ABSTRACT
Title of dissertation: THE INTERACTION OF SPRINKLER
SPRAYS AND FIRE PLUMES
Eric D. Link, Doctor of Philosophy, 2017
Dissertation directed by: Associate Professor Andre´ Marshall,
Department of Mechanical Engineering
The critical factor for successful suppression using fire sprinklers is the delivery
of water to burning surfaces. Water delivery is dependent on initial spray charac-
teristics and subsequent spray interactions with the opposing fire plume, which can
deflect or reverse the sprinkler spray away from the targeted fire source. Measure-
ments provide a comprehensive validation data set for computational fluid dynamics
(CFD) spray models, as well as insight and engineering guidance to the spray-plume
interaction important in fire sprinkler applications. An experimental facility con-
sisting of an array of four sprinklers, similar to that of typical suppression system
installations, is used to evaluate both quiescent spray dispersion and spray-plume
interaction conditions. A 0.2 m×0.2 m centrally located forced air jet, with veloci-
ties ranging up to 4 m/s is used (in place of a fire) to provide a well-characterized,
repeatable kinematic challenge to the spray. Measurements include quiescent case
spray dispersion and local volume flux delivery to the plume source to evaluate spray
penetration through the plume. Additional measurements include air jet centerline
drop velocity and drop size at variable source injection velocities to evaluate plume
penetration behavior. These spray dispersion experiments capture the dominant
transport physics and kinematic behavior of the spray plume interaction. Scaling
analysis of the spray plume interaction is explored for two regimes of spray penetra-
tion; individual drop action and group spray action. In the individual drop action
regime the droplets have a negligible effect on the plume and penetration scales with
the ratio of drop terminal velocity to plume velocity. In the group action regime, a
spray work criterion is proposed, accounting for drag interactions with the plume.
The complete set of spray dispersion and plume penetration measurements comprise
a data set of high resolution and well-characterized boundary conditions (including
detailed initial spray measurements for each sprinkler in the array) useful for CFD
validation.
THE INTERACTION OF SPRINKLER SPRAYS AND FIRE
PLUMES
by
Eric D. Link
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
2017
Advisory Committee:
Associate Professor Andre´ Marshall, Chair/Advisor
Associate Professor Christopher Cadou
Professor Marino diMarzo
Associate Professor Peter Sunderland
Professor Arnaud Trouve´
c© Copyright by
Eric D. Link
2017
Acknowledgments
First I would like to thank my advisor, Dr. Marshall, for his support through-
out my studies at UMD, starting all the way back when I began working in the
lab with FireTEC. His endless ideas, insight, and feedback have made me a better
researcher, scientist, and writer. In addition to my advisor, I would like to thank
the project co-PI’s, Drs. Trouve´ and Sunderland, for their continual support during
my student career and contributions to this research, as well as Dr. Howard Baum
and the other members of my committee for their help. I would also like to acknowl-
edge the Department of Fire Protection Engineering and the faculty and staff who
helped me in my student career. Thanks to Olga for all of her help in the lab, and
to Sharon, Mary Lou, and Nicole for their instrumental roles in the department.
A special thanks goes to the suppression research group, including Taylor
Myers, Stephen Jordan, James White, and Sebastien Vilfayeu. Their feedback and
help along the way is greatly appreciated. Additional help is appreciated from
Rodney Bentley eased some of the tedious and wet measurements. Several interns
came through FPE each providing valuable help in the lab—thank you to Jan Felix,
Tim, and Juraj.
I would like to acknowledge and thank FM Global, particularly Drs. Yi Wang
and Bert Yu, for supporting this project, along with the U.S. National Science
Foundation (GOALI Award #1236788). This project would not have been possible
without their support.
And finally, I thank my family for their constant support in everything I do.
ii
Table of Contents
List of Tables vi
List of Figures vii
1 Introduction 1
1.1 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Suppression Spray Research . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Current Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Initial Spray 16
2.1 Experimental Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Sprinkler Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Measurements and Diagnostics . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Sprinkler Array Facility Design 27
3.1 Plume and Sprinkler Arrangement . . . . . . . . . . . . . . . . . . . . 28
3.2 Sprinkler Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Drop Velocity Considerations . . . . . . . . . . . . . . . . . . 30
3.2.2 Spray Momentum Considerations . . . . . . . . . . . . . . . . 31
3.3 Plume Design Considerations . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Dispersed Spray 36
4.1 Experimental Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Measurements and Diagnostics . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Floor Volume Flux Measurement Results . . . . . . . . . . . . . . . . 42
4.3.1 Single Sprinkler . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2 Sprinkler Array . . . . . . . . . . . . . . . . . . . . . . . . . . 44
iii
4.3.3 Nonuniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Resolution Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.1 Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.2 Resolution Results . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 Spray/Plume Interactions 58
5.1 Experimental Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.1 Sprinkler Array . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.2 Plume Velocity Characteristics . . . . . . . . . . . . . . . . . . 61
5.2 Measurements and Diagnostics . . . . . . . . . . . . . . . . . . . . . . 63
5.2.1 Local Volume Flux . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Shadowgraphy . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.3 Optical Volume Flux . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Shadowgraphy Results . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6 Plume Penetration 82
6.1 Plume Penetration Measurement Results . . . . . . . . . . . . . . . . 85
6.2 Penetration Regime Introduction . . . . . . . . . . . . . . . . . . . . 86
6.3 Individual Action Regime . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3.1 Terminal Velocity Scaling Analysis . . . . . . . . . . . . . . . 88
6.3.2 Terminal Velocity Scaling Results and Discussion . . . . . . . 91
6.4 Group Interaction Regime . . . . . . . . . . . . . . . . . . . . . . . . 97
6.4.1 Spray Work Scaling Analysis . . . . . . . . . . . . . . . . . . . 97
6.4.1.1 Comparison to Spray Momentum . . . . . . . . . . . 101
6.4.1.2 Evaluation of Spray Work . . . . . . . . . . . . . . . 103
6.4.2 First Law Scaling Results . . . . . . . . . . . . . . . . . . . . 107
6.5 Scaling Analysis Extension . . . . . . . . . . . . . . . . . . . . . . . . 109
6.5.1 Reach of Current Analysis . . . . . . . . . . . . . . . . . . . . 109
6.5.2 External Data Set . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.5.3 Result Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7 Conclusions 121
7.1 Comprehensive Experimental Dataset . . . . . . . . . . . . . . . . . . 122
7.2 Refinement of Spray-dispersion Measurement Methods . . . . . . . . 123
7.3 Penetration Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A Complete Initial Spray 4S Measurements 126
B SAF Design Details 147
B.1 Velocity Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.2 Momentum Considerations . . . . . . . . . . . . . . . . . . . . . . . . 150
iv
C Shadowgraphy Noise Reduction 153
D Spray Work Calculation 155
Bibliography 158
v
List of Tables
3.1 SAF Design Characteristics . . . . . . . . . . . . . . . . . . . . . . . 35
6.1 Spray penetration test matrix . . . . . . . . . . . . . . . . . . . . . . 84
B.1 Air jet momentum ratio . . . . . . . . . . . . . . . . . . . . . . . . . 152
vi
List of Figures
1.1 Sprinkler array configurations . . . . . . . . . . . . . . . . . . . . . . 14
2.1 4S schematic diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Tyco D3 spray nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Sprinkler initialization sphere orientation . . . . . . . . . . . . . . . . 23
2.4 Initial-spray volume flux measurements . . . . . . . . . . . . . . . . . 25
3.1 Potential spray-plume interaction alignment . . . . . . . . . . . . . . 29
4.1 Sprinkler array facility – spray dispersion . . . . . . . . . . . . . . . . 37
4.2 Volume flux collection calibration . . . . . . . . . . . . . . . . . . . . 40
4.3 Quiescent dispersion volume flux – single sprinkler #1 . . . . . . . . 43
4.4 Quiescent dispersion volume flux – sprinkler array . . . . . . . . . . . 45
4.5 Spray dispersion non-uniformity . . . . . . . . . . . . . . . . . . . . . 46
4.6 Initial spray photograph from D3 sprinkler . . . . . . . . . . . . . . . 47
4.7 Volume flux spatial averaging methodology . . . . . . . . . . . . . . . 49
4.8 Volume flux resolution analysis . . . . . . . . . . . . . . . . . . . . . 52
4.9 Volume flux resolution error . . . . . . . . . . . . . . . . . . . . . . . 54
4.10 Low-flux resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1 Sprinkler array facility – spray plume interaction . . . . . . . . . . . . 60
5.2 Spatial variations in plume velocity . . . . . . . . . . . . . . . . . . . 62
5.3 Plume velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Sample shadowgraph image pair . . . . . . . . . . . . . . . . . . . . . 67
5.5 Optical flux calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.6 Plume-centerline drop velocity measurement . . . . . . . . . . . . . . 71
5.7 Terminal velocity comparison . . . . . . . . . . . . . . . . . . . . . . 73
5.8 Plume region drop distribution . . . . . . . . . . . . . . . . . . . . . 75
5.9 Plume influence on local drop size distribution . . . . . . . . . . . . . 76
5.10 Flux vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.11 Volume flux profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
vii
6.1 Plume penetration ratio . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2 Penetration regime diagrams . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Single drop free-body and kinetic diagram . . . . . . . . . . . . . . . 90
6.4 Local drop size distribution . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Terminal velocity scaling results . . . . . . . . . . . . . . . . . . . . . 94
6.6 Terminal velocity vs. drop size correlation . . . . . . . . . . . . . . . 96
6.7 Plume control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.8 Spray work integration region . . . . . . . . . . . . . . . . . . . . . . 106
6.9 Spray work penetration scale . . . . . . . . . . . . . . . . . . . . . . . 108
6.10 Penetration regime results . . . . . . . . . . . . . . . . . . . . . . . . 111
6.11 Expanded penetration regime results . . . . . . . . . . . . . . . . . . 118
A.1 Sprinkler #1 volume flux . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.2 Sprinkler #1 dv50 drop size . . . . . . . . . . . . . . . . . . . . . . . . 128
A.3 Sprinkler #1 drop size distribution width . . . . . . . . . . . . . . . . 129
A.4 Sprinkler #1 initial drop velocity . . . . . . . . . . . . . . . . . . . . 130
A.5 Sprinkler #1 break-up radius . . . . . . . . . . . . . . . . . . . . . . 131
A.6 Sprinkler #2 volume flux . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.7 Sprinkler #2 dv50 drop size . . . . . . . . . . . . . . . . . . . . . . . . 133
A.8 Sprinkler #2 drop size distribution width . . . . . . . . . . . . . . . . 134
A.9 Sprinkler #2 initial drop velocity . . . . . . . . . . . . . . . . . . . . 135
A.10 Sprinkler #2 break-up radius . . . . . . . . . . . . . . . . . . . . . . 136
A.11 Sprinkler #3 volume flux . . . . . . . . . . . . . . . . . . . . . . . . . 137
A.12 Sprinkler #3 dv50 drop size . . . . . . . . . . . . . . . . . . . . . . . . 138
A.13 Sprinkler #3 drop size distribution width . . . . . . . . . . . . . . . . 139
A.14 Sprinkler #3 initial drop velocity . . . . . . . . . . . . . . . . . . . . 140
A.15 Sprinkler #3 break-up radius . . . . . . . . . . . . . . . . . . . . . . 141
A.16 Sprinkler #4 volume flux . . . . . . . . . . . . . . . . . . . . . . . . . 142
A.17 Sprinkler #4 dv50 drop size . . . . . . . . . . . . . . . . . . . . . . . . 143
A.18 Sprinkler #4 drop size distribution width . . . . . . . . . . . . . . . . 144
A.19 Sprinkler #4 initial drop velocity . . . . . . . . . . . . . . . . . . . . 145
A.20 Sprinkler #4 break-up radius . . . . . . . . . . . . . . . . . . . . . . 146
B.1 Sprinkler array facility design – spray velocity . . . . . . . . . . . . . 150
B.2 Local spray momentum estimate, 0.4 m below sprinkler . . . . . . . . 151
C.1 Shadowgraphy noise reduction . . . . . . . . . . . . . . . . . . . . . . 154
D.1 Close spacing drop size distribution . . . . . . . . . . . . . . . . . . . 156
D.2 Local spray drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D.3 Drag elevation profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
viii
Chapter 1: Introduction
1.1 Research Objectives
The use of automatic sprinklers to provide suppression in the event of a fire
continues to be a popular and effective strategy for reductions of loss of life and
property. The overall success and performance of such protection systems depends
heavily on the interaction and competition that exists between the water spray from
ceiling mounted sprinklers and the upward motion of the fire plume. While these
systems have been effective, particularly through the development of application
specific sprinkler head designs, there is limited understanding of the interactions
between the spray and the fire plume governing spray penetration and the resulting
surface wetting. For the fire sprinkler, it is the spray penetration through the fire
plume that will produce the greatest contribution toward fire suppression [1, 2].
Better performance and efficiency may be achieved through understanding of spray-
plume interactions dominating sprinkler spray penetration and suppression.
There is a large gap in protection system design and specification. In general,
design methods include the codified density/area method [3], or the use of more
complex computational fluid dynamics (CFD) models to justify deviations from the
1
code. In either case, system design is done independently from knowledge about
the specific sprinkler spray characteristics and the interaction with the fire environ-
ment and ultimate delivery of water to the surface. An intermediate complexity
engineering-level tool for evaluation of sprinkler spray penetration may provide ad-
ditional guidance to system design without adding the complexity of full scale fire
modeling. However, performance-based design is becoming a widespread alternative
protection strategy over prescriptive codes. To support engineering decision making,
CFD models are being used extensively to design and justify fire protection system
designs, including sprinkler suppression performance. The fidelity of sprinkler sub-
models in current CFD codes lags behind the desired predictive performance, in
part due to the lack of accurate spray representation and sufficient validation data.
With these motivations in mind, the primary objectives of this research were
to:
• provide a comprehensive experimental data set useful for CFD spray model
validation, from initial spray to plume interactions to surface delivery
• refine methods for measurement of spray dispersion and spray-plume interac-
tion
• establish a framework identifying potential plume penetration performance
based on quiescent spray characteristics for engineering application
In support of these objectives, a medium-scale laboratory experimental facility
was developed giving extra attention to precise experimental conditions and config-
2
uration alignment so that model inputs can be made consistent with experimental
data. These details are crucial model inputs that are often absent in previous data
sets. This experimental study was divided into four parts: characterization and
measurement of initial spray properties, a study of spray dispersion from a sprin-
kler array in a quiescent environment, measurements of the spray-plume interaction
in the presence of an upward momentum source, and an analysis of spray pene-
tration to identify and evaluate governing scaling parameters. The experimental
configurations yield detailed measurements for the purpose of model validation and
an additional analysis of the measurements highlights improvements to dispersion
measurement methods, provides deeper understanding to the physics of the spray-
plume interaction, and suggests scaling laws for prediction of spray penetration
performance.
1.2 Background
Fire continues to pose a challenge to life and property around the world, con-
tributing to an estimated loss of more than $11 billion and more than 3000 deaths
in the United States in the year 2014 [4]. While the total number of fires has been
steadily declining over the past several decades, the death rate per 1000 fires and the
estimated dollar loss per fire has remained constant [4]. These losses come despite
updated building codes and technological improvements, attesting that fire suppres-
sion remains essential to the safety of occupants and the preservation of property.
Water-based fire suppression methods are widely used for their effectiveness, sim-
3
plicity, and availability. Water-based methods include the suppression hose-streams
typically applied by firefighting personnel, as well as automatically activated fixed
position suppression systems utilizing water-mist nozzles or fire sprinklers. In partic-
ular, automatic fire sprinkler installations represent a predominant fire suppression
strategy that has been established as a reliable and effective method to reduce prop-
erty and life safety losses since their introduction in the late 1800s, and are widely
used in all building occupancy types. An example of their success is presented in
statistics by the National Fire Protection Association (NFPA) for residential fires
(occurring between 2007 and 2011), where an 82% reduction in the fire death rate
per 1000 homes and a 68% reduction in property damage was observed when sprin-
klers were installed [5]. Applications for commercial property protection are also
important, as evidenced by the development of the early suppression, fast response
(ESFR) sprinkler, ongoing research into special hazards protection, and the signifi-
cant attention given to storage protection in the design codes [3].
The automatic fire sprinkler has become a ubiquitous fire safety system around
the world, protecting property and occupants. Installations protect a range of de-
sign hazards from relatively straightforward cases like office buildings and residential
property, to more challenging warehouse storage applications. Since the first auto-
matic sprinkler in 1874, hundreds of different sprinklers have been designed attempt-
ing to improve performance in different applications, and dozens of sprinkler designs
are commercially available today. Each sprinkler produces a unique spray dispersion
pattern depending on the deflector shape, orifice diameter, and water pressure. Per-
4
formance is often characterized through evaluation of the spray pattern in terms of
a water volume flux distribution on wetted surfaces; these spray patterns govern fire
suppression efficacy. In fact, sprinklers may be designed to produce a specific spray
pattern depending on the application. For example, ESFR type sprinklers with a
downward biased spray pattern for plume penetration are used in warehouse storage
applications [3,6] while residential type sprinklers with a wide spray pattern for wall
protection are used in residential occupancies. These sprinklers are approved for fire
protection use according to their performance in various standard tests, including
spray pattern evaluation [7–9].
Development of model codes (e.g. NFPA 13 [3]) and legislation such as manda-
tory sprinkler protection provide guidance for best practices and instruction for
proper system design and installation. As buildings are becoming more architec-
turally complex and the fire hazards being protected by sprinklers have evolved,
cases that do not fall under the scope of the prescriptive codes are more common.
The performance-based design concept uses engineering judgment and justification
for fire protection designs that deviate from the codes. Often, CFD programs are
employed to establish alternate designs to evaluate the expected performance of a
given protection system, including suppression systems. Therefore, it is necessary
for these calculations to produce accurate predictions of fire suppression behavior
to justify design decisions. Reliable modeling could enhance safety and design code
development and improve performance-based design techniques. Various challenges
arise when predicting suppression performance, and this research aims to provide
5
a comprehensive data set for model validation, including measurements of initial
spray characteristics, spray dispersion/propagation, and the interaction with a fire
plume.
While it is acknowledged that water-mist and the evaporation of small drops
(with nominal diameters less than 0.2 mm) to remove heat from the gas-phase flame
region are used for suppression, in many applications, surface cooling of the burning
fuel via delivery of water to the burning fuel surface is the most effective way to
suppress a fire [1, 2]. To deliver the water spray to the burning surface, the spray
must penetrate through the fire plume, overcoming the buoyant upward momen-
tum. The level of penetration depends on the individual sprinkler spray patterns,
plume strength, and relative location of the plume and spray sources. While these
factors are of engineering interest, spray penetration is ultimately determined by
clearly defined local spray-plume interactions. Without analytical methods to eval-
uate or predict performance, protection designs often depend on past experiences
or empirical data from costly, specific large-scale fire suppression testing. Devel-
opment of this experimental study included the goal of identifying critical scaling
and engineering analyses that may predict suppression performance of fire sprinkler
sprays through quiescent spray measurement and plume characterization, bypassing
expensive empirical testing in fire situations.
6
1.3 Suppression Spray Research
Suppression spray research generally falls into several categories including dis-
persed spray volume flux measurement (spray patternation), initial spray measure-
ment and characterization, spray-plume interaction, and numerical modeling. Addi-
tional research topics focus on water mists, gas-phase cooling, as well as identifica-
tion of critical water application rates to achieve suppression. However, the current
study is limited to fire sprinkler sprays and the penetration of such sprays to the
surface. While these additional topics are important to water-based suppression
including the use of fire sprinklers, these additional effects on the fire are beyond
the scope of the analysis presented in this research.
Early measurements of sprinkler dispersion were conducted by Beyler [10] to
investigate the influence of several variables on the volume flux distribution, includ-
ing sprinkler installation orientation, flow rate, and frame arm position. Water was
collected in 0.3 m square bins arranged on the floor in either radial or rectangular
gridded patterns. For measurement of multiple sprinklers, the rectangular grid pro-
vided a simpler coordinate system and more complete floor coverage than the radial
grid configuration. This early study introduced a spatial volume flux measurement
method, but since that time only limited improvements have been implemented in
subsequent studies. Results of these measurements show the significant influence
that pressure, orientation, and water supply have on the resulting spray pattern.
Due to experimental uncertainties, large collection bins, and lack of sprinkler char-
7
acterization, the data set is limited and inappropriate for model validation.
FM Global has provided many of the large-scale spray dispersion studies avail-
able in the literature. These studies focused on quantifying spray patterns through
measurement of volume flux distribution, also termed local delivered density, both
under quiescent conditions and in the presence of a fire, aiding in the development
of the ESFR type sprinkler [6,11,12]. Local density measurements were reported by
Yao [11], also using a series of 0.3 m square bins, arranged in a radial line and swept
around the centerline to provide an azimuthal average measurement of the spray
distribution area at various heights below the sprinkler. Other measurements using
a radial sampling technique similar to Yao were performed by Prahl and Wendt [13]
using 0.25 m square bins, although with an idealized axisymmetric sprinkler. In the
large-scale testing by Factory Mutual (FM Global today), density measurements
were taken in the presence of a fire in rack storage applications, where water was
collected in a grid of 16 square pans approximately 0.5 m in width [12]. A more
spatially-resolved measurement technique was used by Chow and Wong [14], who
implemented a rectangular grid of 120, 0.25 m square collection bins to measure the
spray penetration ratio in the presence of a wood crib fire. Their findings focused on
the penetration ratio and the influence of the fire on spray dispersion rather than on
spray measurement details. Overall, the technique for measuring spray dispersion
has not changed significantly, and still relies on collection of water in large contain-
ers. Even in industries such as agricultural irrigation, where large-scale dispersion
of sprays is critical, spray uniformity and distribution is measured using an array of
8
rain-measurement gauges [15].
As use cases for computational modeling in fire protection design become in-
creasingly ambitious, validation of spray dispersion simulations has emerged as a
critical research activity for the development of methods and models to predict
water-based fire suppression performance. Missing from previous spray dispersion
efforts is a complete data set resolving the details of spray dispersion (from initializa-
tion to delivery) for comparison with simulations. Several questions remain regard-
ing sprinkler spray dispersion, such as the extent of spray pattern non-uniformity
and best practices for accurate measurement of spatial variations in the spray, par-
ticularly for the purpose of model validation. The current industry standard for
sprinkler tests is reflected in a number of standards by both Underwriters Laborato-
ries and FM Approvals [7–9], using large 0.3 m (1 ft) collection pans and evaluating
spray dispersion with pass/fail criteria based on a maximum allowable number of
pans having a volume flux below a critical threshold value.
Additional studies have focused on measurement of spray properties, such as
drop size and velocity distributions [16–18], developing ways to characterize and de-
scribe the spray as it is dispersed. Advancements in measurement technology have
allowed expansion of the early data sets, yielding in-depth comprehensive descrip-
tions of the spray [19–21]. One aspect of fire sprinkler sprays and the accompanying
modeling efforts receiving detailed attention is the spatial variation of the spray
characteristics. Unlike many other spray nozzles, fire sprinklers do not produce
spatially uniform sprays. Even from visual observation of an operating sprinkler,
9
initial spray non-uniformities and their impact on far-field propagation are appar-
ent, motivating the need for detailed spray measurements. More recent studies have
quantified spatial variations in spray characteristics, such as volume flux distribution
and drop size distribution, to support detailed analysis of fire suppression perfor-
mance [19–25]. These measurements reveal elevation and azimuthal angle variations
in near-field volume flux and other important spray characteristics, such as drop size
and velocity, which appear to correspond to geometric features of the fire sprinkler
head. These near-field spatial variations impact far-field volume flux and, in turn,
may affect sprinkler performance. Implementation of these detailed initial-spray
measurements can have a significant influence on the outcome of the model solu-
tion, providing more realistic results [25, 26]. Given the variations in volume flux
variations in the near- and far-field, the variations in near-field measurement of drop
sizes suggest that there are also variations in drop size at spatial resolutions com-
parable to the variations in volume flux (in addition to the natural drag filtering
caused by the range of drop sizes within the spray). While volume flux might not
be sub-critical for suppression, in these locations there may be differences in drop
size that would influence the penetration ability on similar length scales to those
identified as important for resolving the spatial volume flux.
Few experiments detailing water spray penetration through a fire plume have
been conducted, presumably due to the high cost and complexity of large scale
fire tests. Early measurements identify the effect of drop size on penetration [16],
confirming that smaller drops, while effective at cooling the hot gases within a ceiling
10
jet or through entrainment, are ineffective at penetrating to the surface; larger drops
(nominal diameter >0.5 mm) are needed for more efficient suppression. Much of the
experimental data is from FM Global and the large-scale actual delivered density
(ADD) apparatus which collects water on the floor in large collection pans below
a heptane spray burner [12, 14, 18, 27, 28]. More recent experiments by Schwille
[29, 30] explore penetration and the reaction of a fire plume to the momentum and
drag imparted by a suppression spray and measure the velocity of drops in the
plume region, showing substantial penetration reduction with increasing fire size.
Additionally, the concept of a characteristic drag effect, rather than momentum
competition between the spray and plume, was introduced. Redirection, velocity
reduction, and reversal of drops was observed using PIV measurement techniques.
Improved characterization of the plume boundary condition, as well as increased
spray volume flux resolution, including at the location of the fire plume, would
advance the comparisons to CFD models and provide a more complete validation
data set. Schwille also looked at the effect of the interaction of the spray on the
plume, identifying modified plume equations describing the effect a spray may have
on the plume characteristics through drag forces [30, 31] as well as how the plume
may affect drop motion [29] in the direct competition of aligned sprays and real fire
from burners. Other small-scale experiments such as those by Zhou [24] investigate
the directly opposed configuration with water mist and small plume configurations.
Due to the complexities of fire plume and spray interaction experiments, sev-
eral studies using CFD simulations of sprinklers have been performed. Early sprin-
11
kler models used relatively low fidelity sprinkler injection and transport models
simulating only a few trajectories with uniform drop sizes [32–34]. While insight
to the penetration phenomena can be gained from these numerical experiments, re-
sults could be improved with increased spray fidelity and complete and appropriate
measurements for validation of the models. More recently, higher fidelity models
have been developed based on near-field initial spray characterization [22,23]; these
models have been successfully used to simulate complex dispersion [35] and suppres-
sion [36] scenarios. The complexity of these simulation scenarios provides a realistic
challenge for model capabilities, but limits insights into spray physics and utility for
validation of the models.
The experiments conducted in this study seek to address gaps regarding CFD
model validation and engineering insight of spray-plume interactions using a medium
scale laboratory experiment with well-documented spray conditions in both quies-
cent and spray-plume interaction studies, using an array configuration with the
plume located away from the sprinklers rather than the common centerline config-
uration used in the detailed studies to date. Measurements of initial spray charac-
terization, delivered volume flux, local spray-field characteristics, and penetration
measurements with both strong plume and strong spray conditions will contribute a
comprehensive data set for model validation and physical insight to the spray-plume
penetration.
12
1.4 Current Work
Multiple measurements and diagnostics were implemented to explore the phys-
ical phenomena involved in the spray-plume interaction and to obtain experimental
data suitable for CFD model validation. The measurements consist of four different
sets, including
1. Initial spray characterization
2. Quiescent spray dispersion
3. Spray-plume interaction
4. Spray-plume penetration
These measurements were accomplished using two experimental facilities in a
wet lab designed to contain water spray experiments. Initial spray characterization
was performed using the spatially-resolved spray scanning system (4S) [25], detailed
in Ch. 2. The dispersed spray and spray-plume interaction measurements were con-
ducted in the sprinkler array facility (SAF), and are detailed in Ch. 4 and Ch. 5,
respectively.
The SAF consisted of a square grid of 4 sprinklers, typical of sprinkler suppres-
sion system installations, allowing the use of multiple sprinklers and a configuration
where the suppression target was located in-between sprinklers representative of a
potential worst case scenario where the fire is not directly below a given sprinkler.
Measurements in the SAF required two configurations of the facility, sketched in
13
Figure 1.1: The sprinkler array facility was configured in two ways for (a)
spray dispersion and (b) spray-plume interaction measurements. Active
measurement areas in each configuration are highlighted.
Fig. 1.1. Quiescent spray dispersion measurements were taken from the full array
of sprinklers, indicated in Fig. 1.1a by the highlighted measurement areas of initial
spray locations and the full floor coverage. For measurement of spray-plume interac-
tion, the modified configuration shown in Fig. 1.1b was utilized with two sprinklers
and a central vertical plane region for measurement of spray characteristics and
behavior using optical methods.
The detailed spatial measurements of the spray, both at initial formation and
during interactions with the plume, with careful attention given to alignment, reso-
lution, and operating conditions, provide a comprehensive data set useful for CFD
spray transport model validation. Along with the validation data sets from detailed
measurements of spray dispersion and spray-plume interaction, additional insight
and understanding can be derived from the results. The analytical approach in-
cludes a resolution analysis of the spray dispersion measurements providing insight
14
into sprinkler spray length scales and guidance for accurate measurement of sprin-
kler sprays. A scaling analysis framework for evaluating spray-plume interactions
to predict spray penetration to the target surface is also presented. Specifically, the
penetration scaling analysis is based on a sprinkler’s unique spray pattern quantified
through quiescent dispersed local spray characteristics (obtained from either far-field
measurements or from predictions informed by initial spray measurements). The
goal of this analysis was to provide a foundational suppression engineering frame-
work based on recent sprinkler measurement and analysis innovations to support
design analysis and to reduce reliance on large scale fire testing.
15
Chapter 2: Initial Spray
Various sprinkler designs are available for different hazard protection appli-
cations, and each produces a unique, non-uniform spray depending on deflector
geometry and operating pressure. Because the formation of the spray is dependent
