooling through their influence on the contact angle, ?. Later correlations [Eq. 1.3 (Rohsenhow, 1962), Eq. 1.4 (Cooper, 1984), and Eq. 1.5 (Stephan and Abdelsalam, 1980)] provide an estimate of nucleate boiling heat transfer (1.3) (1.4) (1.5) from relatively large heaters in earth gravity. The Rohsenow model is based on microconvection theory in which the heat transfer is attributed to local agitation due to liquid flowing behind the wake of departing bubbles. The equation is a modification of a single-phase forced convection correlation using the appropriate length (bubble departure diameter) and velocity scales. The correlation developed by Stephan and Abdelsalam is a curve fit of available data and its accuracy varies widely depending on the operating conditions. 1.2.1.2 Critical Heat Flux. If the wall superheat is further increased along the nucleate pool boiling curve, Fig. 1.3, CHF will eventually occur. CHF is the maximum heat flux that can be achieved without a significant rise in the heater wall temperature. CHF is () ( ) ? ?? ? vl s fg p sf satw g h c C TT q ? = ? ?? 32 3 3 3 Pr () 55.0 10 5.0 67.0 )log(55 ?? ???= r m r PPMqh Pr,,,207 651 533.0 6 581.0 5 745.0 1 == ?? == XX kT q XXXXNu l v w ? ? 13 perhaps the most critical design parameter for two-phase cooling systems and accurate modeling of this phenomenon is paramount to predicting the operating range and reliability of cooling systems. Many mechanisms have been proposed to explain the behavior of CHF in earth gravity. In one mechanism, a Helmholtz instability results from vapor columns that break down to form local dry patches on the heater. The breakdown results from severe vapor drag on rewetting liquid that is flowing in the opposite direction and causes a liquid flow crisis to the heater surface. The Helmholtz wavelength is shown in Fig. 1.7 as ? h . Zuber?s CHF model for an infinite horizontal surface assumes that vapor columns formed by the coalescence of bubbles become Helmholtz unstable, blocking the supply of liquid to the surface (Zuber, 1959). These vapor columns are spaced ? D apart (Eq. 1.6), Fig 1.7. In this equation, the critical wavelength, ? c, is the wavelength below which a vapor layer (1.6) can be stable underneath a liquid layer. Only perturbations with a wavelength greater than ? c will grow and cause interfacial instabilities. The critical wavelength for a number of fluids is provided in Table 1.2. The Zuber model predicts a maximum heat transfer of the form given by Eq. 1.7. It is important to note that the gravitational dependence on Critical Wavelength ? c (mm) Fluid Low-g (0.01g) 1-g high-g (1.7g) FC-87 47.02 4.70 3.61 FC-72 49.08 4.91 3.76 R113 75.40 7.54 5.78 R22 75.92 7.59 5.82 Water 170.48 17.05 13.08 Table 1.2: Critical wavelength for different fluids. () c vl D BoL g ?? ?? ? ?? 33232 2/1 2/1 == ? ? ? ? ? ? ? = ? 14 () 4 1 2 '' max 149.0 ? ? ? ? ? ? ? = v vl fgv g hq ? ??? ? (1.7) CHF predicted by Zuber?s model, indicates that CHF in a zero-g environment would be zero. This prediction differs greatly from experimental findings in low-gravity which will be presented in the next section. Furthermore, the critical wavelength increases dramatically in low-g environments making it difficult to observe Taylor instabilities in low-g. Another popular model assumes CHF is governed by a hydrodynamic instability where large vapor bubbles hovering slightly above a surface are fed by smaller vapor columns (Haramura and Katto, 1983), Fig 1.8. This model postulates that CHF occurs if the hovering time exceeds the time necessary to evaporate the liquid film between the hovering bubble and the heater causing the heater to dry out. This model assumes the Bond number to be the governing parameter controlling the development of CHF in earth gravity and for horizontal flat plates is predicted by Eq. 1.8. (1.8) Increasing the wall superheat beyond CHF causes a decrease in boiling performance. In the transition boiling regime (f-g, Fig 1.3), the boiling process is increasingly dominated by dryout of the heater surface. Eventually, a local minimum in heat transfer occurs when vapor completely covers the heater surface, commonly referred to as the Liedenfrost point. Physically, this is the beginning of film boiling where a stable vapor film forms between the heater surface and the surrounding bulk liquid. The major transport mechanism in this regime is conduction and radiation exchange through () 165 5316585161 211 4 41 2 1 16 11 11 32 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? v l v l w v w v v vl fgv CHF A A A Ag h q ? ? ? ?? ? ??? ? 15 Figure 1.8: Helmholtz instability mechanisms (Courtesy of Van Carey, 1992). the vapor film. The transport characteristics of this regime are quite poor and therefore operating conditions that create film boiling in two-phase cooling systems are largely avoided by the practicing design engineer. 1.2.2 Terrestrial Pool Boiling Enhancement At first glance, the microconvection models provide some insight into the parameters which affect the heat transfer performance during the pool boiling process. In addition to electrohydrodynamic and acoustic field bubble removal which focus on 16 altering the bubble departure frequency and departure diameter, other system operating parameters have been shown to dramatically influence heat transfer performance during pool boiling in earth gravity. A commonly applied method for increasing heat transfer performance is to cool the bulk liquid below the saturation temperature under the system operating conditions, commonly referred to as subcooling the fluid. The effect of bulk liquid subcooling on nucleate pool boiling heat transfer has been of particular interest to some researchers over the years due to the enhancement in heat transfer that can be achieved by the additional sensible energy storage mode. An increase in subcooling is thought to provide higher heat transfer rates during the initial rewetting process in which the cool liquid contacts the heated surface and the mechanism for heat transfer is conduction and micro-convection. Subcooling has been experimentally shown to influence bubble geometry as reported by Gunter and Kreith who observed a decrease in bubble size with an increase in bulk subcooling. In addition departing bubbles rapidly collapsed in the presence of higher subcooling (Gunter and Kreith, 1949). At first glance one might expect to measure an enhancement in heat transfer under highly subcooled conditions in the nucleate boiling regime. Smaller, rapidly collapsing bubbles provide less resistance for rewetting liquid and may increase the bubble density on the heated surface. Despite such enhancement effects, experimental investigations have shown subcooling to have no effect on heat transfer during nucleate boiling in earth gravity (Forster and Grief, 1959). Such measurements may be explained by the effect of subcooling on bubble departure frequency. As condensation is increased from the top surface of growing bubbles that are attached to the heated surface, the bubbles tend to 17 grow much more slowly, increasing the bubble growth time and reducing the liquid rewetting frequency. In addition, higher bulk subcoolings may tend to reduce the active site density on the heated surface. In total, subcooling effects on bubble departure frequency, bubble size, liquid rewetting temperature, and active site population density act to mitigate heat transfer differences compared to near saturated bulk conditions in the nucleate pool boiling regime. Although negligible subcooling effects have been measured during nucleate pool boiling, it appears to significantly increase CHF. From a hydrodynamic perspective, an increase in subcooling acts to condense the vapor generated at the heated surface providing less resistance for bulk liquid to rewet the surface, delaying the onset of CHF to higher wall superheats. Kutateladze postulated that CHF in subcooled boiling should increase above similar saturated conditions by the amount of energy required to bring the subcooled liquid to a saturated state, Eq. 1.10 (Kutateladze, 1962). Ivey and Morris (1962) suggested C o =0.1 and n=0.75 based on available data. (1.10) 1.2.3 High-g Boiling Boiling mechanisms at higher gravity levels are not thought to differ significantly from earth gravity. The dominant effect of higher gravity levels on boiling is the increase in buoyancy driven flows such as bubble motion and natural convection. Most natural convection correlations predict heat transfer of the form given by Eq. 1.11, with C and n being empirical constants (Incropera and Dewit, 2002). Studying natural convection ( ) fg bulksatp n v l satCHF subCHF h TTc C q q ? ? ? ? ? ? ? ? ? += ? ? 0 , , 1 18 using a centrifuge at up to 1200g, Eschweiler and Benton provide a representative natural convection heat transfer correlation given by Eq. 1.12 (Eschweiler and Benton, 1967). (1.11) (1.12) As mentioned previously, boiling is dramatically affected by the bulk liquid conditions of the system. The increase in natural convection at higher gravity levels can dramatically influence the bulk liquid characteristics and thus the boiling dynamics. An increase in natural convection can delay boiling incipience or suppress boiling completely depending on the level of liquid subcooling, the gravity level, and wall superheat (Koerner, 1970). Studies performed by Beckman and Merte focused on the influence of acceleration on pool boiling of water up to 100g. They found an increase in acceleration caused a decrease in the number of active nucleation sites on the heated surface. This was attributed to a thinning of the superheated boundary layer near the surface as buoyancy driven flows increased (Beckman and Merte, 1965). Some pool boiling studies performed on horizontal heaters in high-g show similar trends to those mentioned above. Using a centrifuge, Ulucakli and Merte studied boiling from a horizontal heater. At 10g, they observed low heat flux boiling to be independent of subcooling for subcooling levels up 50?C. Such observations agree with the 1-g results previously mentioned. A further increase in bulk subcooling at this g-level suppressed boiling activity, and heat transfer was dominated by natural convection. At high heat flux, an increase in subcooling resulted in an increase in the wall superheat (at 50?C subcooling, a 35% increase in wall superheat was measured), holding all other ( ) ?? ? 3 Pr LTTg GrRaCRaNu s LL n LL ? ? === 107363.0 10810215.0 ????= LLL RaRaNu 19 variables constant. At 100g, little effect of subcooling on wall superheat for subcooling up to 30?C was observed and boiling was completely suppressed as the subcooling was increased further (Ulucakli and Merte, 1990). In addition, bubble departure frequency increased while the bubble growth rate was found to be essentially constant and independent of acceleration. This indicates that the bubble departure diameter was reduced at higher gravity levels and is consistent with the Fritz model. Ulucakli and Merte used the Mikic and Rosenhow Model (Mikic and Rosenhow, 1968) as the basis for explaining why, under certain conditions, a decrease in heat transfer at higher subcoolings and heat flux are observed compared to near saturated conditions. This model assumes the net heat transfer from a surface can be approximated by the sum of the boiling and natural convection components Eq. 1.13. In this equation, f represents the mean area fraction of the heater surface not experiencing boiling. Based (1.13) on this model, Ulucakli and Merte stated that the degradation of heat transfer at higher heat flux with increased subcooling resulted from a reduction in the superheated boundary layer thickness. This caused the suppression of some active nucleation sites and increased the non-boiling natural convection component to overall heat transfer. The natural convection contribution to the total heat flux began to outweigh that associated with the active nucleation sites as the subcooling was increased further, and eventually complete suppression of all boiling on the surface occurred (Ulucakli and Merte, 1990). Such experimental results clearly contradict what is predicted by Kutateladze and others and emphasizes the need for additional gravity dependent parameters in such correlations. ncb qfqq ?? + ?? = ?? 20 The contradictory results summarized here suggest that relatively little is known on the coupling between g-level and bulk subcooling. Current models do not accurately account for this effect and further research is needed in order to clarify the conditions where gravity and subcooling combine to increase or decrease the level of heat transfer. 1.2.4 Summary of Classical Boiling In summary, nucleate boiling at scales larger than the capillary length under terrestrial gravitational conditions are dominated by gravity effects such as buoyancy. Buoyancy driven convection is the fundamental transport mechanism at the macroscale and affects bubble departure characteristics and the complex interaction between vapor and liquid flows. Heat transfer enhancement occurs in the nucleate pool boiling regime if the bubble departure frequency is increased, bubble departure diameter decreases, active nucleation site density increases, or any combination of these. In high-gravity, the effects of liquid subcooling are still unclear and this has hindered the development of analytical and numerical models in this area. Many models estimate performance based on various physical mechanisms such as surface tension and buoyancy. Much less experimental work has been devoted to studying the phenomena at significantly smaller scales and at lower gravity levels where buoyancy effects are less significant, and where the heater size is much smaller than the capillary length. Microgravity environments provide an intriguing setting to study smaller scale boiling activity due to the large increase in the capillary length with decreasing g-level. Microgravity environments may also provide a more desirable setting to study heat transfer mechanisms such as microlayer evaporation. 21 In conclusion, the models presented above tend to predict a very small heat transfer in low-g. The heat and mass transport process is expected to be much less efficient as buoyancy driven flows become less significant. The following section addresses this issue. 1.3 MICROGRAVITY BOILING Although buoyancy driven flows have been shown to dominate the transport process at higher gravity levels, relatively little is known of the boiling phenomenon in the microgravity environment. The principle reason for this can be related to the difficulty in creating a quality microgravity environment for long periods of time and the relatively high costs involved in space studies. The microgravity environment provides a setting in which some of the complex mechanisms previously mentioned are decoupled, simplifying the physical process. As a result, microgravity environments provide an ideal setting to study reduced gravity effects as well as gather information about significant earth gravity mechanisms that are typically masked by natural convection. A strong reduction in buoyancy driven flow is thought to dramatically affect the thermal boundary region near the heated surface. In the case of a small heater submerged in a large pool of liquid without the presence of bubbles, the thermal boundary layer can be modeled assuming semi-infinite solid conduction. In contrast, in earth gravity, the boundary layer is much thinner due to rising and falling convection cells near the surface. As a result, in low?g under constant heat flux conditions, the temperature of the heated surface tends to rise more quickly and reach a higher temperature at steady-state. Energy transport within the fluid is dominated by diffusion transport and the thermal boundary 22 region is much larger than under comparable earth gravity conditions where advection tends to dominate the process, Fig. 1.9. Such characteristics may explain why boiling incipience tends to occur at lower wall superheats and lower heat fluxes in low-g. The thermal boundary layer is much larger and therefore nucleating bubbles have more energy within the superheated region to sustain growth. Figure 1.9: Single phase thermal boundary layer development at various times. As mentioned previously, extensive research has been conducted on heaters larger than the capillary length while less is known of boiling on the smaller scale and at lower gravity levels. Under low-g and microgravity conditions, the capillary length becomes quite large, raising questions about its scaling effectiveness. Analyzing the boiling mechanisms at the small scale in earth gravity, Bakru and Lienhard studied boiling from small wires. Boiling curves presented in their work deviate significantly from classical X - distance Temp q?? 23 boiling behavior in that no transitional boiling regime from nucleate boiling to film boiling was observed, and the formation of ?patchy? boiling partially covered the wire. The Liendenfrost point and CHF were not observed in their study, leading to the conclusion that such regimes vanish for heater sizes smaller than L h /L b < 0.01. They concluded that classical pool boiling behavior is observed if the heater length is of the order L h /L b > 0.15 (Bakru and Lienhard, 1972). Keshok and Siegel were one of the first researchers to study boiling from flat heaters. They observed that a reduction in gravity resulted in a decrease in buoyancy and inertial forces acting on vapor bubbles caused them to grow larger and stay on the surface longer (Keshok and Siegel, 1964). Drop tower tests performed by Susumu showed that boiling in low-g can produce large primary bubbles that are surrounded by smaller satellite bubbles. Susumu measured small changes in heat flux compared to normal gravity conditions and observed occasional bubble departure which was attributed to induced inertial effects within the liquid resulting from explosive bubble growth during nucleation (Susumu, 1969). DiMarco and Grassi performed additional studies of boiling on thin wires in low- g where no remarkable effect of gravity on heat transfer was found. Although the boiling heat transfer coefficient was largely unaffected by gravity, bubble dynamics were strongly affected. The bubbles in low-g grew much larger than in earth gravity and occasionally departed the wire, Fig. 1.10. The departure mechanisms in low-g were thought to be bubble coalescence and induced liquid motion from rapidly growing bubbles. Such results indicate the inability of the Bond number to scale both effects of heater size and gravity level on boiling heat transfer (DiMarco and Grassi, 1999). 24 Figure 1.10: Pool boiling from wires (Courtesy of DiMarco and Grassi, 1999). Additional studies performed by Steinbichler et al. on boiling from a small hemispherical heater and wire under microgravity conditions demonstrate that the overall heat transfer coefficient under microgravity conditions is very similar to normal gravity. They measured a slight enhancement in the heat transfer at saturated and slightly subcooled conditions. This was attributed to bubble departure caused by bubble coalescence and induced liquid motion around the vapor bubble (Steinbichler et al. 1998). All of these results indicate that the nucleate boiling correlations mentioned previously (Eq. 1.2-1.8) do not accurately account for the gravitational dependence on boiling in low-g. For flat horizontal heaters, the observations indicate the formation of a primary bubble that causes significant dryout over the heater surface. At low heat flux, some researchers have measured a higher heat transfer compared to similar 1-g conditions (Merte et al., 1998), Fig. 1.11. Under such conditions, bubble departure can be non-existent and bubble dynamics associated with the classical ebullition cycle no longer occur. Under highly subcooled conditions in low-g, it has been shown that for heater sizes where the primary bubble does not cause total dryout, bubble coalescence on the peripheral regions of the heater array causes similar heat transfer performance to classical 25 Figure 1.11: Comparison between low-g boiling and 1-g boiling predictions (Courtesy of Herman Merte). 1-g nucleate boiling (Kim et al. 2002). Parametric studies dealing with the effects of fluid type on boiling in low-g have been performed by a few researchers. Preliminary research has identified a significant impact on heat transfer in low-g for various fluids. Oka et al. found CHF in low-g from a flat horizontal heater in n-pentane and CFC-113 are lowered by 40 percent when compared to earth gravity. At smaller heat flux, only a slight change was measured, which agrees with previously mentioned measurements. Studies using water as the working fluid showed a significantly higher deterioration (> 50%) in CHF at low-g. The differences in performance can be attributed to the thermophysical properties of the fluids 26 and in wetting characteristics on the heater surface. For organic fluids, a smaller contact angle was measured and hemispherical bubbles shapes were observed while for water the contact angle is much larger causing the bubbles to be nearly spherical on the surface in low-g causing dryout to occur more rapidly (Oka et al., 1995). Studies on boiling in low-g indicate a strong gravitational dependence on CHF. For example, Kim et al. (2002) observed bubble coalescence to be the primary mechanism for CHF, which differs from the hydrodynamic instability model proposed by Zuber, Fig. 1.12. CHF in low-g was measured to be significantly smaller and occurred at Figure 1.12: Pictures of the Boiling Process in Low Gravity at Various Superheats and Subcoolings (Courtesy of J. Kim). lower wall superheats compared to higher gravity boiling. They measured a gravitational dependence on CHF shown in Fig. 1.13. This gravitational trend further emphasizes deficiencies in Kutateladze?s CHF model (Eq. 1.10). 27 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 T bulk =23.0 o C T bulk =30.9 o C T bulk =39.5 o C T bulk =49.6 o C CH F (W / c m 2 ) Gravity Level (g) Figure 1.13: Gravitational dependence on CHF (Courtesy of J. Kim). In contrast to horizontal heater studies in low-g, Shatto and Peterson studied the mechanisms for CHF from cylindrical heater cartridges and found that the previously mentioned Taylor-Helmholtz instability governs the critical heat flux mechanism in low- g for this geometry (Shatto and Peterson, 1999). Clearly, additional research is needed in order to clarify the mechanisms responsible for CHF in low-g on different heater geometries in addition to identifying the gravitational dependence on this critical value. Earth gravity CHF mechanisms, such as Taylor and Helmholtz instabilities do not accurately predict performance in low-g as measured by most researchers. 28 1.3.1 Thermocapillary Convection The absence of gravity increases the contribution of other mechanisms normally masked by natural convection and buoyancy, such as Marangoni or thermocapillary convection. Thermocapillary flow results from surface tension gradients along a two- phase interface which can form due to temperature gradients, material composition, and electrical potentials (Ostrach, 1982), Eq. 1.14. In equation 1.14, t is the tangential coordinate direction along the bubble interface. (1.14) Thermocapillary effects were first observed by Trefethen and McGrew where it was shown that flow around vapor and air bubbles can be very similar. They predicted that thermocapillary flow is the primary mechanism for boiling in low-g supplanting ebullition cycle heat transfer mechanisms, although it should be noted that they were unable to validate this claim (Trefethen, 1961; McGrew, 1966). Raake and Siekmann studied temperature and velocity fields near an air bubble in silicon oil in the presence of a uniform temperature gradient and observed strong surface tension driven flows. They measured convective velocities near the surface of a bubble on the order of 10 -3 m/s which provided an additional force preventing departure in low- g. This additional force increased the departure size and decreased the bubble departure frequency (Raake and Siekmann, 1989). Numerical studies performed by Kao and Kenning (1972) on gas bubbles showed that the magnitude of thermocapillary liquid flow is determined primarily by the Marangoni number (Ma, Eq. 1.15), the Prandtl number (Pr), and the Biot number (Bi). They also found that the flow is very sensitive to surface active contaminants, a small amount of which can entirely suppress the thermocapillary tt c ct T Tdt d ? ? ? ? + ? ? ? ? + ? ? ? ? = ? ? ???? 29 motion. In addition, most of the driving surface tension gradient develops close to the liquid-vapor-solid interface and this driving gradient moves closer to the heater surface for higher Marangoni numbers (Kao and Kenning, 1972). (1.15) Wang et al, used high-speed photography and laser PIV techniques to investigate liquid jets emanating from boiling on ultrathin wires during subcooled boiling in 1-g. Bubbles diameters were typically 0.03 mm and affected liquid velocities above the bubble ranging from 15mm/s to 140 mm/s. Their results indicate that near the bubble, superheated liquid near the nucleation site is drawn toward the bubble and then expelled along its cap, Fig. 1.14. These experimental results agreed very well with 3-D numerical simulations which predicted velocities between 20-40 mm/s above the bubble. Figure 1.14: Suspended particle tracing during Marangoni convection, heat flux 6.0x10 5 W/m 2 , 379 K, bulk temp 325K (Courtesy of Wang et al, 2005). Most of the above mentioned studies (except Wang et al.) were performed in a binary system with either gas bubbles injected into the chamber or large amounts of dissolved gases already present. For a gas bubble on a vapor surface, it is clear that temperature gradients can exist along the liquid-gas interface due to the lack of latent heat transport across the interface. For pure fluids however, much debate has centered on the 11 2 ? ? a L t T T Ma ? ? ? ? ? = 30 ability of the bubble?s liquid-vapor interface to maintain a temperature gradient during phase transition. Recent studies in low-gravity show the formation of strong thermocapillary convection under highly subcooled conditions around a vapor bubble in systems with very low to minimal gas concentrations (nominally pure systems). As first suggested by Straub, thermocapillary flows can form in such systems in the following manner. In subcooled boiling, the top of a growing bubble may extend out of the superheated boundary layer and start to condense. With evaporation occurring near the three-phase contact line, impurities such as dissolved gas in the liquid are liberated and carried along with vapor to the top of the bubble. The vapor subsequently condenses while the noncondensable gases accumulate along the interface. Under steady-state conditions, the presence of the noncondensables reduces the vapor pressure locally along the interface and therefore the saturation temperature is decreased locally. A negative temperature gradient along the bubble interface forms which induces a thermocapillary motion directed from the base of the bubble to its top. A diagram of some of the key transport mechanisms of this theory is presented in Fig. 1.15. A force balance along the interface yields the boundary equations (Eq. 1.16-1.17). Under near saturated boiling conditions, this theory predicts an absence of thermocapillary motion due to a nominally constant temperature interface (Straub, 2000). Marek and Straub found the bubble growth time to have a major effect on the accumulation of noncondensable gases. Under saturated conditions, the bubble grows so fast (microseconds) that no accumulation of gas inside the bubble can occur. In contrast, under subcooled conditions where the growth time can be on the order of milliseconds, significant gas accumulation occurs. In addition, Straub measured strong thermocapillary 31 Figure 1.15: Thermocapillary flow transport mechanisms. (1.16) (1.17) flow in systems with extremely low gas concentrations (Marek and Straub, 2001). The strength of thermocapillary convection has been observed to alter the wall heat transfer by changing the size of the bubble and allowing additional liquid to wet the surface in low-gravity. Part of this thesis documents the important role this phenomenon plays in limiting the extent to which the heater temperature can rise in the post-CHF HEATER heat conduction Evaporation, coalescence and dissolution of gas from boundary layer and microlayer Condensation and gas diffusion LIQUID VAPOR AND GAS FLOW Thermocapillary convection Accumulation of gas ? hot ? cold > ? hot e n e t ( ) ( ) 02 11 = ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ++? n v n v RR PP An A Bn B AB AB ??? () () ( ) ( ) ( ) () n v n v dt d n v n v n v n v At A Bt B AnAt A BnBt B ? ? ? ? ? ==? ? ? ? ? ? ? ? + ? ? ?? ? ? ? ? ? ? ? + ? ? ?? ? ?? 32 regime. The complex nature of thermocapillary flows involving vapor/gas flow through the bubble, a dynamic phase boundary, accumulation of non-condensable gases, the dissolution of the gas in the liquid, and diffusion of gas through the liquid vapor interface poses a tremendous challenge. 1.3.2 Summary Although no analytical models have been developed that accurately predict boiling behavior in microgravity, many of the research efforts to date share common observations including: 1) The formation of a primary bubble in low-g and coalescence with smaller bubbles seems to dominate the boiling heat transfer process. At low heat flux, boiling performance can exceed comparable 1-g boiling. 2) Different heater geometries appear to affect bubble departure in low-g. 3) The influence of thermocapillary motion increases significantly in low-g in the absence of natural convection. Further research is necessary in order to quantify this effect. Current theories such as those developed by Marek and Straub need to be investigated further. 4) Low-g environments appear to cause boiling incipience to occur at lower wall superheats, which is attributed to a thicker superheated liquid region in the absence of natural convection. 5) The use of the Bond number as a single scaling parameter is in serious doubt and additional non-dimensional numbers are needed to predict boiling behavior across different gravity levels. 33 Although CHF has been researched extensively in earth gravity, strong disagreements still exist over conditions just before CHF, the trigger mechanisms responsible for initiating CHF, and the combined influence of system parameters on CHF. In low-g a fundamental identification and understanding of the relevant mechanisms is desired. The ability to both greatly increase and predict the magnitude of CHF is of importance to high heat transfer applications in space. A summary of the relevant low-gravity work to date is presented in Table 1.3. 35 RE F E RE NCE DA T E E N V F L U I D HE A T E R SUM M A RY R . S i eg el and K esh ock 1961- 1967 D T w a t e r f lat smoo t h ni ckel sur f ace 22 m m dia. ni chr o me r i bb on 3.2 x 22.2 m m S t r a ub et al . 1986 - 2 001 O F R 1 2 W ir e, 0. 2 / 0. 5 mm D T R 1 1 P i p e, 8mm o. d. P F R 1 2 3 Fl at pl at e 40 x 20 mm ( gol d co at ed ) R 1 1 3 H e m i spher i cal heat er 0. 26 mm di am et er C i r c u l ar heat er s, 1 / 1.5 / 3 mm di a. M e r t e et al 1992 - 2 002 D T l i q u id ni t r ogen F l a t heat er , S i O 2 , 19 x 38 mm 2 22 mm d i a. copp er sph e r e D i M a r c o and G r assi 1999 - 2 002 P F R 1 1 3 Wir e , 0. 2 mm d i amet er SR F C 7 2 A b e and O k a 1992- 1999 P F n - p e nt ane gl ass heat er , f l at I T O coat in g 30 x 30 m m 2 D T C F C 12- C F C 1 12 ar t i f i c i al cav it i e s wa t e r CF C1 1 3 CFC 1 1 O h t a et al . 1996- 2002 P F w a t e r t r a nspar e n t sur f ace, f l at I T O , 50 m m dia. SR e t ha no l D h = 5 0 m m D h ir et al 1999- 2002 P F w a t e r F l a t heat er , st r a in gage heat er , 45 mm di a. K i m et al 2000 - 2 004 S R FC 72 M i cr oh eat er ar r a y 2.7 x 2.7 mm 2 PF LEG E N D : D T - D r o p T o w e r , O F - O r bit a l Fl igh t , P F - P a r a b o li c F l i ght , SR - S oun din g R o c ket e n hancement at low heat f l ux, unaf f ect ed b y s u bcoo lin g bubb le depar t ur e obser v e d f r om mi cr omachin ed nucleat i on sit e s incr easi ng subcoo li ng incr ease C H F , sat el li t e bubb le heat t r ansf er i ndep e ndent of sub c ool ing a n d g r a v i t y l e ve l lar g e bub bles w i t h coalescen c e e n hancement at low heat f l ux, unaf f ect ed b y s u bcoo lin g S u m m ar y o f L o w- Gr av ity Bo ilin g Resear ch T h er mocap ill a r y conv ect io n i m pell s l a r g e b ubb le t o w a r d heat er , 3 0 % enh a ncem en t at l o w e r heat flux no, app r eciabl e ef f ect on heat t r ansf er c o ef f i cient C H F r e duced by 50% r e duced C H F , obser v e d micr o l ay er , mar a ng oni e f f ect o b ser v e d Table 1.3: S u mm ary of Low-g Experim e ntal W o rk 36 1.4 PROBLEM STATEMENT / RESEARCH OBJECTIVE Considerable resources have been expended in recent years toward the study of phase change phenomena in low-g environments. Particular attention has been given to the pool boiling process which is relatively well characterized under terrestrial conditions. Despite such efforts, relatively little is known about the mechanisms responsible for energy, momentum, and mass transfer during the boiling process in low-g environments, placing considerable constraints on the nature and type of designs that can be incorporated into space based hardware. If the boiling process can be quantified and modeled accurately, significant advances in the design and manufacture of space based hardware can be made. This thesis summarizes a mechanistic approach developed to identify measure, characterize, and model the fundamental heat and mass transfer mechanisms associated with the boiling process in space. Experimental, analytical and numerical techniques are employed to provide further insight into the phenomenon. This study aims to further the state of the art in low-g pool boiling by providing accurate and reliable information for future scientists and engineers. In addition to being a validation of previous work, the research objectives of this study include: 1. Obtain spatially resolved heat flux information a. Develop optimized sensor for local temperature and heat flux measurement b. Obtain boiling data from small scale heaters (< capillary length scale) 2. Characterize boiling in the absence of ebullition cycle behavior a. Determine applicability of 1-g models 37 i. Recommend revisions to current models 3. Identify scaling parameters 4. Identify boiling enhancement parameters 5. Validate / identify the mechanisms responsible for boiling a. Model analytically and numerically 6. Develop / recommend new mechanistic approaches where applicable 38 Chapter 2: Experimental Method 2.1 INTRODUCTION The experimental methodology was focused on measuring and characterizing the primary mechanisms important to the pool boiling process in low-g. The mechanisms identified through literature surveys and experimentation mentioned in the previous chapter includes: bubble coalescence, thermocapillary convection, and interfacial molecular kinetics. System parameters, such as bulk subcooling, wall heat flux and wall superheat, appear to affect these mechanisms in a systematic manner. The experimental research objective aims to identify, quantify, characterize, and model the relationships between system operating factors and boiling mechanisms as summarized in Fig 2.1. A brief study of the primary physical mechanisms identified above reveals a great deal about where to begin an experimental investigation. The initial research effort was aimed at identifying, measuring, and characterizing important factors that are thought to influence the primary mechanisms and the phenomenon as a whole. Such factors include; heat flux, wall superheat, bulk subcooling, pressure, and others. Experimental factors were identified that would most dramatically influence coalescence and thermocapillary convection in low-g. After identifying the global system factor space, a parametric experimental investigation was performed for a selected subset of the factor space. In some cases, the results provided the impetus for modification of the experimental test apparatus allowing additional factors to be measured. The results were also used to characterize the physical mechanisms and the relationship between factors 39 and mechanisms, and develop quantitative models to be presented in the following chapters. This chapter provides a summary of the design of the experiments. It is organized to provide a discussion of the experimental design logic, a description of the various systems factors identified and parametrically investigated, and also to provide a rationale for design and fabrication of the experimental apparatus used. The quantity and quality of the experimental data to be presented in the next chapter is largely dependent on the quality of the experimental design methodology presented below. Figure 2.1: Block diagram of research process. 2.2 EXPERIMENTAL METHODOLOGY The experimental methodology followed a fractional factorial approach which provides a number of advantages over a total factorial plan. The primary advantage of this method rests in the ability to selectively study interaction effects between factors as opposed to a complete factorial plan which looks at interaction effects over the entire factor space. A complete factorial design usually involves extensive experimentation which correlates to long periods of time and large data sets that can be difficult to obtain if significant constraints associated with cost and availability exist. The experimental approach first aimed to identify and quantify two types of factors; control factors and noise factors (non-controllable factors). Control factors are variables that can be controlled in both the experiment and the physical process. Control 40 factors include; wall superheat, bulk subcooling, g-level, fluid type, heater size, and heater aspect ratio. The wall superheat is a critical parameter to study in any pool boiling experiment due to its influence on heterogeneous bubble nucleation, vapor formation, thermal boundary layer thickness, and liquid ?vapor hydrodynamics as summarized in the previous chapter. Bulk liquid subcooling plays a very strong role in the boiling dynamics primarily through its influence on the thermal boundary layer and vapor liquid hydrodynamics. The capillary length scale has been proposed as a governing length scale for nucleate pool boiling performance and therefore an effort was made to study various heater sizes and heater aspect ratios that were on the order of and significantly smaller than this length. The primary objective of this effort, quantifying the pool boiling phenomenon in low-gravity environments, necessarily identifies g-level as a parametric variable. A complete list of the control factors studied in this experiment is shown in Table 2.1. Experimental factors investigated Factor Wall Temperature / Wall Superheat Bulk Temperature / Bulk Subcooling Gravity Level Heater Size Heater Aspect Ratio Fluid Type Table 2.1: Experimental factors The design factors were chosen based on their suggested effects on the pool boiling process as identified from the literature review. Factor operating ranges were determined from an iterative design process that looked at experimental design capability, NASA safety requirements, previous experimental ranges mentioned in the literature review, and preliminary experimental results mentioned in the next chapter. For 41 example, the heater array control circuitry used in this study was designed for a maximum operating temperature which was later found to be too low to provide information about important trends in the low-g boiling curve. As a result, redesign of the control circuits for the heater array focused on increasing the temperature range to a desirable limit that provided the maximum amount of information possible while ensuring safe and reliable operation of the heater. Similar design scenarios were often encountered throughout the duration of this effort. Noise factors are predominately control factor uncertainties. Noise factors naturally arise in any experiment. The primary noise factor in this experiment is the g- level uncertainty referred to as g-jitter. Other noise factors include nucleation site location and bubble motion. An effort is made throughout this thesis to quantify and explain the effect of noise factors on both the control factors and the phenomena being investigated. 2.3 PARAMETRICALLY INVESTIGATED FACTORS 2.3.1 Gravitational Environment Gravitational effects on the pool boiling process are the primary motivation for this study. Over the years, microgravity environments have been difficult to create due to the technological, environmental, and economic challenges encountered. Such an environment presents unique design, safety, and economic requirements that are not trivial. Traditionally, drop towers, parabolic flight, sounding rocket flight, orbital flight, and space station operation have been thought of as ?microgravity? platforms although in almost all cases, 10 -6 g levels are not attained. Throughout this thesis the term 42 ?microgravity? and ?low gravity? will be used interchangeably referring to a gravitational environment (10 -2 g) produced in parabolic flight. As mentioned above, different means of achieving microgravity conditions exist and the various platforms provide different levels of quality and duration of microgravity periods. Drop towers provide microgravity conditions without having to travel into space. A drop tower is typically a vertical shaft which provides microgravity conditions during the free fall of the experimental package for a duration that depends on the length of the tower. Two drop towers currently exist in the US and are operated by NASA in Cleveland, Ohio. The major disadvantages of drop towers are the short duration of microgravity conditions and in some cases the cost. Parabolic flight can circumvent one of these disadvantages by providing microgravity conditions for up to 25 sec at comparable costs. The major advantages of parabolic flight include the frequency of experimentation, and the ability to modify the experimental package preflight, in-flight, and post flight. The primary disadvantage is that the quality of microgravity achieved is low, 10 -2 g, and the duration is limited compared to other techniques such as orbital flight. Sounding rockets have the ability to reach 400 km during parabolic flight and can achieve good microgravity levels (10 -5 ? 