ABSTRACT Title of Document: TWO-PHASE HEAT TRANSFER MECHANISMS WITHIN PLATE HEAT EXCHANGERS: EXPERIMENTS AND MODELING. Valentin Solotych, PhD, 2015 Directed By: Professor, Jungho Kim, Department of Mechanical Engineering Two-phase flow heat exchangers have been shown to have very high efficiencies, but the lack of a dependable model and data precludes them from use in many cases. Herein a new method for the measurement of local convective heat transfer coefficients from the outside of a heat transferring wall has been developed, which results in accurate local measurements of heat flux during two-phase flow. This novel technique uses a chevron-pattern corrugated plate heat exchanger consisting of a specially machined Calcium Fluoride plate and the refrigerant HFE7100, with heat flux values up to 1 W cm-2 and flow rates up to 300 kg m-2s-1. As Calcium Fluoride is largely transparent to infra-red radiation, the measurement of the surface temperature of PHE that is in direct contact with the liquid is accomplished through use of a mid-range (3.0-5.1 µm) infra-red camera. The objective of this study is to develop, validate, and use a unique infrared thermometry method to quantify the heat transfer characteristics of flow boiling within different Plate Heat Exchanger geometries. This new method allows high spatial and temporal resolution measurements. Furthermore quasi-local pressure measurements enable us to characterize the performance of each geometry. Validation of this technique will be demonstrated by comparison to accepted single and two-phase data. The results can be used to come up with new heat transfer correlations and optimization tools for heat exchanger designers. The scientific contribution of this thesis is, to give PHE developers further tools to allow them to identify the heat transfer and pressure drop performance of any corrugated plate pattern directly without the need to account for typical error sources due to inlet and outlet distribution systems. Furthermore, the designers will now gain information on the local heat transfer distribution within one plate heat exchanger cell which will help to choose the correct corrugation geometry for a given task. TWO-PHASE HEAT TRANSFER MECHANISMS WITHIN PLATE HEAT EXCHANGERS: EXPERIMENTS AND MODELING. By Valentin Solotych. 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 2016 Advisory Committee: Professor Jungho Kim, Chair Professor Michael M. Ohadi Professor Gary A. Pertmer Professor Reinhard Radermacher Professor Christopher Cadou © Copyright by Valentin Solotych 2016 ii Acknowledgements There are a lot of people that helped me during my time as a graduate student. I will list everyone alphabetically so no one should feel bad about their position. If you are not on the list than it does not mean that I don’t like you, it just means that you did not help me that much in completing my dissertation (I am looking at you, Jason). My thanks goes to: Aerospace Machine shop (Howard and Mike): Always had a couple of minutes to help me with designing parts and using their equipment. Amalfie, Luca (Collaborator): Did great work on creating data bases for single and two- phase correlations to which he then compared my data to. Our hour long discussions about the common topic helped me tremendously. Aroom, Majid (ME Machine shop director): Helped me in many situations when it came to fabricating parts for my experiment. Dessiatoun, Sascha (Intern): Did a wonderful job helping me over the summer, with figuring out how to CNC machine. Dessiatoun, Serguei (Mentor): Thought me most of my practical engineering knowledge. He also never denied me any help whenever I asked him for advice, whether he let me use his lab equipment, borrowing tools or helping to build parts for my experiment. Russian engineering ftw. Flores, Giovanni: For helping me polishing samples. Greeve, Hannes: We had a lot of discussions about electronic design, which helped a lot. Kafri, Dvir: For helping me with Matlab. iii Ketchum, Christina (My wife): For being my second advisor, she helped me with my writing, listened to my boring presentations and rants about work and always gave me advice and comfort. Kim, Jungho (Advisor): For letting me graduate, and also being a good professor/advisor. We sure had our differences when it came to research and working in the lab, but in the end he was always willing to listen to my theories, or he would take the time to explain to me why I was wrong. I also really appreciated his commitment to his students, which included: answering annoying emails, helping to write papers, hands on help for experiments and in general have the best interest of the student on mind. Lee, Donghyeon (Intern): Became a CNC master during his short visit and reduced my work load by a lot. Also no matter what task you would throw at him he would come up with a solution. Reich, Marius (Intern): Did most of the Labview coding, which was a little buggy, but nonetheless, good job Root, TJ (Terp Racing): Allowed and helped me to use his CNC machine. Scammel, Alex (Lab mate): For being in the same boat as me. Without his help and presents I am certain that my GPA would have been lower. He also helped me a lot by just listening and discussing my engineering problems. Solotych, Juri (My dad): Truly a life saver, who sacrificed 5 month of his life to take care of our new born daughter, without him the last months of this work would have been much more difficult. Спасибо! Warehime, Mick: For all the Matlab help. iv Table of Contents Acknowledgements ii Table of Contents iv List of Figures vi List of Tables xiv Nomenclature xv 1. Introduction 1 2. Fundamentals 4 2.1 Geometry 4 2.2 Single Phase Flow 8 2.2.1 Heat transfer 8 2.2.2 Pressure drop 9 2.3 Fundamentals in Flow Boiling 11 3. State of the Art Literature review 16 3.1 Single Phase flow 16 3.1.1 Averaged HTC and frictional factor measurements 16 3.1.2 Local HTC measurements 19 3.2 Two-Phase Flow 23 3.2.1 Flow Patterns 23 3.2.2 Two-Phase heat transfer and pressure drop measurement 28 3.3 Conclusion and motivation 37 4. Experimental Technique 39 4.1 Experimental Setup 39 4.1.1 Test Section 39 4.1.2 Experimental Apparatus 43 4.2 Heater Setup 44 4.3 Infrared Thermography 48 4.4 Data Reduction 51 4.4.1 General heat flux and HTC calculation 51 4.4.2 Eliminating film heater defects 55 v 4.4.3 Data reduction for Single phase flow 57 4.4.4 Data reduction for two-phase flow 58 4.5 Uncertainty analysis and preliminary validation 62 5. Single Phase flow results 66 5.1 Pressure Drop 66 5.1.1 Single Phase friction factor measurements 67 5.1.2 The effect of Inlet/Outlet port and herringbone pattern 72 5.2 Area averaged HTC 75 5.3 Local Heat transfer Measurements 79 5.4 PHE performance comparison 83 6. Two-Phase flow results 86 6.1 Flow Visualization 86 6.2 Pressure Drop 88 6.3 Area averaged HTC 92 6.4 Local Heat transfer Measurements 99 6.5 Dryout observation 106 6.6 PHE performance comparison during two-phase flow 107 7. Conclusion and future outlook 110 8. Appendices 114 8.1 Thermal conductivity measurement of 200RS100 film 114 8.2 Outlook for transient HTC analysis 116 8.2.1 Black dot sizing 117 8.2.2 Black dot spacing 118 8.3 Consideration of alternative heating methods 121 8.3.1 Silicon heater 121 8.3.2 Gold coated polyimide tape 129 9. Bibliography 133 vi List of Figures Figure 1.1: Schematics of a typical PHE 1 Figure 2.1: Showcase of the different PHE designs 5 Figure 2.2: Corrugation features of a typical chevron plate: 6 Figure 2.3: Nomenclature to characterize a PHE geometry 7 Figure 2.4: Vertical heated tube exhibiting sequential stages of two-phase flow boiling from the bottom to the top (Collier and Thome [1]) 12 Figure 3.1: Heat transfer coefficients on the surface of a unitary cell at Re = 2120. CFD Simulation with a) SST turbulence model (left), b) RSM–EASM (middle) and (c) TOIRT measurement (right). (Freund and Kabelac [16]) 21 Figure 3.2: Regular bubbly flow Tribbe and Müller-Steinhagen [24] 24 Figure 3.3: Irregular bubbly flow Tribbe and Müller-Steinhagen [24] 25 Figure 3.4: Churn flow Tribbe and Müller-Steinhagen [24] 25 Figure 3.5: Film flow Tribbe and Müller-Steinhagen [24] 26 Figure 3.6: Partial film flow Tribbe and Müller-Steinhagen [24] 26 Figure 4.1: Schematic of the two plate geometries that were machined into CaF2 and the location of the thermocouples in their polycarbonate counter plate: (a) test section L5.7A1.0B60-60, (b) test section L3.7A0.5B65-65 40 Figure 4.2: L5.7A1.0B60 polycarbonate plate with attached heater, silver busses, electrical insulating tape at the contact points, and TCs to measure bulk fluid temperature. 41 Figure 4.3: Experimental setup: cross section view of the test section, including the inlet and outlet flow distributors, pressure taps and valve system to measure absolute and differential pressure. 42 Figure 4.4: Schematic of flow loop. 44 vii Figure 4.5 SEM image of Dupont 200RS100 cross section identifying the conducting (tC) and non-conducting layers (tP) and their thicknesses. The film was potted into an epoxy carrier and polished before viewing. The average values and the standard deviation about these averages are noted. 45 Figure 4.6: Device used to create a uniform layer of adhesive between the CaF2 substrate and the 100RS200 film, without entrapping air bubbles and not fracturing the CaF2, cross section view of the CAD model (a) and assembled device (b) 46 Figure 4.7: Schematic of test wall construction. 48 Figure 4.8: IR-camera calibration for three random pixels for (a) single phase measurements and (b) two-phase measurements. 50 Figure 4.9: IR-temperature measurement of the heater surface during calibration: Before (a) and after calibration (b). 51 Figure 4.10 Heat generation distribution within the heating film after 8ms of heating, when applied to the corrugated surface. 52 Figure 4.11: Heater film shape required to cover a rectangular PHE plate along with silver bussbars shaped to provide uniform heat flux (top); the temperature distribution on the PHE surface measured by the IR camera during transient heating of the film to test the heater uniformity (ΔT is the temperature difference between the heated and unheated state after 8 ms of heating (bottom). 53 Figure 4.12: Initial image from the IR-camera after 8 ms of heating (a), detection of pixels that are below a certain threshold (b), identifying areas and filling the gaps in each area (c). 56 Figure 4.13: Visualization of change in quality along a PHE channel. 59 Figure 4.14: Energy Balance across a channel section, to calculate the change in quality 59 viii Figure 4.15: Result of the energy balance calculation for several experiments with different flow parameters and heat fluxes. 64 Figure 4.16: Temperature difference between heater and fluid during adiabatic two- phase operation, (a) Temperature map of the entire PHE plate, (b) over the width averaged heater temperature vs. fluid temperature interpolated using the 5 TCs that are placed in the flow channel. 65 Figure 5.1: Pressure drop along the L5.7A1.0B60-60 PHE at various Re. Pressure drop is measured between the furthermost upstream tap (z=0 mm) and a downstream tap (z=20 mm, 40 mm, 60 mm, or 80 mm). 67 Figure 5.2: Comparison of friction factor correlations from other studies with the results of the (a) L5.7A1.0B60-60 and (b) L3.7A1.0B60-30, values that are within the red circle need to be ignored since the measurement uncertainty was too high for these low Reynolds numbers. 68 Figure 5.3: Comparison of experimental friction factor of the L3.7A0.5B65-65 data with other studies. 70 Figure 5.4: Comparison of experimental friction factor for all tested geometries. 71 Figure 5.5: Pressure drop over the inlet and outlet compared with the frictional pressure drop within the (a) L5.7A1.0B60-30 PHE and (b) L3.7A0.5B65-65 PHE. 73 Figure 5.6: Single-phase pressure drop for the oblique washboard geometry and herringbone pattern at different Reynolds number for the L3.7A0.5B65-65 PHE. 74 Figure 5.7: Transversal cross section of two sinusoidal plate heat exchanger for the L3.7A0.5B65-65 PHE: (a) Oblique washboard, (b) herringbone pattern. 75 Figure 5.8 Horizontal and vertical variation of heat transfer coefficient at Re=1700 and heat flux of 0.45W cm-1 for the L5.7A1.0B60-60 PHE. The white rectangles indicate the areas of the nine unit cells that were used to calculate the local heat transfer distribution within a unit cell. 76 ix Figure 5.9 Horizontal and vertical variation of heat transfer coefficient at Re=1300 and heat flux of 0.45W cm-1 for the L3.7A0.5B65-25 PHE. The white box representing the area that was used for the overall HTC computation. 77 Figure 5.10: Comparison of experimental Nusselt number of the (a) L5.7A1.0B60-60 and (b) L5.7A1.0B60-30 data with other studies. 78 Figure 5.11: Comparison of experimental Nusselt number of the (a) L3.7A0.5B65-65 and (b) L3.7A0.5B65-25 data with other studies. 78 Figure 5.12: Heat transfer data from all geometries. 79 Figure 5.13: HTC distribution within a representative cell for the (a) L5.7A1.0B60-60 PHE, (b) L5.7A1.0B60-30 PHE, (c) L3.7A0.5B65-65 PHE, and (d) L3.7A0.5B65-25 PHE. 80 Figure 5.14: HTC distribution over a range of Re: (a) L5.7A1.0B60-60 PHE, (b) L5.7A1.0B60-30 PHE, (c) L3.7A0.5B65-65 PHE, and (d) L3.7A0.5B65- 25 PHE 82 Figure 5.15: Weighted standard deviation of the heat transfer coefficient distribution within a representative cell for the (a) L5.7A1.0B60-60, (b) L5.7A1.0B60- 30, (c) L3.7A0.5B65-65 (d) L3.7A0.5B65-25 PHE. 83 Figure 5.16: Comparison of experimental friction factor during single phase flow, for all tested geometries. 85 Figure 6.1: Two-phase flow visualization for L5.7A1.0B60-60 at G = 100 kg m-2 s-1: (a) bubbly flow x = 0.02, (b) churn flow x = 0.05, (c) film flow x = 0.30. The red circles indicate contact points between the plates. 87 Figure 6.2: Two-phase flow visualization for L3.7A0.5B65-65 at G = 100 kg m-2 s-1: (a) bubbly flow x = 0.05, (b) churn flow x = 0.15, (c) film flow x = 0.4. The red circles indicate contact points between the plates. 87 Figure 6.3: Two-phase pressure drop results: (a) mean frictional pressure gradient versus mean quality for L5.7A1.0B60-60 geometry and (b) L5.7A1.0B60- 30 geometry 88 x Figure 6.4: Two-phase pressure drop results: (a) mean frictional pressure gradient versus mean quality for L5.7A1.0B60-60 geometry, (b) L5.7A1.0B60-30 geometry, and (c) L3.7A0.5B65-65 geometry. 89 Figure 6.5: Two-phase frictional pressure drop data compared to the most quoted prediction methods from the literature: (a) Nilpueng and Wongwises [28], (b) Khan et al. [46]–[48], (c) Lee et al. [54], (d) Amalfi et al. [50,51]. 90 Figure 6.6: Two-phase heat transfer results at G = 100 kg m-2 s-1 and xi = 0.5: (a) time averaged HTC distribution for L5.7A1B60-60 with red dots indicating the contact points and the white box representing the area that was used for the overall HTC computation, (b) saturation temperature and mean heater temperature averaged over the partial width of the plate against the time averaged temperature along the dotted black line. 93 Figure 6.7: Partial dryout for L3.7A0.5B65-65 at G = 100 kg m-2 s-1 and xi = 0.8: (a) instantaneous temperature distribution, with dots indicating the contact points and arrows show the direction of increasing dryout area, (b) time average HTC, with the white box indicating the area that was used for the overall HTC, (c) saturation temperature and mean heater temperature averaged over the partial width of the plate versus the time averaged temperature along the dotted black line. 94 Figure 6.8: Average two-phase heat transfer results: (a) HTC versus quality for L5.7A1.0B60-60 and (b) HTC versus quality for L5.7A1.0B60-30. Dryout occurred for the data to the right of the dotted line and are therefore unreliable. 