on a solid jet impinging on a shaped deflector, the geometry of the deflector plate
is a significant factor in the spray pattern each sprinkler generates. These variables
determine the spray pattern and characteristics of the spray, including the volume
flow rate, the spatial distribution of the volume flux, the drop size distribution, and
the initial velocity of the drops. These three main parameters, volume flux, drop
size, and drop velocity, influence how the spray will interact with the plume.
A critical factor for successful modeling of spray dispersion is the fidelity of the
boundary conditions. Due to the complexities in deflector design, it is beyond the
scope of current analytical approaches for a direct calculation of the initial spray.
Work by Myers [37] pushes the boundaries of such calculations, predicting sheet
formation and velocities from a simple deflector geometry, which could be used for
further calculation of spray distributions. Nevertheless, current implementation of
sprinkler sprays in computer modeling is dependent on the specification of general
spray characteristics, including drop size distribution, initial velocity, and volume
16
flux [26, 38, 39]. Given that each sprinkler is unique, the precision of a spray model
is highly dependent on the initialization characteristics. Therefore, measurement of
the initial spray characteristics is essential to providing high fidelity CFD boundary
conditions as well as inputs to more general engineering analyses to predict sprinkler
performance.
2.1 Experimental Facility
Detailed near-field initial spray measurements were obtained using the 4S.
This facility, first conceived by Ren et al. [20, 40], and further developed by Jordan
et al. [25], measures the total volume flux of the spray along with the diameter,
velocity, and number density of drops after their initial atomization. Because these
spray characteristics vary spatially with respect to the sprinkler, measurements are
taken along a continuous spherical surface surrounding the sprinkler, known as an
initialization sphere [19,21]. A significant feature of the 4S is its ability to rotate the
sprinkler while keeping the measurement devices fixed in place, providing spatially
continuous measurement around the sprinkler. A schematic diagram of the 4S shows
the configuration of the facility in Fig. 2.1. The centrally located sprinkler is situated
between two measurement devices; an array of water collection funnels are positioned
on one side, while a LaVision laser/camera optical system is positioned on the
opposite side.
Water is supplied to the system by a pump from an underground storage tank.
The water flow rate is controlled by an electronic valve monitored by a proportional-
17
Figure 2.1: Schematic diagram of the 4S initial spray facility. Mechanical
collection of volume flux is achieved with the funnel caps and collection
cylinders, while optical measurement of drop size, velocity, and volume
flux is achieved with a LaVision laser system.
integral-derivative controller (PID controller) to maintain a constant flow condition.
18
2.2 Sprinkler Details
For accurate spray initialization in CFD models, future model validation, and
compilation of a comprehensive data set in the current research study, measure-
ments must pay significant attention to consistent and repeatable spray conditions.
Particularly important are sprinkler details and alignment. A set of four Tyco D3
spray nozzles was used throughout this study, each numbered for identification. The
Tyco D3 spray nozzle used for this study produces widely-dispersed sparse sprays
consistent with standard pendant sprinklers. This particular nozzle has a horizontal
deflector consisting of 12 rotationally symmetric slot/tine pairs with no geometric
abstractions, shown in Fig. 2.2. Also shown in Fig. 2.2 is a reference datum iden-
tified by the frame arm to maintain a known angular orientation. This position
identification is important to maintain consistency between sprinklers and in the
initial spray measurements for accurate model input values. Position around the
sprinkler is identified by an azimuthal angle, φ, and an elevation angle, θ, also iden-
tified in Fig,2.2. The elevation angle is measured from the upward vertical direction
at θ = 0◦ to θ = 180◦ directly below the sprinkler. The azimuthal angle is set such
that the frame arms are positioned at φ = 90◦ and 180◦. Azimuthal angle is positive
in the counter-clockwise direction, following a right-hand rule convention with the
sprinkler in its operational orientation (e.g., pendant) and the vertical axis in the
upward direction.
19
𝜙=0˚𝜙=180˚
𝜙=90˚
𝜙=270˚
Reference Frame Arm
x
y
BB
SECTION B-B
A A
B B
2
2
1
1
Tyco D3
SHEET 1 OF 1SCALE: 1:1 WEIGHT: 
REVDWG.  NO.
A
SIZE
𝜃=180˚
𝜃=90˚
Figure 2.2: The Tyco D3 spray nozzle with k-factor 33 LPM/bar1/2 was
used throughout this research. The deflector consists of 12 slot/tine
pairs, and sprinkler were aligned according to the labeled reference frame
arm.
2.3 Measurements and Diagnostics
Characteristics of the initial spray, including volume flux, drop size, and drop
velocity, are measured along the initialization sphere, a location where the initial
water jet has atomized and broken into a spray, using the physical collection tubes
and optical imaging equipment shown in Fig. 2.1. For the Tyco D3 sprinklers used
in this study, the initialization sphere radius was 0.4 m from the sprinkler.
The primary measurement of volume flux is achieved by collecting water as it
passes through the initialization sphere. An arc of 11 collection funnels is located at
a radius of 0.4 m from the sprinkler, covering elevation angles centered from θ = 80◦–
180◦, measured from the upward vertical axis, shown in Fig. 2.1. Water is collected
20
in each of the 11 elevation angle collectors continuously as the sprinkler makes a
full 360◦ azimuthal rotation. The rate of water accumulation is measured in each
collection tube to determine the volume flux. Simultaneous water collection in each
of the elevation angle tubes allows the volume flux to be completely characterized
in one revolution. The azimuthal angle of the sprinkler is recorded as the sprinkler
rotates, allowing for the volume flux measurement to be mapped to a precise location
on the initialization sphere.
Located 180◦ across from the flux collectors is a traversing LaVision laser
shadowgraphy system used to capture images of the spray used to optically measure
the diameter, velocity, and number density of the drops. The optical equipment is
positioned at the initialization radius at discrete elevation angles. As the sprinkler
rotates, images are captured at a rate of 6 Hz. Rotation times extend as long as
50 minutes to acquire a sufficient number of images at each azimuthal location to
ensure the motion does not influence the results and blur the spatial gradients.
Accumulated over the 11 elevation angles, raw image data for an entire sprinkler
characterization consists of over 150,000 image pairs and approximately 600 GB of
data. This massive amount of data is processed using the DaVis LaVision software
package to identify and measure millions of individual drops, reducing the dataset to
a nominal 500 MB size listing all of the drops identified. Similar to the mechanical
measurement, the azimuthal and elevation angle location relative to the sprinkler
is known for each image that is captured, and the drop size distribution and drop
velocity can be extracted from the images and mapped onto the initialization sphere.
21
Additionally, volume flux can be calculated from the optically measured quan-
tities, providing a validation of the mechanical collection method. Due to the rig-
orous alignment procedure of the sprinkler datum and the automated control of
sprinkler rotation and flow rate, repeatability of the measurement is very good.
Errors associated with position and local flux error are less than ±1% and ±2%,
respectively [25].
2.4 Measurement Results
Each individual sprinkler used in this study was measured with the 4S, provid-
ing detailed quantification of the spatial variations in drop size, velocity, and volume
flux. The result is a complete description of the initial spray that comes from each
sprinkler which can be used for high-fidelity model initial conditions for spray dis-
persion modeling and engineering analysis. The initialization sphere is shown in
Fig. 2.3, where the shaded region indicates an example of the quarter of the hemi-
sphere directed into the array. Results of the 4S characterization measurements are
plotted using this template.
Volume flux measurement results are presented in Fig. 2.4 for the four sprin-
klers used throughout this research, the Tyco D3 sprinkler with k-factor
33.1 LPM/bar1/2 operating at 1.38 bar, labeled with their corresponding identifi-
cation number. Multiple characteristics of the particular deflector geometry can be
seen in the spatial distribution of volume flux. The slot-tine pattern can be iden-
tified by the repeating areas of high flux near the equator caused by flow off the
22
sprinkler 
deflector
r = 0.4 m
𝜙=270˚
Reference 
Frame Armx
y
z
𝜙=0˚
Figure 2.3: The initialization sphere is located around the sprinkler,
with the azimuthal angle reference positions φ = 0◦ and 270◦ identified
with the short dashed lines. Sphere measurement results are plotted as
a quarter hemisphere shown by the shaded region.
tine, alternating with vertical streaks corresponding to spray flowing from the slots
following a more vertical initial trajectory. Frame arms of the sprinkler are also
seen to have an effect, situated at azimuthal angles of 90◦ and 270◦. The effect is
particularly pronounced in sprinkler #2, where a significant spray shadow is cast in
the φ = 270◦ direction. Additionally, due to the geometry of the sprinkler deflector,
a significant flow of water is observed coming from a deflection off the frame arm.
These non-uniformities will propagate as the spray is dispersed, and may have a sig-
nificant influence on plume interactions and suppression. Each quarter hemisphere
represents the quadrant of the spray that was directed into the square array area,
with measurements spanning from directly below the sprinkler to 10◦ above horizon-
tal (elevation angles θ = 80–180◦), as highlighted in Fig. 2.3. The circled numbers
23
correspond to the sprinkler identification number, consistent throughout this study.
While Fig. 2.4 shows measurement results of volume flux, similar non-uniform pat-
terns are observed in the other quantities measured from the 4S shadowgraphy.
Complete initial spray characterization results of volume flux, volume median drop
size, drop distribution parameter, initial drop velocity, and drop break-up radius are
presented in Appendix A for each sprinkler.
Although there are similarities between sprinklers, as shown in Fig. 2.4, it is
apparent from these measurements that even sprinklers of the same model produce
different spray patterns despite the same deflector design and operating conditions.
In the interest of providing experimental data for model validation, it is important
to measure the exact variations between sprinklers so that the accuracy of the model
can be validated. By measuring each sprinkler independently, sprinkler-to-sprinkler
variations are accurately documented and the relation of spray patterns in the near-
field can be linked to subsequent spray dispersion. While there are similarities
between the general patterns, the differences of the initial spray will propagate,
leading to unique spray patterns on the floor, discussed in Ch. 4.
24
180˚ 270˚
0˚ 90˚
360˚
180˚
1
3 4
2
�
��������
Volume Flux (mm/s)
0 2 4 6 7 ≥81 3 5
Figure 2.4: Spatial volume flux measurements of the initial spray
plotted on quarter hemispheres for the four Tyco D3 sprinklers,
k=33.1 LPM/bar1/2 operating pressure was 1.38 bar, directed into the
sprinkler array configuration. See Fig. 2.3 for definition of the quarter
hemisphere.
25
2.5 Summary
Detailed measurements of the initial spray were taken for each of the four
Tyco D3 sprinklers used throughout this research. The particular sprinklers had
a k-factor of 33.1 LPM/bar1/2 and were operated at a pressure of 1.38 bar, flowing
38.9 LPM. Measured quantities include spatially-resolved volume flux, drop size,
and drop velocity. From these measurements, the drop size distribution parameter,
γ can be determined, as well as the sheet break-up radius. The collection of these
important spray parameters completely describe the initial spray from the sprinkler.
Accompanied by the installation orientation and identification of the individ-
ual sprinklers, the measurements provide a complete set of injection parameters
that can be used for modeling of sprinkler sprays, including relatively simple drop
tracking models, or more comprehensive CFD models such as FireFOAM. The data
set provided will allow for more accurate sprinkler spray initialization and allow for
increased confidence in CFD spray modeling validation.
26
Chapter 3: Sprinkler Array Facility Design
Measurements of spray dispersion and spray-plume interactions were taken
using the sprinkler array facility, seen in the schematic of Fig. 1.1. Several variables
have an influence on spray-plume interactions and ultimately spray penetration,
including sprinkler height, spacing, flow rate, operating pressure, drop size distri-
bution, fire plume size, and fire momentum. While all of these parameters have an
influence on the penetration effectiveness, when considered all together they define
the localized interactions that govern the spray-plume interaction. The sprinkler
array facility was designed with the goal to provide a medium-scale experimental
facility which maintained similarity to real-world sprinkler applications while provid-
ing two general localized spray-plume interaction regimes, supporting experimental
conditions where penetration was achieved through individual drops in the spray
(Sec. 6.3), or where the accumulated drag forces of the spray contributed to the
penetration (Sec. 6.4). The sprinkler arrangement, sprinkler operating condition,
and plume strength were all considered together to develop the SAF.
27
3.1 Plume and Sprinkler Arrangement
The square array configuration allowed the exploration of different plume lo-
cations within a typical arrangement of sprinkler protection systems, with different
possibilities shown in Fig. 3.1. Much of the previous research with detailed mea-
surements has been conducted with a single sprinkler located directly above the fire
source [24,29–34,41]. While such a configuration is simple and allows for the direct
study of the interaction of the spray and plume, it is not a general representation of
the suppression problem. A fire may be located anywhere in relation to the sprin-
kler locations, including a potential worst-case scenario in-between the sprinkler
spacing. The grid configuration allowed for this variable location arrangement, and
has been explored on a large scale with limited local diagnostics [11, 12, 16, 18, 28].
Spray characteristics from the given sprinklers vary depending on location, and
through different spacing of the sprinklers from the central plume, different inter-
action regimes could be achieved. The facility design accommodates a maximum
sprinkler spacing of 2.65 m, on the same order of magnitude with typical sprinkler
installations which range from 2.4 m–6 m spacing depending on the sprinkler type.
28
Figure 3.1: Possible plume locations (×) included direct alignment (left),
centered alignment (center), or a random alignment (right) closer to one
sprinkler.
3.2 Sprinkler Selection
The Tyco D3 spray nozzle, previously introduced in Sec. 2.2, was selected for
its simple repeating geometry while maintaining consistent geometric features of typ-
ical pendant fire sprinklers, such as the tine/slot deflector design and the inclusion
of frame arms, depicted in Fig. 2.2. The Tyco D3 nozzle is available in a variety of
orifice diameters to provide a range of flow rates and drop size distributions. Drop
sizes from the Tyco D3 are nominally 0.7 mm, within the range of typical sprin-
kler drop sizes, predicted between 0.4 mm and 2.4 mm based on a median volume
diameter drop size.
Limitations of the lab space water flow rate and minimum operating pressure
requirements constrained the size of sprinklers for selection. To ensure good spray
formation, a constraint for minimum operating pressure at the orifice of 0.5 bar
was imposed, also consistent with minimum operating pressures of fire sprinkler
29
installations [3]. Based on lab water flow capability, a maximum of approximately
224 L/min was available, leaving a maximum of 56 L/min from each of the four
sprinklers in the SAF. This maximum flow rate can also be viewed in terms of an
operating pressure, P , through the relation Q = k
√
P , where Q is the flow rate, and
k is the sprinkler k-factor. The limiting case where the flow rate and minimum pres-
sure constraints meet occurred at a nominal k-factor of 80 LPM/bar1/2. Therefore,
any sprinkler larger than this orifice size is unsuitable for the current facility.
Along with the operating pressure considerations, drop velocity and spray
momentum were considered to further determine the specific sprinkler selection.
3.2.1 Drop Velocity Considerations
Penetration of individual drops in the spray through the plume is dependent
on the velocity of the drops. To reach the target surface, drops must maintain
a downward velocity. Because drop size is directly related to the drop terminal
velocity, the drop size distribution was estimated for various operating pressures
to help determine an appropriate pressure and sprinkler size. Details about the
drop velocity calculations and considerations are presented in Appendix B. The
goal was to use a sprinkler that generated a sprinkler spray within the general
operating conditions found in fire sprinkler applications, while also providing drops
with terminal velocities in a range that could be challenged by the competing plume
velocity.
30
3.2.2 Spray Momentum Considerations
The relationship of momentum of the spray and plume have also been iden-
tified as important parameters in the spray-plume interactions [6, 11, 12, 24, 30, 34].
Initial design of the facility considered this momentum competition. From previous
suppression testing, the spray was observed to to penetrate to the fuel source if the
ratio of spray momentum to plume momentum was greater than 1 [41]. In order to
provide a range of possible conditions where the spray momentum was in a typical
range for penetration, a range of spray/plume momentum ratios was considered,
from 0.2 < M˙s/M˙p < 2.
What was not clear from the outset was the appropriate characteristic momen-
tum. Previous work has identified characteristic spray momentum as the injection
momentum, or the initial momentum measured on a strike plate near the injection
location. Others consider the momentum of the spray distributed over the entire
reach of the spray. A general first order estimate of the spray momentum can be
calculated by the product of the volume flux, V˙ ′′, and spray velocity, v, M˙s = V˙ ′′v.
In the current analysis, a local momentum is considered based on the location and
coverage area of the spray and plume. Rather than use a strict momentum ratio
where the spray momentum is considered as a characteristic injection value, it may
instead be considered as a local area based value,
M˙s(As)/As
M˙p/Ap
(3.1)
where the momentum is considered as a localized area modified momentum ratio.
31
The selected area of influence determines the relevant spray momentum. This area
could be the total area of the spray at a characteristic height, or it could correspond
to the area of the plume that it is competing against. Multiple estimates of spray
momentum based on different characteristic areas were considered, and details of the
calculations are presented in Table B.1 in Appendix B. Additional discussion about
spray momentum, and the applicability to the spray-plume interaction phenomena
is discussed in Sec. 6.4. While the spray pattern and distribution of volume flux
has a significant influence on the downward spray momentum, based on the typical
volume fluxes and drop velocities produced by the spray, it is assumed that the
spray momentum is also typical of a typical standard spray or residential sprinkler.
3.3 Plume Design Considerations
One of the important parameters governing the spray-plume interaction and
eventual penetration of the spray to the surface of the burning fuel is the relative
velocity of the drops within the spray and the competing fire plume. Two char-
acteristic velocities were considered for the plume, determined through ratios to
relevant spray velocities. Penetration based on individual drop behavior has been
shown to depend on drop size and corresponding drop terminal velocity. The ratio
of drop terminal velocity to the plume velocity (discussed in more detail in Sec. 6.3)
is the more important factor governing drop penetration, while the kinetic energy
of the plume, determined by ρau
2/2, is important when considering the influence of
accumulated drag forces from the spray (discussed in Sec. 6.4).
32
For repeatable, well-characterized experimental conditions, a forced-air jet at
ambient temperature was used throughout the experimental testing. In the forced-
air method of plume generation, the plume design considered two main variables,
diameter and flow velocity, with the objective of providing a range of velocity con-
ditions to compete with the spray. As the plume diameter increases, the volume
flow rate required increases for the same plume velocity. However for smaller plume
sizes, the pressure drop due to duct sizing is increased, restricting the amount of
airflow available. The plume design converged on the 0.2 m×0.2 m size based on
preliminary testing of pressure drop and flow rate from air ducting to deliver the
plume to the center of the array. The maximum sustained velocity was 3.7 m/s.
More details of the plume velocity profile and construction are presented in Sec. 5.1.
While the current plume region is defined by an ambient temperature air jet,
the characteristic velocity still maintains reasonable similarity to velocities within
real-world medium scale incipient fires. For example, using fire plume centerline
correlations developed by Heskestad [42], the centerline plume velocity for a 300 kW
fire is approximately 6 m/s. While the 3.7 m/s velocity is slightly lower than this
fire plume velocity, the important velocity relationship with the plume is ultimately
not the absolute velocity, rather the velocity and kinetic energy ratios presented in
Sections 6.3 and 6.4.
33
3.4 Summary
Design of the sprinkler array facility considered the arrangement of sprinklers
and the relative velocity and momentum competition between the spray and the
plume. The array configuration allowed for a more general and potentially worst-
case location of the fire plume suppression target in relation to the sprinkler lo-
cations. Selection of the sprinkler operating condition considered the influence of
orifice diameter and operating pressure on the drop size distribution that would be
produced, and the resulting ratio of drop terminal velocity to plume velocity. While
it was unclear from the beginning of the research what the critical spray and plume
momentum comparison was, previous research indicated a range of spray/plume
momentum ratios.
The design parameters of the sprinkler array facility are summarized in Table
3.1. A sprinkler k-factor 33.1 LPM/bar1/2 was selected at an operating pressure of
1.38 bar. At this operating condition, the characteristic drop velocity and momen-
tum criteria were met and drop characteristics and plumes compared favorably on
the same order of magnitude with length and velocity scales present in sprinkler
applications.
34
Table 3.1: Predicted test capabilities of the sprinkler array facility for design deci-
sions.
Parameter Design Value Typical Range
k-factor 33.1 LPM/bar1/2 43–360 LPM/bar1/2
Operating pressure 1.38 bar 0.5–12 bar
Spacing 2.65 m 1.8–6 m
Height 1.5 m 2–15 m
Predicted dv50 0.72 mm 0.4–2.4 mm
Max. uplume 3.7 m/s 5–10 m/s
35
Chapter 4: Dispersed Spray
Because sprinklers are a reactive means of protection and cover a general
area without adjustable aiming direction, dispersion of the spray is critical for fire
suppression and surface cooling. Prior to the additional complication of a competing
fire plume, initial measurements were taken of quiescent spray dispersion within a
square array configuration, previously presented in Fig. 1.1. Volume flux delivery
to the floor 1.5 m below the level of the sprinklers was measured for a quadrant
of a single sprinkler, as well as for the simultaneous operation of a full array of
four sprinklers. Important outcomes of the quiescent spray dispersion case include a
dataset for model validation of spray dispersion which partners with the initial spray
measurements from Ch. 2 to form a complete dataset describing the distribution of
the spray, as well as an analysis of the spatial-resolution of such measurements. The
spray dispersion measurement and analysis presents validation data and physical
insight for a basic quiescent environment.
36
Figure 4.1: Drawing of the experimental facility showing the arrange-
ment of the sprinklers and the water collection tubes. The circled num-
bers identify each sprinkler.
4.1 Experimental Facility
The sprinkler array facility (SAF) was developed for far-field dispersed spray
measurements. The SAF incorporates the common grid building block found in typ-
ical sprinkler installations, with unique sprinklers located at each corner identified
by the numbers in Fig. 4.1. Sprinklers were located in a square configuration spaced
by 2.65 m on each side of the array.
All four sprinklers are the Tyco D3 spray nozzles shown in Fig. 2.2. The four
sprinklers were operated simultaneously at 1.38 bar. With a k-factor 33.1 LPM/bar1/2,
37
the total flow rate was 38.9 LPM from each sprinkler. As was shown in Fig. 2.4 the
measured spray pattern is unique for each individual sprinkler, so all sprinklers were
given identifying numbers and the angular position of each was carefully aligned,
with the reference directions and angles consistent with those shown in Figs. 2.2 and
4.1. Sprinkler frame arms were parallel to the y-axis in Fig. 4.1 and the 0◦ azimuthal
angle directed to the positive x-axis.
Water was supplied to the system by an underground storage tank and pump.
Flow rate was regulated with a valve coupled to an electronic controller monitoring
the total pressure just upstream of each sprinkler. Pressure measurements were
acquired with an Omega PX302 pressure transducer, with range 0–13.8 bar and
accuracy 0.25% BFSL. Timed bucket-filling tests were performed to verify the flow
rate and to confirm equal flow rates from each sprinkler.
4.2 Measurements and Diagnostics
Dispersed spray volume flux measurements over the floor area, V˙ ′′, were ob-
tained with a linear array of collection cylinders as seen in Fig. 4.1, with openings
located 1.5 m below the sprinkler deflectors. The inner diameter of each collection
cylinder measured 52 mm, with an outer diameter of 60 mm. The measurement area
of the cylinders covers 85% of the total measurement area. The linear array was
manually positioned parallel to the x-axis at y-position increments of 0.05 m such
that the entire floor area within the sprinkler array was measured over a series of
tests. The test procedure began with the collection tubes covered while the water
38
flow-rate stabilized at a steady-state operating pressure. At this point the tubes
were uncovered and water was collected for 10 minutes before the tubes were cov-
ered once again. After the water flow was terminated, the water pressure head in
each tube was measured.
Consideration was given to flux collection in a radial coordinate system similar
to previous researchers [10, 13, 14] due to the two-dimensional radial motion of the
spray from the sprinkler. However, this convenience breaks down in two ways. First,
the use of multiple sprinklers are implemented in a square, guiding measurements to
a grid configuration. Additionally, the radial configuration also leads to insufficient
measurement resolution as the radius from the sprinkler increases. Details about
the spatial resolution of the flux measurement are discussed in Sec. 4.4.1.
Volume flux is calculated by determining the volume of water collected in the
collection tubes during the specified test duration. A Setra 209 pressure transducer,
range 0-0.07 bar and accuracy ±0.25% FS, measured the pressure head of water
accumulated in each tube. Using the cross-sectional area of the collection tube, At,
the area of the tube opening, Ao, the measured pressure head, ∆h, and the collection
time duration, t, the volume flux was determined by
V˙ ′′ = (At∆h)/(Aot) (4.1)
An in-place calibration of the pressure transducer was performed to establish
the accuracy and repeatability of the water column height measurement by adding
a known volume of water to the collection array. The calibration incorporated
possible sources of error in the water height measurement, including the leveling of
39
●●●●●●●
●●●●●
●●● ●●●●●
●●●●●●●
● ●●●●
●●● ●●
● ●
●
0 50 100 150 200 250
0
50
100
150
200
250
Measured Δh (mm)
A
ct
ua
lΔh
(mm
)
Figure 4.2: Calibration of the volume flux pressure transducer shows the
actual height of the water column is 1±0.26% higher than the measured
value, contributing minimal error to the measurement. Best fit line is
y = 1.01x.
the collection array, manufacturing differences in tube diameters, and the fraction of
water drops that remained on the side or edge of the tube. Calibration of the pressure
transducer measurement determined the measured height to be linear within 0.26%
of the actual height at a 95% confidence level, with calibration results shown in
Fig. 4.2. This component of the measurement contributes very little to the overall
measurement uncertainty due to the high accuracy of the pressure transducer. The
larger sources of uncertainty are presented by other variables including positioning of
the collection tubes, water pressure variations, temperature, room airflow, or other
variations in spray pattern from day to day. The repeatability of measurements
including all of these factors is detailed in Sec. 4.4.1.
40
Due to the stochastic nature of a spray, a given volume flux measurement
may not provide a statistically resolved value of spray flux. To ensure statistical
resolution, a minimum number of drops must be collected in each sample. It is
accepted that a large sample size of 10,000 collected drops provides a well resolved
measurement. A minimum volume flux may then be established by using the volume
of that number of drops.
For the current experimental configuration, the minimum measurable flux was
limited by the statistical volume requirement rather than the ability to measure
small changes in height. One complication with this method requires the knowledge
of the droplet sizes to determine the volume of the sample collected. The spray in
the current experiment has a measured volume median diameter, dv50, of 0.55 mm
using the 4S. By using a drop diameter of 1 mm for the calculations, the statisti-
cally determined volume will provide a conservative value for the minimum flux by
overestimating the volume of each drop. Using the 1 mm drop diameter, the collec-
tion area of 0.002 m2, and test duration of 10 minutes, the minimum statistically
significant flux is 0.25 mm/min. Any data measured lower than this threshold are
not considered to be reliable in terms of a time average measurement.
Based on the fluxes expected in a given measurement, the experimental pa-
rameters in Eq. (4.1) can be controlled by the experimenter to fine tune the con-
figuration. For example, given a statistically large number of drops, the minimum
measurable flux can be lowered to a more precise value by increasing the test dura-
tion or decreasing the cross sectional area of the tube. By placing a funnel on top
41
of a smaller cylinder, the collection area can remain the same while improving the
response of the pressure transducer by increasing the accumulated height within the
cylinder.
4.3 Floor Volume Flux Measurement Results
4.3.1 Single Sprinkler
Volume flux measurements at the floor were taken for a single sprinkler (sprin-
kler #1) located in the corner of the array facility, with results plotted in Fig. 4.3.
In this case, the data set consists of 1296 measurements on a uniform 0.1 m×0.1 m
grid with the sprinkler located at (x, y) location (0, 0) as indicated by the identifier
in Fig. 4.3. Funnel caps with diameter 0.1 m were placed on the collection tubes
to reduce the resolution and the number of measurement sets to complete the full
spatial map. Figure 4.3 depicts the measured dispersion volume flux of D3 sprinkler
#1 at 1.35 bar from a height of 1.5 m. Placing the sprinkler in the corner allowed for
the total throw radius of the spray to be measured with a mean of 3 m, indicated by
the white contour line at a measured flux of 0.2 mm/min. Additionally, because the
total throw was captured, a mass conservation check was possible. The integrated
flow to the quadrant totaled 26.6% of the total flow rate. While a 25% fraction
would be expected based on the 1/4 coverage area collected, this slightly increased
value agrees well with the 25.9% measured in the corresponding section of the initial
spray measured with the 4S. This indicates that the initial spray itself is not equally
42
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
Location (m)
Lo
ca
tio
n
(m)
���������
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Location, x (m)
Lo
ca
tio
n,
y
(m)
Fl
oo
r V
ol
um
e 
Fl
ux
 (m
m
/m
in
)
0
2
4
6
7
≥8
1
3
5
Figure 4.3: Volume flux of a single sprinkler (#1) was measured on a
0.1 m grid at 1296 locations on the floor 1.5 m below the sprinkler. The
edge of the spray is indicated by the white outline.
distributed around the sphere, agreeing with the spatial variations seen in the initial
spray measurements. The combined measurement of the initial spray (Ch. 2) and
the volume flux at the floor capturing the full extent of the spray provides a useful
validation data set for quiescent spray modeling before introducing the increased
complexity and computational expense of multiple sprinklers.
43
4.3.2 Sprinkler Array
Volume flux measurements on the floor from the simultaneous full array of four
fire spray nozzles is shown in Fig. 4.4, consisting of 2970 measurement locations. The
individual sprinklers are also identified in the figure, along with the orientation of
the frame arms along the y-axis. Non-uniformities in the dispersion are evident by
the radial finger-like structures from the centerline of each sprinkler that appear
to correlate with the specific deflector geometry and frame arms. Note the same
features exist in the initial spray volume flux measurements in Fig. 2.4 due to the
slots and tines of the deflector geometry. Another notable non-uniformity is the
spray shadow caused by the frame arms along the vertical borders of the domain,
indicated by the blue areas with low volume flux.
44
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Location (m)
Lo
ca
tio
n
(m)
���������
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Location, x (m)
Lo
ca
tio
n,
y
(m)
Fl
oo
r V
ol
um
e 
Fl
ux
 (m
m
/m
in
)
0
2
4
6
7
≥8
1
3
5
12
3 4
Figure 4.4: Volume flux of the four-sprinkler array was measured on a
0.05 m grid at 2970 locations on the floor, 1.5 m below the deflectors at
a pressure of 1.35 bar. Sprinkler locations and orientations are identified
in each corner.
4.3.3 Nonuniformity
Measurements of the quiescent spray dispersion identify the non-uniformity
of the sprinkler spray. Radial patterns in the spray distribution can be identi-
fied and are similar to the geometry of the sprinkler deflector. Histograms of the
volume flux distribution are shown in Fig. 4.5, showing a wide range of water dis-
tribution amounts. In the array configuration, the average density of 5.9 mm/min
compares favorably with the overall value determined from the flow rate divided
45
by the protected area of 5.6 mm/min, or approximately 0.14 gpm/ft2. This value
also compares well to the design density for Ordinary Hazard (Group 1) occupancy
conditions stipulated in the NFPA 13 density/area curve [3].
0 2 4 6 8 10 12
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Volume Flux, V


