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Generative Design Optimization of Thermal Management Systems for High Output Power Electronics
by
Andrew Michalak
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by Andrew Michalak 2019
ii
Generative Design Optimization of Thermal Management
Systems for High Output Power Electronics
Andrew Michalak
Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
2019
Abstract
Power electronic converters are becoming a critical part of the continuing electrification of
transportation technology. With the increasing popularity of electric vehicles, high demands are
being placed on the performance and reliability of these on-board modules. To meet these
challenges, novel architectures and advanced design techniques are being utilized to address the
growing issue of proper thermal management for compact power electronic devices. This thesis
proposes a novel design methodology that utilizes genetic algorithms to optimize the liquid
topologies of compact heat sinks for power electronic systems. By incorporating precise
electrical design data into detailed thermal models, the optimization process accurately captures
the heat spreading within these complex systems. The intelligence nature of this iterative
program identifies ideal design characteristics to improve heat sink performance and generate
optimized cooling structures, specifically tailored to target converter systems.
iii
Acknowledgments
The work outlined in this thesis would not have been possible without the support of several
crucial individuals that have played significant roles throughout this process.
First, I would like to express my sincere gratitude to my supervisors, Dr. James K. Mills and Dr.
Olivier Trescases. Their assistance and continual guidance through this process has helped me
overcome the difficult obstacles this project so graciously put in my way, time and time again. I
came to the University of Toronto hoping to learn more about the intricacies of electric vehicles,
their underlying technology and the design process behind it all. If nothing else, I know I have
been successful in this regard, thanks to the shared knowledge and experience of both these
professors.
Thanks to Dr. Wai Tung Ng and Dr. Kamran Behdinan for serving on my defense committee, I
appreciated hearing your thoughts, comments and advice on the presented work. I would also
like to thank to my awesome lab mates, Simarjot Sidhu and Ihab Abu Ajamieh, for always being
available to work through problems with me, brainstorm ideas or simply grab the occasion free
coffee. My good friends Omri Tayyara and Marinus Lurz were also an essential part of my
academic experience, always offering welcomed advice or needed distractions.
Special thanks to Dr. Steven Kinio for guiding me through the initial construction of my genetic
program. His advice and mentorship was an invaluable component of this project. I would also
like to acknowledge NSERC for providing the funding to make my project and my degree
possible.
Special thanks to my roommates, Bethany Litner, Jessica Germano and Maxime Larcheveque,
who always kept life light and fun, especially when school was not. Thanks also goes out to both
the rats in our first apartment, Toronto has definitely been a wild ride right from the get-go and I
wouldn’t have changed a thing.
Lastly, I would like to express my deepest gratitude to my parents, Timothy and Loreen, along
with my sister Sharon, for providing me with all the encouragement, patience, love and support I
needed as I pursued this degree. The University of Toronto has provided me with one of the most
memorable experiences of my life, my greatest thanks to everyone involved.
iv
Table of Contents
Acknowledgments.......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................ vii
List of Figures .............................................................................................................................. viii
Nomenclature ............................................................................................................................... xiv
Chapter 1 ..........................................................................................................................................1
Introduction .................................................................................................................................1
1.1 Problem Statement ...............................................................................................................1
1.2 Proposed Solution ................................................................................................................3
1.3 Thesis Layout .......................................................................................................................4
Chapter 2 ..........................................................................................................................................6
Background .................................................................................................................................6
2.1 Basic Technologies and Practices ........................................................................................7
2.2 Air Cooling ..........................................................................................................................9
2.2.1 Natural Convection ..................................................................................................9
2.2.2 Forced Convection .................................................................................................11
2.3 Indirect Liquid Cooling......................................................................................................13
2.3.1 Liquid Cold Plates..................................................................................................13
2.4 Direct Liquid Cooling ........................................................................................................15
2.4.1 Packaging ...............................................................................................................16
2.4.2 Micro Channel Heat Sinks .....................................................................................20
2.4.3 Jet Impingement Heat Sinks ..................................................................................24
2.4.4 Integrated Coolers ..................................................................................................28
v
2.4.5 Double-Sided and Stacked Modularized Cooling ..................................................30
2.5 Design Optimization ..........................................................................................................32
2.5.1 Practical Techniques ..............................................................................................33
2.5.2 Topology Optimization ..........................................................................................34
2.5.3 Genetic Algorithms ................................................................................................36
Chapter 3 ........................................................................................................................................40
Methodology and Construction of Optimization Program for Liquid Heat Sink Topologies ..40
3.1 Stage I: Genetic Optimization Logic .................................................................................41
3.1.1 Constructing Model and Defining Workspace ......................................................43
3.1.2 Grid Indexing .........................................................................................................44
3.1.3 Mutate Seed Design ...............................................................................................46
3.1.4 Validation ...............................................................................................................48
3.1.5 Evaluation ..............................................................................................................49
3.1.6 Selection, Crossover and Mutation ........................................................................52
3.1.7 Convergence and End Process ...............................................................................53
3.1.8 Preliminary Results ................................................................................................54
3.2 Stage II: Integrating Three-Dimensional Liquid Heat Sink Topologies ............................59
3.2.1 ANSYS Icepak .......................................................................................................59
3.2.2 Changes to Modeling Procedure and Genetic Functions .......................................63
3.3 Overview of Genetic Optimization Process for Three-Dimensional Liquid Heat Sinks ...71
Chapter 4 ........................................................................................................................................73
Simulation Results & Discussion ..............................................................................................73
4.1 Introducing the Test Model ................................................................................................73
4.2 Case Study .........................................................................................................................77
4.2.1 Preparing the Seed Model ......................................................................................78
4.2.2 Defining the Simulation Environment ...................................................................81
vi
4.2.3 Initializing Genetic Logic ......................................................................................83
4.2.4 Design Optimization ..............................................................................................84
4.3 Optimization Testing .........................................................................................................89
4.3.1 Weighting Fitness Function ...................................................................................90
4.3.2 Inlet Temperature Variation ...................................................................................93
4.3.3 Flow Rate Variation ...............................................................................................96
Chapter 5 ........................................................................................................................................99
Conclusion ................................................................................................................................99
5.1 Contributions......................................................................................................................99
5.2 Prototyping Tool ..............................................................................................................100
5.3 Closing Remarks and Future Works ................................................................................103
Bibliography ................................................................................................................................105
Appendix: Details of Heat Sink Design Optimization .................................................................116
vii
List of Tables
Table 1: Heat Dissipations of Various Cooling Methods for T of 353.15K. - [19] ....................... 6
Table 2: Manufactured Power Module Packing Technologies. - [53] .......................................... 19
Table 3: GaN Transistors Manufacturer Provided Thermal Characteristics. ............................... 76
Table 4: Icepak Material Assignments. ........................................................................................ 82
Table 5: Genetic Variables for Case Study Trial. ......................................................................... 84
viii
List of Figures
Figure 1: Classification of Power Semiconductor Modules. - [15] ................................................ 3
Figure 2: Thermal Stack up for Conventional IPM. - [21] ............................................................ 7
Figure 3: Thermal Resistances of Common Heat Sink Materials. - [26] ........................................ 8
Figure 4: CFD Analysis of Passive Heat Sink Designs. - [29] ..................................................... 10
Figure 5: Study on Pin Design for Heat Sink Performance. a) Conventional Pin Fin Array.