10 -6 g) for 5 to 6 minutes. Disadvantages include the need for recovery and high cost. Recoverable satellites provide an on-orbit laboratory for conducting research in microgravity typically 500 km above earth in low earth orbit. The space shuttle is a typical recoverable spacecraft that orbits the earth at 300 km and can provide microgravity conditions for up to two weeks. Last, the international space station provides a nearly indefinite microgravity condition to 43 researchers. This facility offers microgravity levels of 10 -6 g for months or years and can include isolation techniques for reducing the g-level even further (Thomas et al, 2000). Unfortunately, the latter microgravity platforms mentioned above are very expensive. A summary of the various microgravity platforms and their respective quality and duration can be seen in Table 2.2. Microgravity Platform Duration Gravity level Drop tower/shafts 2-9 sec 10 -2__ 10 -5 g Parabolic flights (aircraft) 25 sec 10 -2__ 10 -3 g Balloon-drop 60 sec 10 -2__ 10 -3 g Sounding rocket 6 min 10 -3__ 10 -4 g Space shuttle > 9-11 days 10 -3__ 10 -5 g Space station/recoverable satellite > months 10 -5__ 10 -6 g Table 2.2: Microgravity platform characteristics (Thomas et al, 2000). Selection of the appropriate microgravity platform for this particular study was motivated by cost, microgravity duration, ability to continually modify the test apparatus, and logistics. The NASA operated KC-135 provided a relatively low cost and long duration microgravity environment and allowed continual test modification during flight operations. All experimental data to be presented were taken aboard the NASA operated KC-135 in parabolic flight. Data presented in this paper was taken over a 6 week period totaling 24 flights. During portions of the parabolic flight, low-g (0.01g) and high-g (1.7g) levels are produced. A typical flight consisted of 40 parabolic maneuvers. Each parabolic maneuver consisted of a high-g pull-up (1.7g), a low-g period of about 25 s, followed by a high-g pullout (1.6g-1.7g), Fig. 2.2. Data acquisition for a particular wall temperature was initiated during the transition from high-g to low-g, Fig 2.3. Data were obtained for 90 s throughout the entire low-g period and into the high-g pullout and pull- up. 44 Figure 2.2: KC-135 flight profile (left); KC-135 in flight (right) (Courtesy of NASA). Figure 2.3: Gravitational profile for a typical parabola (Courtesy of J. Kim). Experimentation aboard the KC-135 requires comprehensive design, analysis and testing of each experimental subsystem and the overall system. Some of the design 45 considerations encountered include: physical constraints such as size, weight, structural considerations, power requirements, physiological issues, in-flight spatial constraints, setup, and logistical design & management. A comprehensive description of the experimental design challenges and an in-depth analysis of the experimental system is included in Appendix A (TEDP). Logistical challenges included: apparatus testing and preparation, transport to and from NASA facilities, loading onto the KC-135, and pre- flight testing and qualification. Experimentation during parabolic flight is not a trivial endeavor, requiring diligence and attention to detail surpassing the norm, Fig. 2.4. Physiological challenges encountered during flight included disorientation, nausea, lightheadedness, fatigue. Figure 2.4: Pictures of the Test Environment 46 The g-level was a parametrically investigated parameter having a maximum and minimum value of 0.01g and 1.7g respectively. The majority of experimental data obtained during flight was taken at these gravity levels. A few data points were obtained at lunar, 0.17g, and earth gravity, 1g. A summary of the g-level range studied and the percentage of experiments conducted at each level is shown in table 2.3. Parameter: Gravity-Level 0.01g 47 10 -2 g 0.3g 1 10 -2 g 1g 5 10 -2 g 1.7g 47 10 -2 g Uncertaintyg-level % exp Table 2.3: Gravity level parameter range 2.3.2 Fluid Pool boiling is strongly dependent on the type of fluid undergoing phase transition. Organic and inorganic fluids differ in both heat transfer performance and hydrodynamic manifestations at similar operating conditions. The primary considerations in selecting a suitable working fluid for this experiment were the thermophysical properties and electrical properties of the fluid. As mentioned in the introduction, direct immersion electronic cooling applications require the use of an electrically inert working fluid. The heater array used to initiate and sustain boiling activity in this experiment also required an electrically inert fluid. The maximum heater array temperature studied was 100? C and in order to study an adequately large wall superheat range, the fluid boiling point need to be between 40? C and 70? C. Last, the fluid needed to be non-toxic and non-flammable and satisfy stringent safety requirements set forth by NASA for operation aboard the KC-135. 47 A class of fluids which satisfied all of these conditions was the 3M fluorinert electronic liquids. These fluids are part of a family of fully-fluorinated compounds known as perfluorocarbons. Such liquids have been used as heat transfer media for direct immersion cooling, automated testing, reflow soldering, etching, CVD, and more. In addition, these fluids were selected due to their good material compatibility, low toxicity, nonflammability, and documented working history. The working fluid, FC-72 (C 6 F 14 ), was chosen from this class of fluids primarily based on the boiling point of the fluid at room pressure. FC-72 is a clear, colorless, odorless, highly wetting, dielectric fluid manufactured by 3M. Its dielectric properties and relatively low boiling point (T sat = 56 ?C, at 0.1 MPa) make it a desirable fluid for thermal management solutions in the electronics industry. Of particular interest is the fluid?s relatively high density, low viscosity, and low surface tension, Table 2.4. FC-72 Properties, P = 1 atm, saturated fluid properties Boiling Point (K) 329.15 ? l (kg/m 3 ) 1614 ? v (kg/m 3 ) 14.8 ? (kg/ms) 6.40e-04 C p (J/kgK) 1097 h fg (J/kg) 83536 k l (W/mK) 0.0522 ? (N/m) 0.008 ? (1/K) 0.0094 MW (kg/kmole) 338 Dielectric constant 1.75 T crit (K) 451.15 solubility of water (ppm) 10 solubility of air (ml/100ml) 48 Table 2.4: FC-72 saturated fluid properties. 48 Current theories on the origin of thermocapillary convection indicate that surface active contaminants may play a significant role in the interfacial kinetics at the two-phase interface. As a result, significant effort was made to accurately quantify the purity of the fluid. For FC-72, two impurities are typically present: dissolved gases and the fluid isomers. 2.3.2.1 Dissolved Gas Measurement. A thorough distillation process was followed to remove less volatile contaminates in the fluid. Unfortunately this process did very little to reduce the isomer concentration within in the fluid. After distillation, the fluid was degassed by periodically reducing the pressure inside the boiling chamber down to the vapor pressure of FC-72 at room temperature. The air concentration in the liquid was reduced to less than 3 ppm by repeatedly pulling a vacuum on the vapor/air mixture above the liquid. For a given partial pressure of gas (P g ) above the liquid, the dissolved gas concentration C g (moles gas/mole liquid) in the liquid phase is given by Henry?s law C g =H(T) P g where H(T) is Henry?s constant. For air in FC-72, H has been measured to be 5.4x10 -8 mole/mole-Pa between 31 ?C 2 heaters away from boundary), q sc,i is 1-D and not affected by T bulk with excellent agreement between analytical, numerical and experimental results (to be presented). 2) For edge and corner heaters, q sc,i is 2-D and 3-D respectively. When strong thermocapillary motion is present, T bulk appears to have a negligible effect on q sc,i (< 1% over the experimental ranges studied. 95 3) Substrate conduction from corner and edge heaters can decrease with an increase in h b for T bulk = 55 ?C. This effect is eventually offset by higher heat transfer across the top boundary surface for larger h b values. 3.3.3 Experimental Results Three different experimental methods for determining q sc,i were designed and are analyzed below. The first method, method 1, focuses on experimentally locating relatively long time periods during which vapor totally covered a heater (such as occurs when a large bubble causes dryout over a heater in low-g) element and attributing the heat flux at this time to substrate conduction. The heat transfer from the heater through the vapor is very low due to the comparatively low thermal conductivity of FC-72 vapor with quartz (k FC-72 / k q < 0.038). Assuming a vapor thermal conductivity equal to that of the liquid, a vapor layer thickness of 0.5 mm, and a maximum temperature difference equal to the maximum wall superheat tested (47?C), a conservative estimate of q vap = 0.5 W/cm 2 is obtained, Eq 3.13. This value is an order of magnitude smaller than the numerically and analytically calculated substrate conduction values. In addition, radiation heat transfer between the wall and the liquid is also negligible (0.016 W/cm 2 ). As a result, all heat transferred to the bulk liquid during times when dryout occurred was assumed to be negligible. (3.13) Experimentally determined q sc,i values using method 1 are shown in Fig. 3.14. Higher substrate conduction values are observed near the corner and edge heaters due to the increased area for 2-D and 3-D conduction effects which were confirmed 27272 5358.0 cm W x T k dx dT kq FCFC = ? ? ?=?? ?? 96 numerically. At T bulk = 55?C and h b = 10 W/m 2 K, there is excellent agreement between numerically and experimentally determined q sc,i values for a 96 heater array (Fig. 3.14 - 3.15). Figure 3.14: Comparison of numerical and experimental (method 1)q sc,i for a 96 heater array (T bulk = 55?C, h b = 10 W/m 2 K). At higher bulk subcoolings (T bulk = 28?C, 35?C, 45?C) the experimental method for determining q sc,i appears to be flawed (Fig. 3.16). For middle and edge heaters at low wall superheats, T bulk appears to have a negligible effect on q sc,i as confirmed by the numerical results mentioned previously. In contrast, at higher wall superheats a strong dependence on T bulk is observed contradicting the numerical results which showed a < 9 % increase in q sc,i from edge heaters at higher bulk subcoolings. Such observations indicate the experimental method (method 1) for determining q sc,i at higher bulk subcoolings is inaccurate. The reason for this can best be explained by Fig. 3.17. At T h = 70?C T h = 80?C T h = 90?C T h = 100?C q sc,i [W/cm 2 ] Numerical Ex p erimental 97 Figure 3.15: Comparison of numerical and experimental (method 1) q sc,i for middle (h-1), edge (h-5), and corner (h-6) heaters (T bulk = 55?C, h b = 10 W/m 2 K). T bulk = 55?C, the primary bubble that forms in low-g causes dryout over most of the heater array. As shown in Fig. 3.17, heaters 1 and 5 are completely covered by vapor throughout the low-g boiling process and therefore the adiabatic assumption used to obtain the experimental q sc,i values is justified. For corner heaters (6 and 7), times do occur when the primary bubble covers most of the heater element (> 90%) and therefore the surface averaged condition for such heaters is also sufficiently adiabatic justifying method 1. For T bulk = 28 ?C, heater 1 is also completely covered throughout the low-g boiling process which is why there exists good agreement between experimental and numerical values (Fig. 3.15). At higher wall temperatures, 100?C, strong thermocapillary convection causes the primary bubble to shrink in size allowing bulk liquid rewetting of 98 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 65 70 75 80 85 90 95 100 105 T h (?C) q sc , i (W /c m 2 ) Numer. heater #1 Analytical heater #1 Exper. heater #1 (Tbulk =28 ?C) Exper. heater #1 (Tbulk =35 ?C) Exper. heater #1 (Tbulk =45 ?C) Exper. heater #1 (Tbulk =55 ?C) Numer. heater #5 (h=10) Exper. heater #5 (Tbulk =28 ?C) Exper. heater #5 (Tbulk =35 ?C) Exper. heater #5 (Tbulk =45 ?C) Exper. heater #5 (Tbulk =55 ?C) Figure 3.16: Comparison between analytical, numerical, and experimental q sc,i values. Emphasis should be placed on the large deviations between the experimental and numerical values for higher bulk subcoolings. the edge and corner heaters (heaters 5, 6, 7, Fig. 3.17). The strong thermocapillary motion causes the primary bubble to remain stationary and therefore corner and edge heaters never experience adiabatic conditions above them. As a result, the heat transfer measured during such conditions for these heaters is a combination of boiling heat transfer to the liquid and substrate conduction and unfortunately the magnitude of each is unknown. This results in the large deviations observed in Fig. 3.16. At T bulk = 35?C and 45?C, the primary bubble size is in between these two cases and intermediate deviations are observed. 99 Figure 3.17: Low-g boiling for extreme subcoolings tested (96 heater array, T h = 100?C). Based on these observations a modification to the experimental method for determining q sc,i was made. The new method, method 2 involved using the T bulk = 55?C q sc,i values for edge and corner heaters (obtained using method 1) for all other bulk temperatures. Middle heater q sc,i values were calculated using method 1 for all subcoolings. This method is justified by the numerical results showing little to no effect of bulk temperature on q sc,i . The third experimental method, method 3, incorporates a minor variation to method 2 in that all of the q sc,i values obtained for T bulk = 55?C were used as the baselines for the other bulk subcooling cases (for all heaters including interior ones). The three different experimental methods are summarized below: 1) Method 1: q sc,i was calculated from the lowest heat flux measured during low-g 1 5 5 7 6 5 5 1 T bulk = 55?C T bulk = 28?C 6 7 100 2) Method 2: q sc,i was calculated from the lowest heat flux in low-g for middle heaters and the T bulk = 55?C q sc,i values (obtained using method 1)were used for the corner and edge heaters. 3) Method 3: q sc,i was calculated using T bulk = 55?C (using method 1) experimental baseline for all subcoolings. The three methods described above provide a statistical error range for the q sc,i measurement. Method 2 most accurately calculates the q sc,i experimentally and methods 1 and 3 provided an estimate of the experimental error in method 2. Method 2 provides the most accurate experimental value of substrate conduction because the air jet flow rate was set to be constant throughout a given flight week (regulator setting fixed) and therefore the backside boundary condition remained consistent across various days (subcoolings as mentioned in the experimental test matrix section). Therefore qsc,i should be subcooling independent as identified from the numerical models presented previously. It should be noted that at very low wall temperatures (T h = 70?C,75?C) natural convection dominates the heat transfer process and therefore no primary bubble exists allowing q sc,i to be measured. Under such conditions it appears that the experimental method of taking the lowest heat flux value during low-g appears to give good results that agree with correlations for the magnitude of natural convection in high-g. Such results will be presented in the next chapter. In conclusion, estimating substrate conduction involves two methods and is based on the magnitude of the wall superheat. For low wall superheats, method 1 and method 2 provide almost identical results. For higher wall superheats (with thermocapillary 101 convection present) method 2 appears to be the most accurate experimental method for determining substrate conduction. A complete listing of the experimental, analytical, and numerical results can be seen in Table 3.2. Based on the results presented above, the good agreement between analytical, numerical, and experimental data provides an estimate of the uncertainty in the experimentally measured substrate conduction values of ?10% (largest error for a given data point between experimental models). Performing another propagation of uncertainty analyses yields an uncertainty in the heat flux due to boiling of ?11%. The resulting uncertainty in q i , the heat transfer from a heater to the bulk liquid, is due primarily to uncertainties in q sc,i . 3.4 BOILING HEAT FLUX Boiling heat transfer data was computed from data obtained in high-g and low-g where the heat transfer had reached steady state over an interval of 5s to 10s where the g- levels were within (? 0.05g). Low-g (0.01) time periods were determined from the accelerometer signal and confirmed by the pressure signal. Fig. 3.18 shows the typical gravitational environment with respect to time during one parabola (taken from both the pressure and accelerometer signals). Spatially averaged, time resolved heat transfer data was obtained using the following equation, (Eq. 3.14): (3.14) where the subscript i denotes the heaters and n is the total number of powered heaters. A typical q total (t) is shown in Figure 3.19 and illustrates the variation in heat transfer during () ()[] ? ? = = ? = n i i n i iisciraw total A Aqtq tq 1 1 ,, 102 the low-g and high-g environments. The space and time averaged heat flux were obtained using Eq. 3.15: () t T j total total T ttq q ? = ? = 1 (3.15) where ?t is the time between data points and T t is the total time over which the average is obtained. The Matlab codes used for data reduction are given in Appendix D. Figure 3.18: Time resolved gravitational environment for 1 parabola aboard the KC-135, (Courtesy of J. Kim). 103 Figure 3.19: Spatially averaged, time resolved heat transfer, 96 heater array, T bulk = 28?C, ?T sat = 32 ?C. 3.5 ADDITIONAL PARAMETERS Uncertainties associated with the heater wall superheat, ?T sat , are due to errors in the heater temperature resolution (2 digital potentiometer settings), calibration temperature errors, and errors in the saturation temperature of the fluid which arise from uncertainties in the pressure measurement. Considering the worst case scenario, the saturation temperature of the fluid, T sat , was calculated from a measurement of the time resolved pressure at the heater surface and the saturation curve data for FC-72 (3M Product and Contact Guide, 1995). The pressure transducer was calibrated with an uncertainty of ? 0.01 atm. Incorporating this uncertainty into the saturation curve data, the resulting uncertainty in the time resolved saturation temperature is ? 0.25?C over the 104 ranges tested. A propagation of uncertainty analysis of the heater wall temperature yields an error due primarily to the uncertainty in the temperature resolution of the heater of ? 0.80?C. The final uncertainty in the wall superheat is ? 0.84?C. The thermistor used to measure the fluid temperature and the RTD used to the control the chamber sidewall temperature were calibrated in a constant temperature water bath using a NIST traceable liquid-in-glass thermometer. Although the thermistor measurement represents a local temperature value, it was assumed to be a representative average temperature of the bulk fluid. The micropump adequately dissipated any thermal gradients within the fluid between runs. For a given flight, the bulk temperature reading never varied by more than 2 ?C and therefore represents a good measure of the uncertainty in T bulk . The primary bubble departure frequency in high-g was determined from q total (t). For example, times when a peak in heat transfer occurs in Figure 3.19 (bottom) are thought to correspond to bulk liquid rewetting the heater surface. The number of heat flux peaks per unit time was taken to be the average rewetting frequency. For frequencies well below the video framing rate (29.97 Hz), the rewetting frequency as computed in this manner agreed exactly with the average primary bubble departure frequency obtained from the video. Therefore uncertainties in the frequency measurement are on the order of ? 1 %. Table 3.2 summarizes the uncertainties in the experimental variables. 105 Variable Uncertainty (2s) q total [W/cm 2 ]? 2 W/cm 2 q w,i [W] ? 0.46 % q sc,i [W/cm 2 ] ? 1.7 W/cm 2 q raw,i [W/cm 2 ] ? 5.02 % f [Hz] ? 1 % T h [ o C] ? 0.80 ?C T bulk [ o C] ? 2.0 ?C T sat [ o C] ? 0.25 ?C ?T sat [ o C] ? 0.84 ?C ?T sub [ o C] ? 2.02 ?C A i [cm 2 ] ? 5.0 % V i [volts] ? 0.11 % R i [? ] ? 0.4 % Table 3.2: Summary of experimental uncertainties 106 Chapter 4: Experimental High-g Boiling Results 4.1 INTRO The experimental results of the fractional factorial experimental investigation described in the previous chapter are presented in the chapter. Both qualitative and quantitative descriptions of the boiling behavior under the various conditions investigated are considered. A discussion of boiling in a high-g environment is first discussed and the relevant physical mechanisms and models are analyzed. This is followed by a brief description of the gravitational effects on the bubble shape and primary bubble departure frequency. Such findings provide insight into the complexities of the low-g boiling environment which constitutes the majority of the discussion mentioned thereafter. To this end, detailed experimental, analytical, and numerical results are presented and analyzed. 4.2 BOILING FROM SQUARE HEATERS 4.2.1 7 x 7 mm 2 , 96 Heater Array High-g boiling curves for a 7x7 mm 2 heater array are shown in Fig. 4.1. At low wall superheats, the heat and mass transfer process is dominated by natural convection. In this regime, the measured heat transfer is in good agreement with predictions of natural convection heat transfer from the upper surface of a horizontal heater plate, Eq 4.1 (McAdams, 1954). At higher wall superheats, the boiling dynamics are dominated by the ebullition cycle. As described in the introduction, this cycle is characterized by rapid ( ) 74 4 1 101054.0 ??= LLL RaRauN (4.1) 107 0 2 4 6 8 10 12 14 16 18 20 5 101520253035 Wall Superheat (?C) H e a t Fl ux (W / c m 2 ) 7 mm 96 Heater Array ? Tsub=31?C 7 mm 96 Heater Array ? Tsub=20?C 7 mm 96 Heater Array ? Tsub=11?C McAdams NC Correlation Rosenhow Correlation, Csf = 0.0041 Figure 4.1: High-g boiling curves for a 7 x 7 mm 2 heater array. bubble growth, departure, and coalescence that tend to occur in a periodic fashion. This transport process enhances the heat transfer from the surface as the phenomenon transitions from single phase natural convection to nucleate pool boiling. As expected, the onset of nucleate pool boiling is characterized by a dramatic increase in the boiling curve slope. The measured surface and time averaged nucleate boiling heat flux is in good agreement with the Rosenhow correlation, Eq. 4.2, C sf = 0.0041 (n-perfluorohexane on quartz heater), Fig. 4.1. In Eq. 4.2, C sf is a constant that is used to fit the data and varies depending on the surface/fluid combination. (4.2) () ( ) ? ?? ? vl s fg p sf satw g h c C TT q ? = ? ?? 32 3 3 3 Pr 108 Bottom view images of the boiling process in high-g are shown in Fig. 4.2. As seen from these images, the isolated bubble departure diameter appears to be approximately the size of an individual heater, 0.7 mm, and is consistent with that observed for the smaller heaters. The isolated bubble departure diameter refers to the diameter of a single growing bubble (just after departure) that is not influenced by adjacent bubbles. In practice, an isolated bubble is difficult to create experimentally due to multiple active nucleation sites on the heated surface and therefore the isolated bubble departure diameter is calculated throughout this thesis using a number of models (i.e. Fritz, 1935). The characteristic length scale, assumed to be equal to the heater length, is 7 mm. This value is larger than the isolated bubble departure diameter (0.34 -0.72 mm) calculated from Eq. 4.3-4.5, and is approximately eleven times larger than the capillary length scale, Eq. 1.1. ?0208.0 2 1 =Bo (Fritz, 1935) (4.3) mmHG P Bo 1000 2 1 = (Cole and Shulman, 1966) (4.4) () ( ) ? ?? ? ? 2 4 5 2 1 ,, dvl fgv lpc dg Bo h cT JaJaCBo ? === (Cole and Rosenhow, 1968) (4.5) Over the entire range of wall superheats studied, no evidence of Taylor instability was observed. This can be attributed to a number of factors. First, the highest wall superheat investigated may not have reached the required level for the formation of vapor jets that are predicted from Taylor Instability. Second, the heater length scale is sufficiently small so that if vapor jets were to form, the diameter of a single jet plus the spacing between adjacent jets would exceed the characteristic length scale of the array, as shown in Fig. 4.3. A vapor column that forms in high-g has a diameter of approximately 109 Figure 4.2: 7 x 7 mm 2 array, high -g tim e averag ed spatially resolved h e at flux (wall s uperheat direc tly b e low each im age and each row corresponds to the bulk subcooling le vel defined at the f a r left). 10 20 W/ c m 2 110 Figure 4.3: Predicted vapor column size and spacing from Taylor instability. 3.26 mm (0.5*? d ) and a spacing between adjacent jets of 6.5 mm. This indicates that only a single vapor jet would tend to form on the heated surface at higher wall superheats as shown in Fig. 4.3. At the highest wall superheat investigated, ?T sat = 31 ?C, the formation of a single primary bubble began to occur and was measured to be approximately the same size (2.8-3.5 mm) as the vapor jet diameter predicted above, Fig. 4.2. The primary bubble in high-g did not grow to cover the entire array, as was observed for the smaller heater arrays. As will be discussed later, a single primary bubble was observed above the heated surface at higher wall superheats for smaller heaters. If the heater size is smaller than a vapor column diameter predicted from Taylor instability, the boiling characteristics are qualitatively different than if the heater size is much larger than this length scale. For the cases where the heater size is smaller than the predicted vapor jet diameter (all heaters except the 7 x 7 mm 2 ), a single primary bubble the size of the heater is observed at high wall superheats. Lastly, a distinction should be made regarding primary bubbles and individual bubbles. Firstly, the primary bubble forms due 7mm 7mm ? d = 3.0mm Vapor Columns ? d = 3.0mm bD L32?? = d = 3.0mm d = 0.5*? d 111 to bubble coalescence that results in a bubble that is much larger in size than individual bubbles. Individual bubbles tend to feed the primary bubble and are significantly smaller. 4.2.2 2.7 x 2.7 mm 2 , 96 Heater Array High-g boiling curves for a 2.7 x 2.7 mm 2 heater array are shown in Fig. 4.4. As in the larger heater case, at low wall superheats the process is dominated by natural convection and in agreement with correlation predictions. At higher wall superheats, the boiling behavior is similar to that observed during nucleate boiling at normal gravity 0 5 10 15 20 25 30 35 5 1015202530354045 Wall Superheat (?C) H e a t F l u x ( W /c m 2 ) 2.7 mm 96 Heater Array ? Tsub=30?C 2.7 mm 96 Heater Array ? Tsub=25?C 2.7 mm 96 Heater Array ? Tsub=16?C 2.7 mm 96 Heater Array ? Tsub=9?C McAdams NC Correlation Rosenhow Correlation, Csf =0.0037 Figure 4.4: High-g boiling curves for a 2.7 x 2.7 mm 2 heater array. levels. At low wall superheats, boiling activity on the surface is characterized by the formation of multiple bubbles on the heated surface. These bubbles had diameters ranging from 0.27 mm to 0.81 mm and were similar in size to those measured for the 112 larger heater. The bubbles tend to grow, depart, and merge with other bubbles on the surface and the rate of coalescence appears to increase as the wall superheat is increased. The measured heat transfer was found to be independent of bulk liquid subcooling as predicted from chapter 1. The Rosenhow correlation provides a good estimation of the data up to a wall superheat of approximately 30?C. Bottom view images of the boiling process over the whole range of superheats and subcoolings are shown in Fig. 4.5. The Rosenhow correlation coefficient, C sf , which quantifies the fluid/surface interaction effects is slightly lower (C sf = 0.0037) than that used for the 7 x 7 mm 2 boiling curve fit (C sf = 0.0041). There may be two explanations for this. First, in the 7 x 7 mm 2 case, the fluid was 99% n-perfluorohexane that was completely degassed. Data presented for the 2.7 x 2.7 mm 2 array, Fig 4.4, was taken with FC-72 that had a purity slightly higher than 70%. The slight difference in the purity of the fluid may result in different surface fluid interaction. Second, the heater size is slightly smaller than the predicted diameter of a vapor jet (from Taylor theory) and the qualitative differences in the boiling behavior may explain the slight quantitative differences. Taylor instability predicts the formation of a primary bubble in high-g that tends to cover the entire array at higher wall superheats. The ramifications of this are discussed below. The formation of a single primary bubble is predicted at higher wall superheats and was experimentally validated at a wall superheat of ?T sat ~ 40 ?C, ?T sub ~ 9?C, Fig. 4.6. The observed size of the primary bubble is in good agreement with the Taylor instability prediction of a vapor column diameter of approximately 3 mm, slightly larger than the array (Fig. 4.6a). For ?T sub = 31?C and ?T sub = 25?C, the primary bubble that formed at the highest wall superheat fractured into four primary bubbles (e.g., Fig. 4.7 113 ? T sa t = 11 o C ? T sa t = 21 o C ? T sa t = 31 o C ? T sa t = 41 o C ? T sa t = 9 o C ? T sa t = 19 o C ? T sa t = 29 o C ? T sa t = 39 o C ? T sa t = 10 o C ? T sa t = 20 o C ? T sa t = 30 o C ? T sa t = 45 o C 1020 30 40 50 60 W/cm 2 T bulk = 35 o C T bulk = 28 o C T bulk = 45 o C ? T sa t = 27 o C ? T sa t = 37 o C ? T sa t = 7 o C T bulk = 55 o C ? T sa t = 17 o C Figure 4.5: Time-averaged, spatially resolved heat flux maps of boiling process for 96 heater array in high-g at various ?T sat and T bulk . 114 (a) Figure 4.6: bottom and side view images of the boiling process in high-g showing vapor column formation at high wall superheats, ?T sub = 9?C. (a) (b) (c) Figure 4.7: bottom and side view images of the boiling process in high-g showing the formation of 4 primary bubbles at high wall superheats, ?T sub = 31?C. (c), ?T sat =41?C). The mechanism for fracture is unclear but may be due to the increased level of liquid subcooling which brings cooler liquid closer to the heated surface causing increased condensation from the top of the primary bubble. As the primary bubble gets ?T sat = 37?C ?T sat = 28?C ?T sat = 17?C 2.7 mm 3 mm 10 20 30 50 40 60 W/cm 2 ?T sat = 41?C ?T sat = 31?C ?T sat = 21?C 10 20 30 50 40 60 W/cm 2 115 smaller, surface tension forces the bubble to fracture into four bubbles. These four bubbles occasionally coalesce and depart the heated surface forming a single vapor jet above the heater array. At the highest wall superheats, a large time averaged heat transfer was measured from the edge heaters in the array, Fig. 4.8. The measured heat flux also deviates significantly from the Rosenhow correlation prediction. The trends in the boiling curve data as well as the time resolved boiling heat flux indicate that the boiling activity is close to CHF. It is clear from Fig. 4.8 that dryout of the center of the array occasionally occurs which lowers the time averaged heat transfer. As vapor is generated and departs from the center of the array, a strong rewetting flow from the stagnant fluid medium at the edge heaters replenishes the departing fluid. As the primary bubble departs, the resistance of liquid flow to the center of the array is larger than for the edge region due to the increased rate of vapor formation and coalescence at the center of the array. Figure 4.8: Time averaged, spatially resolved heat flux (W/cm 2 ) from a 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 37?C, ?T sub = 9?C. 10 20 30 50 40 60 W/cm 2 96 8 116 The time resolved heat transfer at high wall superheats from an edge heater (Fig. 4.8, heater #96) and center heater (Fig. 4.8, heater #8) is shown in Fig. 4.9. For the interior heater, #8, complete dryout of the heater occurs periodically as indicated by the heat flux curve going to zero. For the corner heater, #96, smaller oscillations about the mean heat transfer were measured and the heat flux was always above 10 W/cm 2 indicating that dryout did not occur. This signal also contains higher frequency signals, indicating faster vapor bubble growth and departure in this region. Figure 4.9: Time resolved heat transfer from two heaters in the 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 37?C, ?T sub = 9?C. Such trends provide information regarding the mechanisms for CHF. Firstly, at low wall superheats, the time averaged heat transfer from the array is evenly distributed 117 across the heater area, Fig. 4.10. As the wall superheat is increased, dryout of the interior portions of the heater occur due to the increased rate of vapor generation, and as the wall superheat is increased even further, most of the measured heat flux occurs around a small area along the edge of the heater where rewetting liquid has less resistance to flow. Figure 4.10: Time resolved heat transfer from two heaters in the 2.7 x 2.7 mm 2 heater array in high-g, ?T sat = 27?C, ?T sub = 9?C. The Rosenhow model is not expected to predict the decrease in slope of the boiling curve at higher wall superheats near CHF. More importantly, very little predictive modeling is available from literature regarding CHF for heater sizes smaller than the Taylor wavelength. The Zuber CHF model predicts a CHF value of 16 W/cm 2 which is approximately 50% lower than the measured maximum heat flux, but the Zuber model is based on mechanisms that are proposed for large heaters. Additional 118 correlations used to predict CHF for finite-sized surfaces have been written in a form given by Eq. 4.6. For an infinite, heated flat plate, the predicted CHF is 18.2 W/cm 2 (L/L b > 30), (Leinhard and Dhir, 1973) which is again significantly smaller than the measured value. This indicates that current CHF models do not account for the boiling performance seen from heaters with L/L b < 5. () () 4 1 2 max, max, max 131.0 ? ? ? ? ? ? ? =?? ? = ? ? ? ? ? ? ? ? = ?? ?? v vl fgvZ vl b bZ g hq g L L L f q q ? ??? ? ?? ? (4.6-4.8) The time and surface averaged heat transfer appears to be larger for the 2.7 x 2.7 mm 2 array than for the 7 x 7 mm 2 array across the entire range of wall superheats. This again may be due to the differences in the purity of the fluid and/or the fact that the heater size is smaller than the Taylor wavelength which can cause edge heat transfer to increase dramatically. The formation of a single vapor column and single primary bubble was observed at higher wall superheats for the 2.7 x 2.7 mm 2 array. The time averaged edge heat transfer was measured to be dramatically higher from the heater edge (250%) indicating occasional dryout of the center of the array at higher wall superheats. The mechanism for dryout and CHF is clear from Fig. 4.11. As the wall superheat increases, vigorous boiling from the center of the array occasionally creates vapor at a rate greater than can 119 0 5 10 15 20 25 30 35 40 5 10152025303540 ?T sup (?C) H e a t Fl ux ( W / c m 2 ) Heaters 1-64 Heaters 65-96 Figure 4.11: High-g surface averaged heat transfer from interior heaters (1-64) and exterior heaters (65-96), ?T sub = 9?C. be removed from the surface. This causes occasional dryout of the interior portion of the array reducing the time and surface averaged heat transfer. The rapid formation and departure of vapor causes a stronger liquid flow from the edge of the array which enhances the heat transfer in this region. It is posited that the heat transfer from the edge region (near the edge of the primary bubble) levels off as the wall superheat is increased further and the surface averaged heat transfer from the total array begins to decrease indicating CHF. It is interesting to note that for ?T sat = 41?C and ?T sub = 29?C, Fig. 4.7, multiple primary bubbles form and the heat transfer in between bubbles is similar to the heat transfer at the heater edge for ?T sub = 9?C, Fig. 4.6. Such trends indicate the mechanism for CHF in high-g. 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 67 3918 5 161514315686 68 40 19 6 1 4 13 30 55 85 69 41 20 7 2 3 12 29 54 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 120 4.2.3 1.62 x 1.62 mm 2 , 36 Heater Array Boiling curves for the 36 heater array are shown in Fig. 4.12. Boiling images over the entire range of conditions investigated are shown in Fig. 4.13. At low wall superheats, the process is again dominated by natural convection and agrees with predictions. Trends similar to the 2.7 x 2.7 mm 2 array boiling curve are observed and the heat transfer was measured to be almost identical over the ranges investigated. See the previous section for an in-depth discussion of the boiling dynamics on the surface. 0 5 10 15 20 25 30 35 5 10152025303540 Wall Superheat (?C) H e a t Fl ux ( W / c m 2 ) 1.62 mm 36 Heater Array ? Tsub=30?C 1.62 mm 36 Heater Array ? Tsub=25?C 1.62 mm 36 Heater Array ? Tsub=16?C 1.62 mm 36 Heater Array ? Tsub=9?C McAdams NC Correlation Rosenhow Correlation, Csf =0.0036 Figure 4.12: High-g boiling curves for a 1.62 x 1.62 mm 2 heater array. Similar to the larger heater arrays, the formation of a primary bubble occurred at higher wall superheats and this bubble periodically departed the surface allowing the entire heater to be rewetted with liquid. Although the bulk liquid subcooling had a 121 ? T sa t = 16 o C ? T sa t = 31 o C ? T sa t = 26 o C ? T sa t = 36 o C ? T sa t = 41 o C ? T sa t = 14 o C ? T sa t = 34 o C ? T sa t = 29 o C ? T sa t = 24 o C ? T sa t = 19 o C ? T sa t = 39 o C ? T sa t = 15 o C ? T sa t = 20 o C ? T sa t = 25 o C ? T sa t = 30 o C ? T sa t = 36 o C ? T sa t = 40 o C 1020 30 40 50 60 W/cm 2 ? T sa t = 21 o C T bulk = 35 o C T bulk = 28 o C T bulk = 45 o C ? T sa t = 32 o C ? T sa t = 17 o C ? T sa t = 23 o C ? T sa t = 28 o C ? T sa t = 9 o C T bulk = 55 o C ? T sa t = 38 o C Figure 4.13: Time-averaged, spatially resolved heat flux maps of boiling process for 36 heater array in high-g at various ?T sat and T bulk . 122 negligible effect on the surface and time averaged heat flux, the size of the primary bubble was measurably smaller for higher subcoolings, as observed for the 96 heater case, Fig 4.13. The formation of a primary bubble is again predicted from Taylor instability theory at higher wall superheats because the heater size is much smaller than ?? d . The time resolved heat flux data allowed the primary bubble departure frequency to be measured at higher wall superheats. The departure frequency was determined from q total (t), as discussed in the data reduction section. For cases in which the departure frequency was less than 20 Hz, the measured value was corroborated by the frequency obtained from the side view video images. Although the subcooling level was measured to have a negligible effect on time and space averaged heat flux, increased subcooling was shown to dramatically reduce the departure frequency of the primary bubble as shown on Fig. 4.14. As seen in this figure, the bubble departure frequency increases by over 100% as the bulk subcooling decreases from ?T sub = 31?C to ?T sub = 9?C at a superheat of 32?C. An increase in the bulk subcooling increases condensation at the cap of a growing primary bubble, reducing its growth rate. The longer time needed for the bubble to reach departure size results in a decreased departure frequency, decreasing the time-averaged heat transfer. It appears this effect is compensated by a larger heat transfer to the rewetting fluid due to a larger temperature difference between the heater surface and the bulk liquid at higher subcoolings (sensible heating effect). This can be seen from Fig. 4.15 where at low subcoolings, Fig. 4.15a, a higher frequency signal is measured indicating a higher departure frequency. At higher subcoolings, Fig. 4.15b, although the departure frequency is reduced (as indicated from a lower frequency signal), the peaks in 123 0 10 20 30 40 50 60 15 20 25 30 35 40 45 Wall Superheat (?C) D e par t u r e Fr equency ( H z ) ? Tsub= 8 ?C ? Tsub= 16 ?C ? Tsub= 25 ?C ? Tsub= 31 ?C Figure 4.14: Primary bubble departure frequency in high-g for a 36 heater array (1.62 x 1.62 mm 2 ). the heat transfer are 20-30% higher and wider compared to the lower subcooling case. If a peak in heat transfer in Fig. 4.15 is associated with a rewetting event (post bubble departure) then there exists a time in which the rewetting liquid will increase to the saturation temperature of the fluid, at which point it is assumed vapor formation occurs which is followed by dryout of the interior heaters and low heat transfer. The total heat required from the heater to bring the rewetting fluid up to the saturation temperature is estimated by Eq. 4.9. Furthermore, if the heat transfer just after primary bubble departure is approximated by a semi-infinite conduction model, the time required to heat the rewetting fluid to the saturation temperature (given by Eq. 4.9) is estimated by Eq. 4.10. ( ) rewetsatpsens TTmcq ?= (4.9) ) 9 ?C 124 a) ?T sub = 9?C b) ?T sub = 30?C Figure 4.15: High-g time resolved heat flux from interior heaters in the 1.62 x 1.62 mm 2 array. T wall = 100?C. 94 93 92 91 90 89 63 62 61 60 59 58 36 35 34 33 32 57 5 1615143156 6 1 4 133055 7 2 3 122954 125 () ( ) ()( ) ()[] ()( ) 2 22 2 5.0 0 2 2 2 ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? = ? = ? = ? ? ?? ?? ???? rewetwalllheat rewetsatp rewetwalllheat senssens rewetwalllsensheat t rewetwalllheat sens TTkA TTmc TTkA qt TTktA dt t TTkA q sens (4.10) This equation was derived by integrating the semi-infinite conduction heat flux and solving for the time required to sensibly heat the fluid to T sat . Considering the two cases shown in Fig. 4.15, if the rewetting temperature is estimated to be the bulk liquid temperature and the rewetting liquid mass is assumed the same in both cases, the estimated time required to bring the rewetting fluid up to the saturation temperature (from Eq. 4.10) is 4.5 times longer for ?T sub = 30?C (Fig. 4.15b) than for the ?T sub = 9?C case (Fig. 4.15a). From Fig. 4.15 it is observed that the width of the heat flux spike in the ?T sub = 30?C case is approximately four times that for the ?T sub = 9?C case. This calculation supports the idea that the measured spike in heat flux may be due to rewetting fluid on the heated surface and the primary mechanism of heat transfer is transient conduction over this short time period. Experimental data taken by Kim and Demiray (2004) also support this idea. As measured for the 2.7 x 2.7 mm 2 array, the edge and corner heat transfer was measured to be much higher than the center heat transfer at higher wall superheats. This trend again indicates the mechanism for CHF for these heater sizes, Fig. 4.16. First, dryout of the center of the array occurs due to high rate of vapor generation. Second, most of the time and surface averaged heat transfer eventually occurs at the edges of the heater array as the wall superheat is increased. Also note that the primary bubble tends to 126 break down into multiple primary bubbles as the subcooling is increased, Fig. 4.17. This trend was also observed for the 2.7 x 2.7 mm 2 array and is again attributed to increased condensation at the primary bubble cap as the bulk subcooling level increases reducing the primary bubble size until surface tension acts to pull the bubble apart. Also note as Figure 4.16: Bottom and side view images of a 36 heater array at low subcoolings, ?T sub = 9?C. Figure 4.17: Bottom and side view images of a 36 heater array at high subcoolings, ?Tsub = 30?C. ?T sat = 26?C ?T sat = 16?C ?T sat = 36?C 10 20 30 50 40 60 W/cm 2 ?T sat = 38?C ?T sat = 28?C ?T sat = 17?C 10 20 30 50 40 60 W/cm 2 127 the primary bubble breaks down, interior regions of the array are wetted which can enhance the time averaged heat transfer, Fig. 4.18. Figure 4.18: High-g time averaged boiling heat transfer at high bulk subcooling, ?T sub = 30?C and high wall superheat, ?T sat = 41?C. Based on the departure frequency shown in Fig. 4.14, an estimate of the amount of heat transfer due to condensation can be obtained if it is assumed that the measured heat transfer is due to a combination of three energy removal modes during the ebullition cycle. These modes include: sensible heating of the rewetting fluid after bubble departure (q s ), latent heat transfer (q e ) from the heater surface which is responsible for the formation of a bubble of mass m v , and condensation from the bubble (q c ) while the bubble is in contact with the heater surface. For the analysis that follows, these variables were calculated in joules and the heat transfer rate was determined by summing the three modes and then multiplying this value by the measured bubble departure frequency. The three different modes are graphically depicted in Fig. 4.19. As mentioned above, these heat transfer modes occur cyclically with a frequency shown in Fig. 4.14 at various 1.62 x 1.62 mm 2 , 6 x 6 heater array 10 20 30 50 40 60 W/cm 2 2.7 x 2.7 mm 2 , 10 x 10 heater array 128 Figure 4.19: Boiling heat transfer modes in high-g. subcoolings. A complete cycle occurs over time ?t which is equal to the inverse of the measured bubble departure frequency. If these three modes are the only contributors to the measured heat transfer, an estimate of the heat transfer due to condensation can be obtained from Eq. 4.11. In this equation, the total sensible heat transferred to the fluid is ( ) heat fgsubpbv measccesmeas A hTcfV qqqqqq +? ???