experimental investigation and numerical simulation of a
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Louisiana Tech UniversityLouisiana Tech Digital Commons
Doctoral Dissertations Graduate School
Summer 2016
Experimental investigation and numericalsimulation of a copper micro-channel heatexchanger with HFE-7200 working fluidEric Borquist
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EXPERIMENTAL INVESTIGATION AND NUMERICAL
SIMULATION OF A COPPER MICRO-CHANNEL HEAT
EXCHANGER WITH HFE-7200 WORKING FLUID
by
Eric Borquist, B.S., B .S .C h.E , M.S., M.S.E.
A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
COLLEGE OF ENGINEERING AND SCIENCE LOUISIANA TECH UNIVERSITY
August 2016
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LOUISIANA TECH UNIVERSITY
THE GRADUATE SCHOOL
May 18, 2016
D a t e
W e hereby recommend that the dissertation prepared under our supervision
by Eric G eorge Borquist
entitled__________________________________________________________________________________________________
Experimental Investigation and Numerical Simulation of a Copper
Micro-Channel Heat Exchanger with HFE-7200 Working Fluid
be accepted in partial fulfillment o f the requirements for the D egree o f
Ph.D in Engineering
Superv iso r o f D isse rta tio n R esearch
H ead o f D epartm en t
D epartm en t
Recommendation concurred in:
S.2
A dvisory Committee
Approved:
D irec to r o f G rad u a te S tud ies
fjepLoD ean o f the C o lleg e
Approved
D ean o f the G rad u a te S chool
GS Form 13a ( 6 /0 7 }
ABSTRACT
Ever increasing cost and consumption of global energy resources has inspired
the development of energy harvesting techniques which increase system efficiency,
sustainability, and environmental impact by using waste energy otherwise lost to the
surroundings. As part of a larger effort to produce a multi-energy source prototype,
this study focused 011 the fabrication and testing of a waste heat recovery micro-channel
heat exchanger. Reducing cost and facility requirements were a priority for potential
industry and commercial adoption of such energy harvesting devices. During develop
ment of the micro-channel heat exchanger, a new fabrication process using m ature
technologies was created th a t reduced cost, time, and required equipment,. Testing
involved filling the micro-channel heat exchanger with 3M™ Novec™ HFE-7200 work
ing fluid. The working fluid was chosen for appropriate physical and environmental
properties for the prototypes intended application. Using a dry heat exchanger as
the baseline, the addition of the working fluid proved advantageous by increasing
energy output by 8% while decreasing overall device tem peratures. Upon successful
experimental testing of the physical device, internal operation was determined based on
implementation of the lattice Boltzmann method, a physics-based statistical method
th a t actively tracked the phase change occurring in a simulated micro-channel. The
simulation dem onstrated three prim ary areas of phase change occurring, surfaces
adjacent to where the heat source and heat sink were located and the bulk vapor-liquid
interface, which agreed with initial device design intentions. Condensation film thick
ness grew to 5/xm over the time interval, while the bulk interface tracked from initial
12f im from the lid to 20urn from the lid. Surface tension effects dom inating vapor
pressure kept the liquid near the heat source; however, the tem perature and pressure
VLE da ta suggested vapor interface growth from the heated surface to 5f im above
the heated copper plate. Reinforcing the simulation results, including location and
movement of phase interfaces, was accomplished through a thorough ten dimensionless
number analyses. These specialized ratios indicated dominant fluid and heat transfer
behavior including phase change conditions. Thus, fabrication and empirical results
for the heat energy harvesting prototype were successful and computational modeling
provided understanding of applicable internal system behavior.
APPROVAL FOR SCHOLARLY DISSEMINATION
The author grants to the Prescott M emorial Library o f Louisiana Tech University the right to
reproduce, by appropriate methods, upon request, any or all portions o f this Dissertation. It is understood
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author o f this Dissertation. Further, any portions o f the Dissertation used in books, papers, and other
works must be appropriately referenced to this Dissertation.
Finally, the author o f this D issertation reserves the right to publish freely, in the literature, at
any time, any or all portions o f this Dissertation.
Author Eric Borquist_____________
Date 0 7 / 1 7 / 2 0 1 6
(iS Form 14 ( 5/0 3 )
DEDICATION
First and foremost, I would like to dedicate this document and all other academic
endeavors to my ever-loving and supportive parents, Nils and Susan Borquist. The
dedication to education and the constant quest to explore new challenges was a seed
planted early on in my life. I cannot thank them enough for their sacrifice, effort,
and inspiration in getting me to the point I am at in life today. Secondly, I dedicate
this document to my three siblings, Karl, Kristina, and Nils, who have assisted and
supported my lengthy academic career. While not always constructive, you three have
consistently steered me back on the path I should not have wavered from. Lastly, I want
to dedicate my academic career and this document to my grandfather, Nils Borgkvist,
who sadly was never able to capitalize academically on his immense creativity and
intelligence in science and engineering due to strict old country traditions. Your
natural abilities, coupled with your kind spirit, continually inspire me to push beyond
my own expectations.
vi
TABLE OF CONTENTS
A B STR A C T............................................................................................................................. iii
DEDICATION......................................................................................................................... vi
LIST OF TABLES.................................................................................................................. x
LIST OF FIGURES................................................................................................................ xi
ACKNOW LEDGM ENTS....................................................................................................... xv
NOMENCLATURE.................................................................................................................xix
CHAPTER 1 INTRODUCTION ..................................................................................... 1
1.1 Objective and Thesis S tru c tu re ......................................................................... 8
CHAPTER 2 GENERAL LABORATORY COPPER MICRO-CHANNELFABRICATION.......................................................................................... 10
2.1 Review of General Laboratory Fabrication and Lithography Techniques. 10
2.2 Fabrication M ethodology..................................................................................... 13
2.2.1 Mold P rep ara tio n ...................................................................................... 14
2.2.2 E lectroplating............................................................................................. 20
2.3 Results and Discussion........................................................................................... 24
2.4 Conclusion................................................................................................................ 30
CHAPTER 3 MICRO-CHANNEL HEAT EXCHANGER TESTING FORWASTE HEAT RECOVERY EFFIC IE N C Y ..................................... 32
3.1 Review of Previous and Current Micro-Channel Heat Exchangers............ 33
3.2 Working Fluid Description................................................................................... 37
3.3 Test S e tup ..................................................................................................................39
3.4 Results and Discussion......................................................................................... 43
3.5 Conclusion................................................................................................................ 47
CHAPTER 4 NUMERICAL SIMULATION OF A MICRO-CHANNELW ITH THE LATTICE BOLTZMANN M E T H O D ............................ 49
4.1 Review of Lattice Boltzmann M ethod ............................................................. 50
4.2 Model Description............................................................................................... 55
4.2.1 Fundamentals of the LBM ........................................................................ 55
4.2.2 Working Fluid Model P roperties............................................................. 61
4.3 Performance S e tup ................................................................................................ 66
4.4 Simulation R esu lts ................................................................................................ 71
4.5 Conclusion................................................................................................................ 80
CHAPTER 5 NUMERICAL MODEL DIMENSIONLESS ANALYSIS................. 81
5.1 Fluid Flow A nalysis.............................................................................................. 83
5.1.1 Reynolds N um ber........................................................................................ 83
5.1.2 Bond N um ber............................................................................................... 89
5.1.3 Weber N um ber............................................................................................ 91
5.1.4 Capillary N um ber........................................................................................ 92
5.1.5 Fluid Flow Conclusion................................................................................ 93
5.2 Heat Transfer Analysis......................................................................................... 94
5.2.1 Prandtl N um ber.......................................................................................... 94
5.2.2 Nusselt Num ber........................................................................................... 96
5.2.3 Peclet Num ber.............................................................................................. 99
5.2.4 Condensation N um ber............................................................................ 100
5.2.5 Fourier N um ber.........................................................................................101
5.2.6 Heat Transfer Conclusion.......................................................................103
5.3 Phase Change A nalysis....................................................................................... 104
5.3.1 Jakob N um ber...........................................................................................104
5.3.2 Phase Change Conclusion.......................................................................105
5.4 Conclusion................................................................................................................. 106
CHAPTER 6 CONCLUSION..........................................................................................107
APPENDIX A LETTER OF COPYRIGHT PERMISSION FROM A SM E 112
BIBLIOGRAPHY....................................................................................................................134
LIST OF TABLES
Table 2.1: Ordyl® parameters [1]..................................................................................... 14
Table 2.2: Electropolishing param eters [2]...................................................................... 20
Table 2.3: Electroplating parameters [3]......................................................................... 21
Table 2.4: Average deposition rates for 75/im and 225/im sam ples......................... 27
Table 3.1: HFE-7200 environmental and safety properties [4].................................. 38
Table 3.2: 3M™ thermal management fluid properties [5]........................................ 39
Table 3.3: Error for fabrication and experimental measurem ents............................ 43
Table 3.4: Energy input, ou tput, and side losses for dry andwetted te s ts ........................................................................................................ 45
Table 4.1: Peng-Robinson EOS param eters................................................................... 71
Table 5.1: Summary of MHE simulation behavior....................................................... 106
x
LIST OF FIGURES
Figure 2.1: Initial MHE topology with two reservoirs and 27 m icro-channels 14
Figure 2.2: Akiles® Pro-Lam U ltra X-6 autom atic laminator [6] ............................ 15
Figure 2.3: Printed MHE pattern on a transparency sheet....................................... 17
Figure 2.4: Kinsten® KVB30D UV Exposure Box [7]................................................ 18
Figure 2.5: Example 75/un mask prior to electroplating............................................ 19
Figure 2.6: Sample plated with non-optimal 0.5A curren t........................................ 21
Figure 2.7: Example 75/im mask height channels plated at 0 .4 A ............................ 22
Figure 2.8: Example 225/im mask height channels plated at 0.4A.......................... 22
Figure 2.9: Preparation steps for the MHE: (a) clean substrate andelectropolish if desired; (b) apply dry-film photoresist, single or multi-layers; (c) UV expose the photoresist with appropriate mask geometry; (d) remove unexposed photoresist with developer; (e) electroplate the sample;(f) remove exposed photoresist with stripper leavingthe finished device............................................................................................ 23
Figure 2.10: Sample radial MHE with 100/im channel w idth and50/im height....................................................................................................... 24
Figure 2.11: Plating profile for 75/un sam ple................................................................... 26
Figure 2.12: P lating profile for 225/im sam ple................................................................. 26
Figure 2.13: SEM image of channel walls at 500/un scale............................................. 28
Figure 2.14: SEM image of channel walls at 500nm scale............................................. 29
Figure 3.1: Fluid cycle interaction in the MHE, where each channel is simultaneously boiling and condensing due to the heat source and heat s in k .............................................................................. 37
40
41
45
46
58
63
63
64
65
65
68
70
72
72
73
74
75
75
76
77
77
Completed MHE sample with lid and working fluid access p o r t ..............................................................................................
Test setup with thermocouple locations shown as yellow circles
Heat flux data from dry and wetted te s ts .......................................
Tem perature data from dry and wetted te s ts ................................
Particle progression for D2Q9 LBM schem e..................................
Empirical and modeled equation for dynamic viscosity
M 8]......................................................................................................................
Empirical and modeled equation for surface tension a [8].........
Empirical and modeled equation for thermal conductivity
* [9]..................................................................................................
Empirical and modeled equation for specific heat cv [10]...........
Calculated points and modeled equations for thermal diffusivity a .............................................................................................
Boundary and initial conditions prior to sa tu ra tio n ....................
Boundary and initial conditions after sa tu ration ..........................
Time progression for density a r ra y ...................................................
Percent change in density array time progression.........................
Time progression for tem perature a rra y .........................................
Percent change in tem perature array time progression...............
Time progression for pressure array .................................................
Percent change in pressure array time progression......................
Steady-state VLE plot of LBM d a ta ................................................
Color map of pressure at time t = 0 in the m icro-channel........
Color map of pressure at steady-state in the micro-channel......
xiii
Figure 4.18: Side-by-side comparison of the initial and steady-state pressure color maps. The arrows indicate the three phase interfaces and their movement over tim e ....................................... 79
Figure 5.1: Param eters for determining D h in Reynolds num ber........................... 84
Figure 5.2: Reynolds number progression for simulated copper channel............... 85
Figure 5.3: Reynolds number progression for condensing vaporinterface near the MHE l id ........................................................................... 87
Figure 5.4: Reynolds number progression for the bulk vapor-liquidinterface in the MHE channel....................................................................... 88
Figure 5.5: Reynolds number progression for boiling liquid interfacenear the MHE b o tto m .................................................................................... 89
Figure 5.6: Bond number as a function of time for the simulatedMHE channel.................................................................................................... 90
Figure 5.7: Weber number as a function of tim e and position forthe simulated MHE channel.......................................................................... 92
Figure 5.8: Capillary number as a function of time for the threeinterface regions............................................................................................... 93
Figure 5.9: Prandtl number as a function of time and position forthe simulated MHE channel............................................................................ 95
Figure 5.10: P rand tl number as a function of tim e for the threeinterface regions............................................................................................... 96
Figure 5.11: Nusselt number as a function of time and position forthe simulated MHE channel.......................................................................... 98
Figure 5.12: Nusselt number as a function of time for the bulkvapor-liquid interface...................................................................................... 98
Figure 5.13: Peclet number as a function of time and position forthe simulated MHE channel.......................................................................... 100
Figure 5.14: Condensation number as a function of tim e for thesimulated MHE lid ........................................................................................... 101
Figure 5.15: Fourier number as a function of time and position forthe simulated MHE channel.......................................................................... 103
xiv
Figure 5.16: Jakob number as a function of time for the simulatedMHE lid ..............................................................................................................105
ACKNOWLEDGMENTS
Over iny fifteen years at Louisiana Tech University, there are many people,
both faculty and fellow classmates, who I thank for their support, influence, assistance,
and guidance. While I have not always been the easiest person to work with or help
for that m atter, there are numerous generous people who have put me in the position
th a t I am in currently. I began my university experience as an undergraduate at
Louisiana Tech in September of 2001. W ithin the first week of being a student, one of
the most influential events of my generation occurred which cast a immediate shadow
on the otherwise enjoyable collegiate years. Finishing my Louisiana Tech journey in
2016, the events of 2001 continue to reflect on the world which I will be entering as a
graduate. W ith tha t said, the time I have spent at Louisiana Tech has been extremely
enjoyable and frustrating all while being ultimately academically fulfilling as I finally
complete my fifth and final degree.
The first degree path I chose was Mathematics. Though my family thought I
should select a less rigorous program, I was steadfast in pursuing a degree in a difficult
yet globally relevant subject. The professors who had the most impact and influence
on me were Bernd Schroeder, Ph.D, Weizhong Dai, Ph.D , and Richard Greechie,
Ph.D. All three professors were very demanding which I did not agree with initially
but now realize it was in my best interest professionally. The inherent complexity of
advanced mathematics has benefited my academic and professional career immensely
xv
xvi
by requiring understanding of any problem and designing the most advantageous
solution. The progression I have m ade in tim e as both an engineer and a scientist
stems from my initial development in mathematics.
After graduating in 2006 w ith my bachelor’s degree, I was fortunate to find
employment with Ventech Engineers International. My drafting and design capacity
with the company required working under some of the most experienced and insightful
designers in the United States. Their invaluable advice while working on both civil and
piping projects in the process industry opened my eyes to the engineering profession
and how to effectively manage tim e constraints and deadlines. For their help in my
development, I would like to thank Stacy Williams, Jerry Young, Cliff Tarver, Andy
Brown, and M att Johnston. The three years that I worked with them greatly assisted
me in my engineering endeavors.
Soon after starting employment with Ventech, my superiors asked whether I
would be amenable to re-enrolling at Tech for an engineering degree. I began my second
undergraduate degree program in 2007 for Chemical Engineering. The previous degree
and Ventech prepared me for many of the struggles which ensued in the engineering
curriculum. However, the excellent faculty at Louisiana Tech definitely found ways
to increase course difficulties and increase student interaction. In particular, Brad
Cicciarelli, Ph.D , Daniela Mainardi, Ph.D , Scott Gold, Ph.D , and James Palmer,
Ph.D found ways to engage all of the students and ultimately develop better engineers.
Over the course of three years in the program, I would also like to acknowledge the
help and interaction with fellow students including Jonathan Wheelis, Brian Criswell,
xvii
and Ryan Redding. Upon graduating in 2010, I began looking for career options and
eventually settled on continuing my education in graduate school.
Wavering in graduate school for various reasons, I found myself enrolled in
the Physics M aster’s program at Tech in 2011 while being hired by Schlumberger
Industries in Lafayette, LA to perform offshore Coil Tubing Services. Though I gained
experience in personnel management, equipment operations and m aintenance, and
overall knowledge of the oil industry, the largest benefit from my time at Schlumberger
was the friendships developed with all operators, maintenance, and supervisors tha t I
worked with over my year in Lafayette. Thanks Kris K ottingham , Cory Babineaux,
Mitch Barras, Guy Edmonds, Toby Falcon, Kirk Girouard, Rodney Green, Joe
Harrison, Brent James, Steve Meyer, Carl Patin , Shawn Rabel, Brandon Thibeaux,
and Josh Walsh. All of you taught me valuable lessons and kept me laughing while
struggling through the twelve hour shifts.
During my experience at Schlumberger, the enrollment in the Louisiana Tech
Physics M aster’s program inspired the basis for my present academic journey. While
m athem atics taught me to open my mind and engineering taught me to always
approach problems with the entire team, physics taught me to embrace the ambiguity
of science and to happily stum ble on the pa th to solution however winding. W hile
I have had classes with many of the faculty, I would like to especially thank Lee
Sawyer, Ph.D, Zeno Greenwood, Ph.D, Pedro Derosa, Ph.D , Dentcho Genov, Ph.D,
and Klaus Grimm, Ph.D. Physics is a demanding subject, yet the initial struggle belies
the extremely good feeling from solving or even better understanding the problem.
The doctoral program I am soon to finish has tested my patience, intellect,
and personal relationships. Since being in the program, I want to thank my academic
advisor, Professor Leland Weiss, for all of his guidance, assistance, and support. I
likely would not have finished the program without his infinite wisdom and knack
for putting me back in my place. Dr. Weiss has pushed me both technically and
administratively, demanding high-quality program work, effective voice for presenting
findings, and accountability for program and school deliverables. Thank you for all of
your efforts to steer me towards my ultim ate goal.
It would not have been possible to complete th is degree and work full-time
without the ability to overlap program responsibilities and the help of a number of
individuals. As part of the whole energy harvesting Phase I and Phase II STTR effort,
I want to thank Mitchell Belser, Dr. Heath Berry, Aryn Hays, Emmanuel Ogbonnaya,
Chris Porter, Tyler Sonsalla, Suvhashis Thapa, Dr. Leland Weiss, and Dr. Sandra
Zivanovic for all of their hard work, diligence, and collaborative focus on finishing
the prototype. I also want to thank our NASA (Mr. Tom Stanley and Mr. Scott
Jensen at SSC) and NSF counterparts for their patience and funding under contracts
NNX13CS09P, NNX14CS11C and grant number ECCS-1053729.
Currently, I am working at Radiance Technologies, Inc. on Louisiana Tech’s
campus. My supervisor, Dr. Heath Berry, has continually supported me in progressing
my academic career. Since we had sophomore English class together in high school,
we have crossed paths many times over the past 17 years. Heath and the rest of the
Radiance team , most definitely including myself, provide a work environment th a t
can be technically, emotionally, and socially challenging. Cheers!
NOMENCLATURE
Acronyms
F D M finite difference method
F E M finite element method
I L G immiscible lattice gas
L B M lattice Boltzmann method
LGA lattice gas autom ata
M H E micro-channel heat exchanger
P D E partial differential equation
T E G thermoelectric generator
Constants
R gas constant
g gravitational acceleration
Dimensionless Numbers
Bo Bond number
xix
XX
Ca Capillary number
Co Condensation number
Fo Fourier number
Ja Jakob number
N u Nusselt number
Pe Peclet number
Pr Prandtl number
Re Reynolds number
We Weber number
Geometry Properties
A cross-section area
D n hydraulic diameter
dc critical diameter
Lattice Boltzmann M ethod
a Peng-Robinson equation of state parameter
b Peng-Robinson equation of state param eter
cs lattice sound speed
e* particle i velocity
fi particle distribution function
equilibrium distribution function
<7i tem perature distribution function
gf '^ tem perature equilibrium distribution function
r position
p momentum
t time
V maximum velocity
x position
St change in time
4> source term
r relaxation time
Tr tem perature relaxation time
uii weighting coefficients
M a te r ia l P ro p e r t ie s
k therm al conductivity
cp specific heat capacity
h heat transfer coefficient
h fg Heat of vaporization
xxii
P i partial vapor pressure
T tem perature
yi mole fraction of component i
a thermal diffusivity
7 vapor-liquid interfacial surface tension
/x dynamic viscosity
v kinematic viscosity
p density
a surface tension
uj acentric factor
Subscripts
L liquid
V vapor
Units
cP centipoise
cSt centistokes
g gram
J Joule
xxiii
K Kelvin
L characteristic length
m meter
m L milliliter
m N millinewton
mol molar mass
P pressure
Pa Pascal
W W att
fiL microliter
lim micrometer
°C Celsius
CHAPTER 1
INTRODUCTION
The ever-growing consumption of finite global energy sources and their envi
ronm ental cost is constantly encouraging the development of processes and systems
th a t promote increased sustainability, efficiency, and environmental responsibility.
Energy harvesting is a process th a t captures residual fractions of energy th a t would
otherwise be lost to the environment as heat, light, sound, vibration, or movement in
order to improve efficiency and encourage new technologies. The m iniaturization of
modern devices is increasing avenues for waste harvesting possibilities, such tha t energy
harvesting is proposed to potentially replace batteries for smaller, low-power electronics
in the future. The advantages and benefits from employing energy harvesting include
increased efficiency and sustainability, minimal maintenance time and cost, improved
environmental responsibility, and the ability to deploy devices in hostile environments
since direct interaction with personnel is not necessary.
While there are several energy harvesting sources, one of the most promising is
waste thermal energy recovery due to many standard thermodynamic processes having
low efficiencies, whereby much of the therm al energy generated is rejected to the
surrounding environment [11]. Many scales of waste thermal energy harvesting have
been proposed, from large industry down to the individual user personal computer and
1
2
electronics [12, 13, 14]. However, there has been a large research thrust over the past
decade into using waste energy for low-power electronics for remote sensing networks
and health monitoring of process systems [15, 16, 17, 18]. Harnessing the rejected
thermal energy via transduction mechanisms allows existing physical effects to power
additional systems, such as remote and hazardous location sensors [19].
The ability to use “affordable and abundant power” while increasing “available
power” are two of NASA’s Top Technical and G rand Challenges which require
research into waste energy harvesting [20]. As part of a larger research objective, this
study reports on the development of waste therm al energy harvesting enhancements
pertaining to a copper micro-channel heat, exchanger (MHE) with HFE-7200 working
fluid. The overall prototype includes waste energy harvesting of vibration, solar, and
thermal energies all feeding into a single circuit package to provide multiple avenues
of sensor power. However, the necessary thermoelectric generator (TEG) to convert
the waste therm al energy to usable electrical power is not the priority topic for the
present study. In addition to promoting generator efficiency, there is a need to develop
and optimize the heat exchanger incorporated in the harvesting system [21]. The
consistent deployment of TEG-based waste heat harvesting devices hinges on the
advancement of the associated heat exchanger [14, 21, 22].
MHEs use multiple fluid-filled channels which, at such reduced scales, produce
effective heat and mass transfer due to the development of dynamic boundary
layers [22]. Maximizing harvesting of waste heat for sensor power with MHEs
necessitates optimizing channel fluid dynamics while minimizing therm al resistance
[22, 23]. Therm al resistance is reduced using two-phase flows and m aterials with
3
high thermal conductivities [22, 23]. Priority for this investigation is the development
and understanding of the copper-based MHE fabrication and overall efficiency and
the multi-phase flows achieved during operation. The investigation includes design,
fabrication, and experimental testing of the MHE as well as numerical simulation of
phase change within the MHE and subsequent dimensionless analysis of the vapor-
liquid phase interfaces.
The introduction of micro-electronics ushered in a new age of prototyping
and m anufacturing technologies. As scales decreased down to the micro- and nano
levels, new fabrication methodologies and techniques were established, including
development and advancement of processing equipment. Unfortunately, increasing
facility capabilities has come at a price. Companies and universities with less funding
and purchasing abilities quickly found themselves a t a disadvantage while trying to
maintain technological pace [24, 25]. However, recent attem pts are establishing general
laboratory techniques for producing high-quality micro- and nano-scale devices without
the requirements of clean-room conditions and equipment constraints [26, 27, 28].
These a ttem pts at general laboratory fabrication m ethods serve two benefits for
furthering research. First, advancements in general laboratory techniques allow less
fortunate facilities the ability to continue im portant research in micro- and nano
technology. Secondly, the ability to fabricate small-scale devices in a general laboratory
environment enables lower cost of manufacturing, thereby allowing production and
adoption of such devices on a global scale. There has been no research regarding
general laboratory methods for fabricating metal-based MHEs up to this point. Thus,
a general laboratory m ethod producing MHEs would further promote the adoption
4
of waste therm al energy harvesting, increasing the efficiency and sustainability of
primary and auxiliary processes.
The potential of MHEs was first suggested by Tuckerman and Pease in 1981 for
cooling electronics for very-large-scale integrated (VLSI) circuits [29]. In their seminal
article, Tuckerman and Pease announced th a t by using heat exchangers fabricated
a t micrometer dimensions, power densities of kilowatts per square centim eter were
feasible [29]. While initially conceived for electronics, including MEMS, the widespread
embrace of micro-scale devices drove researchers to study the possibilities of micro
scale transport phenomena and how it differed from traditional macro-scale transport
processes [30, 31, 32, 33], The first, studies of MHEs examined channel geometry, fluid
flow characteristics, and heat transfer characteristics for single-phase flows [34, 35, 36].