'' (mm/min)
P
ro
ba
bi
lit
y
D
en
si
ty
(mm
/min)
-1
0.0
0.2
0.4
0.6
0.8
1.0
C
um
ul
at
iv
e
D
is
tri
bu
tio
n
0 2 4 6 8 10 12
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Volume Flux, V


'' (mm/min)
P
ro
ba
bi
lit
y
D
en
si
ty
(mm
/min)
-1
0.0
0.2
0.4
0.6
0.8
1.0
C
um
ul
at
iv
e
D
is
tri
bu
tio
n
(a) (b)
Figure 4.5: Histograms of the spray dispersion volume flux at a height
of 1.5 m for (a) single sprinkler, and (b) sprinkler array configurations
over the entire measurement area.
4.4 Resolution Analysis
4.4.1 Analysis Method
The slot/tine geometry of the typical fire sprinkler deflector is used on many of
the sprinklers manufactured today. Both visual observation and detailed measure-
ments of the initial spray with the 4S reveal a strong dependence on the deflector
geometry in the spray pattern produced. Figure 4.6 shows a photograph of the
D3 sprinkler deflector and the influence of deflector geometry on the initial sheet
46
Figure 4.6: The initial spray of the D3 sprinkler shows dependence on
the deflector geometry. Sheet formation from the slots and tines of the
deflector can be clearly seen.
formation; distinct sheets can be seen corresponding to the slots and tines. Mea-
surements of the sprinkler array show strong spatial variations in far-field volume
flux as well, corresponding to the variations seen in the initial spray. While the
spatial distribution of volume flux is an important measurement for model valida-
tion, additional insight can be found from the results. Quantification of the spatial
variations, as well as the spatial resolution required in measurements, is established
with the following analysis.
Current industry standard approval tests, such as those published by Under-
writers Laboratories and FM Approvals [7–9], recognize that non-uniformities exist
within the spray and may negatively impact suppression performance. These tests
are similar to the current procedure, however large 0.3 m (1 ft) sided square col-
47
lection bins cover the floor. For approval, a limited number of collection bins are
permitted below a certain critical flux. However, these tests do not account for the
resolution with which the flux measurements are evaluated. Error relative to the
true spray pattern will be introduced if the measurement resolution is inadequate;
as collection devices increase in area, the true variations in the spray pattern will
be averaged out and the measurement may suggest that the spray is more uniform
than it really is.
Resolution error was quantified by evaluating local differences in volume flux
between the measured high-resolution data set and several low-resolution data sets
constructed by averaging neighboring data points. These constructed data sets
represent the spatial averaging that would occur if the collection cylinders were
of a larger area. Figure 4.7 illustrates the procedure used for the development of
low-resolution data sets. First the neighboring data points are binned together and
averaged. This new reduced data set is interpolated to get a continuous function
over the entire domain. Finally, the interpolated data set is evaluated at all of
the original measurement locations to provide a data set with the same number of
points as if the spatially averaged data set were collected with larger devices and
interpolated between points.
The characteristic grid cell size, dx, describes the coarseness of the spatial
grid. The error associated with the spatial averaging was determined by comparing
the interpolated low-resolution data sets to the high-resolution reference case. The
48
HRi LRiinterpolate
bin sample
dxz }| {
Figure 4.7: Neighboring grid points were averaged together to con-
struct low-resolution data sets of the volume flux measurement. The
low-resolution data was interpolated and then sampled at the original
measurement locations to evaluate the errors introduced by insufficient
spatial resolution.
error, , was calculated with a normalized standard deviation by
 =
[∑N
i=1(HRi − LRi)2∑N
i=1HR
2
i
]1/2
(4.2)
where HRi is the individual high-resolution measurement at each location i, and
LRi is the value of the low-resolution data at each measurement location, and N is
the total number of measurement locations.
It is also recognized that a measurement repeatability error is present due
to variables including positioning of the collection tubes, water supply pressure
variations, temperature, room airflow, or other variations in spray pattern from
day-to-day. Rigorous alignment and flow control procedures were implemented to
reduce the effects of such variables. Alignment of the sprinklers was achieved by
attaching a long metal rod to the sprinkler to check that the frame arms were
installed according to Fig. 2.2 and Fig 4.4. The linear collection array was aligned
with measured markings on the floor and walls, and verified using the line emitted
49
from a laser level directed along the length of the array.
Resolution is determined by the number of measured points in a length scale
of interest, not explicitly by the spacing of the points. Therefore, resolution must be
discussed relative to a characteristic length rather than in terms of absolute length.
For a sprinkler spray, one characteristic length scale is the spray reach, R, or radial
distance from the sprinkler head that encompasses all of the wetted area. The
simplest estimation of spray reach, R, assumes the drops follow projectile behavior
with no drag [13,43],
R = (v0)r
(
2h
g
)1/2
(4.3)
where (v0)r is the initial radial velocity, h is the height of the sprinkler from the floor,
and g is gravitational acceleration. This model, while simple, may significantly over
predict the spray reach by omitting drag and viscous influences. The initial radial
velocity of drops is measured at velocities above 12 m/s, leading to reach predictions
of more than 6 m. A more accurate calculation of the spray reach would be a
numerical solution of the differential equation for droplet momentum, incorporating
the effects of drag. The most accurate method, used in the current analysis, is
the direct measurement of spray reach by measurement of the spray pattern and
determination of the wetted area.
Of more specific concern to regulatory testing bodies is the accurate identi-
fication of the low-flux areas of the far-field spray [7]. These low-flux areas are
associated with insufficient wetting, the primary suppression mode used in sprinkler
protection. These ‘dry’ regions are identified through a threshold criterion applied
50
to the volume flux measurement, and can be quantified by simply counting the num-
ber of discrete bins with insufficient volume flux. However, if the collection bin area
is too large, errors caused by the discretization will contaminate the evaluation of
the low flux regions, suggesting that the sprinkler provides better coverage than it
does. These errors can be reduced with better bin resolution or through a simple
interpolation scheme.
4.4.2 Resolution Results
Resolution of the spatial dispersion measurements was evaluated using the
method described in Sec. 4.4.1. Two metrics of resolution were explored, one looking
at the total error associated with decreased resolution, and one looking at the error
associated with resolving low flux areas as related to standard acceptance tests in
the sprinkler industry.
Results of the binning method for simulating the spatial averaging effect of
larger collection cylinders is shown in Fig. 4.8, showing how the decrease in resolu-
tion removes spatial variation compared to the true spray pattern measured at a
0.05 m grid resolution (Fig.4.8a and previously in Fig. 4.4). Each successive plot in
Fig. 4.8 corresponds to a nominal doubling of the spatial averaging size. Through
this binning, spray details are smoothed out, gradients are obscured, and the ex-
tremes of flux measurement are lost. This effect is evident in the 0.20 m bins in
Fig. 4.8c, where only the large scale trends are resolved. At this resolution the ex-
tent of the low flux regions, identified as locations with volume flux less than one
51
���������
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Location, x (m)
Lo
ca
tio
n,
y
(m)
Fl
oo
r V
ol
um
e 
Fl
ux
 (m
m
/m
in
)
0
2
4
6
7
≥8
1
3
5
(a) (b) (c)
(d) (e) (f)
Figure 4.8: Spatial averaging of the data indicates the effect of collection
tube size and resolution to capture the variations in the spray distribu-
tion. The contour lines outline the areas identified as dry spots for each
of the collection bin sizes. Grid sizes shown are (a) 0.05 m, (b) 0.10 m,
(c) 0.20 m, (d) 0.45 m, (e) 0.90 m, (f) 1.35 m.
standard deviation below the mean volume flux, are misrepresented. Minimal in-
formation about spatial gradients is present after bin size exceeds 0.20 m, and the
results in Fig. 4.4f essentially only reports the overall mean flux with no spatial
information.
Analysis of the binned and spatially averaged data provides insight to an
adequate resolution for an accurate depiction of the spray dispersion. The solid
line in Fig. 4.9 illustrates how the spatial averaging caused by increased collection
cylinder size produces an error compared to the highest resolution measurement
52
at dx=0.05 m, defined by Eq. (4.2). Typical of many measurements, as the res-
olution increases repeatability is sacrificed. Several sources of repeatability error
are present in the current measurement, including test-to-test variations in pressure
control, water temperature, and collection tube positioning and leveling. As the
resolution increases toward the high resolution measurement (left on the x-axis),
the repeatability error increases, shown by the dashed line in Fig. 4.9. Repeatability
error improves from 7.5% at the highest resolution to 1.5% for the lowest resolution.
As the spatial detail of the measurement is reduced, local mean flux may be more
accurately measured. A comparison between the two errors highlights the compro-
mise between spatial resolution and measurement repeatability. Assuming the two
error types are non-additive, the lowest total error occurs at the near-intersection of
the lines at dx/R = 0.04, where the error from both resolution and repeatability are
low and of comparable magnitude. To the left of this intersection point the mea-
surement is of a high resolution but introduces increased repeatability error. To the
right, at low resolutions, the improved repeatability comes at a significant increase
in resolution errors, providing a good measurement of spatially filtered flux, which
has limited utility. Further discussion of repeatability and resolution error on local
volume flux measurements is provided after the following discussion of resolution
errors on the integral measurement of low flux area.
Resolution errors in the integral measurement of the low flux areas become ap-
parent from simply totaling the number of low flux bins. Areas outlined in Fig. 4.8
indicate low flux areas, in this case defined as areas with flux below 3.9 mm/min, cor-
53
  