=?++=?? ? (4.11) assumed to be that required to bring the bulk fluid temperature up to the saturation temperature. V b is the volume of the primary vapor bubble that is generated and f is the measured primary bubble departure frequency. V b was calculated based on the bubble departure diameter measured just after the bubble leaves the heater surface. As seen in Table 4.1, for pool boiling under nearly saturated bulk conditions, the primary mode of heat transfer is latent heat while for highly subcooled bulk conditions, condensation accounts for the majority of heat transfer from the surface. It should be noted that these results are for cases where a distinct primary bubble forms in high-g. Lastly, existing CHF correlations do not accurately account for the measured peak heat transfer as discussed for the 2.7 x 2.7 mm 2 array. 129 Table 4.1: Condensation heat transfer at two different subcoolings. 4.2.4 0.8 x 0.8 mm 2 , 9 Heater Array Boiling curves for the 9 heater array in high-g are presented in Fig. 4.20. A set of images of boiling from the 0.81 x 0.81 mm 2 array are shown in Fig. 4.21. At low wall superheats, the images show few active nucleation sites and the process is again dominated by natural convection. At higher superheats, the images clearly indicate the formation of a single primary bubble surrounded very occasionally by satellite bubbles, similar to what is observed in low-g for larger heaters. The measured heat transfer at low 0 5 10 15 20 25 30 35 5 1015202530354045 Wall Superheat (?C) H e a t F l u x ( W /c m 2 ) 0.81 mm 9 Heater Array ? Tsub=30?C 0.81 mm 9 Heater Array ? Tsub=25?C 0.81 mm 9 Heater Array ? Tsub=16?C 0.81 mm 9 Heater Array ? Tsub=9?C McAdams NC Correlation Rosenhow Correlation, Csf =0.0036 Figure 4.20: High-g boiling curves for a 0.81 x 0.81 mm 2 heater array. 20.3529.56.52.654128 ~026.1242.83389 q c (W/cm 2 ) q meas (W/cm 2 ) q e (W/cm 2 ) q s (W/cm 2 ) ?T sat (?C) ?? sub (?C) 130 Figure 4.21: Time-averaged, spatially resolved heat flux maps of boiling process or 9 heater array in high-g at various ?T sat and T bulk . ? T sa t = 1 6 o C ? T sa t = 2 1 o C ? T sa t = 2 6 o C ? T sa t = 3 1 o C ? T sa t = 3 6 o C ? T sa t = 4 1 o C T bu l k = 2 8 o C NO D A TA A VAIL. ? T sa t = 1 5 o C ? T sa t = 2 0 o C ? T sa t = 2 5 o C ? T sa t = 3 0 o C ? T sa t = 3 6 o C ? T sa t = 4 0 o C NO DATA A VAIL. T bu l k = 3 5 o C No r e p r e s ent a t i ve boil ing im ages av ail a ble ? T sa t = 1 4 o C ? T sa t = 1 9 o C ? T sa t = 2 4 o C ? T sa t = 3 9 o C ? T sa t = 3 4 o C ? T sa t = 2 9 o C NO DATA A VAIL. T bu l k = 4 5 o C No b o il . im age avail . ? T sa t = 1 2 o C ? T sa t = 2 7 o C ? T sa t = 1 7 o C ? T sa t = 2 2 o C ? T sa t = 3 3 o C ? T sa t = 3 7 o C NO DATA A V A I L. T bu l k = 5 4 o C 1020 30 40 50 60 131 wall superheats agrees fairly well with the Rosenhow correlation but deviates significantly at higher wall superheats ?T sat > 25?C. Primary bubble departure from the heater surface was not observed except for one case (?T sat =37 ?C, ?T sub = 8 ?C) in which departure was infrequent (< 1 Hz). Surface tension clearly dominated the boiling dynamics over the superheat and subcooling ranges investigated. The boiling curves shown in Fig. 4.20 indicate what appear to be two distinct boiling regimes. At low wall superheats, ?T sat < 25?C, multiple bubbles tend to form on the 3 x 3 heater array and tend to coalesce with a larger primary bubble which dominates the boiling activity, Fig. 4.21 - 4.22. As indicated by the presence of multiple bubbles on the surface, there appears to be few active nucleation sites and vapor appears to be Figure 4.22: High-g boiling images from a 0.81 x 0.81 mm 2 heater array, ?T sub = 9?C. generated at a small rate. Heat transfer in this regime appears to be due primarily to the movement of the individual bubbles on the heated surface which tends to enhance local mixing. At higher wall superheats, ?T sat > 25?C, another boiling regime appears to occur W/cm 2 132 and is characterized by the formation of a single primary bubble on the heated surface. Coalescence of the satellite bubbles with the primary bubble, surface tension, and increased condensation at the cap of the bubble due to natural convection prevented the primary bubble from reaching the size required for departure. A strong jet was observed above the bubble indicating the presence of natural convection and/or thermocapillary convection which served to regulate the primary bubble size by enhancing condensation at the bubble cap. The condensing vapor flux was balanced by vapor addition from smaller coalescing bubbles at its base. The occasional departure mentioned previously may indicate that the bubble is close to the required isolated bubble departure diameter for the specified operating conditions. At first glance, the primary bubble appeared to be an isolated bubble. Further analysis showed the primary bubble has a number of interesting characteristics. First, it appears to be fed by microscopic bubbles that form around the edge of the array and coalesce with it, Fig. 4.23. Second, it remains relatively stable in both size and position throughout high-g. Figure 4.23: High-g boiling from a 0.81 x 0.81 mm 2 heater array. T bulk = 28?C, ?T sat = 34?C. Colored area represents powered heaters. Microscopic vapor generation and coalescence Primary bubble 133 Due to the stability and size of the primary bubble on the heated surface, the mechanism of heat transfer is not solely dominated by buoyancy driven flows but is instead a combination of thermocapillary and natural convection. As mentioned in Chapter 1, for small bubbles that do no depart the heated surface, experiments have shown thermocapillary convection to be the dominant heat and mass transport mechanism and buoyancy effects play a much smaller role (Wang et al, 2005). From the side view images, an estimate of the force balance acting on the bubble can be calculated. The surface tension and coalescence force that counteracts buoyancy can be estimated based on the primary bubble size to be ?3 x 10 -6 N. This force is calculated based on the buoyancy force acting on a bubble, F b = ?? lv V b g where V b is calculated from the bubble diameter measured from the bottom view images. Side view images of the bubbles in high-g show a contact angle of approximately 90 degrees with a resulting surface tension force of approximately 20 x 10 -6 N. This surface tension force is an order of magnitude larger than the buoyant force acting on the bubble and therefore explains why the bubble remains on the heated surface. Increased subcooling was measured to have a negligible effect on heat transfer over the ranges tested. This tends to indicate that the thermocapillary and/or buoyancy driven flow above and around the bubble is not strongly influenced by the level of bulk subcooling. The heat transfer from the array at higher wall superheats appears to be the result of a competition between increase in heat transfer associated with the satellite bubble region and the decrease in heat transfer due to growth of the dry area under the stable primary bubble. Further analysis of the boiling images indicates that the primary bubble acts as a pump, bringing liquid in from the side of the heater array and pumping it 134 out at the top of the vapor bubble where it is transported upward due to natural convection and the momentum of thermocapillary flow. The primary bubble shape and position on the heater caused local dryout over the center of the array. The heat transfer from the heater under and outside of the primary bubble is shown in Fig. 4.24. The presence of the primary bubble causes very large heat transfer from the edge of the array due to presence of strong thermocapillary and/or buoyancy driven flows toward the center of the bubble. In addition, interior heaters (8,22-24,46, Fig. 4.24), or heaters that are >50% covered by a primary bubble appear to reach a surfaced average CHF at relatively low superheat. 0 5 10 15 20 25 30 35 40 45 20 25 30 35 40 45 ?T sup (?C) H e a t Fl ux ( W / c m 2 ) Heaters 9,21,45,47, ? Tsub = 9 ?C Heaters 8,22,23,24,46, ? Tsub = 9 ?C Heaters 9,21,45,47, ? Tsub = 30 ?C Heaters 8,22,23,24,46, ? Tsub = 30 ?C Figure 4.24: High-g surfaced averaged boiling heat flux from representative heaters in the 0.81 x 0.81 mm 2 heater array. ?T sub = 9?C. 21 8 9 22 23 24 45 46 47 135 It should be noted that the heater array size is close to the predicted bubble departure diameter from correlations and is significantly smaller than the Taylor wavelength, lending support to the idea that boiling at such scales is not governed by the models and methods presented in Chapter 1. The mechanisms for CHF are clearly not Taylor and Helmholtz instabilities as predicted from Zuber model and others. 4.3 COMPARISON OF BOILING CURVE AND HEATER SIZE RESULTS Boiling curves for all four square heater arrays investigated in high-g are shown in Fig. 4.25. At low wall superheats, the data is in good agreement with natural convection correlations for a horizontal heated surface facing upward for all subcoolings and heater sizes as mentioned previously. The fact that natural convection correlations are in good agreement with the experimental data serves additionally to validate the substrate conduction estimation method described in the previous chapter. At higher wall superheats, there appears to be a negligible subcooling dependence on the heat flux over the ranges tested for all heater sizes. This may be attributed to the fact that CHF was not measured for all the cases studied, although it can be approximated based on the trends in the data. These findings agree with classical boiling models, correlations, and experimental data which show a negligible subcooling dependence in the nucleate pool boiling regime. In addition, the data for the 1.62 x 1.62 mm 2 array shows the primary bubble that tends to form at higher wall superheats in high-g departs less frequently as the liquid subcooling increases. It is thought that a reduction in the departure frequency would cause a reduction in the heat transfer but this effect is counteracted by larger sensible heating to the rewetting fluid and additional condensation as discussed in detail previously. 136 0 5 10 15 20 25 30 35 5 1015202530354045 Wall Superheat (?C) H e a t Fl ux ( W / c m 2 ) 0.81 mm 9 Heater Array ? Tsub=31?C 0.81 mm 9 Heater Array ? Tsub=25?C 0.81 mm 9 Heater Array ? Tsub=16?C 0.81 mm 9 Heater Array ? Tsub=8?C 1.62 mm 36 Heater Array ? Tsub=31?C 1.62 mm 36 Heater Array ? Tsub=25?C 1.62 mm 36 Heater Array ? Tsub=16?C 1.62 mm 36 Heater Array ? Tsub=8?C 2.7 mm 96 Heater Array ? Tsub=31?C 2.7 mm 96 Heater Array ? Tsub=25?C 2.7 mm 96 Heater Array ? Tsub=16?C 2.7 mm 96 Heater Array ? Tsub=8?C 7 mm 96 Heater Array ? Tsub=31?C 7 mm 96 Heater Array ? Tsub=20?C 7 mm 96 Heater Array ? Tsub=11?C Figure 4.25: High-g boiling curves for various square heater arrays. Depending on the size of the heater, boiling in high-g appears to be defined by at least two distinct regimes. For heater sizes smaller than the predicted isolated bubble departure diameter, surface tension dominates the process and classical models fall short of explaining the behavior. Under such conditions, the primary bubble that forms on the heater surface does not depart and the transport mechanisms appear to be a combination of thermocapillary and buoyancy driven flow. Current nucleate pool boiling correlations used to predict the heat transfer cannot explain the differences in performance seen across heater sizes indicating the need for new models and correlations that more effectively 137 account for appropriate length scales such as the Taylor wavelength and isolated bubble departure diameter. Boiling from the smallest heater array is clearly surface tension dominated, although natural convection may play a role in enhancing condensation from the bubble cap which tends to regulate the primary bubble size. The corner and edge heat transfer compared to the larger arrays, 36 and 96 arrays, is slightly less due to the fact that vapor is not removed from the heated surface by bubble departure. For heaters that are larger than the isolated departure diameter and smaller than the vapor jet diameter predicted from Taylor instability (1.62 ? 2.7 mm arrays), the heat transfer at higher wall superheats was measured to be 100% higher than for the 0.81 x 0.81 mm 2 array. This enhancement is due to primary bubble departure that occurs frequently allowing rewetting of the heated surface and an enhancement in heat transfer. For the largest heater size investigated (7 x 7 mm 2 ), the boiling measurements appear to fall in between the two cases mentioned above. As indicated previously, this may be due to the purity of the fluid and/or the given surface/fluid combination which may act to slightly alter the heat transfer from the surface. In summary, the data appears to show three different boiling regimes in high-g. These regimes are directly related to the heater size relative to the bubble sizes. The important non-dimensional length scales that govern pool boiling performance in high-g are: the ratio of the heater length to the bubble departure diameter predicted from the Fritz correlation, and the ratio of the heater length to the Taylor wavelength. The heater hydraulic diameter (ratio of surface area to perimeter) may also play a significant role by determining the relative effect of heat transfer from the edge of the heater, which has 138 been shown to be dramatically enhanced under certain conditions. These length scales were found to be equally important across gravity levels as will be discussed in the next section. It is hypothesized that the transition from buoyancy to surface tension dominated boiling occurs when the bubble departure diameter (D b ) and the heater size are of the same order. The largest bubbles observed for the 1.62 mm and 2.7 mm heater cases in high gravity have a diameter of approximately 0.8 mm, supporting this hypothesis. In addition, the bubble departure diameter in high-g predicted from correlations is 0.72 mm. In summary, the three distinct boiling regimes are shown in Fig. 4.26. This figure shows the three boiling regimes defined by the relative size of the heater to the predicted 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 G-level Le ngt h ( m m ) Predicted Departure Diameter 1/2 Taylor Wavelength 3 x 3 array, 0.81 mm x 0.81 mm 6 x 6 array, 1.62 mm x 1.62 mm 10 x 10 array, 2.7 mm x 2.7 mm 10 x 10 array, 7 mm x 7 mm Figure 4.26: Boiling regime map. departure diameter (Fritz correlation) and Taylor wavelength. If the heater length is smaller than both of these length scales, boiling is surface tension dominated. If the Buoyancy Dominated Boiling Surface Tension Dominated Boiling 139 heater is larger that both of these length scales then buoyancy dominated boiling results. The various heater sizes investigated in this thesis are shown by the symbols in Fig. 4.26. 4.4 TRANSITION FROM HIGH TO LOW-G 4.4.1 Gravitational Effects on the Bubble Departure Diameter The gravitational environment produced aboard the KC-135 provides a transition from high-g to low-g over approximately five seconds. Although the transient gravitational environment produced does not allow a steady-state boiling process to be observed, significant information can be obtained nonetheless. Consider first the measured primary bubble departure frequency for the 0.81 mm to 2.7 mm heater arrays (Fig. 4.27-4.29). The departure frequency was reduced dramatically as the g-level declined, as expected, and can be explained by the reduction in buoyant forces acting on the bubble. It should be noted that a consistent primary bubble was not observed across gravity levels for a 7 x 7 mm 2 array because the heater size was much larger than a vapor column diameter and sufficiently high wall superheats that cause the formation of a primary bubble in high-g were not investigated. Looking first at the g-level dependence on the primary bubble departure frequency for various heater sizes, as the gravity level is reduced, the primary bubble was observed to depart less frequently, Fig. 4.27. An interesting trend can be observed from Fig. 4.27. It appears that for the 1.62 and 2.7 mm heaters, the bubble departure frequency is a function of the ratio of the heater length, L h , to the Taylor wavelength, ? D . Best fit curves of the data shown in Fig. 4.27 were used to calculate the data shown in Fig. 4.28. For the few data points that can be considered, the data appears to fall along the same 140 curve indicating once again the importance of the Taylor wavelength on the dynamics of the primary bubble. 0.0 2.0 4.0 6.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 G-level Depar t u r e F r equency ( H z) 0.81 mm x 0.81 mm, 9 Heaters 1.62 mm x 1.62 mm, 36 Heaters 2.7 mm x 2.7 mm, 96 Heaters Figure 4.27: Effect of Heater Size on primary bubble departure frequency (T bulk = 54 o C, T wall = 100 o C). 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 5 10 15 20 25 30 35 40 ? D /L h D e par t u r e F r eq uency ( H z ) 1.62 mm x 1.62 mm, 36 Heaters 2.7 mm x 2.7 mm, 96 Heaters Figure 4.28: Effect of the ratio of the Taylor wavelength to heater length on primary bubble departure frequency (T bulk = 54 o C, T wall = 100 o C). () vl D g ?? ? ?? 32 2/1 ? ? ? ? ? ? ? = 141 The frequency of bubble departure vs. gravity level is shown in Fig. 4.29 for the 1.62 x 1.62 mm 2 array at higher bulk subcoolings. A higher subcooling reduces the bubble departure frequency for a given wall temperature, g-level, and heater size since the size of the primary bubble decreases due to increased condensation at the top of the vapor liquid interface. As mentioned previously, the effect of bubble coalescence at the base of the primary bubble is thought to significantly influence the primary bubble departure 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 G-level Depar t ur e Fr eq uen c y ( H z) Tbulk=55 ?C Tbulk=45 ?C Tbulk=34 ?C Figure 4.29: Effect of bulk fluid temperature and g-level on bubble departure frequency. Data taken from a 36 heater array (1.62 x 1.62 mm 2 ), T wall = 95?C. frequency. Higher wall superheats increase vapor generation from satellite nucleation sites, increasing the rate of coalescence. The dynamic effects of the coalescence process are thought to provide a net force that holds the bubble onto the surface, counteracting buoyancy as shown in Fig. 4.30. 142 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 G-level Depar t u r e Fr equency ( H z) Twall= 90 ?C Twall= 95 ?C Twall= 100 ?C Figure 4.30: Bubble departure frequency for 1.62 x 1.62 mm 2 heater array T bulk = 55?C. 4.4.2 Gravitational Effects on Primary Bubble Size The transition from high-g to low-g also had a dramatic effect on the primary bubble diameter for the 0.81 x 0.81 mm 2 array. A plot of the gravity level vs. time with representative bottom view images of the boiling process is shown in Fig. 4.31. It is interesting to note that the boiling behavior for this heater size at all gravity levels studied is strikingly similar to what is observed in low gravity boiling for all heater sizes, Fig. 4.32. The primary bubbles in high-g were seen to be significantly smaller than those observed in low-g for the same heater size. This boiling is dominated by the formation of a stable primary bubble that does not depart the heated surface. Surface tension clearly dominated the boiling process for a 9 heater array across gravity levels which indicates that if the heater size is smaller than the bubble departure diameter, the boiling heat flux is dramatically affected. 143 Figure 4.31: Bubble size vs. gravity level, ?T sat = 38?C, T bulk = 28?C. Figure 4.32: Boiling on a 3 x 3 Heater Array (.8 mm x .8 mm) at 1.6 g, T bulk = 28?C, ?T sat = 34?C. Colored area represents powered heaters. 1.4 mm, low-g 0.75 mm, high-g 144 Observations showed the primary bubble (formed in high-g) increases in size as the gravity level decreases. The increase in primary bubble diameter may be due to a decrease in natural convection causing decreased condensation at the top of the bubble. At equilibrium the bubble was nearly 100% larger in low-g. 4.5 HIGH-G CONCLUSIONS In conclusion, the data presented in this section serves to validate previous work for boiling from heater sizes larger than the isolated bubble departure diameter. In addition, the Rosenhow correlation accurately predicts the pool boiling performance at relatively low wall superheats. The primary mechanism for heat transfer during nucleate pool boiling was different for various levels of subcooling. Under near saturated bulk conditions, the majority of heat removal from the surface occurs due to sensible heating to the rewetting fluid as well as latent heat transfer required for bubble formation. Under high bulk subcoolings, the primary bubbles that formed tended to stay on the heated surface longer and large heat transfer due to condensation was identified. For large heaters, the mechanism for CHF was identified to be dryout of the interior portion of the heater which is accompanied by a strong increase in heat transfer from the edges. High gravity boiling on small heaters can be surface tension dominated, similar to boiling in low gravity. Surface tension dominated boiling results in a dramatically lower heat flux and the transition to surface tension dominated boiling is not a function of Bo B alone but depends additionally on wall superheat, bulk fluid subcooling, heater size, and gravity level. 145 Chapter 5: Low-g Boiling Results 5.1 INTRO Buoyancy was found to be the primary bubble departure mechanism at higher g- levels. The primary effect of a reduction in the gravitational level is a reduction in the buoyant force acting on bubbles which causes them to grow large and depart the heated surface less frequently. Bubble departure from the heated surface was found to account for the majority of the heat transfer during saturated pool boiling while under highly subcooled conditions, condensation from the bubble cap was identified as the primary heat transfer mechanism in the presence of strong buoyancy driven convection around the primary bubble. Because the transport process is enhanced by bubble removal and buoyancy driven convection, it can be expected that a reduction in bubble departure frequency in addition to a reduction in buoyancy driven convection tends to reduce the time and surface averaged heat transfer. This chapter discusses in detail the heat and mass transport characteristics due to bubbles that do not depart the heater surface. In low-g, bubbles tended to grow much larger than their high-g counterparts and the heat flux in most cases were found to be dramatically reduced. Although this might be expected at first glance, physical mechanisms not thought to be significant were found to dominate the transport process. Extensive experimental data is presented throughout this chapter which serves to support the many inferences made. This chapter is organized in a similar manner to Chapter 3. Experimental results for the square heater arrays are first presented and analyzed. The effects of bulk liquid subcooling and wall superheat are discussed in detail for each heater size. This is 146 followed by a brief discussion on the effects of boiling in low-g from heaters of larger aspect ratio. Lastly, information is presented which identifies the effect of dissolved gases on the boiling performance in low-g which was found to be dramatic. Throughout this chapter, experimental data is discussed alongside analytical and numerical models. These models are meant to facilitate understanding of the phenomena in addition to providing a predictive capability for future design. Last, a summary of the significant contributions of this work and design recommendations for a passive thermal control system in space are discussed. The conclusions section discusses recommendations for future work in this area. 5.2 HEATER SIZE EFFECTS 5.2.1 7 x 7 mm 2 , 96 Heater Array Boiling curves for a 7 x 7 mm 2 heater array in low-g are shown in Fig. 5.1 for all bulk liquid subcoolings. Images of the boiling process for a 7 x 7 mm 2 array are shown in Fig. 5.2. At low wall superheats, the process is dominated by single phase conduction through the liquid. This transport process is much less efficient than the natural convection process observed in high-g at similar superheats and is the reason why a smaller heat flux is measured. In a zero-g environment, the heat transfer from the heater during single phase transport can be modeled at first approximation using a steady state conduction model assuming the liquid located a distance, x, away from the heater is at constant bulk temperature. As an example, assuming the temperature of the bulk liquid located 1 cm away from the heater surface is at T bulk then the resulting heat transfer due to conduction is 0.02 W/cm 2 . This value is much smaller than the measured heat flux which may be due to residual buoyancy driven fluid motion. Steady natural convection 147 0 2 4 6 8 10 12 14 16 18 20 5 101520253035 Wall Superheat (?C) H e a t Fl ux ( W / c m 2 ) LOW-G, 7 mm 96 Heater Array ? Tsub= 29 ?C LOW-G, 7 mm 96 Heater Array ? Tsub= 19 ?C LOW-G, 7 mm 96 Heater Array ? Tsub= 9 ?C LOW-G Rosenhow Correlation, Csf = 0.0041 HIGH-G, 7 mm 96 Heater Array ? Tsub= 31 ?C HIGH-G, 7 mm 96 Heater Array ? Tsub= 20 ?C HIGH-G, 7 mm 96 Heater Array ? Tsub= 11 ?C McAdams NC Correlation HIGH-G Rosenhow Correlation, Csf = 0.0041 Figure 5.1: Boiling curves for a 7 x 7 mm 2 heater array in low and high-g. that is set up in high-g may not be significantly damped out in the amount of time the g- environment transitions from high to low-g (< 5 sec). Therefore, it is concluded that the residual fluid motion within the system enhances the single phase heat transfer process in low-g. In a true microgravity environment, the steady-state time and surfaced averaged heat flux is predicted to be much smaller. As bubble formation occurs at low wall superheats, 15?C < ?T sat < 25?C, the measured heat transfer in low-g is similar to what was measured in high-g, Fig. 5.1. This is due to the formation of small bubbles on the heater that move around and coalesce with other bubbles on the heater surface. Under such conditions, the nucleation site density was relatively small, and the formation of a primary bubble was not observed and may be 148 Figure 5.2: Surface reso lved tim e averaged bo iling heat trans f er in low-g from a 7 x 7 mm 2 heater array 149 due to the fact that vapor is not generated at a sufficient rate to sustain a larger bubble on the surface, Fig 5.3. For all of the subcooling levels investigated, condensation from the W/cm 2 Figure 5.3: Boiling in high and low-g at low wall superheats, ?T sat = 21?C. bubbles was observed which regulates their size. The bubble coalescence process in low- g mentioned above appears to have the same effect on the heat transfer as in high-g where much smaller bubbles were observed, Fig. 5.3. As seen from Fig. 5.3, the heat transfer appears to be evenly distributed across the heater array for both g-levels and although the bubbles are much larger in low-g, the time and spatially averaged heat transfer is nearly the same and independent of subcooling. It appears that the lateral bubble motion on the surface low-g can create the same heat flux as smaller departing bubbles in high-g. In this boiling regime which can be defined as, ?isolated satellite bubble regime?, the bubbles act as turbulence generators and their relative movement across the heater surface allows the surrounding cooler liquid to wet the surface, enhancing the heat transfer. In low-g at low wall superheats, the primary heat transfer mechanism appears to Low-g, ?T sub = 9?C High-g, ?T sub = 21?C 150 be single phase conduction to the rewetting liquid although an appreciable condensation component may exist. This will be discussed in greater detail for the smaller heater arrays. It is interesting to note that the Rosenhow correlation, which was shown to be a good predictor of performance in high-g, predicts a heat transfer that is much smaller than the measured value in low-g, Fig 5.1. It is clear from this data that such models need to be modified to account for the pertinent mechanisms in low-g. At higher wall superheats, the boiling curves in low-g are strongly dependent on the level of subcooling. Consider first the lowest subcooling investigated (?T sub =9?C). The heat transfer increases with superheat up to 26?C, then decreases at higher superheats. The primary bubble that formed at ?T sat = 26?C increased in size as the superheat increased but did not grow large enough to cover the entire heater, Fig. 5.2. The primary bubble moved around the heater surface coalescing with smaller satellite bubbles. Primary bubble movement in low-g may be due to induced liquid motion from the surrounding satellite bubbles and/or the significant g-jitter in all three axial directions aboard the KC-135. G-jitter has a much larger effect on the primary bubbles that form on the 7 mm array than on the smaller heaters. Thermocapillary effects were not observed to be significant at this particular subcooling. CHF is clearly indicated from the trend in the boiling curve and measured to be approximately 7.8 W/cm 2 at ?T sat = 27?C, Fig 5.1. The mechanism for CHF appears to be breakdown of the satellite bubble region into a single primary bubble which tends to insulate most of the heater area. The CHF at the highest subcooling (?T sub =29?C and 31?C) was much higher than for the case mentioned above. As indicated from Fig 5.1, CHF was not reached for this particular subcooling over the range of the wall superheats measured. Coalescence with 151 the primary bubble was observed to be the satellite bubble removal mechanism at all wall superheats investigated. As the wall superheat was increased from 25?C < ?T sat < 30?C, the size of the primary bubble increases slightly causing dryout over a larger portion of the array. This effect is counteracted by higher heat transfer around the primary bubble due to increasingly active nucleation sites and strong coalescence that increases as the wall superheat is increased. As the superheat is increased to 30?C, the primary bubble size reaches a maximum, but does not cause complete dryout on the heater. The heat flux continues to increase, however, due to a higher nucleation site density and heat transfer around the primary bubble. As the wall superheat is increased above 30?C, the primary bubble size decreases due to the onset of strong thermocapillary driven flows. This allowed increased satellite bubble formation and an enhancement in heat transfer. Further increases in superheat were accompanied by increases in thermocapillary convection which reduced the primary bubble size and increased the overall heat transfer. CHF was not reached since the derivative of the satellite bubble heat transfer w.r.t the wall superheat was positive, Eq. 5.1. In this equation, q?wet refers to the average heat (5.1) flux over the satellite bubble area, A wet . In addition, it is assumed that the heat transfer beneath the primary bubble is negligible. The derivatives shown in Eq. 5.1 were calculated using a backward differencing scheme. As shown in Fig. 5.4, this value is positive at ?T sat = 30?C. A comparison between high-g and low-g boiling at high subcooling is shown in Fig. 5.5. Clearly, the presence of the primary bubble in low-g causes a reduction in time and surface averaged heat transfer. () () () 0? ?? ??? + ?? ? ??= ?? ? sat wet wet sat wet wet sat T q A T A q T q 152 Figure 5.4: Wetted area heat transfer calculation. Figure 5.5: Boiling in low and high-g, ?T sub = 29?C. Top row corresponds to boiling in high-g and bottom row corresponds to boiling in low-g. At the intermediate subcooling (?T sub =19 ?C) the boiling process is again dominated by the primary bubble. Trends similar to the high subcooling cases are observed in both the heat flux data and the images for all heater sizes. As expected, the primary bubble size falls between the high and low subcoolings sizes as does the measured time and surface averaged heat flux, Fig. 5.6. A wet = 26.2 mm 2 7 mm ()() ()() sat wet sat wet sat wet sat wet T q T q T A T A ? ?? ? ?? ??? ? ? ?? ? ? ? ? ? q" wet (W/cm 2 )16.4 A wet (cm 2 )0.262 dA wet /d(?T sat ) (cm 2 /C) -0.036 dq" wet /d(?T sat ) (W/cm 2 C) 2.8 dq/d(?T sat ) (W/C) 0.1432 ?T sat = 30?C, ?T sub = 29?C 153 Figure 5.6: Bulk liquid subcooling effect in low-g pool boiling from a 7 x 7 mm 2 array, ?T sat = 32 - 33?C. 5.2.2 1.62 x 1.62 mm 2 , 36 Heater Array and 2.7 x 2.7 mm 2 , 96 Heater Array 5.2.2.1 Low Subcooling. Boiling curves for the 1.62 x 1.62 mm 2 and 2.7 x 2.7 mm 2 heater arrays are shown in Fig. 5.7. At low subcoolings (?T sub = 6?C), a large primary bubble was observed over most of the wall superheat range investigated. At low wall superheat, ?T sat = 9?C, no bubbles were observed on the heated surface and the heat transfer mechanisms were similar to those describe previously for the larger heater. At higher wall superheats, ?T sat > 15?C, vapor generated at active nucleation sites coalesced into a stable primary bubble that caused dryout over nearly all of the heater area resulting in a very small heat transfer, Fig. 5.8-9. Although the bubbles sizes remain nearly the same, the heat transfer from the edge of the array, heaters 65-96, appears to reach a time and surface averaged maximum at ?T sat = 30?C, Fig 5.10. This is due to two competing effects, 1). an increase in heat ?T sub = 29?C ?T sub = 19?C ?T sub = 9?C W/cm 2 154 0 2 4 6 8 10 12 14 16 18 5 101520253035404550 Wall Superheat (?C) H e at Fl ux ( W / c m 2 ) LOW-G, 2.7 mm 96 Heater Array ? Tsub= 29 ?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 23?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 14?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 6 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 29 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 23 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 14 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 6?C Figure 5.7: Low-g boiling curves for a 1.62 x 1.62 mm 2 & 2.7 x 2.7 mm 2 heater arrays. ?T sat =38.9 o C ?T sat =29.0 o C ?T sat =19.0 o C Figure 5.8: Bottom and side view time averaged low-g boiling images of a 2.7 x 2.7 mm 2 heater array at low subcooling, ?T sub = 6?C. 155 ?T sat =19.0 o C ?T sat =29.0 o C ?T sat =39.0 o C Figure 5.9: Bottom and side view time averaged low-g boiling images of a 1.62 x 1.62 mm 2 heater array at low subcooling, ?T sub = 6?C. 0 1 2 3 4 5 6 7 8 9 10 5 15253545 ?T sat (?C) H e a t Fl ux ( W / c m 2 ) Heaters 1-64 Heaters 65-96 Figure 5.10: edge (black,#65-96) and center (gray, #1-64) boiling from a 2.7 x 2.7 mm 2 heater array at low subcooling, ?T sub = 6?C . 10 155 20 W/cm 2 96 95 94 93 92 91 90 89 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 67 3918 5 161514315686 68 40 19 6 1 4 13 30 55 85 69 41 20 7 2 3 12 29 54 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 156 transfer from the wetted heaters outside the primary bubble as the wall superheat increases, and 2). an increase in the size of the primary bubble which reduces the wetted heat transfer area as described previously for the larger heater array. 5.2.2.2 High Subcooling. As the subcooling is increased, the low-g boiling curve takes a dramatically different shape. At low wall superheats ?T sat < 13?C, the heat transfer process is again dominated by conduction and residual buoyancy driven convection. Consider first the 1.62 x 1.62 mm 2 , 36 heater array at the highest subcooling investigated, ?T sub = 29?C, Fig 5.11. At low superheats, the primary bubble is significantly smaller than the heater size and few active nucleation sites are observed. The rapid increase in wall heat transfer as the superheat increases to 23?C (CHF) is due to an increase in the number of active nucleation sites as observed from the bottom view videos. These nucleation sites produce small bubbles that tend to coalesce with the primary bubble that forms. At CHF, the primary bubble was observed to rotate counterclockwise with a frequency of 28 rad/sec or 4.4 Hz as shown in Fig. 5.12. Consider first heater #8 in the 2.7 x 2.7 mm 2 heater array, the colored heater in Fig. 5.12. The time resolved heat flux for this heater is shown in Fig. 5.13 a-b. Considering the movement of the primary bubble at CHF, Fig. 5.12, it is clear from the bottom view images that heater #8 is periodically completed covered by the primary bubble for approximately 0.05-0.1 seconds. During such times, heat transfer is expected to be very small. This is in good agreement with the time resolved heat flux measurement shown in Fig 5.13b which periodically goes to zero. 157 ?T sat =17.8 o C ?T sat =27.9 o C ?T sat =37.9 o C ?T sat =23.0 o C, CHF ?T sat =33.8 o C ?T sat =42.7 o C ?T sat =13.2 o C ?T sat =23.0 o C, CHF Figure 5.11: Bottom and side view time averaged low-g boiling images of a 1.62 x 1.62 mm 2 , 36 heater array (a) and a 96(b) heater array at high subcooling, ?T sub = 29?C. Such trends indicate a number of interesting findings. First, the primary bubble acts as a vapor reservoir that moves around the heater surface, pulling bubbles into it. This causes a significant heat transfer in the region where coalescence occurs. Comparing this performance to high-g, the measured time averaged heat flux appears to be nearly identical. Therefore, it can be concluded that satellite bubble coalescence with W/cm 2 10 20 30 40 50 60 (b) 2.7 x 2.7 mm 2 , 96 heater array, ?T sub = 29?C (a) 1.62 x 1.62 mm 2 , 36 heater array, ?T sub = 29?C 158 Figure 5.12: Time resolved low-g boiling images at CHF, ?T sat =23?C, ?T sub = 29?C for a 2.7 x 2.7 mm 2 heater array. Colored heater corresponds to heater # 8 in the array. the primary bubble replaces bubble departure as the primary mechanism for heat transfer in low-g at relatively low wall superheats and high subcoolings. More importantly, it appears that the effect of the primary bubble is similar to the heat transfer mechanism in high-g indicating that high-g correlations may be able to predict the heat transfer in low-g if the gravitational term is replaced by another term that accounts for primary bubble size. It should also be noted that heat transfer from the corner of the array, heater #96 at CHF is nearly identical to heat transfer in high-g, Fig. 5.14, indicating once again that low-g mechanisms produce the same measurable behavior during high-g. The CHF condition described extensively above can be analyzed further by considering the following scenario. At any given instant in time, the heater has a distribution of satellite bubbles on its surface as seen from Fig. 5.12. The total mass of vapor on the surface in the form of satellite bubbles at each instant in time can be 1.07 s 1.14 s 1.21 s 1.28 s 1.35 s 1.42 s 1.49 s 1.56 s 159 . (a) Time resolved heat flux over entire parabola. (b) Time resolved heat flux over smaller time scale. Figure 5.13: Time resolved boiling heat flux from Heater #8 (Fig. 5.10) at CHF, ?T sat = 23?C, ?T sub = 29?C. Fig. 5.10 does not correspond to the time scale in this graph. 160 Figure 5.14: Time resolved heat transfer for heater #96, 2.7 mm array, at low-g CHF, ?T sat = 23?C, ?T sub = 29?C. calculated by summing the volume of the bubbles, V b,i , and multiplying by the density of FC-72 vapor, 16.4 kg/m 3 . Furthermore, the amount of latent heat required to produce such a bubble distribution on the surface can be estimated by multiplying the mass of vapor by the latent heat of vaporization. As mentioned previously, the primary bubble rotates in a counterclockwise direction around the surface coalescing with satellite bubbles. After one complete counterclockwise revolution, the primary bubble has removed all of the satellite bubbles shown in a given picture at time, t. As the primary bubble coalesces with the satellite bubbles, it is interesting to note that the primary bubble does not increase in size. The vapor addition to the primary bubble from satellite bubble coalescence is balanced by condensation at the top of the primary bubble. In this manner, the primary bubble acts as a vapor sink. Considering the above scenario, an 161 estimate of the latent heat transfer from the heater surface can be obtained from Eq. 5.2. Furthermore, a more accurate estimate of the latent heat transfer to the fluid can be calculated by considering the above scenario for all images, Eq. 5.3, where k is total number of pictures and n is total number of bubbles on a given picture. The analysis described above assumes condensation from satellite bubbles to be negligible which is justifiable by the fact that they do not grow to the size of the primary bubble and therefore are in contact with higher temperature liquid which is possibly superheated. In addition, the absence of buoyancy driven convection enables condensing vapor to remain in the local vicinity of the bubble interface heating up the surrounding bulk liquid. This idea predicts a decreasing rate of condensation as time increases due to the transient increase in the bulk fluid temperature surrounding a bubble locally. This analysis also neglects coalescence between adjacent satellite bubbles which increases the latent heat transfer estimation. Performing this analysis for the image shown in Fig. 5.11 (0.21s image), results in a heat flux estimation of 0.046 W/cm 2 , Table 5.1. ? = =?? n i ib heat pfg V A fh q 1 , ? k V A fh q k j n i ib heat pfg ideal ?? == ? ? ? ? ? ? ? ? =?? 