However, a shift in research towards multi-phase transport was quickly adopted due
to improved transport capabilities of multi-phase devices [35, 36].
Energy transfer using two-phase fluid flows relies on working fluid conversion
from liquid to vapor. Devices which take advantage of the latent heat transfer of fluids
are more effective than devices which only use sensible heat transfer [37]. Though many
of these studies include devices where flow is induced via an external work mechanism,
the nature of micro-channels offers a capillary flow mechanism, whereby fluid naturally
flows through the channels [36, 38]. Removing the external work mechanism allows
the capillary flow-driven MHEs to achieve greater device efficiency and application
in remote and hostile environments due to minimal necessary interaction. However,
experimental testing is necessary to quantify the capillary flow-driven MHE for practical
5
application and experimental boundary conditions are required for further numerical
analysis of the system ’s interior operation.
W hile efficient performance of the MHE is vital to the overall goal of the
research, there are internal operations of the closed system MHE which can provide
fundam ental device performance characteristics. Conducting precise experimental
measurements of the internal flow and temperature fields on a sealed MHE is a difficult
task. One reason numerical modeling and simulation complements empirical work is by
allowing insight into otherwise difficult or impossible measurements. While understood
in practice and application, multi-phase flow is not fully understood theoretically.
Therefore, numerical modeling and simulation also gives researchers the ability to
observe behavior in systems which incur phase change. The traditional m ethod to
model the physical fluctuations at the phase change interface is to perform macroscopic
discretizations of continuum equations, most notably solving for the Navier-Stokes
equations. However, the nonlinearity and constant variations of phases at the interfaces,
where different phases are continually combining, separating, and evolving, present
difficulties for macroscopic numerical schemes. In the physics discipline of statistical
mechanics, it is known th a t behavior of fluids can be determined through statistical
analysis of ensemble systems on the microscopic scale. Though the evolution of
complex systems on the microscopic scale can involve m ultitudes of variables, these
systems can be expanded artificially to the ’’mesoscopic” scale where the physics of
the system is maintained.
In 1986, Frisch, Hasslacher, and Pomeau presented a Boolean case for using
lattice-based gas cellular au tom ata (LGA) to simulate nonlinear fields such as the
6
Navier-Stokes equations [39]. This led to the development of a computational method
named the lattice Boltzmann m ethod (LBM), based on the continuous Boltzmann
equation which has been discretized in time and phase space [40, 41]. When researchers
expanded the LBM to macroscopic systems, the Navier-Stokes equations were recovered
[39, 41, 42]. Soon after, studies began examining the use of LBM to simulate multi
phase and multi-component systems. Initially, these LBM models incorporated a
density distribution function which was then substitu ted into a given equation of
s ta te to provide the pressure function which indicated the location of phase change
interfaces. However, when tem perature differences play a vital role in the system and
boundary conditions, an additional distribution function based on tem perature was
required. Fusing the density and tem perature distribution functions with the chosen
equation of sta te presented numerical difficulties which caused many researchers to
test models using normalized param eters, such as the gas constant, and arbitrary
equation of sta te param eters [43, 44, 45, 46]. Unfortunately, for most fluids, this
generalization and normalization does not determine the phase change interface within
a physical system with a physical working fluid. After experim ental testing of the
copper MHE was completed, boundary conditions for the actual system, along with
HFE-7200 working fluid properties, were numerically modeled for interior operation
of the MHE. Once the model was simulated, reinforcement of interior MHE operation
was attem pted by both the equation of state and dimensionless group analysis.
The extensive literature on MHE fabrication and performance does not include
general laboratory fabrication techniques and an analysis of experimental and numerical
performance of efficiency and phase change with a non-normalized, real working fluid.
While normalizing d a ta and sim ulating analytical solutions to m ature problems
provides mathematical stability properties of a model, the gap in the knowledge arises
from a lack of effective test data from a physical, capillary-flow driven MHE operating
as a closed system to simulation behavior within the channel from real working fluid
phase change. The culmination of testing and simulating this particular MHE and
its application in the overall energy harvesting prototype narrows the knowledge gap,
allowing for greater understanding of the physical system and potential improvements
for MHE application in waste heat energy harvesting.
Incorporation of general laboratory fabrication procedures promotes a much
larger number of researchers who can prepare and explore MHE behavior with different
working fluids. Development of research methodologies for studying working fluid
phase change within the MHE leads to effectively characterizing MHEs for particular
applications and determining which working fluid provides the best performance for
specific environmental conditions. Therefore, the significance of this study is to initiate
investigations into physical working fluids and their behaviors under experimental
conditions to produce highly efficient and sustainable heat transfer devices, thereby
increasing the adoption of waste heat energy harvesting for varied situations and
environments.
Prim ary research questions for this study are whether a general laboratory
procedure can be developed which effectively produces reliable and repeatable MHEs
for testing, whether the fabricated MHE can be experimentally shown to be efficient
for possible energy harvesting applications, and whether a lattice Boltzmann model
of a single channel can provide insight into the working fluid phase change which is
8
occurring during device operation. In addition to answering these questions directly,
further analysis is performed using dimensionless group analysis of the working fluid
behavior within a micro-channel to understand the overall dominant forces governing
operation and the movement of the vapor-liquid interfaces during device operation.
1.1 Objective and Thesis Structure
One independent study examining the fabrication, experimental testing, and
lattice Boltzmann simulation of a copper micro-channel heat exchanger is presented
in this dissertation. The first part of the investigation, C hapter 2, focuses on the
fabrication of prototype devices of various heights, more importantly in a general lab
oratory environment free of clean-room constraints and requirements. The fabrication
procedure uses low-cost materials and minimal equipment to produce highly repeatable
devices. C hapter 3 covers the second part of the study determ ining experim ental
performance of the fabricated devices in conditions applicable to the first field testing
of the overall prototype. A practical low-energy heat source is used to characterize the
MHE efficiency of energy transfer using the HFE-7200 working fluid. Once the device
is produced and tested, the experimental boundary conditions and initial conditions
are input into the lattice Boltzmann model.
While many publications using lattice Boltzmann are normalized and modeled
using standard parameters and fluids including water, this work analyzes the simulated
performance of the device with copper boundaries and HFE-7200 working fluid
properties. C hapter 4 of the study gives an overview of the lattice Boltzmann
procedure, including the fundam ental equations, necessary to produce the device
simulation. After dem onstrating the thermodynamic properties of the simulation as
they evolve over tim e and the phase change occurring within the channel, C hapter
5 examines pertinent dimensionless numbers of the system and how those numbers
increase understanding of system behavior. These dimensionless numbers cover fluid
flow, heat transfer, and phase change during device operation. Finally, C hapter 6
presents a general conclusion of the study and offers recommendations for future work.
CHAPTER 2
GENERAL LABORATORY COPPER MICRO-CHANNELFABRICATION
2.1 Review of General Laboratory Fabrication and LithographyTechniques
The past fifty years have seen the exponential advancement of device and
component m iniaturization in manufacturing. Spurred mainly by the development
of electronics and semiconductor research, many techniques were; invented to allow
fabrication of increasingly smaller components. Unfortunately, along with the ability
to fabricate such technology, the equipment and facilities necessary have progressively
increased in complexity and expense. Such expenditures are not possible for all
research institutions. However, not all fabrication methods and applications require
such stringent laboratory constraints. Micro-scale metal-based waste energy harvesting
devices are one such application where potential harsh environments demand robust
fabrication methods which do not require large investments in equipment and facilities.
Micro-channel heat exchangers (MHEs) have been researched extensively
since Tuckerman and Pease’s study on using micro-channels for electronics cooling
[29]. These specific heat transfer devices use increased surface area to volume
ratios to develop dynamic boundary layers, producing enhanced heat and mass
transfer effects [22]. Traditional micro-fabrication is performed with silicon or glass
10
11
wafers; however, for heat transfer applications, m etal-based MHEs achieve greater
performance due to increased therm al conductivities [47, 48]. While there are five
broad fabrication classifications for processing micro-channels, most techniques require
expensive equipment or cleanroom facilities [49, 50]. Even though these methods are
not all applicable for general laboratory adoption, there are alternatives which require
minimal equipment and facility infrastructure.
Fabrication of micro-metallic components has been dem onstrated for over 25
years, prim arily using the LIGA technique [51, 52]. LIGA (German for lithography,
galvanoformung (electroplating), and abformung (molding)) is a method where thick
photoresists are applied to substrates as molds and filled with electroplated metals
[48]. However, traditional LIGA uses X-ray illumination and requires expensive
synchrotron radiation facilities for exposure [53]. The UV LIGA technique is an
economical alternative which, in addition to costing less in equipment and facilities, is
a more expedient process [53, 54]. The molding component of UV LIGA is exposed
at near-UV (350-400nm) wavelength to polymerize the photoresist, typically using a
negative photoresist such as SU-8 [26, 53, 55]. Traditional photoresists are spin-coated
onto substrates; however, in order to fully minimize overhead equipment and facility
cost, there are photoresist substitutes to act as the LIGA molding component.
The development and subsequent rapid global expansion of the electronics
industry initiated a need for a cost-efficient method to produce printed circuit boards
(PCBs). In the 1970s, Riston® negative film was introduced by DuPont® which was
applied to a substrate via lamination and exposed using a UV source [52]. Outside of
the electronics industry, these dry films have been used for several different applications
12
including electroplating molds and microfluidic channels [52, 54, 56, 57, 58]. The
advantages of using dry-film photoresist included good conformability and adhesion
to any substrate, improved processing speeds and time, excellent thickness uniformity,
low cost, and safety conveniences due to simple handling and no solvent/liquid use,
all of which are favorable especially for general laboratory environment execution
[52, 54, 59].
Exposing dry-film photoresist using an adapted UV LIGA technique requires
modifications to standard lithography mask processing which are developed for low
cost use in general laboratories. Traditionally, chrome masks are generated for
photolithography via e-beam or laser writing [48, 60, 61]. Though resolutions down to
lOnm are possible, fabrication of the masks is time-consuming and requires extensive
and expensive equipment and facilities [60, 61]. Saving time and money without losing
one order of magnitude resolution, microscope projection photolithography, developed
in the 1970s, manages resolution down to 500nm using modified laboratory microscopes
[60, 62, 63]. However, in order to promote a globally acceptable fabrication method, it
must be low-cost for the mask and necessary equipment and allow general laboratory
capability without including cleanroom facilities.
Inkjet printers have evolved greatly from the first dem onstrated printers
developed by Siemens in the 1950s [64], Advancing from continuous deflection print
systems to the widely adopted drop-on-demand method, modern commercial off-the-
shelf (COTS) inkjet printers have achieved resolutions of 5760x1440 DPI, corresponding
to approximately 4^m and 17/im between dots [64]. Resolutions with such precision
have allowed some researchers to develop methods to print the lithography mask with
13
an inkjet printer [27, 28]. However, further reduction in processing steps and economic
cost by using standard office equipment and minimal laboratory equipment is possible
which produces metallic micro-structures down to 300/im scales.
A lithographic micro-fabrication method which incurs little cost to a laboratory,
allowing any facility the ability to m anufacture metallic m icro-structures on any
flat substrate including metals, is presented here. The process shown dem onstrates
copper-based MHEs with channel widths of 100/im and 300//m using negative dry-film
photoresist. The minimal equipment necessary for this fabrication method makes the
micro-fabrication process more accessible for facilities without cleanroom capabilities.
After the fabrication process is explained in detail, sample results are given followed
by an analysis of process capabilities.
2.2 Fabrication M ethodology
The fabrication of MHEs from the modified UV LIGA technique concentrates
on electroplating copper onto copper sheeting substrates in order to take advantage
of copper’s high therm al conductivity. Previous studies established an initial device
topology, shown in Figure 2.1, which requires electroplating copper from solution onto
a copper substrate to produce the reservoir boundaries and micro-channel walls. Using
a rigid substrate provides a platform which reduces plating delamination and cracking
due to operating conditions and handling. Copper sheeting of 600/im thickness is used
for the MHE substrates and lids. Minimizing necessary equipment and fabrication
time, Ordyl® dry-film photoresist is used which is produced by Elga Europe®. Initial
fabrication testing progressed from Ordyl® P50100 dry-film, lOO/urn thick film to the
14
current Ordyl® Alpha 375 dry-film. Alpha 375 dry-film is 75/tm thick photoresist film.
Processing conditions required are equivalent for both dry films, given in Table 2.1.
□ n u l D M A r u A i n
Micro-channels
Figure 2.1: Initial MHE topology with two reservoirs and 27 micro-channels
Table 2.1: Ordyl® parameters [1]
Lamination Development Stripping
k 2c o 3 N aO H
l-3m /m in (Speed) 0.8% Solution 1-3% Solution
105 - 125°C 28°C 40 - 60° C
2.5-6.0 bar 1.5 bar 1.5-4.0 bar
2.2.1 Mold Preparation
Fabricating micro-scale resolution structures w ithout advanced equipment
requires pre-processing the copper substrate in order to decontaminate and smooth the
substrate for further processing. The copper substrate sheet is initially smoothed with
a wire brush and polishing wheel attachm ents with a Dremel® multi-tool. An acetic
B66D
15
acid solution of 50% concentration at 60°C is then used to clean and decontaminate
the substrate. After rinsing w ith de-ionized (DI) water and dried, the substrate is
ready for processing. The first step requires adhesion of the Ordyl® photoresist to
the substrate.
According to Elga Europes Ordyl® datasheet, the optimal conditions to apply
the dry film photoresist is with either a manual or autom atic lam inator [1], The
Akiles® Pro-Lam Ultra X-6 automatic laminator allows for roller tem perature control
and speed control. The lam inator is shown in Figure 2.2. In order to facilitate
lam inating the sample and to ensure th a t the dry film does not adhere to the hot
rollers, the substrate is placed onto a sheet of Teflon® with an additional sheet of
printing paper on top. The paper is placed on top of the substrate to help smooth out
the photoresist, aiding in removing any wrinkles which occur when the film is placed
on the substrate. After laminating the sample, there is a minimum 20 minutes hold
time prior to exposing the sample to allow for adequate sample cool-down [1],
Figure 2.2: Akiles® Pro-Lam U ltra X-6 autom atic laminator [6]
There is an im portant processing objective which bears mention at this point
in the process prior to continuing the fabrication profile. Most dry-film photoresists,
16
including Ordyl®, has a 1:1 ratio of film thickness to maximum resolution. Therefore,
for Alpha 375 the film thickness is 75/mn and the maximum resolution possible is
75/xm . Unfortunately, for 300/im channel widths, 75/im height does not provide ample
height to the channel walls, thereby reducing volume of working fluid and decreasing
effectiveness of capillaries to facilitate good fluid flow, thus reducing efficiency of the
MHE. Therefore, a further study into the possibilities of raising film mold height
without losing resolution is justified for appropriate device height.
Though not explicitly discussed or even mentioned in the literature or product
datasheets, multiple layers of Ordyl® dry-film photoresist can be applied when required
thickness of micro-structures exceeds available dry-film thickness. The dry-film has
wrappings on both sides prior to use; however, once the first layer is applied and the
substrate cools, the top wrapping of cellophane can be removed and another layer of
Ordyl® applied with the laminator. The difficulty in applying multiple layers arises
from the natural adhesion of the Ordyl® dry-film. When the top wrapping is removed
and another layer applied prior to laminating, the layers adhere to one another causing
potential bubbles and inconsistencies in the layers. To reduce this effect, a metal sheet
was placed into a freezer to lower its temperature. Before placing the second Ordyl®
layer, the substra te ’s tem perature was lowered from contact with the m etal sheet.
Lowering the temperature briefly reduces the cling of the two Ordyl® sheets and allows
several attem pts to get the second layer in proper position without adhering to the first
layer. While this technique is not necessary for the lithography process, it provides
researchers with flexibility regarding available m aterials and film thicknesses. This
17
development also extends the capabilities of using dry-film photoresists to previously
unheard of heights.
Once the Ordyl® dry-film is laminated onto the substrate, the next step in the
process is the UV LIGA exposure which requires the lithographic mask. Searching
for a mask technique th a t requires minimal equipment, standard office transparency
sheets are an optimal platform for the mask print. An Epson® Artisan 1430 Inkjet
Printer with 5760x1440 DPI resolution is used to print the mask. An axial symmetric
rectangular mask pattern is drawn in DipTrace®, a PCB design and schematic freeware.
Printing several designs and channel widths to test the printer’s resolution resulted in
minimal possible channel widths of 100/mi . Reducing scales further increasing the
possibility of the mask having alignment issues due to print drops. Therefore, the
300/xm channel width MHE design is well within the capabilities of the printer. Figure
2.3 shows the MHE pattern printed on a transparency sheet.
Figure 2.3: Printed MHE pattern on a transparency sheet
Since the process and dry-film are adapted from PCB use, the light source used
is a Kinsten® KVB30D UV Exposure Box, shown in Figure 2.4. Ordyl® specification
18
for exposing Alpha 375 is 2 5 - 3 0 ^ [1]. For the given MHE pa tte rn geometry, the
exposure time was calculated to be 15 seconds per layer of dry film. The key to using
a transparency mask directly on the sample is the built-in vacuum unit of the UV
exposure box. This minimizes the distance between mask and sample and potential
light diffraction which causes over exposure of the film in locations not desirable. One
im portant note is when the sample is removed from the exposure box, there may
or may not be indication th a t the exposure is successful. The key to the process is
ensuring th a t the sample is not over-exposed. Over-exposure causes the subsequent
development step to fail due to semi-polymerized resist which is to be removed.
Figure 2.4: Kinsten® KVB30D UV Exposure Box [7]
19
The recommended developing properties are given in the Ordyl® datasheet [1],
Potassium carbonate solution of 0.8% concentration is mixed and added to a store
purchased garden sprayer. The sprayer technique allows the developer to be applied
a t proper pressure to remove the unexposed photoresist from narrow channels and
structures. Samples are sprayed evenly for 20 second intervals and rinsed in water to
prevent over-developing the mold. If over-developed, the polymerized channel walls
begin to delaminate and the bulk polymerized film can strip off of the substrate. This
process is continued until all of the unexposed photoresist is removed. The samples
are then dried w ith a laboratory fan and exam ination under a microscope confirms
when all of the unexposed photoresist is removed. Figure 2.5 shows a sample of height
75/xm thickness after development and prior to electroplating.
Figure 2.5: Example 75pm mask prior to electroplating
20
2.2.2 Electroplating
Prior work indicates th a t electropolishing the copper substrate provides an
improved and clean surface for electroplating [65]. Polishing the substrate creates
a surface with enhanced uniformity, prevents delam ination of plating, and allows
for repeatability of MHE samples. A phosphoric acid based solution is used for the
polishing step due to its widespread use and relatively safe handling when comparing
with other possible polishing solutions. Table 2.2 shows the final solution composition
and conditions [2]. After testing, samples indicate th a t the polishing step could be
performed before or after the Ordyl® mask processing. However, for this work, the
polishing step is performed after the dry-film photoresist has been developed.
Table 2.2: Electropolishing parameters [2]
Parameter Working Condition
h 3p o 4 157mL
h 2o 75mL
Al powder 3gCurrent 0.05A
Temperature 55°C
The mature solution of copper sulfate and sulfuric acid is used for electroplating
due to ease of preparation and accounting for chemical hazards. Table 2.3 shows the
final solution composition and conditions for plating. Using the literature current
density of 0 . 6 1 ^ , the appropriate calculated current for the geometry is 0.67A [3].
However, this current was too large. An example of using large current, causing
visually uneven plating, is shown in Figure 2.6. The optim um plating current for
21
the MHE geometry was experimentally determined to be 0.4A [66]. Figures 2.7 and
2.8 show samples plated at 0.4A with a BK Precision 9130 DC Power Supply. After
establishing the initial polishing and plating process, numerous samples prepared
prove tha t the process is reliable and repeatable in a general laboratory. The process
flow chart to create the MHE is shown in Figure 2.9.
Table 2.3: Electroplating parameters [3]
P a ra m e te r W o rk in g C o n d itio n
C uSO i • 5H 20 188f
h 2s o 4 74 £Current 0.4A
Temperature 40 °C
Figure 2.6: Sample plated with non-optimal 0.5A current
Figure 2.7: Example 75/zm mask height channels plated at 0.4A
Figure 2.8: Example 225//m mask height channels plated at 0.4A
23
I Pre-plating Polymer Strip]
✓ ---------Substrate
( b )
UV Exposed Mask(e)
| Completed Plating attar PR Removal j
(c) (f>
Figure 2.9: Preparation steps for the MHE: (a) clean substrate and electropolish if desired; (b) apply dry-film photoresist, single or multi-layers; (c) UV expose the photoresist with appropriate mask geometry; (d) remove unexposed photoresist with developer; (e) electroplate the sample; (f) remove exposed photoresist with stripper leaving the finished device
24
Additional study on MHE geometry focused on 100/un radial channels. While
intially thought to be scalable using the dry-film photoresist, it was quickly determined
th a t fabrication techniques were reduced in repeatability and consistency as the
minimum dry film resolution was approached. However, though the 100/mi geometry
was not used moving forward with the waste heat recovery prototype, some samples
were produced. Figure 2.10 shows a radial 100/im geometry MHE after electroplating
was completed. The few 100/im samples produced proved th a t the general laboratory
procedure was adaptive to varying MHE dimensions.
Figure 2.10: Sample radial MHE with 100/iin channel width and 50//m height
2.3 Results and Discussion
Results for the general laboratory MHE fabrication with dry-film photoresist
were determined for 300/xm channel width, both quantitatively and qualitatively. Tests
were conducted to characterize channel wall plating, both for verticality and overall
height, plating deposition rate, and to provide SEM image analysis for channel wall
25
structure. The analyses for all three tests were performed on both the 75/zm height
film mask samples and the 225/rm height film mask samples.
If the dry film over-develops prior to electroplating, the subsequent processing
steps lead to channel walls with rounded bases. The change in channel wall geometry
from the desired square/rectangular geometry affects both the fluid flow characteristics
and the heat transfer characteristics [67, 68]. Therefore, a Dektak 150 Surface Profiler
is used to determine channel wall verticality and channel wall height for both plated
MHE heights. Figure 2.11 shows a 3mm sample distance for the 75/rm mask height
samples while Figure 2.12 shows a 3mm sample distance for the 225/un mask height
samples. The profile figures both verify the verticality which can be achieved with
proper lam ination and development processing steps. There is little to no vertical
variation until the channel walls exceed the height of the dry-film mask. Note th a t
while the verticality of the channels is m aintained during electroplating, the top
surfaces of the walls are quite rough, according to the profile. This is primarily due
to plating enhancements, such as brighteners and levelers, not being added to the
electroplating bath in order for evaluation of the most cost-effective MHE fabrication.
26
900
800
700
600
2 500£M'5 400x
300
200
100
0
A/S r\A
500 1000 1500 2000 2500 3000Distance (fim)
Figure 2.11: Plating profile for 75/un sample
— 1500
XL,00‘<b
1 1000
500
o ---------- --------- ---------- ---------- ----------0 500 1000 1500 2000 2500 3000
Distance (pm)
Figure 2.12: Plating profile for 225//m sample
27
Determination of the plating deposition was crucial for developing processing
times which produced repeatable MHE samples of approximately equal height. The
calculation for deposition ra te was experimentally verified by plating ten samples,
five of 75/tm mask height and five of 225/tm mask height, for different periods of
time, namely 20 through 100 minutes, in increments of 20 minutes. Surface profiles
of each sample were plotted and measurements of each channel wall height averaged,
per sample. Results indicated an approximate deposition rate of 2.0 — 2.4^% at the
electroplating conditions given in Table 2.3. Sample calculations of 75/rm mask height
and 225/im mask height are given in Table 2.4. The anisotropic nature of electroplating
caused samples to exhibit detrimental properties if deposition exceeded dry film height.
These properties stemmed from the channel walls losing verticality and experiencing
growth in all directions. This “mushrooming” quality reduced effectiveness of channels
and made stripping the photoresist difficult.
Table 2.4: Average deposition rates for 75/im and 225/fm samples
Mask Height Plate Time Ave. Wall Height Ave. Dep. Rate75/tm 40 min 81.75/tm 2 . 0 4 ^m in
225/xm 100 min 233.6/tm 2 .3 3 -^m in
Once the electroplating param eters were measured and characterized for the
MHEs, scanning electron microscope (SEM) image analysis was used to determ ine
the microscopic structure of the plated walls. Images of 120/wn mask height samples,
given in Figures 2.13 and 2.14, depicted the channel walls having porosity which was
estimated at 16% using the SEM. Physical estimation of the porosity was performed
using a linear bulk volume measurement. Given the size of the designed and plated
28
MHE, the fabricated sample was massed and converted to volume using the density
of copper. It was calculated th a t the sam ples’ volumes were 85% of the theoretical
volume of the MHE, thus giving a porosity of 15%. The porous structure increased
usable device surface area and enhanced contact area for the device working fluid.
Though further explained in Chapter 3, the porous result of channel wall fabrication
caused wicking action throughout the entire MHE structure.
Figure 2.13: SEM image of channel walls at 500//.m scale
29
r
C 4 8 0 0 5 ])“ /■».Cr' r k I 00* GC..Vf ;C ' 2 3 / 2 0 12 GOOnm
Figure 2.14: SEM image of channel walls at 500nm scale
30
Similar to capillary flow, wicking is dependent on meniscus curavature and is a
primary flow mechanism in two-phase flow through porous media [69]. Interconnecting
pores vie for fluid flow and a branching competition occurs at every interface throughout
the media’s complex geometry [69]. During two-phase flow of vapor and liquid, any
mixture segregates based on pore size [70]. The separation of phases allows the liquid
to give be tte r w ettability over the channel surfaces w ithout drying out [70]. Liquid
motion throughout the MHE channels and walls provides a continuous surface flow
throughout the lattice which is advantageous for energy transfer through the MHE.