   
 
0.01 0.1 1
0.01
0.1
0.5
Collection Resolution, dx/R
R
es
ol
ut
io
n
an
d
R
ep
ea
ta
bi
lty
E
rr
or
,ϵ
Figure 4.9: Two descriptions of error, , are plotted to show relative im-
portance of resolution and repeatability at different grid sizes. The solid
curve plots error due to resolution of the flux measurements comparing
the coarse spatially averaged data to the high resolution base case mea-
sured at dx/R = 0.016. The dashed line indicates the repeatability of
the measurement at each resolution.
responding to one standard deviation below the mean. Errors are introduced as the
resolution decreases, and the accurate representation of these areas is diminished.
The identification of low flux regions is less accurate at low resolutions because the
bins are too large to resolve the variations in the spray pattern. This type of reso-
lution is important in applications such as acceptance testing, where determination
of the area supplied with a low flux is important for a passing mark. For each grid
resolution, the corresponding fraction of the measurement area with volume flux
below a set threshold was calculated, with the results plotted in Fig. 4.10. The solid
symbols correspond to a low flux threshold 25% below the mean volume flux, while
the open symbols correspond to a threshold one standard deviation (31%) below
54
    

  
0.01 0.1 1
0.00
0.05
0.10
0.15
0.20
0.25
Collection Resolution, dx/R
Lo
w
Fl
ux
A
re
a
Fr
ac
tio
n
Figure 4.10: Low flux area calculation also suggests a resolution of
dx/R=0.04 to resolve 90% of the low flux area.
the mean volume flux. Scatter in the trends indicates errors associated with the bin
discretization, and contributes to additional error in resolving the low flux area. The
smooth lines in Fig. 6 show how an interpolation of the binned volume flux alleviates
discretization errors and improves the resolution of the low flux area. Figure 4.10
shows the resulting areas for two different thresholds, 25% of mean flux (solid) and
31% of mean flux (dashed). The gray lines indicate the measurement resolution re-
solving 90% of the low flux area determined using the high resolution measurement.
In both cases, the critical resolution again lies at approximately dx/R = 0.04.
The results in Fig. 4.9 show that the resolution errors are comparable to the
repeatability error and less than 10% at a resolution of dx/R = 0.04, or at least 25
55
measurements across the spray reach. At dx/R = 0.04, the repeatability is slightly
improved from the best resolution (dx/R = 0.015), and the resolution error has not
increased beyond 10%, indicating a tolerable increase in error with reduction in mea-
surement resolution to this level. The corresponding binned volume flux measure-
ments for dx/R = 0.04 are highlighted in Fig. 4.8b along with the outlined low flux
area allowing visualization of spray pattern structures at this minimum suggested
resolution. Additionally, Fig. 4.10 reveals that the low flux area can be resolved to
within 90% of the best-resolved area at a resolution of dx/R = 0.04 indicated by the
gray lines. The qualitative visual agreement, coupled with quantitative estimates
of minimal error in local flux and integral low flux area measurement, suggest that
the measurement resolution criterion of dx/R < 0.04 is suitable to accurately re-
solve volume flux variations. While the spray reach, R, is used here to provide a
general framework for discussion of resolution, additional length scales such as de-
flector geometry may influence the gradients present in the dispersed spray. While
these other length scales may be present, R provides a readily accessible engineering
length scale a priori, and providing a reasonably general resolution criterion that
does not require an iterative measurement of the dispersed spray to refine the spatial
resolution.
4.5 Summary
A set of highly resolved volume flux measurements, from both a single sprin-
kler and from the four sprinkler array, were collected under quiescent conditions
56
to provide insight into the measurement of sprinkler spray pattern non-uniformities
and to support CFD model validation. The measured volume flux variations of the
initial spray (previously shown in Fig. 2.4) and the far-field dispersed spray near
the floor correlate with sprinkler geometry details (e.g., frame arm positioning and
slot/tine patterns). While measuring volume flux with large area collection bins
reduces the time required to characterize the spray, such a method hides the gradi-
ents in far-field spray volume flux and obscures low-flux areas (i.e., dry regions) that
may influence suppression efficacy. Analysis of the ultra-fine grid measurement data
provides guidance for the measurement resolution required to resolve spray pattern
details. Both qualitative visual inspection of the volume flux and a quantitative er-
ror assessment suggest that a resolution of dx/R = 0.04 is required, corresponding
to at least 25 data points across the spray reach. At this resolution, local error in
spray pattern is not dramatically influenced by the measurement grid size, compar-
isons of the integral low flux areas are favorable, and the resolution is compatible
with current CFD capabilities.
57
Chapter 5: Spray/Plume Interactions
While dispersion of the spray under quiescent conditions is interesting and can
provide insight to the potential of a sprinkler to deliver water to a given design area,
the ultimate goal for suppression is delivery of water in fire conditions. Under these
circumstances, the spray must compete with a buoyant upward plume generated
by the fire and still be able to deliver water to the burning fuel surface. It is this
interaction between the spray and the plume that is of interest for application to fire
suppression with fire sprinklers. Modifications were made to the SAF to investigate
these interactions including the addition of a forced-air jet providing a well-controlled
momentum source to challenge the spray. Detailed measurements of the spray within
the jet region were taken using a non-obtrusive optical shadowgraphy method.
Measurements of local spray-plume interactions within the plume region were
taken in four flow conditions with the intent of providing model validation data,
characteristics of the local spray field for further analysis, and physical insight into
the spray-plume interactions. The flow conditions included cases with close and far
sprinkler spacing, each with quiescent air and strong jet conditions. This chapter
describes the experiments conducted related to spray-plume interactions, as well as
the results and observations from spray measurements within the plume region.
58
5.1 Experimental Facility
5.1.1 Sprinkler Array
The existing sprinkler array facility, described in Sec. 4.1, was enhanced for the
spray-plume interaction study. A forced-air jet was added to the facility, a substitute
for a real fire plume, along with optical shadowgraph diagnostics to measure spray
characteristics within the plume region. Additionally, multiple sprinkler spacing
conditions were investigated to achieve different interaction conditions. Sprinkler
spacing is defined as the distance from the sprinkler to the plume centerline, indi-
cated by the distance ∆r. The modified facility is shown in Fig. 5.1.
The plume generator, with orientation and ducting visible in Fig. 5.1, was
located in the center of the array. This surrogate plume provided an upward jet of
forced air to challenge the spray, simulating the upward flow from a fire source while
providing repeatable boundary conditions for CFD input. The plume generator
provides ambient temperature airflow at a velocity up to 4 m/s from a 1.1 kW,
240 V three-phase centrifugal blower controlled with a variable-frequency drive. Air
was delivered from the blower via a 0.2 m diameter round flexible duct to the plume
exit through a 90◦ elbow with 0.2 m×0.2 m square cross-section. Due to lab space
restrictions, there was limited vertical space available to provide a lengthy flow
conditioning section after the elbow. Care was taken to ensure the flow from the duct
was uniform and did not show significant flow effects caused by the duct geometry.
To provide a uniform exit profile, the airflow was conditioned by passing through six
59
z = 0 m
1.5 m
3
4
1
2
optical
diagnostic plane
x
z
Figure 5.1: Drawing of the experimental facility showing the arrange-
ment of the sprinklers, the plume, the shadowgraphy system, and the
measurement region.
layers of 12 mm thick open-cell polyurethane foam with 20 pores per inch, supported
by a perforated rigid aluminum plate (40% open area). Additional pressure drop was
provided by a layer of stainless steel mesh (50×250 Mesh size) sandwiched between
the foam. The duct exit was positioned 1.5 m below the sprinklers. A wire-screen
cap prevented the foam from blowing out.
Due to the implementation of the shadowgraphy measurement, only two sprin-
klers could be operated at a time (#1 and #3), indicated by the darkened sprinkler
numbers in Fig. 5.1 and previously highlighted in Fig. 1.1b. The reason for the two
sprinkler approach is so that the drops pass perpendicularly through the camera
60
field-of-view, and also to prevent the LaVision system from physically blocking the
spray along the path to the measurement location. For the experiments using the
optical measurement, diagonal sprinklers #1 and #3 were operational, with the
same conditions as the quiescent dispersion measurements operating at 1.38 bar.
5.1.2 Plume Velocity Characteristics
Care was taken to ensure the plume characteristics were well-controlled and
repeatable for experiments and for model boundary conditions. A layer of fine mesh
screening and several layers of open-cell foam were used to provide a pressure drop
sufficient enough to remove major flow structures and imbalances due to the duct
geometry near the exit. The plume exit velocity was characterized using a hot-wire
anemometer positioned 2.5 cm above the opening of the plume. Figure 5.2 indicates
the limited spatial variation in plume velocity measured at 16 locations on a 5 cm
grid for two different fan speeds. For each flow velocity, the local maximum and
minimum measured velocities were within 15% of the mean velocity.
An additional velocity profile measured across the center of the duct exit is
shown in Fig. 5.3 with a mean of 3.7 m/s. Local velocity measurements fall within
12% of the mean velocity in this case, and show uniform top-hat characterization
across the width of the plume.
61
Figure 5.2: Air velocity was measured 2.5 cm above the outlet of the
ducting at locations on a 5 cm grid to evaluate the spatial uniformity of
the velocity profile. Shown are examples of the spatial velocity distribu-
tion at (a) 2.6 m/s (b) 3.7 m/s.




-0.15 -0.10 -0.05 0.00 0.05 0.10 0.150
1
2
3
4
5
6
x-Location (m)
V
el
oc
ity
(m/s)
Figure 5.3: Measured uniform velocity profile across center of plume
(y = 0 m) at 2.5 cm above opening exhibits variations within 12% of the
mean velocity.
62
5.2 Measurements and Diagnostics
Characterization of the spray-plume interaction was done using two measure-
ments, including mechanical measurement of volume flux to the plume surface and
optical shadowgraph measurements within the plume region. Physical collection of
water provided volume flux measurement at the surface of the plume for various
plume velocity conditions, while the optical measurements provided drop sizes and
velocities at locations throughout the plume region to map the interaction of the
spray and plume. Further analysis of the shadowgraph measurements provides an
additional measurement of volume flux that can be applied unobtrusively to loca-
tions within the spray. These measurements and diagnostics are discussed below.
5.2.1 Local Volume Flux
The successful suppression of a fire will depend largely on the volume flux de-
livered to the fuel surface, requiring penetration through the upward plume motion.
Local volume flux delivered to the plume surface was directly measured by physical
collection similar to the previous method in the quiescent case (Sec. 4.2). However,
rather than the collection tube array, a small collection device was used to avoid
disturbing the plume flow. A 42 mm diameter glass beaker was placed centrally
on the surface of the plume generator, obstructing less than 5% of the plume area.
Prior to exposure of the beaker to the spray, the plume air flow was set along with
the sprinkler flow rate. After the water flow from the sprinklers reached a steady
63
state at 1.38 bar, the plume and collection beaker were uncovered and exposed to
the spray for a period of time ranging from 1 to 5 minutes, adjusted according so
the cup did not overflow. The water collected in the beaker was measured with
an electronic mass balance, accurate to ±0.05 g. In this case, the volume flux is
determined by
V˙ ′′ = m/(ρwAot) (5.1)
where m is the mass of collected water, ρw is the density of water, Ao is the collection
opening area, and t is the collection time.
5.2.2 Shadowgraphy
A LaVision shadowgraphy system, including a synchronized laser and camera,
was used to conduct two-dimensional particle tracking velocimetry (PTV) measure-
ments within the plume region, highlighted in Fig. 5.1. The system consists of a
CCD camera aligned with a diffuser to provide a bright backlighting produced by
a diffused laser pulse. The laser/camera system was mounted on a vertical traverse
shown in Fig. 5.1, and could be positioned at different heights above the plume.
Measurements were taken at 5 elevations (z = 0.10, 0.42, 0.74, 1.06, and 1.38 m)
along the plume centerline as well as two additional profiles 0.1 m to the left and
right of the centerline.
Shadowgraphy PTV measurements use a quick diffuse laser backlight flash, ap-
proximately 1µs long, to freeze particles in an image. Two images are taken in rapid
succession separated by a known time delay, 100µs for these measurements. Indi-
64
vidual drops are located and matched between the two images using the LaVision’s
commercial software package, DaVis. Using a calibration from a scaling image, each
drops diameter is determined, and a velocity vector is calculated from the change
in position of the drop between the two images. Over a sufficiently large number of
image pairs, statistics for drop size and velocity distributions can be calculated for
any given location.
A LaVision Imager pro X CCD camera was used, fitted with a Nikon AF DC-
Nikkor 105 mm f /2D lens. A Nikon PK-13 27.5 mm extension ring was necessary to
obtain the proper focal distance to the plume centerline while filling the image frame
with the diffuse laser backlight. The camera lens and 56 mm diameter laser diffuser
were separated by 0.85 m, each located outside the plume influence. The resulting
circular field of view was approximately 26 mm in diameter and the depth of field
was approximately 25 mm, yielding a cylindrical measurement volume. With the
current lens configuration and separation distance, the 4-megapixel camera provided
resolution sufficient to measure drops as small as 0.08 mm in diameter.
The DaVis software package from LaVision was used to process the raw im-
ages and to calculate drop size and drop velocity. The software identifies drops by
searching for light intensity gradients produced by the shadows of drops. Settings
previously used for sprinkler drop measurements were used as a starting point for
the drop identification algorithm thresholds [44]. The software searches for each
identified drop in the second image of the pair to determine the velocity. A search
window around each drop is used to bound the matching area to avoid incorrect
65
matches. Due to the velocity differences between small and large drops, as well as
the multi-directional velocity field, multiple processing steps were required to opti-
mize particle matching between the two images. Significant measurement noise was
observed caused by incorrect particle matching and non-uniform light intensity near
the edge of the images. To reduce measurement noise, processing was performed
using three overlapping drop size ranges. Each image was processed three times,
identifying drops with diameters, d, within the ranges d < 0.4 mm, d > 0.4 mm and
0.25 < d < 0.55 mm. Any drops measured by multiple processing settings were iden-
tified and the duplicates removed from the combined dataset. Appendix C shows
the reduction in measurement scatter achieved by the multiple processing ranges.
A sample image pair is shown in Fig. 5.4; the first image is on the left, while the
second image is on the right. The yellow overlay on the second image shows the result
of the three-pass processing, with the identified drops and displacement vectors.
Additional filtering was required to ignore drops that were found outside a 20 mm
diameter reduced field of view. These drops on the edge of the image introduced
errors due to slight distortion or light intensity variations. The combination of field
of view reduction and multiple processing ranges successfully reduced the scatter
that was present in the initial measurements, and will be shown along with the
measurement results in Sec. 5.3.
66
Figure 5.4: Sample image pair shows identified drops and their velocity
vectors overlaid in yellow. The 20 mm diameter red circle indicates the
reduced field-of-view implemented for noise reduction.
5.2.3 Optical Volume Flux
In addition to the physical collection of water to measure volume flux, a vol-
ume flux was also determined using the optical measurements. Optically measured
volume flux, V˙ ′′o , is derived from the direct measurements of drop size and velocity
from the shadowgraphy results with the summation
V˙ ′′o = C
∑Nd
i=1
(
pid3i
6
vy,i
)
VONim
(5.2)
where d is drop diameter, vy is the downward velocity magnitude, VO is the optical
measurement volume, determined by the image depth-of-field and field-of-view, and
Nim is the number of image frames recorded. The summation is performed over all
drops moving in the downward direction. Upward moving drops are not included
67
in the calculation for downward volume flux. The shadowgraph technique does
not successfully identify all drops within an image, but instead only captures some
fraction of the overall spray. To calculate actual volume flux, a calibration factor, C,
was determined from equating mechanical measurements of the volume flux delivered
to the plume in each test configuration.
The uncalibrated optical flux (C = 1) can be corrected to provide a direct
comparison to the mechanically measured flux using physical collection devices by
accounting for the direction and location of drops within the image field of view.
Drops from the shadowgraph images that have a velocity vector such that they
would not land inside a physical collection cup were discarded, as they would arti-
ficially increase the measured flux. This correction has limited influence at the low
elevations in the plume because of the more vertical drop velocity vectors, however
at higher elevations, more drops are seen in the image that would not be collected
within a physical cup. While the overall optical flux using all drops is a valid cal-
culation, it is not a direct comparison to the mechanical measurements. Therefore,
the correction was used for direct experimental comparison and calibration of the
optically measured volume flux. Figure 5.5 shows the measured optical flux com-
pared to the mechanical measurement of volume flux at the same location. Using
the drop filtering based on trajectory to an imaginary collection cup, the two flux
measurements yield a linear relationship, and the correction factor, C = 1.18 for the
current configuration.
68
-----
--
------
| || |
| ||||||
● ●
●●●●
Optical Flux(Reduced FOV, Filtered)
y = 1.17756 x
R2 = 0.998591
SSR = 0.740916
0 5 10 15 20 25
0
5
10
15
20
25
Optical Flux
M
ec
ha
ni
ca
lF
lu
x
Figure 5.5: Optical flux calculated from the reduced field of view cali-
brated to physical flux measurements.
5.3 Shadowgraphy Results
Four spray conditions were measured for this study by combination of two
sprinkler spacings and two air jet velocities. The sprinklers were positioned at one
of two separation distances, ∆r, measured from the sprinkler to the jet centerline—a
close spacing case where ∆r = 0.65 m, and a far spacing case where ∆r = 1.87 m.
For each spacing configuration, measurements were taken with a quiescent condition
(vp = 0 m/s) and with a strong air jet (vp = 3.7 m/s).
The shadowgraph measurement directly determines drop sizes and velocity
vectors. The scatter plots of measured drop velocity vector components shown in
Fig. 5.6 provide an overview of the spray dynamics and spray-plume interactions
69
at 5 elevations along the jet centerline for the close spacing condition (sprinklers
positioned a spacing of ∆r = 0.65 m from the jet centerline). The quiescent and
vp = 3.7 m/s jet conditions are provided in Fig. 5.6a and Fig. 5.6b, respectively. The
positive x-direction is along the diagonal towards sprinkler #3 and the negative
x-direction towards sprinkler #1. Each data point represents the velocity of each
individual drop measurement realization from the thousands at each location.
At all optical measurement locations the drop velocity scatter plot forms an
inverted “V” shape. Each arm of the “V” corresponds to drops moving in distinct x-
velocity directions, with approximately half of the drops moving to the left and half
moving to the right due to the two different injection locations. In Fig. 5.6a, both
arms can be seen to extend radially from the origin of the plot. Drops along these
lines are all moving in the same direction, but with different velocity magnitudes
according to their initially stochastic drop size characteristics. The influence of the
location within the jet region is observed by the varying angles seen in the scatter
plots. At higher elevations within the jet, drops are traveling mostly in the x-
direction as gravity has not significantly altered the initial trajectory of the drops;
lower down in the jet region, drops have traveled on a different trajectory with a
significant vertical velocity component. In the quiescent case, all drops are moving
downward, however this is not the case when the spray is opposed with the air
jet. Figure 5.6b shows the case where the drops are driven by a strong plume with
velocity vp = 3.7 m/s. The drops in these cases show a shift in z-velocity for all
drops, with the larger and faster drops being slowed only slightly but still falling
70