11 , ? (Eq. 5.2-5.3) It is clear from the above calculation that the amount of heat transferred to the fluid as latent heat at CHF does not account for the amount of heat transfer measured experimentally. In fact, the measured heat flux is 2.5 orders of magnitude higher than the calculated value. This indicates that the majority of heat transfer at CHF in low-g is not due to latent heat transfer but is instead due to sensible heating of the fluid that wets the heater surface as bubbles coalesce and move around the heater. This rewetting process is enhanced by the movement of the primary bubble on the heater surface which acts as a 162 CHF Latent Heat Calculation Bubble # D b (mm) V b,i (m 3 ) q latent (J) 1 0.27 1.030E-11 1.274E-05 2 0.54 8.241E-11 1.019E-04 3 0.4 3.349E-11 4.141E-05 4 0.135 1.288E-12 1.592E-06 5 0.3 1.413E-11 1.747E-05 6 0.15 1.766E-12 2.184E-06 7 0.32 1.715E-11 2.120E-05 8 0.11 6.966E-13 8.612E-07 9 0.135 1.288E-12 1.592E-06 10 0.27 1.030E-11 1.274E-05 11 0.135 1.288E-12 1.592E-06 12 0.2 4.187E-12 5.176E-06 13 0.13 1.150E-12 1.421E-06 14 0.13 1.150E-12 1.421E-06 15 0.1 5.233E-13 6.470E-07 16 0.35 2.244E-11 2.774E-05 17 0.23 6.367E-12 7.872E-06 18 0.27 1.030E-11 1.274E-05 19 0.27 1.030E-11 1.274E-05 20 0.135 1.288E-12 1.592E-06 21 0.35 2.244E-11 2.774E-05 22 0.54 8.241E-11 1.019E-04 23 0.3 1.413E-11 1.747E-05 24 0.135 1.288E-12 1.592E-06 25 0.27 1.030E-11 1.274E-05 26 0.6 1.130E-10 1.398E-04 27 0.6 1.130E-10 1.398E-04 F p (Hz) 4.4 A heat (cm 2 ) 0.069984 q'' (W/cm 2 ) 0.046 Table 5.1: Latent heat flux calculation at CHF. single phase turbulence generator. This finding is also in agreement with the results presented for the larger 7 mm heater array. As the superheat is increased above CHF to 28?C, a sharp decrease in heat transfer occurs due to increased dryout of the heater. Considering the CHF condition described previously, if the rate of vapor addition from the satellite bubbles increases due to an increased satellite bubble density, the condensation from the primary bubble is unable to condense enough vapor to maintain a constant primary bubble size. Therefore 163 the primary bubble tends to grow which decreases satellite bubble formation allowing the bubble to reach a larger stable size. At this point, vapor generation is balanced by condensation from the bubble cap which serves to regulate the primary bubble size. As the superheat is increased above 32?C, a strong increase in thermocapillary convection was observed from the side view video images. The mechanism for the sudden increase in thermocapillary driven flow is currently unknown but may be due to the increased vapor generation from the edge of the array that occurs at higher wall superheats or it may be related to the presence of dissolved gases in the liquid, as suggested by Straub (2001). Similar trends in the heat transfer data are observed for the lower subcooling cases, T bulk = 35? C and T bulk = 45?C, Fig. 5.15-16. For the 2.7 mm 96 heater array, coalescence was again observed to be the primary mechanism for CHF at higher subcoolings (similar to the 36 heater array). Although strong thermocapillary convection was observed at high subcoolings and high superheats, data was not obtained with sufficient superheat resolution to determine whether a local maximum occurs after CHF (as was observed for the 36 heater array). A comparison between boiling in high and low-g for these heater sizes is shown in Fig. 5.17-18. As mentioned previously, correlations do not account for the nearly identical performance at low wall superheats and do not predict the trends at higher wall superheats during the presence of strong thermocapillary flow. At the highest superheat and subcooling, (?T sat = 43?C, ?T sub = 29?C), the heat flux surpassed CHF, suggesting that thermocapillary convection can limit the rise in heater temperature even for an applied heat flux greater than CHF. 164 ? T sa t = 13 o C ? T sa t = 23 o C ? T sa t = 33 o C ? T sa t = 43 o C ? T sa t = 11 o C ? T sa t = 21 o C ? T sa t = 31 o C ? T sa t = 41 o C ? T sa t = 12 o C ? T sa t = 22 o C ? T sa t = 32 o C ? T sa t = 47 o C 1020 30 40 50 60 W/cm 2 T bulk = 35 o C T bulk = 28 o C T bulk = 45 o C ? T sa t = 29 o C ? T sa t = 39 o C ? T sa t = 9 o C T bulk = 55 o C ? T sa t = 19 o C Figure 5.15: Time-averaged, spatially resolved heat flux maps of boiling process for 96 heater array in low-g at various ?T sat and T bulk . 165 Figure 5.16: Time-averaged, spatially resolved heat flux maps of boiling process for 36 heater array in low-g at various ?T sat and T bulk . 18 o C 33 o C 28 o C 38 o C 43 o C ? T sa t = 16 o C ? T sa t = 36 o C ? T sa t = 31 o C ? T sa t = 26 o C ? T sa t = 21 o C ? T sa t = 41 o C ? T sa t = 17 o C ? T sa t = 22 o C ? T sa t = 27 o C ? T sa t = 32 o C ? T sa t = 37 o C ? T sa t = 42 o C 1020 30 40 50 60 W/cm 2 T bulk = 45 o C T bulk = 35 o C ? T sa t = 9 o C ? T sa t = 29 o C ? T sa t = 24 o C ? T sa t = 19 o C ? T sa t = 34 o C ? T sa t = 39 o C T bulk = 55 o C 23 o C T bulk = 28 o C 166 0 5 10 15 20 25 30 35 40 5 1015202530354045 Wall Superheat (?C) H e a t F l u x (W /c m 2 ) LOW-G, 2.7 mm 96 Heater Array ? Tsub= 29 ?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 23?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 14?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 6 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 29 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 23 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 14 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 6?C HIGH-G, 2.7 mm 96 Heater Array HIGH-G, 1.62 mm 36 Heater Array Figure 5.17: Boiling Curves for a 1.62 mm and 2.7 mm heater arrays. Figure 5.18: Boiling behavior on a 6 x 6 array, 1.62 x 1.62 mm 2 powered array for high- g (top row) and low-g (bottom row). Heat flux is in W/cm 2 . 167 5.2.2.3 Thermocapillary Convection. The formation of very strong thermocapillary convection was observed at high subcoolings and high wall superheats. Fig. 5.19 plots 0 10 20 30 40 50 60 10 15 20 25 30 35 40 45 ?T sup (?C) H eat F l u x ( W / c m 2 ) LOW-G, 2.7 mm array LOW-G, 1.62 mm array HIGH-G, 2.7 mm array HIGH-G, 1.62 mm array Figure 5.19: time and surface averaged heat flux from the wetted area in high and low-g T bulk = 28?C, ?T sub ranges from 29-30?C. Wetted heaters are highlighted in black. the heat flux measured in the wetted area for both high and low-g. The wetted heaters are those that are completely outside of the primary bubble dryout region. It is interesting to note that the heat transfer in the wetted area in low-g is slightly larger than in high-g, indicating that the rate of vapor generation and removal is more efficient in low-g than in high-g. The primary bubble is able to sustain a large vapor influx from around its edges as thermocapillary convection is increased. At certain wall superheats, ?T sat = 33?C and ?T sat = 37?C, the wetted area heat transfer is slightly larger in low-g than in high-g. The time resolved heat flux plot for heater #96, corner heater, is shown in Fig. 5.20a-b. As indicated from the heat flux trace in low-g, the corner heaters are always outside the 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 68 40 19 6 1 4 13 30 55 85 69 41 20 7 2 3 12 29 54 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 68 40 19 6 1 4 13 30 55 85 69 41 20 7 2 3 12 29 54 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 168 (a) Time resolved boiling in high and low-g throughout parabolic maneuver. (b) Time resolved boiling over one second. Figure 5.20: 2.7 x 2.7 mm 2 heater, T wall =100?C, T bulk = 28?C heater #96 (corner heater). 169 primary bubble area and continuously wetted with bulk liquid. As shown in Fig 5.21a, vapor generated in this region is removed by the primary bubble allowing continuous thin film vapor generation throughout low-g. In high-g, the corner heater is occasionally partially covered with a bubble and this causes the heat transfer to drop dramatically, Fig 5.21b. When this bubble departs a spike in the heat transfer is measured. (a) Low-g time resolved image sequence. ?T sat = 43?C , ?T sub = 29?C (b) High-g time resolved image sequence. ?T sat = 41?C, ?T sub = 30?C. Figure 5.21: Time resolved boiling images in high-g (b) and low-g (a). 0.0 s 0.20 s 0.40 s 0.0 s 0.20 s 0.40 s 0.60 s 0.80 s 96 96 96 96 96 96 96 96 96 96 0.60 s 0.80 s 170 At high wall superheats and bulk subcoolings, the presence of strong thermocapillary convection was observed. Analyzing the wetted area in low-g further shows a number of interesting trends. First, the effect of bulk liquid subcooling on wetted area heat transfer is shown in Fig. 5.22. In high-g the time averaged wetted area heat flux is independent of bulk subcooling. This agrees with the data presented in the previous chapter which showed that subcooling had a negligible effect on the boiling heat flux in the nucleate boiling regime and agrees with the work of other researchers presented in Chapter 1. In low-g, a nearly linear dependence of subcooling on wetted area heat flux is observed. This indicates that the bulk liquid subcooling in low-g influences the thermocapillary flow as mentioned previously. The data from various subcoolings and wall superheats is plotted in Fig. 5.23 showing that the data tends to 10 15 20 25 30 35 40 10 15 20 25 30 ?T sub (?C) He a t F l u x ( W / c m 2 ) LOW-G, 2.7 mm array HIGH-G, 2.7 mm array LOW-G, 1.62 mm array HIGH-G, 1.62 mm array Figure 5.22: Wetted area heat flux at various subcoolings for T wall = 90?C. 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 684019 6 1 4 13305585 694120 7 2 3 12295484 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 684019 6 1 4 13305585 69 41 20 7 23122954 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 171 y = 3.1092e 0.0392x R 2 = 0.9796 10 15 20 25 30 35 40 45 50 55 60 30 40 50 60 70 80 T wall -T bulk (?C) H eat F l u x ( W / c m 2 ) 2.7 mm Heater Array, Twall = 100?C, Tbulk = 28?C 2.7 mm Heater Array, Twall = 105?C, Tbulk = 35?C 2.7 mm Heater Array, Twall = 100?C, Tbulk = 45?C 2.7 mm Heater Array, Twall = 90?C, Tbulk = 28?C 2.7 mm Heater Array, Twall = 90?C, Tbulk =35?C 2.7 mm Heater Array, Twall = 90?C, Tbulk = 45?C 1.62 mm Heater Array, Twall = 100?C, Tbulk = 28?C 1.62 mm Heater Array, Twall = 100?C, Tbulk = 35?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 28?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 35?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 45?C Figure 5.23: Low-g time and surface averaged heat transfer from the wetted area for various heater arrays and different wall superheats and subcoolings. collapse onto a single curve indicating that the driving temperature difference for such flows is the wall temperature minus the bulk temperature. The heat transfer coefficient obtained from the wetted area and the wall temperature minus the bulk temperature, which appears to be the driving temperature difference, is shown in Fig. 5.24. It can be inferred that increased subcooling enhances the thermocapillary flow rate around the bubble which acts to enhance the heat transfer coefficient in the wetted area. Further information about the thermocapillary phenomenon can be obtained by considering a number of different analytical models. An estimate of the liquid velocity around the primary bubble during thermocapillary convection can be obtained by considering the bubble shape and heat transfer measured. This model will be referred to as the ?latent heat transfer model?. If it is assumed that all of the measured heat flux 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 68 40 19 6 1 4 13 30 55 85 69 41 20 7 2 3 12 29 54 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 96 95 94 93 92 91 90 89 o 65 37 64 63 62 61 60 59 58 88 66 38 17 36 35 34 33 32 57 87 673918 5 161514315686 684019 6 1 4 13305585 69 41 20 7 23122954 84 70 42 21 8 9 10 11 28 53 83 71 43 22 23 24 25 26 27 52 82 72 44 45 46 47 48 49 50 51 81 73 74 75 76 77 78 79 80 172 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 30 40 50 60 70 80 T wall -T bulk (?C) h co r n er (W / m 2 K) 2.7 mm Heater Array, Twall = 100?C, Tbulk = 28?C 2.7 mm Heater Array, Twall = 105?C, Tbulk = 35?C 2.7 mm Heater Array, Twall = 100?C, Tbulk = 45?C 2.7 mm Heater Array, Twall = 90?C, Tbulk = 28?C 2.7 mm Heater Array, Twall = 90?C, Tbulk =35?C 2.7 mm Heater Array, Twall = 90?C, Tbulk = 45?C 1.62 mm Heater Array, Twall = 100?C, Tbulk = 28?C 1.62 mm Heater Array, Twall = 100?C, Tbulk = 35?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 28?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 35?C 1.62 mm Heater Array, Twall = 90?C, Tbulk = 45?C Figure 5.24: Low-g time and surface averaged heat transfer coefficient from the wetted area. from the wetted heater area goes into latent heat transfer, the vapor generated near the base of the bubble must condense somewhere along the primary bubble surface area, Fig. 5.25. From the bottom view images, the wetted area can be calculated by subtracting the heater area by the primary bubble dryout area. The area for vapor condensation to occur across the primary bubble interface is assumed to be some fraction of the total surface area of the primary bubble, f. It is assumed that the majority of the primary bubble area has condensation occurring across it and vapor is only generated in a small region near the contact line. From the equations shown in Fig. 5.24, an estimate of the average liquid velocity normal to the bubble interface can be obtained, 2.5 mm/s < v liq < 10 mm/s. These equations represent a simple energy balance near the heater surface and assumes all of the measured heat transfer goes into vapor generation and a mass balance over the 173 Figure 5.25: Thermocapillary convection velocity analytical model example for following condition, 2.7 x 2.7 mm 2 heater array, ?T sat = 43?C, ?T sub = 29?C. same region equates the vapor mass flux to the liquid mass flux. The calculated velocity values provide a good analytical estimate of the minimum liquid velocity directly above the bubble interface and is in good agreement with experimentally measured values (15 mm/s -140 mm/s, Wang et. al, 2005). During the presence of thermocapillary convection, the actual liquid velocity above the bubble is expected to be higher than this value due to the presence of thermocapillary stresses which provide additional impetus for flow. The second analytical model developed, referred to as the ?sensible heating model?, was created based on the experimental results shown in Fig. 5.23 which identifies the bulk fluid temperature and wall temperature as the driving temperature difference for thermocapillary flow. This model assumes the primary bubble acts as a heat pump bringing in liquid from the bulk fluid at its base and pumping the fluid along the two-phase interface until it is expelled at the top of the bubble in a saturated thermodynamic state. A diagram of the model is shown in Fig. 5.26. This model A wet = 1.81 mm 2.57 mm q" wet (W/cm 2 ) 56 A wet (cm 2 ) 0.018 m dot (kg/s) 1.21E-05 A cond (m 2 ) 1.30E-06 f 0.5 V liq (mm/s) 5.80 m m locallocal Aq?? frAwhere Ah Aq vAvm h Aq m pbcond condfgl wet lcondllliq fg wet vap 2 2? ? ? = ?? === ?? =  174 predicts a zero liquid velocity in low-g under bulk saturated conditions which is similar to what was observed at the lowest subcooling measured experimentally. This model assumes the heat transfer is directly proportional to the bulk subcooling level which has been shown to strongly influence the strength of thermocapillary convection, Fig 5.26. Figure 5.26: Sensible analytical model for the liquid velocity above the vapor bubble. Example for following condition, 2.7 x 2.7 mm 2 heater array, ?T sat = 43?C, ?T sub = 29?C. 5.2.3 0.8 x 0.8 mm 2 (9 heater array) Images of the boiling behavior for a nine heater array are shown in Fig. 5.27. Boiling curves for the nine heater array in low-g are presented in Fig. 5.28. At low wall superheats, ?T sat < 15 ?C, the transport process was dominated by single phase conduction and convection to the bulk fluid. For the nine heater array, a primary bubble was observed to form and cause dryout over significant portions of the heater surface. Subcooling was found to have little effect on the size of the dry area. At low wall superheats, the primary bubble oscillated laterally on the surface. The cause of such oscillations is currently unknown but may be due to g-jitter aboard the aircraft. The magnitude of oscillations decreased with increasing wall superheat and the size of the dry q" heat (W/cm 2 ) 12.5 A 0.5h (cm 2 ) 0.036 m dot (kg/s) 1.38E-05 v liq (mm/s) 1.215 175 ?T sat =18.9 o C ?T sat =29.1 o C ?T sat =39.0 o C ?T sat =18.1 o C ?T sat =27.9 o C ?T sat =37.9 o C (a) ?T sub =6 o C, T bulk =55 o C (b) ?T sub =29 o C, T bulk =28 o C Figure 5.27: Low-g time averaged boiling images from a 0.81 x 0.81 mm 2 heater array. 0 2 4 6 8 10 12 14 5 101520253035404550 Wall Superheat [?C] H e a t Fl ux (W / c m 2 ) LOW-G, 0.81 mm 9 Heater Array ? Tsub= 29 ?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 23 ?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 14 ?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 9 ?C Figure 5.28: Low-g boiling curves for a 0.81 x 0.81 mm 2 heater array. 176 area increased, resulting in a lower average heat flux. CHF appears to occur at very low superheats immediately following boiling incipience. Also, in contrast to boiling from larger heaters, the onset of thermocapillary convection was not observed. This may be due to the heater size and amount of satellite bubble formation in addition to the size of the primary bubble which is much smaller and therefore may not grow large enough to grow out of the superheated liquid layer. This observation suggests that if the growing primary bubble is within the superheated region, then the onset of thermocapillary convection cannot occur. Furthermore, this also suggests that the superheated boundary layer thickness is an important scaling parameter and its value relative to the heater length appears to strongly influence thermocapillary behavior. A complete listing of the boiling images from this array is shown in Fig 5.29. 177 T bulk = 2 8 o C ? T sat = 1 8 o C ? T sa t = 38 o C ? T sa t = 3 3 o C ? T sat = 28 o C ? T sa t = 2 3 o C ? T sat = 4 3 o C ? T sat = 1 6 o C ? T sat = 26 o C ? T sa t = 2 1 o C ? T sat = 36 o C ? T sat = 4 1 o C ? T sa t = 3 1 o C T bulk = 4 5 o C No boil. im age ava il. ? T sat = 1 7 o C ? T sa t = 37 o C ? T sat = 27 o C ? T sat = 4 2 o C ? T sa t = 3 2 o C T bulk = 3 5 o C ? T sat = 1 4 o C ? T sa t = 1 9 o C ? T sat = 24 o C ? T sat = 3 9 o C ? T sat = 34 o C ? T sa t = 2 9 o C T bulk = 5 4 o C ? T sa t = 2 2 o C 1020 30 40 50 60 Figure 5.29: Time-averaged, spatially resolved heat flux maps of boiling process for a 9 heater array in low-g at various ?T sat and T bulk . W/cm 2 178 5.3 LOW-G HEATER SIZE EFFECTS SUMMARY Boiling curves from all of the square heaters investigated in this study are shown in Fig. 5.30. It appears that low-g boiling behavior on square heaters appears to be dominated by the dynamics of the primary bubble. At low wall superheats (?T sat < 18?C), boiling performance appears to be constant across gravity levels. At higher wall superheats, boiling performance is significantly reduced in low-g. Increased subcooling decreases 0 2 4 6 8 10 12 14 16 18 5 101520253035404550 Wall Superheat [?C] H eat F l u x ( W /cm 2 ) LOW-G, 2.7 mm 96 Heater Array ? Tsub= 29 ?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 23?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 14?C LOW-G, 2.7 mm 96 Heater Array ? Tsub= 6 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 29 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 23 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 14 ?C LOW-G, 1.62 mm 36 Heater Array ? Tsub= 6?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 29?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 23?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 14?C LOW-G, 0.81 mm 9 Heater Array ? Tsub= 9?C LOW-G, 7 mm 96 Heater Array ? Tsub= 29?C LOW-G, 7 mm 96 Heater Array ? Tsub= 19?C LOW-G, 7 mm 96 Heater Array ? Tsub= 9?C Figure 5.30: Low-g boiling curves for various heater sizes and subcoolings. the size of the primary bubble, allowing satellite bubbles to form with a corresponding increase in heat transfer. CHF for the intermediate sized heaters, appeared to be a result 179 of the competition between increasing heat transfer associated with the satellite bubbles and the decrease in heat transfer due to growth of the dry area under the primary bubble as the wall superheat increases. It was shown that the primary mode of heat transfer at CHF was single phase conduction to the rewetting fluid. Depending on the heater size, there appears to be an initial CHF which is dominated by satellite bubble coalescence. This is attributed to heater dryout and the reduction of bubble removal mechanisms such as buoyancy. Increased subcooling appears to delay the reduction in boiling performance (compared to high-g) to higher wall superheats. Thermocapillary convection may be responsible for the post-CHF increase in heat flux observed on the two intermediate sized heaters (2.7 mm-6x6 and 2.7 mm-10x10) at higher subcoolings. For the largest heater (7 mm-10x10), CHF was not observed at high subcoolings although the thermocapillary mechanism was still dominant. Multiple models were presented that predict the liquid flow velocity above the bubble at higher wall superheats and subcoolings (post CHF). It is thought that increased subcooling causes increased condensation at the bubble cap, resulting in a smaller bubble, which in turn increases the temperature gradient along the surface of the bubble. This leads to an increase in the strength of the thermocapillary convection, which brings cold liquid to the bubble cap increasing condensation and causing the bubble to shrink even further. The ultimate size of the primary bubble results from a balance between vapor removal by condensation and vapor addition by evaporation at the base which is primarily due to coalescence with the satellite bubbles. The size of the heater appears to strongly affect the primary bubble size and onset of thermocapillary motion through its effect on the superheated boundary layer near the 180 surface. As indicated, the boiling performance for the smallest heater 0.8 x 0.8 mm 2 is very different from boiling from larger heaters in low-g. In a low-g environment, the thermal boundary layer during the initial growth of the bubble near the heater can be modeled using a single phase axisymmetric transient conduction model. Assuming no vapor generation, the model is shown in Fig 5.31. In this figure, boundary 4 represents the heater which is at bulk temperature at time =0 and then set to T wall for t>0. Boundaries two and five are constant temperature boundaries where T = T bulk . Boundary 1 is an insulated boundary and boundary 3 is an axisymmetric boundary. The length of boundary four relative to the length of all other boundary is sufficiently small such that the effects of boundary 2 and 5 are negligible over the time scales considered. The transient conduction model was developed and Figure 5.31: 2-D axisymmetric model of the thermal boundary layer near the heater surface in low-g. analyzed using FEMLAB. In Fig 5.31, the two pertinent length scales should be noted, L heater , or the length of the heater array, and L sat , or the superheated boundary layer 1 2 3 5 4 L heater L sat = f(time) 4 1 3 y 181 thickness which is defined as the vertical distance away from the heater element where the temperature of the liquid is above the saturation temperature. It should also be noted that L sat is a function of time. Different numerical results were obtained by varying L heater to correspond to the actual heater lengths encountered in this experiment. Representative results obtained in FEMLAB at a given time are shown in Fig. 5.32. In this figure a hemispherical boundary is drawn on the contour plot which would represent the maximum size of a growing Figure 5.32: Axisymmetric transient conduction results for a 7 mm heater at t = 1000 s. The x and y axis represent the distance in meters, and the colors represent the temperature, T wall = 100?C. T bulk = 28?C. bubble on the heater surface (constrained from growing larger than the heater). A growing bubble is constrained from growing by two different mechanisms. Firstly, if the bubble reaches a diameter the size of the heater array, it is constrained from further 182 growth and secondly, the bubble may reach a height above the heater (bubble radius) where cool liquid at the two-phase interface prevents further growth by allowing significant condensation. A plot of the thermal boundary layer development as a function of time is shown in Fig. 5.33. It is significant to note that the boundary layer does not develop in a hemispherical manner. This has profound effects for a hemispherically growing bubble that is on the heated surface. Firstly, consider the various length scales mentioned above, Figure 5.33: Time resolved boundary layer development. Colors represent temperatures and the vertical axis represents various times. L sat and L heater . A non-dimensional number can be defined which is the ratio of these lengths. This value is plotted as a function of time in Fig. 5.33 for the various heater lengths investigated experimentally. It is interesting to note that the growth of the 183 superheated region is much faster for the smaller heater array than for the larger heaters. Furthermore, it is assumed that a hemispherically growing bubble on the surface is limited in radius by L sat or L heater , whichever is smaller. In Fig 5.34, for the smallest heater array, L sat is equal to L heater in a much smaller time than for the larger heater arrays which may explain why the bubbles for this array cause dryout over the heater array for all conditions investigated. The experimentally measured bubble shapes for this heater are shown in Fig 5.35. It is clear from the data that the bubbles that grow from a 0.8 x 0.8 mm 2 heater array are much less hemispherical than the bubbles observed from the larger arrays. It can be inferred that the bubble wants to continue to grow vertically above the heater surface but is constrained from growing laterally by the heater boundary. This indicates that the bubble has not reached sufficient height to allow significant 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0123456 Ln (time) [sec] L sa t / L he a t 0.81 mm heater 1.62 mm heater 2.7 mm heater 7 mm heater Figure 5.34: Development of the superheated boundary layer for various heaters (numerical results obtained using FEMLAB). 184 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 15 20 25 30 35 40 45 Wall Superheat (?C) B h / h L 9 Heater Array Tbulk = 28?C 9 Heater Array Tbulk = 35?C 9 Heater Array Tbulk = 45?C 9 Heater Array Tbulk = 55?C 36 Heater Array Tbulk = 28?C 36 Heater Array Tbulk = 35?C 36 Heater Array Tbulk = 45?C 36 Heater Array Tbulk = 55?C 96 Heater Array Tbulk = 28?C 96 Heater Array Tbulk = 35?C 96 Heater Array Tbulk = 55?C Figure 5.35: Primary bubble geometric characteristics for different heaters. condensation to occur above the bubble. It appears that the constraining mechanism on bubble size is not growth of the superheated boundary layer but is instead the heater length. For the 7 mm heater array the observation is completely the opposite. Firstly, note that CHF was not observed experimentally for this array at high subcoolings as opposed to the two intermediate sized heaters where CHF was defined as the breakdown of the satellite bubbles into a single primary bubble on the heater surface. For the 7 mm heater array, a single primary bubble was never observed to cover the entire array. This might again be explained by Fig 5.34 which shows that for a 7 mm array, the time required for the thermal boundary layer to grow to the size of the heater length is very large. In other words, it appears the constraining bubble growth mechanism is the development of the superheated boundary layer and not the heater length. 185 The above model is valid for short times after nucleation where the bubble begins to grow and remains inside the superheated region. Once the bubble reaches a stable size, which occurs at later times, thermocapillary motion and additional mass fluxes across the vapor bubble interface (condensation) may significantly affect the thermal and velocity boundary layers around the bubble. For the larger heaters, strong thermocapillary motion was observed at higher wall superheats and it is acknowledged that the model presented is less valid. The above analysis should be used instead to understand the growth of the boundary layer around the small heater array, 0.81 x 0.81 mm 2 , where liquid motion was not observed and dryout occurred under all conditions. A more vigorous model would account for evaporation, condensation and thermocapillary effects along a two-phase interface. In summary, it appears that the size of the primary bubble compared to the heater size determines the heat transfer. The wall superheat, heater size, subcooling, and the development of thermocapillary convection all impact the size of the bubble that forms. In conclusion, as the heater gets larger, it takes a much longer time for the thermal boundary layer thickness, measured directly above the center of the heater, to reach a length equal to the heater length. If the growing bubble extends out of the superheated layer, condensation and thermocapillary effects become increasingly significant. As an example, consider a hemispherically growing bubble. As the bubble grows, if the bubble quickly extends out of the superheated region and begins to condense before the bubble can reach a diameter that is equal to the heater length then the governing length scale is the superheated boundary thickness (as is in the larger heater, 7 mm). In contrast, consider a hemispherically growing bubble that reaches a diameter that is equal to the 186 heater length and is within the superheated boundary layer. Under such conditions, the bubbles is constrained from further lateral growth by the heater and grows vertically within the superheated boundary layer. If the heater is completely covered by vapor, the bubble may not extend out of the superheated region (as in the small heater case, 0.81 mm). 5.4 HEATER ASPECT RATIO EFFECTS 5.4.1 Comparison of 2 x 2, 1.4 x 1.4 mm 2 array and Baseline Heater (1.62 x 1.62 mm 2 ) The 2x2 array on the 7x7mm 2 heater was of similar overall size (1.92 mm 2 ) to that used to obtain the baseline data, 1.62 x 1.62 mm 2 (Fig. 5.7). At low superheats (?T sat < 29.5?C) nucleation did not occur and the heat transfer was due to conduction and convection to the fluid. G-jitter in the three coordinate directions during the low-g portion of parabolic flight and undamped natural convection may have caused small scale convection within the test chamber. Compared to the baseline boiling curve, differences can be attributed to a lower wall superheat used to initiate boiling in the larger 7 mm case compared to the baseline case. In those cases where nucleation did occur at low wall superheats, a clear reduction in active nucleation sites compared to the baseline case was observed. This may be attributed to the fact that these two heater arrays were made approximately two years apart and the oxide deposited on the surface may not have the same structure. The width and length of the serpentine resistance elements were also different, perhaps leading to a different surface morphology. Lastly, the extensive degassing process used for the larger array may have resulted in a deactivation of nucleation sites that might have been active if a small amount of gas were present. 187 An increase in superheat to 29.5?C resulted in the formation of a stable primary bubble which caused dryout over most of the heated surface, similar to what was observed for the baseline data at a similar superheat. Increasing the superheat to 34.7?C increased the strength of the thermocapillary convection and reduced the primary bubble size, allowing additional wetting of the heater edges and corners. The ratio of wetted to heated area was measured from the images to be from the images to be 68% for the 2x2 array, and 31% for the baseline data at similar superheats. The increase in wetted area is directly proportional to the increase in the heat transfer (roughly 50%). 0 5 10 15 20 10203040 7 mm array, 2x2, Tsub=9 ?C 7 mm array, 2x4, Tsub=9 ?C 7 mm array, 2x6, Tsub=9 ?C 7 mm array, 2x8, Tsub=9 ?C 7 mm array, 2x10, Tsub=9 ?C 7 mm array, 2x2, Tsub=19 ?C 7 mm array, 2x4, Tsub=19 ?C 7 mm array, 2x6, Tsub=19 ?C 7 mm array, 2x8, Tsub=19 ?C 7 mm array, 2x10, Tsub=19 ?C 7 mm array, 2x2, Tsub=29 ?C 7 mm array, 2x4, Tsub=29 ?C 7 mm array, 2x6, Tsub=29 ?C 7 mm array, 2x8, Tsub=29 ?C 7 mm array, 2x10, Tsub=29 ?C Heat Flux (W/cm 2 ) TllTt(C) Figure 5.36: Boiling curves for various aspect ratio heaters at various bulk subcoolings. ?T sat (?C) 188 5.4.2 Aspect Ratio Effects Boiling curves for heaters of various aspect ratio (2x2, 2x4, 2x6, 2x8, and 2x10 heaters powered on the 7 mm array) at three subcoolings (9?C, 19?C, and 29?C) are shown on Fig. 5.36. Images of the boiling behavior obtained through the heater array are shown on Fig. 5.37. In general, higher subcoolings for a given aspect ratio result in higher overall heat transfer. The boiling behavior at various subcoolings is described below. The heater aspect ratio was changed by varying the number of heaters powered (2x2, 2x4, 2x6, 2x8, 2x10, and 10x10) on a 7x7 mm 2 array. 5.4.2.1 Low subcooling. For all aspect ratios at low superheats (<20?C), the nucleation site density was very low as described above. The heat transfer process is this regime is dominated by conduction and convection to the bulk liquid. At low subcooling, the heat flux appears to increase with increasing aspect ratio, especially at higher superheats. Thermocapillary motion around the bubble was observed to be very weak. For example, at ?T sat =31.4?C (Fig. 5.38), it can be seen that large increases in the wetted area fraction occur as the aspect ratio increases from 2x2 to 2x6. On non-square heaters, surface tension acts to pull the bubble away from the ends of the array, allowing liquid to partially rewet the surface and the bubble shape becomes less spherical. As seen from the images, the wetted area fraction increases from nearly 0% (2 x 2 array ) to 25% (2 x 6 array) and correspondingly larger increases in heat flux are observed. The wetted area fraction increases less dramatically between 2x6 and 2x8 (25-28%) with smaller increases in heat flux. On the 2x10 array, two large bubbles are observed, Fig. 5.38, which may result in a nominally larger increase in wetted area and larger heat transfer. In the absence of thermocapillary effects, larger aspect ratio heaters may enhance the heat 189 Figure 5.37: Im ages of boiling on heaters of various aspect ratio. The superheat at w h ich the im ages were obtained are listed below each im age. Each heater in the array has been shad ed accord ing to the time av erag e wall heat trans f er. W/cm 2 2x2 2x4 2x6 2x8 2x10 190 transfer by allowing multiple bubbles to form on the surface increasing the wetted area. Also, the presence of multiple bubbles allows bubble coalescence which has been shown to account for the majority of the heat transfer in low-g near CHF. The aspect ratio can have a dramatic effect on the heat transfer by affecting the shape of the bubble which dictates the wetted area fraction. Figure 5.38: Time averaged heat transfer from heaters of various aspect ratio, ?T sub = 9?C, ?T sat = 32?C. 5.4.2.2 High Subcooling. At low superheats (<20?C), the nucleation site density was very low as described above. At higher wall superheats, the heat transfer tends to decrease as the aspect ratio is increased from 2x4 to 2x10. At a superheat of ~24.6?C, a single oblong bubble is observed on the 2x4 array. This bubble moved slightly back and forth on the surface as it merged with smaller bubbles nucleating at the ends of the array, accounting for the higher heat transfer at the ends. As the aspect ratio increases, the single bubble split into two bubbles (2x6 and 2x8) due to surface tension effects. On the 2x2 2x4 2x6 2x8 2x10 191 2x10 array, the increased heater area allows for additional nucleation sites, but similar heat transfer levels are observed. At high subcooling (?T sub = 29?C) the heat flux increases slightly with aspect ratio at low superheats (<20?C). Visual observations indicated that the nucleation site density was very low under such conditions. At higher superheats, the heat flux decreases as the aspect ratio increases, contrary to what was observed at low subcooling. Heat fluxes up to 30 W/cm 2 are seen around the three phase bubble interface. Bubble motion for a superheat of ~29.7?C is shown on Fig. 5.39. Boiling on the 2x4 array was the result of the interplay between thermocapillary convection and bubble coalescence. The thermocapillary convection decreased the size of the primary bubble, allowing additional bubbles to form. Two bubbles occasionally merged into a single bubble at the center of the heater (which subsequently shrinks due to thermocapillary convection) allowing new bubbles to nucleate at the ends. The large bubble then merges with one of the growing bubbles, and the cycle repeats. Figure 5.39: Time lapse images for the (a) 2x4 and (b) 2x8 arrays at ?T sat = 29.7?C. 192 To a first approximation, the trends in the high subcooling data might be due to the increasing two dimensionality of the flow field around the heater. The 2x2 array experiences thermocapillary convection from all four sides of the array equally, causing the primary bubble size to shrink to its minimum value. As the aspect ratio increases, thermocapillary convection from the ends of the array become less important, and the bubble is cooled only on two sides. Thermocapillary convection dominated boiling is observed at the highest superheat (34.7?C). The size of the bubbles on all of the heaters decreases as the superheat is increased, which is due to increased thermocapillary flow causing enhanced condensation on the top of the bubbles. More of the heater surface is wetted by liquid, allowing nucleation to occur. The nucleating bubbles merge with the larger bubbles, resulting in higher heat transfer. The large bubbles on the 2x4 and 2x6 arrays were stable, while the large bubbles on the 2x8 and 2x10 arrays occasionally merged with the nucleating bubbles, disturbing the steady thermocapillary convection that had been developed and decreasing the heat transfer from the edges. 5.4.2.3 Intermediate Subcooling. At the intermediate subcooling (?T sub = 19?C), the data tends to collapse onto a single curve. This case represents a case where both thermocapillary convection and surface tension are important. 5.4.3 Summary of Heater Aspect Ratio Effects With varying aspect ratios, there appears to be two boiling mechanisms at play: thermocapillary convection and surface tension. In both cases, as the wetted area increases so does the heat transfer. At low subcooling, it appears that the heat transfer increases due to an increase in wetted area fraction when surface tension acts to pull the 193 bubble away from the heater edges at higher aspect ratios. At high subcooling, thermocapillary convection causes the primary bubble to shrink due to increased condensation, resulting in more wetted area. At high wall superheats and subcoolings, boiling performance appears to decrease with an increase in aspect ratio. Again as for the square heaters, strong thermocapillary convection was observed even for gas concentrations in the liquid <3 ppm. The origins for the thermocapillary convection are not known, but may be due to contaminants in the liquid. The effect of heater aspect ratio on the boiling performance is shown in Fig. 5.40. It is predicted that as the aspect ratio is increased above the measured values, multiple bubbles would form on the heater surface causing the performance to be independent of the heater aspect ratio. 0 2 4 6 8 10 12 14 16 18 20 012345 L h /W h H e a t Fl ux ( W / c m 2 ) ? Tsub = 29?C, ? Tsat = 35?C ? Tsub = 19?C, ? Tsat = 33?C ? Tsub = 9?C, ? Tsat = 32?C Figure 5.40: Heater aspect ratio effects on boiling heat transfer in low-g at relatively high wall superheats. W h L h 194 5.5 DISSOLVED GAS EFFECTS The effect of dissolved gas content was investigated during a single flight week in October, 2003 by conducting experiments with pure fluid (n-perfluorohexane) that was completely degassed (< 3 ppm) for two days, and then opening the boiling chamber to allow ingassing to occur until an equilibrium gas concentration was reached at room temperature and pressure (Cg = 3600 ppm). The boiling performance with very small gas concentrations has been discussed in detail throughout this chapter. All of the data previously shown was taken with a negligible gas concentration in the working fluid. For cases where the liquid gas concentration is very high, the boiling characteristics and performance are dramatically different. In a gassy system, the bubbles tended to grow much larger and cause dryout over a larger portion of the heater surface, Fig 5.41b. The reason for this may be due to the dissolution of gas as vapor is generated near the contact line. As more and more gas is released into the bubble, the bubble grows larger until its size has reached sufficient surface area for gas diffusion back into the liquid, balancing the rate of gas addition near the contact line. It is thought that the bubble that forms is predominately a gas bubble and the partial pressure of vapor inside the bubble is quite small. Boiling curves at the two different dissolved gas concentrations are shown in Fig 5.42. In high-g, it appears that the dissolved gas level has little effect on the measured heat transfer or on the qualitative boiling dynamics as observed from the side view images. Since conduction to rewetting liquid after bubble departure was shown to be the dominate mechanism in high- g, higher gas concentrations, although they may affect the bubble composition, do not seem to interrupt the bubble growth and departure process. 195 (a) C g < 3 ppm (b) (b) C g = 3600 ppm Figure 5.41: Time resolved boiling images from a 7 x 7 mm2 heater array at low and high gas concentrations in the fluid a,b, ?T sub = 28?C. 20 40 60 W/cm 2 ?T sat = 42?C ?T sat = 28?C ?T sat = 52?C ?T sat = 29?C ?T sat = 43?C ?T sat = 53?C 196 0 5 10 15 20 25 30 10 15 20 25 30 35 40 45 50 55 Wall Superheat [?C] H e at Fl ux ( W / c m 2 ) LOW-G, NO-GAS, FLIGHT 10/03, ? Tsub= 28 ?C LOW-G, NO-GAS, FLIGHT 8/04, ? Tsub= 28 ?C LOW-G, GAS, FLIGHT 8/04, ? Tsub= 28 ?C HIGH-G, NO-GAS, FLIGHT 10/03, ? Tsub= 30 ?C HIGH-G, NO-GAS, FLIGHT 8/04, ? Tsub= 30 ?C HIGH-G, GAS, FLIGHT 8/04, ? Tsub= 30 ?C Figure 5.42: Boiling curves for a 7 x 7 mm 2 heater array for various dissolved gas concentrations. In low-g, at higher wall superheats a single large primary bubble forms for high gas concentrations and the heat transfer is small and independent of wall superheat. For a degassed fluid, the boiling performance is quite different. It appears the a thin film of vapor is located on the heater surface post CHF and a strong liquid jet above the heater was observed and is attributed to thermocapillary convection. It is interesting to note that for negligible gas concentrations in low-g, CHF is 19 W/cm 2 or 70% of the high-g CHF, 27 W/cm 2 . This value is much higher than expected and is not predicted from any contemporary correlations. The dramatic enhancement in CHF for negligible gas concentrations is due to the dynamics of the boiling process which causes a thin vapor region to form near the heater and strong thermocapillary convection carries the 197 condensing vapor away from the heater at a high rate accounting for the large heat transfer measured. At the highest wall superheat investigated in low and high-g, ?T sat = 50-52?C, there appears to be no difference in the boiling performance for a degassed fluid, Fig 5.43. For this particular case, the boiling regime is in the transition region and surprisingly the boiling dynamics in high and low-g are identical. This indicates that a degassed fluid might provide significant enhancement in heat flux at high wall superheats and subcoolings for a passively cooled two-phase system in space. Figure 5.43: Time resolved boiling in high and low-g for a degassed fluid, C g = 3 ppm. ?T sat = 50 ? 