96 Figure 6.9: Average two-phase heat transfer results: (a) HTC versus quality for L3.7A0.5B65-65 and (b) HTC versus quality for L3.7A0.5B65-25. Dryout occurred for the data to the right of the dotted line and are therefore unreliable. 96 xi Figure 6.10: Two-phase heat transfer data compared to the most quoted prediction methods from the literature: (a) Donowski and Kandlikar [61], (b) Han et al. [34], (c) Hsieh and Lin [62], (d) Amalfi et al. [50,51]. 98 Figure 6.11: Local time averaged HTC distribution in a single cell for L5.7A1.0B60- 60 at G = 100 kg m-2 s-1, the white squares shows the location of the contact point and the white arrow in (a) the flow direction, quality and heat flux are listed in the upper right corner 101 Figure 6.12: Local time averaged HTC distribution in a single cell for L5.7A1.0B60- 30 at G = 100 kg m-2 s-1, the white squares shows the location of the contact point and the white arrow in (a) the flow direction, quality and heat flux are listed in the upper right corner. 103 Figure 6.13: Local time averaged HTC distribution in a single cell for L3.7A0.5B65- 65 at G = 100 kg m-2 s-1, the white squares shows the location of the contact point and the white arrow in (a) the flow direction, quality and heat flux are listed in the upper right corner. 104 Figure 6.14: Local time averaged HTC distribution in a single cell for L3.7A0.5B65- 25 at G = 100 kg m-2 s-1, the white squares shows the location of the contact point and the white arrow in (a) the flow direction, quality and heat flux are listed in the upper right corner. 105 Figure 6.15: Local temperature distribution in a single cell for L3.7A0.5B65-65 at G = 50 kg m-2 s-1, the white squares shows the location of the contact point and the white arrow in (a) the flow direction, quality and heat flux are listed in the upper right corner. 107 Figure 6.16: Average two-phase heat transfer results vs frictional pressure drop data: (a) L5.7A1.0B60-60, (b) L5.7A1.0B60-30, (c) L3.7A0.5B65-65, and (d) L3.7A0.5B65-25. 108 Figure 6.17: Average two-phase heat transfer results vs frictional pressure drop gradient for all data points 109 xii Figure 8.1: Schematics of the test configuration for determining the thermal conductivity of the electrically conductive layer in the 200RS100 film. 115 Figure 8.2: Comparison of the numerical and measured film temperature distributions at a voltage of 1 V using a thermal contact resistance of 10-3 m2 K W-1 and a thermal conductivity of 7 W m-1K-1. 116 Figure 8.3: Infrared image of the razor blade edge placed in front of a heated black body (right) and the temperature profile across the edge (left) 118 Figure 8.4: Schematic representation of the forced boundary condition in the form of a step function 119 Figure 8.5: Steady state heat spreading within the multilayer 120 Figure 8.6: Calculated temperature profile along the CaF2-adhesive interface and the interpolated temperature profile using the temperature measurements of the virtual dots that are 3 mm spaced apart. 120 Figure 8.7: Transmission @ 3.0 um through an uncoated polished 0.5 mm thick sample, data provided by Lattice [64] 122 Figure 8.8: Schematic of the test section (a). Silicon plates covered with transparent polyimide film (a) and black polyimide film (b) along with the test section (c), where the mechanical electrical contact is shown. 123 Figure 8.9: Raw temperature output of the IR-camera during pool boiling within the PHE geometry, Left: Silicon plate with transparent polyimide film, right: silicon with black polyimide film. 124 Figure 8.10: Ray tracing of the L5.7A1.0B60-60 geometry, with the starting point located between trough and crest, showing the initial light cone and the first refraction 126 Figure 8.11: Qualitative intensity distribution along the wave pattern of a uniform heated silicon plate, when measured with an IR-camera, with the initial intensity being unity. 126 xiii Figure 8.12: Ray tracing of the altered geometry so at least one ray of the initial light cone will exit the flat side of the silicon plate perpendicular, when the starting point is located between the trough and crest. 127 Figure 8.13: Continuation of the ray tracing from Figure 8.12 adding 1st (top), 2nd reflection (center) rays and 2nd refracted rays (bottom). 128 Figure 8.14: Qualitative intensity distribution along the wave pattern of a uniform heated CaF2 plate, when measured with an IR-camera, with the initial intensity being unity. 129 Figure 8.15: Black polyimide tape with gold sputtered layer while being attached on the corrugated plate (a), non-uniformity of the gold layer becomes visible after detaching the tape from the plate (b) 131 Figure 8.16: Black polyimide tape with gold sputtered layer while being attached to a flat surface (a), non-uniformity heating of the gold layer due to the small radii of the corrugations seen by the IR-camera during heating (b) 132 xiv List of Tables Table 4.1: Geometric characteristics of chevron plates tested in the present study 39 Table 4.2: Properties of HFE7100 44 Table 4.3: Physical properties of the transparent/translucent materials 48 Table 4.4: Uncertainties of the instruments used in this study 63 Table 5.1: Single phase pressure drop and heat transfer correlations appropriate for the current geometry. 66 Table 6.1: Summary of the prediction methods for two-phase pressure drops including experimental test conditions 91 Table 6.2: Summary of the prediction methods for two-phase heat transfer including experimental test conditions 99 xv Nomenclature A abbreviation for the plate corrugation a amplitude of the corrugation [m] B abbreviation for the chevron angle Bo Boiling Number, 𝐵𝑜 = 𝑞″ 𝐺𝐻𝑙𝑣 Bd Bond number, 𝐵𝑑 = 𝑔𝜌𝑙𝑑ℎ 2 𝜎 b corrugation pressing depth [m] Ci specific constants or functions cp specific Heat [J kg -1 K-1] d diameter [m] f Fanning friction factor, 𝑓 = 𝑑𝑃 𝑑𝑧 𝜌𝑑𝑒 2𝐺2 F correction factor G mass Flux [kg m-2s-1] g gravitational constant, g = 9.81 [m s-2] H specific enthalpy [J kg-1] h heat transfer coefficient [W m2K-1] i current supplied to the heater [A] k thermal conductivity [W m-1K-1] L abbreviation for corrugation pitch LH length of the section with constant heat generation [m] Nu Nusselt Number, Nu = h dh/k ?̇? mass rate [kg s-1] n number of data points n index of refraction p specific constants to calculate Nu and f P pressure [Pa] Pr Prandtl Number, 𝑃𝑟 = 𝑐𝑝𝜇/𝑘 𝑞″ heat flux ?̇? heat [J s-1] xvi 𝑞″ heat flux generated by the heater [W m-2] ?̇? volumetric heat generation by the heater [W m-3] r reflectance R function for uncertainty analysis 𝑅ℎ𝑒𝑎𝑡𝑒𝑟,Ω/□ Sheet resistance of the heater [Ω m/m] Re Reynolds number, Re = G dh/μ U Liquid velocity [m s-1] T Temperature t Wall thickness [m] W Width We Weber number, 𝑊𝑒 = 𝜌𝑣2𝑑ℎ 𝜎 v flow velocity [m s-1] ?̇? Volumetric flow rate [m3 s-1] x quality 𝑋𝑡𝑡 Lockhart-Martinelli parameter X, Y, Z Coordinates Greek 𝛼 angle between bulk fluid motion and corrugation pattern 𝛽 corrugation angle [°] 𝛾 corrugation aspect ratio 𝛾 = 𝑏/𝜆  emissivity Θ angle of incident 𝜆 Wavelength of the corrugation [m] 𝜇 Dynamic viscosity [kg m-1 s-2] 𝜇𝑤 Dynamic viscosity at the wall [kg m -1s-2] 𝜈 Kinematic viscosity [m2 s-1] 𝜑 Area enhancement factor Φ place holder for unknown function 𝜌 Density [kg m-3] 𝜎 surface tension [kg s-2] xvii ϒ Array of values for MAE Subscripts a acceleration C Carbon filled polyimide cb convective boiling e equivalent exp experimental G Glue gen generation H constant heat generation i running variable l liquid lo liquid only lv liquid to vapor m mean meas measured nb nucleate boiling o outlet pool pool boling pre predicted P Polyimide S Surface sat saturation tot total tp two-phase v vapor Acronyms BD black dot CaF2 calcium Fluoride CNT carbon nano tubes HTC heat transfer coefficient xviii IR infra-red MAE mean absolute error PHE plate heat exchanger TC thermocouple 1 1. Introduction Plate heat exchangers (PHE) as shown in Figure 1.1, are widely used in many applications (food, oil, chemical and paper industries, HVAC, heat recovery, refrigeration, etc.) because they are smaller and lighter, have lower pressure drops, and require less structural support than tube and shell heat exchangers. Furthermore, by allowing the easy removal or addition of plates to the PHE, it is easy to clean the assembly and provide flexibility for different heat load configurations. Figure 1.1: Schematics of a typical PHE (http://www.dairyprocessinghandbook.com/chapter/heat-exchangers) The increased heat transfer performance of PHEs is primarily due to the very large surface area per unit volume that facilitates the heat transfer between the two 2 fluids. The plate design, which usually consists of sinusoidal corrugations arranged in chevron patterns with opposite pitch angles within a plate pair, also contributes to the high heat transfer efficacy through mixing and agitation of the fluid. To further improve the performance of a PHE, it is possible to operate the PHE in a two phase regime. Two phase flow has the ability to transfer large amounts of energy away from a heated surface, due to the change in phase of the fluid. The penalty for the increase in heat transfer is a higher pressure drop due to the rapid acceleration of the vapor phase, which needs to be compensated though an increase in pumping power. However, given a constant pumping power the heat transfer achieved with two- phase cooling is, in almost all cases, higher than the single phase alternative. A considerable amount of experimental and numerical research has been performed to develop correlations from which the overall heat transfer and pressure drop can be predicted for specified plate geometries and fluids with reasonable accuracy. However, very little information is available regarding local measurements of heat transfer. Local measurements can serve as benchmarks for numerical models and can provide insight into heat transfer mechanisms which can lead to improved PHE designs. This work focuses on developing a new technique using infra-red (IR) thermography to measure local heat transfer distributions within typical PHE geometries operated as evaporators. Quasi local pressure drop measurements and two phase flow visualization are also performed to give a complete picture of the heat transferring process. This thesis is divided into seven chapters. Chapter 2 gives a brief introduction to the operation and properties of a PHE as well as fundamentals in heat transfer for single and two-phase flow. Chapter 3 provides an extensive literature 3 review on single and two-phase cooling of a heated PHE wall. Chapter 4 focuses on the experimental aspects of this work. The experimental technique of measuring the local heat transfer and the data reduction is described in detail followed by the uncertainty analysis of all measurements. In Chapter 5 the new technique is evaluated by comparing the measured heat transfer and pressure drop values for single phase flow, to correlations from previous publications. Local heat transfer data will be presented and analyzed. In the Chapter 6 an overview of two-phase results will be given followed with a conclusion and proposed future work. 4 2. Fundamentals This section covers all the knowledge necessary to fully understand PHE and the heat transfer within the PHE. First the characteristics of the PHE geometry are explained with the commonly used nomenclature. Afterwards a brief introduction to single and two-phase heat transfer is given. 2.1 Geometry PHEs consist of thin, rectangular, pressed sheet metal plates that are sandwiched between full peripheral gaskets and clamped together in a frame or welded/brazed, such that the hot and cold fluid streams alternate through the inter-plate passages. The plates are stamped with corrugated patterns that not only provide larger effective heat transfer surface area but also modify the flow field, thereby promoting a significantly enhanced thermal-hydraulic performance. The corrugations also help to improve the rigidity of the stack. Among a variety of surface corrugation patterns that are commercially available for the PHEs, the sinusoidal chevron corrugation geometry or a variation known as a herringbone or zig-zag pattern is the most popular used in diverse applications due to its ease of manufacturing, reduction in fouling and thermal- hydraulic performance (Figure 2.1). 5 Figure 2.1: Showcase of the different PHE designs To increase mixing within the channel that is formed by the two sinusoidal plates, a corrugation angle was added to the plates. This forces the liquid to move in a zig-zag pattern rather than moving along the wave. The corrugation angle is measured in most scientific literature as shown in Figure 2.2. However in some engineering field work the corrugation angle is measured by its complimentary angle as shown in Figure 2.2. The steeper the corrugation angle the more turbulent mixing occurs within the channel and thus the thermal performance increases. The laminar-turbulent transition in a typical PHE channel is lower than in a comparable tube flow. The penalty for this, however, is a higher pressure drop. To change the corrugation angle, it is possible to have two plates with different corrugations pressing against each other. The resulting corrugation angle for both plates is the average of both angles. In general, PHEs with a β >45 are defined as hard plates and for β <45 as soft plates. 6 Figure 2.2: Corrugation features of a typical chevron plate: In order to rate and compare the performance of PHEs, several non-dimensional parameters were introduced, which are the plate corrugation aspect ratio 𝛾, and the enlargement factor 𝜑 a are given by Equation 2.1 and 2.2 respectively: 𝛾 = 4𝑎 Λ 2.1 𝜑 = 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝐴𝑟𝑒𝑎 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝐴𝑟𝑒𝑎 = ∫ √1 + ( 𝛾𝜋 2 ) 2 cos ( 2𝜋 Λ 𝑥) 2 𝑑𝑥 Λ 0 Λ 2.2 7 Where 𝑎 and Λ are the respective amplitude and wavelength (pitch) of a sinusoidal surface corrugation as show in Figure 2.2. For characterizing flow and heat transfer parameter such as Reynolds number, friction factor and Nusselt number, a hydraulic diameter (𝑑ℎ) is introduced: 𝑑ℎ = 4𝑎 𝜑 = 2𝑏 𝜑 2.3 With the help of Equations 2.1-2.3 any sinusoidal PHE characteristic can be fully explained. The nomenclature used in this paper to characterize the corrugation patterns is shown in Figure 2.3. The wavelength and amplitude of the corrugation are indicated by L and A respectively. The chevron angle B is followed by two numbers since PHEs can be arranged in a mixed configuration resulting in an overall angle which is the average of both plates, e.g., mixing a 60° and 30° plate would result in a 45° arrangement. As an example of the nomenclature, the PHE L3.7A0.5B65-65 would have a corrugation wavelength of 3.7 mm, an amplitude of 0.5 mm, and two plates both having chevron angles of 65°. Figure 2.3: Nomenclature to characterize a PHE geometry 8 2.2 Single Phase Flow 2.2.1 Heat transfer When a fluid moves across a solid or liquid surface of different temperature, a convective heat transfer occurs. The convective heat transfer describes the energy transport through the collective movement of molecules from one place to another, in contrast to heat conduction which is based on the energy transport between molecules. Heat transfer through convection and conduction happens when a fluid flows over a wall. Depending on the physical properties of the wall and the fluid, one heat transfer mechanism will dominate the other. The temperature and velocity profile of the moving fluid are strongly coupled and thus influence each other. The definition of the convection coefficient according to Newton’s law of cooling is: ℎ = 𝑞″𝑤𝑎𝑙𝑙 𝑇𝑤𝑎𝑙𝑙 − 𝑇𝐹𝑙𝑢𝑖𝑑 2.4 This law indicates that the heat transfer between the fluid and the wall is linearly dependent on the heat transfer coefficient. Due to the nature of the fluid’s boundary layer which is closest to the wall, the velocity of the fluid approaches zero at the fluid-wall interface. This region is known as the viscous sublayer. Thermal conduction is the dominating heat transfer mechanism in this layer. Consequently, convective heat transfer depends on conduction over the temperature profile in the viscous sublayer and the temperature gradient near the surface determines the convection coefficient. With conduction in the stagnant fluid near the wall and 𝑘𝐹𝑙𝑢𝑖𝑑 the thermal conductivity of the fluid, the heat flux is 9 q″𝑤𝑎𝑙𝑙 = −𝑘𝐹𝑙𝑢𝑖𝑑 ( 𝛿(𝑇 − 𝑇𝑤𝑎𝑙𝑙) 𝛿𝑦 ) 𝑤𝑎𝑙𝑙 2.5 Substituting Equation 2.5 into 2.4 will result in the following expression: ℎ = 𝑘𝑤𝑎𝑙𝑙 ( 𝛿(𝑇𝑤𝑎𝑙𝑙 − 𝑇) 𝛿𝑦 ) 𝑤𝑎𝑙𝑙 𝑇𝑤𝑎𝑙𝑙 − 𝑇𝐹𝑙𝑢𝑖𝑑 2.6 The ratio of 𝑘/ℎ is an illustrative estimation of the thermal boundary layer thickness. Furthermore, when taking the inverse of the mentioned ratio and multiplying it with a characteristic length (e.g. the equivalent diameter of a channel flow) one would get the dimensionless Nusselt number which is used to describe the ratio between convective and conductive heat transfer: 𝑁𝑢 = ℎ𝑑𝑒𝑞 𝑘 2.7 The Nusselt number is commonly used to compare heat transfer performance within single phase cooled channels. Single-phase heat transfer correlations have been proposed by several investigators. Most correlations for PHE are similar to the Dittus Boelter equation that is used to calculate Nu in turbulent pipe flow: 𝑁𝑢 = 𝐶1 𝑅𝑒 𝐶2𝑃𝑟𝐶3 With 𝑃𝑟 = 𝑐𝑝𝜇/𝑘 being the Prandtl number which gives a ratio of momentum diffusivity to the thermal diffusivity of a liquid, and adjustable constants Ci 2.2.2 Pressure drop During convective cooling an energy source is required to keep the liquid in motion, which in most cases is done by a pump. The energy consumed by the pump depends 10 heavily on the frictional losses between the fluid and the wall and viscous losses if the fluid is turbulent. These losses can be described as a pressure drop Δ𝑃, since the static pressure in the flow will continuously decrease downstream of the pump. The goal of the PHE geometry is to create a turbulent flow which is more desirable for high heat transfer rate, due to the strong mixing within the turbulent boundary layer. Calculating pressure losses during turbulent flow cannot be done analytically. However it is known that in fully developed turbulent flow, the pressure drop in a horizontal constant-area pipe depends on pipe diameter 𝑑, pipe length 𝐿, pipe roughness 𝑒, average flow velocity ?