2.4 Conclusion
An efficient method of fabricating copper-based MHEs with minimal equipment
is established using dry-film photoresist. While dry films have thickness lim itations
for structures needing sufficient height, such as MHEs, this previously unpublished
novel method proves that layering multiple films produces MHE molds over 200/xm in
height w ithout reducing photoresist resolution. This general laboratory preparation
process allows for global adoption of micro-fabrication of structures and devices,
even if electroplating is not the desired m ethod for metal deposition. In the case
of MHEs, using the m ature electroplating process further reduces required overhead
expenditures and processing equipment. Though the literature for electroplating is
well established, the 100/xm and 300/xm channel width geometries require altering the
suggested literature current densities to produce reproducible samples of approximately
equal height and smoothness. While the 100/xm samples are possible, the consistency
of the 300/xm samples far exceeds them; thus the 300/xm channel width geometry is
31
used for the energy harvesting prototype. After fabricating several samples of various
channel wall heights, analysis of the reproducibility, deposition rate, and channel wall
structure shows th a t the 300/rm process is repeatable with excellent channel wall
geometry where the deposited copper provides added wicking potential due to an
approximate 15% porosity.
Once the fabrication process is determined, numerous samples of equal 120/iin
channel wall height are prepared for experimental performance testing of the MHE. The
nature of the first prototype for delivery demands an immediately reproducible solution
and maintains an adequate aspect ratio of channel width to height. Characterizing the
fabricated MHEs experimentally for overall heat transfer efficiency is the objective of
the following chapter. Enhancing the heat transfer qualities of MHEs through general
laboratory fabrication methods is a key component to the global adoption of such
technologies for greater system efficiency and sustainability.
CHAPTER 3
MICRO-CHANNEL HEAT EXCHANGER TESTING FOR WASTE HEAT RECOVERY EFFICIENCY
Processes which convert energy into usable forms are ubiquitous in everyday
life. Unfortunately, many processes in use today are inherently inefficient. Industry is
developing techniques, such as cogeneration, which attem pt to recover fractions of the
expended waste heat for reducing costs and pollution emissions [71, 72], For smaller
scale waste heat recovery, the benefits are reduction of equipment costs, potential
independence from batteries, and simple maintenance [16]. Adoption of waste heat
recovery techniques for small-scale application therefore requires greater efficiencies
than large industry processes like cogeneration since the usable input energy is much
lower than the large-scale applications.
Most therm al energy conversion processes require heat exchangers which
transfer therm al energy from one fluid to another fluid. However, the process and
equipment can be simplified if the aim of the device is not conversion of therm al
energy but only transfer of thermal energy. For small-scale waste heat recovery using a
thermoelectric generator (TEG), the objective is supplying as much energy to one side
of the TEG while keeping the other side from increasing in potential energy. Therefore
for the current program, an effective means of transferring energy to either a TEG or
32
33
thermal storage unit is desired. Reducing thermal resistances and taking advantage of
therm al conductivities for optimizing efficiency, cost benefit, and device robustness
encourages the use of metals such as copper. Scaling opportunities for potential device
environments and magnitudes of available energy on such small scales for device use
drives the approach toward employing micro-channel heat exchangers (MHEs).
3.1 Review of Previous and Current Micro-Channel Heat Exchangers
Compared w ith conventional heat exchangers, MHEs produce be tter heat
transfer performance prim arily due to higher surface area to volume ratios [36, 37].
Scaling effects from the enhanced surface area to volume ratio increases the impact
of surface forces and viscous forces while enhancing axial heat conduction a t the
micro-channel wall [73]. Large heat transfer coefficients, driven by the MHE channel’s
hydraulic diameter, are achievable w ith MHEs [33, 74, 75]. Therefore, using an
MHE for the small-scale waste heat recovery prototype application provides the best
performance with a minimal footprint.
Initially, much of the research on MHEs was conducted with single-phase flow
devices at only a few institutions [36]. This was done since fluid flow characteristics
through the micro-channels did not always follow classical theory [74], As researchers
learned more about MHE behavior and potential, the larger focus changed from
single-phase flows to two-phase flows. The addition of phase change enhanced MHE
performance due to larger heat transfer coefficients, reduced coolant flow requirements,
reduced therm al resistance, and greater channel tem perature uniformity [76, 77, 78].
Two-phase heat transfer occurred when the lower tem perature liquid experienced
34
partial conversion to vapor. While sensible heat transfer was occurring in these
systems, the prim ary heat transfer performance relied on the latent heat exchange
[78].
Using two-phase flow MHEs with small hydraulic diam eters results in sub
stantial pressure drops across channel lengths [79, 80]. Countering the pressure
drop requires many researchers to rely on external work mechanisms such as pumps
to provide the necessary fluid flow pressure [22, 81]. Unfortunately for the current
program, including addtional devices remove essential efficiency for waste heat recovery.
Therefore, the current MHE employs capillary flow for fluid motion. Capillary flow
is a product of driving forces due to hydrostatic pressure, inertial force of liquid in
the channel, inertial force at channel inlet, capillary force, and viscous drag [82]. The
study MHE has a reduced hydrostatic pressure due to approximate two-dimensional
operation. For axially symmetric channels with laminar flow, Brody calculated an exact
analytical solution to flow velocity distribution with a specific boundary condition
of zero velocity halfway down the channel [82], Due to the two-phase flow in the
channels, there is also an evaporative factor which causes meniscus deformation and
recession as the fluid travels farther from the inlet [83]. The current study MHE shows
that the bi-directional fluid flow and symmetry of both reservoir inlets causes minimal
meniscus recession along the channel axis.
In addition to capillary flow along the micro-channels, the porous result of
channel wall fabrication causes wicking action throughout the entire MHE structure.
Similar to capillary flow, wicking is dependent on meniscus curvature and is a primary
flow mechanism in two-phase flow through porous media [69]. Interconnecting pores
35
vie for fluid flow and a branching com petition occurs at every interface throughout
the m edia’s complex geometry [69]. During two-phase flow of vapor and liquid, any
mixture segregates based on pore size [70]. The separation of phases allows the liquid
to give better w ettability over the channel surfaces w ithout drying out [70]. The
combination of capillary flow and wicking action provides a liquid motion throughout
the MHE channels and walls which gives continuous surface flow throughout the
lattice, further increasing surface area to volume ratios contributing to larger energy
transfer capability in the MHE.
Applications for MHEs have ranged from electronics cooling to harnessing
waste energy [29, 84], Recent research has explored system level waste heat energy
harvesting solutions by characterizing heat transfer devices coupled with thermoelectric
generators [85, 86 , 87, 8 8 , 89, 90]. However, researchers have noted tha t in addition to
improving the conversion efficiency of thermoelectric material itself, there is a parallel
need to research and develop advanced associated heat exchangers [91, 92, 93, 94],
In fact, researchers prom ote the optim ization of TEG based systems rather than
individual components in order to maximize the output power. The use of advanced
heat transfer devices is critical to efficient TEG operation and future deployment [93].
Therefore, while researchers continue to investigate system level solutions for energy
harvesting, the optimization of energy transfer via the MHE is the prim ary priority
presented here.
Though current publications have shown developed waste heat recovery pro
cesses and techniques from multiple energy sources and industries, including automo
tive, engines, oil and gas, steel, and steam, focus here is on maximizing energy transfer
36
via the MHE for any low-temperature waste heat source [95, 96, 97, 98, 99, 100, 101].
Low-temperature heat sources allow the production of power from renewable energy
sources, such as solar radiation. Much of the most recent research has been facilitated
by developing mid- to large-scale Organic Rankine Cycle (ORC) systems; however,
there is still continued interest in the possibilities of micro-scale energy harvesting
[102, 103, 104, 105, 106].
The MHE in the current study creates a robust piece of equipment with minimal
laboratory equipment while m aintaining a high heat transfer capacity. Once made,
such a device can be coupled w ith other devices, such as therm al storage systems.
Heat exchanger development, along with materials research, are the cornerstones in
developing effective and renewable thermal energy storage [107]. One challenge, when
studying the phase change m aterials (PCMs) which are vital to the therm al energy
storage, is tha t most PCMs have low thermal conducitivities leading to low charging
and discharging rates [108]. The MHE studied attem pts to maximize structural heat
transfer, while providing a platform capable for use in varied environments.
The intentional ambiguity of design parameters, in fabrication and in operation,
makes the MHE multi-faceted, both in environmental condition and cost. Economic
and situational demands may dictate the use of an alternative metal and working
fluid. Following fabrication of the MHE systems are evaluated in therm al testing
and therm al absorption of sim ulated heat sources. The MHE is designed for closed
system operation whereby no external work mechanism is needed for fluid movement.
Therm al and momentum transport are driven by using phase change of a working
fluid. The micro-channels drive capillary action of the fluid such th a t the working
37
fluid is dispersed over the heat source area, improving heat transfer to the working
fluid. The boiling working fluid travels to the MHE copper lid where heat transfer
to the heat sink allows condensation to occur and the working fluid returns to either
the micro-channels or the reservoirs on the MHE ends. The boiling and condensation
process within the MHE is shown in Figure 3.1. This internal action is further explored
and detailed in Chapter 4 through unique LBM modeling and validation.
Heat Sink
Heat Source
Figure 3.1: Fluid cycle interaction in the MHE, where each channel is simultaneously boiling and condensing due to the heat source and heat sink
3.2 Working Fluid Description
3M™ Novec™ Engineered Fluids have been produced for extreme environ
ment therm al management applications [5]. Based on initial tem perature estimates
for the intended environment of the MHE, Novec‘M HFE-7200 was chosen as an
appropriate working fluid candidate. The bulk component of Novec™ HFE-7200,
ethoxy-nonafluorobutane (C4F9OC2/ / 5), was designed to replace ozone-depleting
substances and to offer favorable environmental properties such as low toxicity and
nonflammability [4, 5]. A summary of HFE-7200 environmental and safety properties
is given in Table 3.1.
38
Table 3.1: HFE-7200 environmental and safety properties [4]
Properties HFE-7200Ozone Depletion Potential - ODP 0.00Global Warming Potential - GW P 55
Atmospheric Lifetime (yrs) 0.77Flashpoint None
Flammability Range in Air 2.4 - 12.4%Exposure Guidelines, 8hr TWA (ppm) 200
Acute Toxicity, 4hr LC50 (ppm) >92,000
There are three particularly noteworthy properties regarding HFE-7200 fluid
properties integrating with MHE operation. First, the low surface tension, even at
ambient temperatures, provides a superior wetting agent for the porous micro-channels.
Since low surface tension corresponds to larger surface area dispersion, HFE-7200 is
an excellent choice for infiltrating the porous channel walls as well as wetting along
the channel length. Increasing fluid distribution increases effective surface area for
convective heat transfer. The low heat of vaporization enhances vapor saturation
and requires less energy to begin the internal MHE cyclical process. Reducing energy
input necessary to begin effective heat transfer means less residence tim e of liquid
once the heat source power is input into the MHE, increasing tim e efficiency of the
device. Lastly, the large m aterials com patibility of HFE-7200 allows optim ization
for MHE m aterials of construction [109]. Table 3.2 provides physical properties of
HFE-7200, mostly at ambient tem perature and pressure. Therefore, depending on
the application and intended environment, HFE-7200 can be used regardless of device
composition. Initial analysis of working fluid possibilities confirms the appropriate
choice of HFE-7200 based on favorable environmental characteristics and favorable
physical properties for the MHE application.
39
Table 3.2: 3M™ therm al management fluid properties [5]
U n itsN ovec
H F E -7 2 0 0Boiling point °C 76
Molecular Weight _2_mol 264
Critical Temperature °c 210Critical Pressure M P a 2.01Vapor Pressure kPa 16
Heat of Vaporization ukg 119
Liquid Density kgm 3 1420
Coefficient of Expansion K ~ l 0.0016Kinematic Viscosity cSt 0.41Absolute Viscosity cP 0.58
Specific Heat jkgK 1220
Thermal Conductivity W_m K 0.068
Surface Tension m /v __m 13.6
3.3 Test Setup
Prior to testing with working fluid, the fabricated MHEs were baselined in a
dry condition. Devices were tested with no fluid first and then working fluid was added
to the MHEs. The baseline measurement was performed to determ ine the energy
lost to surroundings. The amount of fluid necessary to fill the MHE reservoirs and
channels was 150/xL based on the device geometry. This value was used to determine
an appropriate volume of working fluid for testing. A vapor-liquid interface was desired
so the MHE was not filled entirely with working fluid and forced into a pressurized
pool boiling operating mode. In this operating mode, the capillary channels would be
ineffective. Based on the necessity to have the vapor-liquid interface and condensation
at the MHE lid, the volume of working fluid added to the MHE was 120/iL, or 80% of
total MHE volume. The MHE was designed to have multiple applications in multiple
environments. In this work, a low-temperature waste heat environment was targeted
40
TMwith tem peratures of the MHE below 100°C. Therefore, 3M HFE-7200 engineered
fluid was selected as the working fluid. The low liquid viscosity increased capillary flow
through the channels and the boiling point of 76°C was low enough to provide a testing
platform for low-power input applications. Loading of the MHE fluid was performed
by manually filling the MHE using a Gilson® Pipetman™ pipette. Following filling
of the MHE, the devices were ready for testing. Figure 3.2 shows an example of a
finished MHE.
Figure 3.2: Completed MHE sample with lid and working fluid access port
Tests were conducted to characterize energy absorption and transfer of the
MHE and tem perature profiles of MHE bottom and lid. The fabricated MHEs were
tested in a setup depicted in Figure 3.3. Minimizing energy losses to surroundings
due to test setup, the testing was performed on a balsa wood platform. Balsa wood
has a therm al conductivity only twice th a t of air but the same order of magnitude,
0 .0 4 8 ^ for balsa versus 0 .0 2 4 ^ for air. Low thermal conductivities helped reduce
unnecessary energy losses into the test setup platform. Omega® k-type bare wire
41
thermocouples (TC) were used to measure tem perature at discrete points on the
heater, heat sink, heat flux sensors, and the MHE. Omega® listed the error of each
TC as ±0.5°C'. The heat source of the test device was provided by an Omega®
KHLV-101/10-P resistance heater. The heater was connected to a power supply with
a measured 3.6W input power maintained for every test. This power was selected to
ensure the bottom of the MHE reached tem peratures above the working fluid boiling
point in order to cause the required and desired phase change.
Energy output from MHE
Energy Input from Heater
Figure 3.3: Test setup with thermocouple locations shown as yellow circles
To quantify the thermal energy transfer through the setup, an Omega® HFS-4
thin film heat flux sensor (HFS) was placed between each layer as noted in Figure 3.3.
Worth noting was a method used to minimize energy loss through the test setup under
Heater #2. Heater # 1 and HFS # 1 , from Figure 3.3, were included in order to offset
heat output from Heater # 2 towards the setup base. The additional HFS underneath
Heater # 2 was used to minimize energy loss through the balsa base by tracking HFS
# 1 from Figure 3.3 and maintaining a heat flux measurement of zero, such tha t Heater
# 1 acted as a guard heater. This ensured th a t the m ajority of ou tput from Heater
42
# 2 was directed towards the MHE. The nominal sensitivity of each HFS-4 has a
sensitivity of ±10%, according to Omega®. Each HFS was calibrated and verified by
Omega®.
The heat sink used in the test setup was a Xigmatek A 10 S80DP, typically used
for cooling PC processors. The heat sink had enough thermal mass to hold constant
tem perature during device testing. A lab jack was used to ensure good therm al
contact between the MHE, all sensors and heaters, and the heat sink. As shown
in Figure 3.3, this setup was m aintained for all tests. Care was taken to maximize
therm al contact between setup layers by using Omega® Omegatherm®201 therm al
paste. D ata was recorded and analyzed via a Lab-Vicw program on a connected PC.
The two heat flux sensors (HFS # 2 and HFS # 3 ) provided heat flux data which was
used to calculate energy transference and losses. The heat flux transfer through the
MHE and tem perature data allowed characterization of the MHE as described in the
Experimental Results section.
Experim ental work carries with it an inherent uncertainty when quantifying
measurements. For fabrication of the MHE, there are two process steps which
have measurable error: printing the MHE mask and the channel wall height due to
electroplating. Once fabricated, the MHE experimental testing has three occurring
measurement uncertainties: the amount of working fluid added to the MHE with the
micro-pipette, instrumentation error due to the heat flux sensors, and instrumentation
error due to the thermocouples. Results of the fabrication and testing error are
summarized in Table 3.3.
43
Table 3.3: Error for fabrication and experimental measurements
Measurement AbsoluteError
RelativeError Notes
MHE Mask Transparency
4pm ; 17pm 1.3%; 5.7%Based on 5760x1440dpi. Depends on print orientation.
Dektak Plating Height 3pm 4%; 1.3%
Profiler absolute error. Relative error given for 75um and 225um samples.
Omega®Thermocouple 0.5°C
Thermocouple 0.5% Heat sourceThermocouple 0.53% Dry MHE bottom plateThermocouple 0.58% Wet MHE bottom plateThermocouple 0.78% Dry MHE top plateThermocouple 0.9% Wet MHE top plateThermocouple 1.4% Heat sinkOmega® Heat Flux Sensor
10%sensitivity
Based on Omega® product sheet
Heat flux sensor 0.261pVyVF/ra2 0 .002% HFS-4 (#15120163)Heat flux sensor 0.061pVyVF/m2 0.0004% HFS-4 (#14120030)Heat flux sensor 0.161pVyVF/m2 0 .001% HFS-4 (#14030129)
Micro-pipette lp L 0.83% Working fluid added to MHE
3.4 Results and Discussion
Tests were conducted to characterize the operation of the dry copper-based
MHE versus a working fluid wetted MHE. The therm al testing reported how added
thermal energy to the device altered heat flux and temperature measurements in order
to characterize heat transfer and energy transference of the device. This was utilized
in subsequent model evaluation and validation work.
Though the given energy input to the heater was 3.6W, resistive losses reduced
energy input supplied to the MHE to 3.44W. This corresponded to a heat flux entering
the MHE of 8 .7 ^ - . For the dry MHE, the output heat flux, measured at the interface
between top MHE surface and heat sink, was 7.6^y while the wetted MHE output
44
was 8 . 3 ^ , depicted in Figure 3.4. The percentage of input flux which exited through
the MHE was 87.5% for the dry MHE and 95.4% for the wetted MHE. Through
the use of the working fluid, energy transfer through the device was increased by
approximately 8%. Energy rejected from the sides of the MHE was assumed negligible
versus the overall thermal energy passing from source to sink. This was based on the
operating temperatures, heat flux, and side cooling tha t was restricted to radiation or
free convection. Direct calculation of the side losses for both the dry and wetted MHE
tests yielded less than 1% of the to ta l input power to the device. Remaining input
which was lost to the surrounding environment was the result of energy absorbed by
the copper MHE due to the increase in experimental temperature, energy lost through
the MHE bottom plate into the balsa wood base, energy absorbed by the working fluid
and vapor due to increases in tem perature, and the energy absorbed by the working
fluid during phase change. The heat flux summary of input, output, and side losses is
given in Table 3.4.
Hea
t Fl
ux
(kW
/m:|
45
10
500 1000 1500
Time (s)
Input to MHE MHE drv output -«-MHE wet output
2000 2500
Figure 3.4: Heat flux data from dry and wetted tests
Table 3.4: Energy input, output, and side losses for dry and wetted tests
Dry Test W etted TestInput Heat Flux 8 .7 ^ (100%) 8.7*$ (100%)
O utput Heat Flux (Measured) 7.6^$ (87.5%) 8.3*$ (95.4%)
Heat Flux Lost Through Sides 0.08^$ (0.92%) 0.05*$ (0.57%)
46
The tem perature profile of the dry and wetted MHE also yielded interesting
results. The working fluid acted as a heat sink, which lowered the measured thermo
couple temperatures an average of 9°C except for the actual heat sink and heat source.
Both the dry and wetted MHE testing yielded a heat sink tem perature of 37°C while
the heat source maintained a temperature of 109°(7. While the temperature difference
between MHE bottom plate and lid for dry and wetted tests remains at approximately
35°C, the reduction in tem perature due to added working fluid increases possibilities
for adjusting working fluids dependent on MHE application. Use of TEGs in power
generation requires the largest temperature possible on the TEG “hot side” . However,
the more efficient transfer of energy due to the addition of working fluid provides
steady energy throughput to the TEG with less continued waste heat loss to the
environment. The tem perature d a ta for the dry and wetted MHE tests is shown in
Figure 3.5.
120
110
100
90
80
70
E 60
50
40
30
200 200 400 600 800 1000 1200 1400 1600 1800 2000
Time (s)
-•-Heat Source MHE Bottom ■ Dry MHE Bottom • W etted— MHE Lid - Dry— MHE Lid - W etted— Heat Sink
Figure 3.5: Temperature data from dry and wetted tests
47
The underlying key to these tests was the contribution to efficiency through
the use of the working fluid within the MHE. In the dry tests, there was only air
in addition to the copper channels between the top and bottom which reduced the
thermal conductivity and the energy transference of the MHE. However, after adding
working fluid, the pocket was filled 80% with working fluid. The vapor-liquid interface
allowed greater conductivity but also introduced phase change. The capillary action
of the micro-channels pulled liquid over the heat source. Vaporization of fluid caused
micro-channels to pull additional liquid and the temperature of the MHE lid indicated
condensation of working fluid back to the channels and reservoirs to begin the cycle
anew as shown in Figure 3.1. Subsequent modeling work examined this behavior in
greater detail in Chapter 4.
Capillary and wicking action allowed working fluid to inundate the entire
channel system, not just the capillary micro-channels. Liquid distribution in the
MHE is prim arily driven through the bi-directionality capillary flow in the main
channels; however, because the channel walls are porous, there is also liquid distribution
throughout the walls tha t act as a sponge. This behavior was previously noted using
nickel-based porous channels [23]. Though the system is closed, this structure promoted
a highly interactive vapor-liquid interface which increased overall heat transfer of the
device.
3.5 Conclusion
The testing of the fabricated copper-based MHE yielded several im portant
results. Most im portant, addition of working fluid increased energy transfer through
48
the MHE by 8%. The low profile height of the MHE minimized thermal losses through
MHE sides. Though the addition of working fluid lowered overall temperatures of MHE
surfaces, the overall benefit of more energy throughput was greater than additional
increases in tem perature supplied for TEG power output.
Using the low thermal conductivity of air and balsa wood, the test setup reduced
potential energy losses through the test apparatus. Additionally, the introduction of
the guard heater allowed for the reduction of input energy not releasing into the MHE.
This is not vital for field testing but it gives a better indication of device efficiency
due to decreasing potential alternate routes for energy input.
CHAPTER 4
NUMERICAL SIMULATION OF A MICRO-CHANNEL WITH THE LATTICE BOLTZMANN METHOD
Traditionally, team s of engineers and scientists produce experimental testing
prototypes in order to progress toward a finalized equipment design. The development
of computer systems over the past sixty years, exponentially increasing in speed and
performance, has driven the process of design to shift towards numerical modeling.
Computational simulation increases the speed of product or process development while
reducing overhead costs [110]. However, unlike strict experimenting and prototyping,
numerical simulation of physical phenomena requires mathematical descriptions [111].
Governing equations must be selected and then the modeler m ust adopt or devise
methods to solve such equations [111]. The development of these solving techniques
has become ubiquitous in science and engineering, especially for developing computer
simulations of complex physical phenomena such as two-phase flow.
The m ature numerical m ethods of mesh discretization such as the Finite
Difference M ethod (FDM) and the Finite Element M ethod (FEM) attem pt to solve
partial differential equations (PDEs) for successively smaller meshes in order to
converge on a solution. Unfortunately, for systems with multi-phase flow and potential
moving phase interfaces, these traditional numerical schemes have difficulty converging
49
50
towards a solution. The FDM uses structured meshes to solve differential equations,
where derivatives are approximated with difference equations [112]. Two major issues
with the FDM are difficulty of solution convergence due to discontinuities at the phase
interface and complex geometries producing regions of low resolution [112, 113]. While
the FEM uses unstructured meshes, which can help the resolution issue, there is still
a challenge where PDEs fail to approximate solutions at interface discontinuities [113].
For a system such as the micro-channel heat exchanger (MHE), the inherent behavior
and operation introduces a potentially active vapor-liquid interface which must be
tracked to fully understand device operation. In order to successfully implement
a numerical procedure for such a transient system, a physics-based com putational
approach called the lattice Boltzmann method (LBM) is used for more efficient system
simulation.
4.1 Review of Lattice Boltzmann M ethod
The development and acceleration of modeling and simulation over the past
thirty years has led to considerable advancement in understanding nonlinear dynamic
systems. Though many m ethods exist for numerically solving these systems of
equations, researchers have developed specific methods which reduce com putational
cost and time. One such idea is the lattice gas autom ata (LGA), originally meant to
solve incompressible Navier-Stokes equations for fluid flows [114]. These LGA models
are described by discretizing phase space and tim e where particles only operate on
the lattice and control of collisions is by specified rules [114, 115]. Lattice sites then
obtain values of 0 and 1, giving the term ’’Boolean molecules” [114]. W hile this
51
allows for simulations to exhibit macroscopic thermodynamic equilibrium, there are
serious challenges with LGA models [114]. Most prominent are th a t the models can
be difficult to extend to multiple dimensions for complex flows and the Boolean nature
gives rise to an excessive statistical noise [115, 116].