52?C, ?T sub = 28?C. LOW-G HIGH-G 20 40 60 W/cm 2 198 Chapter 6: Summary of Gravitational Effects on Pool Boiling At low wall superheats, boiling performance appears to be independent of gravity level although the heat and mass transfer mechanisms are different. In high-g, buoyancy dominates the process which is characterized by the ebullition cycle. In low-g, satellite bubble coalescence is responsible for the heat transfer. At higher wall superheats, boiling performance is significantly reduced in low-g. This is attributed to heater dryout and the reduction of bubble removal mechanisms such as buoyancy. Increased subcooling appears to delay the reduction in boiling performance (compared to high-g) to higher wall superheats. The heater size appears to strongly affect thermocapillary induced heat transfer that occurs post CHF. Surface tension dominated boiling was observed in both high and low-g under certain conditions. In high-g, if the heater size is smaller than the isolated bubble departure diameter predicted from the Fritz correlation then bubble departure does not occur and the formation of a single primary bubble is observed. The transport process is dominated by natural convection and thermocapillary transport around the primary bubble interface. In low-g, surface tension dominated boiling occurred under all of the conditions investigated. The absence of buoyancy means that thermocapillary convection around the primary bubble is the dominant heat and mass transport mechanism. It appears that the primary bubble dominates the boiling performance in low-g. If the primary bubble grows in size to completely dryout the heater surface then low heat transfer results. Contrastingly, the smaller the primary bubble relative to the heater surface, the larger the heat transfer. The effect of bulk liquid subcooling was found to have a more dramatic relative effect on heat transfer in low-g. This is attributed to the 199 strong dependence of thermocapillary convection on the bulk liquid subcooling level in low-g. Thermocapillary effects are less significant in high-g due to the presence of buoyancy driven convection around the bubble which tends to compensate for a reduction in thermocapillary convection at lower subcoolings. In low-g, CHF appeared to be a result of the competition between increasing heat transfer associated with the satellite bubble and the decrease in heat transfer due to the growth of the dry area under the primary bubble as the wall superheat increases. It is hypothesized that the primary bubble size in microgravity is affected by a number of parameters including the thickness of the superheated boundary layer and the heater length. For a growing bubble in microgravity, the bubble is constrained from growing either vertically or laterally depending on the thickness of the superheated boundary layer or the heater length. For smaller heaters, it appears that the heater length determines the maximum size of the primary bubble while for larger heaters, the superheated boundary layer thickness determines the size. If the heater size is the dominant parameter affecting bubble size then thermocapillary convection may be very small and low heat transfer results. The presence of dissolved gases in the system was shown to have a dramatic effect on boiling performance in low-g. The presence of non-condensables changes the composition of a growing bubble. Consider a binary system of n-perfluorohexane and nitrogen. As a bubble forms on the surface and grows, nitrogen is carried into the bubble along with vapor. At equilibrium, the bubble reaches a size whereby vapor and gas addition at its base is balanced by vapor and gas removal near the top of the interface. Gas transport across the bubble interface is governed by diffusion and is directly 200 proportional to the concentration gradient of gas near the bubble interface. The equilibrium gas concentration in the bubble causes it to grow larger than it would if no gas was present. This larger bubble causes increased dryout of the heater surface and a reduction in heat transfer. In high-g, the composition of the bubble is less significant due to buoyancy effects. The bubble departure size, departure frequency (and heat transfer) are unaffected by the composition of the bubble in this case because the density of the two components are nearly identical. Thermocapillary flow is important due to its local transport of the hot thermal boundary layer near the heater. It appears that the thermocapillary flow velocity near the bubble can be approximated if the heat flux and bubble size are known. It was also observed that during thermocapillary dominated boiling, heat transfer from the wetted region in low-g is comparable to heat transfer in high-g under similar conditions. The driving temperature difference for the flow was found to be the wall temperature minus the bulk temperature. Although very strong thermocapillary flow was observed throughout these experiments, its origins are not known. It is believed that the thermocapillary motion observed in these experiments is not due to dissolved gas effects as suggested by Straub (2000) since the gas concentration was reduced to well below 3 ppm and strong liquid jets above the bubbles were still observed. Its presence may instead be due to contaminants in the system. Although reasonable care was taken to clean the system, it was not possible to remove all contaminants. Contaminants may have been introduced into the system from the O-rings used to seal the system, or the small amount of silicone RTV used to seal the PGA containing the heater array to the bottom of the test chamber. 201 Chapter 7: Contributions and Future Scope 7.1 CONTRIBUTION TO THE STATE OF THE ART This thesis provides a much needed basis for future research concerning two- phase flows in space. In addition to providing an in-depth discussion of the boiling process in a variable gravity environment, this effort has identified some of the pertinent pool boiling mechanisms in low-g including thermocapillary convection and bubble coalescence. A comprehensive discussion of the CHF mechanisms in low-g was presented and provides a firm groundwork for future two-phase thermal design in space. In addition, contributions to the state of the art include: 1) Development of an optimized sensor capable of heat flux and temperature measurement at the small scale 2) Development of analytical and numerical methods for interpreting sensor data 3) Characterization of pool boiling in the absence of ebullition cycle behavior a. Applicability of classical models was determined 4) Identification of pertinent scaling parameters 5) Fundamental boiling mechanisms in low gravity identified and analyzed 7.2 FUTURE WORK 7.2.1 Numerical A number of numerical investigations were presented in this thesis. Although these models provide support for the experimental observations made, additional models could be developed which account for: a dynamic bubble interface, energy and mass 202 transport across the two-phase interface, surface tension effects near the three-phase contact line, and the effects of multiple components in the fluid. In addition, statistical thermodynamic modeling (molecular dynamic simulations) could serve to identify the governing mechanisms for the onset of thermocapillary flow. 7.2.2 Experimental This thesis focused on a single fluorocarbon fluid. Additional research should be conducted that investigates the performance of various other fluids including organic and inorganic compounds. The selection of such fluids would have to meet the most stringent of design specifications for testing in space. These specifications, noted earlier in this thesis, are extensive and may require redundant safety systems and containment vessels that could prove costly for future space experimentation. The effect of g-jitter on bubbles is still unclear. This effect needs to be quantified entailing experimentation aboard microgravity platforms that are more robust and significantly more expensive than the KC-135. The thermocapillary phenomenon is discussed throughout this thesis. Future experimentation should focus on the origin of such flows. This would entail measurements (temperature, pressure, velocity) near the two-phase interface. In conclusion, while some recent studies shed light on the complex phenomena governing pool boiling in microgravity, these studies are mostly qualitative in nature and inconclusive at best. This effort provides a discussion of extensive experimental measurements taken aboard the KC-135. 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AEC Report AECU-4439. 209 Appendix A: TEDP Report Prepared by: Jungho Kim (PI) Christopher Henry University of Maryland Dept. of Mechanical Engineering College Park, MD 20742 (301) 405-5437 (O) (301) 314-9477 (FAX) kimjh@eng.umd.edu Technical Grant Monitor: Mr. John McQuillen (216)-433-2876 John.B. McQuillen@nasa.gov Support Provided by NASA MSAD Under Grant No. NCC3-783 FLIGHT WEEK: July 2005 210 A.1 CHANGE PAGE Doc. Version Date Process Owner Description Basic Aug, 2004 J. Kim/C.D. Henry TEDP submitted for KC-135 flight Revision 1 June, 2005 J. Kim/C.D. Henry ? Revised according to NASA TEDP 0205 requirements. ? Maximum Temperature Raised to 120 deg C ? Added PIV capability (laser) ? Integrated power supply and monitor into a single test apparatus. ? Removed UPS and replaced with surge suppressor A.2 QUICK REFERENCE DATA SHEET Principal Investigator: Jungho Kim Contact Information: University of Maryland, Dept. of Mechanical Engineering, College Park, MD 20742, 301-405-5437 (O), kimjh@eng.umd.edu. Experiment Title: Pool Boiling Heat Transfer Mechanisms in Microgravity Flight Date(s): July 2005 Overall Assembly Weight (lbs.): Test Package (est. 256) Assembly Dimensions (L x W x H): Test Package: 24?wide x 24? deep x 42? high, Equipment Orientation Requests: Facing back of aircraft Proposed Floor Mounting Strategy (Bolts/Studs or Straps): Bolts,/Studs Gas Cylinder Requests (Type and Quantity): Air, 1 per day Overboard Vent Requests (Yes or No): No Power Requirement (Voltage and Current Required): Aircraft AC Power: 110 VAC (<6.5A) Aircraft DC Power: 28VDC (<4A) Free Float Experiment (Yes or No): No 211 Flyer Names for Each Proposed Flight Day: Christopher Henry, Jonathan Coursey, Hitoshi Sakamoto, Jungho Kim Camera Pole or Video Support: No A.3 FLIGHT MANIFEST Minimum number of personnel required to operate test apparatus during flight: 2 Trained Test Operators: 1) Christopher Henry, experienced test operator having previously flown aboard the KC-135 during: March 2004 (GRC), October 2003 (GRC), May 2003 (GRC), July 2002 (GRC). 2) Jungho Kim (PI), PI and experienced test operator having previously flown aboard the KC-135 during: March 2004 (GRC), October 2003 (GRC), May 2003 (GRC), July 2002 (GRC). 3) Jonathan Coursey, flew aboard KC-135 during: July 2002 (GRC) 4) Hitoshi Sakamoto, never flown aboard KC-135 A.4 EXPERIMENT BACKGROUND Experimental Purpose The physics of systems incorporating phase change processes needs to be better understood in order to provide a predictive capability for design. The current work aims to identify, measure, characterize, and model the fundamental heat transfer mechanisms associated with the boiling process in space. Experiment History The experiment is a follow-up of a previous experimental system that included a microgravity payload to study subcooled pool boiling heat transfer. This payload was flown on a Terrier-Orion sounding rocket in December, 1999 from NASA Wallops. The 212 test was considered to be very successful, with the exception of obtaining video data. The payload was therefore repackaged to fly on the KC-135, and was flown in April, 2000 from GRC. Additional data was taken in January 2001 from JSC and May, 2001 using the same test rig, but with slight modifications. The modifications include the addition of a PI supplied accelerometer in place of SAMS-FF, a temperature controller on the boiling chamber to vary the liquid subcooling, the addition of high-speed digital video, and a low-pressure air jet for cooling the bottom of the microheater array. This system was then transferred into a flight qualified rack supplied by NASA and flown in 2002, 2003, and 2004. In this series of tests, we have integrated the experimental system into a single test apparatus. A Sorenson 35 volt DC power supply, and LCD monitor have been integrated into the payload eliminating the need for an additional rack for instrumentation purposes. This dramatically reduces the space required aboard the KC-135 during flight. In addition, Particle Image Velocimetry (PIV) experimental capabilities have been incorporated into the test apparatus. The goal of this technique is to provide experimental information regarding the velocity field in the fluid around a stationary bubble in low-g under the influence of thermocapillary convection. This is achieved by seeding the fluid with glass microspheres and illuminating a plane of these spheres using a class II laser. High-speed video images are then used to track the particle motion providing information about the velocity and vorticity fields. We will be performing a series of tests to look at the effect of heater size and thermocapillary convection on microgravity boiling heat transfer. The effective heater size will be varied by turning on and off a different number 213 of heaters in the array. This series of experiments are in direct support to a space flight experiment (BXF/MABE) being developed by NASA Glenn. A.5 EXPERIMENT DESCRIPTION The experimental test apparatus aims to characterize pool boiling mechanisms in a variable gravity environment. The experimental system uses a microheater array (2.7 mm x 2.7 mm) to measure time and spatially resolved heat flux during pool boiling. The heaters are made up of an array of 96 individually controlled heater elements that are maintained as an isothermal surface through the use of feedback control circuits. PIV measurement techniques have been incorporated into the system. The experimental fluid (n-perfluorohexane) has been seeded with glass microspheres (app. 1-10 ?m diameter) at relatively small concentration levels. During the experiments, the particles become entrained in the liquid flow field around growing bubbles and, if illuminated, reflect light allowing high-speed cameras to track their position with time. Successive images can be correlated using various software algorithms providing information about the velocity and vorticity field. A plane of particles is illuminated by a class II laser directly in the center of the boiling chamber. Visualization of the bubbles during their growth and departure with high-speed cameras will be correlated to periods of high heat transfer ? this should lead to better understanding of the mechanisms by which heat is transferred during boiling. Boiling curves will be obtained at various subcooling levels under low and high gravity. The scientific objectives of the project are: 1) Obtain microgravity data with a test package hard mounded to the floor of the aircraft. 214 2) Obtain and correlate microscale heater data with video data. 3) Obtain PIV measurements of the liquid flow field around the primary bubble. 4) Compare data and observations against existing models and develop new mechanistic models where appropriate. This test will be operated with the test apparatus mounted to the floor of the aircraft. Data will be obtained regarding: 1) The time required for the heat transfer from the surface to reach a steady state after exposure to a microgravity environment. 2) Boiling curves under various subcooled conditions, including critical heat flux. 3) Low-speed visualization of bubbles using a regular CCD camera, and high-speed visualization using a Phantom digital camera. 4) The effect of heater size on boiling heat transfer. 5) Thermocapillary convection and its effects on heat and mass transfer in low- gravity The maximum temperature within the test rig will never exceed 120 ?C. Temperatures this high may occur at small areas on the heater surface (2.7 mm x 2.7 mm) for very short periods of time (< 2 sec) in order to initiate nucleate boiling. This situation poses minimal risk to operators because the system is hermetically sealed and inaccessible. Three sides of the boiling chamber are inaccessible to the user and the front side of the boiling chamber has a video camera in front of it, making unintentional contact unlikely. 215 A.6 EQUIPMENT DESCRIPTION The experimental package consists of a single main component. This component is a PI built sounding rocket payload mounted in a NASA supplied Vertical Equipment Rack (VER). This component also contains a PI supplied monitor, keyboard, and DC power supply. A photograph of the test package along with the components is shown on Fig. A.1. The components are described in greater detail in Tables 1and 2. The total weight of the package is approximately 256 lb. The dimensions of the test section are 24?x24?x42?. The ideal test operator location during experimentation is to sit fore or aft of the experimental package. To satisfy the structural requirement, the VER handles must also face fore and aft. Straps bolted to the floor of the aircraft will be used to restrain the test operators during the microgravity maneuvers. Table A.1: Description of components in VER. Type Descriptio n Component Description & Considerations Experimenta l Test rig Sounding rocket payload. This contains the boiling chamber, the high-speed camera for taking pictures from below, a computer, flash disk, control electronics, keyboard, class II laser, and temperature readout. This structure is very rigid, and has survived numerous vibration tests in preparation for the sounding rocket flight. The structure was designed to handle 50g loads in all directions. Experimenta l Frame This flight qualified frame was supplied by NASA. It bolts directly to the floor of the aircraft using four bolts at each corner. The frame will have lexan panels on each side to prevent damage to the payload from aircraft personnel, and will also keep any loose parts within the frame envelope. Experimenta l DC Power Supply This is a Sorenson LH35-10 capable of supplying 35 V, 10 A. Experimenta l Computer Monitor This is a flat panel 15" LCD monitor. Power required: 110 VAC, 1.2 A. 216 The experiment will not free float. The current test package (VER) will be mounted in the same orientation. Lexan panels are attached to the each side of the VER to prevent unintentional damage to the test rig. The lexan is 0.1?? thick, and bolted to holes in the VER. These panels are to prevent unintentional contact with the test rig by research personnel?they are not structural. The test fluid to be used will be either FC-72 or n-perfluorohexane, which is the mail constituent of the FC-72. Approximately 3 liters of one of the fluids will be used. Both fluids are completely inert at the temperatures encountered in this experiment. A hazards analysis and MSDS? for these fluids are included later in this report. Equipment to be taken on-board the flight other than the main components listed above include a pen, notepad, hand held digital video camera with power supply, a laptop computer to acquire data from the high-speed camera, and a small digital still camera. A list of equipment for each flight is given below: 1). VER 4). Clipboard with checklists 5). Pens (4) 6). 2 digital video cameras 7). Videotapes (4) 8). PCMCIA flash disks (2) 9). Digital still camera 10). Laptop The VER has handles by which it can be carried onto the plane and moved about. The VER can be handled by 2 people if necessary. The experiment can be located in any 217 location aboard the aircraft that provides enough room around the experiment for 2 people. During setup and disassembly aboard the aircraft, a tool box containing various tools will be brought aboard the aircraft if troubleshooting of the experimental system is required. The tool box is completely inventoried and this inventory will be checked anytime the tool box is taken off the aircraft. A clipboard, and laptop can be secured Figure A.1: Photograph of modified test package (the VER) and its components. Frame Test Chamber DC Power Supply High Speed Camera Class II Laser 218 to the floor of the aircraft with VELCRO during flight. The remaining items will be carried in a backpack. This backpack will be stored in storage bins provided by the aircraft facility for takeoff and landing. During the flight, the equipment in the backpack will be taped or velcro?d to the floor, held by hand (e.g. video cameras and pens), or placed in pockets in the flight suits. A.7 STRUCTURAL VERIFICATION This report summarizes the testing that has been conducted on the VER. Included in this report is a listing of flight load requirements, component weights, results of the stress test, and turning moment calculations. This report concludes that the VER structure is well within flight regulations set forth in AOD 33897, Rev A: Experiment Design Requirements and Guideline -NASA 932 C-9B. For the purposes of this test, the sounding rocket payload will be considered to be an independent and structurally sound member of the VER. The sounding rocket payload was designed to withstand 50 g loads in all directions, has undergone severe vibration testing, and has successfully withstood rocket launch with no damage to any of the systems. For these reasons, and since no modifications have been made to the core payload, it will be considered a structurally sound and rigid component of the test package, and no further analysis of the payload will be performed. The VER the test rig is housed in was sent to us by NASA, and is flight certified. An analysis of the frame is included in the appendix for reference. The frame we are using is actually stronger than the analysis suggests since the basebar and original baseplate were replaced by a 24? x 24? x 1/2? aluminum plate. The new plate is much wider than originally analyzed, and is capable of handling much higher shear loads. The sounding rocket payload is in exactly 219 the same configuration it was in when it flew on the Terrier-Orion except that the VCR is not being used. AOD 33897, Rev. A outlines five possible flight load scenarios that must be considered in conducting a structural analysis. These five scenarios are listed in Table A.3. The component weights are listed in Table 4. The rack capabilities, per Vertical Equipment Rack: Structural Analysis for Use on Aircraft are summarized in Table A.5. Scenario Load Direction One 9g Forward Two 3g Aft Three 2g Lateral Four 2g Upward Five 6g Downward Table A.2: Maximum Flight Loads Table A.3: Component weights & moment arms about base Component Weight (lbs) Component?s Center of Gravity (in) Moment arm (in?lbs) Test rig 146 24 3504 Frame 57 22 1254 DC Power Supply & mounting plate 45 44 1980 High Speed Camera 5 14 70 Monitor 3 30 90 Total 256 27 6898 Table A.4: VER Rack capabilities Allowable weight (lbs) 500 Actual Weight (lbs) 256 Rig C.G. from floor of rack (in) 27 Rig turning moment 7071 220 The philosophy behind the testing is a follows. Because both the test rig and the VER are structurally sound, a test only needs to be performed to ensure that the connections between the two are sound. Since stress testing on the actual test rig was risky, a model of the test rig was built that mounts to the frame in exactly the same way as the test rig. The exact same bolts and holes are used in both the model and test rig. A photograph of the model is shown on Figure A.2. The model was mounted in the VER, as shown in Figure 3. The model is bolted directly to the 1/2? thick base plate of the VER using four 5/16? steel bolts. The top of the test rig is bolted to a 0.25? thick aluminum plate using eight 5/16? steel bolts. The corners of this plate are attached to existing holes on the VER using 1/4? aluminum angle using 1/4? steel bolts. Stress testing for the forward direction (9 g) for the test rig (146 lbs.) was performed using an Instron SRV017 machine. The model/frame was mounted as shown in Figure 4, and model loaded at a rate of 1000 lb/min up to 1600 lbs through the steel pipe shown on Figure A.3. This pipe imparted the load directly to the model. The load was held at 1600 lbs for a few seconds. The test rig weighs no more than 150 lbs, so the 1600 lb loading represented at least 10 g of loading. No creaking or cracking of the test rig was observed during the test. Because the test rig is mounted in the frame symmetrically in the forward and aft directions, the load capability in the aft direction is similar to that in the forward direction. Stress testing in the other directions (lateral, and upward) for the test rig (146 lbs.) was performed by having two people (Combined weight of 325 lbs) stand on the model close to the center of gravity of the model after the model was rotated to various orientations. Testing in the lateral and upward directions is shown in Fig. A.5. The 221 weight of the two people combined with the weight of the model resulted in a loading in each direction that was close to 3 g. Stress testing in the downward direction was not performed. Because the test rig is mounted directly to the bottom of the frame (which is mounted to the floor of the aircraft) there is nothing that can break. The center of gravity of the test rig is 27 inches from the floor of the rack. This results in a turning moment of the test rig about the baseplate of 6912 in-lbs (assuming a 1-g loading in the forward and aft direction). A high speed camera and side view camera will be used in this series of tests, similar to what was done in April 2001. As part of the TEDP for that series of flights, the camera mounting was stress tested by placing the appropriate weights in all three directions. Figure A.2-3: Model of test rig used for stress testing & model of test rig mounted in the frame. 222 Figure A.4: Testing of model/frame in forward (9 g) direction. (a) (b) Figure A.5: Stress testing in various directions: (a) lateral, and (b) upward. 223 Stress analysis for monitor: The 15? LCD monitor is held in place between two aluminum U-channel (1-1/4? x 0.125?) brackets which are themselves held in place by two 1/4? bolts to the VER. The mass of the LCD monitor and brackets is less than 4 lbs. For a 10g loading, the stress the two bolts are subjected to can be computed to be 4x10 lbs ? 0.25 in () 2 4 ? ? ? ? ? ? ? ? 2 bolts () = 410 psi which is roughly two hundred times smaller than their yield strength. Two additional bolts on either side of the monitor prevent the monitor from sliding back and forth within the channels. These bolts also hold a 1/8? thick lexan sheet in front of monitor to protect it from unintended impact. Stress analysis for power supply: The power supply (Sorensen LH35-10) weighs 45 lbs, and is mounted onto a 6061 Al top-plate (24?x24?x1/8?) using two nylon straps (minimum 800 lb ultimate tensile load). It is positioned on the top plate by four Al angle brackets, each of which is bolted to the top-plate using two 1/4? bolts. The stress the bolts would experience under a 10g load is the weight of the power supply distributed over two bolts: 45x10 lbs ? 0.25 in () 2 4 ? ? ? ? ? ? ? ? 2 bolts () = 4600 psi The stresses on the bolts are about seventeen times smaller than their yield strength. The top-plate is attached to the VER using four 1/4? bolts. The mass of the top plate is 3.2 224 lbs. The stress these bolts would experience under a 10 g load is the sum of the weight of the power supply and the top-plate distributed over four bolts: 48x10 lbs ? 0.25 in () 2 4 ? ? ? ? ? ? ? ? 4 bolts () =2400 psi The stresses on the bolts are about thirty times smaller than their yield strength. The top plate was also stressed over 6g?s in the downward direction by having two people stand on it (total weight 330 lbs). Stress analysis for laser mount: The mounting apparatus for the laser consists of a laser mounting block which is bolted to a micro-positioner (using three -1/8? bolts). The micro-positioner is bolted (using two 1/4? diameter bolts) to a cantilever beam with a diagonal support member (both 6061 Al). This system is then bolted to the experimental system by two 1/4? bolts, see Figure below. The laser mounting block, micro-positioner, and cantilever beam weighs 2 lb, 4 lb, and 1 lb respectively. Analyzing first the mounting block, the maximum shear stress a given 1/8? bolt would experience is 600 psi well below the yield strength (10g loading assumed). A similar analysis at the micropositioner and cantilever levels results in a maximum stress of 350 psi and 611 psi respectively. The cantilever support system is designed to withstand a 6g downward loading as shown in the figure below. Under such conditions a maximum load of 36 lb is supported. Under such conditions the maximum stress within the support structure will occur along the diagonal support member (400 psi, cross sectional area 0.125 in 2 ). This number is 140 times below the yield strength limits of 6061 Al (58,000 psi). 225 Figure A.6: Laser mounting system: laser mounted block (orange square), micro- positioner (red square), cantilever support (maroon square). A.8 ELECTRICAL LOAD ANALYSIS An electrical schematic of the test apparatus is shown in Fig.A.7. Lists of the components along with their electrical characteristics are listed in Table A.8 The total current draw on the aircraft 110 VAC source is no more than 5.3A. Total power required is less than 700 W. A PID temperature controller is used to control the temperature of the liquid in the boiling chamber. The output of the RTD in the boiling chamber is input to the temperature controller. The output of the temperature controller is a 0?5 V pulse width modulated signal to a solid state relay (SSR) that determines whether or not current flows through the heaters surrounding the boiling chamber. Both the sounding rocket payload (Test Apparatus) and the heaters are protected using a slo-blo fuse rated at 10A. All wire gauges shown interior to the test apparatus are either 16-18 gauge and are well within the load limits specified in Table 8. 14 gauge wires are used to connect the test apparatus to the aircraft power supply. 7.1? 3.75? 36 lb (6g downward loading) 58? 226 The wires in the test apparatus were sized according to Table 7: Table A.5: Wire Gauges Current (A) Wire size (Ga) < 0.25 22 < 0.50 20 < 1 18 < 5 16 < 12 14 Figure A.7: Electrical schematic. Test Apparatus 110 VAC from aircraft 28 VDC from aircraft Digital camcorders (2) Laptops (1) High Speed Digital Camera Emergency Shutdown Switch DC Power Supply SSR Surge Suppressor PAYLOAD Pump Computer Monitor 6.4 A, 14 AWG 3.4 A, 16 AWG 4.0 A, 16 AWG, 10A fuse 3.0 A Temp Cont. RTD Heaters 3.4 A 14 AWG 18 AWG 18 AWG 16 AWG 18 AWG 18 AWG 16 AWG, 1A fuse 16 AWG, 5A fuse Class II laser DC < 1mW 20 AWG 227 These wire sizes are more conservative than those suggested in the JSC User?s Guide. Two mini digital video cameras will be used to record images of the boiling process. These cameras are manufactured by Canon (model Elura). A.9 LOAD ANALYSIS The total current draw on the rack 28 VDC power supply no more than 4.0 A. The total current draw on the aircraft 28 VDC source is no more than 3.4 A. Table A.6: Components and their power requirements. The master kill switch for the experiment is on the top of the VER. By depressing this red knob, all power to the experiment is cut off. The experiment has been designed to allow for a sudden loss of power without permanent damage to the experimental system and automatically defaults to a safe configuration. Alternatively, power to the VER can be turned off by turning off the power strip located at the bottom of the rig and turning off the power to the SSR. For the payload, an alternate kill switch is on the DC Power Source Details Load Analysis Name: 110 VAC 2 video cameras: 0.03 Amps Monitor: 1.2 Amps High-speed camera: 0.25 Amps Laptop: 0.15 Amps Laser: 0.005 DC Power Supply: 1.5 Amps Description: Aircraft 110 VAC Micropump: 3.0 Amps Wire Gage: 14 Total power: 550 W Outlet Current: 20.0 A Total current draw: 5.0 A Power Source Details Load Analysis Name: Aircraft 28 VDC Power Heaters for boiling chamber: 3.4 Amps Description: 28 VDC from aircraft Wire Gage: 14 Total power: 96 W Outlet Current: 20.0 A Total current draw: 3.4 Amps 228 power supply. The Micropump utilizes a 2A fuse. There is also a switch on the front that is easily accessible to shut the pump off in an emergency. The wire size used by the pump is regulated by the pump manufacturer. A.10 PRESSURE VESSEL CERTIFICATION The only chamber that experiences a pressure differential is the dome/boiling chamber, figure 8. This chamber has been pneumatically tested to 37 psia (over night) by pressurizing the chamber around the bellows. The pressure difference on the boiling chamber (the chamber containing the FC-72) will be 22.4 psig (37.1 psia). The chamber will be sealed off while the aircraft is on the ground so that the pressure will be 14.7 psia, and all tests will be performed at this pressure. In the event of a catastrophic decrease in cabin pressure at altitude, the pressure around the boiling chamber could decrease to 3.5 psia. The maximum pressure differential possible during Figure A.8: Low-pressure air cooling jet schematic (Courtesy of J. Benton). 229 the flight is therefore 11.2 psig. Since this is 2 times smaller than the pressure difference at which the chamber will be tested, the risk of the boiling chamber failing and releasing FC-72 or normal perfluorohexane is very small. Even if the test fluid is released into the cabin, the it poses no health risks since there are no toxicity limits below the temperatures at which we are operating. As an added measure of protection, a pressure relief valve (Nupro SS-RL3S4) has been installed onto the dome to relieve the pressure whenever the dome pressure exceeds the cabin pressure by 10 psig. The other pressure system being used on this flight is the low-pressure air impingement nozzle. This system is shown is Figure A.8. The system consists of a K- bottle of compressed air, a pressure regulator, a flexible hose, a needle valve, and a nozzle. The pressure downstream of the regulator will be maintained at 5 psig or less. A certified hose and pressure regulator to connect the K-bottle to the needle valve and nozzle will be supplied by NASA. The nozzle exits to the cabin. Figure A.9: Low-pressure air cooling jet schematic. 230 Table A.7: Pressure System Component MAWP (psi) Relief Valve Setting (psi) Regulator Setting (psi) Supplied/Built By 1. Air K-Bottle 2200 N/A N/A GRC 2. Pressure Regulator 2200 N/A 15 Victor MF43011 3. Needle Valve 400 N/A N/A Hoke 4. Nozzle 500 N/A N/A Custom Built Dome/boiling chamber 37 psia 10 psig N/A Custom build A.11 LASER CERTIFICATION A diode type class II laser manufactured by Diode Laser Concepts will be used as part of the PIV measurement system. The laser has internal electronics that provide static, surge, and reverse polarity protection. The laser operates at 5 VDC and draws a maximum total power of 1 mW. Included as part of the laser assembly is a lens that converts the laser beam into a sheet of laser light at an angle of 45?. The laser wavelength is 635 nm. The line width is 1mm @ 1 meter and the fan angle is 10?. The laser is used to illuminate a plane of the boiling fluid, and the light reflected off neutrally buoyant glass microspheres is imaged using a high-speed camera. Power to the laser is controlled by a switch located on the front of the experimental test rig and will be used only during parabolic maneuvers. The laser light is completely enclosed by the experimental system. Black protective mats have been attached to all viewport holes on the experimental system so that minimal laser radiation leaves the experimental chamber. No protective eyewear is required due to the laser class and since minimal laser radiation leaves the boiling chamber. The laser will be aligned and fixed in place prior to travel to NASA facilities and therefore no alignment is necessary during the flight week. 231 A.12 PARABOLA DETAILS AN D CREW ASSISTANCE We will be testing with both the test apparatus and the instrumentation rack attached to the aircraft floor for all flights. Accelerometers on the package will be used to measure the g-levels the package experiences. Data will be taken using an on-board data acquisition system throughout the parabolas for every other parabola. Ideally, a one minute window will be provided prior to the start of microgravity periods after aircraft turns for camera preparation and manual data recording. Thirty or more standard parabolas per day are desired. No crew assistance is required to operate the test equipment. A block diagram of the relevant procedures are shown in Fig. A.10. Figure A.10: In-flight operational procedure (left), pre-flight routine (right). I have some updated sheets of this to put in the Appendix. 1. Accelerometer data acquisition 2. Begin recording side view images to DV cam to (100s) 3. Initiate heater data acquisition routine (90s) 4. Pause image recording and accelerometer acquisition when finished 5. Record by hand run information to data sheets and begin second initiation 6. Turn on pump in turns 2. Set bulk temperature 3. Ensure backside airside is operating correctly 4. Create manifest flight manifest 5. Connect digital video cameras to CCD outputs 7. Test in-flight data acquisition routine 6. Test accelerometer data acquisition 3. Power on instrumentation rack and test rig IN-FLIGHT PROCEDURE PRE-FLIGHT ROUTINE 232 A.13 HAZARDS ANALYSIS REPORT GUIDELINES HAZARD SOURCE CHECKLIST Enumerate or mark N/A _N/A_ Flammable/combustible material, fluid (liquid, vapor, or gas) __5__ Toxic/noxious/corrosive/hot/cold material, fluid (liquid, vapor, or gas) __1__ High pressure system (static or dynamic) _N/A_ Evacuated container (implosion) _N/A_ Frangible material _N/A_ Stress corrosion susceptible material __3__ Inadequate structural design (i.e., low safety factor) _8_ High intensity light source (including laser) _N/A_ Ionizing/electromagnetic radiation _N/A_ Rotating device _N/A_ Extendible/deployable/articulating experiment element (collision) _N/A_ Stowage restraint failure _N/A_ Stored energy device (i.e., mechanical spring under compression) _N/A_ Vacuum vent failure (i.e., loss of pressure/atmosphere) _N/A_ Heat transfer (habitable area over-temperature) _N/A_ Over-temperature explosive rupture (including electrical battery) __6__ High/Low touch temperature __7__ Hardware cooling/heating loss (i.e., loss of thermal control) _N/A_ Pyrotechnic/explosive device _N/A_ Propulsion system (pressurized gas or liquid/solid propellant) _N/A_ High acoustic noise level _N/A_ Toxic off-gassing material _N/A_ Mercury/mercury compound _N/A_ Other JSC 11123, Section 3.8 hazardous material _N/A_ Organic/microbiological (pathogenic) contamination source __4__ Sharp corner/edge/protrusion/protuberance _N/A_ Flammable/combustible material, fluid ignition source (i.e., short circuit; under-sized wiring/fuse/circuit breaker) __2__ High voltage (electrical shock) _N/A_ High static electrical discharge producer _N/A_ Software error or compute fault _N/A_ Carcinogenic material _____ Other:______________________________________________________ _____ Other:______________________________________________________ 233 Appendix B: Optimization of a Constant Temperature Microheater Array Feedback Control Circuit 234 B.1 PROBLEM DEFINITION The primary goal of this optimization analysis is to maximize the temperature resolution of the heater array while maximizing a user defined operational temperature range. Such results serve two purposes: Firstly, the goal of experimental research is to maintain the highest fidelity in measurement and, secondly, the microheater array operates ideally when there is a minimum temperature difference between adjacent heaters. A minimum temperature difference reduces lateral substrate conduction between heaters providing a better estimate of the heat transfer due to boiling. In addition, lateral substrate conduction can cause adjacent heaters to ?turn off? during the boiling process which is problematic because the array no longer provides an isothermal boundary condition locally making it difficult to infer information about the boiling process. The control circuit mentioned previously can be modeled analytically based upon electrical circuit theory. A single and multiobjective formulation is presented alongside a host of linear and nonlinear constraints. This set of mathematical equations defines the optimization formulation that is solved using a number of methods in Matlab. A parametric investigation is performed on a number of the design parameters providing additional information about the optimized solution. A schematic of the feedback control circuit is shown in Fig. 2.1. The circuit is characterized by three main electronic components: resistors, an operational amplifier, and a transistor. Resistors, represented by R 1 , R 3 , R 4, R 5, R h, and the digital potentiometer (R DP ), define a wheatstone bridge that characterizes the performance of the control circuit. R 1 , R 3 , R 4, R 5, are metal film resistors with a manufacturer specified tolerance of 1% and are rated at 0.6 Watts. High tolerance metal film resistors are used for their 235 relative insensitivity to temperature, high power dissipation, and commercial availability. These resistors, in addition to R DP , form the set of design variables which are optimized in the analysis that follows. R DP is a dual digital potentiometer consisting of two digitally controlled potentiometers manufactured by Dallas Semiconductor. It consists of 512 resistive sections providing a resistance range of 0 ? 20 k? . R h represents the resistance of a specific heater element. As mentioned previously, each heater element can be modeled as an equivalent temperature dependent resistance (R h has a temperature coefficient of Figure B.1: Feedback Circuit Schematic resistance 1000 times larger that the metal film resistors described above). The circuit regulating op-amp, labeled ?Chopper Op-Amp? in Fig B.1, is a high-voltage, high- performance operational amplifier. An additional op-amp is used to measure the voltage, Chopper Op-Amp Digital Potentiometer V o + ? + ? R h R 3 R 4 R 1 R 2 236 V o , across the heater element but does not directly influence the performance of the control circuit. The transistor shown in Fig. B.1 is a high current, low voltage, NPN switching transistor that is used to provide power to the heater elements. It is important to note that the analysis presented subsequently applies to a single heater and its respective feedback control circuit. Similar analysis can be performed for each heater in the array to obtain an optimized heater array. The control circuit operates in the following manner: The chopper op amp is used to sense an imbalance in the wheatstone bridge, represented by R 1 , R 3 , R 4, R 5, R h, and R DP . If an imbalance exists, the op-amp outputs a proportional voltage to the gate of the transistor allowing additional current to flow from the 24 volt source through the bridge. This current causes an increase in the temperature of the heater (joule heating) with a corresponding increase in resistance. The resistance of the heater will continue to rise until a new equilibrium state is reached corresponding to a balance in the wheatstone bridge. This entire process occurs very quickly, in approximately 66?s, and much faster than the dynamic behavior of the heater boundary surface. Based on these functional characteristics, the heater resistance can be controlled by controlling R DP . During data acquisition, the time-varying voltage across the heater resistance, V o in Fig. B.1, is measured and used along with the heater resistance at the given temperature to determine the total power dissipated by the heater to maintain it at constant temperature. In summary, the design variables are defined as R 1 , R 3 , R 4, R 5, R DP (see Fig. B.1). The optimization goal involves optimizing these variables for maximum temperature resolution of a given heater in the array subject to constraints described subsequently. All design variables are approximated as continuous variables. 