 








 

 




 


 

 






 

 

 







 


 
 




 




 









 





















 




 



 





 

 







 






 
 
 








 





 

 




 




 



 





 


 


 
 




 

 











 


























 










 




 



 




 










 


 





 
 



 
 






 


 















 












 
 


























 























 








 
 


 














 

 






 



 











 








 








































 





 





















 




 














 

 
 








 










 

















































 


 





























 





 

















 







 





















 
 




















 
 



 

















 





 


 






 








 




















 































 
 




















 
































 










 
 

















































 


 

















 























 

 







 



























 



 

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-5
0
5
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X-velocity (m/s)
Z-ve
lo
ci
ty
(m/s)
(a) (b)
Figure 5.6: Plume-centerline drop velocity measurement results from the
close spacing case (∆r = 0.65 m) at 5 elevations in the plume (0.10 m,
0.42 m, 0.74 m, 1.06 m, 1.38 m, bottom to top). (a) quiescent, (b) vp =
3.7 m/s plume.
71
downward, while the smaller drops are reversed and blown upwards by the plume as
indicated by the data points above the x-axis. While the scatter is mostly symmetric
over the y-axis, slight asymmetry is observed, and is caused by local spray variations
that exist between the two sprinklers as observed in the initial spray measurements
discussed in Ch. 2.
At injection, all drops are moving at an approximately uniform velocity, ra-
dially away from the sprinkler [26]. After injection and initial drop formation, dif-
ferences in velocity magnitude can be attributed to varying drop size, where small
drops are preferentially slowed by air drag to approach their terminal velocity. The
length of the arms in Fig. 5.6 indicate differences in velocity, but does not explicitly
highlight the relationship of drop size and velocity. Figure 5.7 illustrates the influ-
ence drag has on small drops, causing the spread of velocity magnitude correlation,
in the quiescent condition, for the two spacing configurations. The red line indi-
cates the calculated terminal velocity, vt, for a given drop diameter determined by
iteratively solving the steady-state force balance on a drop, resulting in the relation
vt =
(
4ρddg
3ρaCD
)1/2
(5.3)
where ρd is the drop density, ρa is the air density, d is the drop diameter, g is the
gravitational acceleration, and CD is the Re dependent drag coefficient defined with
the correlation
CD =