b) Array with Expanded Pin Fin Diameter. .................................................................................. 11
Figure 6: Structural Examples of Commonly Manufactured Cold Plates. a) Deep Drilled Capped
Cold Plate. b) Pocketed Folded-Fin Cold Plate. - [46] ................................................................. 13
Figure 7: Common Embedded Tube Heat Exchanger. – [53] ...................................................... 14
Figure 8: Comparison of Conventional and Advanced Heat Sink Designs. a) Indirect Cold Plate
Arrangement. b) Direct Cooling Arrangement. - [26] .................................................................. 16
Figure 9: Comparison of Material Stacks for Varying Heat Sink Design Principles. a) Indirect
Cooling Structure and Associated Materials. b) Direct Cooling Structure and Associated
Materials. - [58] ............................................................................................................................ 17
Figure 10: Coefficient of Thermal Expansion Values for Common IPM Materials. - [63] ......... 18
Figure 11: Micro Pin Fin Heat Sink Arrangement. - [70]............................................................. 21
Figure 12: Straight Channel, Staggered Pin and MDT In-Line Pin Heat Sink Formations. - [76]22
Figure 13: Demonstration of Fin Deformation Heat Sinks a) Micro Deformation Tools and
Process. b) Micro Deformed Heat Exchanger Array. - [76] ......................................................... 23
Figure 14: Common Jet Impingement Arrangements. a) Free Surface Jet. b) Submerged Jet.
c) Confined Submerged Jet. - [42] ................................................................................................ 24
Figure 15: Impingement Based Heat Exchanger Designs. - [86] ................................................ 27
ix
Figure 16: Formation of Flow Vortices by Variations in Impingement Angles. a) Perpendicular
90° Impingement angle. b) 70° Impingement Angle. c) 45° Impingement Angle. - [86] ............ 27
Figure 17: Danfoss Shower Power Cooling Design. - [97] .......................................................... 28
Figure 18: Direct Integrated Heat Sink Arrangement. - [26] ....................................................... 29
Figure 19: Construction of MMC Heat Sink Prototype. - [102] ................................................... 30
Figure 20: Double Sided Heat Sink Approach. a) Conventional Liquid Cooling Arrangement.
b) Double Sided Cooling Arrangement. - [104] ........................................................................... 30
Figure 21: Demonstration of Double-Sided-Stacked Cooling Structure. - [106] ......................... 32
Figure 22: Heat Sink with Increased Fin Density Topology. - [121] ........................................... 35
Figure 23:Optimized Heat Sink Designs with Constant Gr Value and Mesh Size of 329 x 640 x
320 Elements. - [122] .................................................................................................................... 35
Figure 24: Basic Genetic Optimization Workflow. - [125] .......................................................... 36
Figure 25: First Stage Conventional Genetic Optimization. ......................................................... 37
Figure 26: Second Stage Perturbation Genetic Optimization. - [125] .......................................... 38
Figure 27: Two Stage Genetically Optimized Air-Cooled Heat Sink. - [132] ............................. 38
Figure 28: Content Breakdown for Chapter 3. .............................................................................. 41
Figure 29: Structure of Genetic Optimization Process. ................................................................ 42
Figure 30: Visualization of Structural Bit Array. ......................................................................... 43
Figure 31: Defining the Design Optimization Workspace. .......................................................... 44
Figure 32: Created Global Array. ................................................................................................. 45
Figure 33: Assigning Element Labels to Partitioned Workspace. ................................................ 45
x
Figure 34: Linking Element Labels to Global Array. ................................................................... 46
Figure 35: Seed Mutation.............................................................................................................. 47
Figure 36: Utilizing Solution Vector and Global Array to Form Structural Bit Matrix for New
Individual. ..................................................................................................................................... 47
Figure 37: Validating New Design Candidate with Blob Analysis and Image Morphology. ...... 48
Figure 38: 2D Example Population of Initial Design Candidates. ................................................ 49
Figure 39: File Structure of Evaluation Stage............................................................................... 50
Figure 40: Evaluation Stages. a) Candidate Solution Vector. b) Representative Bit Array.
c) ANSYS CFD Model. ................................................................................................................ 50
Figure 41: Evaluation Process. a) Generated Bit Arrays. b) Converted to ANSYS CAD
Structures and Simulated in FLUENT. c) Ranked and Assigned Breeding Probability. ............. 51
Figure 42: Generating Child Design. ............................................................................................ 52
Figure 43: Convergence Window with Objective Tracking. ........................................................ 53
Figure 44: Genetic Optimization Process on a 2mm Grid Mini-Channel Design. a) Convergence
Plot. b) Intermediate Designs. c) Final Thermal-Flow Contours. ................................................. 55
Figure 45:Genetic Optimization Process on 1mm Grid Central Channel Design. a) Convergence
Plot. b) Intermediate Designs. c) Final Thermal-Flow Contours. ................................................. 57
Figure 46: Additive Topologically Optimized Heat Sink. a) Smoothed 3D View. b) 2D Profile. -
[140] .............................................................................................................................................. 58
Figure 47: Typical Icepak Workflow. ........................................................................................... 60
Figure 48: Example Icepak Project on Half-Bridge DBC Converter Module. ............................. 61
Figure 49: Icepak Semiconductor Package Design. ..................................................................... 62
xi
Figure 50: Icepak ECAD Import Structure. .................................................................................. 62
Figure 51: Workflow of Model Construction. .............................................................................. 63
Figure 52: Partitioning of Optimization Workspace with Three-Dimensional Voxels. ............... 64
Figure 53: Indexing Workspace Elements. ................................................................................... 64
Figure 54: Formation of Heat Sink Topology. a) Allocation of Structural Elements via Design
Modeler Boolean Functions. b) Forming Fluid Domain. c) Forming Solid Domain. d) Initial Seed
Model. ........................................................................................................................................... 65
Figure 55: Setting Simulation Conditions in Icepak GUI ............................................................. 65
Figure 56: Defining Output Parameters. a) Icepak GUI. b) Variables Exported from Workbench
Project as CSV File. ...................................................................................................................... 66
Figure 57: Formation of Three-Dimensional Global Array. ......................................................... 67
Figure 58: Mutating the Three-Dimensional Workspace to Achieve New Fluid Domain. .......... 67
Figure 59: Operations for Generating New ANSYS Models. a) Starting with Previous Design. b)
Clearing Liquid and Solid Boolean Functions. c) Selecting New Fluid Elements. d) Reapplies
Boolean Functions to Generate New Design Topology. .............................................................. 69
Figure 60: Stage II Convergence Window with Objective Tracking. .......................................... 71
Figure 61: Design Progression of Genetic Optimization Process. ................................................ 72
Figure 62: Base Model for Simulation Testing............................................................................. 74
Figure 63: Electrical DBC Design. ............................................................................................... 74
Figure 64: Compact HB Heat Sink Design. a) Integrated Cooler Approach. b) Inlet/Outlet
Manifold Design. .......................................................................................................................... 75
Figure 65: GaN Power Transistors. a) GaN Systems GS66508B Schematic. b) Corresponding
CAD Model. .................................................................................................................................. 76
xii
Figure 66: Footprint of Heat Sources on PCB. ............................................................................. 77
Figure 67: Electrical Simplification of HB Converter System. .................................................... 78
Figure 68: Simplification of Fluid Domain. a) Elimination of Manifold Sections. b) Comparison
of Old vs New Inlet/Outlet Connections. ...................................................................................... 79
Figure 69: Generating Optimization Workspace for HB Convert Model. a) Defining Active and
Passive Regions. b) Sizing Structural Voxel Elements. c) Partitioning Active Region into Array
of Workspace Elements. ............................................................................................................... 80
Figure 70: Forming Base Optimization Model into Starting Seed Design. .................................. 80
Figure 71: Icepak Modeling Environment & Example Surface Mesh. ........................................ 81
Figure 72: Objective Tracking Window for HB Converter Case Study. ...................................... 85
Figure 73: Design Progression of Case Study Optimization Process. .......................................... 87
Figure 74: Comparing PCB Temperatures Contours. a) Starting Seed Design. b) Final Optimized
Design. .......................................................................................................................................... 88
Figure 75: Comparing Fluid Domain Pressure Contours. a) Starting Seed Design. b) Final
Optimized Design. ........................................................................................................................ 88
Figure 76: Comparing Cross-Sectional Temperature Contours of Heat Sink Cooling Structure.