The next progression moving from the LGA model was the conversion of LGA
from Boolean operators, which can only follow evolution of each individual molecule, to
continuous real numbers between 0 and 1 which then allows for one-particle distribution
functions [115, 117]. W hile the continuous approach removed fluctuations due to
ensemble averages, there was one prim ary problem with the Boltzmann equation
(BE) approach and the LGA [115, 117]. The lack of Galilean invariance due to the
lattice discretization caused scaling issues with multi-phase flows due to fluid interface
velocities constrained by conservation of particles equaling average particle velocity
which did not have the same scaling [114, 115, 118]. A subsequent lattice Boltzmann
model, presented by Gunstensen et al., was designed for immiscible two-phase flows
and included a Galilean invariant collision operator [116]. This suggested lattice
Boltzmann model simulates surface tension a t the interface using a perturbation of
the linear collision operator which forces the pressure tensor to be locally anisotropic
at the interface [116]. This model used an existing immiscible lattice-gas (ILG) model
from Rothm an and Keller with a modification to the ILG collision operator with a
two-step approach: first, they added the perturbation creating the correct surface
tension, and second, they kept the immiscibility by not allowing mass diffusivity from
one fluid to another [116]. While the perturbed model allowed for easier extension
to multiple dimensions, the difficulty in interface tracking of multi-phase flows led to
52
multiple lattice Boltzmann methods which attem pted to rectify these non-ideal fluid
difficulties [119].
Transport phenomena seen in nature is a complex and dynamic behavior. As a
collection of microsystems, these phenomena can be considered statistical probabilities
of the microsystem ensemble evolution. Unfortunately, it is impractical to a ttem pt
calculating properties of such systems due to involvement, of extreme degrees of
freedom. After development of initial LBM models, two models, one based on particle
interaction potential and the other on free energy, accomplish conservation constraints
and effectively contain non-ideal fluid behavior leading to proper fluid flow simulation
[42, 119, 120]. The interaction potential model, by Shan and Chen, contributes a
potential to the collision term which adds either attractive or repulsive energy to every
collision [42]. Swift et al. suggest a model which specifies collision term rules such
th a t the system develops toward the minimum of a non-local free-energy function
[120]. W hile both models show promise, there are potential inconsistencies in the
interaction potential model leading to inaccurate system property calculations and
the free energy model initially does not satisfy Galilean invariance when the phase
space is discretized [42, 120]. While all the given models provided initial fluid flow
phenomena simulation, none of the models included tem perature variations in the
system. Newer research is incorporating such phase-change transition behavior due to
both fluid flow characteristics and energy transfer within the system.
Therm al lattice Boltzmann models can be given in three broad categories:
multi-speed approach, passive scalar approach, and the He et al. model which includes
the internal energy density distribution function [121]. Macroscopic properties of
53
any system use the same distribution function as the multi-speed approach [121].
The variation in speed is due to the necessity to m aintain mass, momentum, and
kinetic energy for every collision [121, 122]. Since there are multiple speeds, the higher
order velocity term s tend to introduce numerical instability [121, 123]. The passive
scalar approach uses two distribution functions: one for velocity and density and a
second scalar function for tem perature [121, 124], While numerical stability is better
for passive scalar than for multi-speed, the scalar function for tem perature does not
affect flow but does progress through the flow field due to advection [121, 123, 124].
The model given by He et al. introduces an internal energy density distribution
function, derived from the Boltzmann equation [121, 125]. While the He et al. model
is an effective model for real therm al problems, the introduction of the complex
gradient operator appearing in the evolution equation eliminates the simplicity of the
LBM [121, 126]. The coupling of distribution functions for density and tem perature
provides challenges to practical models, the introduction of an equation of state allows
simulations of phase transition, both single component and multi-component.
The use of LBM to simulate phase transitions started with the Shan and Chen
pseudo-potential model [42, 127]. Soon after, Yuan applied a sign function which
greatly increased application of the Shan and Chen model [127, 128]. Another model
from Zhang introduced a body force term directly into the evolution equation; however,
the Zhang model proved more numerically unstable for a smaller tem perature range
than the Shan and Chen model [127, 129]. As phase transition models progressed,
there was a trend towards improving numerical stability and accuracy by incorporating
multiple relaxation times and removing the decoupled double distribution function of
54
flow and temperature fields [46, 130]. In 2012, Gong and Cheng published papers using
a new model technique which used a density distribution function and a tem perature
distribution function [43, 44], The Peng-Robinson equation of sta te then used both
distribution functions to simulate pressure changes resulting in phase change [43, 44].
Using normalized parameters, Gong and Cheng successfully simulated the coexistence
curve of the Peng-Robinson equation of state and bubble growth and release during
pool boiling [44],
While previous literature establishes an excellent precedent for moving forward
with LBM implementation, there are many additional factors which must be included
to produce a working model of the MHE system. The inclusion of all real properties of
the HFE-7200 working fluid being the primary focus. Constructing a computationally
efficient and realistic model requires using as many experim ental and empirically
determined parameters as possible. Subsequent sections explore the properties of the
working fluid, as needed by the model, a full description of the simulated model, and
the results and discussion of the simulation.
The m ajor achievement for the current study simulation is the preservation
of all SI units throughout the model. While the m ajority of LBM literature uses
normalized and non-dimensionalized model properties, this is not advantageous for the
system under study. Behavior of the physical fluid under MHE operating conditions is
desired. Therefore, maintaining all units provides simulation data which is immediately
accessible for qualitative feasibility analysis and potential errors in the program. In
addition to the LBM phase simulation, C hapter 5 reinforces system behavior using
the working fluid physical da ta equations with dimensionless number analysis. This
55
additional method of analysis is not possible if system properties are normalized prior
to simulation.
4.2 M o d e l D e sc rip tio n
Since the MHE system includes multiple phases of working fluid, there is a
need to establish both a density distribution function and a tem perature distribution
function. These two functions fully capture the particle evolution through space and
time, allowing for further analysis including equation of state pressure determination
and subsequent dimensionless analysis to understand additional system behavior. One
key component to ensuring an accurate simulation is the correct model of the working
fluid. Therefore, an additional review of HFE-7200 properties is also explored prior to
simulation performance setup.
4.2.1 F u n d a m e n ta ls o f th e L B M
The MHE study involves a bounded fluid system with an external heat
source. From initial conditions and tim e to the steady-state tim e where working
fluid phase interfaces have reached equilibrium, the internal fluid system is continually
undergoing evolution of density, tem perature, and pressure, allowing for the vapor-
liquid interface tracking. W hile non-equilibrium statistical mechanics attem pts to
characterize thermodynamic systems which are out of equilibrium, it is not necessary
to integrate equations of motion for all constituent particles [131]. For situations such
as the MHE with external forces and constraints, local equilibrium throughout the
system can be determined from the mean free path and collision time. Assume a
function / of point particles, / ( r, p, t)d3rd3p, defined as the number of particles with
56
position within d3r of r and momenta within d3p of p of time t [132]. Differing from
semi-classical mechanics, when collisions are included and particles with momenta
collide and convert to conserved momenta, the collision integral is given by:
?L + — ?L + = (?l\ ( a 11dt dt dr dt dp \ d t ) collusum
Rearranging the terms, the Boltzmann equation can be written as
(at) {si) (42)
such tha t
' d f \
. ^ / stream d t d r S P(4.3)
is the streaming term. Therefore, there are two contributions to particle motion over
time: streaming and collision [131].
The LBM describes a system by these evolutions of the particle distribution
functions stream ing and colliding on a lattice network. Initializing the velocity of
particles requires the implementation of the Chapman-Enskog distribution for non
equilibrium systems as well as a discretized collision operator for the lattice network,
such as the traditional Bathnagar-Gross-Krook (BGK) model [133, 134]. The density
distribution function, / , evolves using the traditional BGK collision operator, as
given in Equation 4.4. A corresponding equilibrium distribution function relates the
relaxation of the system, which is given in Equation 4.5. The last term in Equation 4.4
57
introduces a body force term as presented by Gong and Cheng and given in Equation
4.6 [44], This force term includes three forces which change associated velocity terms
during collisions: the interparticle interaction force, the interaction force between
surfaces and liquids, and the gravitational force [44],
f i {x + eiSu t + St) - f i { x , t ) = - ~ ( f i ( x , t ) - f i g(x , t )) + A /j(x , t) (4.4)r
f leq UiP 1 +
u (e* • u )2+
uc2 cl 2c2
(4.5)
A /i(x , t ) = r ( p ( x , t), u + A u) - f - q{p{x, t), u) (4.6)
where
A u = F • 8t/p (4.7)
is the velocity change due to body force during the time step. The force term, F , is
given by
F = F int(x) + F s(x) + F fl(x). (4.8)
Prior to describing the tem perature distribution function, there are some
notation and scheme clarifications which must be made. While there are several
different LBM schemes based on system dimensionality and potential locations in the
58
lattice available for particle movement, the proposed model uses the D2Q9 lattice
scheme due to system symmetry. The D2Q9 scheme is shorthand for two dimensional,
nine discrete velocities within the momentum discretization [45]. Figure 4.1 depicts
the velocities for the D2Q9 scheme. The nine potential velocities, e*, each has an
associated probability, Ui, for a particle’s likelihood to move to th a t lattice node.
Equation 4.9 gives the probabilities for the D2Q9 scheme.
3
Figure 4.1: Particle progression for D2Q9 LBM scheme
U)i
I, i — 0
I i = L 2 , 3 , 4
3g, i = 5,6 ,7,8
(4.9)
The nine velocity vectors are given by Equation 4.10. Note tha t m = ^ where
lattice spacing and 8t = tim e spacing, which is based on the particular lattice
scheme chosen. For the MHE study, both the lattice and tim e spacing are equal to
59
1 (im and 1 sec, respectively. Specific mention must be given to the two relaxation
times, t and t t - For LBM simulations, the fluid kinematic viscosity, v , is defined as
in Equation 4.11 while the thermal diffusivity, a, is defined as in Equation 4.12. Since
the working fluid has physical properties which can be experimentally tested, the
relaxation times can be empirically determined from the fluid da ta in the following
subsection.
Analogous to the density distribution function evolution equation, the tem
perature distribution function, g , has an evolution equation given by Equation 4.13.
The equilibrium function geq, given by Equation 4.14, is very similar to the density
equilibrium function f l q. The main difference between the two distribution functions
is the last term of each equation. W hile the density evolution incorporates a body
force term A /j(x , t), the tem perature evolution uses an energy source term given in
Equation 4.15. The weighting coefficients for both set of distribution functions are
based on the statistical probabilities in Equation 4.9.
(0 , 0 ), i=0
e* = S (± l ,0 )m ,(0 ,± l)m , i= l,2 ,3 ,4 (4.10)
( ± l ,± l ) m , i=5 ,6,7,8
(4.11)
(4.12)
60
gi(x + e<(5t, t + St) - 5i(x, t) = - — (&(x, t) - g ^ ( x , t)) + &tu)i<j> (4.13)t t
9iq = UiT 1 +e f U ( a - U )2 u 2
2c2(4.14)
4> = T ' - mpj
v-u ( 4 , 1 5 )
The density and tem perature distribution functions allow calculation of the
pressure field which provides the vapor-liquid interface motion via an equation of state
(EOS). The Peng-Robinson EOS is chosen for its stability and accuracy [43, 44]. The
Peng-Robinson EOS is
P =p R T ap2e(T)
1 — bp 1 + 2 bp — b2p2( 4 . 1 6 )
such tha t
2
(4.17)
where u is the acentric factor. From the density, tem perature, and pressure fields,
the internal operation of the MHE channel can be analyzed for behavior. However,
attem pting to simultaneously solve for the density and tem perature fields can lead
to convergence difficulties and model instabilities. This presents challenges using
normalized and ideal fluid data. One option to remove the model abstraction employs
e(T) 1 + 0.37464 + 1.54226a; - 0.26992a;
61
using all available physical da ta for the working fluid. Prior to implementing the
LBM, the following subsection explores potential opportunities for optimizing and
stream lining com putational cost and simulation time by using HFE-7200 physical
properties.
4.2.2 Working Fluid Model Properties
The environmental benefits and operational advantages of using 3M® HFE-
7200 as a working fluid is explained in C hapter 3. For the numerical model, there
is available information of specific working fluid properties. Unfortunately, much of
the m anufacturer published literature is at room tem perature [4], Since the MHE
system is experiencing transient density, tem perature, and pressure fields prior to
reaching steady-state conditions, much of the available OEM d a ta is not applicable
for the simulation. However, there is some manufacturer published data coupled with
several researchers studying HFE-7200 that is of great benefit for the simulation. Two
equations given in the 3M® HFE-7200 datasheet correlate density and tem perature,
allowing transformation of the temperature field data into density field data [4]. Since
there is a direct linear equation associating temperature T and density p, the difficulty
in fusing two distribution functions for solving simultaneously is simplified to include
just density distribution data. As the external heat source is applied, changes in
density p correspond to changes in tem perature T. The 3M® equations are given as
Equations 4.18 and 4.19.
(4 . 18 )
62
p = 1.4811 - 0.0023026(7' - 273.15) (4.19)
Though the density-temperature relationship is vital to the simulation of phase
change, there are other working fluid properties which must be included with the
simulation, including dynamic viscosity p, surface tension a, therm al diffusivity rr,
and the acentric factor uj. These are necessary for determ ining the two relaxation
times r and t t , part of the body force term, and the Peng-Robinson EOS calculation.
Upon personally corresponding with 3M® engineers, the acentric factor was identified
as u = 0.459 for HFE-7200. Experim ental da ta points for dynamic viscosity p and
surface tension a, recently published, are shown in Figures 4.2 and 4.3 [8]. In order to
simulate continually changing dynamic viscosity p and surface tension a, trendlines
are added to the published d a ta for programmable equations, based on the working
fluid tem perature.
Surfa
ce
Tens
ion,
a (
mN
/m)
Dyn
amic
V
isco
sity
, u
(uR.
i s)
63
12.5
12
11.5
11y ■= 0 0374x - 0.9112
R-’ ̂ 0.999710.5
10
9.5
9270 280 290 300 310 320 330 340 350 360 370
Temperature, T (K)
Figure 4.2: Empirical and modeled equation for dynamic viscosity /i [8]
16 •
15
14y = 0.0881x + 39 92,
R; = 0.999213
12
11
10
9
8
7270 280 290 300 310 320 330 340 350 360 370
Temperature, 7(K)
Figure 4.3: Empirical and modeled equation for surface tension o [8]
Similarly to dynamic viscosity and surface tension, thermal conductivity k and
specific heat capacity Cp experimental d a ta is used to establish a trendline equation
for continual tem perature ranges, which is then programmed into the simulation.
64
Figures 4.4 and 4.5 show the data with trendline equations. Thermal diffusivity a is
determined using Equation 4.20 with the density array determined by the LBM. Using
the thermal conductivity and specific heat equations, the thermal diffusivity equations
programmed into the simulation, for both liquid and vapor, are shown in Figure 4.6.
0.073
0.071
* 0.069 E
5 0.067 -*
f 0.065tj•d 0.063 c0u« 0.061 E01jE 0.059
0.057
0.055
Y = 2E-06x - 0 0012x ♦ 0 2846 R; - 0.9985
V
270 280 290 300 310 320 330 340 350Temperature, T (K)
Figure 4.4: Empirical and modeled equation for therm al conductivity k [9]
ka = —
pCp(4.20)
Ther
mal
Diff
usiv
ity,
m -
Liqu
id (m
:/s)
Spec
ific
Hea
t, cp
(J/g
K)
65
1.7
1.6
y = 0.0044X + 0.082 R2 = 0.9947
1.5
1.4
1.3
1.2
1.1240 260 280 300 320
Temperature, T (K)340 360
Figure 4.5: Empirical and modeled equation for specific heat Cp [10]
0.24
0.235
0.23
0.225
0.22
0.215
0.21
0.205
0.2
0.195
y = 3E-06x - 0.0013x + 0.3514 R2 = 0.9999
y = 2E-06x -0 0017x^0.3021 R‘ - 09999
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0250 270 290 310 330 350
Temperature, T (K)370 390 410
Figure 4.6: Calculated points and modeled equations for thermal diffusivity a
Ther
mal
Diff
usiv
ity,
u - V
apor
(m
/s)
66
4.3 Performance Setup
Prior to performing the simulation, the program which solves the LBM equations
needs to be selected. Given the objectives of observing the density, temperature, and
pressure fields and how the arrays develop over time, Matlab® is used for the LBM
simulation. The first step in implementing the LBM is the determ ination of model
lattice size, boundary conditions of the channel, and initial conditions for the working
fluid in the channel.
The physical micro-channel has dimensions of 20mm length, 300/un width,
and 120/un height. Therefore, the ratio of length to height is 166:1. While this
ratio simulates conditions along the entire channel, sym m etry and bi-directionality
of fluid motion due to capillary action allows the physical ratio of the program to
run at half of the channel size. Thus, the initial ratio of the program is 83:1. The
height of the simulation was then halved such th a t LY (the length of the y-axis) is
set to 60/un for scaling and reducing the com putational power needed to perforin
the simulation, effectively producing a model having 2//m of physical dimension per
/an of the simulation dimension. Therefore, the horizontal lattice length is set to
4800/im to give proper dimensionality of the simulated channel. However, once again,
due to channel axial symmetry and bi-directionality of fluid flow in the channel, the
horizontal lattice is reduced to efficiently conduct the simulation. After determining
the model lattice size, the boundary conditions of the simulation are established.
The micro-channel is bounded on top and bottom by copper plates. These
two boundaries influence both the momentum gradient and the therm al gradient
along the channel length. Since the fluid particles are constrained within the channel,
67
a traditional bounce-back condition is implemented which causes particle motion
to return from the lattice fringe back into the lattice network. The bounce-back
condition is commonly referred to as the no slip boundary condition in macro-scale
calculations [135]. The copper plates are modeled in the lattice network as boundaries
occurring between lattice nodes, effectively ceasing particle motion in the boundary
direction, causing the particle’s momentum to return the particle to the node from
which it arrived [135]. Therm al boundary conditions for the copper plates is set
to the experim ental conditions of the heat source and the heat sink. Tem perature
data from the experimental testing fixed the bottom plate tem perature a t 85°C and
the top plate tem perature at 50°C for simulation. Given the previous discussion of
channel geometry and symmetries, the vertical boundaries of the lattice network are
programmed for periodic boundary conditions whereby the fluid flow, assuming one
direction, particles reappear on the adjacent vertical boundary. Establishing lattice
geometry and boundary conditions for the channel prior to sat,m at ion as shown in
Figure 4.7, initializing fluid and air conditions must then be calculated to determine
initial fluid motion and composition of air/fluid mixture due to evaporative properties
of the working fluid.
68
Heatsink
Dry Vapor
Heat Source
Figure 4.7: Boundary and initial conditions prior to saturation
Product information for 3M® Novec® HFE-7200 fluid included Equations 4.18
and 4.19 which provided correlation between vapor pressure, density, and temperature
[4], Maintaining the experimental setup parameters, 80% of the channel is filled with
working fluid and 20% is air at room tem perature. Thus, the inner array has initial
densities of 1 -4 3 ^ for the working fluid and 0 .0 0 1 2 ^ for dry air. Immediately after
inserting working fluid into the MHE, the working fluid began evaporating until the
dry air was saturated. In order to fully understand the system equilibrium initial
conditions with saturated vapor and bulk working fluid, R aoult’s Law for a single
condensable species was used which is given by Equation 4.21,
69
Pi = PiVu (4-21)
where p* is the vapor pressure of the pure component and yi is the mole fraction
of component i in the mixture. Therefore, for the HFE-7200/air system at ambient
conditions, the 3M® partial pressure equation, Equation 4.18, was used with Equation
4.21 to calculate molar composition as shown in Equations 4.22 and 4.23.
0.163 _ mo/7200* ™ = n n 3 S = 0 1607S S ^ ' 4 '22>
!/<„, = 1 - 3/7200 = 0.8393- (4-23)m olm ixture
Using density properties and channel geometry measurements, the calculation
of the initial density condition gave the saturated vapor density as less than the bulk
working fluid density, at ambient temperature, by approximately 0.002%. Thus, upon
saturating the dry air of the channel, the system was assumed to have relatively
uniform initial density. The dry air/w orking fluid interface tracked downward to
provide the initial interior composition conditions of the simulation, shown in Figure
4.8. Regarding initial fluid motion, the horizontal velocity component can be found
by measurement of the physical device. Testing provided a flow velocity along the
channel length of 1 7 ^ . At ambient tem perature, 3M® published viscosity allows
calculation of the Reynolds number to initially be approximately 700, giving laminar
micro-channel fluid flow. Gravity and buoyancy effects were also accounted for in
70
the flow profile. However, Cheng and Wu published a correlation shown in Equation
4.24 [136]. For the system in question, channel diam eter was much less than the
equation requires, revealing th a t gravity effects on the symmetry flow was negligible.
Establishing the physical system, boundary and initial conditions, and fluid momentum
within the model allows solutions of LBM collisions. This is coupled with the two
OEM equations and the equation of state to determine phase transitions within the
channel.
Host Sink^ ^ ̂ ^ ^ ^ ̂ ^ ^ ̂ ̂ A ^ A A ^ ^ ̂ ̂ ^ ^ ^ ̂
Saturated Vapor
Heat Source
Figure 4.8: Boundary and initial conditions after saturation
dc = 0.224lc (4.24)
71
In order to develop the pressure field, the param eters of the Peng-Robinson
equation of state needed to be determined. Table 4.1 was generated from calculation
and working fluid information from 3M®. Note th a t all units were m aintained
due to the requirement th a t all model results be comparable to the experiment
and experim ental units. Taking all conditions and the physical system param eters
into account, simulations were performed to solve for the phase change interface
transitions. The results suggested promising simulations of the phase change regimes
which occurred within the micro-channel, reinforcing the fundam ental MHE design
and initial considerations of internal fluid flows.
Table 4.1: Peng-Robinson EOS parameters
a 3 -6 7 0 5 ^
b 0 . 0 0 0 1 6 - ^
R 8 3 1 4 STc 4 8 3 .1 5 KPc 2 .0 1 M Pa
4.4 Simulation Results
The initial simulations are plotted in intervals of 40 time steps for the density
p, tem perature T, and pressure P arrays. The density array at the initial time step
show the dry air and bulk working fluid density difference. Time progression of the
density as a function of position from the lid is given in Figure 4.9 while the percent
change from each time step to the next is given in Figure 4.10. As time steps progress,
three interfaces form, one at the lid, one at the bulk vapor-liquid interface, and one at
the bottom plate. The time-based progression of the central vapor-liquid interface
moves 12pm from the lid down to approximately 20pm from the lid in the density
72
array. After 360 time steps, there is less than 1% change between the densities at time
step 320 and step 360, suggesting th a t the density array had reached steady-state
conditions.
1.5 1.4
1.3
E 1-2M 1.1 2 1
OQJ 0.8| 0.7
t) 0-6- 0 .5
I£ 0.3 a
0.2 0.1
00 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— t = 1 — t = 40 — t = 80 t = 120 — t = 160 — t = 200 — t = 240 — t = 280 t = 320 — t = 360
Figure 4.9: Time progression for density array
100%90%
80%
70%
c 60%fljuc8
20 500 10 30 40
50%
40%
30%
20%
10%
0%
— At = 1:40
— At = 200:240
60Distance (microns, 2pm actual per pm of axis) from MHE Lid
— At = 40:80 — At = 80:120 At = 120:160
At = 240:280 — At = 280:320 — At = 320:360
-At = 160:200
Figure 4.10: Percent change in density array time progression
73
The temperature array is simulated using Equation 4.19 and the density array.
The tem perature as a function of position from the lid is plotted in Figure 4.11.
Initially, the bulk fluid is at room tem perature w ith the vapor showing a warming
trend due to the heat sink remaining at constant tem perature and the bulk liquid
absorbing initial bottom plate heat source energy . The time progression shows bulk
vapor increasing in tem perature while the bulk liquid acts as an internal heat, sink.
While temperature increases near the lid, the density and temperature arrays indicate
liquid conditions, indicating th a t condensation is occurring at the lid. The large
increase in temperature at the bottom plate indicates boiling occurring, given density
and tem perature da ta from 3M®. Similar to the density array, the largest changes
were found in the span between tim e step 1 and tim e step 40, as shown in Figure
4.12. After 360 tim e steps, the tem perature array changes less than 1%, indicating
steady-state conditions.
360
Boiling Point350
340
u 330
8. 320
310
300
2900 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— t =l — 1 = 40 — 1 = 80 t = 120 -*-t = 160 -»-t = 200 — t = 240 -»-t = 280 t = 320 -•-t = 360
Figure 4.11: Time progression for tem perature array
74
6%
5%
4%
3%
OJ2%
1%
0%10 20 30 40
Distance (microns, 2nm actual per pm of axis) from MHE Lid50 60
- a t = 1:40
- a t = 200:240
— At = 40:80 — a t = 80:120 a t = 120:160 — At = 160:200
— a t = 240:280 a t = 280:320 — a t = 320:360
Figure 4.12: Percent change in tem perature array time progression
Both the density and temperature arrays are used to produce the pressure array
from the Peng-Robinson EOS, indicating where the phase change is occurring in the
channel profile. Shown in Figure 4.13, the pressure array appears similar in pattern to
the density array. The pressure array is the key to determining phase change within the
micro-channel. Figure 4.14 reinforces Figures 4.10 and 4.12 suggesting the steadying
of conditions after 360 tim e steps. Curiously, the pressure array does not suggest
a developing phase interface at the heat source surface. Taking the tem perature
array d a ta and the pressure array data, coupled with the working fluid vapor-liquid
equilibrium data, Figure 4.15 shows the steady-state plot as a function of position
within the channel. The VLE data suggests confirmation of the conclusions tha t there
is liquid condensate from the MHE lid to between 4 — 5//m, vapor from 5 — 20/rm, bulk
vapor-liquid interface between 20 — 21/im, liquid from 21 — 54/im, boiling interface
between 54 — 55fim, and nucleate vapor from 55/xm to the heated copper surface.