̅?, fluid density 𝜌, and fluid viscosity 𝜇. In functional form this can be written as: Δ𝑃 = 𝑓(𝑑, 𝐿, 𝑒, ?̅?, 𝜌, 𝜇) 2.8 Through dimensional analysis Equation 2.11 can be rewritten as a non-dimensional pressure drop: Δ𝑃 𝜌?̅?2 = 𝑓 ( 𝜇 𝜌?̅?𝑑 , 𝐿 𝑑 , 𝑒 𝑑 ) 2.9 Experiments have shown that the non-dimensional pressure drop is directly proportional to the term 𝐿 𝑑 . In addition we introduce the dimensionless Reynolds number as 𝑅𝑒 = 𝜇/(𝜌?̅?𝑑) and the number 1 2 into the denominator of the left side, so it becomes the ratio of the pressure drop to the kinetic energy per unit mass of flow: Δ𝑃 𝜌?̅?2 = 𝐿 𝑑 Φ (𝑅𝑒, 𝑒 𝑑 ) 2.10 We can now define the unknown function 𝛷(𝑅𝑒, 𝑒/𝑑) as the friction factor 𝑓 which can be determined experimentally. In general it can be said that convective cooling 11 application are desired to have a high HTC while keeping the friction factor low, by means of optimizing geometry and flow parameters. 2.3 Fundamentals in Flow Boiling During condensation and evaporation processes in channels, the liquid and the vapor take up a variety of configurations known as flow patterns. Flow patterns for circular tubes have been extensively studied, and similarities to flow patterns in PHE have been observed. Therefore, this section will give a brief introduction of flow patterns within circular tubes. Figure 2.4 shows a vertical heated tube with liquid passing through the tube from the bottom to the top. In the beginning of the tube (Section A) the heat is only transported throughout the diameter of the tube through convective heat transfer. After a certain entrance length the temperature of the fluid that is in direct contact with the heated wall is so high that small bubbles begin forming on the surface although the average bulk temperature of the liquid is below saturation temperature, which is referred to as subcooled boiling (Section B). 12 Figure 2.4: Vertical heated tube exhibiting sequential stages of two-phase flow boiling from the bottom to the top (image reproduced with permission from Collier and Thome [1]) Once bubbles begin to form, a new metric (other than just temperature), is required to fully define the state of the system. A useful variable for this purpose is the thermodynamic mass quality (𝑥) of the fluid. The thermodynamic mass quality of the fluid at a given distance, z, from the beginning of the tube is given by : 𝑥 = 𝐻(𝑧) − 𝐻𝑠𝑎𝑡 Δ𝐻𝑣𝑎𝑝 2.11 13 where H(z) is the enthalpy of the layer of fluid at distance z, Hsat is the enthalpy of the fluid at the saturation temperature, and ∆Hlv is the change in enthalpy required for vaporization of the liquid. Negative values of 𝑥 give a measure of how far the enthalpy of the liquid is from the saturation point. For 𝑥 = 0 the liquid is exactly at saturation. When 𝑥 is a small positive quantity (0 < 𝑥𝑚 < 1) the quality gives an approximate ratio between the amount of vapor in the system to the total volume. For values greater than one the vapor is oversaturated. The transition between regions B and C, from the subcooled nucleate boiling region to the saturated nucleate boiling region, can be clearly defined thermodynamically although the transition may not be visually so obvious. This is the point at which the liquid reaches the saturation temperature (thermodynamic equilibrium quality, 𝑥 = 0). Due to the continued presence of vapor bubbles from the subcooled boiling region, there is a requirement that some of the liquid must be subcooled to ensure that the liquid bulk enthalpy equals that of saturated liquid. This effect is due to the temperature gradient inherent in any cross-section of the tube. The subcooled liquid flowing in the center of the channel will only reach the saturation temperature at some distance downstream of the point 𝑥 = 0, where the liquid bulk enthalpy will be greater than that of saturated liquid. In the regions C to G the thermodynamic mass quality of the fluid can be employed as a description of how much of the volume is occupied by vapor. As the quality increases in the saturated nucleate boiling region a point may be reached, where transition in the heat transfer mechanism occurs. This transition is preceded by a change in the flow pattern from bubbly or slug flow to annular flow (regions E and F). This transition signals the change over from the 14 process of boiling to the process of evaporation. In the boiling regime bubble nucleation was the vector for heat transfer. The transition is made to the evaporation regime due to the thinning layer of liquid film coating the inside surface of the tube. As the thickness of the liquid film on the heating surface is such that the effective thermal conductivity is sufficient to prevent the liquid in contact with the wall from being superheated, bubble nucleation is no longer possible. Thus, heat is carried away from the wall by forced convection in the liquid film to the interface between liquid and vapor in the core of the tube where evaporation can take place. Since nucleation may be completely suppressed, the heat transfer process may no longer be called boiling. The region beyond the transition has been referred to as the two-phase forced convective region of heat transfer (Regions E and F). The next major transition step in the flowing liquid occurs at some determinable value of the thermodynamic mass quality where the liquid film coating the inside of the tube is heated enough to have completely evaporated. This particular critical heat flux (CHF) is known as “dryout”. Subsequent to dryout the wall temperature for a channel with controlled surface heat flux will begin to rise. Eventually, with continued heat flux, all transported droplets in this vapor column will also evaporate, which is known as the saturated vapor region as seen in Region H of the tube. The region between dryout and complete elimination of droplet flow is known as the liquid- deficient region as shown in Region G. This is where post-CHF heat transfer occurs. The dryout transition often limits the amount of evaporation which should be allowed to occur for a channel at a particular heat flux. 15 Understanding the fundamental knowledge of liquid evaporation in a smooth tube is necessary as it forms a basis for understanding almost all correlations for PHE evaporators. Most of the correlation in the literature for flow boiling in tubes can be summarized by the general equation first proposed by Chen [2] and improved by Steiner and Taborek [3]: ℎ = (ℎ𝑛𝑏 ′ 𝐶1 + ℎ𝑐𝑏 ′ 𝐶2) 1 𝐶3 = ((ℎ𝑛𝑏𝐹𝑛𝑏) 𝐶4 + (ℎ𝑐𝑏𝐹𝑐𝑏) 𝐶5)𝐶6 2.12 The model assumes that the local flow boiling heat transfer coefficient can be obtained by summing the nucleate boiling heat transfer coefficient (ℎ𝑛𝑏 ′ ) and the forced convection heat transfer coefficient (ℎ𝑐𝑏 ′ ). 𝐹𝑛𝑏 is the correction factor for the nucleate boiling which accounts for the partial or total suppression of nucleate boiling sites in two-phase flows and 𝐹𝑐𝑏 is the correction factor for convective boiling which accounts the enhancement of convection in a two-phase flow due to the higher velocity of the two-phase flow with respect to the liquid only flow. For a PHE this formula is used by adding new empirical constants or by modifying the correction factors. Some literature uses a two-phase Nusselt number with the characteristic length being the equivalent diameter as defined in Equation 2.3. To quantify the pressure drop during two-phase flow a similar approach as for single phase flow can be performed. However during two-phase flow applications several pressure components are added to the frictional pressure drop due to the gaseous face in the fluid. This will be discussed in detail in the data reduction section 4.4.4 16 3. State of the Art Literature review Summaries of the extensive work-to-date into PHEs have been provided by Ayub [4], Manglik et al. [5] and Abu-Khader [6]. A review of recent PHE publications most pertinent to the current study (i.e., those that involve changes in geometry, local measurements, IR techniques or flow visualization) is provided below. 3.1 Single Phase flow 3.1.1 Averaged HTC and frictional factor measurements Okada et al. [7] was one of the first research group that extensively analyzed the effect of geometrical properties of a corrugated PHE on heat transfer and pressure drop. They used water as testing fluid in a Reynolds number range of 400 to 15000. Six plates were manufactured in total. Four of them had identical wave pattern (L10A2.8BXX/XX) and only changed in corrugation angle: 30°, 45°, 60° and 75°. Three of the plates had identical corrugation angle (60°) and changed in wavelength: 8 mm, 10 mm, 15 mm and amplitude: 2.6 mm, 2.8 mm, 3.2 mm respectively. They measured that the HTC and the frictional pressure drop increases exponentially with increasing Reynolds number. HTC clearly increased with increasing corrugation angle. The rate of increase for all angles remained approximately constant by a factor of approximately 2. The pressure drop behaved similarly, with the exception that the pressure drop increased by a factor of 4 when increasing the angle from 45° to 60°, whereas the other angle changes produced lower factors (30° to 45°: increase by a factor of 2; 60° to 75°: increase by a factor of 1.4). When changing the wave length of the corrugation the HTC remained 17 nearly constant, however for the pressure drop a clear decrease was observed when increasing the wavelength from 10 mm to 15 mm by a factor of nearly 2. Heavner [8] made friction factor and HTC measurements on an industrial PHE using water as the working fluid. Three plates with identical corrugation geometry and different corrugation angle were used to create 5 chevron-angle combinations: 45°/90°, 23°/90°, 45°/45°, 45°/23°, and 23°/23°. No information of the corrugation amplitude and wavelength were given in their paper, nor how they reduced their pressure data, since the pressure was measured before and after the PHE. They found that the friction factor decreases exponentially with increasing Reynolds number. The friction factor decreased with decreasing corrugation angle. When reducing the corrugation angle from 67.5° (45°/90°) to 45° (45°/45°) the friction factor decreased by a factor of 3, a further decrease to 23° reduced the friction factor by a factor of 2. For the HTC a similar relation was observed, however the ratio of decreasing HTC with decreasing corrugation angle was lower, for example the difference between the HTC for the hardest plate and softest plate was a factor of 3. Focke et al. [9] used a PHE with the corrugation wavelength of 10 mm, an amplitude of 2.5 mm (L10A2.5BXX/XX) and corrugation angles of 0°, 30°, 45°, 60°, 72°, 80°, and 90°. They saw that the pressure drop increases with an increasing corrugation angle up to 60° with an increasing rate, after that angle the rate of increase decreased until reaching the pressure drop maximum at 80°. At 90° they observed a local minimum with similar values as the 60° plate. For heat transfer a similar trend was observed, as the global maximum accrued at an angle of 80°, and a local minimum at 90°. They concluded that an increasing corrugation angle (0°-80°) at constant 18 Reynolds number increases the pressure drop over 2.5 orders of magnitude, whereas the HTC only increases by a factor of 4-10. Flow visualizations showed that at an angle of 45° the fluid moves along the furrows and gets reflected into the furrow of the opposite side when reaching the edge of the plate. For 60° and 72° plates no flow visualization were available but they expected a similar flow pattern. Crossing streams induce secondary swirling motions in the flow along the furrows since the opposite furrow has liquid that moves in a direction perpendicular to the flow. When increasing the corrugation angle theses streams have a retarding effect on each other due to the velocity components being in the opposite directions. This was confirmed by a flow visualization of a 80° plate which showed a zig-zag pattern since the reflections occurred between contacts points. Muley and Manglik [10] used two plates (L9.0A1.25B30, L9.0A1.25B60) to create two symmetric and one mixed PHE. They used water as working fluid and were able to measure pressure and overall HTC in a range of 6000.1 ms) and low air velocities a continuous liquid phase pervades the channel area. At an intermediate up to high superficial air and water flow velocities, they observed a mixture of both regimes or slug flow. The heat transfer coefficient was calculated to be higher with injected air than without it, which is especially true for low superficial water velocities. Hsieh et al. [26] used a L10A1.5B60-60 PHE with an acrylic plate to visualize two-phase flow of R-134a. With an increase in heat flux at a given mass flux, larger bubbles formed before departing the surface. When the heat flux was constant and the mass flux changed, the bubble size was noticeably affected. Small, individual bubbles were observed at high subcooling, whereas bubbles would coalesce and move vigorously at lower subcooling. The visualization of air/water two-phase flow was studied by Asano et al. [27] for a commercial PHE. These plates were opaque in the visible light spectrum so visualization was performed using thermal neutron radiography. The liquid and air distributions were found for one channel and also a multichannel PHE from which a distribution of phases was derived. Two-phase flow was introduced into the PHE, 28 where the gaseous phase occupied the center of the channel while the liquid phase occupied the sides. Nilpueng and Wongwises [28] used a similar visualization technique as Vlasogiannis et al. [25], by removing the end plate of a commercial PHE and replacing it with an identical plate made out of transparent polyurethane. They used a non- symmetrical plate with chevron angles of 55∘ and 10∘. By switching the flow direction they were able to see different flow patterns that were based on the inlet quality and gravity effect. For the vertical upward flow, bubble recirculation flow and bubbly flow were observed, whereas for the vertical downward flow slug flow, annular-liquid bridge/air-alone flow were observed. Annular-liquid bridge flow which describes a thin water film that is present over the whole plate surface while the air flows between the water films, was observed in both cases. All of the above mentioned analysis of flow patterns is based on the experimental results of adiabatic gas and liquid mixture. Certainly, the fluid may experience significantly different flow patterns if either condensation or evaporation is involved. 