a) Starting Seed Design. b) Final Optimized Design. ................................................................... 89
Figure 77: Convergence and Optimized Fluid Topologies for Fitness Testing. a) Temperature
Dependent Fitness Scoring (a=1, b=0). b) Temperature Biased Fitness Scoring (a=0.7, b=0.3). 91
Figure 78: Performance Comparisons of Fitness Testing Models. ............................................... 92
Figure 79: Convergence and Optimized Fluid Topologies for Inlet Temperature Testing. a) 0°C
Inlet Fluid. b) 15°C Inlet Fluid. c) 50°C Inlet Fluid. .................................................................... 94
Figure 80: Performance Comparisons of Inlet Temperature Testing Models. ............................. 95
xiii
Figure 81: Convergence and Optimized Fluid Topologies for Flowrate Testing a) Inlet Flow 0.25
LPM. b) Inlet Flow 0.5 LPM. c) Inlet Flow 1.0 LPM. ................................................................. 97
Figure 82: Performance Comparisons for Flowrate Testing Models............................................ 98
Figure 83: Workflow of Genetic Optimization is Prototyping Process. a) Starting Design
Temperature Profile. b) Optimized Design Temperature Profile. c) Thermal Deformation of
Optimized Design. ...................................................................................................................... 102
xiv
Nomenclature
Acronyms
SiC Silicon Carbide
GaN Gallium Nitride
Si Silicon
DGT Dispersed Generation Technology
PV Photovoltaic
IPM Integrated Power Modules
EV Electric Vehicle
HEV Hybrid Electric Vehicle
CFD Computational Fluid Dynamics
FEA Finite Element Analysis
IGBT Insulated Gate Bipolar Transistor
MOSFET Metal-Oxide-Semiconductor Field-Effect Transistor
GTO Gate Turn-Off Thyristor
SCR Silicon Controlled Rectifier
HDD Heat Dissipating Device
PCB Printed Circuit Board
DBC Direct Bonded Copper
xv
DBA Direct Bonded Aluminum
AlN Aluminum Nitride Ceramic
Al2O3 Alumina Ceramic
Al Aluminum Alloy
Cu Copper Alloy
TIM Thermal Interface Material
CTE Coefficient of Thermal Expansion
MMC Metal Matrix Composite Materials
MDT Micro Deformation Technology
GA Genetic Algorithm
DM Design Modeler
HB Half-Bridge
Heat Transfer Variables
QFluid, Coolant Flow Rate
TFluid,In Coolant Inlet Temperature
RTH Thermal Resistance of Heat Sink
TD Device Temperature
ΔPInlet-Outlet Pressure Drop
TD,Base Device Temperature of Base Seed Design
xvi
ΔPBase Pressure Drop of Base Seed Design
a Temperature Weighting in Fitness Function
b Pressure Weighting in Fitness Function
ρ Material Density
kth Thermal Conductivity
cp Specific Heat Capacity
Genetic Optimization Variables
MB Design Candidate Bit Matrix
MP Partitioned Optimization Workspace Matrix
ΔxPixel x Dimension of 2D Structural Pixel Element
ΔyPixel y Dimension of 2D Structural Pixel Element
XWS x Dimension of Optimization Workspace
YWS y Dimension of Optimization Workspace
ZWS z Dimension of Optimization Workspace
MG Global Array of Indexed Workspace Values
xS Workspace Size Vector
xFE Design Candidate Solution Vector Identifying Fluid Elements
Δxvoxel x Dimension of 3D Structural Voxel Element
Δyvoxel y Dimension of 3D Structural Voxel Element
xvii
Δzvoxel z Dimension of 3D Structural Voxel Element
Nx,voxels Number of Voxel Elements in x Direction of Workspace
Ny,voxels Number of Voxel Elements in y Direction of Workspace
Nz,voxels Number of Voxel Elements in z Direction of Workspace
1
Chapter 1
Introduction
1.1 Problem Statement
With the increasing emphasis towards an electrified world, energy is quickly becoming a critical
requirement for almost all human ventures. One of the most vital aspects of this growing field is
the control and conversion of the energy itself, which is achieved through the utilization of
specialized electronic circuits and systems known as Power Electronics [1]. These units are
essential in almost all power conversation applications, controlling the flow of electrical energy
at much higher levels than conventional devices could handle. It is anticipated that all electrical
power will flow through a power semi-conductor in the very near future [2]. The more recent
developments in semiconductor materials, such as Silicon Carbide (SiC) and Gallium Nitride
(GaN) devices allows for higher breakdown voltages and forward current densities leading to
greater efficiency and better thermal stability as compared to conventional silicon (Si) devices
[3], [4].
Much of the rise in demand is attributed to the increasing popularity of dispersion energy
systems or Dispersed Generations Technology (DGT) [5]. These systems, both renewable and
non-renewable, include energy sources such as photovoltaic (PV) generators, micro-hydro
systems, wind turbines and fuel cells, which can operate at highly fluctuating levels of
intermediacy. Power electronics are the ideal interface technology to match the output
characteristics of these systems to the conventional grid connection requirements.
Due to the versatile nature in which they can operate, power electronics are also becoming a
fundamental component of industrial, commercial, residential, aerospace and military sectors.
Moreover, the energy range at which they can function make them ideal for use in mobile
transportation systems [6]. Specifically, in terms of the automotive industry, electronic Integrated
Power Modules (IPM) have an important role in the rising popularity of Hybrid Electric and
Electric Vehicles (HEV/EV). Their reduced size and cost along with high efficiency, reliability
and power capacity have made them an integral part of advanced modularized inverter systems
2
[7]. In modern day designs, these can be found in electric drivetrains, battery charging units and
a variety of vehicular power accessories [8]–[11].
As mobile applications put higher objectives on power density a growing area of concern has
become proper thermal management of these semiconductor devices. While controlling the
energy transfer of electronic systems, power electronic devices experience losses in electrical
efficiency, leading to the generation of waste heat [12]. It is this waste heat that can lead to major
issues such as material degradation, internal thermal stresses, decreased efficiency and overall
system degradation [13]. The task of thermal-mechanical designers to achieve significant levels
of heat removal through the study and utilization of fluid cooled electronic heat sink structures.
One of the most important metrics in this area of thermal design is the semiconductor junction
temperatures1. To operate at peak performance, these semiconductor junctions must be
maintained at acceptable temperatures, depending on their material composition [14]. Different
applications can call for various levels, ranges and durations of power, depending on the function
[15]. Heat load can be categorized by the nature of the corresponding electrical design or the
structure of the associated power semiconductor devices, as shown in Figure 1. The problem then
falls on thermal designers to identify the required level of heat removal based on the expect
device efficiency and chose a suitable cooling method. With the move to electric mobility
applications, shape, weight and volume can become major cost variables while heightened
constraints on things like ambient conditions, fluid structures and performance reliability can
greatly limit design flexibility [16].
1 Junction Temperature: The highest operating temperature of a semiconductor within an electronic device or
package
3
Figure 1: Classification of Power Semiconductor Modules. - [15]
By utilizing the fundamentals of heat transfer, the increasing power of Computational Fluid
Dynamics (CFD), Finite Element Analysis (FEA) and innovative methods of design and
optimization, thermal engineers can achieve advanced cooling structures to handle this rising
issue of waste heat removal. Developing novel solutions for these high energy applications is the
key to unlocking higher levels of power density and assisting in the continued electronification
of all the technology surrounding transportation and mobility.
1.2 Proposed Solution
The cases of electric cars present a unique and challenging environment for design optimization.
Being a mobile platform, it is always advantageous to reduce the size and weight of any internal
technology. Traditionally, electronic heat sinks and liquid cooling systems are comprised of
heavy metal components, requiring a significant amount of valuable volumetric space. Thus, this
thesis will seek to investigate the development of an optimization process to achieve compact
heat sink topologies for EV specific power electronics.