24
Re
(
1 + Re
2/3
6
)
, Re < 1000
0.424, Re ≥ 1000
(5.4)
72
(a) (b)
●
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●
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●●
●
● ●● ●
●●●
●
● ●
●
●●●
●
●
●
●
●
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0.0 0.5 1.0 1.5 2.0
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Diameter (mm)
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el
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ag
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12
Diameter (mm)
V
el
oc
ity
M
ag
ni
tu
de
(m/s)
Figure 5.7: Drop diameter vs. velocity magnitude correlation in the qui-
escent case at z = 0.74 m. (a) close spacing (∆r = 0.65 m), (b) far
spacing (∆r = 1.87 m).
In the far spacing case, drops have had sufficient travel time and distance to
slow to near their terminal velocity (Fig. 5.7b) compared to the close spacing case
where drops are traveling significantly faster (Fig. 5.7a).
In addition to drop velocity correlations, an additional observation in Fig. 5.7
suggests a difference in drop size distributions measured in the different spacing
conditions. The near spacing condition results in a more complete range of drop
sizes, while the close spacing shows fewer overall drop measurements, and very few
drops with diameters less than 0.5 mm. In the far spacing, smaller drops influenced
by drag have already slowed in the radial direction of travel and do not reach the
plume centerline measurement location. Figure 5.8 shows the drop size distribution
cumulative volume fractions (CVF) at each measurement location on the plume
73
centerline for the quiescent no plume condition (left) and the plume condition with
vp = 3.7 m/s (right). Each plot contains the CVF for the close spacing (blue) and far
spacing (orange) configurations. The most noticeable result of the CVF comparison
is the rightward shift of drop distribution in the far spacing case compared to the
close spacing. Comparing the curves in the left column to the right (with the plume),
a less noticeable shift is observed where all of the smaller drops are driven higher in
the plume region. Each figure also highlights the number of drops measured in each
location.
The resulting changes in drop distribution can be compared using a normalized
volume fraction to show the shift in drop size and the re-distribution of the spray
volume within the plume region. A modified volume fraction is used to describe drop
size weighting of the local spray with respect to that at the base under quiescent
conditions for each spacing configuration. The normalized volume fraction, VF ∗, is
described by the equation
VF ∗(z, d) =
V˙ ′′CL(z, d)∫ (
V˙ ′′CL(z0, d)
)
Q
dd
(5.5)
where V˙ ′′CL(z, d) is the volume flux distribution as a function of drop size with diame-
ter d at a specific elevation z in the plume region. The denominator
∫ (
V˙ ′′CL(z0, d)
)
Q
dd
is the total volume flux measured in the quiescent condition at the base of the plume
at z0 = 0 m integrated over all drop sizes. This normalization reveals how the spray’s
local drop size distribution and overall volume flux may change (reflected in a non-
unity
∫
VF ∗(z, d)dd) when challenged by a plume.
74
(a) (b)
� = ���� � = ��
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ���
d��� = ���� d��� = ���
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ���
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ����
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ����
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ���
d��� = �� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ����
d��� = ��� d��� = ���
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ����� � = ����
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ���� � = ����
d��� = ���� d��� = ���
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
� = ���� � = ���
d��� = ���� d��� = ����
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
Figure 5.8: Drop size distribution at 5 elevations within the plume at 5
elevations (0.10 m, 0.42 m, 0.74 m, 1.06 m, 1.38 m, bottom to top). (a)
quiescent, (b) 3.7 m/s plume. (black: near, gray: far).
75
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
N
or
m
al
iz
ed
V
ol
um
e
Fr
ac
tio
n,
V
F*
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
N
or
m
al
iz
ed
V
ol
um
e
Fr
ac
tio
n,
V
F*
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
N
or
m
al
iz
ed
V
ol
um
e
Fr
ac
tio
n,
V
F*
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
N
or
m
al
iz
ed
V
ol
um
e
Fr
ac
tio
n,
V
F*
(a) (b)
(c) (d)
Figure 5.9: Normalized volume fraction probability density functions
comparing quiescent flux (blue) to flux delivered with a strong plume
(orange).
(a) close spacing, z = 1.38 m, (b) far spacing, z = 1.38 m,
(c) close spacing, z = 0.10 m, (d) far spacing, z = 0.10 m.
Figure 5.9 shows VF ∗ distributions at two heights for the close and far sprinkler
spacing. In each figure, quiescent and strong plume conditions are compared.
The first observations can be made in the close spacing cases on the left of
Figure 5.9 (a and c). Focusing on the quiescent condition drop size distribution
indicated with the blue curves, it is clear that there are significantly more small drops
at the base of the jet (Fig. 5.9c) compared to those at higher elevations (Fig. 5.9a).
When the spray is subject to the air jet, these small drops are rejected from the
76
low elevations, as seen by comparing the orange curve in Fig. 5.9c (representing the
jet condition distribution) with the blue curve (representing the quiescent condition
distribution). Essentially all small drops are rejected, as there is no volume fraction
of drops less than 0.5 mm. At the higher elevation, however, the volume fraction of
small drops has increased because the small drops are carried by (and in the direction
of) the jet flow, also reflected in Fig. 5.6b. Small drops having terminal velocity less
than the velocity of the jet will be turned away and cannot penetrate to the jet
surface. While these drops will not contribute to direct fuel surface cooling, they
may still contribute to ultimate suppression or mitigation through ceiling jet cooling
or redistribution to other surfaces, preventing fire spread, or improving tenability
within a compartment. In the far spacing case, on the right of Fig. 5.9 (b and d),
there is essentially no volume at the higher elevation location in the quiescent case
(Fig. 5.9b) because the measurement location is above the umbrella-shaped sprinkler
spray. However, in the jet challenge case also depicted in Fig. 5.9b, the volume is
non-negligible (orange curve) where a significant amount of spray has been redirected
upwards. The larger drops capable of reaching the more remote jet centerline in the
far spacing are also more capable of penetrating the jet (being driven by their own
momentum and less influenced by jet drag). This is reflected by the drop distribution
in the far spacing case remaining relatively unchanged compared to the quiescent
case for that condition.
Comparison of the drop distributions in the quiescent case (blue curves) be-
tween the close and far sprinkler spacings (left and right of Fig. 5.9) highlights the
77
natural drop filtering due to drag influence. A very small volume is carried to the
plume centerline by small drops for the far spacing, while at the close spacing nearly
50% of the volume fraction is delivered in drops smaller than 0.5 mm in diameter.
This drop size filtering due to drag effects is also demonstrated in Fig. 5.10
which depicts velocity vectors for characteristic drop sizes (determined by volume
fraction) at a select location (plume centerline at z = 0.42 m) in the close spacing
configuration. This depiction identifies drop size dependent behavior of velocity
measurements presented in Fig. 5.6. Each vector represents an equal fraction of
volume flux from each sprinkler according to increasing discrete drop size bins (dv05–
dv95) as described in the legend. The length of each vector corresponds to the mean
velocity of each drop size class (and corresponding equally weighted flow fraction).
Vectors for each sprinkler can be clearly identified by their respective x-directions
and correspond to 100% of the volume flux from each individual sprinkler. Figure
5.10a shows the quiescent case where all vectors are directed downward. The drag
influence of the smaller drops is shown by the shorter velocity vectors and the
orientation at an angle closer to vertical. Large drops maintain a larger velocity
magnitude and preserve more of their initial x-velocity outward from the sprinkler.
Figure 5.10b shows the same measurement but in the vp = 3.7 m/s case. Small drops
are influenced by the jet and have been re-directed upwards, while intermediate drop
vectors have been turned from their quiescent direction (maintaining x-velocity, with
significant reduction in z-velocity) but have not been completely overcome by the
jet. Large drops are slowed to a lesser extent, indicated by the warmer colored
78
��������� ���������
0 0
.2
0
.4
0
.6
0
.8
1
.0
dvX 10 20 30 40 50 60 70 80 900 100
1 m/s
x
z
(a) (b)
Figure 5.10: Volume flux vectors representing equal volume fractions for
the close spacing at z = 0.42 m on plume centerline. (a) vp = 0 m/s, (b)
vp = 3.7 m/s.
vectors (i.e. red) that maintain more of their quiescent direction.
The downward volume flux of the spray, particularly when opposed by a plume,
is a key quantity for predicting fire suppression. The spray must deliver enough vol-
ume to extract sufficient heat from the fuel to suppress the fire. This volume delivery
is further complicated when the spray must penetrate through an opposing plume to
the base of the plume surface. Measurements of volume flux were calculated using
the optical shadowgraph images at 5 elevations within the plume region. The results
are shown in Fig. 5.11 for each spacing configuration in the quiescent case and the
plume case. The shaded region indicates a flux ±15% from the optically measured
value. In each configuration, the optical flux is also compared to a mechanically
79
(a) (b)
●
●
●
●
●
●
●
●
●
⨯
⨯
⨯ ||
||
|
0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Volume Flux (mm/min)
E
le
va
tio
n
(m)
●
●
●
●
●
●
●
●
●
●
⨯
⨯
⨯ | |
| |
||
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Volume Flux (mm/min)
E
le
va
tio
n
(m)
Figure 5.11: Volume flux was measured optically along the plume cen-
terline at 5 elevations in the quiescent (black) and plume (gray) case.
The × symbols represent physically collected volume flux data points.
(a) near spacing, (b) far spacing.
measured flux, indicated by the × symbols. The mechanically measured flux results
provided very repeatable results, with measurement errors within ±6%, as indicated
by the error bars.
5.4 Summary
Spray-plume interactions and the ability of the spray to penetrate through the
plume govern the suppression effectiveness of fire sprinklers. Detailed measurements
of spray-plume interactions with multiple sprinkler and forced-air jet configurations
were performed using unobtrusive optical shadowgraphy. Measurements of drop
size, velocity, and volume flux show along vertical profiles in the plume region re-
veal complexities associated with drop transport under quiescent conditions, which
80
are only enhanced further when the spray interaction with an opposing jet is cap-
tured. The non-uniformity of sprinkler sprays means that small changes in location
can lead to significant changes in spray characteristics such as drop size distribution
and volume flux, which may have direct influence on penetration and suppression
performance. Additionally, the measurements provide data for CFD model valida-
tion along intermediate locations of spray dispersion computations.
81
Chapter 6: Plume Penetration
The predominant suppression mechanism of sprinkler sprays is the surface
cooling of the burning solid fuel. This is achieved when drops are able to penetrate
through the upward motion generated by the fire plume. Current protection de-
sign methods use a general quiescent design density (overall average volume flux)
delivered to a design area to determine system flow requirements with no direct
consideration given to the ability of the spray produced to penetrate to the surface.
Understanding the phenomena and physical scaling behind penetration can aid in
protection design evaluation and in potential technological development in sprin-
klers. While penetration will be correlated with suppression effectiveness, there are
additional factors to consider—100% penetration to the surface will not guaran-
tee suppression if the delivered volume flux is below the critical value required for
suppression. Additional suppression phenomena, such as gas cooling through drop
evaporation in a fire compartment, radiation attenuation, and surrounding surface
wetting are not accounted for in the penetration ratio metric. However, these effects
are beyond the scope of this analysis, and will work to improve the suppression ef-
fectiveness of a particular sprinkler if direct penetration to the burning surface can
be achieved.
82
This chapter presents measurements of penetration and a scaling analysis to
predict the degree of penetration depending on local spray properties. Penetration
of the spray to the surface of the plume was determined by measuring volume flux
from the SAF as a function of variable plume velocity. A majority of the measure-
ments were done with the two sprinkler configuration which provided local spray
details. Observation of suppression events and physical intuition suggests there
are two contributing mechanisms that may determine penetration effectiveness of a
spray [6,29]. Analysis of the trends observed from the current penetration measure-
ments considers two regimes of spray-plume interaction with different mechanisms
of penetration to identify scaling laws to predict the penetration. First, individual
drops are considered independently as they interact with the plume, and second,
consideration is given to the drag force interactions induced by the spray onto the
plume by the collection of all drops within the spray. The measurements of local
spray properties from the quiescent condition (no plume) measured in Ch. 5 includ-
ing drop size, velocity, and volume flux, were used to inform the scaling laws.
A scaling analysis in terms of quiescent spray characteristics is desirable as
prediction and measurement of such values is easier compared to the more com-
plex condition including spray-plume interactions. The quiescent spray condition
presents the total potential the spray has to penetrate or influence the plume dy-
namics. Recent advancements in model development show accurate prediction of
local spray characteristics [45]. Even simplified models, given the accurate initial
spray input (presented in Ch. 2), can accurately predict important local spray char-
83
acteristics in quiescent conditions. Development of scaling laws for prediction of
penetration performance of a given sprinkler would provide an engineering analysis
to determine protection system effectiveness.
Experiments measuring spray penetration to the plume surface were attempted
such that the two penetration mechanisms had different relative contributions (i.e.
dominated by individual drops or total drag force work applied to the plume). Table
6.1 highlights the general test conditions that were explored to measure the different
penetration regimes. Four different test conditions were achieved by leveraging two
different sprinkler spacing conditions (close and far spacings presented in Ch. 5) and
either two or four sprinklers operating in the array. In general, due to drag filtering,
the far spacing case provided larger drops with higher terminal velocities, while the
near spacing provided smaller drops. The number of sprinklers was used to control
the drag influence of the spray through variation of the volume flux. The plume
velocity was varied over a range of velocities in each of the test configurations. The
penetration regimes are described in Sec. 6.2.
Table 6.1: Test matrix of desired general spray-plume interaction conditions and
required facility configuration.
Penetration Regime Test Configuration
up/vt W/KE Spacing # Sprinklers
Low Low Far 2
Low High Far 4
High Low Close 2
High High Close 4
84
6.1 Plume Penetration Measurement Results
Measurements of volume flux delivered to the local plume surface were taken
as described in Sec. 5.2.1, using a small collection cup at the plume surface, under
the influence of a range of plume strengths to determine the penetration of the spray
through the plume. The degree of successful penetration can be quantified by a ratio
of measured volume flux in the quiescent no plume case to the actual delivered flux
when the plume is present,
PR =
V˙ ′′
V˙ ′′Q
(6.1)
indicating the fraction of water delivered to the target location relative to the max-
imum possible amount through a quiescent environment.
Measurements of plume penetration calculated according to Eq. (6.1) from the
two-sprinkler configuration are plotted in Fig. 6.1 as a function of the opposing air
jet strength. As the jet velocity increases the penetration ratio is reduced. This
result was expected when the jet velocity creates a condition where drops are no
longer able to penetrate to the plume surface and are turned around and redirected
by the stronger air jet. It is notable that the critical plume velocity for penetration
occurs at different values depending on the configuration and whether the sprinklers
are located close or far from the jet centerline. The vertical dashed lines indicate
a critical velocity for 50% penetration, and aligns closely to a critical point where
penetration ratio transitions rapidly. At first glance, results indicate that the spray
is better at penetrating if it is spaced far from the centerline. One may assuming
85
(a) (b)
0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
Plume Velocity (m/s)
P
en
et
ra
tio
n
R
at
io
0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
Plume Velocity (m/s)
P
en
et
ra
tio
n
R
at
io
Figure 6.1: Penetration ratio measurements for the two sprinkler con-
figuration with (a) close and (b) far spacing. The vertical dashed line
represents the jet velocity corresponding to a 50% penetration ratio and
a rapid transition in penetration ratio.
that the closer spacing has a more dense spray with higher spray velocities and
stronger momentum, but this result is counterintuitive. A look at the scaling for
plume penetration is presented in the following sections to identify the behavior of
the spray-plume interactions and to provide an engineering assessment of a given
spray condition, identifying the contributing factors for plume penetration.
6.2 Penetration Regime Introduction
In the first regime, spray penetration depends on the ability of individual drops
to maintain sufficient momentum on their own to avoid being turned away from the
competing gas flow [16]. This suggests that smaller drops, being more susceptible
86
to individual drag interactions, will be unable to penetrate to the fuel surface. In
the first regime, drops are considered individually to determine their penetration
ability. In this case it is assumed that the drops are relatively large and the spray
is relatively sparse so there is not a significant impact on the plume dynamics, as
indicated by the cartoon in Fig. 6.2a, where the plume velocity is unchanged by
the spray. This is considered the individual action regime, conventionally termed
as one-way coupled to the gas phase, where the spray is dominated by individual
drag interactions. In this regime, a critical scaling factor using the drop terminal
velocity is explored, where only drops with supercritical terminal velocities penetrate
the plume. Smaller drops may still be able to penetrate depending on the specific
velocity vector and plume entry location, but are largely redirected by the opposing
gas flow such that they do not land at the targeted location and do not significantly
contribute to suppression.
However, sprays with drops that are relatively small compared to the plume
velocity and the drag induced by the gas flow are often used with successful sup-
pression, suggesting there is a second regime of spray-plume interaction. Examples
of such events include water mist spray nozzles or the suppression of large fires with
significant buoyancy induced flows, often a challenge in storage applications. In
the second regime, penetration is influenced by the spray as an ensemble, where
a significant drop number density and/or velocity causes the plume dynamics to
change [30,31], allowing drops that would otherwise be redirected if they were pene-
trating alone to penetrate the plume and reach the surface [6,24]. This is represented
87
Individual Action
Local plume 
volume Vdrop
Uplume
Group Action
Figure 6.2: Two regimes of penetration dynamics are considered; in-
dividual action and group action regimes. The interaction regime is
characterized by the influence the drops have on the dynamics of the
gas-phase plume.
in Fig. 6.2b by the increased number of smaller drops, and a change in the plume
velocity induced by the drag force of the spray as a group. In this regime, it is
proposed that the accumulated work effects of the spray, due to the drag imparted
on the plume, relative to the characteristic kinetic energy of the plume is a critical
penetration scaling parameter. An analytical framework to identify scaling param-
eters for plume penetration of a certain spray is detailed in the following sections,
considering the two behaviors.
6.3 Individual Action Regime
6.3.1 Terminal Velocity Scaling Analysis
At the most basic level of penetration, a drop must maintain a net downward
velocity throughout its trajectory. In the individual action regime, drops are consid-
88
ered independent of one another and with one-way coupling to the gas phase through
drag interactions, meaning the gas velocity is unchanged. In the limiting case, all
drops will reach a terminal velocity as they are influenced by drag. If the terminal
velocity is sufficiently large to maintain a net downward velocity in the presence of
the plume motion, it is possible for the drop to penetrate the plume. Therefore,
a critical scale for an individual drop to penetrate an opposing plume may be the
drop’s terminal velocity. Drops that have subcritical terminal velocities cannot be
guaranteed to penetrate. Unless trajectory conditions are favorable, the subcritical
drop will be redirected away from the target, and there will be no suppression from
these smaller drops.
Penetration analysis in this regime considers the forces acting on a drop falling
through the air. A free body diagram is shown in Fig. 6.3 including the gravitational
body force, FG, acting downward and the drag force, FD, acting opposite the relative
velocity vector shown by the kinetic diagram. If the drag force is not strong enough
to reverse the direction of motion, the drop is unstoppable and is therefore considered
to penetrate the plume. The critical force condition is determined using the force
balance between the gravitational and drag forces. Beginning with Newton’s second
law,
ΣF = ma = m
dv
dt
(6.2)
and substituting in the equations for drag and gravitational forces
m
dv
dt
=
1
2
CDρaAd|u− v|(u− v) +mg (6.3)
89
Figure 6.3: Free-body and kinetic diagrams of a single drop traveling
through air includes gravitational body force and a drag force.
where m is the mass of the drop, CD is the drag coefficient, ρa is the air density,
Ad is the frontal area of the drop, u is the air velocity vector, v is the drop velocity
vector, and g is the gravitational acceleration vector.
For the remainder of the single drop analysis only velocity in the vertical z-
direction is considered, which is a reasonable simplification when discussing both
terminal velocity and vertical plume penetration. In this case, the falling drop
motion directly opposes the upward air velocity. To determine the critical drag force
that a drop is able to resist without stopping or reversing direction, the vertical
component of Eq. (6.3) is set to a zero acceleration and after simplification, the
relationship of the velocity difference is found to be
uz − vz =
(
4ρddg
3ρaCD
)1/2
(6.4)
where uz is the magnitude of the upward plume velocity and vz is the magnitude
of the downward drop velocity. Recall the equivalent Eq. (5.3), which now shows
90
that the terminal velocity is the relative velocity between the drop and the air,
vterm = uz − vz. For penetration the drop must maintain a net downward velocity,
vz > 0. This critical condition is found when vterm > uz. If the plume velocity is
less than the opposing drop terminal velocity, it is not possible for the drop to be
stopped or reversed, and the drop cannot be rejected from the plume.
The spray can be considered in terms of individual drop penetration through
a measured (or predicted) drop size distribution. The cumulative volume fraction,
CVF(d), quantifies the fraction of the measured spray that is contained in drop
sizes smaller than a given diameter. The complement of this value, 1 − CVF(d),
determines the fraction of the spray volume that is greater than a given size, or
corresponding critical terminal velocity. Thus, it is proposed that the penetration
can be scaled according to the equation
PR(uz) ∼ [1− CVF(vterm = uz)] (6.5)
where the CVF(vterm) is the CVF in terms of a local drop terminal velocity dis-
tribution, evaluated at the critical terminal velocity equal to the competing plume
velocity.
6.3.2 Terminal Velocity Scaling Results and Discussion
Penetration through the plume will depend on local spray characteristics. Non-
uniformities stemming from the formation of the spray will influence the specific
characteristics of the interaction depending on the target location relative to the
91
(a) (b)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
V
F
0 1 2 3 4 5 6 7 8
0.0
0.2
0.4
0.6
0.8
1.0
Terminal Velocity (m/s)
C
V
F
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Diameter (mm)
V
F
0 1 2 3 4 5 6 7 8
0.0
0.2
0.4
0.6
0.8
1.0
Terminal Velocity (m/s)
C
V
F
Figure 6.4: Local drop size distributions of the (a) close spacing and (b)
far spacing configuration, along with corresponding terminal velocity
(upper axis) measured at z = 0.1 m. Lines represent the PDF (dashed),
CVF (solid), and dv50 (red).
sprinkler. As identified in the proposed scaling, the local drop size distribution is
important for the terminal velocity analysis. Drop size distributions were calculated
for each of the sprinkler spacing configurations in the quiescent no plume condition,
measured at a location 10 cm above the base of the plume, and are plotted in Fig. 6.4,
characterizing the drops that were delivered to the plume target location. Drops
higher in the plume region pass through the plume, but are not on a trajectory to
reach the target at the plume.
The probability density of each drop size is plotted by the gray dashed line
(values read to left), while the cumulative volume fraction is plotted by the black
92
line (values read to right), indicating the fraction of the spray volume with drop
diameters less than a given size. The characteristic volume median drop size, dv50,
is identified by the red leading lines where the CVF reaches 0.5. The terminal
velocity corresponding to the given drop diameter is indicated on the upper x-axis.
Due to the location of the plume within the spray, a significant difference is observed
in the local drop size distributions and associated drop terminal velocities. In the
far spacing configuration, the distribution has shifted to the right, where there are
essentially no drops smaller than 0.5 mm. In the near spacing case, more than 50%
of the spray is contained in drops smaller than 0.5 mm. These differences in drop
size will directly influence the penetration behavior based on the terminal velocity
criterion.
Results of the penetration measurements and the scaling prediction of Eq. (6.5)
using the measured drop size distributions are presented in Fig. 6.5 as a function of
plume velocity. The plume velocity is presented as a ratio with a characteristic spray
velocity, vt50, the terminal velocity of the local dv50 drop size. This permits com-
parison between spacing configurations based on the terminal velocity criterion for
penetration that vt/vp > 1. Low plume velocities appear to the left of the plot with
high penetration. Penetration reduces to the right as the plume velocity increases.
Experimental results are shown by the black points, while the scaling prediction
Eq. (6.5) is shown by the lines. As the plume velocity exceeds the characteristic
terminal velocity at a ratio of 1, a steep reduction in penetration is observed. The
details of the drop size distributions accurately predict the shape of the experimen-
93
(a) (b)
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
vp /vt50
P
en
et
ra
tio
n
[1-C
V
F(v p
/v t50
)]
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
vp /vt50
P
en
et
ra
tio
n
[1-C
V
F(v p
/v t50
)]
Figure 6.5: Measurements of penetration (points), and predictions based
on measured local drop size distributions using terminal velocity scaling
law (lines) in the close (a) and far (b) spacing configurations.
tal results, including the extended tail observed in the near spacing case due to the
wider drop size distribution.
Predictions from the terminal velocity scaling may show a conservative es-
timate, particularly in the close spacing case where drops are often still traveling
faster than their terminal velocity, as shown in Fig. 5.7a. Smaller drops that enter
the plume region at the base of the plume and have a short residence time may
not be reversed by the plume prior to reaching the surface, contributing more pen-
etration than predicted by the scaling alone, resulting in experimental data points
above the predicted line. Any influence of group spray drag interactions will also
increase the actual penetration compared to the terminal velocity scaling, and will
be discussed later.
94
The results indicate that the reason the far spacing case initially appears to be
a better suppression condition (on the basis of penetration ratio) in Fig. 6.1 is due to
the spray characteristics at the interaction location. The larger dv50 drop diameter
at the far spray radius indicates that, overall, the individual drops will resist the
opposing drag forces better and maintain more momentum than the smaller drops
that are found closer to the centerline of the sprinkler. This result suggests that a
solution to the penetration problem is just to use larger drops throughout, which
has been recommended before and is a desired characteristic of large orifice and
large drop sprinklers. One of the largest orifice sprinklers today is an ESFR type
sprinkler with k-factor 363 LPM/bar1/2 (25.2 gpm/psi1/2). Based on the minimal
operating pressure of 0.5 bar stipulated by NFPA 13 [3] and the dv50 drop size
correlation [20], the largest expected volume median drop size is estimated to be
approximately 2.4 mm, with a terminal velocity of 8 m/s. While this is significantly
larger than the terminal velocity of the current tested Tyco D3 sprinkler, it is still
less than maximum plume velocities in excess of 10 m/s observed in high-challenge
storage fires [27, 46]. An additional consideration for a maximum drop size is
that drops exceeding a critical diameter will breakup a second time into smaller
drops when surface tension forces cannot resist the inertial forces due to the motion.
This is described by the drop Weber number, We = ρav
2d/σ, where ρa is the air
density, v is the relative velocity of the drop and air, d is the drop diameter, and
σ is the water surface tension. The breakup limit is generally observed when We
exceeds 12 [47]. Combining the terminal velocity equation and the critical We ≈ 12
95
0 1 2 3 4 5
0
2
4
6
8
10
12
Diameter (mm)
Te
rm
in
al
V
el
oc
ity
(m/s)
Figure 6.6: Terminal velocity versus drop diameter.
condition yields a maximum drop diameter of 5 mm. This provides a generous
upper limit as the injection velocity is generally much greater than the terminal
velocity, and therefore secondary breakup would occur at a smaller drop size. An
additional consideration of the ESFR type sprinkler is the central spray core that is
generated directly beneath the sprinkler, acts more as a jet stream of water rather
than a spray of drops. This will provide locally enhanced penetration, however if
the main target for suppression is off-axis, the drops and spray dispersion will be the
more important factor for suppression. The increased drop size approach reaches
impractical limitations and leads to the second interaction regime, which leverages
smaller drop sizes.
96
6.4 Group Interaction Regime
6.4.1 Spray Work Scaling Analysis
An additional consideration for scaling penetration of the spray through the
plume, particularly for the near spacing case, is the accumulated influence of the
spray as a whole. As previously described, the group action regime is considered
when the spray produces a significant drag force on the plume, causing the plume
dynamics to change. In this case, drops are no longer considered on an individual
basis because the one-way coupled relationship between the drops and gas phase no
longer accurately reflects the plume interaction dynamics and the drop trajectory
behavior. In the group interaction regime, it is possible for smaller drops with
subcritical terminal velocities to penetrate the plume and reach the target surface;
such drops would be overcome by the plume and be redirected if considered in
the individual action regime. Several previous studies indicate these small drop
interactions have an impact on penetration, identifying a characteristic global value
for either spray momentum [6,24] or drag imparted by the spray on the plume [30].
This characteristic momentum or force acting on the plume causes a change in the
plume dynamics, allowing the spray to penetrate. While these previous studies
investigated the relationship between a characteristic value, the current approach
considers the distance over which the spray and plume interact. The drag force
experienced by the drops is also acting in the opposite direction against the motion
of the plume, reducing the kinetic energy within the plume. It is proposed that the
97
ability of the spray to influence the plume dynamics through a reduction in plume
kinetic energy corresponds to the ability of spray to penetrate a weakened plume.
To evaluate the influence of the spray on the plume dynamics, an energy
balance is considered around a control volume of the plume, selecting only the gas
phase, shown in Fig. 6.7. The spray in this area is considered for the amount of
work the drag forces from the drops will impart onto the gas phase. The analysis
is considered in the vertical direction. The first law of thermodynamics states that
the rate of change of energy within the control volume, dE/dt, as the relation
dE
dt
= Q˙net − W˙net (6.6)
where dE/dt represents the rate of change of energy within the control volume,
consisting of internal, kinetic, and potential energies, Q˙net represents the rate of
heat added to the control volume, and W˙net is the rate of work done by the control
volume.
Recognizing the dE/dt term to be d(met)/dt, where m is the mass within the
control volume and et is the total energy per unit mass, the derivative term can be
expanded to (
et
dm
dt
+m
det
dt
)
= Q˙net − W˙net (6.7)
Continuing with the assumption that the mass flow from the plume is steady
in time and is conserved into and out of the control volume, and there is no heat
gained or lost by the plume system due to its interaction with the spray, the dm/dt
98
fd
dz
m˙
A1
A2
m˙
Figure 6.7: Control volume of plume containing only the gas phase,
enclosing the full area of the plume cross section and a differential height,
dz. The spray is treated as an obstruction to the flow within the volume
and imposes a downward force on the flow.
and Q˙net terms can be removed, leaving
m
det
dt
= −W˙net (6.8)
The time derivative can be converted to a position derivative using the relation
of dz = u(z)dt, yielding
mu
det
dz
= −W˙net (6.9)
In the open boundary flow case, the atmospheric hydrostatic pressure provides a
balance between the gravitational body force and pressure forces, resulting in no
net work done on the control volume. The cancellation of those terms leaves only
the kinetic energy, ek, remaining on the left hand side, and means the W˙ term on the
right hand side consists of only drag body forces from the drops. This can be written