3.2.2 Two-Phase heat transfer and pressure drop measurement Danilova et al. [29] was one of the first researchers to investigate heat transfer in PHE geometries during evaporation. R12, R22, R113 and ammonia were used as working fluids. His group measured that the HTC increased almost linearly with an increase in quality. A correlation of a two-phase Nusselt number was established, that included the Bond number, which takes into account gravitational and surface tension force. 29 Engelhorn and Reinhart [30] tested R22 in an industrial PHE. They observed when elevating heat flux and mass flux, that the heat transfer increased. On the other hand, heat transfer decreased with increasing evaporation temperature. In addition, they analyzed the effect of flow distribution and found out that the maldistribution of two- phase flow can significantly decrease the heat transfer. Tribbe and Müller-Steinhagen [31] also investigated the effect of the corrugation angle and quality on the frictional pressure drop. They were able to insert small syringe needles, with an OD of 1.2 mm through the rubber gasket, and thus measuring the pressure drop inside the PHE. The frictional pressure drop increased linearly with an increase of flow quality for all PHE tested. When changing the corrugation angle the pressure within the PHE changed significantly. When changing the angle from a 60°/60° to a 60°/30° configuration, the frictional two-phase pressure drop decreased by a factor of roughly 7.5. When further decreasing the angle from 60°/30° to 30°/30° the pressure drop decreased by a factor of approximately 2. During all tests the inlet and outlet distribution systems remained the same, as did the pressure drop over them. Therefore it became evident that the inlet and outlet distribution pressure drop has a much higher effect on the overall pressure drop for lower corrugation PHE angles. Kumar [32] was one of the first who observed a decrease in heat transfer after reaching a certain quality (𝑥 = 0.7). R22 and ammonia were used in his experiments. Thonon et al. [11] gave a review of available two-phase research in PHE at that time. They were able to divide the two-phase flow into two categories, namely: nucleate boiling dominated and convective boiling dominated and provided correlations for both 30 of them. The criteria for categorizing the flow was a function of the boiling number (𝐵𝑜) and the Lockhart-Martinelli parameter (𝑋𝑡𝑡). Margat et al. [33] investigated the evaporation of R134 in a PHE in a mass flux range of 35 𝑘𝑔 𝑚−2𝑠−1 ≤ 𝐺 ≤ 120 𝑘𝑔 𝑚−2𝑠−1 with a 60∘ corrugation angle and 2 mm corrugation height and an unknown wavelength. Void fraction measurement were conducted in the PHE by using a specially adapted quick closing valve technique before and after the PHE. After the valves were closed the remaining liquid in the PHE was drained in a bottle and was then weighed. They measured that the volumetric void fraction is affected by velocity and that conventional models underestimated their values. For pressure and heat transfer measurement, they saw that both are governed by mass flux and quality but not heat flux, which provided the conclusion that the main heat transfer mechanism in PHE is convective boiling (as opposed to nucleate boiling, which in general is dependent on heat flux). As previously mentioned Ayub [4] provided an extensive summary of research carried out for single and two-phase flow in PHEs. In addition, he proposed a correlation for the evaporation of ammonia. His correlations includes parameters such as the Reynolds number, liquid thermal conductivity, and geometrical parameters like corrugation angle and overall length of the PHE channel. Han et al. [34] used 3 different PHE geometries L4.9A1.1B70-70, L5.2A1.1B55-55, L7.0A1.1B45-45. A broad range of qualities (0.15 < 𝑥 < 0.9) were tested for the liquids R410a and R22 in a mass flux range of 13 𝑘𝑔 𝑚−2𝑠−1 ≤ 𝐺 ≤ 34 𝑘𝑔 𝑚−2𝑠−1. They noted that with increasing corrugation angle the heat transfer increased but only for higher qualities. For the two-phase pressure drop they saw that 31 the effect of changing the chevron angle became more evident at higher qualities. Varying the mass flux showed a significant effect on the HTC. Whereas changes in quality affected the HTC noticeably, only for the 70° plate. Heat flux affected the overall HTC slightly only at low qualities and low mass fluxes, due to the abrupt changes of flow path and strong turbulences within the PHE which suppresses nucleate boiling heat transfer. Correlations including equivalent Reynolds number, boiling number and geometrical parameters have been developed from the experimental data. Park and Kim [35] investigated the evaporation heat transfer and pressure drop characteristics of R-134a in an oblong shell and PHE in a mass flux range of 40 𝑘𝑔 𝑚−2𝑠−1 ≤ 𝐺 ≤ 80 𝑘𝑔 𝑚−2𝑠−1. The heat exchanger consisted of four oval shaped L9.0A1.4B45 plates that only had 2 ports, which were all lined up to create three parallel channels for the refrigerant. The plates were installed in a shell through which hot water was pumped, creating four vertical counter flow channels. They measured HTC and frictional pressure drop while changing quality, heat flux, system pressure, and mass flux. The data showed that HTC and frictional pressure drop are heavily dependent on mass flux and quality, whereas heat flux had almost no effect. At high qualities the saturation temperature of the fluid had a noticeable effect on the mean HTC and frictional pressure drop, when changing Tsat from 0 to 10°C an HTC increase of 20% was observed. This was attributed to the lower specific volume of the working fluid vapor at higher saturation temperatures, which decreases the vapor velocity and therefore decreases the shear forces to the liquid film on the heat transfer surface, and the smaller latent heat of vaporization at higher saturation temperatures. They also compared their results with standard PHE from the literature and found that the oblique 32 shell PHE produce higher evaporation heat transfer and higher pressure drops although the rise in heat transfer was more pronounced than that of the pressure drop. Palm and Claesson [36] used a variety of plates with different geometries to analyze single and two-phase flow heat transfer using R134a and R22. They observed that the HTC is mainly dependent on the heat flux and less on the mass flux. Six different chevron angles ranging from 53° to 65° were analyzed to determine which angle produces the highest HTC. Their tests showed that all evaluated chevron angles produced similar HTC when varying the heat flux, however there was a modest increase at the angle of 61°. These results did not include any pressure measurement data, making it impossible to judge the performance of a PHE which includes HTC and pressure drop. A variety of different flow distributors were tested, showing that flow distribution plays a significant role for the overall HTC due to the homogeneous fluid distribution. In addition, they tried to fit their data to established pool boiling correlations. The final result was a modified correlation by Cooper [37]. Sterner and Sunden [38] tested five different PHE geometries with ammonia as the working fluid. The geometries were very similar, since the first three PHEs only differ in wavelength and only the last plate had a different corrugation angle (60∘ as opposed to 54∘). A noticeable difference in performance between the first three PHEs was measured. The PHE with the shortest wavelength outperformed the other two. They also analyzed the effect of inlet flow distribution and observed that when adding a flow distributor the heat transfer will always increase, however the pressure loss was significant which led to the conclusion that flow distributors can be removed if pumping power is limited. 33 Djordjevic and Kabelac [39] used an array of thermocouples in two PHEs (L12A1.6B63-63 and L12A1.6B27-27) to measure quasi local heat transfer in a PHE during the evaporation of R134a and ammonia. The length of the PHE was 0.8 m, meaning that they could calculate the local quality and correlate the heat transfer to that quality value. They observed as many other groups that the HTC is independent of the heat flux, but heavily depends on the vapor quality. They also concluded that the HTC rises for high mass flux but decreases for lower mass fluxes at a vapor quality of (𝑥 = 0.5). When analyzing the effect on chevron angle on the overall HTC they observed that the low chevron angle produced a higher HTC during the evaporation of ammonia. They concluded that low chevron angles are more favorable for evaporation in PHEs especially for higher qualities (x>0.7), where strong deflections are not as effective and potentially cause local dry outs. Finally, they compared their data to previous correlations, and they found that a modified Steiner and Taborek [3] and Danilova et al. [29] model fits their data the best. Táboas et al. [40] studied boiling heat transfer in a L9.6A1.0B60-60 PHE with an ammonia/water mixture as working fluid and a mass flux range of 50 𝑘𝑔 𝑚−2𝑠−1 ≤ 𝐺 ≤ 140 𝑘𝑔 𝑚−2𝑠−1. At higher mass fluxes (𝐺 ≥ 100 𝑘𝑔 𝑚−2𝑠−1) they saw an increase in HTC with increasing quality, whereas at lower mass fluxes (𝐺 ≤ 70 𝑘𝑔 𝑚−2𝑠−1) HTC decreased with increasing quality. Heat flux affected the HTC only in the low quality region where the HTC slightly increased. Convective boiling HTC normally increases and nucleate boiling HTC decreases with decreasing system pressure, due to the changes in vapor density. When increasing the system pressure from 7 bar to 15 bar, however, no changes in HTC were detected. On the other hand, 34 the frictional pressure drop was reduced with an increasing system pressure, since the vapor density is higher and therefore has a lower velocity. They concluded that the main parameter that influences the HTC and the frictional pressure drop is the mass flux. Later they analyzed their data in depth and compared it to other data and correlations in Táboas et al. [41]. The group was only able to test low flow qualities (𝑥 < 0.2) for which they recommended a slightly modified Chisholm [42] correlation to fit their data. Huang et al. [43] used the refrigerants R134a, R507A, in an industrial PHE evaporator with a mass flux range of 6 𝑘𝑔 𝑚−2𝑠−1 ≤ 𝐺 ≤ 31 𝑘𝑔 𝑚−2𝑠−1. With two similar plate patterns, where the only difference was the corrugation angle, they created three different channels by using each plate pattern separately and combining the two different patterns (L8.1A1.0B28-28, L8.1A1.0B28-60, L8.1A1.0B60-60). All three PHE showed similar results for two-phase HTC. They concluded that the heat transfer mechanism is nucleate boiling dominated and therefore is strongly dependent on heat flux and less dependent on quality, mass flux and chevron angle. The frictional pressure drop however showed a strong dependence on mass flux, quality and chevron angle. A linear increase of the frictional pressure drop was observed with kinetic energy per unit volume. The pressure was measured before the inlet and after the outlet of the PHE, meaning that the inlet and outlet pressure losses had to be estimated using Shah and Focke [44]. Finally, they used statistical regression to come up with a correlation for a two-phase Nusselt number including non-dimensional groups, based on saturation temperature, thermal diffusivity and surface tension of the fluid. 35 Recently Khan et al. [45]–[49] gained a lot of data for the evaporation of ammonia in plate heat exchangers. A wide spectrum of plate geometries were tested with a goal to come up with empirical correlations for a two-phase Nusselt number and fanning friction factor. In Khan et al. [48] the group looked at heat transfer and pressure drop characteristics of one PHE with three different corrugation angles using ammonia as the working fluid. They showed that the overall HTC depends less on the chevron angle than the frictional pressure drop. It was also observed that the HTC depends strongly on saturation temperature and less on quality and heat flux. Furthermore, the group was very focused on industrial applications, which is why in the most recent study (Khan et al. [49]) they were the first to include miscible oil in the flow and compare it to flow without oil. They found that the oil concentration had a significant effect on the heat transfer of ammonia and friction factor. Amalfi et al. [41, 42] provided a comprehensive literature survey of flow boiling heat transfer and two-phase frictional pressure drops mechanisms within chevron PHEs. In this study, the prediction methods available in the open literature from 1981 until 2014 were detailed and a consolidated experimental database from 13 research studies were culled that included 3601 data points. The authors carried out a sensitivity analysis to investigate the effect of plate geometrical parameters on the thermal and hydraulic performance, and an extensive statistical comparison of all available two-phase prediction methods against the above mentioned databank was also furnished. Using dimensional analysis coupled with the multi-regression technique, new methods for predicting local HTC and local frictional pressure gradient within 36 plate heat exchangers were developed and shown to work better than the available methods. Recently, Vakili-Farahani et al. [43 - 44] examined the local heat transfer and pressure drop within a PHE channel (L3.7A0.5B65-65, port-to-port length of 228 mm) created by two plates that were electrically heated. The fluid was R245fa. The plates were pressed together by two PVC plates to stabilize and insulate the test section. Six windows along the length of the PHE were machined into the PVC plates allowing the outer surface temperature (and thus the local HTC) to be measured with an IR-camera. Through adiabatic two-phase flow tests, the authors were able to measure the saturation temperature of the refrigerant and thereby calculate the quasi local pressure for each window. They concluded that the two-phase behavior in PHEs is similar to pipe flow, and the flow distributions at the PHE inlet and outlet have a significant effect on the overall thermal and hydraulic performance. In another recent publication, Lee et al. [54] used water as a working fluid in a L10A1.3B60-60 PHE evaporator at low mass fluxes (14.5 ≤ 𝐺 ≤ 33.6 𝑘𝑔 𝑚−2𝑠−1). Quality values of (0.15 < 𝑥 < 0.9) where achieved by heating the plates with an electrically heated copper block. They also observed that with an increase in quality the HTC decreased due to the partial dry-out of the liquid film. They compared their data with correlation from the literature and concluded that the correlations either over or under predict the experimental data. Therefore, the group developed a new correlation to fit the data. 37 3.3 Conclusion and motivation There has been much research conducted on PHE evaporators. However, no group has analyzed the local heat transfer distribution and local pressure drop data in a PHE during evaporation at different quality levels. Also, most of the developed correlations are highly dependent on the apparatus that they were gained from. In almost all cases, researchers included inlet and outlet fluid distribution in their measurements and calculation for HTC and friction factor. There are a variety of distribution systems available and chances are small that two research groups used the same system. The pressure drop over the distributors can be significant, especially for soft PHE plates. The pressure drop in two-phase systems governs the saturation temperature of a fluid, therefore potentially falsifying the energy balance that is solved in order to calculate overall HTC. One group was able to measure the pressure drop within the PHE but was not able to measure HTC. Other groups were able to measure local HTC for single phase flow but did not include any pressure drop measurement. This thesis presents results of truly local pressure drop and HTC measurements for four PHE geometries for single and two-phase flow. The performance of each PHE can be analyzed by comparing the overall HTC and the pressure drop with each other. In addition, high spatial resolution HTC measurements of a unit cell within a PHE coupled with adiabatic flow visualization will be presented. Measurement of the local HTC distribution within the heat exchanger in conjunction with flow visualization allows researchers to gain insight into the mechanisms by which heat is transferred during boiling in compact heat exchangers– 38 this will greatly facilitate the development of new, innovative, higher performance designs based on a solid understanding of the underlying physics. Local measurements can serve as benchmarks for numerical models and can provide insight into heat transfer mechanisms, which can lead to improved PHE designs. The ability to measure local HTC for various plate geometries will lead to correlations that will be more universal. 