A custom designed program constructed in MATLAB 2018a utilizes the proven power of binary
genetic optimization and treats the layout of liquid cooling channels with heat exchangers as a
topological optimization problem to produce optimal cooling designs, unique to any electrical
4
layout [17]. Using a specialized toolbox and Python scripting, this program is able to iteratively
communicate with the ANSYS 19.2 Workbench to model and simulate potential designs
generated by the genetic optimization algorithm coding. By pairing the principles of unique
optimization process with the modelling capabilities of ANSYS Icepak, CFD simulations can
accurately capture the influence of all components and materials within the electronic designs to
feed back into the genetic optimization learning process loop. This genetic optimization
approach, coupled with ANSYS and Icepack, results in three-dimensional heat exchanger
designs with optimized geometry to remove the maximum amount of heat generated form
integrated circuit power transistors.
Initial results show a robust functionality of the custom optimization program and a significant
ability to achieve novel designs and distinct improvements. A series of trials are run to determine
how the established program adapts to changes in the environmental conditions applied to the
simulation space. This, for example, includes optimization at various heat exchanger inlet
temperatures, and coolant fluid pressure. Key genetic variables are also investigated in an
attempt to identify key operating points in the code structure.
Lastly, the resulting geometries produced by the code are analyzed with the goal of
manufacturability. Several options are presented of how to tie the optimization capabilities of the
program to some advanced manufacturing techniques in order to produce these unique models
for real world applications. Specific variables and functions within the coding structure are
identified as key areas to improve the efficiency, functionality and effectiveness moving forward.
The programs flexibility for optimizing any style of heat sink as well as applications to any other
topology problems, capable of being simulated in ANSYS, is discussed as a final note on the
usefulness and future potential.
1.3 Thesis Layout
This thesis is organized as follows: Chapter 2 reviews the wide spectrum of existing methods for
electronic cooling as well as techniques for heat sink design. Various examples of conventional
thermal management systems are presented along with more innovative approaches to high
density cooling, all with the focus of power electronic applications for EV/HEVs. Chapter 3
details the construction of the proposed design optimization program for liquid heat sinks. A
genetic optimization base logic is developed in MATLAB and linked to ANSYS Workbench
5
using an AAS toolbox in order to simulate and evaluate various topologies for these liquid heat
sink geometries. Chapter 4 demonstrates the operation of the Generative Design Process applied
to a compact, power dense converter module. The optimization process is run on this model at
varying operating parameters in an attempt to characterize the programs behavior and investigate
how changes in system parameters influence the optimal geometries generated. Chapter 5
discusses the conclusions drawn from the tested results, the contributions of the work presented
in this thesis and considers a variety of future opportunities to further improve the efficiency and
effectiveness of this process for generative topology optimization.
6
Chapter 2
Background
In this section, the basics of power semiconductor thermal management is reviewed. This chapter
provides a review the methodologies for the thermal management of power electronics specific
to hybrid and electric vehicles. Basic design approaches are presented as well as a review of the
more recent advancements being made to address the growing issue of electronic cooling and
waste heat dissipation. Power semiconductor devices can be classified by their application and
the corresponding current and voltage levels [18]. Some current industry examples of common
power electronic devices include: Insulated Gate Bipolar Transistors (IGBT), Metal-Oxide-
Semiconductor Field-Effect Transistors (MOSFET), Gate Turn-Off Thyristors (GTO) and
Silicon Controlled Rectifiers (SCR). A variety of cooling options are available depending on the
extend of the waste heat generated by these power electronic devices. These different approaches
to electronic thermal management have be categorized by Scott [19] in Table 1 by the
corresponding level of heat removal that can be achieved.
Table 1: Heat Dissipations of Various Cooling Methods for T of 353.15K. - [19]
Although there exists a large variety of cooling options for high power electronics, several major
constraints must be considered when identifying suitable options for a given system design.
Particularly, in the case of on-board mobility applications, spatial restrictions and weight
requirements may lead to significant constraints on thermal designs. EV’s can also be a
challenging environment for electronics devices. Standards on ambient conditions, coolant
temperatures and performance reliability create a harsh environment for thermal designers to
work within [20].
7
2.1 Basic Technologies and Practices
As a result of the growing performance requirements, most IPM’s are designed with integrated
cooling systems to extract the waste heat and maintain suitable overall temperature levels. A
convectional IPM stack is presented in Figure 2. The main heat dissipating device (HDD) usually
takes the form a silicon chip or package. However, as mentioned earlier, advances in device
packaging and the utilization of bare die SiC or GaN components help reduce thermal resistances
in close proximity to the junction heat source [3], [4]. These devices are usually solder bonded to
a printed circuit board (PCB), which provides electrical isolation as well as housing any other
passive/active components required by the power system layout [21]. More recent designs seek
to replace conventional PCBs with Direct Bonded Copper (DBC) or Direct Bonded Aluminum
(DBA) modules. The ceramic materials within DBC stacks, such as Aluminum Nitride (AlN) or
Alumina (AL2O3) allow for much higher levels of heat transfer through the isolation material
when compared with the FR-4 epoxy commonly used for PCB isolation [22].
Figure 2: Thermal Stack up for Conventional IPM. - [21]
While the electrical aspect of IPM designs seek to reduce thermal resistances cause by material
layers, the mechanical components attempt to utilize heat spreading and convective heat transfer
to dissipate the waste energy away from the HDD [23]. The system represented in Figure 2
depicts a conventional finned heat sink design, usually machined from a highly conductive metal
alloy such as Aluminum (Al) or Copper (Cu). These heat sinks are in turn mounted to the
corresponding electrical design via a Thermal Interface Material (TIM) which usually takes the
form of thermal grease or solder [21].
The final component required by any thermal management system is a working fluid or coolant.
The role of this moving fluid is to act as the mechanism for convective heat transfer from the
8
heat sink, carrying the excess heat away from the IPM stack, and rejecting it from the system
altogether [24]. With regards to HEV/EV systems, there are historically two main fluids
available for electronic cooling, which are air and automotive antifreeze (water/ethylene glycol
mix) [25]. Each carries its own set of benefits and draw backs, which will be discussed in the
coming sections. The inclusion of a coolant system introduces several variables, such as: flow
rate (QFluid), fluid temperature (TFluid,In), required plumbing, ducting and reservoir storage, which
can all have major influence on the performance and architecture of the overall thermal system
design [24].
The data presented in Figure 3 compares the associated Thermal Resistance (RTH) values
expected from conventional IPM materials as well as the convective resistance between the heat
sink and working fluid [26]. Such information is important for thermal designers looking to
improve on the current approaches to electronic cooling.
Figure 3: Thermal Resistances of Common Heat Sink Materials. - [26]
In order to achieve innovative designs and novel solutions, all materials and layers within the
IPM stack must be considered individual design components and analyzed accordingly. By
integrating these different components into the design process, advanced thermal management
systems can meet the rising needs of high-level power electronics.
9
2.2 Air Cooling
One of the most well established and widely utilized methods of electronic cooling is that of
convective heat transfer with air as the working fluid. Air is still the most flexible and least
expensive options in terms of a heat transfer medium. In addition, air cooled systems require
very little complexity, resulting in significantly lower material and equipment costs when
compared with other methods [27]. Regarding thermal management in automotive settings, high
velocity air can be readily available, further reducing the system requirements and parasitic
loads. It is also important to note that for moving vehicles all heat, either directly or indirectly,
must be rejected to the surrounding ambient air. Thus the use of air cooling can greatly reduce
the overall size and of a coolant loop [21].
2.2.1 Natural Convection
Many designers in the past have utilized the heat transfer phenomenon known as Natural
Convection to achieve very simplistic, robust designs for handling low power electronic systems.
Bouknadel et al. carried out extensive CFD analyses on several heat sink configurations,
investigating various fin arrangements as well as conductive metals. Results indicated that heat
sinks composed of Graphite-metal provided lower thermal resistances when compared to
conventional Aluminum and Copper designs. Elliptical style fins were also found to achieve
higher levels of heat dissipation, as shown in Figure 4, outperforming parallel plate fins as well
as staggered circular and square fin arrangements [28].