Perc
ent
Cha
nge
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— t = 1 — t = 40 — t = 80 t = 120 — t = 160 — t = 200 — t = 240 — t = 280 t = 320 — t - 360
Figure 4.13: Time progression for pressure array
100%90%
80%
70%
60%
50%
40%
30%
20%
10%
0%0 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— a t = 1 :4 0 — a t = 40:80 — a t = 80:120 At = 120:160 — At = 160:200
— At = 200:240 — At = 240:280 At = 280:320 — At = 320:360
Figure 4.14: Percent change in pressure array time progression
The large natural surface tension dominant behavior of fluid flow in micro-
channel deters bubble growth as the tem perature rises above the boiling point. At the
increased pressure shown in the array, the large surface tension increases boiling point
76
1.2
1.15
1.1
T 1.05 2Sc 13<TJ- 0 .9 5aa 0.9l/l<U& 0.85
0.8
0.75
0.7295
The plot indicates that boiling interface at steady- state is located between 54-55umfrom the lid.
sectionBulk liquid
The plot indicates that bulk interface a t steady-state is located between 20-2 lum from the lid.
305 315
VIE line
325 335Temperature, T(K)
345
The plot indicates that condensation at steady-state is located between 4- 5um from the lid.
Bulk vapor section
355 365
Figure 4.15: Steady-state VLE plot of LBM data
of the working fluid. Thus, the working fluid absorbs more energy before yielding
to boiling. Though the lack of bubble growth decreases introduction of nucleation
sites, vapor bubbles th a t do initiate growth do not coalesce. This phenomena causes
an increase in bubble population over time on the heated surface [137]. The process
ends with the small bubbles deforming under surface tension and releasing, therefore
contributing to the cyclical operation of the MHE [138].
Beyond the array plots, Figures 4.16 and 4.17 depict the time step progression
of the pressure array with color maps in MATLAB™ . The phase interfaces at the
MHE lid and bottom are small in comparison with the bulk vapor-liquid interface,
shown in yellow. The white shade indicates conditions where the working fluid is
increasing in tem perature past the boiling point. The orange and light red shades
indicate conditions where liquid condensate is interacting with the bulk vapor.
77
Figure 4.16: Color map of pressure at time t = 0 in the micro-ehannel
100 t30 " 'in CKm m I Lanfh (UQ
Figure 4.17: Color map of pressure at steady-state in the micro-channel
78
The simulated cyclical operation of the MHE provides reinforcement tha t the
experimental device is operating effectively as designed. Given the conditions of phase
change at the heat source and heat sink and the large tracking vapor-liquid interface,
the model reassures the operation of the experimental MHE as having a real internal
fluid-vapor-fluid loop. Phase change verification by experimental working fluid data
confirms the LBM simulation. For final color map comparison, Figure 4.18 shows both
color maps side-by-side. The three arrows indicate the movement of the interfaces
over time.
79
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4.5 C o n clusion
The development of a simulated copper micro-channel filled with working fluid
began with looking for an approach which could successfully track phase change in
the channel while being com putationally efficient for implementation on a desktop
or laptop personal computer. Recent statistical approaches for com putational fluid
dynamics led to performing the numerical solution to simulation with the lattice
Boltzmann method. The implementation of the LBM provided an excellent avenue
for determining internal operation approximations for the prototyped MHE.
Separate from much of the literature which normalized and non-dimensionalized
system properties and conditions, the approach in this study prioritized the preservation
of all required param eters. While this process introduced potential unit conversion
difficulties initially, the overall result of the simulation showed immediately availability
for feasibility analysis. W hile th is process differed from much of the literature, it
proved a viable alternative if modeling a physical system.
Information from 3M® allowed for the simulated results to be analyzed. The
density, tem perature, and pressure arrays showed that there is movement of the bulk
vapor-liquid interface from approximately 12firn to 20gm and there is development of
boiling and condensing interfaces at the heat source and heat sink surfaces. Prior to
concluding successful operation of the MHE via the simulated model, further analysis
was conducted with dimensionless numbers, only possible due to the inclusion of
physical data and units, to provide conclusions for simulation-based channel fluid flow
and heat transfer behavior.
CHAPTER 5
NUMERICAL MODEL DIMENSIONLESS ANALYSIS
Chapter 4 established the development and execution of the lattice Boltzmann
sim ulated copper micro-channel w ith HFE-7200 working fluid. The pressure field
was calculated from the Peng-Robinson equation of state using the dual distribution
functions of the density and tem perature fields. W hile the pressure field indicated
the phase change occurring in the channel, secondary equations exist which can
complement the pressure field data by reinforcing understanding of system behavior
and performance, namely dimensionless numbers.
The history of dimensional analysis begins with such luminaries as Newton,
Euler, Fourier, Maxwell, and Stokes [139, 140]. However, it was not until Osborne
Reynolds popularized one of George Stokes’ concepts, later introduced as the Reynolds
number by Sommerfeld in 1908, on fluid flow patterns th a t led to an abundant
development of dimensionless numbers in the late nineteenth and early twentieth
centuries [140, 141, 142, 143, 144]. Dimensionless numbers, specific experimental
instances of dimensional analysis, are mathematical expressions typically composed of
either products or ratios w ith dimensions of unity [139, 145]. Though largely used
in engineering, especially chemical engineering, dimensionless numbers exist in most
engineering and science disciplines [139, 146, 147]. Most occur as coefficients when
81
82
non-dimensionalizing conservation laws and constitutive equations [139]. However,
dimensionless numbers are predominant in transport phenomena, a field of study in
engineering where momentum, energy, and mass transfer are analyzed.
All necessary physical properties and equations of the LBM simulation are
intentionally incorporated in the model without normalization or dimensional analysis
to the copper wall or HFE-7200 working fluid, thereby removing ambiguity from
model im plem entation and subsequent simulations. Therefore, all resulting system
characteristics, from viscosity to equation of state parameters to pressure, are kept in
SI units which benefits the immediate determination of model feasibility in the physical
world. However, there are several reasons for examining dimensionless numbers and
their influence on understanding system behavior and performance. Dimensionless
numbers can reduce the number and complexity of variables affecting a system
[139, 145]. Scaling different sized models is simplified with dimensionless numbers,
producing effective methods for researchers to advance from a model to a prototype
with less difficulty [139, 145], Most im portantly for the current study, dimensionless
numbers indicate dom inant transport processes which govern the behavior of the
system, providing a clearer physical understanding of phenomena within the system and
predicting vapor-liquid interface movement [145]. Due to the enormity of dimensionless
numbers in the literature, the current micro-channel system with free surface working
fluid is examined with specific numbers pertinent to the physical and simulated system.
Investigating two-phase flows in micro-channels with free surfaces, there are ten
dimensionless numbers which must be studied for greater system transport behavioral
understanding: Reynolds number (Re), Bond number (Bo), Weber number (We),
83
Capillary number (Ca), P randtl number (Pr), Nusselt number (Nu), Peclet number
(Pe), Condensation number (Co), Fourier number (Fo), and Jakob number (Ja)
[74, 139, 148, 149, 150, 151, 152]. These ten numbers cover specific energy and
momentum transport characterization of the system while including vapor-liquid
interface analysis. In addition to providing additional system behavior, movement
and position of the phase interfaces, first shown with the LBM simulation, can be
reinforced through the dimensionless group investigation.
5.1 F lu id F low A n aly sis
5.1.1 R ey n o ld s N u m b e r
Reynolds number may be the most ubiquitous dimensionless number, especially
in fluid mechanics. It specifically relates the inertial forces to viscous forces pertaining
to fluid flow within a channel; it also gives an indication of whether fluid flow is
laminar or turbulent based strictly on its numeric magnitude. The typical equation
for Reynolds number is
= (5.1)fi
However, for flow in a pipe or tube, Reynolds number is a ratio of density p, fluid
velocity V , hydraulic diameter D u, and dynamic viscosity //,
Re = f>y/Dl‘ , (5.2)fi
where the hydraulic diameter is given by
84
D m = - j . (5.3)
The parameter A is the cross-sectional area of the pipe or tube and P is known as the
wetted perimeter. For the simulated copper channel, Figure 5.1 gives the geometry of
these parameters.
Copper Lid
Air/Vapor
Copper Bottom1 W________________
A = H x W P = h + h + W + W = 2h + 2W
Figure 5.1: Parameters for determining D H in Reynolds number
Laminar flow occurs when a fluid flows in parallel layers. At low velocities,
the fluid tends to flow without lateral mixing. In this flow regime, particle motion of
the fluid is very orderly with all particles moving in straight lines parallel to the pipe
walls. Laminar flow occurs when Re < 2040. Figure 5.2 shows the progression of the
Reynolds number over time with respect to the channel height.
For the simulated micro-channel, since Re < 450, flow is laminar. Such low
Re implies large viscous forces compared to the inertial forces. While inertial forces
85
450
400
350
a;* BOO$E 2503C2 200ocJ 150ct
100
50
00 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid)
—-t = 1 -*-t = 40 — t = 80 t = 120 -*-t = 160 — t = 200 t = 240 — t = 280 t = 320 -»-t = 360
Figure 5.2: Reynolds number progression for simulated copper channel
are weak overall for the given Re, there is one location where inertial forces are the
strongest, namely the bulk liquid. This is a reasonable result given liquid velocity
in the channel due to capillary action. There are three; locations of interest based
on Figure 5.2: system boundary phase interfaces with the top and bottom copper
plate and the development of the phase interfaces between vapor and liquid. At t = 1,
there is definite separation of the air and working fluid. The small deviations a t the
boundaries are the result of immediate temperature differences, leading to immediate
density differences, at the source and sink. As time progresses, note the saturation of
air by the increasing Re. Immediately after t = 1 and progressing until steady-state
is reached, two disjointed locations begin to develop. These are the locations of
liquid-vapor interfaces, the development of a film condensation layer near the copper
boundary lid and the bulk interface occurring in the channel. Similarly to the color
86
map plots in Chapter 4, these phase interfaces move over the time steps agreeing with
the pressure array plot and color map of the Peng-Robinson EOS.
Analyzing the three phase change interfaces enlarged at their respective scales
reveals potential behavior of fluid phase interaction. Figure 5.3 explores the fluid
behavior near the MHE lid by expanding the view of Figure 5.2 for all tim e step
simulations at the location of the disjointed region, namely from 1/rra to 5//m from
the MHE lid. Initially a t t = 1, the slope of Re is negative with an extremely low
Re, decreasing from 66 to near 0 for the bulk air in the channel. However, as tim e
progresses, Re increases meaning inducement of flow due to increasing density. Initially,
the MHE lid surface tem perature is causing condensation to occur which is apparent
by the negative slopes from t = 1 to t — 80. However, between t — 120 and t — 200,
there is a change from negative to positive slope. At this point the condensing film
is thickening which encourages the development of boundary flow where the relative
velocity of the fluid layers decreases as the surface is approached. Interestingly, at
certain points, the Re decreases but corresponds to an increase in the distance from
the MHE lid, suggesting an influx of saturated vapor which increases the thickness of
the condensing film on the MHE lid.
87
350
Increasing film thickness from the MHE lid
Increasing condensation shown by increasing Re
0 '■'»1 1.5 2 2.5 3 3.5 4 4.5 5
Distance (microns, 2pm actual per pm of axis) of the condensing interface from the MHE Lid
-•-t = 1 -*-t = 40 -«-t = 80 t = 120 -*-t = 160 -*-t = 200 -*-t = 240 -*-t = 280 t = 320 -«-t = 360
Figure 5.3: Reynolds number progression for condensing vapor interface near the MHE lid
The color map plot of Chapter 4 indicates th a t the bulk vapor-liquid interface
increases in distance from the MHE lid over the time progression. At t — 1, there is a
clear delineation of the air and working fluid in the channel. However, for analyzing
the interface over time, the slope at the interface assists in indicating fluid behavior
between phases. Figure 5.4 shows the changing slope of the three median points of
the interface location. From t — 1 to t = 40, the phase interface transitions from a
positive slope to a local saddle point which continues until steady-state is reached. The
continual form of each successive time step suggests the development of a continuously
evolving interface with mixing of vapor and liquid contributing to the local saddle
point while moving away from the MHE lid until steady-state conditions are reached.
The vapor-liquid interface begins to steady in behavior starting at t = 200 with
each successive tim e step remaining in the same location w ith slightly reducing Re
88
values. Prom the simulation, it appears th a t the bulk vapor-liquid interface for the
experimental device settles at approximately 40/xm from the lid.
4S0
400
350atp o o
Ec 250 2c 200 >■ajo:
150
100
5010 12 14 16 18 20 22
Distance (microns, 2pm actual per pm of axis) of bulk vapor-liquid interfaces from MHE Lid
-•-t = 1 -*-t = 40 -e-t = 80 t = 120 -e-t = 160 -•-t - 200 -*-t = 240 -e-t = 280 t = 320 -*-t = 360
Figure 5.4: Reynolds number progression for the bulk vapor-liquid interface in the MHE channel
The final Re location for further analysis is located at the bottom where the
heat source is applied. At t = 1, the heat source has only initiated heat transfer to
the working fluid, as depicted in Figure 5.5 by the large slope directly a t the MHE
bottom surface. However, as time steps progress, more therm al energy is absorbed
into the working fluid, contributing to the reduction of Re at the MHE bottom surface
due to potential locations of nucleate boiling. Similarly to Figure 5.3, the boiling
behavior acts in the following fashion. As more heat is absorbed by the working fluid,
bubbles begin to form at local boiling locations causing Re to decrease due to vapor
introduction into the bulk fluid velocity profile. Continual heat flux at the surface
prom pts further localized boiling to the point where some locations merge to form
89
pool boiling pockets, creating larger areas of vaporization which expands toward the
MHE lid.
440
420
a 400IEc 380 tjo cJ 360oc
340
32052 52.5 53 53.5 54 54.5 55 55.5 56 56.5 57 57.5 58
Distance (microns, 2pm actual per pm of axis) of boiling interface from the MHE Bottom
-•-t = 1 -*-t = 40 -»-t = 80 t = 120 -*-t = 160 -*-t = 200 -»-t = 240 -*-t = 280 t = 320 -*-t = 360
Figure 5.5: Reynolds number progression for boiling liquid interface near the MHE bottom
Based on the simulation results, including the density array and dynamic
viscosity, the Re appears to reinforce the interior operation of the MHE agreeing with
the arrays and color maps in Chapter 4. However, before stating th a t MHE interior
operation simulation converges toward a singular ideal, other dimensionless numbers
must be compared for system behavior concordance.
5.1.2 Bond Number
The Bond number, Bo, gives the ratio of body forces to surface tension
forces using both vapor and liquid densities pv and p i, gravitational acceleration g,
characteristic length L, and surface tension a . The equation for Bo is
Increasing vaporization shown by decreasing Re
Increasing pool boiling from the MHE bottom
The Bo for the channel simulation is given in Figure 5.6. First, note the continuously
decreasing Bo. Due to the num erator containing the difference of liquid and vapor
densities, the Bo at t — 1 has the largest difference. The gravity term and characteristic
length are constants so they do not contribute to the changing Bo. However, the
surface tension in the denominator contributes greatly to the Bo of the system. As the
densities converge due to saturation, the increasing tem perature of the system causes
surface tension to begin decreasing. From Figure 5.6, the surface tension is decreasing
slower than the density difference causing the Bo to decrease overall. Regarding the
magnitude of the Bo < 1, this indicates tha t surface tension dominates body forces in
the channel.
o.i
0.09 *
O 0.08CO41c 0.07flj-Cuo 0.06
it= 0.05-QCm 0.04
0.03
0.020 40 80 120 160 200 240 280 320 360
Time Step
Figure 5.6: Bond number as a function of time for the simulated MHE channel
91
5.1.3 Weber Number
The determination so far suggests viscous forces dominating the Re and surface
tension forces dominating the Bo. The Weber number, We, comparing inertial forces
to surface tension forces with density p, fluid velocity V, characteristic length L, and
surface tension a, is given by
W e = ^ . (5.5)
Based on the Re and Bo, surface tension forces should dominate leading to a
W e of small magnitude. Figure 5.7 shows the W e for the MHE channel as a function
of tim e and position. The m agnitude of the W e axis for Figure 5.7 immediately
indicates th a t surface tension dominates inertial forces. There are three locations in
Figure 5.7 which correspond directly with the Re plot, the boundary interfaces and
the bulk vapor-liquid interface. Comparing Figure 5.2 and Figure 5.7, the development
of the three interfaces occurs at exactly the same distances from the MHE lid. This
is particularly noteworthy since the equations for Re and W e only have density and
velocity in common. Comparing Equations 5.2 and 5.5 and removing like terms and
constants, such as velocity and characteristic length, reveals magnitudes on the order
of
— and —. p a
(5.6)
92
Since the viscosity and surface tension are programmed from fitted experimental data
points, shown in Figure 4.2, and including the magnitude of both Figures 5.2 and 5.7,
surface tension dominates viscosity for the MHE simulation.
o.oi0.009
0.008
0.007
£ 0.006
§ 0.005 cj j 0.004
0.003
0.002
0.001
00 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— t = 1 -*-t = 40 — t = 80 t = 120 -»-t = 160 -*-t = 200 -«-t = 240 -«-t = 280 t = 320 -»-t = 360
Figure 5.7: Weber number as a function of time and position for the simulated MHE channel
5.1.4 Capillary Number
The last direct dimensionless number ratio compared for fluid flow is the viscous
forces to the surface tension forces, given by the Capillary number, Ca. The Ca,
comparing dynamic viscosity /z, fluid velocity V, and interfacial surface tension 7 , is
given by
93
During simulations this variable was isolated and calculated at each time step interval.
This was done by running the simulation for the given time step and calculating the
surface tension from the tem perature using the trendline from C hapter 4, whereby
the particular cell from the tem perature array was determ ined by the three arrays
from Chapter 4. C a as a function of time is shown in Figure 5.8. Note the magnitude
of the y-axis. Since Ca « 10~5 order of magnitude and the inherent porous nature of
the MHE fabrication shown in Chapter 2, flow is dominated by capillary forces with
negligible viscous forces contributing. Thus, the m agnitude of the Ca reinforces the
Re, Bo, and W e numbers comparison by indication of surface tension dominance.
5.50E-05
5.00E-05
4.50E-05
4.00E-05
c 3.50E-05
= 3.00E-05
2.50E-05
2.00E-05
1.50E-050 40 80 120 160 200 240 280 320 360
Time Step
-•-lid bulk bottom
Figure 5.8: Capillary number as a function of time for the three interface regions
5.1.5 Fluid Flow Conclusion
The fluid flow dimensionless numbers, Reynolds, Bond, Weber, and Capillary,
all point toward surface tension forces dom inating fluid flow motion in the channel.
94
W hile the Bond and Capillary numbers are plotted as functions of tim e only, the
Reynolds and Weber numbers both converge on the appearance of three regions of
interest where phase change occurs. W hile it is intuitive th a t these regions exist
due to boundary conditions and initial conditions, the direct comparison presents an
interesting behavior requiring further analysis. In order to understand internal behavior
of the MHE through simulation, heat transfer analysis must also be performed.
5.2 Heat Transfer Analysis
5.2.1 Prandtl Number
Moving directly from fluid flow to heat transfer analysis, a dimensionless
number which compares the two is beneficial to determine which transport phenomena
dom inates in the MHE system. The P rand tl number, P r , is a ratio of momentum
diffusivity and therm al diffusivity comparing specific heat cp, dynamic viscosity //,
and fluid thermal conductivity k. It is given by Equation 5.8.
p r — (5.8)k
Figure 5.9 depicts P r for the MHE channel. All three variables for P r are
discussed in the C hapter 4 section covering the working fluid modeling. Note the
immediate similarity of Figure 5.9 and Figure 5.7. Interestingly, Pr is only dependent
on fluid characteristics, whereas W e has dependence on system channel geometry as
well. However, just as Figure 5.2 and Figure 5.7 before, Figure 5.9 agrees on the three
interface regions in exactly the same location relative to the MHE lid.
95
0.22
0.21
0.2
0.19a.«D 0.18
= 0.17
0.16
0.15
0.14
0.13
0.120 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
-«-t = 1 — t = 40 — t = 80 t = 120 •— t = 160 — t = 200 — t = 240 — t = 280 t = 320 —-t = 360
Figure 5.9: Prandtl number as a function of time and position for the simulated MHE channel
In addition to the comparison with previous dimensionless figures, the magni
tude of Pr indicates greater thermal diffusivity than momentum diffusivity throughout
the channel. Since the fluid flow is lam inar with low velocity, the bulk vapor and
liquid components exhibit the smallest momentum diffusivity to therm al diffusivity.
However, a t the phase interfaces, the molecular motion due to phase interaction
contributes to a larger influence by momentum diffusivity. The region which is larger
in Figure 5.9 than Figure 5.2 and Figure 5.7 is the liquid/vapor behavior near the heat
source. This can be explained strictly by the tem perature array and how it affects
both liquid and vapor. Even if the liquid is not boiling near the heat source, the
tem perature of the liquid through the MHE depth causes molecules to move more
freely, allowing increased momentum transfer. Figure 5.10 shows the Pr for the three
interfaces as a function of time. Based on the simulation, therm al diffusivity is 6.86
96
times more influential than momentum diffusivity for the MHE lid and bottom at
t = 1 whereas the therm al diffusivity is 5.66 times more influential than momentum
diffusivity for the bulk vapor-liquid interface at t = 1. As steady-state conditions are
reached, therm al diffusivity m aintains dominance over momentum diffusivity for all
three regions, though the influence diminishes to 5.46 for the bottom, 4.93 for the lid,
and 4.87 for the bulk interface.
0.21
0.2
0.19a5 0.18
1 0.17
0.16
0.15
0.140 40 80 120 160 200 240 280 320 360
Time Step
-•-lid bulk -*-bottom
Figure 5.10: Prandtl number as a function of time for the three interface regions
5.2.2 Nusselt Number
The Nusselt number, Nu, provides the ratio of convective to conductive heat
transfer occurring when there is heat transfer across a boundary. Since there are two
boundaries supplying and removing heat, the N u is simulated for the entire channel
depth. N u is typically given by comparing heat transfer coefficient h. characteristic
length L, and fluid therm al conductivity k shown in Equation 5.9.
However, based on experimental testing, there is constant wall heat flux at both the
source and sink surfaces. Constant heat flux at the boundary surfaces causes the
energy equation can be reduced, combined with Fourier’s law of conduction, and
solved for the heat transfer coefficient. The reduction yields h = 4.364k / L which
therefore yields N u = 4.364. Using the fluid flow conditions and the constant heat
flux boundary condition, Shah and London published a correlation for therm ally
developing, hydrodynamically developed laminar flow, Re < 2300, where
N u = 4.364 + 0.0722 (^RePr
which was used in the simulation for N u [153]. Figure 5.11 displays the simulated
results of the Shah correlation. The magnitude of N u indicates convection is at least
4.364 times more influential on heat transfer than conduction for the entire channel.
This is logical since air and working fluid have such low therm al conductivities even
though fluid velocity in the channel is low. The behavior of Figure 5.11 is interesting
at the bulk vapor-liquid interface, exhibiting multiple saddle points at most time step
intervals. Therefore, the key locations of the bulk interface are shown in Figure 5.12
only as a function of time. Note tha t over time, the N u slope begins to settle toward 0
meaning tha t the interface is steadying between 4.36503 and 4.36509 and the interface
composition has mixed to become equal vapor and liquid.
R e P r ^ < 33.3 (5.10)
98
4.3656
4.3654
4.3652
z 4.365
| 4.36483±L 4.3646
= 4.3644
4.3642
4.364
4.36380 10 20 30 40 50
Distance (microns, 2pm actual per pm of axis) from MHE Lid
- t = 1 —- t = 40 -*-t = 80 t = 120 -»-t = 160 — t = 200 — t = 240 -«-t = 280 t = 320 -*-t = 360
60
Figure 5.11: Nusselt number as a function of time and position for the simulated MHE channel
4.3654
4.3652
a 4.365
3 4.3648
Z 4.3646
4.3644
4.3642
•t = 80 t = 120 — t = 160 t = 200 — t = 240t = 1 t = 280 t = 320 t = 360
Figure 5.12: Nusselt number as a function of time for the bulk vapor-liquid interface
99
5.2.3 Peclet Number
Based on the importance of convection in the simulation, given by the Nu, a
further look into components of convection is beneficial to understanding transport
phenomena in the channel. Convection is a combination of advective transport and
diffusive transport. These two quantities are compared, with characteristic length L,
fluid velocity V, and therm al diffusivity a, using the Peclet number, Pe., given by
Equation 5.11.
= — (5.11)a
Pe compares the advective transport rate to the diffusive transport rate. Figure
5.13 shows the Pe as a function of time and position in the channel. The magnitude
of Pe indicates large dependence on advection to the overall convection. However, at
t = 1, the diffusive transport is dominant in the bulk vapor. This particular location
and tim e experiences the largest diffusion of working fluid into the air due to large
molecular movement down the concentration gradient. As time steps progress and the
vapor becomes saturated, advection begins to supercede diffusion as the dominating
transport mechanism.
100
70
60
50
30
20
10
00 20 30 4010 6050
Distance (microns, 2pm actual per pm of axis) from MHE Lid
— t = 1 — t = 40 -«-t = 80 t = 120 — t = 160 — t = 200 •—t = 240 — t - 280 t = 320 -»-t = 360
Figure 5.13: Peclet number as a function of time and position for the simulated MHE channel
5.2.4 Condensation Number
The Condensation number, Co, gives the ratio of number of molecules condens
ing on a surface compared to the total number of molecules striking the surface [154].
For the MHE simulation, the surface which experiences condensation is the MHE lid.