39 4. Experimental Technique This section will describe in detail the experimental setup, which includes test section and flow apparatus. The heating method and temperature acquisition method are explained next. The chapter will close with the uncertainty analysis. 4.1 Experimental Setup 4.1.1 Test Section Representative PHE geometries L5.7A1.0B60 and L3.7A0.5B65 (Figure 4.1) were machined into CaF2 plates using a CNC mill. Since CaF2 is expensive, brittle, hard to machine, and since the surface temperature measurement was only required on one plate, it was decided to fabricate the opposing plate using polycarbonate. In addition two polycarbonate plates where machined with different corrugation angle to create a mixed plate configuration with a L5.7A1.0B60-30 and L3.7A0.5B65-25 geometry. The L5.7A1.0B60-60 geometry is similar to commonly used PHE evaporators, whereas the L3.7A0.5B65-65 geometry is a novel configuration that minimizes refrigerant charge, is more compact, and tries to gain higher performances by decreasing the pressing depth and corrugation wavelength. A summary of important geometrical parameters of all the plates tested in this study is shown in Table 4.1. Plate LP [mm] WP [mm] 𝜆 [mm] a [mm] 𝛽 [°] 𝜑 [-] Area [cm2] L5.7A1.0B60 99 50 5.7 1 60 1.25 62 L5.7A1.0B30 99 50 5.7 1 30 1.25 62 L3.7A0.5B65 99 50 3.7 0.5 65 1.16 57 L3.7A0.5B25 99 50 3.7 0.5 25 1.16 57 Table 4.1: Geometric characteristics of chevron plates tested in the present study 40 (a) (b) Figure 4.1: Schematic of the two plate geometries that were machined into CaF2 and the location of the thermocouples in their polycarbonate counter plate: (a) test section L5.7A1.0B60-60, (b) test section L3.7A0.5B65-65 A polycarbonate and CaF2 plate, both with film heaters attached, were pressed together in the test section whose cross section is shown in Figure 4.3. To prevent the two heater films from shorting at the contact points, small pieces (~ 2x2 mm) of Scotch MagicTM tape (60 m) were attached to the heated film on the polycarbonate plate at each contact point (Figure 4.2). Two T-type thermocouples were used to measure the inlet and outlet temperatures, and five T-type thermocouples were inserted into the flow. These five thermocouples were equally spaced apart along the plate (19.8 mm spaced apart, see 41 Figure 4.1 and Figure 4.2). They were fixed by drilling 0.6 mm holes into the polycarbonate plate and epoxying the wires so the tip would extend two times the amplitude into the channel created by the two plates. Figure 4.2: L5.7A1.0B60 polycarbonate plate with attached heater, silver busses, electrical insulating tape at the contact points, and TCs to measure bulk fluid temperature. In addition five pressure taps (1 mm diameter holes spaced 19.8 mm apart, on the same height as the thermocouple) drilled into the side wall of the test section (Figure 4.4) were used to measure the pressure drop along the test section. Another two pressure taps where located upstream of the inlet and downstream of the outlet. To measure the pressure difference between the taps, a system of valves was used to connect the furthermost upstream tap in the PHE and any of the other taps to a single differential pressure transducer (Validyne DP15, 0-22000 Pa). Since the fluid enters and exits the test section perpendicular to the channel created by the two plates through a single inlet in the center, two 3D printed flow distributors were added between the inlet and outlet 42 of the channel to minimize flow maldistribution. The flow distributors were designed to continue the current PHE geometry. In addition, the flow distributors were used to hold the electrodes that connect to the silver leads painted on the film heater as well as hold thermocouples that were used to measure the channel inlet and outlet temperatures. Figure 4.3: Experimental setup: cross section view of the test section, including the inlet and outlet flow distributors, pressure taps and valve system to measure absolute and differential pressure. 43 4.1.2 Experimental Apparatus A schematic of the flow loop is shown in Figure 4.4. The working fluid in the primary flow loop was HFE7100 (see Table 4.2 for a summary of the properties). The fluid was chosen based on its boiling point (61°C @ 1 bar) which is ideal for the current setup since it is high enough to reduce ambient noise during IR measurements and low enough to avoid damaging heat sensitive components in the test section. It is a nontoxic fluid and is representative of other refrigerants. The fluid was pumped through a coil preheater to create the desired inlet condition for the test section. The coil heater was electrically powered by two generic 12 VDC/80 A computer power supplies combined with a solid state relay controlled using a PC through pulse-width modulation at 2 Hz. The fluid exiting the test section entered a counterflow concentric tube heat exchanger cooled by a secondary water loop. A membrane accumulator (Hydac SBO210-0.75 E1) was used to keep the pressure in the main loop at 1 atm. Liquid degassing was performed by pumping the liquid past a polyolefin membrane (Radial Flow SuperPhobicTM) and using a vacuum pump to remove gas from the liquid. Two flow meter (Omega FLR 1000, 400-5000 ml/min and 0-500 ml/min), a pressure transducer (Omega PX309-030AV, 0-1 bar) and twelve T-type thermocouples were installed in the apparatus to measure the flow conditions at various locations within the loop. Two USB based National InstrumentsTM systems were used for data acquisition (NI 9213 for all T-type thermocouples and NI 6211 for all other analog voltage measurements and preheater control). 44 @25°C @50°C @61°C @65°C @70°C Liquid density [kg m-3] 1513 1443 1414 1400 1386 Vapor density [kg m-3] 2.902 6.965 9.581 11.16 12.94 Thermal conductivity [W m-1 K-1] 6.9x10-2 6.4x10-2 6.2x10-2 6.1x10-2 6.0x10-2 Kinematic Viscosity [m2 s-1] 3.7x10-7 2.8x10-7 2.5x10-7 2.4x10-7 2.3x10-7 Specific Heat of liquid [J kg-1K-1] 1183 1233 1255 1263 1273 Evaporation enthalpy [J kg-1] 1.23x10-5 1.15x10-5 1.11x10-5 1.1x10-5 1.08x10-5 Pr [-] 9.70 7.88 7.57 7.56 7.55 Table 4.2: Properties of HFE7100 Figure 4.4: Schematic of flow loop. 4.2 Heater Setup The principle by which the local heat transfer distribution was measured in this study is described below. A thin, flexible film heater (Dupont 200RS100) consisting of a 45 polyimide layer containing electrically conductive carbon (the resistance of the film was measured to be 100 /☐) bound to an electrically insulating polyimide layer, was used as the heating element. Since the carbon is dispersed throughout the polyimide layer, the heating was uniform and resistant to damage and cracking, unlike metallic or Indium Tin Oxide (ITO) films (see Section 8.3.2). The carbon also made this layer opaque and of high emissivity (>0.94). The thickness of the two layers were measured using an SEM (Figure 4.5). Figure 4.5 SEM image of Dupont 200RS100 cross section identifying the conducting (tC) and non-conducting layers (tP) and their thicknesses. The film was potted into an epoxy carrier and polished before viewing. The average values and the standard deviation about these averages are noted. The film heater was attached to an IR transparent CaF2 plate (Alkor Technologies) using a UV curing optical glue (Norland Optical Adhesive 61). Since the film is relatively stiff and would not stay in the trough of the corrugation without the application of force, a device was needed to hold the film in place while the adhesive could harden. The device is depicted in Figure 4.6 and consists of individual rods with the same radius as the radius of the corrugation at the trough. The rods were pushed into the through trough individual aluminum bars, so that the film would constantly be pressed against the plate. A window was machined into the baseplate of the device to 46 allow UV-radiation to shine though the CaF2 plate and harden the adhesive. Using that device it was possible to create a uniform layer of adhesive without entrapping any air bubbles for most of the surface and not cracking the brittle substrate. (a) (b) Figure 4.6: Device used to create a uniform layer of adhesive between the CaF2 substrate and the 100RS200 film, without entrapping air bubbles and not fracturing the CaF2, cross section view of the CAD model (a) and assembled device (b) Electrical connections to the edges of the heater were made using silver loaded paint (SPI #5001-AB). The contact resistance between the paint and the heater was measured using a 4-wire method to be <0.25% of the overall heater resistance. 47 To measure the heat flux conducted into the substrate, the temperature distribution on top of the CaF2 substrate must be known. Opaque, square dots 1x1 mm 2 were attached to the CaF2 at select locations so this temperature could be measured. The size of the dots was large enough to ensure the camera pixel reading at the center of any dot was not influenced by the slit response function (SRF) of the camera as explained in Vollmer and Moellmann [55]. To determine the center-to-center spacing between adjacent dots, a 2-D numerical heat conduction simulation was carried out to simulate the amount of heat spreading within the polyimide film and the optical glue. A step function in temperature was used as the boundary condition on the carbon heater film and the temperature profile along the optical glue-CaF2 interface was computed. The spacing between the dots (3 mm in our case), was chosen such that the temperature profile between the dots could be accurately reconstructed using spline interpolation (see Section 8.2.2 for a more detailed explanation). To produce the dot pattern, a negative mask made of polyimide tape was prepared using a laser cutter and attached to the CaF2 plate. A solution containing Carbon nano tubes (CNT) dispersed within DMSO was obtained from International Technology Center, Raleigh and spray coated onto the masked surface–details of the CNT solution and the deposition procedure are described in Gokhale et al. [56]. To ensure the dots were opaque, chromium was deposited onto the CNT layer. Chromium has excellent adhesion when applied through vapor deposition and requires a relative thin layer in order to become fully opaque. The polyimide mask was then removed leaving the dots on the CaF2 surface. The final thickness of the dots was measured to be less than 2μm. Figure 4.7 shows the schematic of the final multilayer. 48 Figure 4.7: Schematic of test wall construction. Properties of the materials used in the wall construction are summarized in Table 4.3. The thermal conductivity of the electrically conductive layer was measured to be >5 W/m-K using the technique described in Section 8.1. Table 4.3: Physical properties of the transparent/translucent materials 4.3 Infrared Thermography Infrared thermometry is an established technology whereby the measurement of infrared wavelength energy emission combined with knowledge of the surface emissivity of a substance can be used to determine its temperature. A major advantage Layer k [W m-2K-1] ρ [kg m-3] Abs. coefficient [m-1] Index of Refraction [-] cp [J kg-1K-1] CaF2 12 3180 3.5x10-4 1.41 854 Polyimide Film 0.12 1420 7110 1.7 1090 Optical glue 0.17 1231 4200 1.527 - 49 of this temperature measuring technique is its non-invasive nature; therefore the flow would not have to be disturbed by any mechanical means. An overview of IR thermography in heat transfer research within the last decades is given by Astarita et al. [57]. IR imaging done with scientific grade cameras can yield reasonable frame rates although the local measurement accuracy may only be as good as 2 °C due to factors such as noise and uncertainty. However, when a pixel-by-pixel calibration is carried out the accuracy can be greatly improved to around 0.2 °C. The calibration procedure for all experiments was carried out in a standardized fashion. The camera was rigidly mounted to the same structure as the test section. This will not allow any relative movements between the camera and the CaF2 plate, thus every pixel will have the same field of view of the test section during the experiments. Liquid with constant temperature is then pumped through the test section without powering the heater film. The camera records 100 frames and takes the average temperature value for each pixel. The quasi local temperature along the PHE channel, which is interpolated using the 7 thermocouples in the test section, is then used to calibrate each pixel of the camera. Using this technique it is possible to account for non-unity emissivity values and multiple reflections from the surroundings and from within the CaF2 layer itself. Figure 4.8a shows the calibration curve from 3 randomly selected points across the plate. As expected the raw temperature from the IR-camera is lower than the temperature measured by the TCs due to the previously mentioned effects. 50 (a) (b) Figure 4.8: IR-camera calibration for three random pixels for (a) single phase measurements and (b) two-phase measurements. The calibration is limited to the point where the liquid reaches saturation temperature, whereas the temperature of the heated film is higher than that during evaporation. However, as can be seen by the linear behavior of the calibration curve of one pixel (Figure 4.8a), it can be assumed that the linearity will be preserved up to temperatures higher than saturation. To ensure that the linear assumption is correct a test was performed by increasing the pressure in the test loop which would raise the saturation temperature. This was done by pressurizing the open side of the accumulator. The IR-camera calibration was then carried out for higher temperatures and the linearity of the calibration remained, as can be seen in Figure 4.8b. A final validation of the calibration was done by visually inspecting the overall calibration as seen in Figure 4.9. 