10
Figure 4: CFD Analysis of Passive Heat Sink Designs. - [29]
A similar study carried out by Arefin found that expanding the outer diameter of conventional
pin fin arrays had the potential to increase the heat transfer capabilities of passive aluminum heat
sinks. A 1° expansion of the pin diameter along the length of the fins [Figure 5] was found to
results in a 5°C temperature drop for a 50-Watt heat load [30].
11
Figure 5: Study on Pin Design for Heat Sink Performance. a) Conventional Pin Fin Array.
b) Array with Expanded Pin Fin Diameter.
Christen et al. sought to compare the efficiency of forced convection to natural convection for air
cooled heat sinks. Considering the power consumption required by active cooling fans and
blowers, it was found that thermal losses and volumetric requirements can be reduced by parallel
mounting the associated semiconductor devices as well as increasing the number of switching
devices within the system. These methods were found to make passive cooling a more feasible
option for specific systems, reducing the complexity of the associated thermal system while
increasing the power density [31]. With a focus on the formation of laminar versus turbulent air
plumes, Kitamura et al. characterized the geometric variables of a vertical cylinder array in
relation to heat transfer and natural convection [32].
2.2.2 Forced Convection
In general, air offers low thermal conductivity and density, which can result in low rates of
convective heat transfer across heat exchangers. Thus, much of the work in this area has focused
on maximizing the available heat transfer area for the fluid and improving the exchange of
energy. This is why, following the work of Tuckerman and Pease on the enhancement of liquid
cooling via micro-channels, many sought to apply these same principles to active air cooling
12
concepts [33]. As was the basis for the design work by Hilbert et al. which investigated the use
of laminar air flow through micro channels to offer low thermal resistivity level at <1.7K/W with
very low internal pressure drops [34]. Following this Knight, Goodling and Gross found that
higher rates of heat transfer could be experimentally achieved if channel heat exchangers were
optimized to induce turbulent flow [35]. A later investigation carried out by Azar, McLeod and
Caron defined a new style of Narrow channel heat exchangers capable of cooling high powered
components at dissipation levels of 20W/cm2 [36].
Gromoll was able to alter heat exchanger stacking techniques and integrate micro-heat-pipes,
direct air cooling and thermosyphons to his air cooled heat exchangers and reach dissipation
levels otherwise only possible via liquid cooling [37]. Through the use of tubes for directing air
flow, Kleiner et al. was able to theoretical and experimentally attain much higher levels of
cooling than open air systems [27]. Many also found the use of staggered pin arrays could
increase turbulent flow and thus the power density levels heat exchangers could handle. As was
the case with the work of Marques and Kelly who investigated the use of micromachining to
achieve compact, high performing air cooled models [38].
One of the more recent areas of this field that has seen significant improvements has been the use
of jets for the distribution of air across electronic units. Due to its low viscosity, air can be
delivered at high velocities through very small diameter jet arrays at reasonable pressure levels,
dissipating waste heat fluxes to upwards of 4kW/m2 [39]–[41].
Most designs involving air flow will incorporate large bulky heat sinks composed of thermally
conductive metals, making them a large, heavy accessory for vehicular applications where space
and weight are key issues. Moreover, it is becoming a growing consensus that air cooling
techniques are approaching their peak dissipation levels of ~800 W/cm2 via direct jet arrays [42].
The low conductivity and high convective resistances offered by the fluid will keep it from
achieving higher levels of performance. Thus, as power densities and size reductions become key
design factors, the industry moves away from air cooling methods and towards higher
performing methods of convective heat transfer [43].
13
2.3 Indirect Liquid Cooling
2.3.1 Liquid Cold Plates
As power levels rise to meet the needs of more commercial and industrial scale energy
applications, so too does the associated heat losses. Hence more stable and reliable cooling
schemes are required. Liquid cold plate technology is seen as a viable solution for greater heat
removal capability. Cold plates commonly utilizes fluids with high heat capacity pumped
through machined passages in metal bodies compose of thermally conductive metals [44]. The
ideal heat transfer fluid is usually plain water as it offers good thermal conductivity, high density
at a relatively low viscosity, indicating reasonable internal pressures. However this is commonly
supplemented with an ethylene glycol solution to raise the boiling point and lower the freezing
point of the working fluid [45], [46].
Figure 6: Structural Examples of Commonly Manufactured Cold Plates. a) Deep Drilled Capped
Cold Plate. b) Pocketed Folded-Fin Cold Plate. - [46]
Cold plates can come in many different forms, usually dependent on the manufacturing
capabilities of the designer and the heat flux requirements of the specific system. Models such as
Deep Drilled Cold Plates, as shown in Figure 6a, are simple to manufacture and offer an
inexpensive, reliable solution to relatively high heat flux applications. While more complex
designs, such as the Pocketed Fin Cold Plate shown in Figure 6b, require a more intricate
manufacturing process, but thus yield much high rates of heat dissipation [46]. Due to their
widespread use, the performance and optimization of cold plate model is important practice
across various industries. Much of the work with cold plate models has been focused around
improving the design characteristics through a variety of optimization methods. One of the most
commonly used forms for the optimization of heat exchangers is Topology Optimization. Much
work has gone into analyzing the physical parameters of these thermal systems and using
14
established equations for flow and heat transfer to achieve high performing designs [47]–[49].
An investigation by Sparrow et al. analyzed the effect of baffles on flow characteristics and heat
transfer via numerical CFD methodology [50]. Work Nam et al. achieved an algorithm capable
of designing different serpentine channel geometries for fuel cell technology, although further
optimization was recommended to supplement this process [51]. A process carried out by
Fesanghary, Damangir and Soleimani combined Global Sensitivity Analysis and Harmony
Search Algorithms to optimization the design of shell-tube heat exchangers with respect to
multiple variables simultaneously [52].
The most common and widely used styles of heat exchanger is the Formed Tube Cold Plate. This
design, presented in Figure 7, places embedded copper tubes into the machined body of made
from thermally conductive material, usually aluminum alloy. One of the more attractive features
of this design is that the fluid flow within the tube remains completely isolated from the externals
of the system, requiring no rubber seals or hydraulic interfaces that could possible leak due to
wear [46].
Figure 7: Common Embedded Tube Heat Exchanger. – [53]
Due to the safe, reliable and simple design nature of cold plates they have implemented in a
variety of heat removal systems, including various automotive applications. Thermal
management of battery packages has emerged as an ideal area for implementing cold plate
technology. Through CFD analysis, Ghosh showed without stable heat removal from specific
thermal ‘Hot Spots’ the life of HEV/EV batteries can be severely reduced [54]. Pesaran showed
that although the level of heat flux removal by HEV battery packs at a suitable level for air
cooling, EV and more complex HEVs benefit from the ability of cold plate to both heat and cool
effectively [20]. The work presented by Jarrett and Kim showed how, with design modeling
15
optimization, cold plates were ideal at management the non-uniform nature at which of battery
stacks generate waste heat [55].
Although they provide a very stable cooling solution, cold plates still require the purchase and
machining of metals, adding additional space and weight to the electrotonic units they are
assisting. The thermal resistance of these materials has also raised concerns on the technologies
ability to scale with rising power densities [43], [53], [56]. Therefore, much of the research at the
forefront of the automotive power electronics industry is seeking new ways to effectively
eliminate these materials from the system, reducing size, weight, thermal resistance and bring the
fluid closer to the heat sources. The next section of this thesis will focus on the more innovative
solutions being investigated for high level heat flux applications where conventional cooling
systems fall short.