237 B.2 FORMULATION B.2.1 Objective Function 1: Maximize Temperature Resolution As mentioned previously, under steady state operation a balance exists in the wheatstone bridge. Written mathematically, Eq. 1 characterizes this behavior. In Eq. 1, R h is written as the dependent variable and R DP as the independent variable as described in the previous section. Taking the derivative of Eq. B.1 with respect to R DP yields the differential change in heater resistance with respect to a differential change in R DP , Eq. B.2. (B.1) (B.2) Since R DP can only be adjusted in 512 equal increments, the minimum possible change in the digital potentiometer resistance is given as 39 ?. This value also describes the maximum resolution control of the wheatstone bridge. Substituting this value into Eq. B.2 defines the minimum increase in heater resistance for a minimum change in R DP, Eq. B.3. Stated differently, Eq. 3 represents the smallest theoretical change in heater resistance for a step change in digital potentiometer setting. (B.3) In addition to Eq. B.3, the heater resistance is also strongly dependent on temperature. The temperature dependence on the resistance of the heater was measured experimentally and is characterized by the temperature coefficient of resistance, ?. () () 2 335 351 353 51 2 335 351 353 51 RRRR RRRRR RRRR RRR R RRRR RRRR RRRR RR R R DP DPDP DP DP h DP DP DPDP h + ? ? + ? =?? + ? + = ? ? () 335 51 3 41 5 5 4 31 RRRR RRR R RR R RR RR R R R R DP DP h DP DP h + +=? + + = () () 2 335 351 353 51 2 335 351 353 51 3939 RRRR RRRR RRRR RR RRRR RRRRR RRRR RRR R DP DP DP DP DPDP DP DP h + ? + = + ? ? + ? =? 238 Using this parameter, a resistance-temperature relation can be formulated, Eq. 4, where R ref , T h , T ref , and ?T, represent some arbitrary metal reference resistance (corresponding to the reference temperature), heater temperature, reference temperature, and change in temperature (T h -T ref ) respectively. These additional variables are considered design parameters and appear in the optimization formulation summary at the end of this section. Differentiating Eq. B.4 with respect to ?T, yields Eq. B.5. Equation B.5 states that a differential change in heater temperature is proportional to the differential change in resistance. (B.4) (B.5) From the previous analysis, dR h can only be controlled to a minimum value specified by Eq. B.3. Substituting ?R h for dR h (Eq. B.3 into Eq. B.5) yields the temperature resolution of the heater element, Eq. 6. Equation 6 represents the minimum possible theoretical temperature change for a step change in digital potentiometer resistance (temperature resolution or uncertainty). Therefore, the optimization objective involves the minimization of Eq. B.6, or in simplified form Eq. B.7. (B.6) (B.7) () ? ? ref h h h h ref h R dR dT dT dR R Td dR =?== ? () () ? ? ? ? ? ? ? ? + ? + = ? ? ? ? ? ? ? ? + ? + =? 2 5 53 51 2 335 351 353 51 13939391 DP DP DPrefh DP DP DPrefh h RR R RRRR RR RRRR RRRR RRRR RR R T ?? )1( 1 TRRT R R T refhref h ref h h ?+=?+ ? ? ? ? ? ? ? = ? ? () 2 53 2 51 39 min DPrefh h RRRR RR T + =? ? 239 B.2.2 Objective Function 2: Maximize Temperature Range (Single Objective Constr. 4) The second objective considers the maximum operating temperature of the heater. Substituting Eq. B.1 into Eq. B.4 for R h and setting R DP to 20000 (the maximum controllable potentiometer resistance), the high temperature limit is obtained, Eq. B.8. As a constraint, Eq. B.8 states that the maximum temperature that the heater can operate at must be greater than or equal to T high , or the user specified high temperature limit. This constraint is written as an inequality constraint for the single objective formulation. Ideally, the user would like the largest possible temperature range. Therefore, T high is a design parameter and, written in standard form, this constraint is given by Eq. B.9. Formulating Eq. B.8 as a second objective results in Eq. B.10 (note: the second objective function shown in Eq. B.10 is transformed using the epsilon constraint method to a single objective formulation, constraint g 4 , introducing design parameter T high ). (B.8) (B.9) (B.10) ref hrefhrefhrefh high T RRRRR RR RR RR T +? + +? ???? 1 20000 20000 335 51 3 41 0 1 20000 20000 : 335 51 3 41 4 ??+ + ?? ref hrefhrefhrefh high T RRRRR RR RR RR Tg ???? ref hrefhrefhrefh high T RRRRR RR RR RR T +? + += ???? 1 20000 20000 max 335 51 3 41 240 B.2.3 Inequality Constraint 1: Low Temperature Control The lowest temperature that a given heater element can be controlled to is determined by substituting Eq. B.1 into Eq. B.4 for R h and setting R DP to zero theoretically (experimentally this would be a very low value). Setting R DP equal to zero approximates the low end temperature control range. Performing this manipulation and simplifying results in Eq. B.11 with T low representing the lowest controllable heater temperature. Stating Eq. B.11 as a constraint in standard form says that the optimized circuit design must be able to operate to atleast a temperature defined by T low , Eq. B.12. T low is a user specified design parameter. Additional information regarding the operational temperature range of the heater element is given by Eq. B.13. This equation is for the user?s reference and is introduced later in this report and does not enter into the optimization formulation. (B.11) (B.12) (B.13) B.2.4 Inequality Constraint 2: Minimize Power Dissipation Across Right Side of Bridge A physical constraint that arises due to the circuit operation considers the amount of current flow through each side of the wheatstone bridge. Ideally, the user would like ref h ref low T RR RR T + ? ? ? ? ? ? ? = ? 1 3 41 0 1 : 3 41 1 ??+ ? ? ? ? ? ? ? lowref h ref TT RR RR g ? ? ? ? ? ? ? ? ? + = + =?= 20000 20000 20000 20000 53 51 335 51 RRR RR RRRRR RR TTT refhrefhrefh lowhighrange ??? 241 to have the largest current flow through the heater element R h . This situation further validates the assumption that the metal film resistors on the right side of the bridge do not change resistance because very little current will flow through them and thus a negligible amount of heat is generated. In addition, this allows large amounts of power to be dissipated through the heater which can occur during times of large boundary heat flux conditions. The larger the voltage present across the heater, the larger the range of boundary conditions the heater can accommodate. In order to ensure that a small amount of power is dissipated by the right side of the bridge, the resistance R 3 + R 4 should be significantly higher that R 1 + R ref . Stated mathematically, Eq. B.14 represents this constraint with C min being the minimum value of this ratio chosen by the user. (B.14) B.2.5 Inequality Constraint 3: Maximum Voltage Drop Across R 1 The voltage drop across R 1 should not be too high as to decrease the maximum performance of the heater array. Under high heat flux conditions, the heater resistance may require a large voltage to regulate its temperature. If the voltage drop across R 1 is too large, this will not occur. The voltage drop across a resistor in series with another is represented by Eq. B.15. Defining a maximum voltage drop permissible across R 1 , V drop , and substituting in Eq. 1 for R h , an additional constraint is formulated, Eq. 16. (B.15) (B.16) 0: 1 43 min2 ? + + ? ref RR RR Cg () h drop RR R V + ? 1 1 24 0 1 24 : 335 5 3 4 3 ?? ? ? ? ? ? ? ? ? + ++ drop DP DP V RRRR RR R R g 242 B.2.6 Inequality Constraint 5: Op-amp Sensitivity (R 1 Bound) The chopper op-amp has a minimum sensitivity (voltage difference) for accurate operation. The maximum sensitivity in the wheatstone bridge occurs when R 1 and R h are approximately equal. If the ratio of these two resistances becomes extremely large or small, the op amp is incapable of detecting the voltage difference and thus cannot compensate for an imbalance in the bridge. Therefore, an additional constraint on the system is required (Eq. B.17). Similar to equation B.14, design parameter D min is the lowest user specified ratio of R 1 and R ref and is dependent on the specifications of the op- amp. This equation can be restated as the lower bound of the design variable R 1 , Eq. B.18. (B.17) (B.18) B.2.7 Inequality Constraints 6-11: Additional Design Variable Bounds All design variables must be real numbers greater than or equal to zero. In addition, R 1 , R 3 , and R 4 have maximum bounds specified by the design parameters R 1Ubnd , R 3Ubnd , and R 4Ubnd respectively. R 5 can be any real number greater than zero and R DP has a maximum value of 20,000. Equations B.19-B.24 represent additional design variable bounds. (B.19-B.24) 200000 ,0,0 ,0,: 544 3311116 ?? ????? ???? DP Ubnd UbndUbnd R RRR RRRRgg 0 1 min ?? ref R R D min15 : DRRg ref ? 243 B.2.8 Equality Constraint 1: Define Optimized Temperature A brief analysis of Eq.7, the optimization objective function, provides some insight into this next constraint. Firstly, Eq. 7 is nonlinear w.r.t R DP indicating that the temperature resolution increases with the inverse of the quadratic of R DP . This means that the heater temperature resolution will increase with an increase in heater temperature. It can be shown that the temperature uncertainty is monotonically decreasing w.r.t R DP for R DP > 0, Eq. B.25. This indicates that the worst temperature resolution always occurs for a digital potentiometer setting of zero. () ()() () 3 53 2 1 2 5 3 53 51 5 78 178 DPrefhDPDP DP refhDP h RRRR RR RRRR R RR RR R T + ? = ? ? ? ? ? ? + ? + = ? ?? ?? (B.25) Since R DP is controlled by the user and can take on 512 incremental values between 0 and 20 k ?, a particular heater temperature, T opt , is defined which corresponds to the heater temperature being optimized. This constraint forces R DP to take on a single value corresponding to T opt and eliminates the semi-infinite behavior of this variable, Eq. B.26. The monotonic behavior of the objective function w.r.t R DP indicates that all temperatures above T opt will have a temperature resolution that is guaranteed to be better than the temperature resolution at T opt . This characteristic aids the user in selecting this critical design parameter value. (B.26) In summary, equality constraint 1 (Eq. B.26), reduces the optimization goal from optimizing the temperature resolution over the entire temperature range, to optimizing a 0 1 : 335 51 3 41 1 =+?+ + ?? optref hrefhDPrefh DP refh TT RRRRRR RRR RR RR h ???? 244 single heater temperature value. This constraint was formulated as such because in the particular research context that the author is involved, excellent temperature resolution is not required at the low temperature limit, T low , but is instead desired over a temperature range from T opt to T high . The solution therefore optimizes the temperature resolution at T opt and because of the monotonic nature of the objective function w.r.t R DP , all temperatures between T opt and T high are guaranteed to have a temperature resolution better or equal to the temperature resolution at T opt . B.2.9 Optimization Formulation Summary In summary, customization of the feedback control circuits is governed by an optimization formulation that seeks to minimize the temperature resolution of a single heater, Eq. B.6, and maximize the high temperature limit, Eq. B.10, subject to the non- linear inequality constraints, g 1 -g 3 (Eq. B.12, B.14, B.16), non-linear equality constraint, h 1 (Eq. B.26), and the design variable bounds, g 5 -g 11 (Eq. B.18-B.24). The representative multiobjective and single objective optimization formulations are summarized on the following pages (note: the single objective formulation applies the epsilon constraint method to the multiobjective formulation). Design Variables (resistor values, see Fig 1.2): R 1 [? ], R 3 [? ], R 4 [? ], R 5 [? ], R DP [? ] Design Parameters: ? h : temperature coefficient of resistance of the heater [? / ? o C] R ref : reference resistance of the heater array at reference temperature [? ] T ref : reference temperature corresponding to reference resistance [ o C] C min : constant used to minimize power dissipated across the right side of the wheatstone bridge D min : minimize ratio defined by the operation of the chopper op-amp (see 1.2). T high : the highest temperature that the heater must reach [ o C] T low : the lowest temperature the heater must be able to operate at [ o C] T opt : the temperature being optimized [ o C] 245 R 1Ubnd : upper bound of R 1 [? ] R 3Ubnd : upper bound of R 3 [? ] R 4Ubnd : upper bound of R 4 [? ] V drop : max voltage drop across R 1 [V] Single-Objective Optimization Formulation: Objective Function: (B.7) Subject to: (B.12) (B.14) (B.16) (B.9) (B.18-24) (B.26) 0 1 : 3 41 1 ??+ ? ? ? ? ? ? ? lowref h ref TT RR RR g ? 200000 ,0,0 ,0,: 544 3311min115 ?? ????? ????? DP Ubnd UbndUbndref R RRR RRRRDRgg 0 1 : 335 51 3 41 1 =+?+ + ?? optref hrefhDPrefh DP refh TT RRRRRR RRR RR RR h ???? 0: 1 43 min2 ? + + ? ref RR RR Cg 0 1 24 : 335 5 3 4 3 ?? ? ? ? ? ? ? ? ? + ++ drop DP DP V RRRR RR R R g () 2 53 2 51 39 DPrefh h RRRR RR T + =? ? 0 1 20000 20000 : 335 51 3 41 4 ??+ + ?? ref hrefhrefhrefh high T RRRRR RR RR RR Tg ???? 246 Multiobjective formulation: Objective Function: (B.7) (B.10) Subject to: (B.12) (B.14) (B.16) (B.18-24) (B.26) () 2 53 2 51 39 min DPrefh h RRRR RR T + =? ? 0 1 : 3 41 1 ??+ ? ? ? ? ? ? ? lowref h ref TT RR RR g ? 200000 ,0,0 ,0,: 544 3311min115 ?? ????? ????? DP Ubnd UbndUbndref R RRR RRRRDRgg 0 1 : 335 51 3 41 1 =+?+ + ?? optref hrefhDPrefh DP refh TT RRRRRR RRR RR RR h ???? 0: 1 43 min2 ? + + ? ref RR RR Cg 0 1 24 : 335 5 3 4 3 ?? ? ? ? ? ? ? ? ? + ++ drop DP DP V RRRR RR R R g ref hrefhrefhrefh high T RRRRR RR RR RR T +? + += ???? 1 20000 20000 max 335 51 3 41 247 B.3 ASSUMPTIONS The formulation derived previously incorporated a number of assumptions in addition to assuming the ideal behavior of the op-amp and transistor. Firstly, the circuit leads are assumed to have a zero resistance. Parasitic effects associated with inductance and capacitance within the circuits is assumed to have a negligible effect on the circuit performance. Design variables R 1 , R 3 , R 4 , and R 5 are assumed to have negligible temperature dependence. This is a valid assumption for R 3 , R 4 , and R 5 but significant power may be dissipated through R 1 causing a measurable change in its resistance. A more robust model would account for slight changes in this resistance due to joule heating. The heater resistance is assumed to be solely dependent on temperature. In reality, thermal fatigue of the heater array can cause wire bond detachment, cracking of the heater substrate, voids to form between the substrate and epoxy adhesive, and many other problems which can lead to operational transients. This assumption defines what it means to be an ideal heater (one that has uniform temperature and no time varying thermal properties). The heater properties have been measured experimentally and the heater itself has been sufficiently tested so that the ideal heater assumption is valid. For the following analysis, all design variables are assumed to be continuous variables. In reality, the commercial market only sells discrete resistors. It is assumed that multiple resistors can be put together in parallel or series combinations so that, practically speaking, the continuous assumption is valid. Theoretically, R DP is a discrete variable, but can be modeled as a continuous variable with little loss in modeling accuracy. 248 It should be noted that the nature of the current control circuit design allows resistors to be removed and installed quite easily. Through hole mounted sockets are used on printed circuit boards which eliminates the need for any additional soldering. Therefore, optimized resistance values can be installed and modified with little effort and the performance can be validated experimentally with relative ease. B.4 METHODS, RESULTS, AND DISCUSSION The presence of the nonlinear equality constraint, h 1 , makes it difficult to obtain any significant insight into the problem using monotonicity analysis. Nonetheless, the monotonic behavior w.r.t the different design variables for the temperature resolution objective function, ?T h or T unc , is shown for positive valued design variables, Eq. B.27- B.30. (B.27) (B.28) (B.29) (B.30) As mentioned previously, the mulitobjective formulation was converted to a single objective optimization problem using the epsilon constraint method. This was achieved by introducing an additional design parameter, T high , which was used to convert () 0 39 2 53 2 5 1 ? + = ? ? DPrefh unc RRRRa R R T () 0 39 2 5 2 3 2 51 3 ? + ? = ? ? DPrefh unc RRRRa RR R T () 0 78 3 53 51 5 ? + = ? ? DPrefh DPunc RRRRa RRR R T () 0 78 3 53 2 51 ? + ? = ? ? DPrefhDP unc RRRRa RR R T 249 the second objective, Eq. B.10, to a constraint, g 4 (Eq. B.9) which was varied over a specified range to obtain the Pareto frontier. A representative optimum was chosen based on user preferences and is elaborated on later in this report. An initial point sensitivity analysis was performed to assess the affect of the initial point on the optimization results. It was observed that the initial point strongly affects the optimized solutions and further discussion will be provided in the next section. A parametric investigation was performed on the design parameters T low , and T opt and their affect on the optimized design is presented subsequently. These design variables were chosen to be parametrically varied because it was observed that the constraint g 1 was active at the optimum and furthermore, h 1 , has a strong dependence on T opt . Lastly, a custom optimization solution algorithm, based on the exterior penalty method, was developed and used to verify the results obtained using the Matlab function, ?fmincon?. As will be shown, both methods agree very well with one another adding to the validity of the solutions presented herein. Before proceeding any further, it is necessary to define the different values chosen for the design parameters. The lower bounds for design variables, R 3 , R 4 , R 5 , R DP , were chosen to be a very small value, as shown in Table B.1, which avoids any singularity issues associated with the objective or constraint functions. In addition, consideration was given to avoid lower boundary values which became active constraints at the optimized solution. Similar reasoning was applied to the upper boundary limits on the design variables where all resistances except R 5 were specified to be less than 1 M?. R 5 can naturally tend toward infinity without degrading the performance of the circuit. The design parameters ?, R ref , and T ref were determined based on the physical characteristics 250 of the heater array and confirmed experimentally. C min and D min were chosen from experience, where adequate performance of the circuit has been observed. V drop was chosen based upon the maximum operating boundary conditions that are applied to heater. It has been shown through experimentation that the heater can require up to 14 volts in order to accommodate large heat flux boundaries and therefore, V drop was to chosen to be 10 volts (24V ? 14V). For the particular boiling fluid being studied (FC-72), the saturation temperature is 56 o C at atmospheric pressure. Of particular interest are the boiling characteristics at temperatures higher than 70 o C. Therefore, the temperature resolution below this value is not significant and the baseline T opt value was chosen as 70 o C. The low operational temperature limit, T low , was chosen to allow for adequate operation of the heater under ambient room temperature conditions with some margin added for safety. Operation of the heater at room temperature provides time saving diagnostic capabilities that can be used to quickly characterize the heater prior to data acquisition. T high was chosen based on reliability and safety considerations (120 o C). Most industrial electronic devices are rated to 125 o C which makes this a good temperature limit while providing a suitable range for the superheat of the fluid during boiling to be studied. Lastly, T high , T low , and T opt were parametrically studied over a range of values shown in Table 1. The baseline, or user preferred, case is the default design parameter vector used while varying the parametric variables in question. 251 Table B.1: Design parameter values Baseline R 1 89.4 R 3 0.000001 R 4 0.000001 R 5 0.000001 R DP 0.000001 R 1Ubnd 500 R 3Ubnd 1000000 R 4Ubnd 1000000 R 5 inf R DP 20000 ? 0.003 R ref 298 T ref 24.7 C min 20 D min 0.3 T high 120 T low 10 T opt 70 Vdrop 10 Parametric Study LOWER BOUND UPPER BOUND DESIGN PAR. T opt : 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 T low : 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65 T high : 71, 75, 77.5, 80, 82.5, 85, 90, 95, 100, 105, 110, 115, 120, 130, 140, B.5 SINGLE OBJECTIVE RESULTS USING ?fmincon? As mentioned above, the Matlab function, ?fmincon? was used to solve the single objective optimization formulation. This function finds the constrained minimum of a scalar function of several variables starting at an initial point estimate. It takes a number of input arguments including the function to be minimized, nonlinear equality and equality constraints, variable bounds, and others. B.5.1 Initial Point Sensitivity After programming the single objective formulation into Matlab and solving for a number of different initial points, it was observed that each optimized output was 252 quantitatively different. After verifying the Matlab output solutions were feasible, it was determined that a rigorous initial point sensitivity analysis was required to characterize the outputs. The approach developed shares many similarities to Monte Carlo analysis. The first step involved obtaining a representative set of initial points that spanned the entire range of the variable bounds. Considering the fact that there exist 5 variables and a low, medium, and high, value for each variable was desired, the number of different combinations one can obtain from this set is 125. Adding additional robustness, 250 randomly distributed initial value sets were computed in Matlab (for a single design parameter vector, ex. ?Baseline?) and the optimized solution of each was determined using ?fmincon?. The initial design points, used as an input into the ?fmincon? function were calculated by first generating a uniformly distributed random number from zero to one in Matlab and then applying that value on a percentage basis to the design variable bounding limits. Since the high limit bounds are so large for the design variables, a random permutation vector between 2 and 6 was also generated at each iteration to represent the exponent of the high limit (Ex. 10 2 , 10 3 , 10 5 , 10 6 , 20000). This ensured that low value combinations could be obtained in the simulation and provides a better representation of the initial value space. This additional step enabled a more random distribution to be obtained. The process as described above was repeated for all five design variables until a single initial point vector was generated. An iterative process was then used to obtain an initial point matrix with the total number of rows equal to the total number of initial point vectors, 250 (Eq. B.31). This matrix was input into Matlab and a solution was obtained for each initial point vector. 253 The 250 optimized solutions obtained were then plotted on a histogram to observe the distribution of objective function values, Fig. B.2. The majority of the optimized solutions fall very close to the global minimum (lowest optimized objective value) of the formulation. The minimum of these 250 results was then chosen as the ?representative? optimum or the design that most closely represents the global optimum for the particular formulation. In the parametric analysis that follows, this modified Monte Carlo procedure was conducted for each design parameter vector. (B.31) Figure B.2. Example objective function distribution for different initial points numbervectorpoinitiali RRRRR RRRRR RRRRR dp dpiiiii dp int ,2505,2504,2503,2501,250 ,5,4,3,1, ,15,14,13,11,1 = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ##### ##### 254 B.5.2 Pareto Frontier As mentioned previously, the multiobjective formulation was converted to a single objective problem using the epsilon constraint method. The epsilon constraint method is an A posteriori method used to solve multiobjective optimization problems and is of the form: ( ) () Sx ljkjallforxftosubject xfimize jj l ? ?=? ,.....,1 min ? Where S is the feasible design space. The Pareto frontier provides the solution to the multiobjective optimization formulation in k variable space (where k is the total number of objective functions). A decision vector x* ? S is Pareto optimal if there does not exist another decision vector x such that f i (x) less than or equal to f i (x*) for all i = 1,?.k, and f j (x) < f j (x*) for atleast 1 index j 2 . In order to obtain a single optimum design from the Pareto solution set, a user weighting method was applied to the objectives. For the particular problem under investigation, the Pareto frontier is shown in Fig. B.3. From this graph it is clear than the objective space in nonconvex. In addition, the constraint, g 4 (epsilon constraint) was active for all the optimal solutions obtained which helps to validate the choice of the second objective. Applying user preferences to Fig. B.3, a single design is chosen based on the ?baseline? design parameter vector from Table. B.1. This design has a number of interesting characteristics as shown in Fig. B.4. In this figure, the x-axis represents the temperature of the heater and the y-axis is the single objective function value or T unc . 255 When compared to the current design, it is clear that the optimal design performs much better at temperatures above 70 o C. It should be noted that at 70 o C, a slight (< 1%) enhancement in performance in observed. Table B.2 provides additional information regarding the optimal and current designs and Table B.3 summarizes the Pareto results. Figure B.3: Pareto frontier 256 Figure B.4: User specified optimal design (?baseline? design parameter values). Table B.2: Current vs. optimal design comparison (single-objective formulation). OPTIMUM DESIGN CURRENT DESIGN R 1 [? ] 167 237 R 3 [k? ] 27.733 47.6 R 4 [k? ] 47.379 57 R 5 [k? ] 89.786 1000000 R dp [k? ] 9.906 10.7 g 1 0 0 g 2 -142 -175.3975 g 3 -2.08 -0.099 g 4 0 -2.025 h 1 1E-13 1E-13 CONSTRAINTS F 0.2127 0.2157 DESIGN VARIABLES OBJECTIVE FUNCTION 257 Table B.3: Pareto results R 1 246.4 474.02 187 310 410 311 120 168.61 474.3 365 466 253.98 R 3 4033.1 423810 20363 523110 650 64 34150 18231 1780.4 323 5311 479940 R 4 4851 70 3930 770 250 84 675030 60 893.9 11141 91653 85.912 R 5 49.8 6910 345 6480 296700 76373 30 810 457.6 69189 86592 56.331 R DP 5844.3 15520 3010 4590 7880 13268 1114 17738 440.2 2839 19241 12020 R 1 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 R 3 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 R 4 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 R 5 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 R DP 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 1E-06 R 1 500 500 500 500 500 500 500 500 500 500 500 500 R 3 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 R 4 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 1E+06 R 5 inf inf inf inf inf inf inf inf inf inf inf inf R DP 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 ? 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 R ref 298 298 298 298 298 298 298 298 298 298 298 298 T ref 24.7 24.7 24.7 24.7 24.7 24.7 24.7 24.7 24.7 24.7 24.7 24.7 C min 20 20 20 20 20 20 20 20 20 20 20 20 D min 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 T high 71 75 80 85 82.5 77.5 90 95 105 115 120 140 T low 10 10 10 10 10 10 10 10 10 10 10 10 T opt 70 70 70 70 70 70 70 70 70 70 70 70 Vdrop 10 10 10 10 10 10 10 10 10 10 10 10 R 1 241.78 240.13 242 238 89.898 164 231 211.36 106 89.553 167 129.61 R 3 4957 6893 12628 17759 5758 6811 20035 28752 13907 14722 27733 22305 R 4 5840 8176 14875 21243 18246 11802 24707 38750 37422 46830 47379 49021 R 5 1184 1820 3911 6667 5239 2857 8992 21396 25235 67567 89786 1E+11 R DP 15406 10004 9912 1000 9982 10000 9640 11073 9777 10142 9906 9231 OBJ. FUNC. F1 0.0108 0.036 0.0669 0.0936 0.0807 0.052 0.1172 0.1393 0.1725 0.2006 0.2127 0.2535 g 1 000000000000 g 2 0 -8 -31 -52.7 -41.9 -20.3 -64.581 -112.52 -107.1 -138.82 -141.62 -146.8 g 3 0 -0.04 0 -0.09 -4.96 -2.15 -0.2652 -0.7747 -4.2825 -4.979 -2.0795 -3.3548 g 4 000000000000 h 1 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 1E-13 MATLAB OUTPUT (GLOBAL OPTIMUM) DESIGN VAR. INITIAL POINT LOWER BOUND UPPER BOUND MATLAB INPUTS DESIGN PAR. CONSTR. 258 B.5.3 Parametric Study Results of the parametric investigation of T low are shown in Fig. B.5 and Table B.5 (located in Appendix III). In all of the cases studied, g 1 was active at the optimum, Fig. B.5. T low appears to have a linear affect (monotonically decreasing) on the optimized objective function value T unc over the range studied. The second parametric investigation focused on the affect of T opt . T opt has a very interesting affect on the optimal solution as seen in Fig. B.6. For low values (near T low ), T low appears to have no effect on the optimum. At larger values, near T high , strong dependence on the optimized objective function is observed. Table B.6 (Appendix III) details the results of this parametric investigation. Lastly, the optimization effects of T low , T high , and T opt can be represented in a non- dimensional form combining all of effects presented in this section and the previous one. If the non-dimensional values shown in Eqs. B.32, B.33 are defined, and the results from Tables B.3, B.5 and B.6 are written in terms of Eq. B.32, B.33, then Fig B.7 results. Tabular non-dimensional results are presented in Appendix III, Table B.8. The important observation is that the non-dimensional results collapse onto the same curve. This indicates that if the temperature range and optimization temperature is chosen, the optimal temperature resolution can be taken directly from the graph (although a complete solution would have to be obtained using one of the solution methods described herein). This provides the user with a powerful predictive means of determining the optimal design. (B.32,B.33) res T T T T T range unc flat unc non % 512 ===?range TT TT T lowhigh lowopt nonrnage % , = ? ? = 259 The matlab code used to obtain the results presented herein is available in Appendix D. Figure B.5. Parametric effect of T low on optimum solution. Figure B.6. Parametric effect of T opt on optimum solution. 260 0.00 0.20 0.40 0.60 0.80 1.00 0.00 0.20 0.40 0.60 0.80 1.00 % Range % R e s Par. h1 Par. g4 Par. g1 Figure B.7. Non-dimensional results (Par. g4, Par. g1, and Par. h 1 represent the results obtained from Tables 3, 5, and 6 respectively in non-dimensional form). B.6 EXTERIOR PENALTY METHOD A second optimization solution method was developed based on the exterior penalty approach. This method involves converting the constrained single objective formulation to an unconstrained optimization problem which can then be solved using a number of well-developed unconstrained optimization techniques. The method is classified as a transformation method for this reason. The Penalty method considers the transformation of the constrained formulation to unconstrained form given by Eq. B.34, where ?T h is the objective function (Eq. B.7) and g(x) and h(x) are vectors defined in the single objective formulation presented previously. (B.34) lowhigh lowopt range unc TT TT range T T res ? ? = = % 512 % ( ) ( ) ( )( )xhxgtTtRP h ,,, ?+?= 261 For small penalty terms, Matlab was unable to obtain a solution, Fig. B.8. As the penalty term is increased above 100, the optimized solution reaches a steady value. The entire unconstrained exterior penalty formulation can be found in Appendix II. As can be seen in Table B.4, the optimization results obtained using this exterior penalty approach agree very well with the results obtained in Matlab using ?fmincon? (detailed results can be found in Table B.7, Appendix III). Figure B.8. Affect of the penalty term on the unconstrained optimization results. Table B.4. Exterior penalty and ?fmincon? comparison T opt [ o C] T unc ("fmincon") [ o C] T unc EP [ o C] % DEV 71 0.0108 0.0114 5.56% 75 0.036 0.0365 1.39% 80 0.0669 0.0686 2.54% 85 0.0936 0.0947 1.18% 82.5 0.0807 0.0825 2.23% 77.5 0.052 0.0547 5.19% 95 0.1393 0.1386 0.50% 105 0.1725 0.1729 0.23% 120 0.2127 0.2129 0.09% 140 0.2535 0.2535 0.00% 262 Appendix C C.1 FINAL HEATER RESISTANCE VALUES Card # Circuit # Heater # R h (?)R 1 (?)R 2 (?)R 3 (?)R 4 (?)R 5 (?) 017199 66.5 48800 26200 76800 200000 165195 64.8 48800 26200 76800 200000 21811 48800 26200 76800 200000 33199 66.3 48800 26200 76800 200000 466193 64.7 48800 26200 76800 200000 56170 55.9 48800 26200 76800 200000 639193 64.7 48800 26200 76800 200000 767170 55.9 48800 26200 76800 200000 819217 71.3 48800 26200 76800 200000 940191 63.2 48800 26200 76800 200000 10 68 210 69.6 48800 26200 76800 200000 11 1 225 74.7 48800 26200 76800 200000 12 2 226 74.8 48800 26200 76800 200000 13 69 210 69.6 48800 26200 76800 200000 14 41 192 63.2 48800 26200 76800 200000 15 20 219 71.2 48800 26200 76800 200000 16 70 172 57.5 48800 26200 76800 200000 17 42 194 64.6 48800 26200 76800 200000 18 7 200 66.4 48800 26200 76800 200000 19 71 194 64.9 48800 26200 76800 200000 20 43 200 66.2 48800 26200 76800 200000 21 21 227 74.7 48800 26200 76800 200000 22 72 196 64.8 48800 26200 76800 200000 23 22 200 66.2 48800 26200 76800 200000 044218 73 48800 26200 76800 200000 173198 64.6 48800 26200 76800 200000 28221 73 48800 26200 76800 200000 345201 66.5 48800 26200 76800 200000 474189 63.3 48800 26200 76800 200000 523225 74.7 48800 26200 76800 200000 646220 73 48800 26200 76800 200000 775207 68 48800 26200 76800 200000 824223 74.7 48800 26200 76800 200000 976215 71.3 48800 26200 76800 200000 10 47 202 67.9 48800 26200 76800 200000 11 9 239 78.6 48800 26200 76800 200000 12 10 230 76.9 0 26200 76800 200000 13 48 202 66.2 48800 26200 76800 200000 14 77 222 73.1 48800 26200 76800 200000 15 25 224 74.9 48800 26200 76800 200000 16 78 209 69.6 48800 26200 76800 200000 17 49 221 73.1 48800 26200 76800 200000 18 26 226 74.8 48800 26200 76800 200000 19 79 192 63.1 48800 26200 76800 200000 20 50 221 73.2 48800 26200 76800 200000 21 11 223 74.9 48800 26200 76800 200000 22 80 201 66.3 48800 26200 76800 200000 23 51 222 73 48800 26200 76800 200000 0 1 263 Card # Circuit # Heater # R h (?)R 1 (?)R 2 (?)R 3 (?)R 4 (?)R 5 (?) 027204 67.8 48800 26200 76800 200000 181201 66.2 48800 26200 76800 200000 228228 76.8 48800 26200 76800 200000 352203 68.2 48800 26200 76800 200000 48198 66.8 48800 26200 76800 200000 512203 67.9 48800 26200 76800 200000 653197 64.9 48800 26200 76800 200000 78174 57.5 48800 26200 76800 200000 829220 73 48800 26200 76800 200000 954196 64.9 48800 26200 76800 200000 10 84 215 71.3 48800 26200 76800 200000 11 3 227 74.9 48800 26200 76800 200000 12 4 227 74.9 48800 26200 76800 200000 13 85 213 71.5 48800 26200 76800 200000 14 55 195 64.9 48800 26200 76800 200000 15 30 220 73.2 48800 26200 76800 200000 16 86 174 57.6 48800 26200 76800 200000 17 56 196 64.9 48800 26200 76800 200000 18 13 202 66.1 48800 26200 76800 200000 19 87 196 64.8 48800 26200 76800 200000 20 57 202 66.6 48800 26200 76800 200000 21 31 228 76.8 48800 26200 76800 200000 22 88 199 66.6 48800 26200 76800 200000 23 32 203 68.2 48800 26200 76800 200000 058219 73.4 100065 26200 76800 200000 189199 66.6 100054 26200 76800 200000 214222 73.1 100110 26200 76800 200000 359202 66.1 100079 26200 76800 200000 490190 63.3 100053 26200 76800 200000 533226 74.9 100044 26200 76800 200000 660220 73.2 100064 26200 76800 200000 791207 68.2 100133 26200 76800 200000 834208 69.8 100051 26200 76800 200000 992219 73 100007 26200 76800 200000 10 61 INF 0 100036 26200 76800 200000 11 15 231 76.5 100032 26200 76800 200000 12 16 230 76.6 100073 26200 76800 200000 13 62 200 100058 26200 76800 200000 14 93 220 73.1 100076 26200 76800 200000 15 35 222 73.1 100060 26200 76800 200000 16 94 207 67.8 100037 26200 76800 200000 17 63 219 73.2 99998 26200 76800 200000 18 36 225 74.7 100050 26200 76800 200000 19 95 188 61.8 100041 26200 76800 200000 20 64 200 66.3 100055 26200 76800 200000 21 5 221 73.2 100046 26200 76800 200000 22 96 196 64.9 100031 26200 76800 200000 23 37 217 71.6 100058 26200 76800 200000 2 3 264 C.2 COMPRESSIBLE FLOW THEORY For one-dimensional compressible flow, the variation of density makes the continuity and momentum equations interdependent. Under adiabatic, inviscid, and equilibrium conditions the field equations simplify to: Under steady conditions, the continuity equation simplifies to: () A dA v dvd x v vx A Axx v A x A v x vAvA x ++= ? ? + ? ? + ? ? = ? ? + ? ? + ? ? == ? ? ? ?? ? ?? ? ? 111 0 For 1-D steady compressible flow neglecting body forces terms, the momentum equation becomes: . 2 0 1 2 const dpvdp vdv dx p x v v =+?=+? ? ?= ? ? ? ??? the energy equation for an ideal gas becomes: . 2 1 0. 2 1 22 constvTcvdvdTcvdvdhconstvh pp =+?+==+?=+ combining the energy and momentum equations it can be shown along with the second law of thermodynamics that: .0 1 0 consts T dp dhds dp dhTds dp dh =?= ? ? ? ? ? ? ? ? ?= ?= =? ? ? ? This shows that compressible flow under the assumptions stated above is isentropic. The speed at which waves propagate through the fluid is equal to the speed of sound. It is related to the compressibility of the fluid by: 265 s p a ? ? ? ? ? ? ? ?? = ? 2 For an ideal gas, RT p aconstp ? ? ? ? ? ==?= 2 . And the Mach number is used to represent compressibility effects. Combining the momentum and continuity equations and introducing the Mach number it can be shown: 2 1 M A dA v dv ? ?= Therefore M = 1 only at the throat of a tube and cannot go supersonic unless the throat diverges downstream. Combining the energy equation and substituting in for T gives (assuming a reservoir initially with no velocity: . 112 1 2 2 2 ? = ? + ?? o a a v This can be simplified to: ) 2 1 1( 2 2 2 M T T a a oo ? +== ? () .) 2 1 1( 112 ? ? += ? ? M p p o () .) 2 1 1( 112 ? ? += ? ? ? ? M o because and ideal gas that is isentropic becomes: 1? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? = ??? ? ooo T T pp p P/Po must be 0.5532 in order to justify Ma = .96. 266 Appendix D: Data Reduction and Optimization Pr ograms D.1 DATA REDUCTI O N PROGRAMS D.1.1 Program name: qfluxdet.m Description : This program is used to convert heater, pres sure, and accelerometer voltages to SI units. %THIS F I LE ASS U MES T H E DATA FIL E S HAVE BE EN C O NVER TED FROM B I N A RY TO T E XT FORM A T CORRECTL Y AN D ARE STORE D ON THE C U RRE NT M A CHINE IN T H E FIL E FORM AT S P ECIF IE D %TH I S PR O G R AM A N A LY ZES HE AT T R ANS FER D A TA FR OM T H E M I CR OH EATER ARR A Y ( 2 . 7 m m or 7 m m ) IN V A RI OU S GRA V IT AT IO N A L ENV I RO NM E N TS (I NP UT S FROM USER ) %TH I S PR O G R AM IS BRO KEN U P INT O 8 DIS T I N C T TA SK S S U M M A RIZE D AS T H E F O L L O W I NG: % 1) IDE N T I FY RUN AND F I LE CHARACTERISTIC S % 2) CO NS TRUCT VO L T AG E F I LE N A M E AN D IM PORT HE ATE R IN FORM AT IO N % 3 ) CONVERT UPLOAD ED W A LL TEMP TO A C TU A L CA LI BRA T ED W A LL TEMPERA TURE % 4) BRE A K UP M A TRI X OF RE FER E NCE RE SIS T ANC ES IN T O WOR K I N G VECT ORS % 5) UPL O AD V O LT A G E TE XT F I LE S AND CREATE HEAT FL UX MATR IX % 6) ANAL YZE PRESS U RE, ACCEL E ROMETER, AND TIME VE CTORS AND CONC ATE N ATE TO FL UX MATRIX % 7) WRITE D A TA T O AP PROPRI ATE FILE S % 8 ) CREATE SCREEN OUTPUTS % 9 ) D I SPLA Y OV ERA L L OU TPU T %THI S PROGRA M ANA LYZES O N E D A Y S DA TA (FO R K C - 135 DA TA) AN D LO OPS TH ROU G H EA CH RU N NU MBER FO R THE SPECI F IED DA TE %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 1 %THIS S TEP REQUIRES T H E USER TO INP U T THE HEATER TYPE AN D WHER E TH E DAT A WA S T A K E N . IF T H E DA T A WA S T A K E N ABO A RD THE KC-135, % T H E USE R ENTER S T H E DATA AC QUIS IT ION DATE, T H E B U LK T E MPER ATUR E F O R THAT DATE, THE TOT A L NUMBER OF RUNS F O R THAT DATE % I F TH E DA TA W A S TAK E N IN EA RTH G R AV ITY, A DI FFEREN T PR OCE D URE APPL IE S WHERE TH E BUL K T E M P , AN D HE AT ER SIZ E ARE SELECTE D % S U CCES S I VE LY A N D THERE SH O U LD BE 1 6 R U N S OF D A T A F O R A GI V E N B U LK S U BCOOL IN G %THIS S TEP REQUIRES T HAT T H E E X CEL FILE E X IST: ' C :\MATLAB\BO ILINGDATA\fligh t d a ta\sizeTem p , Date' (Date is worksh eet n a me) 267 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % clear all close all clc heater=m enu(' S elect heater t y pe:' , ' Platinu m ( 2 . 7 m m ) ' , ' 7 m m array' ); %i dentifies t y pe of heater data envi ro n=m e nu (' Sel ect heat er envi ro nm ent ' ,'KC - 1 3 5 ' , ' 1 -G' , 'Joh n B e nt o n D a t a ' ) ; %dat a i s st or ed by e n v i ro nm ent f r e q = in pu t( 'EN TER D A TA A C QU ISI T I O N FREQU E NCY [H z]: ') ;d isp ( '- -- -- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- - ' ) ; i f ( ( en vi r o n == 1 ) | (e n v i r on = = 3 )) %m i c rogra v i t y i nput s d a te1 = in pu t('EN TER DA TA A C QU ISI T IO N DA TE: ', 's') ;d isp( '- - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; bi n r em = rem ( dat e ,2); dat e = st r2 n u m ( dat e 1); bu lk_ t em p = i n pu t( 'EN TER BU LK TEMPERA TU RE: ') ;d isp ( '- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; bu lk_ t em p s t = in t2 str(bu lk_ t e m p ) ;bu l k_ temp _un c=2 ; t o talru n s=in put (' ENTER T O TA L RU NS FOR S P ECI F I E D DA TE: ' ) ;d isp(' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); i f e nvi r o n = = 1 hel p fi=' flight data' ; % u sed later t o wri t e data to "flightdata" fol d e r datas= xlsr ead(' C:\MATLAB\BOIL I N G DAT A\flightdata\sizeTe m p' , d ate1); %i m ports theoretical heat er size, theoretical w all te m p , and measu r ed bu lk te m p el sei f en vi r o n == 3 hel p fi=' BENT ON D A T A ' ; datas= xlsr ead(' C:\M ATLAB\BOIL I N G DAT A\BE NT ON D A TA\size T em p ' ,date1); %im ports heater size, wall te m p , and bul k tem p fo r B e n t on dat a e n d elseif (e nvir o n == 2) % 1 - G i n puts b u l k _t em p=m e nu(' S el ect b u l k l i q ui d t e m p erat ure t o be a n al y zed' , ' 28^ {o}C ' , ' 35^ {o}C ',' 45^ {o}C ' , ' 50^ {o}C ' , ' 55^ {o} C ' ) ; gheatsize=menu(' Select hea t er sizes to be analyzed' , ' 9 -16 Heaters' ,' 25-36 Heaters' ); t o talrun s=1 6 ; i f bul k_tem p == 1 %c on ve rt m e nu se lection to strin g fo r file read i ng bt=' 28' ; el sei f b u l k _t em p == 2 bt=' 35' ; el sei f b u l k _t em p == 3 bt=' 45' ; el sei f b u l k _t em p == 4 bt=' 50' ; el sei f b u l k _t em p == 5 bt=' 55' ; e n d i f gheatsize == 1 268 l g ht =' 9_1 6heat e r s' ; elseif gheat size == 2 l g ht =' 25_ 36 heat ers' ; e n d w o r k s h e=st r cat (' Tbul k' ,bt , ' _ ' , l ght ); dat a s= xl srea d(' C : \ M ATLA B \ B O ILI N GD ATA\ On eGR u nHi s t o ry . x l s ' , wor k s h e); %im port s ru n i n f o fo r 1G dat a end %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 2 %THIS S TEP CONS TRUCT S THE VOLT AGE F I LE NAME TO BE UP LO AD ED LATER AN D ALSO BEG I N S TH E RU N NUMBER LOO P %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % for m = 1 :to talru n s bb b = in t2 str(m ) ; p h r =str cat( ' W O RK ING ON RUN :', b b b );d i sp ( ' - - - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; d i sp (p hr ) ; d i sp ( ' - - - - - - - - - - - - - --- -- -- -- -- -- -- -- -- -- -- - ' ) ; i f e nvi r o n = = 1 fi l e nam e 1=st rcat (' C : \ M A TLAB \ B O ILI N G D A TA\ f l i g ht dat a \ ' ,dat e1,' _T bul k' ,bul k_t em pst , ' \ dat a ' , bbb ,' .t xt ' ) ; %fi l e nam e used t o read v o ltage d a ta titl=strcat(d ate1 ,'_ d a ta',bb b); el sei f en vi r o n == 2 filenam e 1=strcat(' C:\MA TLAB\BO IL I N G D A TA\ 1 G d at a\ ' , ' T bul k _ ' , bt ,' \' ,l ght ,' \' ,' data' , bbb,' .txt' ) ; %filenam e used t o read vo ltag e d a ta titl=strcat('Tb u l k_ ',b t ,'_ ' ,lg h t ,'_ ' ,'d a ta ',b b b ); el sei f en vi r o n == 3 filenam e 1=strcat(' C:\MA TLAB\BO ILI N G D A TA\ B E N TO N D A T A\ ' , dat e 1 , ' _ Tb ul k' ,b ul k _ t e m p st ,'\dat a' ,bb b ,' .t xt ' ) ; %fi l e nam e us ed t o read vo ltag e d a ta titl=strcat(d ate1 ,'_ d a ta',bb b); e n d %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% STEP 3 %CO NVER T WALL TEM PERAT U RE ( W RITT EN O N DAT A SH E ET) T O ACT U AL T E M P ER ATUR E O F H E ATER ARR AY %UP L OAD REFERENCE RESIST ANCE FIL E WHICH SPECIFIES T H E RE FERENCE TEMPER A TUR E OF T H E HE ATER ARRAY, ALL 96 RESIST ANCE % V A L U E S AT T H E RE FERENCE RE SIST A N CE, A LL 9 6 HE ATE R AREA S, AL L 9 6 TC OR O R ALP H A %THIS STE P REQUIR ES THAT T H E E X CEL FILE E X IS T: 'C: \ MATLAB\work \Microg r av ityDataAn aly s is\Matlab I n put\Ch r isd a taredu ctio n \ Sev mmHeater \re fresa reaSeve n mm .xls' %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %% heatersize= datas(2,m ) ;wall_tem p =datas(4,m ); bul kt em p=dat a s( 5,m ) ; %b reak up inform ation into heate r size,date, and bul kt e m p i f i s na n ( wal l _t em p) dis p (' OM EGA WAL L T E MPERAT UR E FOR T H IS RUN DATE HAS NOT BEE N S P ECIF IE D IN E X CEL FI LE!! !!' ); dis p (' PRO G RAM E X ITT I N G ' ) ;quit 269 e n d i f ( ( e nvir o n == 1) | (e nvir on == 2)) dis p (' UPL O A D I N G REF E RENCE RE S I ST ANCE CH ARAC TER IS TICS' ) ;disp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); if (heate r == 1) heat_re s _area= xlsrea d( 'C:\MATLAB\work \Micro grav ityDataAn al ysis\Matlab I n p u t\Ch r isd a tared u c tion \ Platinum Heater\refres area.xls' ); acc wall_tem p =1.002*wall_tem p +.3987; %calibration c u r v e f it (5/ 24/ 02) acc wal l _ t e m p_unc = 2 ; elseif ((e nviron == 1) & (heater == 2) & (date > 10200 0) & (rem (date,2) == 1) & (re m (d ate,5) > 0) & (d ate < 110000)) heat_re s _area= xlsrea d( 'C:\MATLAB\work \Micro grav ityDataAn al ysis\Matla bInp ut \ C hri s dat a re duct i o n\ Se vm m H eat er\ r efres a re aSe v enmm1003.xls' ) ; acc wall_tem p =1.0152*wall_tem p -0. 