51 (a) (b) Figure 4.9: IR-temperature measurement of the heater surface during calibration: Before (a) and after calibration (b). 4.4 Data Reduction 4.4.1 General heat flux and HTC calculation The objective of this measurement technique is to enable the heat transfer coefficient distribution on the corrugated surface. The heat generated within the conducting film by applying a voltage across the silver electrodes. The heat generated per unit area within a rectangular area of the film with length LH and width WH is given by ?̇?𝑔𝑒𝑛 ″ = ?̇? 𝐿𝐻𝑊𝐻 = 𝑖2𝑅 ℎ𝑒𝑎𝑡𝑒𝑟, Ω □ ( 𝐿𝐻 𝑊𝐻 ) 𝐿𝐻𝑊𝐻 = 𝑖2𝑅 ℎ𝑒𝑎𝑡𝑒𝑟, Ω □ 𝑊𝐻 2 [ 𝑊 𝑚2 ] 4.1 where i=current through the film [A] and 𝑅 ℎ𝑒𝑎𝑡𝑒𝑟, Ω □ =resistance of a square section of the heater. The film that is attached to the corrugated CaF2 plate is not rectangular, 52 however, but of trapezoidal shape as shown in Figure 4.10. ComsolTM was used to simulate the current flow (and thus the local generation rate) within this trapezoidal shape (Figure 4.10). Heat is generated non-uniformly near the electrodes but a region of relatively uniform heat generation exists within the central portion of the film where Equation 4.1 is valid. The generation rate within the square area (WH=52.5mm, LH=50mm) shown in Figure 4.10 varies by up to 10%. Figure 4.10 Heat generation distribution within the heating film after 8ms of heating, when applied to the corrugated surface. To improve the uniformity of heating, the silver electrodes where extended in such a way that the heated area changed from trapezoidal into a rectangular shape. The silver had to be applied to the heating film after it was attached to the CaF2 substrate, since it is not trivial to predict the final position of the film during the gluing process. The 3D CAD model of the plate was used to determine the two triangles that need to be painted. 53 Masking tape was then applied on the corrugation to assure that the paint would not cover additional areas. The result was that the film was now uniformly heated as can be seen in Figure 4.11. Figure 4.11: Heater film shape required to cover a rectangular PHE plate along with silver bussbars shaped to provide uniform heat flux (top); the temperature distribution on the PHE surface measured by the IR camera during transient heating of the film to test the heater uniformity (ΔT is the temperature difference between the heated and unheated state after 8 ms of heating (bottom). One 600V 1.4A Sorenson power supply was used to power both heaters in series. When creating a mixed PHE arrangement with two plates that only differ in corrugation angle, the plate with the lower corrugation angle would have a lower resistance since the width of the heater film would be larger. To ensure that both plates receive equal amount of heat flux, a rheostat was connected to the CaF2 plate heater in 54 parallel. Since the heated surface area of both plates were approximately identical, the resistance of the rheostat was adjusted that the total heating power to each plate was the same. The resistance of the rheostat was calculated as followed: 𝑃𝐶𝑎𝐹2 = 𝑖𝐶𝑎𝐹2 2 𝑅𝐶𝑎𝐹2 = 𝑖𝑃𝑜𝑙𝑦 2 𝑅𝑝𝑜𝑙𝑦 = 𝑃𝑃𝑜𝑙𝑦 4.2 𝑖𝐶𝑎𝐹2 = 𝑅𝑅ℎ𝑒𝑜 𝑅𝐶𝑎𝐹2 + 𝑅𝑅ℎ𝑒𝑜 𝑖; 𝑖𝑃𝑜𝑙𝑦 = 𝑖 4.3 𝑅𝑅ℎ𝑒𝑜 = 𝑅𝐶𝑎𝐹2(𝑅𝑃𝑜𝑙𝑦 +√𝑅𝐶𝑎𝐹2𝑅𝑃𝑜𝑙𝑦) 𝑅𝐶𝑎𝐹2 − 𝑅𝑃𝑜𝑙𝑦 4.4 The heat generated could be removed by convection into the liquid or by substrate conduction. To estimate the heat lost into the substrate, the IR camera was used to measure the temperature of the black dots on the surface of the CaF2 substrate as well as the conducting film between the dots (Figure 4.7). The heat lost into the substrate can be estimated using: q𝑠𝑢𝑏 ″ = Tw − Tdot 𝑡𝑃 𝑘𝑃 + 𝑡𝐺 𝑘𝐺 4.5 The local thickness of the optical glue (tG) could vary, however, and was not known. An overestimate of the substrate conduction can be obtained by assuming the thickness of the optical glue is zero, i.e, all the measured temperature difference occurs across the polyimide. Even with this assumption, the substrate conduction losses were found to be no more than 1% of the input heat flux. The local heat transfer from the heater to the liquid was obtained by subtracting this small conduction loss from the heat generated: 55 ?̇?𝑓𝑙𝑢𝑖𝑑 ″ = ?̇?𝑔𝑒𝑛 ″ − ?̇?𝑠𝑢𝑏 ″ 4.6 The local heat transfer coefficient can be calculated using ℎ𝑓𝑙𝑢𝑖𝑑(𝑥, 𝑧) = ?̇?𝑓𝑙𝑢𝑖𝑑 ″ (𝑥, 𝑧) 𝑇𝑤(𝑥, 𝑧) − 𝑇𝑓𝑙𝑢𝑖𝑑 4.7 where Tfluid is the local temperature obtained by linearly interpolating the thermocouple readings between the inlet and outlet of the test section. The above analysis assumes the temperature within the electrically conducting film is uniform. The validity of this assumption can be shown using a simple conduction analysis. The conducting layer can be modeled as a plate with internal heat generation, an insulated boundary on one side (to approximate the conduction loss), and a specified temperature on the other (the temperature wall-fluid boundary). The maximum temperature difference within the film is given by Δ𝑇𝑚𝑎𝑥 = ?̇?‴𝑡𝐶 2 2𝑘𝐶 = ?̇?″𝑡𝐶 2𝑘𝐶 4.8 At the maximum heat flux used in the tests below ( =0.8 W/cm2), the maximum temperature difference within the film was calculated to be ~0.02 °C. The temperature variation within the conducting film was thus much smaller than the temperature difference between the film and fluid and could be neglected for all cases. 4.4.2 Eliminating film heater defects During the application of the 100RS200 film to the CaF2 substrate the entrapment of air bubbles was inevitable. These areas needed to be avoided, when taking the average HTC for the entire plate. In addition the black dots and reference markings on the plate 56 should not be included as well. The black dots will have approximately the same temperature as the heater during adiabatic operation when the heater temperature is uniform. However, during steady state heating the heater surface temperature is not uniform and therefore heat spreading occurred within the multilayer (for more details see Appendix 8.2.2). Since this works focus is on the steady state HTC, it was decided to not include the black dots in the data analysis. (a) (b) (c) Figure 4.12: Initial image from the IR-camera after 8 ms of heating (a), detection of pixels that are below a certain threshold (b), identifying areas and filling the gaps in each area (c). To identify the areas that were not included in the data analysis, a similar approach was used as in the previous section where the uniformity of the heat flux distribution of the heater was tested. Before each experimental campaign a step function in high heat flux was applied to the CaF2 plate while recording the heater with 57 an IR-camera at a high framerate (>100 Hz). After 8 ms of heating areas of non uniform heat flux, markings on the plate, entrapped air bubbles in the epoxy layer and black dots became clearly visible as shown in Figure 4.12a. A Matlab algorithm was used to detect the location of each pixel that was below a certain threshold (Figure 4.12b). The final step was to fill and increase each area that was detect by the previous step. 4.4.3 Data reduction for Single phase flow The Nusselt number within plate heat exchangers is usually defined as: 𝑁𝑢 = ℎ𝑓𝑙𝑢𝑖𝑑𝑑ℎ 𝑘𝑓𝑙𝑢𝑖𝑑 4.9 where 𝑑ℎ = 2𝑏/𝜑, and is a function of the Reynolds number, Prandtl number, and geometry factors. The Reynolds number is based on average flow velocity and a characteristic length: 𝑅𝑒 = 𝑈𝑑ℎ 𝜈 = ( ?̇? 𝐴)𝑑ℎ 𝜈 4.10 where 𝐴 is the cross sectional area perpendicular to the flow direction. The range of Reynolds numbers in the present study was between 300 and 3500. The Prandtl number for single phase flow was 7.8 and was assumed to be constant throughout the test section since the bulk fluid temperature only varied by about 3°C. The pressure drop is presented in terms of a Fanning friction factor: 𝑓 = 𝑑𝑃 𝑑𝑧 𝜌𝑑ℎ 2𝐺2 4.11 58 4.4.4 Data reduction for two-phase flow Since all measurements are conducted under the steady state assumption, the calculation of HTC for the two-phase flow is identical to the single-phase regime. The liquid velocity however is commonly defined by the mass flux 𝐺 𝐺 = ?̇?𝜌 𝐴 [ 𝑘𝑔 𝑚2𝑠 ] 4.12 The dimensions of the PHE in this study are small compared to a standard PHE plate. Plates constructed from CaF2 are comparatively costly and difficult to machine, necessitating a scaled down version of the PHE. Typically PHE are up to 10 times larger than our setup allows, therefore they have a much wider range of quality values within the channel during evaporation. This is visualized by the color pattern in Figure 4.13. It can be seen that the experimental plate would only be able to produce a much smaller quality range. However, by changing the inlet conditions of the test channel, it is possible to reproduce separately each section of a full PHE. Integrating over each subsection will give then the performance of a full plate heat exchanger, with the given geometrical parameters. Although the used PHE is relatively small, the change in quality along the channel can be significant. To calculate the local quality during evaporation in the channel, it is necessary to include the change in pressure in the channel. Saturation temperature and liquid/vapor enthalpy are dependent on pressure which could change up to 20 kPa over the PHE. 59 Figure 4.13: Visualization of change in quality along a PHE channel. The quasi local liquid temperature gained from the seven thermocouples indicates the saturation temperature at any point in the channel, since the flow enters the test section at saturation. This means it is possible to write the energy balance across a small channel element only as a function of saturation temperature as is shown in Figure 4.14. Figure 4.14: Energy Balance across a channel section, to calculate the change in quality Writing out the energy balance and solving the equality for 𝑥(𝑧 + Δ𝑧) will result in the following equation: 60                 , , , , , 1 Δ Δ Δ Δ l sat v sat l sat v sat l sat Q x z H z x z H z H z z m x z z z z H zH z                 4.13 Since the local temperature and pressure were known from the five thermocouples and five pressure taps along the PHE, the local values of the liquid and vapor enthalpy Hl,sat and Hv,sat could be determined. A marching procedure was then used to calculate the local quality along the test section. Before entering the test section, the liquid was heated in the preheater to achieve the desired quality at the inlet of the test section. The total power input to the preheater was calculated from the following overall energy balance:  p sat i o lvQ mc T T x Hm   4.14 where cp was evaluated at the average of the preheater inlet and saturation temperature at the outlet of the preheater, and Hlv was computed at the preheater outlet condition. As described earlier, the pressure data were obtained using an absolute pressure transducer to measure the saturation pressure close to the inlet of the PHE. A differential pressure transducer combined with four valves were used to measure the pressure drop along the PHE at four locations. The total pressure drop measured by the differential pressure transducer within the PHE was the sum of three components: , ,Δ Δ Δ Δtot meas g meas f aP P P P   4.15 The measured gravitational pressure drop accounted for the pressure due to the liquid head included in the differential transducer measurement: 61  ,Δ g meas l P P mP gD gD    4.16 which was reduced to ,Δ ( )g meas P m lP D g    4.17 where DP was the distance between two pressure taps and ρm was the mean two-phase density within the PHE defined by the homogeneous model as 1 1 m v l x x            4.18 This distance DP has to be accounted for since the tubes leading to the differential pressure transducer are completely filled with liquid and have a density that is different from the two-phase mixture in the PHE channel. The pressure drop due to the acceleration during evaporation was estimated according to 2 1 1Δ  Δa v l P G x          4.19 The frictional pressure drop ΔPf was computed from the above set of equations which allowed for the calculation of the actual pressure drop in the PHE Δ Δ Δ Δtot g f aP P P P   4.20 where ΔPg represented the gravitational pressure drop within the PHE and was defined as: Δ  g p mP D g 4.21 62 The acceleration pressure drop was of the order of 0.01% of the total pressure drop and could be neglected. Hence, the pressure drop can be assumed to be linear within the PHE channel since the frictional pressure gradient was fairly constant over the short PHE length. The four differential pressure transducer measurements were used to create a linear fit to the experimental data, and the slope of the linear fit was used to determine the pressure drop. The uncertainty of the pressure drop was based on the goodness of the linear fit and is discussed in the last section of this chapter. 4.5 Uncertainty analysis and preliminary validation The uncertainties and ranges of the instruments used in this work are listed in Table 4.4. The overall uncertainty (with 95% confidence) for the friction factor, Nu, Re and HTC were computed using the error-propagation formula of Taylor (1982): 𝜎𝑅 = [( 𝛿𝑅 𝛿𝑣1 𝛿𝜎1) 2 + ( 𝛿𝑅 𝛿𝑣2 𝛿𝜎2) 2 +⋯( 𝛿𝑅 𝛿𝑣𝑛 𝛿𝜎𝑛) 2 ] 0.5 4.22 Where 𝜎𝑅 is the overall uncertainty of the value 𝑅 which is a function of the variable 𝑣1 to 𝑣𝑛 having each an uncertainty of 𝜎1 to 𝜎𝑛 respectively. As mentioned before the error for the pressure drop within the test section was calculated based of the goodness of the linear fit of 5 pressure measurements within the PHE. The linear fit of the pressure distribution inside the PHE would give the following equation: 𝑃(𝑧) = 𝑏𝑧 + 𝑎 4.23 where 𝑏 = 𝑑𝑃 𝑑𝑧 . The uncertainty of 𝑏 is defined by: 63 𝜎𝑏 = 𝜎𝑃√ 𝑁 Δ 4.24 where 𝑁 is the number of data points and 𝜎𝑃 is defined as: 𝜎𝑃 = √ 1 𝑁 − 2 ∑(𝑃𝑖 − 𝑎 − 𝑏𝑧𝑖)2 𝑁 𝑖=1 4.25 with Δ = 𝑁∑𝑧2 − (∑𝑧)2 4.26 In addition the error-propagation are shown by the error bars on the figures. The average uncertainty of the local heat transfer coefficient was calculated to be ±12% and are shown by the error bars on the plots. Model Range (𝑣1…𝑣𝑛) Uncertainty (𝜎1…𝜎𝑛) Flowmeter Omega FLR 1000 400-5000 ml/min ±50ml/min Flowmeter Omega FLR 1000 0-500 ml/min ±5ml/min Pressure transducer Omega PX309- 030AV 0-200000 Pa ±500 Pa Differential Pressure Transducer Validyne DP15 0-22000 Pa ±220 Pa Thermocouple T-type -200-350°C ±0.2°C IR-Camera FLIR5600 30-80°C ±0.2°C Table 4.4: Uncertainties of the instruments used in this study An overall energy balance between the energy input to the heaters and the sensible heating of the liquid (measured using the 7 thermocouples, flow meter, and fluid properties) was carried out. Figure 4.15 shows the results of the energy balanced measured for forty experiments with different combinations of mass rate and heat fluxes. The energy balanced was calculated the following way: 64 ?̇?ℎ𝑒𝑎𝑡𝑒𝑟 = 2𝐴ℎ𝑒𝑎𝑡𝑒𝑟𝑞″ 4.27 ?̇?𝑙𝑖𝑞𝑢𝑖𝑑 = ?̇?𝑐𝑝Δ𝑇 4.28 ?̇?ℎ𝑒𝑎𝑡𝑒𝑟 − ?̇?𝑙𝑖𝑞𝑢𝑖𝑑 ?̇?ℎ𝑒𝑎𝑡𝑒𝑟 = Δ?̇? 4.29 That means if Δ?̇? > 0 heat is lost to the surroundings and values for Δ?̇? < 0 are due to the measurement uncertainty. On average, the balanced agreed to within ±11% or better for all flow rates. Figure 4.15: Result of the energy balance calculation for several experiments with different flow parameters and heat fluxes. To test if the calibration was still valid during an experimental campaign, periodic adiabatic measurements between heated runs were recorded, where the 65 calculated temperature of the heater surface needed to match the temperature of the fluid measured by the TCs. This data was analyzed in real time, so potential adjustments in the calibrations could be performed before taking more data. Figure 4.16 shows the output of the real time data reduction during an adiabatic test run. If the temperature deviation between the heater and the fluid was above the uncertainty, the calibration had to be repeated. (a) (b) Figure 4.16: Temperature difference between heater and fluid during adiabatic two- phase operation, (a) Temperature map of the entire PHE plate, (b) over the width averaged heater temperature vs. fluid temperature interpolated using the 5 TCs that are placed in the flow channel. 