2.4 Direct Liquid Cooling
Conventional indirect liquid cooled plates, such as the one represented by Figure 8a, are a
practiced technology that has been implemented and optimized over a wide range of
applications. One area of focus working towards increasing performance looks at the sequential
thermal resistance network that exists between the heat source device and the coolant fluid. As
presented by the summarized data in Figure 3, the biggest contributors to thermal impedance are
the base of the heat sink body and the TIM responsible for providing a thermal pathway between
the electrical board and the heat exchanger body [26]. A new style of design, known as Direct
Backside Cooling or Impingement Cooling and seen in Figure 8b, addresses this issue by
eliminating these layers of material and bringing the base plate of the electrical module into
direct contact with the working coolant. Usually some geometry is formed into the base of the
electrical module of IPM to induce turbulence or provide greater interface area for the coolant,
increasing the effect of heat spreading as well as convective transfer [26], [57].
16
Figure 8: Comparison of Conventional and Advanced Heat Sink Designs. a) Indirect Cold Plate
Arrangement. b) Direct Cooling Arrangement. - [26]
Direct backside cooling can offer significate reductions in size and weight while simultaneously
reducing in total thermal resistance of electronic models or IPMs. For HEV/EV technology this
can mean more compact systems, operating at lower junction temperatures allowing for more
efficient energy conversion [58], [59]. Yet several drawbacks can result from this method of
design. Without the use of a separated cold plate, the interface between the fluid and IPM must
be sealed via O-Ring or rubber gasket. If not designed properly this seal could fail under thermal
cycling, causing coolant to leak in close proximity to the electrical components. In the likely case
that the working fluid is not a dielectric any leakage could have severe impacts on the system
integrity and safety [46]. Effects of corrosion and material degradation on the IPM base have to
be addressed depending on the materials selected for manufacturing [60].
Direct liquid cooling is a very versatile technology and can be integrated with various
conventional and advanced heat sink geometries to enhance performance. However, if this
method is to be pursued, they are important systematic considerations that must be made with
regards to materials and processing techniques that will be discussed in this section.
2.4.1 Packaging
With the fundamental principle of Direct Liquid Cooling being to eliminate intermediate layers
of materials and provide more compact stacking structures, the matching of material properties
becomes a critical design issue. Comparing the material structure of direct cooling to that of
indirect cooling, presented in Figure 9, several key differences should be noted. With the
elimination of the base plate and thermal grease, due to its low conductivities, the electronic
module is directly bonded to the heat sink geometry. This is done using convectional solder,
brazing or pressure sintering [61].
17
Figure 9: Comparison of Material Stacks for Varying Heat Sink Design Principles. a) Indirect
Cooling Structure and Associated Materials. b) Direct Cooling Structure and Associated
Materials. - [58]
The only major remaining material components in a direct cooling stack are that of the ceramic
substrate within the DBC/DBA board, used for electrical isolation, and the heat sink body itself.
The selection of these materials greatly impacts the thermal conductivity of the material stack.
However a much more important property to now consider is that of thermal expansion,
specifically the associated Coefficient of Thermal Expansion (CTE) values [62]. If proper
material selection is not carried out, the components will expand at different rates during thermal
cycling. This can cause thermo-mechanical stresses resulting in fatigue, internal cracking and
overall system degradation. The various CTE values for some common IPM materials are
presented in Figure 10.
18
Figure 10: Coefficient of Thermal Expansion Values for Common IPM Materials. - [63]
A report compiled by Aranzabal et al. summarizes various commercial IPM systems being
implemented in current automotive designs and the innovative aspects that correspond to each
[53]. These include such models as: Toyota Prius (2004), Nissan LEAF, Toyota Lexus and more.
A summary of this information is seen in Table 2. The report discusses various packaging
aspects of IPM systems, identifying die attachment techniques and interconnection wiring. Most
importantly, the corresponding IPM ceramic substrate materials were discussed, being one of the
critical design areas that can affect the overall performance and lifespan of the modules.
19
Table 2: Manufactured Power Module Packing Technologies. - [53]
20
The early work of Romero et al. set out to evaluate the use of Metal Matrix Composite Material
(MMC) as a base plate/heat sink material for power electronics applications in leu of
conventional aluminum or copper. They found that after 4000 thermal cycles the MMC heat
sinks models (AlSiC in particular) offered much higher reliability over conventional options.
This was due to the low CTE associated with the material that corresponds well with that of IPM
ceramic’s, inducing less thermos-mechanical stress at the bond interface [64]. More recent
innovations have been made with regards to material analysis, such as that of Ivanova et al.,
achieving a 40% drop in IPM junction temperatures by utilizing a process that integrated micro
heat pipes directly into the DBC layering [65]. Weyant et al. determined that temperature
gradients could be reduced by an additional 50% by combining embedded heat pipe technology
with MMC heat sink designs [66]. A recent evaluation of industry trends, carried out by
Stockmeier, identified several areas at the forefront of IPM material stacking procedures. The
replacement of solder contacts by high pressure sintering, bond wires with weld contacts and the
elimination of base plate materials are all major areas of improvement [67]. Uhlemann and
Herbrandt investigated the use of aluminum clad materials for heat sink designs with the notion
that the raw material costs of MMC are too high for mass production applications. Al-Cu clad
materials offer the same matching of CTE values to the IPM ceramics but are more easily
available and machinable. When compared to basic aluminum designs, Al-Cu clad heat
exchangers provided a 10% reduction in thermal resistance and a 30% reduction in overall
weight [68]. Some have even gone to adjust the material structure of the ceramics themselves,
like Xu et al. who simulated a ladder shaped DBC arrangement capable of reducing thermal
stresses and plastic strains within the system during thermal cycling [69].
2.4.2 Micro Channel Heat Sinks
Since the emergence of electronic overheating, one of the most versatile and reliably high
performing methods of cooling has been that of mini and micro channel flow structures. The
basic concept of microchannel flow is to reduce the cross-sectional area of the fluid as is it
passes across the heat sink, improving the local convective heat transfer by increasing the
velocity of the coolant, reducing the development of thermal boundary layers and possibly
inducing turbulent flow [33]. These passages are formed by micro-machining extrusions in the
base plate of the heat sink. Two very common patterns, shown in Figure 11 and Figure 12 are
finned channels and pin-fin arrays [70]. These arrangements are commonly setup up in areas of
21
high temperature gradients such that an even flow of coolant occurs across the width of the
pattern. Although microchannel heat exchangers are a widely established technology, there are
still several associated drawbacks with this method. Machining on this small of a scale can be
difficult or expensive if the required level of equipment is not readily available and the reduction
in cross sectional area can result in high pressure drops across fluid inlet and outlet locations.
Most importantly Thermal Runaway2 is a well-known issue when utilizing liquid cooled
microchannels, as the coolant further downstream of the inlet experiences higher temperatures,
which result in higher junction temperatures of any electronic devices located downstream [71].
This temperature differential between devices can lead to increase thermo-mechanical strain,
decreased efficiency and accelerated material degradation.
Figure 11: Micro Pin Fin Heat Sink Arrangement. - [70]
As mentioned in previous sections, much of the efforts made in this area of electronic cooling is
built off the pioneering work of Tuckerman and Pease, who found that straight forward
integration of compact 50um channeled heat exchangers could greatly reduce thermal resistances
for power dense IC packages [33]. Lee and Vafai compared the performance of microchannel
coolers to that of jet coolers for high heat flux dissipation and found that the microchannel design
options were much more preferable to small dimensional (<5mm2) applications [72]. An
innovative structure, developed by Harris, Despa and Kelly, combined microchannel liquid
cooling with cross-flow forced air to decrease thermal diffusion lengths and provide a function
similar to automotive radiators [73]. An extremely compact integrated design with low thermal
resistance of 0.087K/W was achieved by Steiner and Sittig who also found water to offer much
2Thermal Runaway: A thermodynamic phenomenon in situations where an increase in temperature changes conditions, which in
turn leads to further temperature increases, possibility leading to a destructive result
22
better thermal performance as a working fluid when compared to dielectric fluids [74].
Analyzing the high accuracy of numerical simulations for single phase microchannel flow
structures, Qu and Mudawar also found that a basic fin analysis model, accounting for thermal
entrance effects, could provide reasonably accurate predictions when compared to experimental
results [75].