as the sum of the drag force on all drops within the control volume, W˙ =
∑
(fd ·u),
99
where fd is the drag force on an individual drop.
The total mass within the control volume can be written as ρ dV ,
ρu dV
dek
dz
=
∑
(fd · u) (6.10)
Dividing the right side by u dV , the velocity terms cancel and yields a total drag
force per unit volume,
∑
fd/dV = F
′′′
d . The F
′′′
d term can be calculated based
on locally measured (or model predicted) quiescent spray characteristics, including
drop size, drop velocity, and number density, at various locations of interest so that
a profile of these characteristics is known as a function of height within the plume
region F ′′′d (z). Substituting in ek =
1
2
ρu2 results in the relationship
1
2
ρ
du2
dz
= F ′′′d (z) (6.11)
Separating the variables yields a final form, relating the plume kinetic energy to a
cumulative volumetric work term,
1
2
ρu2 =
∫ Lref
0
F ′′′d (z)dz (6.12)
where the integration along the z-direction is bounded by the ground and a reference
height, Lref , determined by the configuration geometry of the sprinkler and plume
alignment. The height of Lref includes spray that is tracing trajectories to the target
surface. The important parameters for the spray work scaling are the relationship
of the total volumetric work that the spray exerts on the plume,
∫
F ′′′d (z)dz and the
initial volumetric kinetic energy of the plume at the base, ρu2/2.
It is proposed that when the spray drag forces are sufficient to remove the
kinetic energy associated with the plume flow, the plume reaches a critical condition
100
where it cannot overpower the spray, providing a scaling relationship for penetration
PR(vp) ∼
∫
F ′′′(z)dz /KE (6.13)
6.4.1.1 Comparison to Spray Momentum
Previous studies suggest that spray momentum compared to the plume mo-
mentum is an important parameter determining spray-plume interactions. How-
ever, determination of the appropriate scale between the two momenta is unclear.
Through the consideration of the drag forces that the plume and drops exchange,
the evolution of the effect of the momentum can be evaluated. The evaluation of
the spray work can be compared to the spray momentum in the following way.
The momentum of the spray (per unit area), M˙ ′′s , can be calculated from the
product of mass flow rate of water drops, m˙′′, and the velocity of the drops, v,
M˙ ′′s = m˙
′′v (6.14)
Substituting for m˙′′ to introduce the volume flux, V˙ ′′ of the spray,
M˙ ′′s = ρwV˙
′′v (6.15)
and then multiplying by v/v and recognizing that the spray volume fraction can be
written as VF = V˙ ′′/v, the simplification results in
M˙ ′′s = ρwVFv
2 (6.16)
producing a final scaling for spray momentum flux as
M˙ ′′s ∼ VFv2 (6.17)
101
The two terms in the scaling relate to the amount of water delivered, and the
pressure of the injection (influencing both volume and velocity). This value provides
a general integral metric describing the spray momentum, but generally ignores the
localized interactions. It is well suited for a consideration of the interactions present
in a directly aligned configuration where the momentum of the spray acts along the
full direction of the plume.
For comparison, the spray work scaling can be explored beginning from the
total drag force, FD, produced by the spray,
Fd = Nd
(
1
2
ρaCDAdu
2
)
(6.18)
where the term in brackets is the drag force on a single drop. The variable Nd
represents the total number of drops in the spray, which can also be written as
Nd = ndV , where n is the number of drops per unit volume and dV is a differential
volume containing drops. Another relationship for volume fraction can be written
to include the volumetric drop density
VF =
NdVd
dV
= nVd (6.19)
Substitution of these variables results in
Fd =
VF
Vd
dV
(
1
2
ρaCDAdu
2
)
(6.20)
Simplifying the ratio Ad/Vd and dividing each side by dV provides the volu-
metric drag force introduced in Sec. 6.4,
F ′′′d =
3
4
ρaCD
1
d
VFv2 (6.21)
102
and the final scaling of the volumetric drag term becomes
F ′′′d ∼
VFv2
d
(6.22)
Finally, in the spray work scaling, the F ′′′ term is integrated over the height of the
spray-plume interaction, adding the effect of height to the scaling.∫
F ′′′d ∼
VFv2H
d
(6.23)
The additional benefits of the drag work formulation, Eq. (6.23) compared to the
momentum based approach, Eq. (6.17) is the explicit inclusion of drop size effects
and the distance over which the spray and plume interact, through the integral term.
These are important characteristics of the interaction that are not directly included
in the momentum formulation. By introducing the length scale of the interaction,
the formulation is applicable directly to a large range of configurations that can
be considered on a local scale rather than the complete integral comparison of the
spray and plume momenta.
6.4.1.2 Evaluation of Spray Work
Determining the value of the spray-plume interaction parameter requires knowl-
edge of the spray field in the location of the plume to evaluate the drag interactions.
It is possible to use the initial spray measurements as a reasonable first guess, how-
ever the initial spray will be significantly different than the spray that has evolved
along the path to the target location. Drag effects have a large influence on the
spray and will preferentially filter out smaller drops as the radial distance from the
103
sprinkler increases, as observed in the measurements in Ch. 5. Drag also slows the
radial velocity of the drop, curving the trajectory of the drops downward. The com-
bination of these effects will change the characteristic number density and velocity
vector of the spray in a given location.
The F ′′′d term can be calculated based on measured spray characteristics that
are present in the drag equation, including drop diameter and drop velocity, at
various locations of interest so that a function of F ′′′d (z) is known throughout the
plume elevation. Also important is the drop number density n (drops/m3), which
serves as a multiplier of the individual drop drag force to account for all drops in
the spray.
The drag force for a single drop can be represented as shown in Fig. 6.3 and
used in Eq. (6.3). Multiplying the single drop drag by the total number of drops
within the control volume of a given size, Nd, and assuming only the vertical velocity
components for plume penetration, provides the total drag force in the vertical
direction,
Fd = Nd
(
1
2
CDρaAd(u− v)2
)
(6.24)
The volumetric formulation used in Eq. (6.23), F ′′′d , is obtained by dividing
both sides of the drag force by the differential volume, dV , leaving a volumetric
drop number density on the right hand side, n = Nd/dV , where n represents the
number of drops per unit volume.
Inputs to the local drag force equation are sourced from the optical shadow-
graph measurements from the quiescent case, and include Ad and v. Also available
104
from the shadowgraph measurements is the volume flux, V˙ ′′, which is used to de-
termine the drop number density
n =
V˙ ′′
Vdv
(6.25)
where v is the vertical component of the optically measured drop velocity and Vd is
the drop volume of the drop.
Each drop is a different size and is traveling at a different velocity, so precise
accounting of the total drag force would require the evaluation of each drop in
the spray. In practice, the spray can be considered in several drop size “classes”
consisting of drops within a given size range. The measured drops can be collected
into discrete groups so that a characteristic drop size and velocity can be used for
each class, and the measured volume flux can be used to determine the number
density to use for each drop size class.
For this analysis, the drop size distribution for all measurement locations
within the plume was considered, and divided into 10 drop size groups in ranges
of d =(dmin–dv10), (dv10–dv20), (dv20–dv30), etc., such that each class contained equal
volume fractions, or 10% of the measured volume flux. The characteristic diameter
of each class was the median of the class, i.e. dv5,dv15,dv25, etc. The spray properties
n and v were determined for each drop size groups at each elevation location to
provide a profile for each drop size class. For each group, F ′′′(z) was evaluated,
and summed together to obtain the total local spray drag force, which was then
integrated over the height of the spray interaction. Appendix D shows the calcula-
tion of the local drag force profile along the plume elevation for the different drop
105
∆r
Lref
H
Dp
𝜃
Figure 6.8: The function of local drag force is integrated over the inter-
action distance characterized by drops that are directed to the base of
the plume, a function of the configuration geometry.
size groups. The relevant interaction height was determined by the spray that was
directed to the target location through geometry, indicated in Fig. 6.8, and identifies
only drops which have a potential to reach the target area and directly influence
penetration. While the spray above this height has additional drag influence on
the plume, these interactions do not have an influence on the interactions that gov-
ern the local penetration of the spray to the base of the plume. At heights above
this region, the influence of the spray on the plume could be calculated to evaluate
how the plume dynamics evolve, through a solution of Eq. (6.12) where the plume
velocity varies with elevation. In this case, a stagnation point where the spray and
plume meet could possibly be identified. While this would provide an analysis of
the spray influence on the plume, the resulting information about how the plume
106
penetrates through the spray is not the point of interest when determining the spray
penetration through the plume.
6.4.2 First Law Scaling Results
Penetration results viewed in terms of the spray work scaling are seen in Fig. 6.9
for the close spacing and far spacing condition with two operating sprinklers. Circle
points represent the near spacing condition, triangles represent the far spacing. The
data points are again shaded based on a penetration value (white <30%, black
>70%, and gray in-between). Results clearly show that the spray influence is a poor
predictor for penetration in the far spacing case because the spray influence is very
small for all plume velocities. This is expected due to the lower number of drops,
larger drop diameters, and lower volume flux at the far locations. Additionally,
the larger distance from the sprinkler to the plume centerline reduces the effective
interaction height, shown as Lref in Fig. 6.8. The primary factor in this result,
however, is likely the much smaller number density in the far spacing case. In the
close spacing case a correlation between penetration ratio and the penetration scale
exists. In this configuration, the spray work scaling is becoming important, and at
a W/KE ratio near 1, penetration ratio transitions through the marginal range.
The results presented for the two conditions (near and far spacing) in Fig. 6.9
come from the same global spray properties; the overall spray is the same, but the
main difference is due to location effects. From Eq. (6.23), the influence of local
values includes
107
• drop number density
• vertical drop velocity
• drop size
• interaction height based on location geometry
The implementation of a location based analysis including local spray characteristics
allows for inclusion of these additional relevant spray physics compared to an integral
metric based on a global momentum value or an overall drop characteristic such as
a Sauter mean diameter describing the drag influence.
0.0 0.5 1.0 1.5
0.0
0.2
0.4
0.6
0.8
1.0
W/KE
P
en
et
ra
tio
n
Figure 6.9: Plume penetration scaled with spray work. • near spacing,
N far spacing. Shading corresponds to penetration value. White <30%,
black >70%, gray in-between.
However, with the success of the terminal velocity scale, it is not conclusive
that the spray work scale is the dominant scaling of the interaction. For a more
definitive analysis of the scaling, another condition, towards a denser spray with
108
smaller drops, would be required, which is not achieved with the current experimen-
tal set-up. While these drag interactions may play a role in the near spacing case,
the current results are inconclusive about the analysis. Additional study applying
the analysis to centered spray-plume configurations and to sprays with smaller drop
sizes that do not correlate with the terminal velocity may provide more insight, and
is discussed in Sec. 6.5.
In this analysis, drag effects of the spray on the plume were considered in
the current configurations, however, results suggest the overall work and kinetic
energy transfer between the spray and the plume is not a dominating factor when
considering the off-center configuration. Drops that enter the plume from the side
of the plume and at lower elevations along a trajectory directed at the base of
the plume will interact independently from the influence of the spray at higher
elevations. These drops will not be influenced by the plume during their entire
lifetime. Independent of where drops enter the plume is the drag force balance at
the terminal velocity limit. This seems to be an effective scaling for penetration,
when compared to a characteristic plume velocity.
6.5 Scaling Analysis Extension
6.5.1 Reach of Current Analysis
The results of the two scaling analyses indicate that the conditions tested in the
SAF operating with two sprinklers are dominated by the individual drop penetration
109
due to terminal velocity. While a correlation between W/KE is observed in the close
spacing case, there are very few conditions with a supercritical work parameter,
and even in these cases the terminal velocity is still an important factor. The
relationship between the two scaling parameters is seen in Fig. 6.10 which plots the
velocity ratio versus the spray work parameter for each flow configuration, indicating
the relative contribution of each penetration mechanism. The shaded region at the
bottom of the plot indicates the penetration regime where drops penetrate due to
their individual terminal velocities. Data points in this bottom region correspond
to definite penetration based on the terminal velocity scaling. The second shaded
region, to the right of the plot at W/KE > 1 corresponds to the regime where
penetration is achieved due to the spray work interactions with the plume. Points in
the bottom right where the two shaded regions overlap correspond to an inconclusive
condition where both penetration mechanisms are possible. While the two regimes
have been presented separately, and a line marking the shaded region is defined, they
will not work completely independently; the influence of both penetration regimes
may combine and the boundary between regimes is not perfectly clear cut. For
example, a spray imposing moderate work on the plume will slow the plume velocity,
allowing for a lower critical terminal velocity requirement for penetration, and the
combined action of the spray interaction will lead to increased penetration than
when considering the terminal velocity criterion alone. The color of each data point
corresponds to the level of penetration achieved. Black points indicate PR > 0.7
while white points indicate PR < 0.3. The gray points suggest an intermediate
110
0.001 0.010 0.100 1 10
0.5
1
2
W/KE
v p
lu
m
e
/v term
Figure 6.10: Penetration data plotted as a function of scaling parameters
for all data sets, identifying the level of penetration by color. (• near
spacing 2, N far spacing 2,  near spacing 4,  far spacing 4, shading
corresponds to penetration value)
transition zone of marginal penetration. From these points it is observed that the
general penetration regimes correspond to the level of penetration, however there is
some transition region or combination effects where the shaded boundaries have been
drawn. The overlap of the two contributing regimes is seen through the marginal
penetration cases identified by the gray colored data points.
It is noted that the penetration ratio measurements presented this far corre-
spond to the flow condition used in Ch. 5 with two sprinklers activated; this flow
configuration allows for the local spray properties to be measured. The two-sprinkler
results are shown in Fig. 6.10 by the circle points (close spacing) and triangle points
111
(far spacing). These two conditions skirt around the top right quadrant of the plot,
indicating that a condition where successful penetration is independent of the drop
terminal velocity. To increase the spray work independently from the drop size, an
increased number of sprinklers can be used. Additional penetration ratio measure-
ments were taken using all four sprinklers in the SAF simultaneously to nominally
double the volume flux while keeping the drop sizes relatively similar. In these
cases, the work interactions are doubled due to the doubled volume flux, and are
represented in Fig. 6.10 by the square points (close spacing) and the diamond points
(far spacing).
There are notable limitations in the four sprinkler data points, however. First,
these data points assume the same terminal velocity information as measured in the
two sprinkler configuration. This may not be a completely accurate assumption,
particularly in the far spacing case where differences in drop size distribution may
be enhance by the lower drop count and the influence of initial spray variations due
to the slot/tine geometry. This may explain some of the disagreement related to the
far spacing 4 sprinkler case (diamond points) where marginal penetration is noted
below the critical line in Fig. 6.10. If the terminal velocity of the combined four
sprinkler sprays has a slightly lower vterm (due to different localized spray drop size
distributions) these points would move up on the y-axis. For example, adjustment of
the dv50 drop size to 0.57 mm instead of 0.73 mm would adjust the terminal velocity
to 2.3 m/s instead of 2.9 m/s, shifting the diamond points upward to correspond
with the critical line at 1. Additional uncertainty is present in the x-direction as
112
well, assuming that the work calculated from the two sprinkler condition is simply
doubled in the four sprinkler configuration.
Note that there is limited data in the upper right quadrant, where terminal
velocity is too weak but penetration may occur due to drag interactions of the
spray. Based on the spray generated in the current test conditions, the drop size
and spray work conditions are not achievable independently. A condition where the
spray work dominates without a potential for individual drop penetration would be
desired. These conditions would be characteristic of sprays with even smaller drop
sizes than those observed near the sprinklers in the current measurements. While
not possible with the current facility, test data reporting fire suppression ability with
different low to medium pressure (10.3–13.8 bar) water mist nozzle configurations
was explored to expand the current data set.
6.5.2 External Data Set
To explore the scaling in this region, outside experimental data was imple-
mented from water mist fire suppression tests of wood-crib fires [41] which provided
incomplete, yet sufficient, spray information to implement the W/KE analysis with
some assumptions. Including this dataset also presents to opportunity to apply
the current scaling analysis to a case with real fire suppression. There are several
differences between this external data set and the current study. The suppression
experiments consist of a real fire of approximately 275 kW heat release rate, they
use water mist, and the spray nozzle is located directly above the fire at a height of
113
1.3 m above the fuel surface. Each of these differences requires consideration when
the current scaling analysis is applied.
Spray Considerations
For implementation in the W/KE analysis, profiles of spray properties includ-
ing volume flux, drop size, and drop velocity are required. While the complete data
is not presented in the paper, a few assumptions can be made to move forward.
For volume flux considerations, the known flow rate from the nozzle and the
known spray angle can be used along with the assumption that the spray is uniformly
distributed within the solid cone. While the original cone angle is 90◦, the radial
component of spray velocity will decay rapidly and the wide trajectory will not
persist to the floor. Based on trajectory analysis of the small drop size at an initial
angle of 90◦, the maximum diameter of the spray can be estimated at 1.2 m. While
the floor measured volume flux shows some nonuniformity, the calculated fluxes
using this truncated cone method agree well with the reported average delivered
density.
The drop velocity profile is also required, and only the initial velocity is pro-
vided. Additional information from the nozzle data sheet [48] shows the initial
spray cone dissipates into a continuous fog after a listed distance. For calculation,
the drop velocity was assumed to follow the solution to the drop drag equation,
Eq. (6.3). Using initial conditions as measured in the paper, an initial velocity of
10 m/s is considered at a distance 0.2 m below the nozzle. The solution to the differ-
114
ential equation suggests that the drop reaches it’s terminal velocity in a distance that
agrees with the listed reach of the momentum dominated spray region. Therefore,
the solution to the drag equation was used to estimate the drop velocity profile.
The mist was generated by nozzles with a range of orifice diameters and at
two pressures. For some of the test cases, drop size and velocity of the spray was
measured at a distance 0.2 m below the nozzle. The drop size reported is the Sauter
Mean Diameter (SMD), which is typically smaller than the volume median dv50
drop diameter. While these drop sizes are not directly comparable, they compare
reasonably well with a correlation for drop size based on orifice Weber number to
predict dv50. Additionally, no drop size distribution is provided in the reference,
and so increased fidelity is added by using a drop size distribution; a monodispersed
spray is assumed for these conditions.
Because of the configuration differences, the height over which the spray work
is considered spans the entire distance from the fuel surface to the sprinkler, as
opposed to the current SAF configuration where only a small elevation of the spray
is considered for penetration. The local drag force from the spray was integrated
from 0 m up to 1.1 m (0.2 m below the nozzle where the provided spray measurements
were taken). At locations closer to the nozzle, the spray is extremely dense and is
not considered in this analysis.
115
Plume Considerations
In the current study the competition to the spray is provided by an ambient
temperature air jet with a specified initial velocity. This same concept does not
directly apply to the case of the real fire condition in the work by Santangelo.
However, a characteristic peak velocity of the fire is calculated based on a correlation
of the heat release rate, vflame,max = 1.9HRR
1/5 and is approximately 6 m/s for
the wood-crib fires. Additionally, the gas is heated and will have different density
and viscosity characteristics than the ambient jet used in the current study. Using
the plume findings of Heskestad, the temperature rises by 650 K at the flame tip
where the maximum velocity occurs [42], corresponding to a density decrease by a
factor of 3 and an increase in viscosity by a factor of 7 [49]. A conservatively high
kinetic energy of the plume is calculated using the hot temperature density and the
characteristic plume velocity, and the changes in air properties will influence the
drag force produced by the drops on the plume.
Additional Datasets
An additional data set was also considered for inclusion in the current analysis.
Recent measurements of spray-plume interaction by Zhou in a small-scale config-
uration include very small drop water mist [24]. However, several considerations
make application of the current W/KE analysis difficult to this data set. While
very detailed measurements of volume flux, drop size, and velocity were obtained,
116
there is limited information regarding the elevation profile of these spray character-
istics. In this case, the momentum of the spray exhibits a significant influence on
the far-field drop velocity. Despite the drops being very small, nominally 0.05 mm,
they do not slow to their terminal velocity, and are still traveling at nearly 5 m/s
upon interaction with the hot air plume. While this is dramatically slower than
the initial velocity of 18 m/s near the injection, the velocity remains much greater
than the terminal velocity of the small drops. This suggests the spray nozzle used
in this study operates on a different principle where the narrow cone angle of 30◦
yields jet-like behavior, where the core velocity is maintained at elevated levels, and
entrained air contributes significantly to the spray momentum, insulating it from
direct plume influence. In fact, the nozzle used by Zhou uses an orifice atomization,
while the BETE P nozzles used by Santangelo use an impingement atomization,
significantly reducing the injection velocity from the orifice.
6.5.3 Result Discussion
The results of the scaling analysis to the expanded data set from the wood-crib
testing is shown in Fig. 6.11 by the star shaped points. The different test conditions
are also labeled by the spray nozzle used. Immediately noticeable is the influence of
the very small drop sizes present in the spray, resulting in very high vp/vt ratios.
The points are once again colored by the extent of penetration. The P120
test delivers the highest volume of water and is predicted to have the largest plume
influence. Suppression in this case is very successful. In the P66 and P80 cases,
117
0.001 0.010 0.100 1 10
0.1
0.5
1
5
10
50
100
W/KE
v p
lu
m
e
/v term
Figure 6.11: Extension of the results to include application of the scaling
analysis on mist suppression testing of real fires. (• near spacing 2, N
far spacing 2,  near spacing 4,  far spacing 4, F fire suppression tests
from [41], shading corresponds to penetration value)
suppression is not as easy. The reduced volume flux suggests a smaller W/KE ratio
closer to the proposed critical vale around 1. A significant outlier is observed in the
P54 nozzle test condition. It is very possible that the assumptions for the W/KE
calculation are not accurate to the spray conditions. However, it is important to
note that suppression depends on factors other than percent penetration, including
a critical application rate or delivered volume flux. While the point lies in the upper
right quadrant indicating penetration due to spray work interactions, it does not
necessarily mean that a critical volume flux was achieved. This test case supplies
the lowest volume flux in the quiescent condition to begin with, so even though
penetration may be occurring, suppression may not be successful strictly because the
118
actual amount of water available to be delivered is insufficient for suppression. This
result highlights the fact that there are additional factors than solely penetration
ratio that govern suppression. This is a case in the current measurements as well.
Even though the far spacing case shows a high penetration ratio, the actual volume
flux delivered to the target even at PR = 1 (1.5 mm/min) is still less than the volume
flux delivered in the weakest close spacing test condition (2.8 mm/min).
Additional consideration that is not accounted for in the current analysis is
the effect of evaporation. Particularly in the P54 nozzle test, the drop size is very
small at an estimated 100µm, and would be susceptible to very fast evaporation.
6.6 Summary
The ability of a sprinkler spray to penetrate through a simulated fire plume
was investigated for a range of spray characteristics and plume strengths. While
current sprinkler protection design methods do not consider local spray variations
or the ability of a given spray to achieve penetration through a fire plume, a scaling
analysis was explored in to provide a framework useful for evaluation of a given
sprinkler design through knowledge of local quiescent spray characteristics. Two
regimes of spray-plume interaction and penetration were explored—the first based
on individual drops and terminal velocity, the second based on accumulated spray
drag interactions from the entire spray. In both cases, penetration is governed by
very localized spray-plume interactions corresponding to a small fraction of the total
dispersed drops in the vicinity of the plume. It is the local drop characteristics that
119
determine penetration rather than a more global integral representation of the spray.
The analysis framework is used to identify and evaluate the relevant drops in the
spray based on the physical mechanism responsible for penetration.
In the experimental conditions currently tested, the terminal velocity criterion
for penetration yields excellent results to predict the level of spray penetration. The
differences in local spray drop size distributions are a dominating factor regarding
penetration and predict the experimental results well. Viewing the measurements
with respect to the work from spray drag interactions shows that far from the
sprinkler centerline, where the spray is sparse and contains only large drops, there is
limited influence on the plume and the spray work is a poor indicator of penetration
ability. However, near the spray centerline where the spray is comprised of small
drops, work effects show a correlation to penetration. These work effects incorporate
spray number density, drop velocity, drop size, and the effective vertical distance of
the interaction. It is likely that the scaling for each regime overlaps somewhat, and
there are configurations such as the current near spacing case where both scaling
parameters must be evaluated to determine the penetration potential of the spray.
Extension of the analysis to external fire suppression datasets is feasible, and shows
relatively consistent results to the current dataset.
120
Chapter 7: Conclusions
The present work implements a unique multi-sprinkler facility, representing
a fundamental sprinkler protection grid configuration, to investigate the dispersion
and subsequent interactions of fire sprinkler sprays with a competing fire plume.
Understanding of the spray-plume interactions, which dominate the suppression ef-
fectiveness of sprinklers, is critical for improvements in fire sprinkler protection of
increasingly demanding hazards as well as for development of detailed computer
modeling of such suppression sprays. Both the initial and dispersed spray mea-
surements show the complex and spatially non-uniform characteristics of the spray,
and are unique for individual sprinklers. This fact complicates both fire suppres-
sion effectiveness and the ability to accurately model suppression sprays using CFD
solvers. The research objectives were grouped into three areas, including (1) devel-
opment of a CFD spray model validation dataset, (2) refinement of spray dispersion
measurement methods, and (3) development of a framework to identify plume pen-
etration performance for engineering application. The results and contributions are
summarized as follows.
121
7.1 Comprehensive Experimental Dataset
The set of comprehensive spray measurements presented throughout this re-
search provides insight to the mechanisms of plume penetration along with a much
desired dataset for implementation in CFD models, for both initial spray input con-
ditions as well as data for model validation and development. The dataset is com-
prised of measurements describing the spray from initial injection, to volume flux
distribution on the floor, and interaction and penetration through a simulated fire
plume. The complete details of experimental set-up and configuration, along with
detailed local spray measurements, was previously unavailable. The dispersed spray
and plume interaction measurements, while providing physical insight through the
presented scaling analysis, would be relatively unhelpful for model validation with-
out the accompanying initial spray details due to the variations in spray character-
istics that occur naturally in sprinkler sprays. The inclusion of all measurements
from the same configuration allows for the direct application of the presented data
for model validation.
The comprehensive experimental dataset contributes
• detailed spatially-resolved measurements to support model validation
• a complete dataset including relevant initial spray and far-field spray disper-
sion measurements
• critical alignment and experimental configuration details to provide reliable
122
boundary conditions
7.2 Refinement of Spray-dispersion Measurement Methods
Volume flux measurements of spray dispersion from an array of sprinklers, in
a general sprinkler system grid configuration, were taken with a fine resolution of
5 cm. In addition to supporting model validation, these measurements highlight
the limitations of current industry standard acceptance tests in regards to iden-
tifying spatial variations in the spray pattern that may influence the suppression
effectiveness of a particular sprinkler.
The dispersed spray measurements contribute
• spatially-resolved dispersed spray measurements to support model validation
• a high resolution analysis providing insight to critical length scales
• evidence for requirements of the spatial resolution of measurements corre-
sponding to 4% of spray reach
7.3 Penetration Framework
A scaling framework considering the contributions of individual drop terminal
velocities for plume penetration, as well as the accumulated influence of drag in-
teractions from the entire spray was presented to predict penetration performance
based on local quiescent spray characteristics. This analysis may be useful for engi-
neering application by considering the local spray properties and behavior in regard
123
to penetration performance.
The penetration measurements and scaling analysis contribute
• a framework for the analysis of spray penetration capability based on quiescent
spray properties
• results show that local drop size distribution and terminal velocity ratio predict
penetration performance
• an analysis of local accumulated spray work contributions rather than a global
characteristic momentum ratio to predict penetration in the group action
regime
• analysis of additional fire suppression data to apply the current analysis to
expanded conditions and real fire data
This study was limited in terms of available lab capabilities, such as ceiling
height, ability to use a real fire, and the analysis ignores the influence of evaporation,
which may have an impact on the applicability of the spray work analysis for sprays
of very small drops. Future work to include additional spray configurations with
the same spray data could extend the analysis and better determine the limitations
and applications. The current experimental configuration limited the analysis to
conditions where the terminal velocity was still coupled to the spray work scaling
parameter. Additional test conditions with smaller drops are required to better
evaluate the spray work analysis independent of the drop terminal velocity. Future
work regarding the influence of evaporation, application to a real fire plume, and
124
incorporating the complexities of dense sprays with high entrainment, such as fine
water mist, would further advance the understanding of the spray-plume interaction.
For the engineer, this current research shows that the penetration is directly related
to the spray drop size distribution, and the drop terminal velocity is the critical
parameter.
125
Appendix A: Complete Initial Spray 4S Measurements
Measurements of the initial spray are presented here for each sprinkler used in
the study for CFD model spray initialization. Sprinklers were Tyco D3 spray nozzles
with k-factor 33 LPM/bar1/2 (2.3 gpm/psi1/2) operating at a pressure of 1.38 bar
(20 psi).
For each sprinkler, five datasets are presented including volume flux, V˙ ′′, vol-
ume median drop diameter, dv50, drop distribution width parameter γ, break-up
radius, rbu, and the drop velocity at the break-up location, ubu. Measurements in-
clude complete 360◦ azimuthal measurements at 11 elevation angles. The quadrants
of the sprinklers not directed toward the center of the array have been shaded.
The drop size distribution can be defined using the local dv50 and γ measure-
ments at a given elevation angle θ and azimuthal angle φ around the initial spray
through the combined log-normal Rosin-Rammler distribution [17,20],
CVFV,d(d|θ, φ) =