66 5. Single Phase flow results The measured pressure drop and heat transfer data were compared with the relatively recent pressure drop and heat transfer correlations listed in Table 5.1. These correlations were selected since the geometry and parameter range upon which they were based were similar with the current study. Table 5.1: Single phase pressure drop and heat transfer correlations appropriate for the current geometry. 5.1 Pressure Drop The pressure drop along the test section for various Re is shown on Figure 5.1. This data was obtained by sampling the differential pressure transducer at 500 Hz for 5 s, which was enough for the sampling uncertainty to become negligible compared with other uncertainties. The linear fits to the data (solid lines) intercept the ordinate at Reference 𝛽° 𝜑 𝐷𝑒 [𝑚𝑚] Re Pr (Fluid) Correlation Thonon et al. [11] 15, 30, 45, 60 50 -15000 Nu = 𝐶(𝛽)Re𝑚(𝛽)Pr𝑛 𝑓 = 𝐸(𝛽)Re𝑝2(𝛽) Muley and Manglik [10] 30, 45, 60, 75 1.29 5.08 600- 10000 2.0-6.0 (Water) Nu = 𝐶(𝛽)𝐷(𝛽)Re𝑝1(𝛽) Pr0.33 𝑓 = 𝐸(𝛽)𝐹(𝜑)Re𝑝2(𝛽) Talik et al. [58] 60 1.22 4.65 1450- 11460 2.5-5.0 (Water) Nu = 0.248Re0.7 𝑓 = 0.3323Re−0.042 Okada et al. [7] 30-75 700- 25000 (Water) Nu = 𝐶1Re C2 Pr0.4 Heavner [8] 0-67 400- 10000 3.3-5.9 (Water) Nu = 𝐶1(𝜑) 1−𝑚Re𝑚 Pr0.5 𝑓 = 𝐶2(𝜑) 𝑝+1Re−𝑝 Focke et al. [9] 0-90 1.46 10 90 -50000 (Distille d Water) Nu = 𝐶1Re 𝑚 Pr0.5 𝑓 = 𝐶2Re 𝑝 Kumar [59] 30, 40, 45, 60 1.17 >100 (Water) Nu = 𝐶1Re 𝑚 Pr0.33(𝜇/𝜇𝑤) 0.17 𝑓 = 𝐶2Re 𝑝 Present Study 60, 45 65, 45 1.25 1.17 4 2 300 -3500 7.8 (HFE 7100) 67 mostly positive values, likely due to higher pressure losses in the entry region. It is seen that the pressure drop is linear beyond the first downstream pressure tap, however, indicating a hydrodynamically fully developed flow. Figure 5.1: Pressure drop along the L5.7A1.0B60-60 PHE at various Re. Pressure drop is measured between the furthermost upstream tap (z=0 mm) and a downstream tap (z=20 mm, 40 mm, 60 mm, or 80 mm). 5.1.1 Single Phase friction factor measurements Comparison of the friction factor measured using the pressure data, with the correlations in Table 5.1 are shown in Figure 5.2 and Figure 5.3. As can be seen from Table 5.1 most correlations depend only on Reynolds number, some include the corrugation angle 𝛽. In most cases each equation gives a different constant for each common angle. For the L3.7A0.5B65-65 geometry the constants were chosen that correspond to a 60° angle since that is the closest angle for a standard PHE. The only 68 equations that incorporate all geometrical factors is the ones from Muley and Manglik [10]. Figure 5.2a shows the friction factor for the L5.7A1.0B60-60 and L5.7A1.0B60-30 geometry. The data are bracketed by the proposed correlations, but agree best with Kumar [59]. The L5.7A1.0B60-60 data follows the downward trend of the friction factor with increasing Reynolds number as was predicted by Muley and Manglik [10] Focke et al. [9] and Kumar [59]. (a) (b) Figure 5.2: Comparison of friction factor correlations from other studies with the results of the (a) L5.7A1.0B60-60 and (b) L3.7A1.0B60-30, values that are within the red circle need to be ignored since the measurement uncertainty was too high for these low Reynolds numbers. Figure 5.2b shows the frictional pressure drop of the L5.7A1.0B60-30 PHE. The frictional pressure drop decreased by nearly a factor of magnitude when compared with the L5.7A1.0B60-60 PHE. Therefore, the pressure drop at low Reynolds numbers was too small to be reliably measured by the differential pressure transducer. Friction factor values that were measured below a Reynolds number of Re=2000 must be ignored since the overall pressure drop over the entire PHE was lower than the uncertainty of the 69 pressure transducer. The values in question are circled in Figure 5.2b. However, for Reynolds number above 2000 a clear trend could be detected. The data agrees very well with the prediction method proposed by Talik et al. [58]. The correlations that were able to follow the trend for the L5.7A1.0B60-60 plate were not able to do the same for the L5.7A1.0B60-30 plate even though the correlations were dependent on the corrugation angle. This is likely due to the fact that most researchers measured the pressure drop over the inlet and outlet distributor, which becomes more significant for softer plates. Figure 5.3 shows the pressure drop for the L3.7A0.5B65-65. The effect of the small change in chevron angle β of 5° (from 60° to 65°) has less influence on the hydraulic performance, therefore with the exception of Muley and Manglik [10] the correlations are the same as for the L5.7A1.0B60-60 plate. As seen before, the correlations are able to bracket the data, but fail to have a good agreement for both tested corrugation angles. The data agrees best with the correlation of Muley and Manglik [10] for both cases. The downward trend of the friction factor for both geometries was predicted well by the correlations. 70 (a) (b) Figure 5.3: Comparison of experimental friction factor of the L3.7A0.5B65-65 data with other studies. Figure 5.4 shows the friction factor for all geometries in one plot. Muley and Manglik [10] included the dependence on the surface enlargement factor φ. Their correlation suggested that L5.7A1.0B60-60 and L5.7A1.0B60-30 (with φ=1.25) would have a higher friction factor than L3.7A0.5B65-65 and L3.7A0.5B65-25 (with φ=1.17), which is qualitatively consistent and clearly visible with the observed trends for the hard plates. Similar results were also observed by Okada et al. [7] who observed a pressure drop decrease with increasing corrugation wavelength and amplitude. When changing the corrugation from L10A2.3B60-60 to L15A3.4B60-60 the pressure drop decreased by a factor of 2. 71 Figure 5.4: Comparison of experimental friction factor for all tested geometries. For the two soft plates the effect of enlargement factor is less prominent. This could be due to the shift in flow direction when using a mixed plate arrangement. When two identical PHE plates are used the corrugation pattern runs parallel with the bulk fluid direction, however if one plate has a different corrugation angle the corrugation pattern is shifted by an angle 𝛼 which is defined as followed: 𝛼 = |𝛽𝑃𝑙𝑎𝑡𝑒1 − 𝛽𝑃𝑙𝑎𝑡𝑒2| 2 5.1 Therefore, the L5.7A1.0B60-30 and L3.7A0.5B65-25 have a shift angle of 15° and 20° respectively, which could produce a higher pressure drop for the L3.7A0.5B65-25 plate. In the industry where, in general, larger plates are used, it is assumed that this effect is negligible, however for our experiments only a small PHE was implemented which resulted in uneven mixing that will be later shown during HTC measurement. The non-uniform heat flux distribution was more pronounced on the L3.7A0.5B65-25 and is an indicator for higher pressure drop due to uneven liquid distribution. Further 72 tests on how a mixed plate configuration compares to a pure one are needed, and have not been carried out yet by other researchers. 5.1.2 The effect of Inlet/Outlet port and herringbone pattern The pressure loss over inlet/outlet flow distributor within the PHE test section along the pressure drop over the entire PHE is plotted in Figure 5.5, for L5.7A1.0B60-30 PHE and L3.7A0.5B65-65 PHE. As can be seen, the port pressure drop plays a significant role in the overall pressure drop, especially with low corrugation angle plates. The elevated pressure drop at the outlet compared to the pressure drop at the inlet is due to the fact that different fittings were used at the inlet and outlet of the test section. In addition the predicted pressure drop over the port is plotted which is defined by Shah and Focke [44] as: Δ𝑃𝑝𝑜𝑟𝑡 = 1.5( 𝜌𝑙𝑣 2 2 ) 5.2 The data shows that the predicted port pressure drop highly under predicts the measured data. Flow distributors can easily take up 30% of the total length of the PHE, yet in most cases they are neglected in the data reduction, allowing for significant errors in friction factor and Nu measurement. 73 (a) (b) Figure 5.5: Pressure drop over the inlet and outlet compared with the frictional pressure drop within the (a) L5.7A1.0B60-30 PHE and (b) L3.7A0.5B65-65 PHE. Another source of inconsistencies between data sets, is the arrangement of the corrugated pattern. The corrugated pattern is usually stamped into the PHE plate as a herringbone pattern (as can be seen in Figure 2.1), since the manufacturing process becomes easier and fouling can be reduced. In our application we decided against the herringbone pattern and chose an oblique washboard pattern, since it was easier to machine into the CaF2 substrate and it made the attachment of the film heater significantly easier. In addition, it is well known that the herringbone configuration contributes little to none to the local heat transfer of a PHE cell that is located away from the herringbone center. Most correlations were established from experiments using plates with herringbone patterns. To investigate the effect of the pattern structure on pressure drop, a herringbone pattern was machined into two polycarbonate plates and adiabatic pressure measurements were taken. The results are listed in Figure 5.6. 74 Figure 5.6: Single-phase pressure drop for the oblique washboard geometry and herringbone pattern at different Reynolds number for the L3.7A0.5B65-65 PHE. The frictional pressure drop of the herringbone pattern is (up to 25%) higher compared to the oblique washboard pattern. The V-shape of the herringbone pattern, interrupts more frequently the viscous boundary layer at the center of the plate due to the abrupt transition from the minimum to the maximum plate spacing, which can be observed in Figure 5.7. Additionally, the local cross and swirl flows around crest and furrows at the center of the plate in turn produce more turbulence. The increased local mixing would increase the local HTC and therefore also the overall HTC as well. This effect would become less significant with wider plates for the local HTC, however the overall pressure drop and heat transfer data would be affected and is another reason why most correlations do not agree with each other well. 75 (a) (b) Figure 5.7: Transversal cross section of two sinusoidal plate heat exchanger for the L3.7A0.5B65-65 PHE: (a) Oblique washboard, (b) herringbone pattern. 5.2 Area averaged HTC To examine if the flow was thermally fully developed, the heat transfer coefficients were plotted along the direction of the stream and cross-stream directions at the locations shown in Figure 5.8a. It can be seen that the flow became thermally fully developed along the streamwise direction after a relative short entry length (y>15 mm) (Figure 5.8b, top). Similar entry lengths were observed at higher Re values. The heat transfer coefficient in the cross-stream direction was also very regular within the central 30 mm of the plate (Figure 5.8b, bottom). Irregularities in the horizontal temperature distribution as observed by Gherasim et al. [17] were not measured in our experiments for pure PHE arrangement, and may be due to the inlet distribution system that was added to our test section. In addition Figure 5.8a clearly shows the contact points with low HTC and the extended silver contacts (Figure 5.11) with high HTC due to the non-existing heat flux. This behavior was observed for the pure PHE arrangements (L5.7A1.0B60-60 and L3.7A0.5B65-65). 76 (a) (b) Figure 5.8 Horizontal and vertical variation of heat transfer coefficient at Re=1700 and heat flux of 0.45W cm-1 for the L5.7A1.0B60-60 PHE. The white rectangles indicate the areas of the nine unit cells that were used to calculate the local heat transfer distribution within a unit cell. Figure 5.9 shows the HTC distribution for the mixed plate arrangement L3.7A0.5B65- 25. As can be seen the HTC distribution is not as good as with the pure arrangement. As discussed in Section 5.1.1 the bulk flow velocity vector is shifted by an angle 𝛼 to the PHE (Figure 5.9a). The unsymmetrical plate arrangement produces a larger entry length and irregularities in HTC can be observed on the left and right boundary, however the center of the plate marked with a white box in Figure 5.9a provides a relative uniform area regarding HTC. This area was used to create the overall HTC of the PHE by averaging all the HTC values within that area. This perimeter was also used for all other PHE configuration, to eliminate potential boundary effects. 77 (a) (b) Figure 5.9 Horizontal and vertical variation of heat transfer coefficient at Re=1300 and heat flux of 0.45W cm-1 for the L3.7A0.5B65-25 PHE. The white box representing the area that was used for the overall HTC computation. The average heat transfer in the fully developed region was measured in the range of 300 0.5). The time averaged, spatially resolved HTC distribution measurements within a representative PHE cell during two-phase flow indicated a minimum at the contact point, an elevated HTC on the upstream side of a furrow, and a maximum located just upstream of the contact point. As the inlet quality increased, the heat transfer 112 distribution became increasingly non-uniform. At high qualities the maximum HTC located upstream of the contact points began to disappear for the L5.7A1.0B60-60 and L3.7A0.5B65-65 geometry indicating local dryout. The two mixed PHE L5.7A1.0B60- 30 and L3.7A0.5B65-25 showed different HTC patterns than their hard plate counterpart, since mixing two plates with different corrugation angles shifted the flow velocity vector relative to the PHE. Adiabatic two-phase flow visualizations indicated film flow to be the dominant flow regime with the vapor core sandwiched between thin liquid layers. Dryout periodically appeared in the proximity of the contact points, and these dry areas became more stable and smaller as the quality increased. This work did not focus on establishing correlations for singe and two-phase flow since all measured values were obtained within the PHE. Real PHE have additionally a flow distribution system and inlet and outlet port which both can play a significant role on the heat transfer and pressure drop for the PHE system. More research in that field is necessary to predict the performance of a PHE. The main contribution of this thesis is the development of a new technique that allows the measurement of local HTC on corrugated surfaces. This technique can help researchers to identify heat transfer and pressure performance of a corrugated pattern without taking into account inlet/outlet flow distribution systems and ports. We showed that the former can have significant effects on the overall performance of the PHE, especially for plates with small corrugation angles. PHE designers now have a tool to determine the performance of the PHE section exclusively. When performing additional experiments with a real PHE possessing the same properties, designers can easily identify the heat transfer and pressure losses over the fluid distribution systems 113 and ports by subtracting the extrapolated data that was gained using the technique described in this thesis. For future experiments, the geometry of the CaF2 plates can be altered to analyze the effect on changes in , 𝛽, 𝜆, 𝑑𝑒𝑞, and mixed vs pure plate arrangements on heat transfer and pressure drop. The apparatus and the technique described can be extended to the measurement of transient heat transfer, which will enable the analysis of transient two-phase flow within PHE geometries. A technique similar to that developed by Kim et al. (2012) can be used to calculate the instantaneous temperature profiles within the test wall, enabling transient heat transfer coefficients to be computed at the wall-liquid interface. 