Figure 12: Straight Channel, Staggered Pin and MDT In-Line Pin Heat Sink Formations. - [76]
Parametric studies carried out by Zhang et al. determined that performance of microchannel heat
exchangers are greatly influenced by the channel width. This variable defines a significant trade-
off between thermal resistance and pressure drop. It was also found that the effect of base plate
thickness is minimized when aluminum material is replaced with more conductive substances
such as copper or diamond [77]. Building on this Kim investigated the use of different methods
for optimizing microchannel coolers, focusing on analytical fin and porous medium models as
well as a numerical three-dimensional approach. The findings indicated that the main design
variables for optimizing performance are channel height, width and fin thickness [78]. An
analytical and experimental procedure carried out by Peles et al. indicated that pin fin
arrangements provide better design flexibility and thermos-hydraulic performance over channel-
based designs. Moreover, decreasing fin length and increasing array density is preferable when
dealing with high Reynolds number flows [70]. An interesting study performed by Moreno et al.
evaluated the influence of Micro Deformation Technology (MDT) on the performance of
conventional microchannel geometries, presented in Figure 13. MDT is an advanced technique
that seeks to add small scale deformations to fin structures in order to increase the heat transfer
area and induce turbulence. Examples of this technique are provided in Figure 13 .It was found
23
that the MDT pin array provided significant thermal improvements over the conventional
structures [76].
Figure 13: Demonstration of Fin Deformation Heat Sinks a) Micro Deformation Tools and
Process. b) Micro Deformed Heat Exchanger Array. - [76]
Although numerical simulations and analytical models have been found to provide reasonably
accurate predictions for flow and heat transfer in microchannel arrangements, a significant
challenge in this area has been that of flow visualization. However Sajith et al. were able to
attain valid optical measurements of a mini channel system using Mach-Zehnder Interferometry,
eliminating the need for flow disturbing thermocouples [79]. More recent studies have sought to
build on the cooling capabilities of microchannel designs by integrating them with other
advanced flow techniques. As was the case with Husain et al. who investigated the capabilities
of various hybrid designs incorporating different combinations of microchannel, pin fin and jet
arrangements. It was found that the inclusion of microchannels decreases the convective
effectiveness of jet swirl. Thus the most effective design, achieving acceptable thermal
resistances, high convective heat transfer and low junction temperature was the combination of
jet and pin arrays [80].
Microchannel cooling schemes have proven to be a highly utilized means of thermal
management in the field of power electronics. With regards to automotive applications, they
provide compact designs that can be easily integrated into the structures of IPM and IGBT
modules. It has proven to also be a flexible technology, open to a variety of optimization and
hybrid design techniques. The main drawbacks that result from this method of heat sink design
are with respect to manufacturing. Fabrication methods tend to increase in cost as the scale of the
channel dimension decrease [81]. Moreover, as flow areas are reducing factors such as surface
finish and roughness can start to have influence on the already high levels of applied pressure.
24
Microchannels are a suitable option to any application that may require very high-power density
cooling at the tradeoff of cost and pumping power.
2.4.3 Jet Impingement Heat Sinks
A longstanding method of increasing the rate of convective heat transfer between fluids and
heats sinks has been the use of Forced Surface Impingement. The foundation of this method is
that higher turbulence can occur if flow is directed normal to the heated surface and the fluid can
impinge directly on the area of heat transfer. The area around the stagnation point then
experiences a higher level of heat transfer than if the flow was to pass parallel to the heat source
plane through a series of pins or channels [82], [83]. For many years this practice was almost
exclusively utilized for air cooling setups, but with the heat flux levels currently being reach by
power electronics it is becoming more commonly adapted to liquid cooling schemes. The
impingement flow is usually established through the use of small diameter jets or channels that
induce substantial pressure drops, forcing the liquid into a high velocity, turbulent trajectory
perpendicular to the heat source [84]. The style of impingement can be broken down into the
main categories of Free, Submerged and Confined impingement, as shown in Figure 14. These
are dependent on the arrangement of the physical structure as well as the allocation of liquid and
gas. Although confined impingement has be more prevalent in automotive applications, due to
the predicable and controllable nature of the associated flow, all methods offer high levels of
thermal dissipation with a variety of design variables that correspond differently to performance
[42].
Figure 14: Common Jet Impingement Arrangements. a) Free Surface Jet. b) Submerged Jet.
c) Confined Submerged Jet. - [42]
Liquid impingement systems have been seen to achieve some of the highest rates of convective
heat transfer in the industry. There are also several additional benefits associated with this
25
technology. The use of liquid impingement means that the design complexity is usually limited
to the jet or channel structure, allowing the impingement surface to remain untouched. This can
eliminate the need for machined fins or pathways directly on base of the heat sink, or in some
cases, eliminate the need for a base plate altogether [85]. In addition, since heat transfer
completely takes place around the stagnation point of the fluid, the material used for the
impingement structure does not have to handle any of the heat flux. To clarify, the thermal
conductivity of the structure does not matter and could theoretically be made from any material
capable of supporting the flow of coolant [86]. However, all these benefits come at the trade-off
of internal pressure. Since the nature of this cooling method requires high pressure at the
impingement jets or channels, there are usually high pumping requirements associated with these
systems, which translates to larger parasitic loads.
An early report compiled by Jambunathan, Moss and Button analyzed the variables affecting the
local heat transfer occurred at the stagnation point of impinging flow. It was found that
geometric nozzle characteristics along with flow confinement, turbulent intensity and the
dissipation of jet temperatures are the significant factors when attempting to predicting local
Nusselt numbers [87]. The work of Gerimella and Nenaydykh, focused only on the influence of
nozzle geometry for submerged and confined liquid jet arrangements. It was found that the
highest heat transfer coefficient corresponded to smaller nozzle aspect ratios (length/diameter <
1), however the influence of these ratio values reduced as the displacement between the nozzle
and target surface increased [88]. Oliphant, Webb and McQuay carried out an experimental
comparison of common jet array and spray droplet impingement, finding that jet cooling,
dependent on flow velocity and array size, performed at equal levels to spray cooling, which was
found to mostly be dependent on mass flow alone. However, spray impingement was able to
achieve this level of heat transfer at significantly lower mass flow rates of coolant. It was
theorized that this was due to the formation of an evaporative film along the impingement
surface and the unsteady nature of thermal boundary layers experienced in spray impingement
[89]. The more recent work of Mertens et al. focused solely around the performance of spray
impingement, achieving an air-water cooling system capable of dissipating 825 W/cm2 of heat
from and IGBT module [90]. Bhunia, Chandrasekaran and Chen compared the cooling
capabilities of liquid micro-jet arrays to that of conventional air and cold plate technology. Not
only was a significantly low thermal resistance of 0.013 °C/W achieve for the liquid jet based
26
heat exchanger, but the temperature variation between the various IGBT and Diodes being tested
was reduced to approximately 2°C [91]. As the practice has become more establish many
designs, such as the one implemented by Turek et al., have sought to combine impingement
arrangements with two-phase cooling approaches. The pressure atomized evaporative spray
cooling method they presented utilized high temperature fluid (100°C) as to reduce the
condenser size and requirements. The system was able to provide a 3.3 increase in the heat flux
output by the electrical converter under test while maintaining junction temperatures under
125°C [92].
Another example of hybrid cooling scheme was that pursued by Barrau et al. which combined
liquid jet impingement and microchannel design. It was found that the inclusion of the
microchannel structure provided higher rates of heat transfer and more even temperature
distribution across the heat sink at the cost of increasing overall pressure. The channel density
was also found to be the major scaling factor of the hybrid system with respect to Reynolds and
pressure values [93]. Hadziabdic and Hanjalic conducted an in-depth analysis on the influence of
liquid vortices cause by jet impingement on heat transfer. Through direct Eddie simulations the
different flow regimes were characterized and provided insights into the relationship between
stagnation, turbulence and resulting Nusselt values [94].