The Co is determined, using heat transfer coefficient h, fluid thermal conductivity k,
dynamic viscosity p, density p, and gravitational acceleration g, by the equation
C o = ( 5 1 2 )
which is different depending on the situation and geometry [155, 156]. Figure 5.14
shows how the MHE develops a steadying condensation film on the lid surface. The
figure indicates the largest surface condensation occurring a t early tim e steps. Due
101
to vapor saturation of working fluid, this initial data appears logical given the heat
sink location and tem perature of the lid. Over the tim e interval reaching steady-
sta te conditions, note th a t Co -> 0.215. Therefore, roughly one-fifth of molecules
striking the MHE lid, and as time progresses the condensate film, are condensing and
contributing to the condensate film. It must be noted however that while a percentage
of the vapor is condensing, the phase interface experiences constant molecules in the
condensate film vaporizing into the saturated vapor region.
0.4
0.380 •Ua? 0.36u re1 0.34If t
| 0-32 5 0.3E= 0.28 o3 0.26 coj
c 0.243 • • •
0.22 * • •
0.20 40 80 120 160 200 240
Time Step
Figure 5.14: Condensation number as a function of time for the simulated MHE lid
5.2.5 Fourier Number
The final heat transfer dimensionless number considered for the MHE channel
is the Fourier number, Fo. The Fo compares therm al diffusion transport ra te the
therm al storage rate of the medium with therm al diffusivity a , characteristic time t,
and characteristic length L. Fo is determined by Equation 5.13.
• ♦ •
280 320 360
102
a t ,F o = j j (5.13)
As a function of tim e and position, Fo is shown in Figure 5.15. Note the overall
difference in behavior versus all of the other heat transfer dimensionless plots. The
overall m agnitude of Fo shows th a t therm al diffusion dom inates therm al storage,
especially in the bulk liquid region. The interesting behavior occurs a t the three
phase interface locations. The lower Fo corresponding to the phase interaction at
the MHB lid, bulk vapor-liquid interface, and MHE bottom demonstrates the energy
storage via the continual phase interactions at the interfaces. For example, at the bulk
vapor-liquid interface there is ever-evolving interaction between vapor condensing and
liquid evaporating establishing a phase equilibrium. Therefore, some of the energy
input into the system remains at the interface location causing the therm al storage
rate to be larger than in the bulk vapor and liquid regions. Similarly for the MHE lid
and bottom , there is a reduction in diffusion influence which indicates multi-phase
interaction.
103
61
2. 58
S; 56
° 55L, JJ
520 10 20 30 40 50 60
Distance (microns, 2pm actual per pm of axis) from MHE Lid
-*-t = 1 -»-t = 40 -»-t = 80 t = 120 -«-t = 160 -»-t = 200 -*-t = 240 -*-t = 280 t = 320 -*-t = 360
Figure 5.15: Fourier number as a function of time and position for the simulated MHE channel
5.2.6 Heat Transfer Conclusion
The findings from the five heat transfer dimensionless numbers are: therm al
diffusivity dominates m omentum diffusivity, convection is the dom inant transfer
mechanism, and the three phase interface regions appear to increase thermal storage
rates versus the bulk vapor and liquid regions. Considering the combination of
convection, advection supplies the bulk heat transfer. Lastly, the MHE lid, kept at
reduced temperatures with the heat sink, steadies at approximately 21% of molecules
which contact the lid then accumulate in the condensate film. Overall, the heat
transfer numbers agree with the fluid flow numbers, even when heat transfer numbers
rely only on fluid characteristics. Time and position agreement reinforces conclusions
reached by the fluid flow analysis concerning the three two-phase regions and the three
interface movements during simulation.
104
5.3 Phase Change Analysis
5.3.1 Jakob Number
The Jakob number, Ja , is a rarely encountered dimensionless number, yet it is
vital for direct contact processes that involve phase change [157]. For processes which
involve boiling, Ja gives the ratio of maximum sensible heat absorbed by the liquid to
the latent heat absorbed by the vapor [158]. Condensing processes are characterized by
the ratio of maximum sensible heat absorbed by the vapor to the latent heat absorbed
by the liquid [158]. Ja uses specific heat of liquid cPi/, liquid density p , tem perature
difference A T , heat of vaporization h fg, and vapor density pv. Ja is given by Equation
5.14 [159, 160],
Ja = (5.14)' I fgPv
Since Ja shows the am ount of heat transfer occurring during phase change,
Figure 5.16 give the tim e progression for Ja at the MHE lid, MHE bottom , and
the bulk vapor-liquid interface. In agreement with the surface tension dominance of
the fluid flow analysis, Ja < 16 means th a t bubble departure a t the MHE bottom
is controlled strictly by surface tension forces [159]. The lid interface converges to
0.77. Therefore, approximately 44% of interface energy is absorbed via sensible heat
through the vapor while 56% of the interface energy contributes to phase change via
latent heat absorption by the liquid once steady-state conditions are reached. The
boiling occurring at the MHE bottom converges to approximately 0.6. Conversely to
the MHE lid, this means th a t 38% of interface energy is absorbed via sensible heat
105
through the liquid and 62% of the energy is absorbed via latent heat through the
vapor phase. The bulk interface converges to approximately 0.78. Similar in quantity
to the MHE lid, 44% of the interface energy is absorbed via sensible heat while 56%
contributes to phase change of both phases.
0.9
0.8
0.7to
j j o . 6 E3
-Q 0.5 o-xID0.4
0.3
0.20 40 80 120 160 200 240 280 320 360
Time Step
-•-lid bulk -^bo ttom
Figure 5.16: Jakob number as a function of time for the simulated MHE lid
5.3.2 Phase Change Conclusion
The use of the Jakob number demonstrates that the three regions experiencing
multi-phase interaction have larger energy contributions to latent heat absorption.
This indicates energy absorption via a constant temperature process, further reiterating
phase change at th a t specific location. Therefore, the LBM simulation of the MHE
channel supports the idea of interior operation of the MHE developing a boiling region
and a condensing region where effective operation occurs as a continual cycling of
working fluid phase change.
106
5.4 Conclusion
Analysis of fluid flow, heat transfer, and phase change in the simulated MHE
channel via dimensionless numbers yields several interesting results. The prim ary
behavior noted is th a t every dimensionless number plotted as a function of time
and position agreed on the development and movement of the three phase interfaces,
regardlass of variable and system characteristic dependence. The overall result of
the dimensionless number analysis is th a t channel behavior can be summarized as
laminar, capillary-driven fluid flow, bulk heat transfer via convection effects, and
effective boiling and condensing on both surfaces in contact with the heat source and
heat sink, also summarized in Table 5.1.
The density, tem perature, and pressure arrays are used in C hapter 4 to
characterize phase change and internal operation of the MHE channel simulation.
However, the collected analysis via dimensionless numbers, which is initially used to
verify interior condition and behavior, is also verification of channel operation. While
these numbers indicate the system characteristics they are intended to determine,
the collectivized agreement of all numbers open potential avenues for future use of
dimensionless numbers in simulation verification.
Table 5.1: Summary of MHE simulation behavior
T ra n s p o r t M ech an ism M H E C h a n n e l B eh av io r
Fluid FlowLaminar Flow Regime
Surface Tension Dominant
Heat TransferThermal Diffusion Dominant
Convection Dominant Thermal Sinks at Phase Interfaces
Phase ChangeLatent Heat Greater Than Sensible Heat
Absorption at Phase Interfaces
CHAPTER 6
CONCLUSION
The present study set out to determ ine an efficient and low-cost fabrication
method for the production of a copper-based micro-channel heat exchanger to recover
waste therm al energy. In addition to the physical prototype required by the NASA
proposal which provided funding for the development, the investigation sought to
validate internal operation with a numerical model using the lattice Boltzmann method.
Further dimensionless number analysis reinforced results from the numerical simulation.
The importance of this study, after providing NASA with a working prototype which
powers remote sensors w ith multiple energy scavenging mechanisms, allowed the
creation of a simulation which used physical properties of system fluids w ithout
normalization thereby giving results which were immediately available for comparison
against working fluid experim ental data. W aste heat recovery has been researched
to take advantage of thermodynamic inefficiencies, allowing for reduced operational
costs, increased operational efficiency, and increased environmental sustainability. The
study successfully accomplished all objectives including the creation of a cost-effective
MHE fabrication technique, development of an energy efficient waste heat recovery
device, and the creation of the numerical model using a statistical approach which
allowed for efficient phase interface tracking during MHE operation.
107
Specific findings were chapter specific and were summarized with the respective
chapters. However, there were results which bear reiterating at the end of the study.
One of the first aims of the study was determining w hether cost-effective general
laboratory techniques were possible allowing the fabrication of the MHE. The technique
developed, previously not found in literature, promoted an unexplored use of dry-film
photoresist where film layers were stacked allowing micro-structure fabrication with
greater heights and aspect ratios. Layering dry-films also provided an avenue for using
low-cost office equipment and a power supply to produce repeatable samples of MHEs,
shown for heights over 200gm. Therefore, successful fabrication of m icro-structures
was deemed available to any facility with general laboratory capabilities. While the low
profile of a copper-based MHE transferred 87% of energy without using any working
fluid, the use of a working fluid increased energy transference to over 95%. Heat
transfer was enhanced in the device by the inherent porous nature of channel wall
fabrication, increasing surface area by 18%. The overall effectiveness of the MHE
resulted in progressive prototypes produced for the NASA modular energy harvesting
device.
Having fulfilled the fabrication and experimental prototype aspect of the study,
the focus changed from overall device operation to internal operation and phase change
occurring during device use. The lattice Boltzmann method was a recently developed
alternative to the more m ature FEM and FDM techniques for solving multi-physics
and com putational fluid dynamics problems. The LBM required less com putational
resources and actively tracked the development of phase interfaces which occurred at
the heat source, heat sink, and the bulk vapor-liquid interface. The simulated results,
compared with available working fluid data, confirmed th a t the MHE operated as
intended. After completing the simulation analysis, additional simulation verification
was completed through the use of 10 dimensionless numbers appropriate for the MHE.
The simulation indicated tha t condensation at the MHE lid occurred developing a film
thickness of 5gm which due to model setup corresponded to a 10frni film thickness
in the experimental MHE operation. Bulk vapor-liquid interface movement occurred
from 12/im from the MHE lid to 20//m, thereby indicating the interface moved from
24/xra to 40//m in the physical MHE testing. Therefore, the air/working fluid interface
of the channel started at approximately 20% of MHE depth and after saturation and
phase change, the vapor/liquid interface moved down to 33%. Interestingly, pressure
conditions and the natural dominance of surface tension in the channel indicated
potential superheating of working fluid with minimal bubble growth and release.
Moving beyond empirical results, there were three important additional results
from the investigation. Keeping the copper-based MHE in prototype form eliminated
the ability to use site glasses for experimental verification of phase change. However,
using all available physical da ta for the air/working fluid mixture enabled using the
computational model and subsequent analysis for justification of experimental results.
This conclusion resulted in a faster prototyping process which future researchers
can use for expedited projects. The use of physical param eters also introduced the
possibilities of using dimensionless numbers in future simulated systems. Potential
behavior indicators in the system, such as surface tension dominance, increased
confidence th a t the employed numerical model operated similarly to initial design
requirements.
110
As consequence of the s tudy’s outcomes, global adoption of the fabrication
process was determined as financially practical for any facility. This was im portant
to potentially increase study and use of MHEs in industry, academia, and possibly
commercially. The robust, cost-effective, performance efficient MHE provided the
immediate end user with a highly functional energy harvesting device which was
intended for operation in multiple environments. In addition to the MHE, the LBM
approach investigation allowed for immediate fluid alternatives to be modeled. The
ease of transition between operational working fluids provided possibilities for research
teams to quickly explore design alternatives.
Progressing past the current study, several recommendations for future study
are apparent. Concerning fabrication, there are two avenues to explore further with
the dry-film photoresist. The layering technique can be studied to produce taller
m icro-structures at potentially lower film resolutions. The second option examines
other substrates, not necessarily metals, for fabrication of more varied micro-devices.
Regarding the operational MHE, designs with narrower and taller channel walls can
be explored for optimizing heat transfer efficiency. Additionally, the use of different
working fluids for operational necessity, such as high heat flux conditions, needs to
be investigated for increasing potential MHE operating conditions and environments.
The progression of the numerical model should proceed to three dimensions to better
understand transport phenomena occurring during operation, including influence of
wicking through copper lattice pores. Increasing simulation dimensionality would also
allow a more accurate analysis of phase change, especially for tracking interface motion,
and behavior of the system via dimensionless number analysis. After exploring the
I l l
simulation with dimensionless numbers, this additional analysis technique appeared to
be a reasonable step for modeling physical systems. While the use of these numbers
in such a capacity has not appeared in publication to the extent found in the study,
exam ination of these numbers in comparison w ith the EOS model was a highly
successful process which other researchers could use in their studies.
Overall, the objectives set forth by the project to develop an effective fabrication
method for producing an efficiently operational MHE was a success. Further analysis of
internal operation using the lattice Boltzmann method and behavior within the system
by dimensionless number analysis converged on the initial MHE design intentions.
Though built and inspired for an end goal prototype at specific operating conditions,
the three phases investigated herein established a procedure for development and
analysis for future MHE use in various environments.
APPENDIX A
LETTER OF COPYRIGHT PERMISSION FROM ASME
112
Dear Mr. Borquist,113
This permission has been revised to reflect all requests. It is our pleasure to grant you pennission to use all or any part o f the ASME papers:
• Copper Plated MicroChannel Heat Exchanger for MEMS Application, by E. Borquist; E. Ogbonnaya; S. Thapa; D. W ood; L. Weiss, Paper number ICNMM2014-21927
• A Copper MicroChannel Heat Exchanger for MEMS-Based Waste Heat Thermal Scavenging, by E. Borquist; A. Baniya; S. Thapa; D. Wood; L. Weiss, Paper number 1MECE2014-38801
• Exploration o f Phase Change Within a Capillary Flow Driven Square Micro-Channel Using Lattice Boltzmann Method and Experimental Boundary Conditions, by E. Borquist; G. Smith; L. Weiss, Paper number ICNM M 2015-48482
cited in your letter for inclusion in a Dissertation entitled Experimental Investigation and Numerical Simulation o f a Copper Micro-Channel Heat Exchanger with HFE-7200 Working Fluid to be published by Louisiana Tech University.
Permission is granted for the specific use as stated herein and does not pennit further use o f the materials without proper authorization. Proper attribution must be made to the author(s) o f the materials. Please note: if any or all o f the figures and/or tables are o f another source, pennission should be granted from that outside source or include the reference o f the original source. ASME does not grant pennission for outside source material that may be referenced in the ASME works.
As is customary, we request that you ensure full acknowledgement o f this material, the author(s), source and ASME as original publisher. Acknowledgement must be retained on all pages printed and distributed.
Many thanks for your interest in ASME publications.
S I T T I N G T H C S T A N D A R D
Beth DarchiPublishing Administrator ASME2 Park Avenue, 6,h floor New York, NY 10016-5990 Tel 1.212.591.7700 [email protected]
Sincerely,
114
Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting and 12th International Conference on Nanochannels, Microchannels, and
August 3-7, 2014, Chicago, Illinois, USA
FEDSM2014-21927
C O PPER PLATED MICROCHANNEL HEAT EXCHANGER FOR MEMS APPLICATION
E. Borquist, E. Ogbonnaya, S. Thapa, D. Wood, L W eiss ‘Institute for Micromanufacturing
Departm ent of Mechanical Engineering Louisiana Tech University
Ruston, LA 71272 Email: lw eiss@ latech.edu
ABSTRACTDemand fo r increased density circuit architecture, micro-
and nano-scale devices, and the overall down-scaling o f system components has driven research into understanding transport phenomena at reduced scales. One method to enhance transport processes is the utilization o f mini-, micro-, or nano-channels which drive uniform temperature and velocity profiles throughout the system. This work specifically examines a unique heat exchanger. The exchanger is developed as a closed system, with 300pm width channels, fabricated entirely with copper.
The heat exchanger has been designed fo r widespread use in varied environments. Further, the exchanger is working fluid non-specific, allowing fo r different fluids to be specified fo r various temperature ranges. The system design can be used equally well as a standalone heat exchanger or coupled with another device to provide a thermal energy storage system.
Fabricating the heat exchanger with copperfor the substrate as well as the channels themselves allows the exchanger to maintain a high thermal conductivity which aides in the fluid energy transference. The exchanger was fabricated to be a closed system removing any excess equipment such as pumps. In testing, the exchanger showed thermal absorption o f 2 .2 ^ given input o f 2.63 jjjf and working fluid amounts o f 37pL The general design and use o f copper in the exchanger allowed maximum absorption o f 84% o f the input with operation below the boiling point o f the working fluid.
INTRODUCTIOND em and for increased density circuit architecture, m icro-
and nano-scale devices, and the overall dow n-scaling o f system com ponents has driven research into understanding and im proving transport phenom ena at reduced scales. E ffective rem oval o f heat from m icro-electro m echanical system s (M EM S) allow s m ore efficiency and reliability o f devices w hile provid ing an additional p latform for useful pow er output [ 1 ]. M icro-channel heat exchangers (M H Es) use m ultip le fluid-filled channels w hich, at reduced scales, produce effective heat and m ass transfer due to the dynam ic boundary layers [2], M H Es reduce system size w hile im proving efficiency w hich reduces overall system operating costs |2 ] . P roper harvesting o f M EM S w aste heat necessitates an M H E that op tim izes channel fluid dynam ics w hile m inim izing therm al resistance |1 ,3 | . T herm al resistance is reduced using tw o-phase flows and m aterials w ith h igh therm al conductiv ities [1 ,3].
T raditionally, m icro- and nano-scale devices have relied on silicon as substrate o r bulk m aterial o f fabrication . How ever, the low therm al conductiv ity o f silicon, w hen com pared to m etals such as copper, and its frag ility in w afer form dem and viable alternatives fo r m ore effective and varied usage in dynam ic environm ents [4]. M etal-based M H Es w ould produce m ore robust system s w hile im proving system therm al conductiv ity [1], T here are four b road fabrica tion classifications fo r processing m icrochannels: photolithography, solidification, subtractive, and add itive [5],
A n im portant photolithography technique for m etallic mi-
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RESERVOIRS
MICRO-CHANNELS ELECTROPLATED CU
CU SUBSTRATE —
Figure 1. C om ponents of MHE.
crostructures is L IG A (G erm an fo r lithography, galvanoform ung (electroplating), and abform ung (m olding)) w here th ick pho toresists are applied to substrates as m olds and filled w ith e lectro plated m etals [6], A lthough L IG A produces h igh quality m ic rostructures o f h igh aspect ratios, it can be a h igh-cost p rocess [1 ,7 ], An adaptation o f L IG A involves using polyim ide, w idely used as C O TS m aterials, as the applied m olds for e lectro plating w hich is a low -cost alternative to L IG A [7]. Solid ification techniques for m etallic m icro-channels using com pression m olding have been dem onstrated w ith copper [4 ,8 ]. In addition to surface reactions due to h igh tem peratu res and yield strength o f m old insert concerns, com pression m olding requires expensive equipm ent to perform [1 ,4 ,8 ]. Subtractive processes involve m illing m icro-channels from a substra te [1 ,5 ] . M illing has been dem onstrated both w ith trad itional m etal b its and electro-erosion o r m icro-electrical d ischarge m illing (/tED M ) [1 ,5 ,9 —11], Fabrication challenges o f m illing include the loss o f p recision fo llow ing m echanical wear. T he h igh-cost o f equipm ent if using the /rED M m ethod o r electro -erosion also p resen ts m illing challenges [ I ]. A dditive techniques such as con tact p rin ting o r vapor deposition are viable only fo r applications o f m inim al th ickness and u tilize h igh-cost equ ipm ent [6]. Sub-m icron trenches have been electroplated at h igh aspcct-ratios w ith copper w hich validates the proposed level o f p recision involved w ith M H Es [12]. A n electroplating m ethod provides an efficient, h igh-precision , low -cost m ethod w hen coupled w ith a photolithography m ask process.
In this w ork, a low -cost m ethod fo r the fabrication o f a copper M H E w ith m inim al equ ipm ent using an adapted L IG A tech nique w ith electroplating is presented . T he M H E has com ponents as noted in Fig. 1. It is designed to operate as a c losed system needing no external w ork m echanism . T he closed system uses the tem perature grad ien t betw een the M H E bottom and lid to facilita te the liquid-vapor cycling o f the w orking fluid. T he therm al transport is driven by using phase change o f a w orking fluid. M icro-channels drive capillary action o f the fluid as
FLUID FLOW FROM CAPILLARY ACTION
HEAT SOURCE
Figure 2. Transfer m echanism s of MHE.
depicted in Fig. 2. T he boiling w orking fluid travels to the M H E copper lid w here condensation returns the fluid to e ither the m icro-channels o r the reservoir. T he M H E is designed for m ultip le applications. There is no specified w orking fluid in the design . Fluid is selected based on boiling point requirem ents and device conditions. C opper was selected for the M H E due to therm al properties, but any m etal w hich can be electrodeposited could be used. Follow ing fabrication o f the M H E, the devices arc evaluated in therm al testing fo r therm al absorption o f sim ulated w aste heat sources.
EXPERIMENTAL METHODS Fabrication
T h e fabrication o f M H Es w as based on m odified L IG A tech niques focused on electroplating copper onto copper substrates. In general, to create the device from Fig. 1, a layer o f copper was e lectrodeposited to provide the reservoirs and m icro-channels structure. A fter the M H E bottom p late w as developed, a sheet o f copper was polished to produce the M H E lid. T hough a closed system design, an access port w as provided on the lid in o rder to add w orking fluid for testing.
F irst, copper 110 sheeting w as purchased for substrate rig id ity. A dry film pattern ing technique w as em ployed to define channels for e lectroplating . T he dry film m anufacturer suggested that lam ination o f their dry film onto a substra te should be done w ith a hot roll at elevated tem perature [13]. However, previous experim ents have show n the possib ility o f dry film application w ith a ho t flat iron [1], O nce the dry film was lam inated onto the substrate, the photo lithography m ask w as secured onto the dry film. Though the recom m ended dry film exposure w ith a UV lam p o f peak em ission 360 to 380nm , experim ents w ith the dry film proved that a fluorescent lam p developed the film successfully for 300//m w idth channels. A fter a developm ent lim e o f 20 m inutes, the undeveloped film w as rem oved from the substrate w ith the recom m ended KiCO$ solution [13], Figure 3 dep icts a sam ple w ith a developed dry film and substra te w hich was p repared for e lectroplating .
T here w ere several suggested p lating baths for copper in the
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Figure 3. Copper substrate with Ordyl mask.
Table 1. Copper Electroplating Bath [14]CuS 0 4SH20 188 I
h 2s o 4
CurrentDensity 3 s ?
Temperature 37 °C
Table 2. Copper Electropolishing Bath [15]lh P O A 157mL
H20 75mL
Current 0.045A
Temperature 55 °C
literature. However, accounting fo r chem ical hazards and ease o f preparation , the initial bath so lu tion and p lating conditions consisted o f copper sulfate in a sulfuric acid m ixture given in T able 1 [14]. T herefore, given a 300m L basis, and a p lating area o f 202.5m m 2, the inform ation in Table 1 resulted in a bath o f 288m L H%0, 12.07m L H2SO4 , 56.4g CmSO^HjO and a current density o f 3 .
A fter several iterations o f p lating currents rang ing from 0 .6A to O JA , an acceptable current for fabricating the channel areas w as established at 0.4A . T he 0 .4A current y ielded consistent, repeatable p lating fo r the M H E geom etry. This current p roduced channels as show n in Fig. 6 w ith a plating tim e o f 1 hour. It w as desired to determ ine a plating deposition rate in o rder to crea te channels o f required height. D eposition rate w as determ ined by varying plating tim e and m easuring channel height w ith a D ektak 150 Surface Profiler. T he first several sam ples w ere p lated w ith a channel height o f 60/tm and 300/rm channel
PC
lAB-VIEW
I__ HEAT SINKHFS-3MHEHFS-2HEATER
LEGEND • THERMOCOUPLE
TC WRINGH FS WIRING
Figure 4. Testing Setup tor MHE.
w idth. To im prove channel uniform ity and repeatability , as well to prevent delam ination , a further step w as in troduced into the fabrication process. P rio r w ork indicated electropolish ing the copper substra te w ould prov ide an im proved and clean surface fo r deposition . Phosphoric acid w as selected for the po lish ing step [15], Table 2 show s final so lu tions and conditions fo r e lectropolish ing copper w ith a 300g basis after determ ining proper current density fo r the surface area.
O nce the M H E bottom w as electroplated , a copper 110 lid w as cut to bottom p late d im ensions and polished w ith the phosphoric acid solution to enhance therm al con tact w ith the bottom plate. P rior to bonding, an access port w ith d iam eter g inch was drilled into the cen ter o f the lid. C entering the access port p ro vided equal d ispersion o f w orking fluid, v ia the m icro-channels, to the tw o reservoirs. T he bottom p late and lid w ere then co n tacted w ith a press and bonded w ith epoxy on the vertical sides. C are w as taken not to get epoxy on the external heat transfer (horizontal) surfaces.
P rio r to testing w ith w orking fluid, the M H Es w ere base- lined in a dry (no fluid) condition . D evices w ere tested w ith no fluid first and then increasing am ounts o f fluid w ere added to the M H E. T he baseline m easurem ent w as perform ed to determ ine the energy lost to surroundings. T he am ount o f fluid necessary to fill the M H E reservoirs and channels w as 150/tL. T he vapor- liquid interface w as desired so the M H E w as not fully filled w ith w orking fluid. 3M rM N ovec H FE -7200 engineered fluid was selected as the w orking fluid for testing w hich has a boiling point o f 76°C . L oading o f the M H E fluid was perform ed by m anually filling the M H E using a G ilson Pipetm an p ipette. Follow ing filling o f the M H E, the devices w ere ready for testing.