0 882; %calibration c u r v ef it (9/4/ 0 3) acc wal l _ t e m p_unc = 2 ; elseif ( ( e nv iro n == 1 ) & ( h eater == 2 ) & (( d a te == 080 304 ) | (d ate == 08 040 4) | ( d ate == 08 050 4) | (d ate == 0 8060 4) )) acc wall_tem p = wall_t e m p ; acc wal l _ t e m p_unc = 2 ; heat_re s _area= xlsrea d( 'C:\MATLAB\work \Micro grav ityDataAn al ysis\Matla bInp ut \ C hri s dat a re duct i o n\ Se vm m H eat er\ r efres a re aSe v enmm0804.xls' ) ; disp (' ANAL YZ IN G 7 M M HE ATE R DA TA F O R AU G U ST 2 0 0 4 KC- 1 3 5 FLI GHT' ) ;dis p(' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --' ); end %INS ERT elseif ST AT EMENT FOR FUT U RE F L IGHT DAT A %%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%% elseif (e nvir on == 3) accwall_t e m p = wall_te m p ; heat _res _area=xls r ead(' C:\MATLA B\work \Microg r av ityDataAn aly s is\Matlab I n put\C h r isd a taredu ctio n \ Platinum Heater\refresarea JOHN B.x l s') ; e n d dis p (' UPL O AD IN G RE FE RENCE RES I STA N CE C H ARACTER IS TICS' ) ;disp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% STEP 4 %CREA T E RESI STAN CE, A R EA AN D A L PH A VECTO R S %TH E RES I ST ANCE V E CTOR PR OV I D ES TH E RE SIST A N CES CORRESP ON DI NG T O T H E G I V E N R U N TEM P E RA TURE (T HER E FORE IT SH OUL D BE INS I DE T H E LOO P ) %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % al pha= h eat _res_a rea(2:length(heat _res _a rea) ,3) ; alp h a _un c=.0 005 ; %h eat er te m p erature COR (heate r 1-96 in order) res _ run=hea t _res _area ( 2:le ngt h(heat_r es _area),1).*(1+al pha *(accwall_t e m p -heat _res _ar ea(1,1))); % c onve rt to act ual run res istan c e (fro m te m p ) res _ r u n_ u n c = sqrt (( (1+al p h a *(acc wall_te m p -heat_res _a rea( 1, 1) )) .* (res _ r u n* .0 0 5 +1 .5 )).^ 2 +( res _ r u n * (acc wall_tem p - h eat_ r es _are a( 1,1)) ... . *al pha _unc).^2+ (alpha.*accwall_te m p_unc.*res_run).^2); %resistance uncertainty (as vector) r e s_ run _un c_ p e r c =m ean ( r e s_ run _un c./r es_ r un *10 0) ; %resistor perc entage uncertai n ty a r ea= heat_r es_area ( 2:lengt h( heat_res _are a), 2 ); % h eater area s (cm ^ 2) a r ea _u nc=s q r t ( ( 2 *sq r t ( a r ea) *. 00 0 5 ) . ^ 2 ); a r e a _u nc _pe rc =mean(a rea_unc./ a rea*100);%ar ea uncertainty (cm ^ 2) 270 %%%%%% % %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 5 %UP L O A D VOL TA GE T E XT FIL E S F O R SP ECIF IE D RU N N U M B ER AN D D A TE %FL I G H T DAT A FROM 10/ 03 N EED S TO BE CONVERTED BEC A USE THE HE ATER SE T U P WAS C H ANGED. THERE F ORE THE F I RST HEATER IS NOT T H E FIR S T % COL U MN OF T H E UPL O ADE D VOL TAGE FILE. THIS IS TH E REA S ON FO R TH E CO NV ERSI ON FUN C TIO N W H I C H I S USED TO CO NVERT THE VOLT AGE % MATR IX BAC K SO T HAT T H E FIR S T COLUM N CORRESP ONDS T O THE F I RST HE ATE R . %TH E VOL TAG E M A TRI X I S T H E N S C AN NE D AN D NO N-RE G U LA TI NG H E ATER DA TA IS REM OVE D . ONL Y R E G U LA TI NG H E ATER DA TA IS S A VE D T O A NE W % HE AT F L UX M A TR I X AN D T H E HEA TER NU M B ER IS C O NC AT EN ATE D ALO N G WI TH T H E HE A TER ARE A W H IC H I S T H E FIRST R O W %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %% d i sp ( ' CA LCU L ATIN G HEA T FLUX AND U N C ERTA IN TY ') ;d isp ( '- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; vo ltag e =d lm read(filen a m e 1 ) ;vo ltag e _un c=.00 002 2*v o ltag e +458 *10 ^(-6 ); % vol t a ge dat a a n d u n cert a i n t y fr o m Fati h' s PC I- DA S6 4 02/ 16 m a nual [as, bs] = si ze( vol t a ge ); j= 0; if (( en v i ron == 1) & (h eater == 2 ) & (d ate > 102 000 ) & (r em ( d ate,2) == 1) & (rem (date,5) > 0 ) & (d ate < 11 000 0) ) %if th e o ctob er 2 003 f ligh t week dis p (' TH I S IS OCT O BE R 2 0 0 3 FLI G H T W E EK A N D VOL TA GE DAT A FIL E S ARE BE IN G M O D I FI ED BY F A CTRO 1 . 36 2 9 AN D RE ORDERE D T O ACCO UNT F O R H E AT ER ORIE NT ATI O N ERROR S ' ) ; d i sp ( ' - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; ne w volta ge = voltage; %conve rsion f actor for voltage readi ng co n v _ v ect = [ 1 5 16 9 10 31 33 36 18 1 2 21 23 26 28 3 4 58 14 34 35 5 37 6 19 20 7 44 ... . 8 24 25 11 51 12 29 30 13 32 59 60 92 93 63 64 17 38 39 68 69 42 43 22 45 46 76 77 49 ... . 50 27 52 53 84 85 56 57 89 90 91 61 62 94 95 96 65 66 67 40 41 70 71 72 73 74 75 47 48 ... . 78 79 80 81 82 83 54 55 86 87 88 97 98 99 100]; %conver si on vector because heat er ori e nt at i o n was di ffe re nt f o r i = 1:100 new v ol t a ge(: ,c on v _ve ct (i )) = v o l t a ge (: ,i )* 1. 3 6 2 9 ; end clear voltage i vo ltag e = n e wvo ltag e ; elseif (( env i ro n == 1 ) & ( h eater == 2 ) & ( ( d a te == 0 803 04 ) | (d ate == 08 040 4) | ( d ate == 08 050 4) | (d ate == 0 806 04 )) ) d i sp ( ' THIS I S AUG UST 20 04 FLIGH T W E EK AN D V O L TAG E DA TA FI LES ARE BEIN G MO DI FI ED BY FA CTRO 1. 362 9 AND REORD E RED TO ACCO UNT F O R H E AT ER ORIE NT ATI O N ERROR S ' ) ; d i sp ( ' - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; 271 ne w volta ge = voltage; %conve rsion f actor for voltage readi ng co n v _ v ect = [ 9 10 15 16 21 23 26 28 3 4 31 33 36 18 1 2 44 8 24 25 11 51 12 29 30 13 58 ... . 1 4 34 35 5 37 6 19 20 7 22 45 46 76 77 49 50 27 52 53 84 85 56 57 32 59 60 92 93 ... . 6 3 64 17 38 39 68 69 42 43 73 74 75 47 48 78 79 80 81 82 83 54 55 86 87 88 89 90 91 ... . 6 1 62 94 95 96 65 66 67 40 41 70 71 72 9 7 9 8 99 1 0 0 ] ; %c o nve rsi o n vector becaus e heater or ientat ion was differe n t f o r i = 1:100 new v ol t a ge(: ,c on v _ve ct (i )) = v o l t a ge (: ,i )* 1. 3 6 2 9 ; end clear voltage i vo ltag e = n e wvo ltag e ; e n d %IN S ERT elseif STA TEM EN T FO R FUTU RE FLIGHT DA TA D E CO DI NG O R AD DI NG A FACTO R %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %% f o r i = 1: l e ngt h( res _ r u n ) loo = m ean (vo ltag e (4 :length ( v o ltag e ),i)); if (loo > 0.35) % o nly records data for regulating heaters j=j+ 1;onheate r s( j)=i;a rea_ heat( j ) = a r ea(i); %rec or ds re gulating he ater num b er qfl u x(:, j)= v oltage(:,i) . ^2./(r es_r un(i) * ar ea (i)); %heat flux m a trix q f l u x_un c( :,j ) =sqr t( (2* v o ltag e ( : ,i) . /res_ r un ( i )./ar ea(i) .*vo ltag e _unc( : ,i) ) .^2 + ... ( volt a ge(:,i) . ^2./are a (i)./res _run(i ). ^2 .* res _ r u n_ u n c(i) ).^ 2 +( v o ltage(:,i) . ^2 ./are a (i)^2 . /res _r un (i). *area _ unc ( i )).^ 2 ); q f l u x_un c_p e r c ( : ,j ) = m ean (q f l u x_u n c (:,j )./q f l u x ( : ,j )*1 00) ; %calcu lates a p e rcen tag e un cer t a in ty in h e at f l ux end e n d qwrite=cat( 1 ,[area _heat;onheaters] , q flux); %concat enate he ater num b er with heat flux c o lum n qwrite2 = [accwall_ tem p ,bu l k t em p , h eater size,len g t h ( on heaters)]; %seco n d v ect o r to b e written to file %%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %% STEP 6 %ANALYZ E THE PRE S S U RE AND AC CELEROMET ER SIGNAL F O R GIVEN R UN %DE F INES THE PRES SURE (CONVER TI NG VO LTAG E SIG N A L TO PRESSU RE) %FILTERS OUT HIGH F R EQUENC Y NOISE (SM O OTHING F U NCTION) DISP LAYS P L OT S OF THIS %CO N CAT E NA TES TH E TIM E VECT OR, HE AT F L UX M A TR IX , AC TU AL PRE SSURE VEC T OR, SM O O TH ED PR ESS U R E VECT OR, A C TUA L ACC VEC T O R , SM O O T H E D ACC VEC T OR %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %% 272 press_vol=voltage(:, 9 8); %pre ssure si gnal acc _pres s =1*press _vol/. 742; %converts pressure voltage to actual press u re ( ATM ) dis p (' FILTE RIN G HI GH F R EQU E NC Y PRESS U RE S I GN AL' ) ;disp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' ) ; pressure=sgolayfilt(acc_press, 1,1001); % f ilters out high fre que n cies (a pplies a Savitz k y -Go l ay FIR sm o o t hin g filter) accel=sgolayfilt(voltage (: ,100),1,1001); %sm ooths accelerom et er data figu re;sub p l o t (2 ,2 ,1 );p l o t (pressu re);ylab el('p r essu re (ATM)');tit le(titl); s u bpl ot(2,2,2); plot(acc _pre ss);subplot( 2,2,4);plot(voltage(:, 100));ylabel(' acc. voltage' ) ;subpl ot(2,2,3);plot(accel); pressure2=cat(1,[0; 0 ],pr essure);acc_press2=cat(1,[ 0;0],acc_press);voltage2= cat (1,[0;0],voltage(:, 100));accell2=cat(1,[0; 0], accel); tim e1 =[0 : 1 : (len g t h(acc_ p ress2 )) -3 ]'/freq ;time = cat(1 ,[0 ; 0 ] ,ti m e1 ); %ti m e in secon d s datatowrite= cat(2,tim e,qwri te ,acc_press 2 ,pressure 2,voltage2,accell2); %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% STEP 7 %W RI TE DA TATOW R ITE AN D qwr ite2 TO A FI LE FO R U P LOAD IN TO AN OTH E R A N A L Y S IS PROG RA M %A LSO ASK S I F TH E USER W A NTS T O OVER W RITE IF T H E FILE ALREADY E X ISTS %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % d i sp ( ' W R I T IN G H E A T FLU X DA TA TO FI LE') ;d isp ( '- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; i f e nvi r o n = = 1| 3 writefilen=strcat('C:\MA TLA B \ B O ILI N G D A TA\ ' ,he l pfi , ' \ ' , dat e 1,' _ Tb ul k' ,b ul k _ t e m p st ,' \ q fl ux\ q f l u x _ ' , bb b,' . t x t ' ); w r i t e fi l e n 2 = st rcat (' C : \M ATLAB \ B O ILI N G D A T A \ ' ,hel p f i , ' \ ' , dat e 1,' _ Tbul k' ,bul k_t em pst , ' \ qfl ux\ 2 q fl ux _' ,b bb ,' .t xt ' ) ; writefilen3 =strcat('C:\M ATLA B \ B O IL IN GD AT A\ ' , h e l p fi ,' \ ' ,dat e1,' _Tb u l k ' , b u l k _t em pst , ' \ qfl ux\ q f l u x _ ' , bb b,' . m a t'); el sei f en vi r o n == 2 w r i t e fi l e n = st rcat (' C : \ M A TLAB \ B O ILI N G D A TA\ 1 G d at a\ ' , ' T bul k _ ' , bt ,' \' ,l ght ,' \' ,' qfl ux\ qfl u x _ ' , b b b , ' . t x t' ); w r i t e fi l e n 2 =st r cat (' C : \ M ATL A B \ B O IL IN GD AT A\ 1 G dat a \ ' ,' Tbul k _ ' , bt ,' \' ,l ght ,' \' ,' qfl ux\ 2q fl u x _ ' , bb b,' . t x t ' ); w r i t e fi l e n 3 =st r cat (' C : \ M ATL A B \ B O IL IN GD AT A\ 1 G dat a \ ' ,' Tbul k _ ' , bt ,' \' ,l ght ,' \' ,' qfl ux\ 2q fl u x _ ' , bb b,' . m a t' ); e n d search = ex i s t(writefilen); i f sea r ch == 2 u p c hoice = m e nu(' A HE AT F L U X FIL E EX IST S F O R TH IS DA TE , D O Y O U WANT T O OVE R W RITE IT ? ' , ' Y ES' , ' NO' ); if upchoic e == 1 d l m w rite(writefilen,d a tato write,' \t' ) ; %w rite data m a trix to f ile d l m w rite(writefilen2 ,q write2 , '/t'); sa ve(writefilen3,' qwri te' , ' tim e ' , ' acc_press2' , ' p ress ure 2 ' , ' voltage2' ,' ac cell2' , ' accwall_te m p ' , ' bulktemp' ,' heatersiz e' , ' onheaters' ); end else dlm w rite(writefilen, datat o w r ite,' \t' ) ; d l m w rite(writefilen2 ,q write2 , '/t ' ); 273 sa ve(writ e filen3,' qwrite' , ' t ime ' , ' acc_pre ss2' , ' p re ssure 2' ,' voltage2' ,' accell2' , ' accwall_te m p ' , ' bulktem p' , ' heatersize' , ' onheat e r s' ); e n d %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% STEP 8 %CREATE PROGR AM S CREEN OU TP UTS A N D H E AT F L U X M A P %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % ba d_ heat ( 1 , m )=m ; bad_ hea t (2,m )=heat ers i ze; bad_ heat (3,m )=heatersize-length(onheat ers); b ad_h eat(4,m )=wall_ te m p ; ba d_ heat ( 5 , m )=bul kt em p;bad _ h eat ( 6 ,m )=res_ r u n _ unc _ p erc; bad _ h eat ( 7 ,m )=area_ un c _pe rc; b a d _heat (8 ,m )=m ean(qf l ux _u nc _pe rc); s p ri nt f ( ' ru n num ber: % d \ n t h e o ry h eate r size: %d \n ba d heaters: %d \n wa ll tem p : %d \ n b u l k temp : %d \ n resistan ce unc: % d %\n area unc: %d %\ n heat flux unc: %d %\n' ,... ba d _heat ( 1 ,m ),ba d_ heat ( 2 ,m ),ba d_ heat ( 3 ,m ),ba d_ heat ( 4 ,m ),ba d_ heat ( 5 ,m ),ba d_ heat ( 6 ,m ),ba d_ heat ( 7 ,m ),ba d_ heat ( 8 ,m )); %CLEAR VARIABLES F R OM STE PS 2-3 clea r bbb phr filenam e 1 he atersize wall_t e m p bulktem p heat_res_a rea accw all_tem p accwall_tem p_unc titl %CLEAR VARIABLES F R OM STE P 4 clear alph a alp h a _ u n c r e s_ ru n r e s_r un_ unc res _ run_unc_perc area area _unc ne xt a r ea_unc _perc %CLEAR VARIABLES F R OM STE P 5 cl ea r vol t a ge v o l t a ge_ u n c a s bs j ne w vol t a ge c o n v _vect i l oo o nheat e r s a r ea_ heat qfl u x qfl u x _ unc q f l u x_ u n c_ pe rc qw ri t e q w ri te2 %CLEAR VARIABLES F R OM STE P 6-7 clea r press _ vol acc _pres s press u re accel press u re2 acc_pres s 2 voltage 2 accell2 tim e 1 tim e da tatowri t e writefilen writefilen 2 writefilen3 searc h upchoice end %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 9 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%% %DI SPL AY O U TP UTS F O R EAC H RU N %SUMMAR Y OF RES U LTS FOR THE SP ECIFIED DAT E (ALL R U N NUMBERS ) for ccc= 1:m s p ri nt f ( ' ru n num ber: % d \ n heat er si ze: %d \ n b a d h eat ers: %d \ n wall te m p : %d \ n b u l k tem p : %d \n',bad_heat (1,ccc),bad_heat (2,ccc),bad_heat(3, ccc),bad_heat(4,ccc), bad_heat(5,ccc)) end %ba d _heat %figure 274 %h ol d o n %p lo t(vo ltag e (:,9 ),'r') %p lo t(vo ltag e (:,2 3),'b ' ) %p lo t(vo ltag e (:,8 ),'k ') %x lab e l('Data Po in t') %ylab e l('Vo ltag e (V)') %ax is([ 0 225 00 2 9 ] ) %legend(' h eate r 9' ,' heater 23' ,' heater 8' ) %p lo t(vo ltag e (:,2 2)) %p lo t(vo ltag e (:,2 3)) %p lo t(vo ltag e (:,2 4)) %p lo t(vo ltag e (:,4 5)) %p lo t(vo ltag e (:,4 6)) D.1.2 Program name: FLIGHTSUBCOND.m Description : This program analyzes the he at flux data created using ?qfluxdet.m? in both gravitational environmen ts and provides additional ana l ytical capa bilit ies. %THI S PROGRA M ASSU MES TH AT q f lux d e t h a s alr e ady b een exec ute d a n d the m a tla b files alread y ex ist % $$$$$$$$I MPORTA NT $$$$$$$ %M OD FIF Y THI S PR OGR AM A T T H E SUBSTR ATE CON DUCT I O N BA SEL I NE ( L IN ES 240 - 2 7 0 AN D ANA LYZE TH E SA TU RA TION BASELI NE DAT E F I RST (TO CREAT E THE SUB BASELINES ) % $ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$ % 1) IDE N T I FY RUN AND F I LE CHARACTERISTIC S % 2) IDE N T I FY GR A V IT ATI O NAL E N VIR ONM E N T % 2 . 1 ) I D ENT I FY GR A V IT AT IO N A L EN VIR ONM ENT " I F" 1 - G DAT A % 2 . 2 ) IF HEA TER NU M B ER IS 2 8 AN D GRE A T E R THAN 200 [W /CM 2 ] THEN DELE TE IT (10/ 03 DAT A ONL Y) % 3) DETER MINE SUB S T R ATE C O NDUCTION % 3.1) SAVE S U BSTR ATE CONDUC TION VALUE S IF T H E B U L K TEMP E RATURE IS NE AR SAT U RATION TEMPER A TUR E , OT HER W ISE IM PORT % 3 . 2 ) C A LCUL ATE 3R D- 7th BAS ELI NES B A SE D ON BUL K 5 5 SUBSTR ATE CON DUCT I O N AT S A M E WA LL TEM P E RAT U RE F O R ED GE HEATERS AND COR N ER HEATERS % 3.3) SAVE S U BSTR ATE CONDUC TI ON B A SE LINES TO FILE FOR F U T U RE ANAL YS IS 275 % 4) CA LC ULA TE T I M E RESO LVE D BOIL IN G HE AT F L U X ES FOR E V ER Y SUBSTR ATE CON DUCT I O N BA SEL I N E IDE N T I FI ED % 4.1) FILTER OUT HEATER S T H AT ARE ON AND S H OUL D NOT BE ON % 4 . 2 ) C A LCUL ATE A V ERA G E HE AT F L U X IN M I CROGR AV ITY A N D HI G H - G % 5) CALC ULATE WAL L SU PERH EA T A N D S U BCOOL I NG % 6) CA LC ULA TE A ND DIS P L A Y HE AT F L U X IM AGE S % 7) WRITE HE AT FL UX DAT A TO FI L E % 8 ) CREATE A PLO T OU TPU T S % 9) CRE A TE S I N G LE F I G U RE OU TP UT F O R SA VI NG %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 1 %ID E NT IF Y DAT E AN D R U N N U M B ER TO BE AN AL YZE D %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% clear all close all clc heater=m enu(' S elect heater t y pe:' , ' Platinu m ( 2 . 7 m m ) ' , ' 7 m m array' ); envi ro n=m e nu (' Sel ect heat er envi ro nm ent ' ,'KC - 1 3 5 ' , ' 1 -G' , 'Joh n B e nt o n D a t a ' ) ; if ( ( envir o n == 1) | (e nvir on = = 3)) i f e nvi r o n = = 1 hel p fi=' flight data' ; el sei f en vi r o n == 3 hel p fi=' BENT ON D A T A ' ; e n d d a te1 = in pu t('EN TER DA TA A C QU ISI T IO N DA TE: ', 's') ;d isp( '- - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; bi n r em = rem ( dat e ,2); dat e = st r2 n u m ( dat e 1); bu lk_ t em p = i n pu t( 'EN TER BU LK TEMPERA TU RE: ') ;d isp ( '- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; bu lk_ t em p s t = in t2 str(bu lk_ t e m p ) ;bu l k_ temp _un c=2 ; bb =inp u t ( ' EN TER R U N NU MBER TO B E AN ALYZED : ') ;d isp( '$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ ') ;b bb =in t 2 s tr( bb) ; filen=strcat (' C:\M ATLAB\BOIL I N G D A T A\ ' , hel p fi ,' \ ' ,dat e1,' _Tb u l k ' , b u l k _t em pst , '\ qfl ux\ q f l u x _ ' , bb b , ' . m a t' ); a = ex ist(filen ) ; i f a == 2 loa d ( f ilen); % u ploa d heat fl ux inf o rm ation d i sp ( ' MATLA B H E A T FLUX D A TA U P LO AD ED SU CCESSFULLY ') ;d isp( '$ $$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $ ' ); else d i sp ( ' UNA BLE TO FIND H E AT FLUX D A T A FO R THI S RU N NU MBER AND DA TE! ! ! ! ' ) ; d i sp ( ' $$ $$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ $$$ ') ; 276 pa use ( 20) ; e n d %%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% STEP 2 %I DEN T I F Y GRA V IT AT IO NA L E N V I RONM E N T " I F" FL IG HT D A TA %TH E L O A D ED M A T L A B FILE S H O U L D HA VE TH E FO LL O WIN G VAR IABLE S DE FI NE D B Y " q flu x d et.m " % q w r ite, tim e , acc_pre s s2, voltage 2, a ccell2, acc wal l _ t e m p , bul kt e m p, heat er size, onheate r s, pre ssure 2 %TH E HEA T FL UX A V E R AGE S ARE DIS P L AYE D I N E A CH GR A V IT AT IO N A L EN VIR O N E M E NT pressure= p r e ssur e 2(3:lengt h ( p re ssure 2) ); m eanpress= m ean(press ure ) ; j= 0;k= 0; dp r e ss(1 ) = 0 . 0 003 ;d isp ( '- -- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; d i sp ( ' CA LCU L ATIN G MICRO G R AVI TY A N D 2G DA TA PO IN TS') ;d isp( '- - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; f o r i = 2: l e ngt h( pre ssu re) - 2 0 0 dpress(i ) = p ress ure(200+i ) -press ure(i); %cal culate press u re differe n ce if (( pre ssu re(i) < m eanpr ess) & (a bs (d p r ess(i )) < . 0 0 0 2 ) ) j = j + 1; m i ctim e(j)=(i+200); % d ata points i n m i crogravity end if (( pre ssu re(i) > m eanpr ess) & (a bs (d p r ess(i )) < . 0 0 1 ) )% & (i > 4 0 0 0 )) k = k + 1;highgtim e(k)=(i+200); % d ata poi nts in hi gh gra v ity end e n d i f ( ((m ax(m ictim e )- m i n( m i ctim e))/25 0) > 30 ) %identify if tw o m i crogra v ity pe riods e xi st bb= 0 ; f o r nn= 1 :lengt h(m i ctim e)- 1 diff 1 ( n n )=a b s ((m ictim e (nn )-m ictime(n n+ 1) )); if dif f 1 ( n n) > 1000 bb=bb+1; t r ans ( bb)= nn; e nd end m i crange 1=[m i n (m i c t i me(1: ( t r ans ( 1) -5 0) ))+ 2 5 0 , m a x(m i ctim e(1: t r an s(1 ) - 5 0) )- 25 0] ; m i crange 2=[m in(m ictime(tran s ( 1 )+ 5 0 :lengt h(m i ctim e)) ) +2 5 0 ,m ax(m ictim e(trans( 1)+ 5 0:lengt h( m i ctim e)))- 25 0 ] ; hi gh ra nge =[m i n(hi gh gt i m e)+75 0 ,m ax( h i g hgt i m e)-1 0 0 ] ; %hi g h gra v i t y dat a ra n g e ( d at a p o i n t s ) fi gure;hold on %pl o t m i crogra v ity a n d 2G c o m puter define d ra nges pl ot ( p ress ure ) ; p l o t ( [ h i g h r an ge( 1 ), hi g h r a nge ( 1 )] ,[ .8 ,1 . 5 ] , ' k : ' ,[ m i crang e 1( 1) ,m i c range 1( 1)] , [. 8, 1. 5] ,' r: ' , [hi g h r an ge (2 ), h ighra nge ( 2 )] ,[. 8 , 1 . 5 ] , ' k :' ,.... 277 [m i c range 1( 2) ,m i c range1 ( 2 ) ] , [. 8, 1. 5] ,' r: ' , [m i c range2 ( 1 ) , m i c range 2( 1)] , [. 8, 1. 5] ,' r:' , [m icran g e 2 ( 2 ) , m i cran ge 2( 2)] , [. 8, 1. 5 ], 'r :') axi s ([ 0 l e ngt h( pre ssu re) m i n(pre ssu re( 5 : l e ngt h ( p r ess u r e )) )- 0. 05 m a x(press u re)+ 0. 0 5 ] ); y l abel (' Pressure (at m ) ' ); xl ab el (' Da ta Po in t'); title('CO MPUTER IDENTIFIED G-ENVIRONMENT LIM I TS');leg e nd( 'Pressure','h ig h-grav ity li m i ts', 'lo w -grav ity li m i ts ') xa xi s p = [ 1 : l e ngt h( pre s s u re )] / 2 5 0 - 1 5; pze r o = (p ressu re -m in(pr e ssur e ) ) gl e v = pz ero . * ( ( 1 +( 1. 8/ m a x(pze r o ) - 1 )/ m a x(pze r o ) ) * p zero ) ; fi g u re;p lot(x a x i sp ,g lev); x la bel(' t im e (sec)' ) ;ylabel(' g -level (g)' ); e n d i f (m ax(m ictim e)- m in(m ictim e ))/25 0 < 3 0 m i crange 1=[m in(m ictime)+2 5 0 ,m ax(m ictim e )-25 0 ] ; m i cran ge2= 0; %h igh g t i m e = [ 100 00 90 00 ]; hi gh ra nge =[m i n(hi gh gt i m e)+75 0 ,m ax( h i g hgt i m e)-1 0 0 ] ; fi gu re hold on pl ot( p ress ure ) ; pl ot ([ hi g h r an ge( 1 ), hi g h r a nge ( 1 )] ,[ .8 ,1 . 5 ] , ' k : ' ,[hi gh ra n g e( 2) ,hi g h r a n g e (2 )] ,[. 8 , 1 . 5 ] , ' k : ' ,[ m i crange1 ( 1 ) ,m i c range1 ( 1) ] , [. 8,1.5] ,' r:' ,... [ m icr a n g e 1(2 ) , m icr a n g e1 (2 ) ] ,[ .8 ,1 .5 ], 'r :') ; axi s ([ 0 l e ngt h( pre ssu re) m i n(pre ssu re( 5 : l e ngt h ( p r ess u r e )) )- 0. 05 m a x(press u re)+ 0. 0 5 ] ); y l abel (' Pressure (at m ) ' ); xl ab el (' Da ta Po in t'); title('co mp u t er id en tified micro g rav ity t i m e ');le g e n d ('Pressure','h ig h - grav ity li m its ', 'l o w -grav ity li mits') e n d i f m i crange 2(1) > 0; dis p (' LO W- G DA TA RAN G E [ DAT A PO IN T] : ' ) ;disp( [m icrange1; m i crange 2] );di sp(' -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); dis p (' HI G H - G DA TA RAN G E [ DAT A PO IN T] : ' ) ;disp( [hi g h r a nge] ) ; d isp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); else d i sp ( ' LOW - G D A TA RA NG E [D A T A POI N T]: ') ;d isp ( [ m icr a n g e 1 ]);d i sp ( ' - - - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; dis p (' HI G H - G DA TA RAN G E [ DAT A PO IN T] : ' ) ;disp( [hi g h r a nge] ) ; d isp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); e n d s e l ect =m enu ( ' D o y o u l i ke t h e c o m put er d e fi ne d l i m i t s ? ' ,' y e s' ,' no' ); i f select == 2 m i crange 1=(i np ut (' SPE C I FY M I C R O GR A V IT Y LI M I TS: ' )); m i crange 2= [0 0] ; hi gh ra nge =(in put(' SPEC I FY 2 G LIM I T S : ' ));dis p (' -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); e n d cl ea r di f1 d p r ess hi g h g t i m e i j k nn cl ose all else 278 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 2.1 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%% b u l k _t em p=m e nu(' S el ect b u l k l i q ui d t e m p erat ure t o be a n al y zed' , ' 28^ {o}C ' , ' 35^ {o}C ',' 45^ {o}C ' , ' 50^ {o}C ' , ' 55^ {o} C ' ) ; gheatsize=menu(' Select hea t er sizes to be analyzed' , ' 9 -16 Heaters' ,' 25-36 Heaters' ); bb =inp u t ( ' EN TER RU N NU MBER TO AN A L Y Z ED : ') ;d isp ( '- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; bb b = in t2 str(b b) ; i f bul k_tem p == 1 %c onver t m e n u selectio n to stri n g fo r file read ing bt=' 28' ; el sei f b u l k _t em p == 2 bt=' 35' ; el sei f b u l k _t em p == 3 bt=' 45' ; el sei f b u l k _t em p == 4 bt=' 50' ; el sei f b u l k _t em p == 5 bt=' 55' ; e n d i f gheatsize == 1 l g ht =' 9_1 6heat e r s' ; elseif gheat size == 2 l g ht =' 25_ 36 heat ers' ; e n d m i crange 1= [ 5 0 0 , 2 00 0] ; h i g h r an ge=m i c rang e1; % 1 - g data range filen = strcat ('C:\MATLAB\BO ILINGDATA\1Gd a ta\Tbu lk_ ' ,b t,'\ ',l ght ,' \ q fl u x \ q fl u x_' , b b b ,' .t xt ' ) ; heat_res _are a=xlsrea d(' C :\MATLAB\ work \Microg r av ityDataAn alysis\Matlab I np u t\C h r is dat a re duct i on\ Pl at i n um Heat er\ r efr e sarea . xl s ') ; w o r k s h e=st r cat (' Tbul k' ,bt , ' _ ' , l ght ); datas= xlsrea d(' C :\M ATLA B\BOILI N GD ATA\ On eGR u nHist o ry . x ls' , wo rk sh e); %i m p o r ts ru n in fo for 1 G d a ta heatersize= datas(1, bb); wall_tem p =datas(2,bb); %break up info rm ation into heatersize ,date, a n d bul kte m p acc wall_temp=1.002*wa ll_te m p +.3987;bulkte m p=data s(3,bb);accwall_te m p_unc=2; %UP L O A D DAT A FIL E F O R 1 G HE AT FLU X d a ta=d lm read (filen ) ; pressure= d ata(:,length( d ata( 1,:) )- 2); m eanpress= mean(press ure ) ; %1 G HE AT FLU X C H ARACTERI S TIC S m i crom ean=m ean(dat a ( m i cran ge 1( 1): m i c range 1 ( 2 ) ,: ) ) ; m icro u n c=( 2 * s t d ( d at a(m i crange 1( 1): m i c range 1( 2) ,: )) )./ m i c rom ean*1 0 0 ; m i crom i n =m i n (dat a(m i crange 1 ( 1 ) : m i c range 1 ( 2 ) ,: ) ) ; m i c rom a x=m a x(da t a (m i c range 1( 1 ) : m i c range 1( 2 ) ,: )); m i n m eande v=(m icrom ean-m icro m i n)./m i crom ean*100; t o tal m icro =cat(1 ,d ata(1 , :),micro m ean, m icrounc,m i n m e a nde v);dummydata=data; 279 hi g h G m i n=m i n(dat a ( h i g hr ange ( 1 ): hi gh ra nge ( 2 ),: )); %sh oul d be t h e sa m e as m i crang e ave r age end %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 2.2 %%IF HE ATE R NUMBER IS 28 AND GR EATER THAN 200 [W /CM 2 ] THEN IT IS BAD HEAT E R AND NEE D S TO BE DEL ETED FROM THE DAT A MA TRIX %TH I S S H OU LD ON LY OC CUR F O R T H E 7 M M HE A TER ARR A Y OCTOBER FL IG HTS ! %THIS S TEP ALS O DISPL AYS ALL OF THE PERTINEN T HE AT F L UX AVER AGES IN E A C H E N VIRONMENT %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % clear bulk_temp select a m i ctim e press u re 2 a cc_press 2 voltage2 q w rite2 = qwri te; for i = 1 :leng t h (q write(1 ,:)) i f (qwrite(2 ,i ) == 28 & m a x ( qwrite(3 :leng th (q write),i) > 1 50)) j = i; qwrite 2(:, j) = [] ; onheaters ( j) = [] ; e n d end clear qwrite q w rite = q w rite2 ; %HE A T F L U X CH AR ACT E RIST ICS WITHIN SPECIF I ED RANGES data = qwrite(3:length(qwrite),:);area = qwrit e (1,:);heat _num b = qw rite(2,:);tim e = time(3:lengt h(tim e));accell2 = acce ll2(3:le ng th(accell2 )); microm ean= m ean(data(m i crange 1(1):micrange 1 ( 2 ) ,: ) ) ; m i c ro u n c=( 2 * s t d ( d at a(m i crange 1( 1): m i c range 1( 2) ,: )) )./ m i c rom ean*1 0 0 ; hi g h m ean=m ean( dat a ( h i g hra nge ( 1 ): hi gh ra n g e( 2) ,: )); hi g h st d=( 2 *st d (dat a( hi g h ra n g e( 1): h i g h r an ge( 2 ),: ) ) ) ./ hi ghm ean* 1 00; m i crohi g h = m a x( dat a (m i c range1 ( 1): m i c range1 ( 2),: )); m i crom i n =m i n (dat a(m i crange 1( 1): m i c range 1( 2) ,: )); m i crom ax=m ax(dat a ( m i crange1 ( 1 ) : m i c range 1( 2) ,: )); t o t a lm i c ro=cat (1 ,heat _n um b,dat a ( 1 ,: ),m i cromean,microm i n,m i crohigh); h i gh G m in = m i n (d ata(h i gh r a ng e(1 ) : h igh r ange( 2 ) , :)) ; disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); disp (' M I CROGRA V IT Y HE AT F L U X SP ECS ( W I T HT OUT q s ci RE M OVE D) [ H E A TER; F I RST DAT A HE AT FLU X ; M I CR OM EA N; M I C R OM IN; MICROHIGH] : ');d isp ( t o tal m icro ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); clear qwrite 2 i j %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 3 %ID E NT IF Y SUBSTR ATE CON DUCT I O N BA SEL I N E S %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % autom a te=m en u(' D O Y O U W ANT T O AUT OM ATE S U B. CON D . CAL C ULA T I O N S : ' , ' Y ES' , ' NO' ); 280 m a p=[0 96 95 94 93 92 91 90 89 0;65 37 64 63 62 61 60 59 58 88; 66 38 17 36 35 34 33 32 57 87;67 39.... 18 5 16 15 1 4 31 56 8 6 ; 6 8 40 19 6 1 4 1 3 30 55 8 5 ; 6 9 41 2 0 7 2 3 12 29 5 4 84 ;70 42 2 1 8 .... 9 10 11 28 5 3 83 ;71 43 2 2 23 24 2 5 26 27 5 2 82 ;72 44 4 5 46 47 4 8 4 9 50 51 8 1 ; 0 7 3 74 75 7 6 .... 7 7 7 8 79 80 0] ; q sci _ m a p = ze r o s( 1 0 , 1 0); q sci _ m a p2 = qsci _m ap; sub c o n duct i o n = zeros ( 1 ,l en gt h( dat a ( 1 ,: ) )); s u bco n duct i o n 2 = s ub co n duct i o n; base _di f f = h i g h G m i n- m i crom in; jj= 1; ba se2= 0; fo r i = 1: l e n g t h ( h eat _ num b) i f (a utom ate == 1) su bc o n d u c t i on(i ) =m i c ro m i n(i ) ; s u b co n d unc (i )= 2. 5; i f base _di ff (i ) >= 0 s u bconduction2(i)=m i crom in(i); el sei f bas e _di ff (i ) < 0 s u bc ond u c tion2 ( i ) = hig h G m in ( i ) ; base 2( jj, 1 :3)=[ o nheat ers(1 , i),h i g hGmin ( i),m icro m i n ( i)];jj =j j + 1 ; end elseif (a utomate == 2) & (onheaters ( 1,i) > 0) n u m = int2str( on heaters ( 1 , i));fi gu re;h old o n ; pl ot (m i c range 1 ( 1 ) : m i c range 1 ( 2 ) , d at a(m i cran ge1 ( 1 ) :m icran g e 1 ( 2 ) , i)); xlabel(' D A TA POI N T' ); ylabel(' LO W-G H E A T FLU X [ W /cm ^ {2}] ' ) ;phrase= strcat(' Heater Num b er: ',num ); tit le(p hrase); pl ot ([m i c range 1 ( 1 ) ,m i c range 1 ( 2 ) ] , [t ot al m i cro(2 , i ) ,t ot al m i cro(2 , i ) ] , ' r ' ) ; axis ([m icrange 1 ( 1 ) m i crange 1 ( 2 ) m i crom in(i) m i cro m ax(i)] ) su bc o n d u c t i on(i ) =i n put (' ENTER qsc , i F O R SP EC IF IE D HEA TER : ' ) ; d i sp ( ' - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; sub c on ductio n 2 ( i ) = sub c o ndu ctio n( i) ; e n d %M O D IF Y SUBSTR ATE CON DUCT I O N M A TRI X f o r j= 1:10 f o r k= 1:10 if ( h eat_num b(1,i) == m a p(j,k)); qsci _m ap(j,k) = subconduction(i); qsci _m ap2( j, k) = s u bconduction2(i ); e nd end e n d end clear i j k aut o mate jj base _di ff 281 d i sp( ' TH E FOLLOW I NG HEA TERS HAD LOW E R BA SELI NE I N H I G H -G (I F A LO T TH EN MO DI FY PROG RA M) : ') ;d isp ( b a se2 ) ; disp (' AUT OM ATE D S U BST R ATE C O N D U CTI O N V A L U ES I D EN TIF I ED ( q sci_m a p, RO UN DE D): ' ) ;disp( ro u n d ( qsci_m ap)); disp (' AUT OM ATE D S U BST R ATE C O N D U CTI O N V A L U ES W/ HI GH -G M I N ( q sci_ m a p2, R O UN DED ) : ' ) ;disp ( r o u n d ( q sci_m a p2 )); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 3.1 %SAVE SUB S TRATE CONDUCT I ON VALUES IF THE BUL K T E MPERAT URE I S NE AR SAT U RAT I O N TE M P ERAT URE , O T HER W I S E IM P O RT FOR AD D I TI ON AL %SUBSTR A T E CO ND UCTI ON BAS ELI N E S %UP D ATES 1) T H E FIRST IF ST ATEME N T NE EDS T O BE UP D A TE D T O INC O R P ORA TE B U L K S A T U RAT I ON D A TE %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % if (d ate == 0 716 02 | d a te == 07 110 2 | d a te == 10 220 3 | d a t e == 100 903 | d a te == 0 803 04 ) %add ad d ition a l baselin e d a tes as t h e y occur B 5 5_ basel i n e1=s ubc o n d u ct i on; B 5 5 _ m a p=qsci _m ap ; B 55 _ba sel i n e2=s u b co n duct i o n 2 ; B 55 _m ap2=qs ci _m ap2; sub f ile=strcat('C: \ MATLAB\BOILINGDAT A\ ' , hel p fi ,' \ ' ,dat e1 ,' _Tb u l k ' , b u l k _t em pst , '\ su bcond \in pu t\h eater si ze' ,num 2str(heatersi z e),. .. 'wallte m p _ ' ,n u m 2 s tr(accwall_ tem p ),'. mat'); s a ve (s ub fi l e ,' B 55_b asel i n e1 ' , ' B 55_m ap' , ' B 55 _ b asel i n e 2 ' , 'B 55 _m ap2' ); d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ;d isp( 'TH I S I S THE BA SELIN E SU BSTRATE CO NDU CTIO N RU N ' ) ; up file = sub f ile; elseif (d ate == 0 804 04 | d a te == 08 050 4 | d a te == 08 060 4) u p file=strcat('C:\MATLAB\BOILI NGDATA\fligh t d a ta\ 0 803 04_ Tb u l k5 5 \ sub c ond \inp u t\h eat ersize',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n u m 2 s t r(accwall_ tem p ),'. ma t'); elseif ( d ate == 102403 | date == 102303) %uploa d B 5 5 basl ine f o r oct obe r 20- 2 4 f ligh t s u p file=strcat('C:\MATLAB\BOILI NGDATA\fligh t d a ta\ 1 022 03_ Tb u l k5 1 \ sub c ond \inp u t\h eat ersize',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n u m 2 s t r(accwall_ tem p ),'. ma t'); elseif (d ate == 0 712 02 | d a te == 07 090 2 | d a te == 07 150 2 | d a te == 0 710 02 ) %up l o a d B 5 5 b a selin e fo r ju ly 0 2 f ligh t d a tes u p file=strcat('C:\MATLAB\BOILI NGDATA\fligh t d a ta\ 0 711 02_ Tb u l k5 5 \ sub c ond \inp u t\h eat ersize',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n u m 2 s t r(accwall_ tem p ),'. ma t'); elseif (d ate == 1 007 03 | d a te == 10 080 3 | d a te == 10 100 3) %up l o a d b5 5 b a selin e for br ian f lig h t d ate s u p file=strcat('C:\MATLAB\BOILI NGDATA\fligh t d a ta\ 1 009 03_ Tb u l k5 5 \ sub c ond \inp u t\h eat ersize',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n u m 2 s t r(accwall_ tem p ),'. ma t'); %elseif (add add itio n a l fligh t d a te s he re a n d the r e re fer e nce s u bco n d fil e end filex i s = ex ist(u p file); 282 if (filex i s > 0 ) l o ad( u pfile) B 5 5_m apm o d = B 5 5 _ m a p; d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ;d isp( 'SA T U R A T IO N q s ci BA SL I N E UPLOADED SU CCESSFU L LY ') ; d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; else dis p (' SAT U RATE D S U BS TRATE C O N DUCT I O N B A SELI NE D A T A HA S NOT BEEN AN AL YZE D YET !! ! ! ! ! ' ) dis p (' YO U SH OUL D EX I T TH E PR OG RAM A N D A NAL YZ E T H E SATUR A T I ON BAS ELINE DATE FIR S T !!!!!!' ) pa use( 2 0 ) end cl ear fi l e xi s su bfi l e base2 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 3.2 %CALCU LA TE 3R D- 7th B A SEL I N E S B A SE D ON BULK 55 SU BSTRA TE CO NDU CTIO N AT SA ME WALL TEMPER A T U RE F O R E D GE HE ATERS AN D C O RNE R HE ATERS %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % dum m y _ m ap=zeros ( 1 0 , 1 0 ); u no= o n es( 1 0, 10 ); cl ear k; k = 1; sur r = zer os( [ 1 1 00] ); i f ( bul kt em p < 52 ) %IDENTIF Y P O WERE D HEATERS THAT ARE C O MPLETEL Y SURROUNDE D BY OTHER P O WERED HE ATERS f o r i = 2: 9 f o r j = 2:9 if ( q sci _ m a p(i+1, j) > 0) surr ( k )= 1; e nd if ( q sci _ m a p(i-1, j) > 0) surr ( k )=s u r r ( k )+1; e nd if ( q sci _ m a p(i,j+ 1) > 0) surr ( k )=s u r r ( k )+1; e nd if ( q sci _ m a p(i,j- 1) > 0) surr ( k )=s u r r ( k )+1; e nd if (s ur r( k) == 4) | ( h eatersize == 96) dum m y _ m ap(i,j)=1; e nd k=k+ 1; 283 end e n d clea r i j k end qsci _m ap3=( q s c i _ m a p.*d um m y _ m ap)+(r o u n d ( B 5 5 _ m a p m od )) .* ( u n o - d u m m y _ m ap); qsci _m ap4=( q s c i _ m a p2.* dum m y _ m ap)+(r o u n d ( B 5 5 _ m a p m od )) .* ( u n o - d u m m y _ m ap); qsci _m ap5=( q s c i _ m a p.*d um m y _ m ap)+(r o u n d ( B 5 5 _ m a p m od )) .* ( u n o - d u m m y _ m ap)+. 1 5* (( r o u n d (B 55 _m ap m od)) . * ( un o - d u m m y _m ap)); qsci _m ap6=( q s c i _ m a p2.* dum m y _ m ap)+(r o u n d ( B 5 5 _ m a p m od )) .* ( u n o - d u m m y _ m ap)+. 1 5* (( r o u n d (B 55 _m ap m od)) . * ( un o - d u m m y _m ap)); qsci _m ap7=r o un d ( B 5 5_m apm od); %DEC O D E qs ci _m ap 3,4 , 5 , 6 , 7 B A C K F O R B O I L I N G C A LC UL ATI O N sub c o n ductio n 3 =zer os (1 ,len g t h( on heaters ( 1 , :)));s ubc o n d u ct ion 4 =s ubc o n d u ction 3 ; sub c o n duct i o n 5 =su b c o nd uct i o n 3 ; s ubc o n d u c t i on6= su bc on d u ct i o n 3 ; su bcond u c tion7 =sub con d u c tio n3 ; fo r i = 1: l e n g t h ( h eat _ num b) f o r j= 1:10 f o r k= 1:10 if (m ap(j,k) == heat_num b (1,i) ) subc onduction3(i)= q sci_m a p3( j, k) ; subc onduction4(i)= q sci_m a p4( j, k) ; subc onduction5(i)= q sci_m a p5( j, k) ; subc onduction6(i)= q sci_m a p6( j, k) ; subc onduction7(i)= q sci_m a p7( j, k) ; e nd end e n d end %U SER M ODI FIED SU BSTRA TE CO NDU CTIO N BASELIN E ( I F DESI RED , ASS U M E S S O M E A NAL YS IS H A S ALR E A D Y BEEN DO NE ) sub c o n duct i o n 8 = s u bc on d u ct i o n 7 ; q sci _ m a p8 = qsci _m ap7; select2 = m e n u ( 'D O YOU W A N T TO AD D A MODI FIED SU BSTRA T ED COND U C TIO N BA SELINE', 'yes ', 'n o ' ) ; if select2 == 1 dis p (' THIS IS THE C O MP UTER DEF I NED S U BCONDUCT I ON B A SELI NE 1 (fi rs t ro w (su b ) sec o n d r o w ( h eat #) an d wall tem p : ');d isp ([sub co nd u c tion ; onh eat ers]); d i sp (accwall_ tem p ); s u bc onduction8 = (i nput(' INP U T NE W B A SEL I NES VECTOR (MAKE S U RE VE CTOR ELEM ENT C O RRES SPONDS T O CORRECT HEATER ELEMENT: ' )); d i sp ( s ub cond u c tion8 ) 284 dis p (' --- -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ' ) ;disp ( ' ---- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); f o r i = 1: l e ngt h( heat _ n u m b ) f o r j= 1:10 for k=1:10 i f ( h e a t_num b (1,i) = = m a p(j, k) ); qs ci_m ap8(j,k) = subc onduction8(i); e n d e nd end e n d end clear i j k %COLORM A P PL OT A U T O M A TE D SU BSTRATE CO ND UCTI O N M A P fi g u re; r a n ge=[ 0 40] ; c ol orm a p; su bp l o t(4,2,1); i m a g e sc(q sci _ map , ran g e );co l o rb ar('v e rt');titl e('AUTOM ATED SUBSTR ATE CONDUC TION');a x i s squ a re;ax i s tigh t;ax i s o f f su bp l o t(4,2,2); i m a g e sc(q sci _ map 2 , rang e);co l orb a r('v e rt');title('AUTOM ATED SUBSTRATE C O NDU CTION (q_ { sc,i}m ap 2 ' );ax is squ a re;ax i s t i ght su bp l o t(4,2,3); i m a g e sc(q sci _ map 3 , rang e);co l orb a r('v e rt');title('AUTOM ATED MI DDLE (B ULK 5 5 CORNER AND EDGE) (q _ { sc,i}m ap 3 ' );ax is sq uar e ; a xi s t i ght ; a xi s of f su bp l o t(4,2,4); i m a g e sc(q sci _ map 4 , rang e);co l orb a r('v e rt');title('AUTOM ATED SUBSTRATE C O NDU CTION (q_ { sc,i}m ap 2 ' );ax is squ a re;ax i s t i ght su bp l o t(4,2,5); i m a g e sc(q sci _ map 5 , rang e);co l orb a r('v e rt');title('AUTOM ATED MI DDLE (B ULK 5 5 + 15 % C O RNER AND EDGE (q _ { sc,i}m a p 5 ' ) ;ax i s sq uare;ax i s tigh t;ax i s o f f su bp l o t(4,2,6); i m a g e sc(q sci _ map 6 , rang e);co l orb a r('v e rt');title('AUTOM ATED SUBSTRATE C O NDU CTION (q_ { sc,i}m ap 2 ' );ax is squ a re;ax i s t i ght su bp l o t(4,2,7); i m a g e sc(q sci _ map 7 , rang e);c o l orb a r('v e rt');title('BULK 55 (q_ { sc,i}m ap 7 ' );ax is squ a re;ax i s tigh t;ax i s off fi g u re; r a n ge2 = [ 0 55] ; i m ag esc(q s ci _map 3 , rang e2 ); co lorb ar('v e rt') ;tit le('AUTOM ATED MIDDLE (B ULK 5 5 CORNER AND EDGE) [q _ { sc,i}m ap 3 ] ');ax i s squ a re;ax i s t i ght ; a xi s of f %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 3.3 %SA V E SUB S TRATE CO N DUCT I O N B A SELI NES T O FILE FOR F U TURE AN AL YSI S %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % su bcond f ile = strcat('C:\MAT LAB\BOILINGD ATA\',h e lpfi,'\ ' ,d ate1 ,'_ T bu lk ',bu lk_ t em p s t,'\s u b c on d \ h e atersize',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n um 2str(ro un d ( a ccwall_tem p )) ,' . m at' ) ; save( s u b c o n d fi l e ,' subco n duct i on' ,' subc on d u c t i on2' ,' subc o n d u ct i o n 3 ' , ' s ubc o n d u ct i o n4' ,' sub c on d u ct i o n 5 ' , ' s ubc o n d u ct i o n6' ,' subco n d u ction7' ,.. . ' q sci _ m a p' , ' qsci_m ap2' ,' qsci_m ap3' ,' qsci_map4' ,' qsci_m ap5' ,' qsci_m ap6' ,' qsci_m ap7' , ' accwa ll_tem p ' , ' bulktem p ' ,' onheaters' ,' a rea' ); %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 4 %CALCULATE TIME RES O LVED BOIL ING HE AT F L UXE S F O R E V ERY S U BST R ATE C O N D U CTI O N BA S ELI NE IDE N T I FI ED 285 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % %TIM E RE SO LVE D T O T A L BO ILI N G H E AT FL UX ext r a _ b o i l f 1 = [ ( d at a - re pm at (subc o n d u ct i o n,l e ngt h( dat a ), 1 ) ) ] ; ext r a_b o i l f 2= [( dat a - re pm at(su b c o n d u ct i o n2 ,l en gt h ( dat a ) , 1 ))] ; ext r a _ b o i l f 3 = [ ( d at a - re pm at (subc o n d u ct i o n3 ,l engt h( dat a ) , 1 ))] ; e xt ra _b oi l f 4=[ ( dat a - rep m at (subc on d u c t i on4 ,l en gt h ( da t a ),1 ))] ; ext r a _ b o i l f 5 = [ ( d at a - re pm at (subc o n d u ct i o n5 ,l engt h( dat a ) , 1 ))] ; e xt ra _b oi l f 6=[ ( dat a - rep m at (subc on d u c t i on6 ,l en gt h ( da t a ),1 ))] ; ext r a _ b o i l f 7 = [ ( d at a - re pm at (subc o n d u ct i o n7 ,l engt h( dat a ) , 1 ))] ; e xt ra _b oi l f 8=[ ( dat a - rep m at (subc on d u c t i on8 ,l en gt h ( da t a ),1 ))] ; %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 4.1 %FILT E R O U T HE ATER S THA T ARE O N AN D SH OU LD NO T BE ! %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % if leng th (on h eaters) > h eatersize di s p (' # OF HEA TER S O N T H A T S H O U LD N O T B E ON: ' ) ; d i s p ([l e ngt h( o nheat er s ) - heat e r si ze] ); a v g = su bc o n d u ct i o n; [B, I N D E X ] = so rt(a vg ); IN D I CES _ c u t = IN DE X( 1: (len gth( I NDE X) - heatersize ));indices_kee p = IN DE X( (le ngt h( IN DE X) - heatersize + 1 ) : len g th (I N D E X) ); dis p (' THES E HE ATER S WERE ON AND WERE DE LETED FR OM DATA MATRIX [h eat #, avera g e HF]' ); c u t_heaters = sort(onh eaters(INDICES_c u t));dis p ([cut _ heaters;avg(IN DICES _ c u t)] ) ; d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; %delete c u t heaters from boiling heat flux data m a trices fo r i = 1 :leng th(ind ices_k eep ) bo ilf1 ( :,i) = ex tra_b o ilf1 ( :,in d i ces_ k e ep(i));bo ilf2( :,i) = ex tra_b o ilf2 ( :,in d i ces_ k e ep (i ));bo ilf3 ( :,i) = ex tra_ bo ilf3( :,i ndices _keep(i)); bo ilf4 ( :,i) = ex tra_b o ilf4 ( :,in d i ces_ k e ep(i));bo ilf5( :,i) = ex tra_b o ilf5 ( :,in d i ces_ k e ep (i ));bo ilf6 ( :,i) = ex tra_ bo ilf6( :,i ndices _keep(i)); bo ilf7 ( :,i) = ex tra_b o ilf7 ( :,in d i ces_ k e ep(i));bo ilf8(:,i) = ex tra_b o ilf8 ( :,in d i ces_ k e ep (i )); area 2(i ) = area(i ndices _keep(i)); onheaters 2 (i) = onheaters(indices_kee p(i)); e n d a r ea _all = area; onheate r s_al l = onheate r s; a r ea = area 2; onheate r s = onheaters 2 ; else dis p (' NO E X TRA HE AT ERS WERE O N , TH IS IS G O O D ' ) ;disp ( ' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); bo ilf1 = ex tra_ bo ilf1 ; bo ilf2 = ex t r a_bo ilf2;b o ilf3 = ex tr a_ bo ilf3 ; bo ilf4 = ex tra_b o ilf4 ; b o ilf5 = ex tra_b o ilf5 ; bo ilf6 = ex tr a_ bo ilf6 ; bo ilf7 = ex tra_ bo ilf7 ; b o ilf8 = ex tra_ bo ilf8 ; INDICES_c u t = 0;indices _keep = [' all'];c u t_h eaters = 0; area_all = a r ea ;o nheaters _ all = onheate r s; end clear avg INDICES INDEX 286 %TIM E RE SO LVE D M I CR OGR AV IT Y B O IL IN G HE A T FL UX ( H A V E T I M E VE CTOR I N HE RE) t i m e UG = t i m e(m i crange1 ( 1 ) : m i c range 1( 2) ); boi l U G 1 = b o i l f 1 ( m i crange1 ( 1): m i c range 1( 2) ,: ); b o i l U G 2 = b o i l f 2 ( m i crange 1 ( 1 ) : m i c range 1 ( 2 ) ,: ); boi l U G 3 = b o i l f 3 ( m i crange1 ( 1): m i c range 1( 2) ,: ); b o i l U G 4 = b o i l f 4 ( m i crange 1 ( 1 ) : m i c range 1 ( 2 ) ,: ); boi l U G 5 = b o i l f 5 ( m i crange1 ( 1): m i c range 1( 2) ,: ); b o i l U G 6 = b o i l f 6 ( m i crange 1 ( 1 ) : m i c range 1 ( 2 ) ,: ); boi l U G 7 = b o i l f 7 ( m i crange1 ( 1): m i c range 1( 2) ,: ); b o i l U G 8 = b o i l f 8 ( m i crange 1 ( 1 ) : m i c range 1 ( 2 ) ,: ); %TIME RE SOLVE D MICR OGR AVIT Y T O TAL BOIL ING P O W E R (WATTS ) area_m a t = repmat(ar ea,size(boilUG1,1),1); lo wg _ t o t alh eat 1 = bo ilUG1 .*area_ m a t;lo wg_ t o t alh eat 2 = bo ilUG2 .* area_mat; lo wg_ t o t alh eat3 = bo ilUG3.* area_ m at ; lo wg _ t o t alh eat 4 = bo ilUG4 .*area_ m a t;lo wg_ t o t alh eat 5 = bo ilUG5 .* area_mat; lo wg_ t o t alh eat6 = bo ilUG6.* area_ m at ; l o w g_t ot al heat 7 = bo ilUG7 .*area_ m a t; %TI M E RESOLV ED H I G H -G RAV I TY BOI L IN G HEAT FLUX ti m e HG = tim e ( h i g h rang e(1):h igh r ang e (2 ),:); boi l H G 1 = b o i l f 1 ( hi gh ra nge (1 ): hi g h ra n g e( 2) , : ); boi l H G 2 = b o i l f 2 ( hi gh ra ng e(1 ) : h i g h r an ge (2 ),: ) ; boi l H G 3 = b o i l f 3 ( hi gh ra nge (1 ): hi g h ra n g e( 2) , : ); boi l H G 4 = b o i l f 4 ( hi gh ra ng e(1 ) : h i g h r an ge (2 ),: ) ; boi l H G 5 = b o i l f 5 ( hi gh ra nge (1 ): hi g h ra n g e( 2) , : ); boi l H G 6 = b o i l f 6 ( hi gh ra ng e(1 ) : h i g h r an ge (2 ),: ) ; boi l H G 7 = b o i l f 7 ( hi gh ra nge (1 ): hi g h ra n g e( 2) , : ); boi l H G 8 = b o i l f 8 ( hi gh ra ng e(1 ) : h i g h r an ge (2 ),: ) ; %TIM E RE SO LVE D HI GH - G RA VIT Y BOI L IN G HEAT TRA N SFER (W ATTS) clear area _m at area_m a t = repmat(ar ea,size(boilHG1,1),1); HI GH g _ t o t a l h eat 1 = boi l H G 1 . * area _m at ; H IG Hg _t ot al hea t 2 = boi l H G 2 . * area_m a t ; H IG Hg _t ot al heat 3 = b o i l H G 3 . * a r ea_m a t ; HI GH g _ t o t a l h eat 4 = boi l H G 4 . * area _m at ; H IG Hg _t ot al hea t 5 = boi l H G 5 . * area_m a t ; H IG Hg _t ot al heat 6 = b o i l H G 6 . * a r ea_m a t ; HIGHg_ to talheat7 = b o ilHG7 .