114 8. Appendices 8.1 Thermal conductivity measurement of 200RS100 film The film heater used in this study (Dupont 200RS100) consisted of two layers, an insulating layer made of pure polyimide and a carbon-filled, electrically conductive polyimide layer with high emissivity. The thermal conductivity for the polyimide film was available from literature values (k=0.15 W/m2-K), but the value for the carbon filled layer was unknown. The principle for measuring the thermal conductivity of the carbon filled layer was to electrically heat square sections of the film and measure the temperature distribution with an IR camera and compare with numerical simulations. Figure 8.1 shows a schematic of the apparatus. Three pieces of film were cut and suspended between two copper electrodes to produce three square heated areas (2 mm, 4 mm, and 6 mm). The top and bottom edges of the film were kept at a constant temperature by the copper electrodes. The apparatus was mounted in a vacuum chamber to ensure that the heat generated within the film was lost only by conduction through the film to the electrodes and by radiation to the surroundings. The vacuum chamber had a silicon window with an anti-reflection coating (Edmund Optics #47-943) so the temperature distribution within each film could be measured using an IR camera. 115 Figure 8.1: Schematics of the test configuration for determining the thermal conductivity of the electrically conductive layer in the 200RS100 film. For a square heater of a given size, the shape of the temperature profile within the film is dependent on the thermal properties of the film, the heat generated within the film, the energy radiated from the surface of the film to the surroundings, and the thermal contact resistance between the film and the copper electrodes. The total heat generated in all three heaters was the same since the voltages and resistances were identical. Numerical simulations were performed to find the temperature distribution and the thermal conductivity and thermal contact resistance values to match the measured data were found. Comparison of the temperature distributions measured using the IR camera with the temperature distribution from the simulations is shown on. The ratio of the generated heat lost through radiation to that lost by conduction along the film into the copper electrodes increases with heater size, resulting in flatter temperature profiles. The thermal contact resistances and thermal conductivities required to obtain good agreement between the measured and calculated temperature distributions are shown for the three heater sizes. The thermal conductivity of the film is seen to be greater than 6 W/m-K. 116 Figure 8.2: Comparison of the numerical and measured film temperature distributions at a voltage of 1 V using a thermal contact resistance of 10-3 m2 K W-1 and a thermal conductivity of 7 W m-1K-1. 8.2 Outlook for transient HTC analysis To measure the instantaneous HTC during two-phase evaporation in the PHE it is necessary to calculate the instantaneous temperature profile within the multilayer depicted in Figure 4.7. Therefore it is necessary to solve a conduction equation with two temperatures as boundary condition. Since the highest temperature drop is over the adhesive and a polyimide film (due to their low thermal conductivity) it is feasible to have the first temperature measurement at the liquid-heater interface, and the second one at the CaF2-adhesive interface. The heating film has a high emissivity which 117 simplifies the measurement of the first temperature. For the second temperature, thin and highly emissive black dots were attached to the CaF2 substrate. This section discusses the design criteria, such as size and spacing of the black dots. 8.2.1 Black dot sizing The size of the black dots is not only dependent on the distance between camera and object, but also heavily dependent on the properties of the camera, namely optical properties and focal plane array (FPA) resolution. In the case of the Flir Silver 660 the resolution is 640x512 pixels with a horizontal field of view of (HFOV) 20° and vertical field of view (VFOV) of 16°, resulting in an instantaneous field of view (IFOV) of approximately 0.56 mrad. With a perfect camera that is perfectly aligned, so that one detector element would cover the whole black area of the black dot, the minimum edge length s of the black dot could be calculated for a certain camera to object distance d using Equation 8.1. s = IFOV ∗ d 8.1 Knowing that it is impossible to perfectly align the camera with the black dot one would increase the size of the black dot by a factor of 4 (2x2 pattern), so no matter how bad aligned the camera is, at least one detector element would be covered by the black dot. Due to defects of optical lenses, nonlinearity of the electro-optical sensor, wrong focus or vignetting there will always be a degradation of the original image. Each pixel will affect its neighboring pixel by changing its true value. This can clearly be seen, when a razor blade is placed in front of the opening of a heated black body. 118 Figure 8.3: Infrared image of the razor blade edge placed in front of a heated black body (right) and the temperature profile across the edge (left) Figure 8.3 shows that it takes approximately 6-7 pixels in order to go from the high to low temperature value. In the black dot case, we will not be dealing with one edge but rather two edges since the observed object is a dot. This means that theoretically the minimum edge length of the dot needs to be equal or larger than 12-14 pixels. With a minimum focus distance of roughly 110 mm, we would need a dot edge length of approximately 1 mm. 8.2.2 Black dot spacing As mentioned in Section 4.2 the spacing of the black dots needed to be small enough to accurately predict the temperature between the dots using interpolation. A 2-D numerical heat conduction simulation was carried out in Matlab to determine the amount of heat spreading within the polyimide film and the optical glue. Each of the three layers was divided into 40 nodes. A step function in temperature was used as the 119 boundary condition on the top nodes of the polyimide film as depicted in Figure 8.4. The steady state temperature profile along the multilayer was numerically computed and the results are shown in Figure 8.5. The spacing between the dots, was chosen such that the temperature profile between the dots could be accurately reconstructed using spline interpolation as can be seen in Figure 8.6. Figure 8.4: Schematic representation of the forced boundary condition in the form of a step function 120 Figure 8.5: Steady state heat spreading within the multilayer Figure 8.6: Calculated temperature profile along the CaF2-adhesive interface and the interpolated temperature profile using the temperature measurements of the virtual dots that are 3 mm spaced apart. 121 8.3 Consideration of alternative heating methods Numerous alternatives were considered to uniformly heat a PHE geometry, while measuring high resolved heat transfer. Two methods that were applied and failed are discussed in this section. 8.3.1 Silicon heater Initially it was proposed to measure heat transfer and acquire flow visualization by using an IR thermometry technique developed by Kim et al. [60] that takes advantage of the transparency of silicon in the mid-IR range (3–5 μm). Two plates were cut out of single crystal silicon ingot and the L5.7 A1.0 B60-60 was CNC-machined into the material. The provided silicon was intrinsic meaning that it had no defects and therefore did not conduct electricity. Therefore the flat surface of each plate was n-doped using Boron. The amount of dopant determines the emissivity of the silicon (Figure 8.7) which is why a relative low amount of dopant was applied on the flat surface. Leads were mechanically attached on the sides of the silicon. To reduce the contact resistance. The sides were heavily doped and a layer of chromium and silver was additionally deposited similar to the process explained in Kommer [63]. 122 Figure 8.7: Transmission @ 3.0 um through an uncoated polished 0.5 mm thick sample, data provided by Lattice [64] The plates were each coated on the inner wall with a 60 μm layer of polyimide tape as shown in Figure 8.8b. One plate was then covered with an IR opaque paint containing carbon black (Nazdar GV111), which allowed an effective inner wall temperature to be measured through the silicon and polyimide layer (Figure 8.8c). Two strips of the painted polyimide tape were also attached to the outer wall of the plate so the outer wall temperature could be measured. The inside and outside temperature measurements can be used to solve a coupled conduction/radiation problem which accounted for absorption, emission, and reflection of the thermal energy from the layers and the surroundings, to determine the temperature profiles within the multilayer. The heat flux and heat transfer coefficient could then be calculated for every camera pixel of the plate. 123 (a) (b) (c) (d) Figure 8.8: Schematic of the test section (a). Silicon plates covered with transparent polyimide film (a) and black polyimide film (b) along with the test section (c), where the mechanical electrical contact is shown. Two gold mirrors were used to simultaneously capture both plates with the IR- camera, since silicon and polyimide are partially transparent in the IR-spectrum and therefore allowing heat transfer measurements on one plate and flow visualization on 124 the other plate. The two plates along with the test section without the mirrors are shown in Figure 8.8. Figure 8.9 shows the raw temperature output of the IR-camera of both plates during pool boiling. Besides the clearly visible contact points on both plates, dark patches that are located between the trough and crest can be observed. Figure 8.9: Raw temperature output of the IR-camera during pool boiling within the PHE geometry, Left: Silicon plate with transparent polyimide film, right: silicon with black polyimide film. These dark patches were also observed during adiabatic operation, where a uniform temperature distribution would be expected. To understand the forming of the mentioned dark patches a ray tracing simulation had to be performed. Ray tracing follows the path of a light beam accounting for reflection and refraction at each 125 interface between two materials with different index of refraction, according to Snell’s law. sinΘ1 sinΘ2 = 𝑛2 𝑛1 8.2 Where Θ1 and Θ2 are the angle of incident and angle of refraction respectively and 𝑛1 and 𝑛2 are the index of refraction of the two materials. During each reflection/refraction the energy flux of the beam is divided over the two new rays. The ratio between the two new rays is governed by the index of refraction of both materials and can be expressed by Fresnel’s equation: 𝑟 = ( 𝑛1 cosΘ − 𝑛2 cos Θ 𝑛1 cosΘ + 𝑛2 cos Θ ) 2 Θ=0 → ( 𝑛1 − 𝑛2 𝑛1 + 𝑛2 ) 2 8.3 Where 𝑟 is the percentage of the initial ray that gets reflected and (1 − 𝑟) is the percentage that passes through the material and gets refracted. Figure 8.10 shows a simplified 2-D version of the ray tracing simulation. The starting point of the simulation is located between the trough and crest. The initial cone has an angle of approximately 70° due to the thin polyimide layer (not shown) that is attached on the silicon. 126 Figure 8.10: Ray tracing of the L5.7A1.0B60-60 geometry, with the starting point located between trough and crest, showing the initial light cone and the first refraction The simulation shows that none of the initial rays will reach the lens of the camera. In addition more than half of the initial cone will be totally internal reflected, so they will not exit the silicon at all. Figure 8.11 shows the qualitative energy distribution of the wave pattern as the IR-camera would see for an adiabatic case. As can be seen the pattern is very similar to the one observed in Figure 8.9. Figure 8.11: Qualitative intensity distribution along the wave pattern of a uniform heated silicon plate, when measured with an IR-camera, with the initial intensity being unity. 127 The intuitive solution to that problem would be altering the geometry of the corrugation so that at least one ray of the initial cone will exit the flat side of the silicon with a 90° angle. This can be done by either increasing the wavelength or decreasing the amplitude. Figure 8.12 shows the altered geometry of the corrugation. Due to the high index of refraction of silicon (𝑛𝑠𝑖 ≈ 3.5) a relative high amount of radiation gets reflected at the interface between silicon-air (𝑅~0.30) and also silicon-polyimide (𝑅~0.12). Figure 8.12: Ray tracing of the altered geometry so at least one ray of the initial light cone will exit the flat side of the silicon plate perpendicular, when the starting point is located between the trough and crest. As was seen in Figure 8.7 the highest transmission of a silicon waver is of the order of 55%, meaning that the majority of the rays are reflected since absorptivity of silicone in the IR-spectrum is small. When using a flat silicon surface as the heating element, it is possible to calculate all loses due to reflection within the multilayer, as was done in Kim et al. [60]. For a curved surface however the rays do not remain 128 perpendicular as shown in Figure 8.13, which makes a full ray tracing calculation close to impossible. Figure 8.13: Continuation of the ray tracing from Figure 8.12 adding 1st (top), 2nd reflection (center) rays and 2nd refracted rays (bottom). Using a calibration technique as is discussed in section 4.3 would not be able to solve for the steady state temperature of a single pixel either, since neighboring points on the curved surface would interact with other points and therefore falsifying the true 129 temperature value of each pixel. This can be observed in the left image of Figure 8.9 where the black tape that was attached on the flat side of the silicon plate clearly interacts with its neighboring point as well as the center of the plate where the two corrugation of the herringbone pattern meet. Choosing a different material for the PHE geometry, with a lower index of refraction such as CaF2 (𝑛𝐶𝑎𝐹2 ≈ 1.5) proved to eliminate that problem since the effect of reflected rays within the multilayer became negligible as can be seen in the ray tracing simulation in Figure 8.14. However CaF2 is not a semiconductor as is silicon, which meant that a new method for heating the liquid was needed. Figure 8.14: Qualitative intensity distribution along the wave pattern of a uniform heated CaF2 plate, when measured with an IR-camera, with the initial intensity being unity. 8.3.2 Gold coated polyimide tape Before using the 200RS100 film other options for heating the CaF2 plate were considered. The first option was to apply the same black polyimide tape that was used for the silicon plates (section 8.3.1) on the corrugation of the CaF2 and deposit a thin layer of metal on top of the black surface. Sputtering and vacuum vapor deposition were used to apply a 50 nm thick gold layer. However due to the nature of the 130 corrugation the film could not be deposited with a uniform thickness by either method, as can be seen in Figure 8.15. In addition, the working fluid HFE7100 would wash of the gold over time, contaminating the liquid and lowering the resistance of the heater. Therefore it was decided to apply the gold onto the polyimide film and add a protection layer on top of the gold, prior to adhering the film to the CaF2. The protective layer consisted of a uniform thin PMMA film that was created by spin coating. The result was a multilayer that could be uniformly heated and would withstand the dissolving effect of the working liquid (Figure 8.16a). 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