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Test SetupTests w ere conducted to characterize energy transfer o f the
M H E. T he fabricated M H Es w ere tested in a se tup as depicted in Fig. 4. To m inim ize energy losses to the surroundings, the testing w as perform ed on a p iece o f balsa w ood. O m ega k-type bare w ire therm ocouples (TC ) w ere used to m easure tem perature at d iscrete poin ts on the heater, heat sink, heat flux sensors and the M H E. T C s w ere centrally located betw een each layer as show n in Fig. 4. O m ega lists the erro r o f the T C as ± 0 .5 °C . H eat flux to the test dev ice w as accom plished using an O m ega KH LV -101/10-P resistance heater. T he heater w as connected to a pow er supply w ith a m easured 1.1W m aintained for each test. This pow er w as selected to prov ide low energy input. A low en ergy pow er w as se lected to estab lish low tem peratu re potential application fo r the M H E. To quantify the therm al energy transfer through the setup, an O m ega H FS-4 thin film heat flux sensor (H FS) w as p laced betw een each layer as noted in Fig. 4. The nom inal sensitivity o f each H FS-4 has an erro r o f ± 1 0 % based on O m ega.
T he layered test setup, show n in Fig. 4, w as fabricated as a vertical stack o f heater, heat flux sensor, M H E, heat flux sensor, and heat sink. T he heater and heat flux sensors have the sam e area w hich allow ed ease o f stacking. T he M H E, being elongated , w as cen tered betw een the tw o flat heat flux sensors. E ach layer had a T C above and below w hich w as placed in the stack w ithout additional tape so that the tem peratu re results w ere not affected by extraneous m aterials. A laboratory jack w as then used to press the test se tup against the heat sink, w hich ensured good therm al contact betw een every layer.
T his se tup w as m aintained fo r all tests independent o f the quan tity o f M H E w orking fluid. C are w as taken to m axim ize therm al contact betw een setup layers by using O m ega O m egath- erm 201 therm al paste. D ata w as recorded and analyzed via a Lab-V iew program on a connected PC. T he tw o HFS provided heat flux data w hich w as used to calcu late energy throughput and losses. E ach HFS w as calibrated and verified by O m ega. T he calibration num ber w as used to convert the voltage signal received by Lab-V iew in to an energy flux. T he tw o HFS used for each test had calibration num bers o f 1.9 and 1.8 ■T he heat flux throughput allow ed characterization o f the M H E as described in the R esults section.
RESULTSC opper M H Es w ere fabricated as described in the E xperi
m ental M ethods section. T he suggested current density o f 3 ^ j , given surface area o f the M H E, provided a suggested current o f 0.61 A from the literature [14]. T his current density plated copper uncontrollably. R esults o f p lating w ith the curren t low ered to 0 .5A are p resen ted in Fig. 5. T here are m any locations w hich indicated plating selectivity w hich caused d isproportional chan nels. A fter the electropolish ing step w as introduced and the cur-
Figure 5. Copper plated channels with I = 0.5A.
Figure 6. Copper plated channels after polishing with I = 0.4A.
rent low ered further to 0 .4A , the M H E channels exhibited even plating a t a deposition rate o f 1 ^ . T he resu lts o f fabrication are show n in Fig. 6 w hich proved that w ell-defined M H Es o f copper can be p roduced w ith m inim al equipm ent.
T he Experim ental M ethods section described testing setup perform ed after M H E fabrication. T he resu lting test data in Fig. 7 w as generated w ith M H Es o f 90/rm channel heigh t and 300/rm channel w idth. Dry M H E read ings indicated 2.63 ̂ y o f therm al
flux entering the M H E and 2.55 ̂ y leaving the M H E. A pprox im ately 97% o f energy supplied to the M H E transferred through the system . T h is inform ation provided assurance that there w as m inim al energy lost to surroundings and good therm al contact o f the M H E com ponents and testing setup.
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3.00
5 i so
—Input
—Dry
-W e tte d
oso
0.00 0 500 1000 1500
Time (s)
Figure 7. Thermal f l u x o f dry and wetted MHE.
A partia lly filled M H E w as tested w ith a volum e o f 37pL w orking fluid. T his data, depicted in Fig. 7, indicated 2 .2 - j o f therm al flux throughput w ith w orking fluid. T he reduction in p erform ance w as likely to the low er therm al inputs o f these initial tests. H ow ever, if the energy input is increased, the M H E perfo rm ance is expected to be significantly im proved w ith increased m ass transfer and phase change.
T em perature profiles fo r the dry and w etted tests are show n in Fig. 8 and 9. T he low energy input caused a heater tem perature betw een 40°C and 50°C , too low to have significantly caused phase change o f the w orking fluid based on the boiling poin t o f 76°C . T he tem peratu re difference betw een each therm ocouple w as approxim ately 5°C in dry and w etted readings. T he M H E Lid m easurem ent show ed a reduction o f 2°C betw een dry and w etted tests w ithout tem peratu re change o f the M H E bottom . Low energy input w as achieved; how ever, selection o f an alternative w orking fluid w ith reduced boiling po in t w ould im prove the operation o f these devices. Fu ture tests are p resently focused on increased heat input and device perform ance.
CONCLUSIONSM E M S-based copper plated M H E s have been fabricated and
tested for operation . D ue to the large therm al conductivity o f copper, fabrication focused on p rocesses in w hich copper could be used for the en tire M H E. W ithout the electropolish step, deposition w as selective and channels delam inated from the substrate upon m ask rem oval. M ask th ickness se t lim its fo r channel height due to aniso tropic deposition w hen m ask height was exceeded. Fabrication o f the M H E w as perform ed at low cost w ith m inim al equipm ent. Future w ork w ill focus on fabrication o f varying channel heights and w idths to fu rther refine the fabrication p ro
45-*-He»t«r
40MHE Lid
25
200 500 1000 1500 2000
Time (s)
Figure 6. Temperature profile of dry MHE.
45-*-H*ater
40
-**-Hcat Sink
30
2S
200 500 1000 1500 2000
Time {s)
Figure 9. Temperature profile of wetted MHE.
cess depending on M H E application.
T he perform ance o f the dry M H E indicated good testing se tup w ith m inim al energy loss to surroundings. How ever, en ergy input w as no t large enough to fully show case the capability o f the fluid-filled M H E. In both testing scenarios, however, the vast m ajority o f input therm al energy w as transferred from the sim ulated source. This show ed the effectiveness o f the use o f copper substra te and fabrication techniques in general.
Future w ork is presen tly investigating the lim its and perfo rm ance characteristics o f the devices a t increased therm al inputs. Increasing energy input such that tem peratures approach and ex ceed H F E -7200 boiling poin t w ill p rom ote phase change w ithin
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the M H E. A nother approach w ould consider testing under the sam e conditions using a d ifferent w orking fluid. S ince the M H E is w orking fluid non-specific, ano ther fluid could be selected w ith a boiling poin t appropriate to tem peratu res achieved w ith low pow er input.
T he energy inpu t necessary to p rom ote phase change conditions and the use o f therm ally conductive m aterials w ill reduce therm al resistance o f the M H E, allow ing larger energy th roughput. K now ing operating conditions fo r various w orking fluids w ill allow M H E flexibility w ith m ultip le applications dependent on device environm ent.
ACKNOWLEDGEMENTST he authors gratefu lly acknow ledge the support o f th is work
by N ASA and the N SF via G ran t No. EC C S-1053729.
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[3] M athew , B ., Jakub-W ood, B., O gbonnaya, E., and W eiss, L ., 2013. “Investigation o f a m em s-based capillary heat exchanger fo r therm al harvesting” . International Journal o f Heat and Mass Transfer, 58(1), pp. 492 -5 0 2 .
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[6] Jaeger, R. C ., 2001. In troduction to m icroelectronics fabrication , vol. v, m odular series on solid state de- vices,(neudeck, gw and p ierret, rf, eds.).
[7] Frazier, A. B ., and A llen, M. G „ 1992. “H igh aspect ratio electrop lated m icrostructures using a photosensitive poly- im ide process” . In M icro E lectro M echanical System s, 1992, M E M S ’92, P roceedings. A n Investigation o f M icro S tructures, Sensors, A ctuators, M achines and R obot. IEEE, IEEE, pp. 8 7 -9 2 .
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Journal o f Micromechanics and Microengineering, 19(3), p. 035009.
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[12] C honan, Y„ K om iyam a, T., O nuki, J., N agano, T., A ka- hoshi, H ., Itabashi, T., Saito , T., and Khoo, K., 2006. “F illing a narrow and h igh aspect-ratio trench w ith electro-cu p la ting” . Materials transactions, 47(5), p. 1417.
[13] E urope, E. O rdyl dry film p500000 product data sheet form bt-050e.
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Proceedings of the ASME 2014 International Mechanical Engineering Congress & ExpositionIMECE2014
November 14-20,2014, Montreal, Canada
IMECE2014-38801
A C O PPER MICROCHANNEL HEAT EXCHANGER FOR MEMS-BASED WASTE HEAT THERMAL SCAVENGING
E. Borquist, A. Baniya, S. Thapa, D. Wood, L. W eiss *Institute for Micromanufacturing
D epartm ent of Mechanical Engineering Louisiana Tech University
Ruston, LA 71272 Email: lw eiss@ latech.edu
ABSTRACTThe growing necessity fo r increased efficiency and sustain
ability in energy systems such as MEMS devices has driven research in waste heat scavenging. This approach uses thermal energy, which is typically rejected to the surrounding environment, transferred to a secondary device to produce useful power output. This paper investigates a MEMS-based micro-channel heat exchanger (MHE) designed to operate as part o f a micro-scale thermal energy scavenging system. Fabrication and operation o f the MHE is presented. MHE operation relies on capillary action which drives working fluid from surrounding reservoirs via micro-channels above a heated surface. Energy absorption by the MHE is increased through the use o f a working fluid which undergoes phase change as a result o f thermal input.
In a real-world implementation, the efficiency at which the MHE operates contributes to the thermal efficiency o f connected small-scale devices, such as those powered by thermoelectrics which require continual heat transfer. This fu ll system can then more efficiently power MEMS-based sensors or other devices in diverse applications. In this work, the MHE and micro-channels are fabricated entirely o f copper with 300pm width channels. Copper electro-deposition onto a copper substrate provides enhanced thermal conductivity when compared to other materials such as silicon or aluminum. The deposition process also increases the surface area o f the channels due to porosity. Fabrication with copper produces a robust device, which is not limited to environments where fragility is a concern.
The MHE operation has been designed fo r widespread use in varied environments. The exchanger working fluid is also nonspecific, allowing fo r fluid flexibility fo r a range o f temperatures, depending on the thermal source potential. In these tests, the exchanger shows approximately 8.7 o f thermal absorption and 7.6 ^ o f thermal transfer fo r a dry MHE while the wetted MHE had an energy throughput o f 8.3 The temperature gradient maintained across the MHE bottom plate and lid is approximately 30 °C for both the dry and wetted MHE tests though overall temperatures were lower fo r the wetted MHE.
INTRODUCTIONT he grow ing necessity for increased efficiency and sustain
ability in energy system s has driven research in w aste heat scavenging. O ver the past 30 years, the increasing m iniaturization o f devices and p rocessing ab ilities has m ade previously un th inkable developm ent and scaling possible. W ith this scaling dow n o f devices, new avenues o f w aste harvesting possib ilities, such as therm al scavenging, have been realized by researchers. T herm al scavenging can provide pow er for external sensors o r prov ide a p latform for structural health m onitoring o f system s. T he key to taking advantage o f these therm al harvesting possib ilities is the sam e reason that sustainable alternatives are being sought out: inefficiency o f existing system s.
M any standard therm odynam ic cycles have low efficiencies w here m uch o f the therm al energy generated is re jected to the surrounding environm ent [1], H arnessing the rejected therm al
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energy via transduction m echanism s allow s existing physical e ffects to pow er additional system s, such as M EM S devices [2], M icro-channel heat exchangers (M H Es) use m ultiple fluid-filled channels w hich, at reduced scales, p roduce effective heat and m ass transfer due to the dynam ic boundary layers [3]. M axim izing harvesting o f w aste heat fo r M EM S devices w ith M H Es necessitates optim izing channel fluid dynam ics w hile m in im izing therm al resistance [3 ,4 ]. T herm al resistance is reduced using tw o-phase flows and m aterials w ith h igh therm al conductiv ities [3 ,4 ],
Traditionally, m icro-scale devices have relied on silicon as substrate o r bulk m aterial o f fabrication. However, the low thermal conductiv ity o f silicon, w hen com pared to m etals such as copper, and its frag ility in w afer form dem and viab le a lternatives fo r m ore effective and varied usage in dynam ic environm ents [5], A doption o f technologies on the g lobal scale requires low -cost m aterials and processes w hich can be im plem ented w ith m inim al equ ipm ent in frastructure. M ass-produced m etal-based M H Es w ould produce m ore robust system s, im proved therm al conductivity , and allow usage throughout m uch o f the g lobe [4], T hough there is num erous literature on heat spreaders and o ther capillary devices, including heat pipes, the exchanger in this work has been designed to use m icrochannels betw een tw o reservoirs com posed entirely o f copper [3 ,6 -8 ] .
T here are five b road fabrication classifications for p rocessing m icro-channels: photolithography, expansion, solidification, subtractive, and additive [9 ,10 ]. W hile all five fabrication m ethods poten tially include required expensive equipm ent o r clean- room laboratory conditions, there are low -cost options w hich w ould allow for w idespread use o f m etal-based M H Es for therm al w aste scavenging. O ne im portant photo lithography tech nique for m etallic m icrostructu res is L IG A (G erm an for lithography, galvanoform ung (electroplating), and abform ung (m olding)) w here thick pho toresists are applied to substrates as m olds and filled w ith electroplated m etals [11], A n adaptation o f LIG A involves using poly im ide as the applied m old w hich is a low -cost alternative to traditional L IG A [12], T his adapted electroplating m ethod produces an efficient, high-precision , low -cost m ethod w hen com bined w ith a CO TS m ask process.
In th is w ork, a m ethod fo r the fabrication o f a copper M H E using an adapted , L IG A inspired technique is presented . The M H E has com ponents as noted in Figure 1. It is designed for c losed system operation w hereby no external w ork m echanism is needed for fluid m ovem ent. T herm al and m om entum transport are driven by using phase change o f a w orking fluid. T he m icro-channels drive capillary action o f the fluid such that the w orking fluid is d ispersed over the heat source area, im proving heat transfer to the w orking fluid. T h is m echanism is show n in F igure 2. T he boiling w orking fluid travels to the M H E copper lid w here heat transfer to the heat sink allow s condensation to occur and the w orking fluid retu rns to e ither the m icro-channels or the reservoirs. T he M H E is designed fo r m ultip le applications in
MICRO-CHANNELS
Figure 1. MICROCHANNEL HEAT EXCHANGER LAYOUT
C O P P E R PLATING
CAPILLARY ACTION
) HEAT SOURCE
Figure 2. FLUID MOTION OF HEAT EXCHANGER
m ultip le environm ents. T here is no specified w orking fluid in the operational design. F lu id is strictly se lected dependent on boiling poin t requirem ents and conditions o f device operation . C opper w as se lected for the M H E due to therm al p roperties; however, any m etal w hich can be electrodeposited can be used.
T he purpose o f fabricating this particu lar M H E is to create a robust piece o f equipm ent w ith m inim al laboratory equipm ent w hile m aintain ing a h igh heat transfer capacity. O nce m ade, such a device can be coupled w ith o ther devices, such as therm al storage system s. H eat exchanger developm ent, a long w ith m aterials research , are the cornerstones in developing effective and renew able therm al energy storage [13], O ne challenge, w hen studying
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the phase change m aterials (PC M ) w hich are vital to the therm al energy storage, is that m ost PCM have low therm al conductiv ities leading to low charging and d ischarging rates [14], The M H E stud ied in th is w ork attem pts to m axim ize structural heat transfer, w hile providing a p latfo rm capable for use in varied en vironm ents, through the use o f copper.
T he intentional am biguity o f design param eters, in fab rication and operation , m akes the M H E m ulti-faceted, bo th in e n vironm ental condition and cost. E conom ic and situational d e m ands m ay dictate the use o f an alternative m etal and w orking fluid. Follow ing fabrication o f the M H E, described in the fo llow ing section, system s are evaluated in therm al testing fo r therm al absorption o f sim ulated heat sources.
EXPERIMENTAL METHODS Fabrication
T he fabrication o f M H Es from the m odified L IG A technique concentrated on electrop lating copper onto copper substrates. To create the device show n in F igure 1, a 100-200/rm layer o f co p per w as electrodeposited onto a copper substra te to produce the reservoirs and m icro-channels. O verall d im ensions o f the exchangers w ere 22 m m in w idth and 44 m m in length. A fter the M H E bottom p la te w as fabricated , ano ther copper p late was p o lished fo r sm oothness and used as the M H E lid. S ince the system w as designed for c losed system operation , an access port was installed on the lid to allow addition o f w orking fluid fo r testing.
A rigid substra te was necessary to lim it p lating delam ination and p lating cracking due to device handling . C opper 110 sheeting o f 3.175 m m th ickness w as purchased (M cM aster-C arr) for the substra te and lid construction . In o rder to create a process w hich m inim izes equ ipm ent and fabrication tim e, dry film (Or- dyl) w as purchased for the m icro-channel m ask patterning. E lectroplating and polish ing w as perform ed w ith so lu tions o f copper su lfate/su lfuric acid and phosphoric acid (A lfa A esar).
T he copper substrate w as in itially cleaned w ith an acetic acid solution and rinsed . A flat iron w as then heated on a hot plate to approxim ately 80 °C in o rder to lam inate the dry film onto the substrate. O nce the dry film w as lam inated onto the substrate, the 300/jm w idth channel m ask w as secured to the lam ination. Traditionally , a m ask aligner is used to expose the film; how ever, in o rder to facilita te use outside o f laboratory env ironm ents, a fluorescent light was used fo r exposure. A fter a developm ent tim e o f 15 seconds, the undeveloped film w as rem oved from the substra te using O rdyls recom m ended potassium carbonate solution. F igure 3 dep icts a sam ple w ith a developed dry film and substrate prepared fo r electroplating.
P rior w ork indicated that electropo lish ing the copper substrate w ould provide an im proved and clean surface for e lectro p lating . P o lish ing the substra te creates a surface w ith enhanced uniform ity, prevents delam ination o f p lating , and allow s fo r repeatability o f M H Es. A phosphoric acid based solution was se-
P aram ete r W orking Condition
H,PO< 157 ml.
h 2o 75 mL
Current 0.045A
Temperature 55 °C
Table 1. ELECTROPOLISHING CONDITIONS FOR COPPER [15]
P aram e te r W orking Condition
CuS 0 45 H20 188 f
h 2s o 4 W f
Current 0.4A
Temperature 40 “C
Table 2. ELECTROPLATING CONDITIONS FOR COPPER [16]
lected for the polish ing step. Table 1 show s the final solution com position and conditions. T he estab lished m ixture o f cop per su lfate and sulfuric acid w as chosen for e lectroplating due to ease o f p reparation and accounting fo r chem ical hazards. Table 2 show s the final so lu tion com position and conditions for plating. T he optim um curren t fo r the M H E d im ensions was determ ined to be 0 .4A . D eposition rate o f copper was also a required param eter. Several sam ples w ere plated for varying tim es and a D cktak 150 Surface Profiler w as used to m easure the deposited channel heights. U sing the fabrication m ethod presen ted , the deposition rate o f copper plating w as determ ined to be approxim ately 1 £ £ . Sam ples w ere plated from 60/rm in heigh t to 200pm in heigh t, all having channel w idths o f 300pm .
O nce the M H E bottom w as electroplated w ith a height o f 120pm, a second copper substra te w as polished and plated w ith a he igh t o f 120pm , w hich served as the M H E lid. T he additional porosity and surface area o f both the bottom plate and the lid w ere felt to enhance operation o f the M H E. P rior to p lating the lid, an access port w ith d iam eter 3 m m w as drilled into the cen ter o f the lid. C entering the access port provided equal d ispersion o f the w orking fluid, via the m icro-channels, to the tw o reservoirs. T he bottom plate and lid w ere then con tacted w ith a press and bonded w ith steel-based epoxy on the vertical sides. T he relative sm oothness o f the p lating enhanced therm al contact betw een the plates; the external seal covered the en tire vertical sides o f both plates to ensure w orking fluid d id not escape during operation due to the porosity o f the electroplating process. E xam ples o f plated M H Es are presen ted in F igures 4 and 5.
P rior to testing w ith w orking fluid, the M H Es w ere baselined in a dry condition . D evices w ere tested w ith no fluid first and then w orking fluid was added to the M H E. T he baseline m easurem ent w as perform ed to determ ine the energy lost to surroundings
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Figure 3. DRY MASK ON COPPER SUBSTRATEFigure 5. COPPER PLATED MHE CAPILLARY CHANNELS
HtATER 2
h b a t f i u x s e n s o r t
HEATER 1
Figure 6. TEST SETUP - THERMOCOUPLES ARE LABELED TC
Figure 4. COPPER MHE BASE WITH CAPILLARY CHANNELS
and absorbed by air inside the M H E. T he am ount o f fluid necessary to fill the M H E reservoirs and channels o f the bottom plate was 1 50/jL. T his value w as used to determ ine an appropriate vo lum e o f w orking fluid for testing. T he vapor-liquid in terface was desired so the M H E w as no t filled entirely w ith w orking fluid. The se lected volum e o f w orking fluid added to the M H E was 100/rL. 3M™ Novec™ H FE 7200 engineered fluid w as selected as the w orking fluid for testing w ith a boiling poin t o f 76 °C. L oading o f the M H E fluid w as perform ed by m anually fill the
M H E using a G ilson® Pipetm an pipette. Follow ing filling o f the M H E, the devices w ere ready for testing.
Test SetupTests w ere conducted to characterize energy absorption and
transfer o f the M H E and tem perature profiles o f M H E bottom and lid. T he fabricated M H Es w ere tested in a setup dep icted in Figure 6. To m inim ize energy losses to the surroundings, the testing w as perform ed on a piece o f balsa w ood, w hich has a therm al conductiv ity tw ice that o f air. O m ega® k-type bare w ire therm ocouples (TC) w ere used to m easure tem perature at d iscrete poin ts on the heater, heat sink, heat flux sensors, and the M H E. O m ega® listed the error o f the TC as ± 0.5 °C. T he heat source
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9
8
7
65
4
3 — Input
— O utput W etted
— O utput Orv2
10
0 500 1000 1500 2000Tim* (s)
Figure 7. HEAT FLUX DATA FROM DRY AND WETTED TESTS
-H e a te r
-D ry MHE Lid
— Dry MHE Bottom
— Heat Sink
120
100
e
40
20
1000 1500T im e (a)
Figure 8. DRY MHE TEMPERATURE DATA
o f the test device w as p rovided by an O m ega® K H LV-101/10-P resistance heater. T he heater w as connected to a pow er supply w ith a m easured 3.6W m aintained fo r each test. T h is pow er w as selected to ensure the bottom o f the M H E reached tem peratures above the w orking fluid boiling po in t to cause the required phase change.
To quantify the therm al energy transfer through the setup, an O m ega® H FS-4 thin film heat flux sensor (H FS) w as p laced betw een each layer as noted in F igure 6. T he additional H FS underneath the heater was used to m in im ize energy loss through the balsa base by track ing heat flux sensor #1 from F igure 6 and m aintain ing a heat flux m easurem ent o f zero. T he nom inal sensitiv ity o f each H FS-4 has an error o f ± 10% according to O m ega® .
W orth noting w as a m ethod used to m inim ize energy loss through the test se tup underneath the heater. H eater #1 and heat flux sensor #1, from Figure 6, w ere included in o rder to offset heat ou tpu t from heater #2 tow ards the setup base. The heat flux sensor betw een the heaters w as m easured during testing so that there w as no heat flux betw een the heaters. T his ensured that the m ajority o f output from heater #2 w as directed tow ard the M H E.
T his setup w as m aintained for all tests independent o f the volum etric quan tity o f M H E w orking fluid. C are w as taken to m axim ize therm al contact betw een setup layers by using O m ega® O m egatherm ® 201 therm al paste. D ata w as recorded and analyzed via a Lab-V iew program on a connected PC. T he two heat flux sensors (HFS #2 and H FS #3) p rovided heat flux data w hich was used to calculate energy throughput and losses. E ach HFS w as calibrated and verified by O m ega® . T he heat flux th roughput and tem perature data allow ed characterization o f the M H E as described in the R esults section.
— H eater — W e tte d MHE Bottom
— W etted MHE Lid — Heat Sink
120
100
SO
60
40
200 500 1000 1500 2000
T im * (*)
Figure 9. WETTED MHE TEMPERATURE DATA
RESULTST he results o f pro to type testing are included in this sec
tion. Tests w ere conducted to characterize the operation o f the dry copper-based M H E versus a w orking fluid w etted M H E. T he therm al testing reported how added therm al energy to the device altered heat flux and tem perature m easurem ents in o rder to characterize heat transfer and energy throughput.
T hough the given energy input to the heater was 3.6W , resistive losses reduced energy input supplied to the M H E to 3.44W . T h is corresponded to a heat flux entering the M H E o f 8.7 .
For the dry M H E, the output heat flux m easured at 7.6 w hile
the w etted M H E output w as 8 .3 ^ y , depicted in F igure 7. T he percentage o f input flux w hich exited the M H E w as 87.5% for
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Figure 10. SEM IMAGE O F PLATED CHANNELS AT 5<Hty/m SCALE Figure 11. SEM IMAGE O F PLATED CHANNELS AT 500nm SCALE
the d ry M H E and 95.4% for the w etted M H E. T hrough the use o f the w orking fluid, energy th roughput through the device w as increased by approx im ately 8% . E nergy rejected from the sides o f the M H E w as assum ed neglig ib le versus the overall therm al energy passing from source to sink. T h is w as based on the operating tem peratures, heat flux, and side cooling that w as restricted to radiation o r free convection. C alculation o f the side losses for both the d ry and w etted M H E yielded less than 1 % o f the total input pow er to the device.