1√
2pi
∫ d
0
γ
1.15d′ exp
[
− ln (d′/dv50)2
2(1.15/γ)2
]
dd′, d < dv50
1− exp [−0.693 (d/dv50)γ] , d > dv50
(A.1)
126
0150
0 90 180 270 360
V '' (mm/m
in
)
80°
0
150
V '' (mm/m
in
)
90°
0
150
V '' (mm/m
in
)
100°
0
150
V '' (mm/m
in
)
110°
0
150
V '' (mm/m
in
)
120°
0
150
V '' (mm/m
in
)
130°
0
150
V '' (mm/m
in
)
140°
0
150
V '' (mm/m
in
)
150°
0
150
V '' (mm/m
in
)
160°
0
150
V '' (mm/m
in
)
170°
0
150
V '' (mm/m
in
)
180°
Figure A.1: Volume flux measurements, V˙ ′′, for Sprinkler #1 (mm/min).
127
02
0 90 180 270 360
d v
50
(mm
)
80°
0
2
d v
50
(mm
)
90°
0
2
d v
50
(mm
)
100°
0
2
d v
50
(mm
)
110°
0
2
d v
50
(mm
)
120°
0
2
d v
50
(mm
)
130°
0
2
d v
50
(mm
)
140°
0
2
d v
50
(mm
)
150°
0
2
d v
50
(mm
)
160°
0
2
d v
50
(mm
)
170°
0
2
d v
50
(mm
)
180°
Figure A.2: Drop size, dv50, measurements for Sprinkler #1 (mm).
128
05
0 90 180 270 360
γ 80°
0
5γ 90°
0
5γ 100°
0
5γ 110°
0
5γ 120°
0
5γ 130°
0
5γ 140°
0
5γ 150°
0
5γ 160°
0
5γ 170°
0
5γ 180°
Figure A.3: Drop size distribution width measurements, γ, for Sprinkler #1.
129
015
0 90 180 270 360
u b
u
(m/s) 80°
0
15
u b
u
(m/s) 90°
0
15
u b
u
(m/s) 100°
0
15
u b
u
(m/s) 110°
0
15
u b
u
(m/s) 120°
0
15
u b
u
(m/s) 130°
0
15
u b
u
(m/s) 140°
0
15
u b
u
(m/s) 150°
0
15
u b
u
(m/s) 160°
0
15
u b
u
(m/s) 170°
0
15
u b
u
(m/s) 180°
Figure A.4: Initial drop velocity measurements, ubu, at the break-up
radius rbu for Sprinkler #1 (m/s).
130
00.5
0 90 180 270 360
r b
u
(m) 80°
0
0.5
r b
u
(m) 90°
0
0.5
r b
u
(m) 100°
0
0.5
r b
u
(m) 110°
0
0.5
r b
u
(m) 120°
0
0.5
r b
u
(m) 130°
0
0.5
r b
u
(m) 140°
0
0.5
r b
u
(m) 150°
0
0.5
r b
u
(m) 160°
0
0.5
r b
u
(m) 170°
0
0.5
r b
u
(m) 180°
Figure A.5: Break-up radius, rbu, measurements for Sprinkler #1 (m).
131
0150
0 90 180 270 360
V '' (mm/m
in
)
80°
0
150
V '' (mm/m
in
)
90°
0
150
V '' (mm/m
in
)
100°
0
150
V '' (mm/m
in
)
110°
0
150
V '' (mm/m
in
)
120°
0
150
V '' (mm/m
in
)
130°
0
150
V '' (mm/m
in
)
140°
0
150
V '' (mm/m
in
)
150°
0
150
V '' (mm/m
in
)
160°
0
150
V '' (mm/m
in
)
170°
0
150
V '' (mm/m
in
)
180°
Figure A.6: Volume flux, V˙ ′′, measurements for Sprinkler #2 (mm/min).
132
02
0 90 180 270 360
d v
50
(mm
)
80°
0
2
d v
50
(mm
)
90°
0
2
d v
50
(mm
)
100°
0
2
d v
50
(mm
)
110°
0
2
d v
50
(mm
)
120°
0
2
d v
50
(mm
)
130°
0
2
d v
50
(mm
)
140°
0
2
d v
50
(mm
)
150°
0
2
d v
50
(mm
)
160°
0
2
d v
50
(mm
)
170°
0
2
d v
50
(mm
)
180°
Figure A.7: Drop size, dv50, measurements for Sprinkler #2 (mm).
133
05
0 90 180 270 360
γ 80°
0
5γ 90°
0
5γ 100°
0
5γ 110°
0
5γ 120°
0
5γ 130°
0
5γ 140°
0
5γ 150°
0
5γ 160°
0
5γ 170°
0
5γ 180°
Figure A.8: Drop size distribution width measurements, γ, for Sprinkler #2.
134
015
0 90 180 270 360
u b
u
(m/s) 80°
0
15
u b
u
(m/s) 90°
0
15
u b
u
(m/s) 100°
0
15
u b
u
(m/s) 110°
0
15
u b
u
(m/s) 120°
0
15
u b
u
(m/s) 130°
0
15
u b
u
(m/s) 140°
0
15
u b
u
(m/s) 150°
0
15
u b
u
(m/s) 160°
0
15
u b
u
(m/s) 170°
0
15
u b
u
(m/s) 180°
Figure A.9: Initial drop velocity measurements, ubu, at the break-up
radius rbu for Sprinkler #2 (m/s).
135
00.5
0 90 180 270 360
r b
u
(m) 80°
0
0.5
r b
u
(m) 90°
0
0.5
r b
u
(m) 100°
0
0.5
r b
u
(m) 110°
0
0.5
r b
u
(m) 120°
0
0.5
r b
u
(m) 130°
0
0.5
r b
u
(m) 140°
0
0.5
r b
u
(m) 150°
0
0.5
r b
u
(m) 160°
0
0.5
r b
u
(m) 170°
0
0.5
r b
u
(m) 180°
Figure A.10: Break-up radius, rbu, measurements for Sprinkler #2 (m).
136
0150
0 90 180 270 360
V '' (mm/m
in
)
80°
0
150
V '' (mm/m
in
)
90°
0
150
V '' (mm/m
in
)
100°
0
150
V '' (mm/m
in
)
110°
0
150
V '' (mm/m
in
)
120°
0
150
V '' (mm/m
in
)
130°
0
150
V '' (mm/m
in
)
140°
0
150
V '' (mm/m
in
)
150°
0
150
V '' (mm/m
in
)
160°
0
150
V '' (mm/m
in
)
170°
0
150
V '' (mm/m
in
)
180°
Figure A.11: Volume flux measurements, V˙ ′′, for Sprinkler #3 (mm/min).
137
02
0 90 180 270 360
d v
50
(mm
)
80°
0
2
d v
50
(mm
)
90°
0
2
d v
50
(mm
)
100°
0
2
d v
50
(mm
)
110°
0
2
d v
50
(mm
)
120°
0
2
d v
50
(mm
)
130°
0
2
d v
50
(mm
)
140°
0
2
d v
50
(mm
)
150°
0
2
d v
50
(mm
)
160°
0
2
d v
50
(mm
)
170°
0
2
d v
50
(mm
)
180°
Figure A.12: Drop size, dv50, measurements for Sprinkler #3 (mm).
138
05
0 90 180 270 360
γ 80°
0
5γ 90°
0
5γ 100°
0
5γ 110°
0
5γ 120°
0
5γ 130°
0
5γ 140°
0
5γ 150°
0
5γ 160°
0
5γ 170°
0
5γ 180°
Figure A.13: Drop size distribution width measurements, γ, for Sprinkler #3.
139
015
0 90 180 270 360
u b
u
(m/s) 80°
0
15
u b
u
(m/s) 90°
0
15
u b
u
(m/s) 100°
0
15
u b
u
(m/s) 110°
0
15
u b
u
(m/s) 120°
0
15
u b
u
(m/s) 130°
0
15
u b
u
(m/s) 140°
0
15
u b
u
(m/s) 150°
0
15
u b
u
(m/s) 160°
0
15
u b
u
(m/s) 170°
0
15
u b
u
(m/s) 180°
Figure A.14: Initial drop velocity measurements, ubu, at the break-up
radius rbu for Sprinkler #3 (m/s).
140
00.5
0 90 180 270 360
r b
u
(m) 80°
0
0.5
r b
u
(m) 90°
0
0.5
r b
u
(m) 100°
0
0.5
r b
u
(m) 110°
0
0.5
r b
u
(m) 120°
0
0.5
r b
u
(m) 130°
0
0.5
r b
u
(m) 140°
0
0.5
r b
u
(m) 150°
0
0.5
r b
u
(m) 160°
0
0.5
r b
u
(m) 170°
0
0.5
r b
u
(m) 180°
Figure A.15: Break-up radius, rbu, measurements for Sprinkler #3 (m).
141
0150
0 90 180 270 360
V '' (mm/m
in
)
80°
0
150
V '' (mm/m
in
)
90°
0
150
V '' (mm/m
in
)
100°
0
150
V '' (mm/m
in
)
110°
0
150
V '' (mm/m
in
)
120°
0
150
V '' (mm/m
in
)
130°
0
150
V '' (mm/m
in
)
140°
0
150
V '' (mm/m
in
)
150°
0
150
V '' (mm/m
in
)
160°
0
150
V '' (mm/m
in
)
170°
0
150
V '' (mm/m
in
)
180°
Figure A.16: Volume flux measurements, V˙ ′′, for Sprinkler #4 (mm/min).
142
02
0 90 180 270 360
d v
50
(mm
)
80°
0
2
d v
50
(mm
)
90°
0
2
d v
50
(mm
)
100°
0
2
d v
50
(mm
)
110°
0
2
d v
50
(mm
)
120°
0
2
d v
50
(mm
)
130°
0
2
d v
50
(mm
)
140°
0
2
d v
50
(mm
)
150°
0
2
d v
50
(mm
)
160°
0
2
d v
50
(mm
)
170°
0
2
d v
50
(mm
)
180°
Figure A.17: Drop size, dv50, measurements for Sprinkler #4 (mm).
143
05
0 90 180 270 360
γ 80°
0
5γ 90°
0
5γ 100°
0
5γ 110°
0
5γ 120°
0
5γ 130°
0
5γ 140°
0
5γ 150°
0
5γ 160°
0
5γ 170°
0
5γ 180°
Figure A.18: Drop size distribution width measurements, γ, for Sprinkler #4.
144
015
0 90 180 270 360
u b
u
(m/s) 80°
0
15
u b
u
(m/s) 90°
0
15
u b
u
(m/s) 100°
0
15
u b
u
(m/s) 110°
0
15
u b
u
(m/s) 120°
0
15
u b
u
(m/s) 130°
0
15
u b
u
(m/s) 140°
0
15
u b
u
(m/s) 150°
0
15
u b
u
(m/s) 160°
0
15
u b
u
(m/s) 170°
0
15
u b
u
(m/s) 180°
Figure A.19: Initial drop velocity measurements, ubu, at the break-up
radius rbu for Sprinkler #4 (m/s).
145
00.5
0 90 180 270 360
r b
u
(m) 80°
0
0.5
r b
u
(m) 90°
0
0.5
r b
u
(m) 100°
0
0.5
r b
u
(m) 110°
0
0.5
r b
u
(m) 120°
0
0.5
r b
u
(m) 130°
0
0.5
r b
u
(m) 140°
0
0.5
r b
u
(m) 150°
0
0.5
r b
u
(m) 160°
0
0.5
r b
u
(m) 170°
0
0.5
r b
u
(m) 180°
Figure A.20: Break-up radius, rbu, measurements for Sprinkler #4 (m).
146
Appendix B: SAF Design Details
Additional details about the considerations of drop velocity and spray momen-
tum not provided in Ch. 3 are presented in the following sections of this Appendix
chapter.
B.1 Velocity Considerations
Based on the terminal velocity criterion for drop penetration, it was desired
that the SAF be able to provide test conditions where the ratio between the drop
terminal velocity and the plume velocity were either above or below the critical
ratio, vterm/uplume ≈ 1. In consideration of the drop velocity, the range of possible
velocities can be estimated to fall between a maximum at injection and a minimum
at drop terminal velocity. Drops will interact and penetrate the plume between
these velocity extremes, with the terminal velocity being the limiting case. Figure
B.1 shows how several important velocity scales correspond to a given sprinkler k-
factor. The results of various characteristic velocity calculations were used to guide
the final sprinkler k-factor selection.
The injection velocity can be estimated by the Bernoulli velocity as
√
2∆P/ρw,
147
where ∆P is the operating pressure and ρw is the density of water. The black lines in
Fig. B.1 show the limits imposed on the injection velocity due to operating pressure
constraints. The minimum pressure is limited by a pressure of 0.5 bar, while the
maximum pressure is limited by total flow rate capability, capped at 56 LPM per
sprinkler. Note that beyond a k-factor 80 LPM/bar1/2, it is not possible to satisfy
both constraints.
The terminal velocity is also an important velocity scale, and can be calculated
as a function of the drop size. In Fig. B.1, characteristic drop terminal velocities
are indicated by the blue shaded region. As drop terminal velocity is dependent
on drop size, the characteristic drop size was estimated via correlation prior to the
facility design. The volume median drop size, dv50, has been successfully predicted
previously using a scaling of the orifice Weber number, dv50/Do = CWe
−1/3
o , where
the orifice Weber number is defined as Weo = ρwU
2Do/σ. Variable ρw is water
density, U is the injection velocity (governed by operating pressure), Do is the orifice
diameter, and σ is the surface tension of water. The coefficient C is a sprinkler
dependent parameter, where a value C = 3.24 was previously found to be accurate
for the Tyco D3 nozzle at a range of orifice diameters [21]. The upper blue boundary
represents the terminal velocity of the dv50 at the lowest operating pressure, while
the lower bound is determined from the highest allowable pressure determined by
flow rate restrictions.
The velocity range of the forced air plume is indicated by the green shaded
region, below 4 m/s. For reference, a characteristic velocity of a 300 kW fire is also
148
shown in Fig. B.1 with a nominal velocity of 6 m/s at the flame height. Experiments
aim to be conducted to evaluate the proposed critical condition of drop terminal
velocity to plume velocity ratio, vterm/uplume ≈ 1, to evaluate penetration.
The current operating condition is identified by the red point at a k-factor of
33.1 LPM/bar1/2 and injection pressure of 1.38 bar, corresponding to an estimated
dv50 of 0.72 mm and corresponding terminal velocity of 2.9 m/s. Based on an esti-
mated drop size distribution, following the Rosin-Rammler function, the range of
velocities from the dv10 to dv90 drop sizes show the possible range of drop velocities
within the spray. The injection velocity is much larger (e.g. 17 m/s at 1.38 bar).
The selection of the k-factor 33.1 LPM/bar1/2 allowed for smaller drop sizes to be
achieved using a lower pressure while still using 75% of the flow rate capability,
making it suitable for the lab capabilities and desired test conditions.
The plot shows that with the given range of drop velocities in the current
condition, there are plume velocities that the current plume generator can create to
sufficiently test this condition.
149
---
---
0 20 40 60 80 100
0
5
10
15
K-factor (LPM/bar1/2 )
V
el
oc
ity
(m/s) Min. Pressure Constraint
300 kW fire
Max Blower Velocity
Figure B.1: Plot of relevant spray and plume velocities considered for
the design of the sprinkler array facility. The black region indicates pos-
sible injection velocities. The blue region indicates the range of possible
drop terminal velocities depending on operating pressure. The red point
and error bars indicate the operating condition and the range of drop
size velocities within the given drop size distribution. The green region
indicates the range of plume velocities possible from the current blower.
The orange dashed line indicates the estimated plume centerline velocity
of a 300 kW fire.
B.2 Momentum Considerations
For the current Tyco D3 nozzle, the spray momentum was estimated through
a basic trajectory calculation based on initial spray volume flux measurements from
the 4S and an estimated characteristic drop size. The resulting spray distribution is
shown in Fig. B.2. Note that the area directly beneath the sprinkler shows the most
150
Figure B.2: The spray momentum was estimated using a trajectory cal-
culation to map the volume flux from the sprinkler to the horizontal
plane. Using the drop velocity, the momentum is estimated.
significant downward momentum, as expected due to the increased drop velocity
and volume flux in this area.
Integration of the locally estimated momentum flux based on the spatially
resolved 4S measured volume flux and the drop velocity from a simple trajectory
analysis yields a total spray momentum of 4.4 N. This momentum is evaluated based
on the area that it is acting over. Several calculations are considered in Table B.1
with different areas of influence are considered. If the entire spray area is considered,
this is not necessarily the best characteristic value because of the localized inter-
action of the plume. Smaller areas were also considered, and an integration was
performed to find the highest momentum in these local areas. The table suggests
that while the plume velocity of a characteristic fire, at 6 m/s, is a little higher than
151
the possible jet velocity from the current design, the velocity range of the plume
will still permit the momentum of the air jet to be similar to that of the fire plume
due to the density difference between the fire and the ambient temperature air jet.
Table B.1: Momentum ratio calculation results for various spray area considerations.
Ms As M
′′
s up M
′′
p,low up M
′′
p,high up
(N) (m2) (N/m2) m/s (N/m2) (m/s) (N/m2) (m/s)
Spray core1 4.4 5.7 0.77 0.8 0.385 0.56 3.85 1.8
Local spray2 0.11 0.126 0.873 0.85 0.437 0.60 4.36 1.9
Local spray3 0.05 0.031 1.6 1.15 0.8 0.82 8.0 2.6
300 kW fire
estimate
– – – – 10 5 14 6
Current jet – – – – – – 16.4 3.7
1 total spray momentum, integrated over 1.3 m diameter circle
2 momentum from high momentum point spot with diameter 0.4 m
3 momentum from high momentum point spot with diameter 0.2 m
152
Appendix C: Shadowgraphy Noise Reduction
Raw velocity measurements from the shadowgraphy images yielded very noisy
data with clear underlying trends. While the drop size identification worked well
from the single processing step, identification of drop pairs between images was
poor. Visual inspection of the processing output overlay images (e.g. Fig. 5.4b)
identified a significant number of inaccurate particle matches resulting in erroneous
velocity vectors. The solution was to divide the image analysis into three steps,
each optimized for a specific drop size range. The DaVis software allows the user
to specify the minimum and maximum (x, y) dimension of the particle to search
for. Particles that do not meet the size criteria on either axis are ignored. Because
the drops are not perfectly spherical, drops near the edge of the search range are
largely ignored. Therefore, three overlapping ranges were selected for processing,
d < 0.4 mm, d > 0.4 mm and an intermediate range 0.25 < d < 0.55 mm. Because
the larger drops move at a much larger velocity, a change to the search window
size was also implemented to ensure the same drops were identified in both images
of the pair. Figure C.1 shows representative results of the noise reduction. The
gray data points show original drop velocity measurements from the quiescent close
spacing configuration at z = 0.74 m on the plume centerline. After implementing
153
the multiple processing steps for three drop size groups, the scatter was largely
removed, shown by the black data points.
● ● ●●●
●
●
●●
●● ●●
●
●●
●
●
● ●●● ●
●
●●●●●● ●● ●● ● ●●
●
● ●●● ●
● ●
● ●● ● ●●●
●
●●● ●
●
●●
●
●
●
● ● ●● ●●
●
●
●
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-10 -5 0 5 10-10
-5
0
5
10
X-velocity (m/s)
Y
-velo
ci
ty
(m/s)
Figure C.1: Measurements of drop velocity with and without the opti-
mized shadowgraphy processing. Black points are the optimized mea-
surements and gray points are with a single processing step.
154
Appendix D: Spray Work Calculation
Calculation of the spray work through the plume region requires the develop-
ment of elevation profiles of various spray properties. These include vertical drop
velocity, drop size, and drop number density. These profiles are determined based
on the shadowgraphy measurements at 5 elevations within the plume, presented in
Ch. 5. Because drag force depends on the size of the drop, the spray is divided into
discrete drop size groups to account for the different drag force contributions. Ten
discrete drop size classes were determined from the local drop size distribution, with
each group containing equal volume fractions of the spray. The drop size distribu-
tion of the plume centerline is shown in Fig. D.1, where ten equal drop size groups
are identified based on the CVF function.
The local volumetric drag force is determined for each drop size class as a
function of elevation by
F ′′′d (z) = nd(z)
[
1
2
CD(d, v(z)) ρaAd (vd(z))
2
]
(D.1)
where Ad is determined by the class median volume diameter and vd(z) is the mean
velocity of the drop sizes within the class at the given elevation. The local CD is
also determined as a function of the drop size class and the local drop velocity.
155
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Diameter (mm)
C
V
F
Figure D.1: The cumulative volume fraction drop size distribution for
the quiescent close spacing configuration identifies the drop size groups
for the spray drag summation.
The drag force is weighted by the local drop number density, determined by n(z) =
V˙ ′′d (z)/(Vdv(z)), where V˙
′′
d is the contribution of the total volume flux by the given
drop size class, V˙ ′′d (z) = 0.1V˙
′′(z) and Vd is the drop size volume. Figure D.2 shows
the elevation profiles of the measured downward velocity, calculated number density
(based on measured velocity and volume flux), and the calculated volumetric drag
for each of the ten drop size groups.
Summation of the drag force from all drop size classes provides the total local
drag force of the spray and is shown in Fig. D.3. This function is integrated over the
interaction length scale to determine the value of spray work. In the near spacing
case, the length is from z = 0 to z = 0.5.
156
0 0.
2
0.
4
0.
6
0.
8
1.
0
dvX 10 20 30 40 50 60 70 80 900 100
0 2 4 6 8
0.0
0.5
1.0
1.5
2.0
Downward Velocity (m/s)
H
ei
gh
t(m)
1000 104 105 106
0.0
0.5
1.0
1.5
2.0
Number Density (drops/m3)
H
ei
gh
t(m)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
Volumetric Drag Force (N/m3)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
H
ei
gh
t(m)
Figure D.2: Resulting elevation profiles from the near spacing spray
condition of vertical velocity, drop number density, and volumetric drag
force for 10 drop size groups.
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Total Volumetric Drag Force, F''' (N/m3)
H
ei
gh
t(m)
Figure D.3: Summation of the drag forces from each drop size group
yields the total drag profile.
157
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