* area_ m at; %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 4.2 %CA L CULATE AV ERA G E H E A T FLUX IN M I CROG R AV I T Y AN D HI GH- G %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % %AV E RA GE HEA T F L U X OVER M I CR OGR AV IT Y AN D 2 G F O R EVER Y P O W E RED HE ATE R m i crob oi l a ve1 = m ean(boi l U G1 ); m i croboi l a ve2 = m ean(b oi l U G 2 ); m i croboi l a ve 3 = m e an( b oi l U G 3 ); m i crob oi l a ve4 = m ean(boi l U G4 ); m i croboi l a ve5 = m ean(b oi l U G 5 ); m i croboi l a ve 6 = m e an( b oi l U G 6 ); m i crob oi l a ve7 = m ean(boi l U G7 ); m i crob oi l a ve8 = m ean(boi l U G8 ); h i gh gbo ilav e 1 = m ean ( b o ilHG 1 ) ; h i g hgb o ilav e 2 = m ean ( boilH G 2 ) ; h i g hgbo ilav e 3 = m ean (bo ilH G3 ) ; h i gh gbo ilav e 4 = m ean ( b o ilHG 4 ) ; h i g hgb o ilav e 5 = m ean ( boilH G 5 ) ; h i g hgbo ilav e 6 = m ean (bo ilH G6 ) ; h i g hgb o ilav e 7 = mean ( b o ilHG 7 ) ; hi g h g b o i l a ve 8 = m ean(boi l H G8 ); 287 M I C R O M A T = [ o n h eat ers; m i cro boi l a ve 1; m i cro boi l a ve 2; m i cro boi l a ve 3; m i cro boi l a ve 4; m i cro boi l a ve 5; m i cro boi l a ve 6; m i cro boi l a ve 7; m i cro b o ilav e 8 ] ; HI GHM AT = [ o n h eat ers; hi g h g b o i l a ve 1; hi gh gb oi l a ve 2; hi gh gb oi l a ve 3; hi gh gb oi l a ve 4; hi gh gb oi l a ve 5; hi gh gb oi l a ve 6; hi gh gb oi l a ve 7; hi gh gb oi l a ve 8] ; MI CRO MA Tzer o = MI CR OMA T ; HI GHM ATze r o = HI G H M A T; %ZERO NE G A TI VE A V ER AGE H E A T F L UX H E A T E R S (I F S O M E ARE NEG A T I VE) fo r i = 1:len g th (H IG HM A T ( 1 , : )) f o r j = 2: 9 if HI G H M AT( j ,i) < 0 HI GH MATzer o( j,i ) = 0; end if M I CRO MAT( j,i) < 0 MICR OMATze r o ( j ,i) = 0; end e n d end clear i j %CALCULATE T O TAL AVERAGE HE AT TR AN SFE R FROM E A C H HEATER (WATTS ) TOT A LMICR O = [MICROM A T zero(1,:);(MIC R OMATze ro( 2 ,:) . *a r ea);(M I CROMATze r o(3,:). * area ); (M ICROMAT zer o( 4,:) .*a r ea); ( MICROMATz ero(5,:). * area ); ... (M ICR O M A Tzer o( 6,: ) . * area );(M ICR O M A Tze r o( 7,: ) . * area );(M IC ROM A Tze r o ( 8,:) .*a r ea);(M I CROMATze r o( 9,:).*area )]; TOT A L H I G H = [H I GHM AT zero ( 1 , :);( HI G H M A Tze r o( 2,: ) . * area );(H I G HM ATze r o ( 3 ,: ). *area ) ;(H I G H M A Tze r o( 4,: ) . * area );(H I G HM ATze r o ( 5 ,: ). *are a ) ;... ( H I G HMATzer o(6,:). * a r ea) ;(H I GH MA Tzero( 7,:) .* a r ea);(HIGHMATzero(8, :).* area);(HIGHMAT zero(9,:).*a r ea)]; %A DD A L L A V E RAG E HEA T FLU X AN D DI VID E BY SU M O F AREA S ( B OI LIN G CU RV E DA TA PO IN TS) DAT AP O I NT SM ICRO = su m ( TOTALM I CRO(2: 9 ,:) , 2 ) / ( sum ( area) ); DAT AP O I NT SHI G H = sum ( TOT A L H I G H ( 2:9,: ) , 2 )/(s um (area) ); %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 5 %CALCULATE WALL S U PERHE A T AND S U BCOOLING %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %if environ == 2 %if in 1G e n vir onm ent Tsat=2 9. 93 3 * lo g( (m ean(pr e ssur e ( h ig hra n ge( 1 ): hig h ra n g e (2 )) )) -. 00 6 9 2 8 )+ 5 7 . 2 9 9 ;wal lsupe rheat _hi g h G=acc wall_te m p -Tsat; o u tp ut=[re p m at(wallsupe r h eat_m icro,7 ,1 ) D A T A P O I N TS MI CRO r e pmat( w allsu p e rh eat_h igh G , 7 ,1 ) DA TA PO IN TSH I GH ]; else Tsatmicro=29.933*log(m ean(pre ssure(m ic range 1 (1):m i crange 1(2))))+ 57.2 99; wallsuperheat_m icro=accwall_tem p -Tsatm icro; Tsath i ghG =2 9.933 * l o g ( ( m ean (p r e ssur e (hig hr ang e (1) : h i g h r a n g e ( 2 ) ) ) ) - . 0 117 789 2) +5 7.29 9 ; w a llsup erh eat_h igh G =accw a ll_ tem p - T sath ig hG ; sub c o o ling_micr o = Tsatmicr o - b u l k t emp ; sub c o o ling_h igh = Tsath i gh G - bu lk tem p ; o u t p ut 1= [re pm at (wal l s upe rheat _m i c ro,8, 1 ) re pm at (subc ool i n g _ m i cro,8 , 1 ) D A T A P O I N TSM I C R O] ; 288 o u t p ut 2 = [ r e pm at (wal l s up erheat _hi gh G, 8, 1) re pm at (subco o l i n g_ hi g h , 8 , 1 ) D A T A P O INT S H I G H ] ; end disp (' WALL T E M P (C) , S A T TEM P (L O W - G ), S A T T E M P ( H I G H- G) , BULK TEM P: ' ) ;disp ([acc wa ll_tem p ,Tsatm icro ,Tsathi g h G , bul ktem p] ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' RUN NU M B ER: ' ) ;disp(b b b );dis p (' -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -' ); disp (' AC TUAL HEATER SIZE: ');d isp ( leng th(onh eate rs) ) ; disp(' HE ATE R SIZE SH OUL D BE: ' ) ; d i sp( h eater size) ; d i sp( ' - - - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; disp (' WALL S U PER H EA T ( C ), B U L K S U BCOOL IN G [ C ] , LO W AVE RAGE HE AT FLU X ( W /cm 2 ) (bel ow ) HI G H AVER A GE HEA T F L U X ( W / c m 2 )' ); di sp (o ut p u t 1 ); di s p ( out put 2); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 6 %CALCU LA TE A N D DIS P L AY H E A T F L UX IM AG ES %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %clear i j k q b o illo w_ m a p 1 = zero s(10 ,10 ) ; q bo illo w_ map 2 = zero s(1 0 ,10 ) ; q bo illo w_map 3 = zero s(1 0 ,10);qb o illow_ m a p 4 = zero s (10 , 1 0 );qbo illo w_ m a p5 = z e ros ( 10 ,1 0); q b o illo w_ m a p 6 = zero s(10 ,10 ) ; q bo illo w_ map 7 = zero s(1 0 ,10 ) ; q bo illo w_map 8 = zero s(1 0 ,10); q b o ilh igh_ m a p 1 = zero s(10 ,10 ) ; q bo ilh igh_map 2 = zero s(1 0 ,10) ;qb o ilh i g h_ m a p 3 = zero s(10 ,1 0) ;qbo ilh igh _ m ap 4 = zer o s(1 0 ,10 ) ; q bo ilh i g h_m ap5 = zer os( 1 0, 10 ); q b o ilh igh_ m a p 6 = zero s(10 ,10 ) ; q bo ilh igh_map 7 = zero s(1 0 ,10) ;qb o ilh i g h_ m a p 8 = zero s(10 ,1 0) ; for i = 1 :leng th(MICROM A T(1,:)) f o r j= 1:10 f o r k= 1:10 if (MIC ROMAT ( 1,i) = = m a p(j, k) ) & (MICROM A T ( 1,i) > 0); q boi l l ow _m ap1( j, k) = M I C R O M A T(2 , i ) ; q boi l l ow _m ap2( j, k) = M I C R O M A T(3 , i ) ; q boi l l ow _m ap3( j, k) = M I C R O M A T(4 , i ) ; q boi l l ow _m ap4( j, k) = M I C R O M A T(5 , i ) ; q boi l l ow _m ap5( j, k) = M I C R O M A T(6 , i ) ; q boi l l ow _m ap6( j, k) = M I C R O M A T(7 , i ) ; q boi l l ow _m ap7( j, k) = M I C R O M A T(8 , i ) ; q boi l l ow _m ap8( j, k) = M I C R O M A T(9 , i ) ; qboil h igh_m ap1(j,k) = HI G H MAT ( 2,i); qboil h igh_m ap2(j,k) = HI G H MAT ( 3,i); qboil h igh_m ap3(j,k) = HI G H MAT ( 4,i); qboil h igh_m ap4(j,k) = HI G H MAT ( 5,i); qboil h igh_m ap5(j,k) = HI G H MAT ( 6,i); qboil h igh_m ap6(j,k) = HI G H MAT ( 7,i); 289 qboil h igh_m ap7(j,k) = HI G H MAT ( 8,i); qboil h igh_m ap8(j,k) = HI G H MAT ( 9,i); e nd end e n d end %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 7 % W RIT E HE AT F L U X D A T A T O FIL E %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % if env i ro n == 1 | env i ro n == 3 filen = strcat('C:\MATLAB\B O ILINGD ATA\',h e lp fi,'\',d ate1 ,' _ T b u l k ' ,b u l k _ t em p s t,'\BOILHF\',n u m 2 s tr(h eatersize),'wallte m p _ ' ,n u m 2 s tr( ro und (accwall_ tem p )),'.m at' ) ; di s p (' DAT E: ' ) ; d i s p( dat e ) d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; else filen = strcat ('C:\MATLAB\BO ILINGDATA\1Gd a ta\Tbu lk_ ' ,b t,'\ ',l ght ,' \ q fl u x \ q fl u x_' , b b b ,' .m at' ) ; d i sp ( ' - - - - - - --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; filen = strcat ('C:\MATLAB\BOIL IN G D A T A\ 1 G dat a \ T b u l k _' ,bt , ' \ ' , l ght ,' \ s ubc o nd\ s u b s t r at e_r u n' ,bb b ,' . m at' ) ; end save( f i l e n,' b oi l f 1' ,' boi l f 2' ,' boi l f 3' ,' boi l f 4' ,' boi l f 5' ,' boi l f 6' ,' boi l f 7' ,' boi l f 8' ,' M I C R O M A T' ,' HIGHM AT' , ' accwal l _ t e m p ' , ' a rea' ,' bulktem p' , ' heatersize' ,... ' q boi l h i g h _ m ap1' ,' qboi l h i g h _ m a p2' ,' qboi l h i g h _ m a p3' ,' qboi l h i g h _ m a p4 ' , ' onheat e r s' ,' cut _heat ers' ,' IN D I C E S _ cut ' ,' area_al l ' ,' onh eate r s_all' ,'indices_keep' ,... ' qboilhigh_m a p5' ,' qboilhigh_m a p6' ,' qboilh i g h_m a p7' ,' qboi lhigh_m a p8' ,' qboillow_m a p1' ,' qboillow_m a p2' ,' qboillow_m a p3' ,' qboillow_m ap4' ,' qboil l ow _m ap5' ,... ' qboillow_m a p6' ,' qboillow_m a p7' ,' qboillow_m a p8' ,' wallsuperheat _hi ghG' ,'wallsuperheat_m icro ' , ' DATAPOINT SMICR O ' , ' DATAP OINTS H IGH' , ' tim eUG' ,' tim e HG' ,' press u re' , ' boilU G 1 ' , ' boilUG 2 ' ,... 'bo ilU G3 ', 'b o ilU G4 ', 'b o ilUG 5 ', 'b o ilUG 6 ', 'b o ilUG7 ', 'b o ilU G8 ', 'b o ilH G1', 'b o ilH G2 ', 'b o ilH G3 ', 'b o ilH G4 ', 'b o ilH G5 ', 'b o ilH G6 ', 'b o ilHG7 ','b o ilHG8 ',... 'ex t ra_b o ilf1', ' ex tra_b o ilf2 ' ,'ex tra_ bo ilf3 ' ,'ex tra_ bo ilf 4 ' ,'ex tra_b o ilf5 ' ,'ex tra_ bo ilf6 ' ,' ex tra_ bo ilf7 ' ,'ex tra_ b o ilf8 ' ); test = ex ist(filen ) ; if test > 1 dis p (' DAT A WAS WRI T T E N S U CCES S F ULL Y TO: ' ) ;disp( f ilen ) ;d isp ( '- -- -- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- - ' ) ; else d i sp ( ' ERROR I S SAV I NG D A T A TO FILE') ;d isp ( '- -- -- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- - ' ) ; end 290 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 8 %POS T PR OC ESSING (HE A T FL UX MAP S ) %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % %fi g ure; ra n g e = [0 2 0 ] ; col o rm ap; l e g1 = st r c a t (' SA HF = ' , n u m 2st r(out put 1( 1, 3) )); l e g 2 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 1( 2, 3) )); %l eg3 = st rcat ( ' SA HF = ' , n u m 2st r(out put 1( 3, 3) )); l e g 4 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 1( 4, 3) )); l e g 5 = st rcat (' SA H F = ' , n u m 2 s t r ( out put 1( 5, 3) )); %l eg6 = st rcat ( ' SA HF = ' , n u m 2st r(out put 1( 6, 3) )); l e g 7 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 1( 7, 3) )); l e g 8 = st rcat (' SA H F = ' , n u m 2 s t r ( out put 1( 8, 3) )); %titl_ lo w = st rcat('LOW - G B O ILING FLUX: wall sup = :',n u m 2 s t r(wallsu p erh eat_ m ic ro),'su b c oo l = : ' ,n u m 2 s tr(sub co o ling_ m i cro ) ,'wa ll te m p = ;' ,num 2str(accwall_tem p )); %sub p l o t (4 ,2 ,1);i m ag esc(qbo illo w_ m a p 1 , rang e);co l o r b a r('vert');ti tle(strcat(titl_ lo w,leg 1 ));ax i s squ a re;axis tig h t;ax i s o ff; %sub p l o t (4 ,2 ,2);i m ag esc(qbo illo w_ m a p 2 , rang e);co l o r b a r('vert');ti tle(strcat('(q _ { sc,i}m ap 2 ' ,leg 2));ax is sq u a re;ax i s ti g h t; %sub p l o t (4 ,2 ,3);i m ag esc(qbo illo w_ m a p 3 , rang e);co l o r b a r('vert');ti tle (strcat('AUTOMATED MIDDLE (B ULK 55 C O R N ER AND EDGE) (q_ { sc,i } m ap3' ,l eg3 )); %ax is squ a re;ax i s tigh t;ax i s off; %sub p l o t (4 ,2 ,4);i m ag esc(qbo illo w_ m a p 4 , rang e);co l o r b a r('vert');ti tle(strcat('(q _ { sc,i}m ap 2 ' ,leg 4));ax is sq u a re;ax i s ti g h t; %sub p l o t (4 ,2 ,5);i m ag esc(qbo illo w_ m a p 5 , rang e);co l o r b a r('vert');ti tle (strcat('AUTOMATED MIDDLE (B ULK 55 + 1 5 % CORNER AND EDGE (q _{sc,i }m ap5' ,l eg5 )); %ax is squ a re;ax i s tigh t;ax i s off; %sub p l o t (4 ,2 ,6);i m ag esc(qbo illo w_ m a p 6 , rang e);co l o r b a r('vert');ti tle(strcat('(q _ { sc,i}m ap 2 ' ,leg 6));ax is sq u a re;ax i s ti g h t; %sub p l o t (4 ,2 ,7);i m ag esc(qbo illo w_ m a p 7 , rang e);c o l o r b a r('vert');ti tle(strcat('BULK 5 5 (q_{ sc,i}m ap 7 ' ,le g 7));ax is sq u a re;ax i s tig h t;ax i s off; %sub p l o t (4 ,2 ,8);i m ag esc(qbo illo w_ m a p 8 , rang e);co l o r b a r('vert');ti tle (strcat('MODIFIED MAP 8 ' ,leg 8 )); ax is sq u a re;ax i s tig h t;ax i s o ff; %fi g ure; ra n g e = [0 2 0 ] ; col o rm ap; l e g1 = st r c a t (' SA HF = ' , n u m 2st r(out put 2( 1, 3) )); l e g 2 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 2( 2, 3) )); %l eg3 = st rcat ( ' SA HF = ' , n u m 2st r(out put 2( 3, 3) )); l e g 4 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 2( 4, 3) )); l e g 5 = st rcat (' SA H F = ' , n u m 2 s t r ( out put 2( 5, 3) )); %l eg6 = st rcat ( ' SA HF = ' , n u m 2st r(out put 2( 6, 3) )); l e g 7 = st rcat (' SA HF = ' , n u m 2 st r(o ut p u t 2( 7, 3) )); l e g 8 = st rcat (' SA H F = ' , n u m 2 s t r ( out put 2( 8, 3) )); %titl_ h i g h = st rcat('HIGH G BOILING FLUX: wall sup = :',n u m 2 s tr(wallsu p e rh eat _ h i g h G),'su b c oo l = :',n u m 2 s tr(sub coo ling _ h i gh),'w all te m p = ;' ,num 2str(accwall_tem p )); %sub p l o t (4 ,2 ,1);i m ag esc(qbo ilh ig h_ m a p 1 , ran g e );co l o rb ar('v e rt') ;title(strcat(titl_ h i g h ,leg1));ax is squ a re;ax i s tigh t;ax i s off %sub p l o t (4 ,2 ,2);i m ag esc(qbo ilh ig h_ m a p 2 , ran g e );co l o rb ar('v e rt') ;title(strcat('(q _ { sc,i}m a p 2 ' ,leg2 ) );ax is sq uare;ax i s tigh t %sub p l o t (4 ,2 ,3);i m ag esc(qbo ilh ig h_ m a p 3 , ran g e );co l o rb ar('v e rt') ;title(strcat('AUTOM ATED MIDDLE (BULK 55 C O RNER AND EDGE) (q _{sc,i }m ap3' ,l eg3 )); %ax is squ a re;ax i s tigh t;ax i s off %sub p l o t (4 ,2 ,4);i m ag esc(qbo ilh ig h_ m a p 4 , ran g e );co l o rb ar('v e rt') ;title(strcat('(q _ { sc,i}m a p 2 ' ,leg4 ) );ax is sq uare;ax i s tigh t %sub p l o t (4 ,2 ,5);i m ag esc(qbo ilh ig h_ m a p 5 , ran g e );co l o rb ar('v e rt');title (strcat('AUTOM ATED MI DDLE (BULK 55 + 15% CORNER AND EDGE (q _{sc,i }m ap5' ,l eg5 )); %ax is squ a re;ax i s tigh t;ax i s off %sub p l o t (4 ,2 ,6);i m ag esc(qbo ilh ig h_ m a p 6 , ran g e );co l o rb ar('v e rt') ;title(strcat('(q _ { sc,i}m a p 2 ' ,leg6 ) );ax is sq uare;ax i s tigh t %sub p l o t (4 ,2 ,7);i m ag esc(qbo ilh ig h_ m a p 7 , ran g e );co l o rb ar('v e rt');title (strcat('BULK 55 (q_ { sc,i}m ap 7 ' ,leg 7));ax is sq u a re;ax i s tig h t;axis o f f %sub p l o t (4 ,2 ,8);i m ag esc(qbo ilh ig h_ m a p 8 , ran g e );co l o rb ar('v e rt');title (strcat('MODIFIED MAP 8 ' ,leg 8 )); ax is sq u a re;ax i s tig h t;ax i s of f 291 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 9 %F IN A L FI GU RE FO R P R IN T I NG %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % fi g u re; r a n ge=[ 0 60] ; c ol orm a p; l e g1 = st rcat (' ) S A H F = ' , num 2st r (o ut p u t1 (1 , 3 ) ));leg 2 = strc at(' )SAH F = ' , n u m 2 str(o utp u t 1 ( 2 , 3 ) )); l e g3 = st rcat (' S A H F = ' , n u m 2 st r( out put 1( 3, 3 ) ) ) ; l e g4 = st rca t (' SAHF = ' , nu m 2 st r(out put 1( 4, 3) )); l e g 5 = st rcat (' SAH F = ' , num 2st r ( o ut p u t 1( 5, 3) )); l e g6 = st rcat (' S A H F = ' , n u m 2 st r( out put 1( 6, 3 ) ) ) ; l e g8 = st rca t (' SAHF = ' , nu m 2 st r(out put 1( 8, 3) )); titl_ lo w = strcat('LOW - G: Tsu p (' ,n u m 2 s tr(wallsu p e rh eat _ m icro )); su bp l o t(4,3,1); i m a g e sc(qb o ill o w _ m ap 1 , range);co lorb ar('v e rt') ;ti tle(strcat(titl_ lo w,leg1)); ax is sq u a re;ax i s tig h t;ax i s off; sub p l o t ( 4 , 3 , 4 ) ; i m a gesc(q boi l l ow _m ap3, ran g e ); col o rba r(' ve rt ' ) ; t i t l e (st r cat ('Tsu b (' ,n um 2st r(su b c ool i n g _ m i cro) ,l eg 3) ); axi s sq uar e ; ax is tig h t;ax i s off; subpl o t(4,3,7); i m a gesc(qboill ow_m ap5,range); colorba r(' ve rt' ) ;title(strcat('Twall(;' ,num 2str(accwall _ temp),leg5));axis s qua re;ax is ti g h t;ax i s o f f; su bp l o t( 4,3,10);i m a g e sc( q bo il lo w_ m a p 8 , r a ng e) ;co l o r b a r ( ' ver t ');ti tle(strcat(leg8 ) );ax is squ a re;ax i s tigh t;ax i s o f f; l e g1 = st rcat (' S A H F = ' , n u m 2 st r( out put 2( 1, 3 ) ) ) ; l e g2 = st rca t (' SAHF = ' , nu m 2 st r(out put 2( 2, 3) )); l e g3 = st rcat (' S A H F = ' , n u m 2 st r( out put 2( 3, 3 ) ) ) ; l e g4 = st rca t (' SAHF = ' , nu m 2 st r(out put 2( 4, 3) )); l e g 5 = st rcat (' )SA H F = ' , num 2st r ( ou tpu t 2( 5,3) )) ; l e g6 = st rcat (' S A H F = ' , n u m 2 st r( out put 2( 6, 3 ) ) ) ; l e g8 = st rca t (' SAHF = ' , nu m 2 st r(out put 2( 8, 3) )); titl_ h i g h = strcat('HIGH G: Tsu p (' ,nu m 2 s tr(wallsup erh eat_h igh G )); su bp l o t(4,3,2); i m a g e sc(qb o i l h igh _ m ap 1 , rang e);co l o r b a r('vert');ti tle(strcat(titl_ h i gh ,le g1));ax is squ a re;ax i s tigh t;ax i s off; sub p l o t ( 4 , 3 , 5 ) ; i m a gesc(q boi l h i g h_m ap3, ra n g e); c ol or ba r(' v e rt ' ) ; t i t l e (st r cat (' Tsub (' ,num 2st r(s ubc o o l i n g _ h i g h) ,l eg 3) ); ax is sq u a re;ax i s tig h t;ax i s off sub p l o t ( 4 , 3 , 8 ) ; i m a gesc(q boi l h i g h_m ap5, ra n g e); c ol or ba r(' v e rt ' ) ; t i t l e (st r cat (l eg 5) ); ax is sq u a re;ax i s tig h t;ax i s off sub p l o t ( 4 , 3 , 1 1 ) ; i m a gesc(qb o i l hi g h_m ap8, ra n g e); c ol or ba r(' v e rt ' ) ; t i t l e (st r cat (l eg 8) ); axi s s q uare; a xi s t i g ht ; a xi s of f range=[0 60];colorm ap; su bp l o t(4,3,3); i m a g e sc(q sci _ map , ran g e );co l o rb ar('v e rt') ;titl e('AUT SUBC OND 1 ' );ax is sq u a re;ax i s ti g h t;ax i s o f f su bp l o t(4,3,6); i m a g e sc(q sci _ map 3 , rang e);co l orb a r('v e rt ');title('q _ { sc,i}map 3 ' );ax is squ a re;ax i s tigh t;axis o f f su bp l o t(4,3,9); i m a g e sc(q sci _ map 5 , rang e);co l orb a r('v e rt ');title('q _ { sc,i}map 5 ' );ax is squ a re;ax i s tigh t;axis o f f su bp l o t(4,3,12);i m a g e sc(q sci_map 8 , rang e);co l orb a r('v e rt ');title('q _ { sc,i}map 8 ' );ax is squ a re;ax i s tigh t;axis o f f fi g u re; r a n ge=[ 0 10] ; im agesc(q boill ow _m ap1, ran g e );colo rba r(' ve rt' ) ;title(' AUT SUBCOND 1 ' );ax is squ a re;axis tig h t;ax i s o ff %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 9 %TIME RE SOLVE D MOVIE %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 10 %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%% %SURF A CE AVER A GED BOIL IN G FROM SP ECIF IE D HEA TERS %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%% 292 clear i j k choice 2 = m e n u (' AN AL YZE DES I RED H E ATERS TO O B TAI N S U RF ACE AVER A GE' , ' Y ES' , ' E XIT' ); k = 1; whi l e c hoi ce 2 == 1 cho o se = in pu t( 'SPECI FY D E SI RED HEA TER TO O B TA IN SU RFACE AV ERAGE FLU X : ') ;d isp ( '- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; fo r i = 1 :leng th(choo se) fo r j = 1 :len g t h ( h eat_num b ) if choose( i) == h eat _ n u m b ( j ) sum a rea( k) = area ( j ) ; qt ot ( k ) = area ( j ) *hi gh g boi l a ve 3 ( j ) ; QT O TLO W( k) = a r ea(j)*m icroboi l ave3(j); k = k+1; e nd end e n d di s p l a y a vg H I G H = sum ( qt o t )/ sum ( sum a rea); d i sp la ya v g l ow = su m ( Q T OT L O W ) / su m ( s u m a r e a ) ; hig h gdis p = strcat(' AVER A GE HE AT TR AN SFER IN HI GH -G FO R HEA TERS, :', n um 2 s tr(ch o o s e),': IS: '); d i sp (h igh g d i sp ) ; d i sp( d isp l ayav gH IG H) ;d isp ( '- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ') ; l o w g disp = s t rcat(' AVERA GE HE AT TR AN SFER IN L O W-G F O R H E ATERS , :' ,nu m 2str(cho ose ) , ' : IS: ' ) ; dis p (lo w gdi sp); disp (dis pla y avglo w );disp ( ' ----- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); c h oice2 = m e nu (' AN AL YZ E DE SIRE D H E ATERS T O OBTA IN S U R F ACE A V ER AGE' , ' Y ES' , ' E XIT' ); clea r i j s u marea qtot QTOTLOW c h oose end %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%% STEP 11 %INDIVIDUAL HE ATER TIME RES O L V ED BOIL ING %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% %%%%%%% % clear i j k choice 1 = m e n u (' AN AL YZE IN DI VI D U A L HE ATERS' ,' YES' ,' EXIT' ) ; whi l e c hoi ce 1 == 1 s eeheat = input (strcat(' INPUT HE A TER NUMBER TO SEE C HAR ACTERIST I CS: ' )); f o r i = 1: l e ngt h( o nheat er s ) if onhe a ters(i)==see heat i nde xsa v e = i; e nd end 293 %p l o t bo iling h eat fl u x b o i l h eat fl u x s eeheat = [b oi l f 3 ( : , i n dex s ave ) ,[ 1: l e ngt h( dat a )] ' *1/ 25 0] ; figu re; p lo t(bo ilh eatflux seeheat(:,2 ),bo ilh eatflu x s eeh eat(:,1 ),'k '); a x is( [ 0 lengt h ( d ata)/250 0 max(boilheatfl uxs eeheat(:,1))+5]) x l ab el ('ti me (sec)'),ylab e l('h eat fl u x (W/cm^{2 })');titp lo t = strcat('HEATER NUMBER: ', n u m 2 s tr(seeh eat));title(titp lo t) ho ld on %%% pl ot a v g val u es l o wi np 1 = [ m ean(b oi l f 3 ( m i cran ge1 ( 1 ) : m icran g e 1 ( 2 ) , i n d e xsa v e) )] ; l o wi np 2 = [l owi n p 1 ; l o wi np 1] ; l o wa v g = [l o w i n p2 ,m i c rang e1' / 250] ; hi g h i n p 1 = [ m ean(b oi l f 3 ( hi gh ra nge (1 ): hi g h ra n g e( 2) ,i n d e x sa ve) ) ] ; hi ghi n p 2 = [hi ghi np 1 ; hi ghi np 1] ; hi g h a v g =[ h i ghi n p 2 , h i g hra nge' / 25 0] ; p l o t ( l ow avg( :,2) ,low av g( :,1 ) ,'w - ') ;h o l d o n pl ot (hi gha v g ( : , 2 ) , h i g hav g ( : , 1) ,' w-' ) ; hol d on %%% pl ot l o w- g a n d hi g h - g ra nges l o wlim = [0 ; m ax (bo ilh eatfl u x s eeh eat(:,1))+3 ];lo wlim 2 = [lowlim ,r ep mat( ( m icr a n g e 1(1 ) / 2 50 ),2,1) ]; pl ot (l o w l i m 2 (: , 2 ) , l o wl im 2( : , 1) ,' w: ' ) ; hol d o n l o wl i m 2 = [ l owl i m ,repm a t((m i c range 1( 2) ' / 250) ,2 ,1 )] ; pl ot (l o w l i m 2 (: , 2 ) , l o wl im 2( : , 1) ,' w: ' ) ; hol d o n hi g h l i m = [l owl i m ,repm a t ( hi g h ra n g e( 1)/ 2 50 ,2 ,1 )] ; pl ot (hi ghl i m (: ,2 ), hi g h l i m (: ,1) , ' w : ' ); hol d on hi g h l i m = [l owl i m ,repm a t ( hi g h ra n g e( 2)/ 2 50 ,2 ,1 )] ; pl ot (hi ghl i m (: ,2 ), hi g h l i m (: ,1) , ' w : ' ); hol d on %place te xt in scree n l o w t ex t = n u m 2 str ( l o w inp1) l o wte x = str cat(lowte xt); h i gh tex t = nu m 2 str ( h i g h i np 1) te xt((m icran g e1 ( 1 )+ 20 )/2 5 0 ,m ax(b oilheat flu x seeheat (:,1 ))+ 5,lo wtex ) h i gh tex t = nu m 2 str ( h i g h i np 1) ; te xt(( hig h r a nge ( 1 )+ 20 )/2 5 0 ,m ax(b oilheat flu x seeheat (:,1 ))+ 5, hi g h t e xt ); t e xt (( hi g h ra n g e (1 )+2 0 0 )/ 25 0, m a x(b o i l h eat fl uxs eeheat (: , 1) )+5 , 'LOW -G ') t e xt (( hi g h r a nge ( 1 )+ 40 0 ) / 2 50 ,m ax(b oi l h e a t f l uxsee heat (: , 1 ) ) +5 ,' HIG H - G' ); t e xt (( hi g h r a nge ( 1 )+ 40 0 ) / 2 5 0 ,m ax( boi l h eat fl uxsee heat ( : ,1) ) +5 ,' \leftarrow' ) t e xt (( hi g h r a nge ( 1 )+ 40 0 ) / 2 50 ,m ax(b oi l h e a t f l uxsee heat (: , 1 ) ) +5 ,' \ r i ght ar r o w' ) %%%Z OOM IN PL OT fig u re; %H IG H- G DAT A SE QU ENCE z o om l o w = boi l h eat fl u x see h eat (m i c range 1( 1)+ 2 0: m i crange 1 ( 1 ) +2 5 0 ,: ) ; z o om hi gh = boi l h eat fl u x see h eat ( h i g hra n g e (1 )+2 0 : h i g h r a n ge( 1 )+ 2 5 0 , : ) ; 294 xa x = z o om hi g h (: , 2 ) - z oom hi g h ( 1 , 2 ); H= pl ot ( x a x , z oom l o w(: , 1) ,' k: ' ) ; hol d o n ; G =pl o t ( xa x,z o o m hi gh(: , 1 ) ,' k-' ) ; l e gend (' LO W- G' ,' HIGH -G' ) ; a xi s t i g ht title(titp lo t); x lab e l('ti m e (sec) ');ylab e l('h eat flux (W/cm ^ {2 })') set(H,'Lin eW i d th ',2);set(G,'Lin e W i d t h ' ,2 ) %axi s ([ 0 hi g h ra n g e( 2)+ 2 50 0 m a x( boi l h ea t f l uxsee heat (: , 1 ) ) +3] ) %fi g u r e; pl ot (b oi l U G3 (: ,i n d e xsa v e) ); %fi g u r e; pl ot (b oi l H G3 (: ,i n d e xsa v e) ); %clear i i n dexsa v e boilhea tfluxsee heat %%% pl ot hi gh - g a n d pl ot a v g val u es fig u re; %H IG H- G DAT A SE QU ENCE z o om hi gh = boi l h eat fl u x see h eat ( h i g hra n g e (1 )+2 0 : h i g h r a n ge( 1 )+ 1 5 0 , : ) ; xa x = z o om hi g h (: , 2 ) - z oom hi g h ( 1 , 2 ); %H=p lo t(x a x , zo o m lo w(:,1),'k : '); G= pl ot ( x a x , z oom hi gh (: , 1 ),' k -' ); h o l d o n ; Title(titp lo t);x lab e l('ti m e (sec) ');ylab e l('h eat flux (W/cm ^ {2 })') hi g h i n p 1 = [ m ean(b oi l f 3 ( hi gh ra nge (1 ): hi g h ra n g e( 2) ,i n d e x sa ve) ) ] ; hi ghi n p 2 = [hi ghi np 1 ; hi ghi np 1] ; hi g h a v g =[ h i ghi n p 2 , h i g hra nge' / 25 0] ; xl i n e = [ 0 , x a x (l e ngt h( xax ))] ' ; pl ot (xl i n e , hi gha v g (: , 1 ) , ' k : o ' ) ; h ol d o n ho ld on s eeheat = input (strcat(' INPUT a n other HE ATER NUM B ER TO SEE CHAR ACTER IST I CS: ' )); f o r i = 1: l e ngt h( o nheat er s ) if onhe a ters(i)==see heat i nde xsa v e = i; e nd end fi gu re; b oi l h eat fl u x see h e a t = [ boi l f 3(: , i nde xsa v e) ,[ 1: l e ngt h( dat a )] ' *1/ 25 0] ; z o om hi gh = boi l h eat fl u x see h eat ( h i g hra n g e (1 )+2 0 : h i g h r a n ge( 1 )+ 1 5 0 , : ) ; xa x = z o om hi g h (: , 2 ) - z oom hi g h ( 1 , 2 ); pl ot (xa x ,z o o m hi gh(: , 1 ) ,' k-' ) ; hol d o n ; hi g h i n p 1 = [ m ean(b oi l f 3 ( hi gh ra nge (1 ): hi g h ra n g e( 2) ,i n d e x sa ve) ) ] ; hi ghi n p 2 = [hi ghi np 1 ; hi ghi np 1] ; hi g h a v g =[ h i ghi n p 2 , h i g hra nge' / 25 0] ; pl ot (xl i n e , hi gha v g (: , 1 ) , ' k : * ' ) ; 295 %lege n d ( ' H I G H - G' ,' HIG H - G AV G' , ' H IG H- G, # 96' ,' HI GH -G A V G , # 96' );axis tig ht le gen d ( ' H IG H- G' ,' HIGH - G A VG');ax is tigh t;x lab e l('ti m e (sec)') ;ylab e l('h eat fl u x (W/cm^{2 })'); c h oice1 = m e nu (' AN AL YZ E I N D I V I DU AL HE ATERS ' , ' YES' ,' EXIT' ) ; end D2. Opti m i zation (Matlab) clear all close all clc %THI GH PA RETO FRON TIER PLO T T_h i gh = [ 7 1 75 8 0 85 82 .5 7 7 .5 9 0 95 10 5 115 1 2 0 14 0 130 11 0 100 ]; Tob j = [0 .01 08 0 . 03 6 0.066 9 0 . 0 936 0 . 0 807 0 . 0 5 2 0 . 11 72 0.13 93 0 . 17 25 0.20 06 0 . 2 127 0 . 2 535 0 . 2 3 4 0 . 18 72 0.15 64 ]; fi g u re; p l o t ( T _ hi g h ,T o b j , ' ko' ); xl abel (' M a xi m i ze T_{ h i g h} [^ {o}C ] ' ); axi s ([7 0 14 0 0 0. 3] ) ylabel(' Minimize T_{ u nc} [^ {o}C]' );%ti tle('Mu ltio b j ectiv e Paret o Fron tier'); l e gen d (' \ a l pha = 0. 0 0 3 \ O m e ga / \ O m e ga^ { o}C ' ,' R _ {ref} = 29 8 \ O m e ga' , ' T _{re f} = 2 4 . 7 ^ { o}C ' ,' C _ {m i n } = 2 0 ' , ' D _{m i n} = 0. 3' ,' T_{l ow} = 10 ^ { o} C ' ,' T_{opt } = 70 ^{o } C') ; gr id on %RAN GE C O M P ARIS O N P L OT %OPTM I UM @TH I GH = 12 0 al pha = 0 . 0 0 3 ; r _re f = 2 98; T _ r e f = 2 4 . 7 ; x( 1) = 16 7; 296 x( 2) = 27 7 33; x( 3) = 47 3 79; x( 4) = 89 7 86; R _ d p = [ 0 : 1 56: 20 0 00] ; fig u re; Tsens = 39 * x ( 1 ) * x( 4)/ ( al pha *r _re f *x (2 )) * ( 1./ ( x( 4 ) +R _ d p ) -R _ d p . / ( ( x (4 )+ R _ d p ) . ^ 2 )); T_ r a ng e = +x(1 )*x ( 3 ) /( al p h a * x (2 )* r_ r e f ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge, T sens,' k- *' ); xl ab el (' Heat er Te mperat ure [^{o} C ]' );ylabel(' Te m p erature un c . [^{o}C] ' );axis([m in(T_ r an ge ) m a x(T_ ran g e ) 0. 15 0 . 3] ); hol d on %COM PARE TO C U RREN T DE SI GN S O LUT I O N x = [8 9.4 181 79 5 792 4 10 ^8 0 ] ; Tsen s2 = 39* x( 1) *x( 4) /( alph a* r_ r e f* x( 2) )*(1 ./(x (4) + R_d p )- R_d p ./( ( x( 4) +R_ d p ) .^2) ) ; T_ r a ng e2 = +x( 1 ) *x( 3) /( alph a* x(2 ) * r _ r ef ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge 2, Tsens 2 ,' k-' ) ; l e gen d (' O p t i m i zed Desi g n ' , ' C ur rent Desi gn' ) ; %Param etric Tlow Tl ow = [ 1 0 15 20 25 30 35 40 45 50 55 60 65] ; Tob j = [0 .21 27 0 . 2 043 0 . 1 95 0 . 1 853 0 . 1 757 0 . 1 658 0 . 1 561 0 . 1 463 0 . 1 365 0 . 1 268 0 . 1 17 0 . 1 073 ]; fig u re;pl o t(Tl o w ,T o b j,' ko' );xlabel(' T_ {low} [^{o}C]' );axis([5 70 0 0.3]) ylab el('T_ {u nc} [^{o }C ]');%title('Mu ltio b j ectiv e Paret o Fro n tier'); l e gen d (' \ a l pha = 0. 0 0 3 \ O m e ga / \ O m e ga^ { o}C ' ,' R _ {ref} = 29 8 \ O m e ga' , ' T _{re f} = 2 4 . 7 ^ { o}C ' ,' C _ {m i n } = 2 0 ' , ' D _{m i n} = 0. 3' ,' T_{h i gh} = 1 2 0 ^ { o}C ' ,' T_{opt } = 7 0 ^ { o}C ' ); gri d o n %Param etric Topt To pt = [ 2 0 30 40 50 60 70 80 90 10 0 11 0 12 0] ; Tob j = [0 .21 45 0 . 2 15 0 . 2 145 0 . 2 145 0 . 2 145 0 . 2 127 0 . 1 986 0 . 1 702 0 . 1 277 0 . 0 709 0 . 0 216 ]; f i gu r e ;p l o t( Top t ,To b j , 'ko ' ) ; x l ab el( ' T_ {low } [ ^ {o }C]') ; ax is([ 15 12 5 0 0.25]) ylab el('T_ {u nc} [^{o }C ]');%title('Mu ltio b j ectiv e Paret o Fro n tier'); l e gen d (' \ a l pha = 0. 0 0 3 \ O m e ga / \ O m e ga^ { o}C ' ,' R _ {ref} = 29 8 \ O m e ga' , ' T _{re f} = 2 4 . 7 ^ { o}C ' ,' C _ {m i n } = 2 0 ' , ' D _{m i n} = 0. 3' ,' T_{h i gh} = 1 2 0 ^ { o}C ' ,' T_{l ow} = 7 0 ^ { o}C ' ); gri d on 297 D.2 OPTIMIZ A TION PROGRAMS D.2.1 Program name: Fmincon Solution Algorithm %USE D T O S T UD Y TH E E FFECT OF I N ITI A L PO INT ON OPTIM I Z A TION S O L U TION RE SUL T S clear all;clo se all;clc %DES IGN PARAMETER DEFINIT I ON al pha = 0 . 0 0 2 ; r _re f = 2 98; T _ r e f = 2 4 . 7 ; C _ m i n = 20; D _ m i n = .3; T _l o w = 2 0 ; T_o p t = 70 ;V_d rop = 10 ; R1 _ub nd = 500 ;R3_ ubn d = 10 ^6 ;R4_u bnd = 10 ^6 ; T_ hi g h = 1 00; %IN I T I AL P O INT CREAT I ON %G EN ERATE RA NDO M NU MBERS U S ED T O DET E R M I NE IN IT I A L P O INT ran d num = ran d ( 1 50 ,5 ); fo r j = 1:len g th (ra nd n u m ( 1,:)) fo r i = 1 :leng th(ran dnu m ( :,1 ) ) ex p o = ra nd pe rm (5)+1; if j == 1 x 0_v ec( i ,j) = r_ r e f * D_ m i n + r a n dnum ( i ,j ) * ( R 1 _ubn d- r_r e f* D_ m i n ) ; end if j == 2 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 1) )- 1) ; end if j == 3 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 2) )- 1) ; end if j == 4 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 3) )- 1) ; end if j == 5 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(2 000 0- 1) ; end e n d 298 end clear i j %IN I T I AL A N D RU N M A TLAB OPT I M I ZA TI ON for i = 1 :leng th(x0_ v e c(:,1)) %PIC K IN I T IA L P O I N T x0 = x0 _v ec( i ,:) ; %SOLVE FO R OPTI M U M Lb n d = [r _re f * D _m i n 1 0 ^ - 6 10^ -6 1 0 ^ - 6 10^ -6] ; Ub nd = [ R 1_ ubn d R3_u bnd R 4 _ub nd i n f 2 000 0 ] ; o p t i o n s = o p t im set ( ' M axFu nE val s ' , 30 00 ,' M a xIt e r' ,3 0 0 0 , ' T ol C o n' ,10^ -1 0,' T ol f un' ,1 0^ - 1 0 ) ; [ x ,T ob j] =fm i nco n (' Tres opt ' , x 0 , [ ] , [] ,[] , [] ,L bn d, U b n d ,' Tre s No nLi n ' , opt i o ns,al pha ,r _re f , T _re f ,C _m i n ,D_m i n ,T_ h i g h , T_l o w , T_ o p t , V _d rop ) ; clc %O UTP U T OPT I M I ZE D CONS TRA I N T V A L U ES [C,Ce q ] = T r esN o nLin(x,alpha ,r _re f ,T _r ef,C_ m in ,D_ m in ,T_h igh , T_ low,T_op t,V_d r o p ); dis p (' ITERA T IO N N U M B ER' ) ;disp( num 2str (i)); %SAVE RE SULT S IN M A TRIX ONLY IF C O NSTR AINT S ARE S A TISF IE D if (( C(1 ) <= 0 ) & ( C (2 ) <= 0 ) & ( C (3 ) <= 0 ) & ( C (4 ) <= 0 ) ) if ((a bs (Ceq( 1 ) ) < 1 0 ^- 6 )) %& (ab s (Ce q ( 2 ) ) < 1 0 ^- 6) ) Designv ar(i,:) = x ; Tob j ective( i,:) = Tob j ; n on lin con t (i,:) = C;lin co n t (i,:) = Ceq ; end e n d end %FI L TER OUT ZERO SO LU TION S clear i j j = 1; for i = 1 :leng th(Tobj ectiv e) i f T o bjective ( i) > 0 op tim u m s ( j) = Tobj ective(i); va r opt( j ,: ) = Desi gnva r(i, : ); nonlincontopt ( j ,: ) = no nl i n co nt (i ,: ); op tlin con t (j,:) = lincon t (i ,:); in it(j , :) = x 0_v ec(i,:); j = j+1; 299 e n d end %HI S TO GR A M OF OP TIM U M S O L U TI O N S figu re;h ist(op tim u m s,3 0 ) ;x label('Op t i m ized T_ {u n c } [C]'); ylab el('Freq u e n c y (25 0 to tal sam p les)');% t i t l e('In itial Po in t Sen s itiv ity');g rid on ; %leg = str cat( ' V _ {d rop } [vo lts] = ', n u m 2 s tr (V _d rop ) ) ; l e g = st rcat (' T_ {hi g h} [^ {o}C ] = ' , num 2st r(T _hi gh )); %l egen d(l e g,' \ al pha = 0 . 0 0 3 \ O m e ga / \ O m e ga^ { o}C ' ,' R _ {ref} = 2 9 8 \ O m e ga' , ' T _{ref} = 2 4 . 7 ^ { o}C ' ,' C_{m i n } = 20' ,' D_{m i n } = 0 . 3 ' , 'T _ { lo w } = 10 ^ { o}C ' ,' T_{opt } = 7 0 ^ { o}C ' ); gri d o n %LOO K FO R MO ST NO N- LI N E A R SO LUTI ON [w orst , w or] = m i n(var o pt (: , 4 ) ) ; %DETERM I NE THE MINIMUM S O LUT I ON disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' GLOB A L OP TIM U M OBJECTI V E F UNCT I O N V A LU E (Tu n c ) ; @ M O ST N ONL I N EAR' ); [ i nd 1,op t] = m i n ( op ti m u m s ) ; d i sp ( i nd1 ) ; d i sp(o p tim u m s( w o r) ) ; %PARET O P O I N T %DETERM I NE SEC O ND OBJECTIVE VALUE disp (' SECON D OBJECTI V E V A L U E (V DROP )' ); opt DV = var o p t (o pt ,: ); v d ro p = 2 4 / (1 +o p t D V ( 3 ) / op t D V( 2) +o p t D V ( 4 ) *op tDV ( 5 ) / ( op tDV ( 4 ) *op tD V( 2) +o p t D V ( 5 ) *op tDV ( 2 ))) ; d i sp( vdr op ) ; disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' OPTIM U M DES I G N V A RI ABLES ; M O ST N O N - L I NE AR; I N ITI A L DES I G N P O I N T' ); di sp ([ o p t D V] ); di sp (va r opt ( w o r ,: ));IP = in it(op t,:);d isp ( IP) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' INE Q U A L IT Y CO NS T R AI NT VA LU ES @ O P TIM U M (T LO W, CM IN, V D RO P); @ M O S T NO N- LI NE A R ' ) ; opt NLC = n onl i n co nt o p t ( opt ,: ); di sp ( opt NLC ) ; d i s p ( no nl i n c o nt o p t ( wo r,: ) ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp(' EQUALITY C O NSTR AINT VALUE S @ OP TIM U M ; M O ST N O N -L IN EAR' ); o p t LC = op tlinco n t (op t ,:); d i sp(op t LC);d i sp (op tlin con t (wor,: )); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); %PLOT GLOBA L O P TI MUM SO LU TI ON clear x 300 f i gu r e ;R_dp = [ 0 : 3 9 : 2 000 0 ] ; x = o p t D V; Tsens = 39 * x ( 1 ) * x( 4)/ ( al pha *r _re f *x (2 )) * ( 1./ ( x( 4 ) +R _ d p ) -R _ d p . / ( ( x (4 )+ R _ d p ) . ^ 2 )); T_ r a ng e = +x(1 )*x ( 3 ) /( al p h a * x (2 )* r_ r e f ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge, T sens,' r-' ); xl a b el (' Tem p erat ure R a nge [C ] ' ); y l abel (' Te m p erature unc. [C]' );axis([m i n( T_ r a ng e) m a x ( T_ r a ng e) 0 0.5 ] ) ; %COM PARE TO C U RREN T DE SI GN S O LUT I O N hol d on x = [2 27 26 100 3 750 0 400 00 0 ] ; Tsen s2 = 39* x( 1) *x( 4) /( alph a* r_ r e f* x( 2) )*(1 ./(x (4) + R_d p )- R_d p ./( ( x( 4) +R_ d p ) .^2) ) ; T_ r a ng e2 = +x( 1 ) *x( 3) /( alph a* x(2 ) * r _ r ef ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge 2, Tsens 2 ,' b-' ) ; %M OST N O N - LI NE AR S O L U TI O N hol d on x = va ro pt ( w o r ,: ); Tsen s3 = 39* x( 1) *x( 4) /( alph a* r_ r e f* x( 2) )*(1 ./(x (4) + R_d p )- R_d p ./( ( x( 4) +R_ d p ) .^2) ) ; T_ r a ng e3 = +x( 1 ) *x( 3) /( alph a* x(2 ) * r _ r ef ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge 3, Tsens 3 ,' k-' ) ; legen d (' OPT I M I ZED D E SI GN' ,' CURREN T DE SI GN' ,' M O ST N O N L I N EAR DES I G N ' ) ;gri d on axi s ( [ m i n(T_ra nge 3 ) m a x(T_ r a nge 3 ) 0 0. 8] ); d i sp( ' R1 O P T; R1 IN ITIA L') d i sp( [ op tDV ( 1) ,IP(1 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R3 O P T; R3 IN ITIA L') d i sp( [ op tDV ( 2) ,IP(2 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R4 O P T; R4 IN ITIA L') d i sp( [ op tDV ( 3) ,IP(3 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R5 O P T; R5 IN ITIA L') di sp (o pt D V ( 4 ) ); di sp (I P( 4) ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' Rdp OPT ; Rdp I N IT I A L ' ) d i sp( [ op tDV ( 5) ,IP(5 ) ]) 301 D.2.2 Program name: Exterior P e nalty Algorithm %U N C ON STRA IN ED O B JECTI V E FUNCTI ON fu nct i o n T o b j = EXT P E N FU NC ( x ,al p ha, r _r ef,T _re f ,C _m in, D _m i n ,T_ h i g h , T _ l o w,T _ o p t , V _ dr o p ,r p,R 1 U b nd ,R 3 U b n d ,R 4U bn d , R 5 Ub n d ) R1 = x ( 1); R3 = x ( 2); R4 = x ( 3); R5 = x ( 4); R d p = x( 5); To bj = 39 *R 1 * R 5^ 2/ (al pha *r _re f *R 3 * (R 5+ R d p ) ^ 2 ).. .. + r p* (-R 1*R 4/ (al p ha *R 3 * r _ re f) -R d p * R 1 * R 5/ (al p ha*R 5 * R 3* r_ ref+R d p * al p h a*R 3 *r _r ef)+ 1/ al pha -T _ r ef+T _ opt )^ 2. .. . + r p*(m ax([0,(-R 1*R4/(al pha*R3*r _ref )- 20000*R 1*R5/( alpha *R5*R3*r_ref+ 2 0000*a lpha *R3*r _ ref ) +1/alpha- T _re f +T_high)] ))^ 2.... + r p*(m ax([0,((R 1*R4/(R 3 *r_ref )- 1)/alpha +T_re f - T _l ow ) ] ))^2. ... + r p*(m ax([0,((C _m in-(R3+ R4)/(R 1+r _ re f) ))] ) ) ^2. ... + r p*(m ax([0,( 24/ ( 1 +R 4/R3+R5*R dp/ (R5*R3+R dp*R 3) )- V_dr op)] ) ) ^2.... + r p*(m ax([0,(r _ ref * D _ m i n-R1)] ) ) ^2. ... + r p*(m ax([0,(R1-R1U bnd)] ))^2... . + r p*(m ax([0,(R4-R4U bnd)] ))^2... . + r p*(m ax([0,( 10^( - 6 ) - R4)] ) ) ^2. ... + r p*(m ax([0,(Rdp-20000)] ) ) ^2. ... + r p*(m ax([0,( 10^( - 6 ) - Rdp) ] ))^2. ... + r p*(m ax([0,(R5-R5U bnd)] ))^2... . + r p*(m ax([0,( 10^( - 6 ) - R5)] ) ) ^2. ... + r p*(m ax([0,( 10^( - 6 ) - R3)] ) ) ^2. ... + r p* (m ax([0 ,(R3 -R3 U bn d ) ] ))^2; %EXTER IOR PEN A LT Y AP PROAC H clear all;clo se all;clc %FI N D S Y M B OLIC GRA D I EN T OF OBJ E CTIV E sy m s R1 R3 R 5 R d p alph a r_ref To bj = 39 *R 1 * R 5/ (al p ha* r _re f *R 3) *( 1/ (R 5+ R d p )-R dp/ ((R 5 + R d p ) ^ 2 )); gra d = [sim plify((di f f ( Tobj,R 1) )) ,sim plify((diff ( T o bj,R 3) )) ,... . sim p lify((d iff(To bj ,R 5 ) )),sim p lify((d iff(Tob j,Rdp ) ))] pretty (g ra d) h e ss = [ s im p lif y( d i ff (( d i ff (Tob j, R1) ) , R 1) ) , sim p l i f y ( d if f( (d if f( Tobj , R 1 ) ) , R3 )) , . . . 302 sim p lify ( diff (( dif f(T o b j, R1) ) ,R5 ) ) , sim p lify ( diff (( dif f ( T o b j,R1 )),R d p ));.. . sim p lify(diff (( dif f(T obj, R3 ) ) ,R1)) , sim p lify(diff (( dif f ( T obj,R3)),R 3 ) ) ,... sim p lify ( diff (( dif f(T o b j, R3) ) ,R5 ) ) , sim p lify ( diff (( dif f ( T o b j,R3 )),R d p ));.. . sim p lify(diff (( dif f(T obj, R5 ) ) ,R1)) , sim p lify(diff (( dif f ( T obj,R5)),R 3 ) ) ,... sim p lify(diff (( dif f(T obj, R5) ) ,R 5 ) ) , sim p lify ( diff (( dif f ( T o b j,R5 )),R d p ));.. .] sim p lify(diff (( dif f(T obj, Rdp) ) , R1)), sim p lify(di ff (( diff ( T obj,Rdp) ),R 3 )), ... sim p lify ( diff (( dif f(T o b j, Rdp ) ) , R5 )), sim p lify ( di ff (( diff ( T o b j,Rd p) ),R d p) )] ; %DES IGN PARAMETER DEFINIT I ON al pha = 0 . 0 0 3 ; r _re f = 2 98; T _ r e f = 2 4 . 7 ; C _ m i n = 20; D _ m i n = .3; T _l o w = 1 0 ; T_o p t = 70 ;V_d rop = 10 ; R1 Ub nd = 5 00;R3 Ub nd = 10^6 ; R4 Ubn d = 1 0 ^ 6 ; R5U bnd = 10 ^12 ; T_ hi g h = 1 40; fact or = [. 1 1 1 0 10 0 1 0 0 0 1 0 ^ 4 1 0 ^ 5 10^ 6 10^ 7] ; o p tion s = o p t i m se t( 'Max Fu nEv a ls',2 000 0,'Max I t er ',150 00 ) ; %IN I T I AL P O INT CREAT I ON %G EN ERATE RA NDO M NU MBERS U S ED T O DET E RM INE IN IT I A L P O INT ran d num = ran d ( 1 00 ,5 ); fo r j = 1:len g th (ra nd n u m ( 1,:)) fo r i = 1 :leng th(ran dnu m ( :,1 ) ) ex p o = ra nd pe rm (5)+1; if j == 1 x 0_v ec( i ,j) = r_ r e f * D_ m i n + r a n dnum ( i ,j ) * ( R 1 U bnd -r _r ef*D _ m in ) ; end if j == 2 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 1) )- 1) ; end if j == 3 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 2) )- 1) ; end if j == 4 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(1 0 ^ ( e x po( 3) )- 1) ; end if j == 5 x 0_v ec( i ,j) = 1 + r a ndnu m ( i,j ) *(2 000 0- 1) ; 303 end e n d end clear i j fo r i = 1:len g th (facto r) fo r j = 1 :leng th(x0_ v e c(:,1)) %P ICK I N IT IA L P O I N T iter = i; x0 = x0_vec(j,:); r p = factor(i) [ x ,T o b j] = fm i nunc(' EXT P ENF U NC ' , x0 ,o pt i o n s ,al p ha, r _ r ef ,T_ r ef ,C _ m i n ,D_m i n ,T_ h i g h,T _ l o w,T _ opt , V _d r o p , r p , R 1U bn d,R 3 Ub nd ,R 4 U bnd ,R 5U bnd ) %CH E CK T O S EE IF CONS TRA I N T S AR E S A T I SFIE D [C,Ce q ] = Tres N onLi n ( x ,alpha ,r _re f ,T_r ef ,C _ m in ,D _min ,T_h igh , T_lo w , T_op t,V_dr op ) ; dis p (' ITE R ATI O N N U M BE R ' ); di sp([ num 2st r(i ) , n u m 2str(j)] ); %S AV E RESULT S IN M A TRI X ON LY IF C O N S T R AI NTS ARE SAT I SF IE D if ((C (1 ) <= 0 ) & (C( 2 ) <= 0 ) & (C( 3 ) <= 0 ) & (C( 4 ) <= 0 )) if ( ( abs ( Ceq(1)) < 10^ -6)) Desi g n v a r(i,j ,:) = x ; Tob j ectiv e(i,j , : ) = Tob j ; n on linco n t (i,j,:) = C;lin con t (i,j ,:) = Ceq ; e nd end e n d end %FI L TER OUT ZERO SO LU TION S clear i j k = 1; m = 1; mess = size(T o bjective); for j = 1 :iter f o r i = 1:m e ss(2) if T o bje c tive( j,i) > 0 o p tim u m s(k ) = To bj ectiv e(j,i); c h e(m ) = Tobjective( j, i); var o pt( k ,:) = Designvar( j,i,:); nonlinc ont opt (k ,: ) = n onl i n c o nt ( j ,i ,: ); o p tlin co n t (k,:) = lincon t (j ,i,:); 304 in it(k , :) = x0_ v e c(i,:); k = k+ 1;m = m + 1; end e n d i f e x ist(' c he') == 1 optim u m srp(j) = m i n(che ) ; clear c h e m m = 1; e n d end opt i m u m srp fi g u re; s em i l ogx( fact o r , opt i m um srp,' ko' ); xl a b el (' Penal t y Pa ram e t e r ' ); y l abel (' T_{unc} [^ { o }C ] ' ); gri d on; %HI S TO GR A M OF OP TIM U M S O L U TI O N S figu re;h ist(op tim u m s,3 0 ) ;x label('Op t i m ized T_ {u n c } [C]'); ylab el('Freq u e n c y (25 0 to tal sam p les)');% t i t l e('In itial Po in t Sen s itiv ity');g rid on ; %leg = str cat( ' V _ {d rop } [vo lts] = ', n u m 2 s tr (V _d rop ) ) ; l e g = st rcat (' T_ {hi g h} [^ {o}C ] = ' , num 2st r(T _hi gh )); %l egen d(l e g,' \ al pha = 0 . 0 0 3 \ O m e ga / \ O m e ga^ { o}C ' ,' R _ {ref} = 2 9 8 \ O m e ga' , ' T _{ref} = 2 4 . 7 ^ { o}C ' ,' C_{m i n } = 20' ,' D_{m i n } = 0 . 3 ' , 'T _ { lo w } = 10 ^ { o}C ' ,' T_{opt } = 7 0 ^ { o}C ' ); gri d o n %LOO K FO R MO ST NO N- LI N E A R SO LUTI ON [w orst , w or] = m i n(var o pt (: , 4 ) ) ; %DETERM I NE THE MINIMUM S O LUT I ON disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' GLOB A L OP TIM U M OBJECTI V E F UNCT I O N V A LU E (Tu n c ) ; @ M O ST N ONL I N EAR' ); [ i nd 1,op t] = m i n ( op ti m u m s ) ; d i sp ( i nd1 ) ; d i sp(o p tim u m s( w o r) ) ; %PARET O P O I N T %DETERM I NE SEC O ND OBJECTIVE VALUE disp (' SECON D OBJECTI V E V A L U E (V DROP )' ); opt DV = var o p t (o pt ,: ); v d ro p = 2 4 / (1 +o p t D V ( 3 ) / op t D V( 2) +o p t D V ( 4 ) *op tDV ( 5 ) / ( op tDV ( 4 ) *op tD V( 2) +o p t D V ( 5 ) *op tDV ( 2 ))) ; d i sp( vdr op ) ; disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' OPTIM U M DES I G N V A RI ABLES ; M O ST N O N - L I NE AR; I N ITI A L DES I G N P O I N T' ); di sp ([ o p t D V] ); di sp (va r opt ( w o r ,: ));IP = in it(op t,:);d isp ( IP) 305 disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' INE Q U A L IT Y CO NS T R AI NT VA LU ES @ O P TIM U M (T LO W, CM IN, V D RO P); @ M O S T NO N- LI NE A R ' ) ; opt NLC = n onl i n co nt o p t ( opt ,: ); di sp ( opt NLC ) ; d i s p ( no nl i n c o nt o p t ( wo r,: ) ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp(' EQUALITY C O NSTR AINT VALUE S @ OP TIM U M ; M O ST N O N -L IN EAR' ); o p t LC = op tlinco n t (op t ,:); d i sp(op t LC);d i sp (op tlin con t (wor,: )); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); %PLOT GLOBA L O P TI MUM SO LU TI ON clear x f i gu r e ;R_dp = [ 0 : 3 9 : 2 000 0 ] ; x = o p t D V; Tsens = 39 * x ( 1 ) * x( 4)/ ( al pha *r _re f *x (2 )) * ( 1./ ( x( 4 ) +R _ d p ) -R _ d p . / ( ( x (4 )+ R _ d p ) . ^ 2 )); T_ r a ng e = +x(1 )*x ( 3 ) /( al p h a * x (2 )* r_ r e f ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge, T sens,' r-' ); xl a b el (' Tem p erat ure R a nge [C ] ' ); y l abel (' Te m p erature unc. [C]' );axis([m i n( T_ r a ng e) m a x ( T_ r a ng e) 0 0.5 ] ) ; %COM PARE TO C U RREN T DE SI GN S O LUT I O N hol d on x = [2 27 26 100 3 750 0 400 00 0 ] ; Tsen s2 = 39* x( 1) *x( 4) /( alph a* r_ r e f* x( 2) )*(1 ./(x (4) + R_d p )- R_d p ./( ( x( 4) +R_ d p ) .^2) ) ; T_ r a ng e2 = +x( 1 ) *x( 3) /( alph a* x(2 ) * r _ r ef ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge 2, Tsens 2 ,' b-' ) ; %M OST N O N - LI NE AR S O L U TI O N hol d on x = va ro pt ( w o r ,: ); Tsen s3 = 39* x( 1) *x( 4) /( alph a* r_ r e f* x( 2) )*(1 ./(x (4) + R_d p )- R_d p ./( ( x( 4) +R_ d p ) .^2) ) ; T_ r a ng e3 = +x( 1 ) *x( 3) /( alph a* x(2 ) * r _ r ef ) + R_ dp* x( 1)* x (4 )./( alph a*x( 4)* x (2 )* r_ r e f + R _ dp* alph a*x( 2) *r _r ef) - 1 / alpha+T_ r ef ; pl ot (T _ r an ge 3, Tsens 3 ,' k-' ) ; legen d (' OPT I M I ZED D E SI GN' ,' CURREN T DE SI GN' ,' M O ST N O N L I N EAR DES I G N ' ) ;gri d on axi s ( [ m i n(T_ra nge 3 ) m a x(T_ r a nge 3 ) 0 0. 8] ); d i sp( ' R1 O P T; R1 IN ITIA L') d i sp( [ op tDV ( 1) ,IP(1 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R3 O P T; R3 IN ITIA L') d i sp( [ op tDV ( 2) ,IP(2 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R4 O P T; R4 IN ITIA L') 306 d i sp( [ op tDV ( 3) ,IP(3 ) ]) disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); d i sp( ' R5 O P T; R5 IN ITIA L') di sp (o pt D V ( 4 ) ); di sp (I P( 4) ); disp (' --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --' ); disp (' Rdp OPT ; Rdp I N IT I A L ' ) d i sp( [ op tDV ( 5) ,IP(5 ) ])