The tem peratu re profiles o f the dry and w etted M H E also yielded interesting results. T he w orking fluid acted as a heat sink, w hich low ered the m easured therm ocouple tem peratu res an average o f 9°C except for the actual heat sink. B oth the dry and w etted M H E testing y ielded a heat sink tem perature o f 37°C. T he tem peratu re data fo r the dry and w etted M H E tests are show n in F igures 8 and 9. W hile the w orking fluid acted as a heat sink for the entire system , it benefited the tem peratu re d ifference o f the M H E bottom and top an average o f 3°C.
T he underlin ing key to these tests was the contribution to efficiency through the use o f the w orking fluid w ithin the M H E. In the dry tests, there w as a sm all pocket o f air betw een the tw o plates w hich reduced the therm al conductiv ity and the energy th roughput o f the M H E. However, after adding w orking fluid the pocket w as filled approxim ately tw o-th irds w ith fluid. T he vapor-liquid in terface allow ed greater conductiv ity but also introduced phase change. T he capillary action o f the m icro-channels pulled liquid over the heat source. V aporization o f fluid caused m icro-channels to pull additional liquid and the tem perature o f the M H E lid indicates condensation o f w orking fluid back to the reservoirs to begin the cycle anew.
SEM im ages o f the plated copper are show n in Fig. 10 and 11. T h e estim ated porosity w as determ ined to be 15%. T h is esti
m ation w as perform ed using a linear bulk volum e m easurem ent. G iven the volum e o f the designed M H E, the fabricated sam ple w as m assed and converted to volum e using the density o f copper. It w as calculated that the sam p le 's volum e was 85% o f the theoretical volum e o f the M H E, thus giving a porosity o f 15%. T he porous structure increased device surface area and enhanced con tact area for the w orking fluid. U sing phase change allow ed w orking fluid to inundate the entire device, not ju s t the capillary m icro-channels. T hough the system is closed , this structure p ro m oted a h ighly interactive vapor-liquid in terface w hich increased overall heat transfer.
CONCLUSIONSFabrication and operation o f a sm all-scale, M E M S-based
M H E has been investigated. T he M H E acted in a c losed system w ith operation based on developm ent o f capillary m icrochannels w hich provided pum p-like w orking fluid m otion across a heated surface, inducing phase change o f the fluid. T h is operation provided a m ore efficient transfer o f energy across the copper device.
Fabrication o f the copper device w as based on electrop lating techniques that produced channel w idths o f 300 /jm w ith heights o f 120 ftm. T he fabrication m ethodology proved that devices can be m anufactured w ith m inim al equ ipm ent and laboratory necessities. T h is added benefit was m eant to potentially increase the g lobal adoption and use o f such devices, even in rem ote areas o f the world.
T he in troduction o f w orking fluid im proved the energy throughput o f the device by approxim ately 8%. W ith a energy flux supply o f 8 . 7 a dry device show ed output flux o f 7 .6 - ^
w hereas the w etted device show ed output flux o f 8.3 ̂ r . T hese
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resu lts dem onstrated the effectiveness o f using w orking fluid and phase change w ithin the devices. U se o f w orking fluid, coupled w ith the developm ent o f copper techniques allow ed a device to be fabricated entirely o f copper. T h is increased therm al conductivity o f the device w hen com pared to established m aterials such as silicon and alum inum .
Future w ork w ill investigate the ability to decrease the cap illary channel w idth o f the copper exchangers. T his should p ro duce devices w ith greater capillary capability com pared to the 300^mi w idth channels reported in th is w ork. D evelopm ent o f a lternative channel geom etries and the contro l o f p lating porosity m ay be advantageous to im proving heat transfer across the device. Further p rogress on these devices prom ote adoption o f w aste heat scavenging program s and potentially opens diverse avenues o f applicability fo r g lobal developm ent.
ACKNOWLEDGEMENTST he authors g ratefu lly acknow ledge the support o f th is w ork
by N A SA and the N SF via G ran t No. ECCS-1053729.
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Proceedings of the ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems and ASME 13th
International Conference on Nanochannels, Microchannels, and MinichannelslnterPACKICNMM2015
July 6-9, 2015, San Francisco, California, USA
lnterPACKICNMM2015-48482
EXPLORATION OF PHASE CHANGE WITHIN A CAPILLARY FLOW DRIVEN SQUARE MICRO-CHANNEL USING LATTICE BOLTZMANN METHOD AND
EXPERIMENTAL BOUNDARY CONDITIONS
E. BorquisU, G. Smith*, L. W eiss *Institute for Micromanufacturing
Departm ent of Mechanical Engineering Louisiana Tech University
Ruston, LA 71272 Email: lw eiss@ latech.edu
* R adiance Technologies, Inc. Ruston, LA 71272
ABSTRACTPreviously published research examined the overall effi
ciency o f heat transfer through a copper plated micro-channel heat exchanger. However, since the device is sealed and composed entirely o f copper, understanding the phase change, temperature field, and density field o f the working fluid is difficult empirically. Given that the efficiency was shown to be greatly increased by the working fluid phase change, this understanding within the device is important to designing devices o f greater efficiency and different working fluids. One method o f determining device and component performance is numerical modeling o f the system.
Fluids that undergo phase change have long frustrated those attempting to successfully numerically model systems with acceptable stability. Over the past twenty years, the lattice Boltzmann method (LBM) has transformed the simulation o f multi- component and multiphase flows. Particularly with multiphase flows, the LBM "naturally " morphs the phase change interface throughout the model without excessive computational complexity. The relative ease with which LBM has been applied to some multicomponent/multiphase systems inspired the use o f LBM to
track phase change within the previously recorded experimental boundary conditions fo r the copper plated heat exchanger.
In this paper, the LBM was used to simulate the evaporation and condensation o f HFE-7200 within a capillary flow driven square micro-channel heat exchanger (MHE). All initial and boundary conditions fo r the simulation are exactly those conditions at which the empirical data was measured. These include temperature and heat flux measurements entering and leaving the MHE. Working fluid parameters and characteristics were given by the manufacturer or measured during experimental work. Once the lattice size, initial conditions, and boundary conditions were input into MATLAB®, the simulations indicated that the working fluid was successfully evaporating and condensing which, coupled with the capillary driven flow, allowed the system to provide excellent heat transfer characteristics without the use o f any external work mechanism.
Results indicated successive instances o f stratified flow along the channel length. Micro-channel flow occurring due to capillary action instead o f external work mechanisms made differences in flow patterns negligible. Coupled with the experimentally measured thermal characteristics, this allowed simulations to develop a regular pattern o f phase interface tracking. The
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agreement o f multiple simulations with previously recorded experimental data has yielded a system where transport properties are understood and recognized as the primary reasons fo r such excellent energy transport in the device.
INTRODUCTIONM ultiphase flow is a fundam ental phenom enon necessary
for m any prim ary functions in life. W hile understood in p ractice and use, m ultiphase flow is not fu lly understood theoretically. In o rder to p roperly understand w hat occurs during phase change in m any system s, researchers have turned to num erical m odeling and sim ulation. T he traditional m ethod to m odel the physical fluctuations at the phase change in terface is to perform m acroscopic d iscretizations o f continuum equations, m ost notably so lv ing for the N avier-Stokes equations. How ever, the nonlinearity and constant variations o f phases at the interface, w here d ifferent phases are continually com bining, separating, and changing, p resents difficulties fo r m acroscopic schem es. In the physics d isc ip line o f sta tistical m echanics, it is know n that behavior o f fluids can be determ ined through statistical analysis o f ensem ble system s on the m icroscopic scale. Though the evolution o f com plex system s on the m icroscopic scale involves too m any variables, these system s can be expanded artificially to the ’’m esoscopic” scale w here the physics o f the system is m aintained.
In 1986, F risch , H asslacher, and Pom eau presented a B oolean case fo r using la ttice-based gas cellu lar au tom ata (LG A ) to sim ulate nonlinear fields such as the N avier-Stokes equations[1], T h is led to the developm ent o f a com putational m ethod nam ed the lattice B oltzm ann m ethod (LB M ). T he L B M is based on the continuous B oltzm ann equation w hich is then d iscretized in tim e and phase space [2 ,3 ], W hen researchers expanded the LBM to m acroscopic system s, the N avier-Stokes equations w ere recovered [1 ,3 ,4 ] , Soon after, studies began exam ining the use o f LBM to sim ulate m ultiphase and m ulti-com ponent system s, m ost notably by Shan and Chen. T heir pap er in troduced the interpartic le poten tial as a m eans o f adding attraction and repulsion to the lattice elastic conditions [4], O ver tim e, Shan and C h e n ’s pseudo-potential m odel inspired several o ther m odels including Yuan and Schaefer, Z hang and C hen, and Z eng, w ho all incorporated partic le forces into equations o f state [5], Initially, these LBM m odels incorporated a density d istribution function w hich is then substitu ted into a given equation o f sta te to prov ide the p ressure function w hich gives the phase change in terface. H ow ever, w hen tem perature differences p lay a vital ro le in the system and boundary conditions, an additional tem peratu re distribution function is needed. Fusing these tw o distribution functions w ith the chosen equation o f sta te can p resen t difficulties w hich is w hy m any researchers have tested m odels using norm alized param eters, such as the gas constant, and arb itrary equation o f state param eters [5 -8 ]. U nfortunately, for m ost fluids, this generaliza
tion is not valid to determ ine the phase change interface w ithin a realistic system .
Im plem enting the lattice B oltzm ann schem e requires a thorough understanding o f the system in question as w ell as the properties o f the w orking fluid. In o rder to sim ulate the system properly, the physical system m ust be num erically m odeled equivalently and the lattice netw ork m ust be o f sufficient reso lution w ith an appropriate tim e step [9]. T hese constrain ts w ill assist in representing the correc t physics fo r the system . W hile in m any cases the physical system units are nondim ensionalized prio r to d iscretiz ing the lattice, it is not absolu tely necessary [9], T he m odel presented in this w ork m aintained all units w hich allow ed for com parison w ith param eter calcu lations and experim ental data
In th is w ork, an M H E square channel is m odeled w ith prior experim ental boundary conditions applied and the lattice B oltzm ann m ethod. T he channels have been designed fo r c losed system operation w hereby no external w ork m echanism is needed fo r fluid m ovem ent. T herm al and m om entum transport are driven by the cap illary flow w ithin each channel as well as the phase change o f the w orking fluid. T he m echanism o f operation is given in a p revious w ork [10], A pplying the appropriate tim e steps and channel geom etry allow ed for resu lts w hich reached steady-state at approxim ately the sam e tim e as the orig inal ex perim ental work.
EXPERIMENTAL METHODS Model Description
P rior to exam ining specific perfo rm ance o f the proposed m odel, a general descrip tion o f the m odel construction is given along w ith all fundam ental equations. S ince the system has m ultiple phases, there is a need to estab lish a density d istribution function and a tem perature d istribution function in o rder to fully capture the particle evolution th rough lattice space and tim e. T he L B M describes a single com ponent o r m ulti-com ponent system by these evolutions o f the partic le distribution functions. The density d istribution function evolves using the traditional BGK collision operato r as given in Equation 1. A corresponding equ ilibrium distribution function relates the relaxation o f the system , w hich is given in Equation 2. T he last term in E quation 1 in troduces a body fo rce term as presen ted by G ong and C heng[6], T h is fo rce term includes three forces w hich change associated velocity term s during co llisions, the in terpartic le interaction force, the in teraction force betw een surfaces and fluids, and the g ravitational force [6],
/ , ( x + e ,5 ,,r 4 8 ,) - f ( \ , t ) = ~ l- ( f i ( x , t ) - f ^ ( x , t ) ) + Afi{x,t)
( 1)
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1 + ^ + ^Cl C‘■t ^ c
U u' 2 r i
(2)
A nalogous to the density d istribution functions evolution equation, the tem peratu re distribution function has an evolution equation given by Equation 3. T he equilibrium function , given by Equation 4, is very sim ilar to the density equilibrium function. T he m ain d ifference betw een the tw o distribution functions is the last term o f each equation. W hile the density evolution incorporates a body force term , the tem peratu re evolution uses an energy source term . E ach d istribution has w ith it an associated velocity, e,, at position x and tim e t. T he w eighting coefficients, to,, for both equilibrium functions is based on statistical probab ility for partic le m ovem ent.
3
7
Figure 1. Nine discrete velocities lor each lattice node.
'<7 _ to,T
- 7 - ( £ i ( V ) - s ' V . 0 ) + 8 , a > i 0 XT
(3)
er U (c, -U)2' 1 ' 7 El
2c?(4)
w ith specific densities, the difficulty in fusing tw o distribution functions w as sim plified to include only the density d istribution function values. T he tw o equations are given in Eq. 6 and 7 below [11],
T here are m any d ifferent L B M schem es based on system d im ensionality and po tential locations fo r the particles to m ove. For the p roposed m odel the D 2Q 9 lattice schem e w as chosen due to system sym m etry. T he D 2Q 9 schem e is shorthand for two d im ensional, n ine d iscrete velocities w ithin the m om entum d iscretization [7], F igure 1 depicts the velocities for the D 2Q 9 schem e. T here are nine po tential velocities and each has an associated probability , given in Equation 5.
( I i = 0(0/ = U , i = 1,2,3,4 (5)
U , i = 5,6,7,8
B efore in itializing the m odel w ith the density and tem perature d istribution functions, inform ation given by 3M rM w as acquired concern ing the w orking fluid in question, H FE-7200. T he large am ount o f 3M published data allow ed fo r the use o f tw oequations w hich corre la te the density, tem perature, and partialp ressure o f H FE -7200 [11], T his inform ation w as used to transform tem perature data for boundary conditions in to density data. S ince there was a d irec t linear equation associating tem peratures
InP — 22 .289 - 3752.1 (1 /7 ') (6)
p = 1.4811 — 0.0023026(7 — 273 .15) (7)
O nce the density d istribution function is estab lished and the tem perature array is also found for the m odel, the p ressure field m ust be determ ined. S ince the p ressure gives the phase change interface, it is the overall objective o f th is paper. Fn o rder to determ ine the pressure, an equation o f sta te is typ ically used to associate all three variables. T he Peng-R obinson equation o f state w as chosen due to stability and accuracy fo r m ost m odels [5 ,6 ], Equation 8 gives the P eng-R obinson equation o f state. T h e next section describes how the system w as tested and the lattice p a ram eters for m odel sim ulation.
pRT aph (T )1 — i>p 1 + 2bp - b1 p 2
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Heat Source
Figure 2. Boundary and Initial Conditions for the System.
Performance SetupT he initial step in pursu ing an LBM sim ulation is the se lec
tion o f the program w hich w ill solve the m odel. G iven the o b jec tives o f observing the density, tem perature, and pressure fields and the arrays w hich w ill develop during the LB M , M A TLA B 7 M w as selected. F rom the experim ental data published previously, the first step for the p rogram is to determ ine the boundary conditions o f the system as w ell as the initial conditions for the fluid in channel. Sym m etry o f the channel and the bi-d irectionality o f the fluid flow suggest periodic horizontal boundary conditions. T he fixed top and bottom plating provides for the traditional LBM bounce back condition. W hile these boundary conditions apply to the m om entum equations, there are also tw o additional boundary cond itions w hich account for the heat sink and source. T herefore, tem perature boundary conditions m ust also be set. This presents difficulty in program m ing w here an additional tem perature distribution function m ust be defined. How ever, one benefit o f using a m anufactured w orking fluid is the O EM data sheets and inform ation w hich potentially provide alternative avenues to establish ing a second d istribution function. T he boundary conditions and initial conditions fo r the channel m odel are given in Figure 2.
The physical m icro-channel had d im ensions o f 20m m long, 300/im w ide, and 120//m in height. T herefore, the ratio o f length to height is approx im ately 166. W hile this ratio w ould sim ulate conditions along the entire channel, sym m etry and b id irectionality o f fluid m otion due to cap illary action allow ed the physical ratio o f the program to run at ha lf o f the channel size. T hus, the ratio used in the p rogram is approxim ately 80. For
scaling, the height o f the sim ulation was halved such that LY w as set to 60/rm . T herefore, the horizontal lattice w as set to 4800^m to give the p roper d im ensionality o f the sim ulated chan nel. Tem perature from the experim ental testing fixed the bottom p la te tem perature a t 85°C and the top p la te tem perature at 50°C. T im e steps w ere tried to m easure the steps necessary to ensure steady-state conditions. Follow ing application o f boundary and initial conditions along w ith channel d im ensions for the sim ulation, w orking fluid properties w ere considered to provide the L B M -generated p ressure field.
Product inform ation for 3M N ovec 7200 fluid includes Eq. 6 and 7 w hich provide corre la tion betw een vapor pressure, density, and tem perature [11]. G iven these equations, the tem peratu re boundary conditions can be transform ed into part o f the density array fo r the lid and bottom boundary conditions. N ow that the boundaries are established for the density array, the channel in itial conditions m ust be fixed. S ince 80% o f the channel is filled w ith w orking fluid and 10% is air, the inner array has initial d en sities o f 1 .4 3 ^ for N ovec 7200 and 0 .0 0 1 2 ^ for air at am bient tem perature. A fter setting up the static system , fluid m otion m ust be accounted fo r in the channel. In the tw o-dim ensional system , the horizontal velocity com ponent can be found by m easurem ent. Testing provided a flow velocity along the channel at 2 0 ™ . At am bient tem perature, 3M published viscosity allow s calculation o f the R eynolds num ber to be 975.6, g iving lam inar m icro-channel fluid flow. G ravity and buoyancy effects m ust also be accounted fo r in the flow profile. However, C heng and W u published Eq. 9 [12], For the system in question, channel d iam eter is m uch less than the equation requires, revealing that gravity effects on the sym m etry flow should be negligible. E stablish ing the physical system , boundary and initial conditions, and fluid m om entum within the system allow s solu tions o f LBM collisions. This is coupled w ith the tw o OEM equations and the equation o f state to determ ine phase transitions w ithin the channel.
d, = 0.224/, (9)
In o rder to develop the p ressure field, the param eters fo r the Peng-R obinson equation o f state m ust be determ ined. Table 1 w as generated from calculation and w orking fluid inform ation from 3M. N ote that all units w ere m aintained due to requiring m odeling results in appropriate units. Taking all conditions and the physical system param eters in to account, sim ulations w ere perform ed to solve fo r the phase change in terface transitions. Though the program is continually being developed, the fo llow ing resu lts suggest p rom ising sim ulations o f the phase change transition regions w ithin the m icro-channel.
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Table 1. Peng-Robinson EOS parameters [11]a 36705 ^
b 0.00016 £
R 8-3 '4 £ $
Tr 483.15 K
Pc 2.01 MPa
RESULTST he initial sim ulations at the d im ensions o f 4800/m i long
and 60/rm height ind icated that w ith lam inar flow conditions and neglig ib le gravity effects, the p rogram speed is increased by decreasing the length d im ension w ithou t sacrificing accuracy. T herefore, the subsequent sim ulations w ere conducted w ith 60/rm height and 240/rm length. T he pressure array was p lo tted w ith a co lor m ap w hich is default in M A TLAB. T he system in Fig. 3 is in itialized at tim e t = 1 and develops through tim e t = 360.
T he initial im age, and subsequent figures, can be described as follow s. T he yellow line at approxim ate height 48/rm is the liquid-vapor in terface a t equilibrium prio r to any applied heat. T he teal area under the interface is the region o f liquid-vapor m ixture w ith greater concentration o f liquid. B ulk liquid is the large dark b lue region. T he lighter b lue region at the bottom o f the figure is the region experiencing the initial energy input from the heat source. A bove the equilibrium interface, there is an orange region w hich is the liquid-vapor m ixture w ith greater concentration o f vapor. B ulk vapor is the dark red region, w hile the lighter red at the h ighest region is the region experiencing the initial energy ou tpu t from th e heat sink.
A fter tim e t = 90, there is a shift dow nw ard fo r the vapor- liquid equilibrium interface. T he vapor-liquid m ix ture layers have all expanded and the bulk liquid and bulk vapor layers have contracted given the added energy throughput to the system . A t tim e t = 180, the process has executed sim ilarly, expanding the vapor-liquid m ixture reg ions w hile contracting the bulk vapor and liquid regions.
A fter tim e t = 270, the sim ulation has not approached steady-state. T he vapor-liquid equilibrium interface continues to fluctuate and broaden w hile m oving tow ard the base o f the ch an nel as additional bulk fluid is boiling near the top plate. It is also apparen t that the condensation on the top p la te has slow ed due to the bulk vapor m oving upw ard. B oth vapor-liquid m ixture re gion above and below the equilibrium interface have b roadened and the vapor-liquid m ix ture a t the heat source continues to in crease in size.
F rom the tim e o f t = 320 onw ard , the p lo t beg ins to indicate steady-state flow w ith only m inute fluctuations in each region. T he percen t change m aintains less than 1 % o f the pressure array readings. F igure 3(e) show s the channel a t t = 360. T he equ ilib rium interface is in sim ilar position and channel w idth to the p lo t
at t = 270. T he largest difference is the vapor-liquid m ixtures below the equilibrium interface. It has expanded several m icrons dow nw ard. T h e m ixture at the heat source has also roughly doubled in w idth suggesting that nucleation o f w orking fluid has op tim ized at steady-state. T he vapor region has steadied, though the condensation at the heat sink has slow ed such that there is little gradient betw een the top p late m ixture and the bulk vapor flow.
W hile the m odel is being continuously im proved, these in itial resu lts indicate a strong vapor-liquid equilibrium interface which fluctuates over several m icrons but reaches steady cond itions after approxim ately t = 320. T he vapor-liquid m ixtures on either side o f the equilibrium in terface increase in size over tim e until they are roughly th e size o f the equilibrium interface. T hose three transition regions cover approxim ately 12/mi o f the sim ulation w hich corresponds to 25//m o f the experim ental tests. W hile the bulk vapor and liquid regions contract, they m aintain the m ajo rity o f the channel volum e. T he top p la te condensation appears to slow as the larger w orking fluid volum e begins to vaporize and the bottom p late evaporation tends to increase w ith a nucleation zone th ickness o f approx im ately 10/im for the sim ulation and 20/an fo r the experim ental m odel.
CONCLUSIONST he phase change transition regions, w ithin one square
m icro-channel heat exchanger, w ere explored through the use o f the lattice B oltzm ann m ethod. T h is com putational m ethod coup led w ith w orking fluid p roperties a llow ed a m odel to be constructed w hich accounted for body fo rce term s and phase change at the transition regions. E xperim ental resu lts w ere used to im plem ent the boundary conditions for tem peratu re w hile experim ental analysis y ielded fluid flow conditions w hich could be sim plified fo r the program , such as b i-d irectionality and critical diam eter. T he sim plification o f the physical system m odel allow ed for the focus to p laced on incorporating the density and tem peratu re d istribution functions and the final pressure array, given by the P eng-R obinson equation o f state.
Including the tem peratu re boundary conditions produced progression o f the equilibrium in terface dow nw ard in the channel and ind icated that the equilibrium conditions increased to b roaden the in terface in the channel. S tratification w ithin the program appeared correct, w here the vapor-liquid m ixture regions surrounding the in terface also began to broaden until steady- state. T he vaporizing m ixture at the heat source interface expanded p rio r to reaching steady-state; how ever, the difference in tem perature betw een the tw o copper p la tes w as not large enough to m aintain an analogous in terface on the condensing plate. W hile there w as still p ressure d rop at the top plate interface, it d id not have the sam e w idth and large difference as the bottom plate.
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N W H M W rW V
Q m m I M H H........
(a) Simulation at time t = 1
(c) Simulation at time t = 180
w tN w iyw
ttwel ls<MU|
(b) Simulation at time t = 90
(d) Simulation at time t = 270
(e) Simulation at time t = 360
Figure 3. Progression of channel simulation phase change interface versus time
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Future w ork w ill investigate com bining experim ental data w ith the program m odel. A s the m odel develops m ore accuracy, a better p rogression o f the phase change regions will becom e m ore apparent. T here should also be larger data sets for w hich to corre la te the density /tem peratu re array w ith the p ressure array in o rder to gain grea ter insight into the transitions regions. R unning the program on a com puter system w ith larger m em ory w ould also allow for the en tire channel to be sim ulated , g iving a larger picture o f the channel fluid interaction. F urther p rogress on th is m odel prom otes design a lterations w hich w ill take advantage o f know ing how the phase change transition regions change over tim e. W ith th is know ledge, better experim ental testing can occur in o rder to develop m ore efficient, h igher perform ing devices.
[10] B orquist, E „ Baniya, A ., T hapa, S., W ood, D., and W eiss, L ., N ovem ber 2014. "A copper m icrochannel heat exchanger for m em s-based w aste heat therm al scavenging” . Proceedings o f the ASME 2014 International Mechanical Engineering Congress and Exposition(lMECE20\4- 38801), pp. 1-7.
[11] 3M , 2009. 3m rM novec™ 7200 engineered fluid. O riginal docum ent from 3M rw E lectronics M arkets M aterials Division.
[12] C heng, P., and W u, H., 2006. “M esoscale and m icroscale phase-change heat transfer” . Advances in heat transfer, 39, pp. 4 6 1 -5 6 3 .
ACKNOWLEDGEMENTST he authors gratefu lly acknow ledge the support o f th is work
by N ASA and the N S F via G rant No. E C C S -1053729 as well as the U niversity o f M innesota for their H ydra softw are.
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