In recent years the many have noticed that liquid impingement can be an ideal cooling method to
keep up with the ever-increasing requirements of automotive power applications, offering
extremely high levels of thermal dissipation in the form of light, compact designs. Parida, Ekkad
and Ngo compared a variety of jet arrangements utilizing separation walls and different angles of
impingement, as shown in Figure 15 for the cooling of HEV/EV microelectronics.
27
Figure 15: Impingement Based Heat Exchanger Designs. - [86]
It was found that the presence of center walls can increase conduction and assist in the formation
of liquid vortices, shown in Figure 16, caused be low impingement angles, which are found to
increase the convective heat transfer between the fluid and the heat exchanger [86].
Figure 16: Formation of Flow Vortices by Variations in Impingement Angles. a) Perpendicular
90° Impingement angle. b) 70° Impingement Angle. c) 45° Impingement Angle. - [86]
A design achieved by Morozumi et al. integrated the principles of Direct Cooling with
impingement technology to improve the reliability of an HEV power control unit while
simultaneously reducing overall size. Also, the use of an Sn-Sb solder was demonstrated to
account for the disproportional CTE values of ceramic substrates and aluminum heat sinks,
extending fatigue lifetime and improving the overall reliability of the module [95]. Gould et al.
found that a jet impingement cooling solution was ideal for the thermal management of power
28
electronics in military hybrid vehicles, where harsh ambient conditions and high fluid
temperatures can apply. Using water-glycol coolant at inlet temperatures of 100°C at constant
flow rates, the jet impingement design was found to maintain junction temperatures at 169°C, a
substantial improvement other the commercial cold plate and microchannel models also tested
[96]. New innovations utilizing the compact nature impingement cooling are constantly being
developed, such as the “Shower Power” automotive cooling concept presented by Danfoss
Silicon Power, shown in Figure 17. This original design avoids the high pressure drops
commonly associated with impingement cooling by utilizes small-winding microchannel
passageway, attaining a uniform cooling across HEV/EV IPMs [97].
Figure 17: Danfoss Shower Power Cooling Design. - [97]
As automotive designs become more reliant on the performance of power electronics modules,
the trade-offs of pumping demands for high level heat flux dissipation and uniform temperature
distribution, offered by impingement cooling are becoming more appealing. Many see jet
impingement as a promising field for power dense, mobile applications.
2.4.4 Integrated Coolers
The continuous goal to reduced thermal resistance within power electronic structures has led to
one of the more complex but extremely high performing design concepts, referred to as Direct
Integrated Cooling. This cooling arrangement , depicted in Figure 18 , seeks to integrate the heat
sink structure directly into the DBC structure of a power electronic module [26]. This can
essentially eliminate all the conductive thermal resistances associated with any solder, TIM or
29
heat sink materials that would overwise impede the flow of heat between the DBC and the
working fluid [26].
Figure 18: Direct Integrated Heat Sink Arrangement. - [26]
The implementation of this design structure requires the careful selection of materials and
assembly processes. A design by Colgan et al. achieved significant cooling levels of 300W/cm2
and over, using a microchannel design formed by integrated silicon fins. The final thermal
resistance associated with their prototype was 10.5 C-mm2/W [98]. A similar idea was proposed
by Tang et al. who sought to combine the ideal corrosion resistance properties of aluminum with
the superior heat spreading characteristics of copper. A hybrid substrate model was achieved
through a carbon nanofiber bonding process. Performance and reliability testing has yet to be
reported, but early thermal modeling suggests a high level of performance [99].
More recently, Jung et al. achieved experimentally validated embedded silicon microchannel
cooling design with the potential to extract up to 850C/cm2 of waste heat from vehicular power
electronics. Using single-phase water as a working fluid and a unique 3-D manifold design, it
was observed that one of the biggest areas of uncertainty is the accurate prediction of pressure
drop. This is due to the difference between “target” micro channel dimensions and “actual”
channel dimensions as a result of microfabricating [100]. Chen et al. were able to apply the
principles of integrated cooling into the area of thermal management for lithium-ion battery
packs. Combined with a custom optimization process, temperature reductions of ~1.87°C and
deviations of 0.35°C were attained for easily manufacturable design [101].
An innovative design recently developed by Erp et al. utilized a combination of metalized heat
spreading via integrated silicon micro channels and low-pressure liquid distribution via PMMA
30
manifolds. The proposed system, shown in Figure 19, seeks to minimize the pumping
requirements of conventional liquid cooling systems while keeping volumetric sizes tight by
bringing the cooling liquid in close proximity to the active devices[102] .
Figure 19: Construction of MMC Heat Sink Prototype. - [102]
Although their currently exists a high trade-off between assembly costs and complexity, with the
rising cooling requirements of power electronics, DBC Direct Integrated heat exchangers may be
applicable for extremely power dense applications.
2.4.5 Double-Sided and Stacked Modularized Cooling
Another more recent straight forward but effective approach to high power density electronics
double sided and modularized cooling. By integrated a second heat exchange into the IPM stack,
as shown in Figure 20, thermal designer can effectively double the rate of conductive heat
transfer away from power electronics and HDD [103].
Figure 20: Double Sided Heat Sink Approach. a) Conventional Liquid Cooling Arrangement.
b) Double Sided Cooling Arrangement. - [104]
31
This principle is reinforced by the findings of Wang et. Al who computational and
experimentally compared a conventional one-sided IGBT stack to that of a double-sided cooling
stack. The addition of the second liquid heat sink was found to increase system efficiently by
47.9% [105]. With the potential to greatly increase power density in IPMs, this style of design
has become popular in the field of automotive power electronics and EVs [106].
The concept of double-sided cooling allows for simpler and easily manufactured heat sink
geometries, such as macro pin fin arrays or mini channels, to be utilized for high power dense
applications. However, it should be noted that the application of double-sided liquid cooling
arrangements put substantial constraints on the corresponding electrical design. The mounting of
an additional ceramic substrate on the topsides of the electronics devices means that
conventional wire bonds can no longer be utilizes as electrical interconnects. The addition of this
new criteria heavy constraints the design and assembly of the and electrical layout [26].
The issue of electrical interconnects was investigated by Gillot et al. who sought to replace wire
bonds with flip chip solder bumps, allowing the associated IGBT devices to be mounted on both
sides to DBC substrates for double sided cooling. Through thermal simulations and experimental
testing it was found that the ‘sandwiched’ cooling structure provided a 76% increase in heat
dissipation as compared to a corresponding single-sided design [107]. Charbonneau et al. were
able to utilizes Embedded Power Packaging structures, similar to Figure 20b , to achieve the
electrical requirements of a proposed double-sided cooling scheme. Through experimental
analysis a 60% improvement in thermal performance was achieved [104]. A high performing
design was achieved by Schneider-Ramelow, Fraunhofer and Hoene by combining the principles
of Direct Cooling with a double-sided structure. A 40% increase in thermal resistance resulted
from the additional heat sink. It should also be noted that very low thermal resistances of ~0.08-
0.09 K/W were achieved with very low pumping requirements (<2 lpm) [63]. A different
approach carried out by Chang et al. used copper-clip packaged for the electrical connection of
wafer thin IGBTs between two liquid cooled heat sinks. The major finding were a 200% increase
in the power handling capabilities of the IGBTs, a 40% reduction in thermal resistance and a
260% increase in the predicated number of cycles due to the wireless connections [108].
As the technology around, double sided cooling becomes further establish, more inventive
structures are being developed. One of the major innovations in this area is the formation of
32
Stacked liquid cooling schemes, shown in Figure 21. Utilizing the double-sided cooling
approach, multiple IPMs and liquid heat sinks can be bundled to provide extremely compact,
multipurpose, high performance electrical systems.
Figure 21: Demonstration of Double-Sided-Stacked Cooling Structure. - [106]
The benefits of this approach have been especially apparent in the power electronics sector of the
transportation industry, where many companies such as: Toyota, Denso, Alstom are developing
compact innovative designs based on multi-level stacked cooling [26]. As the automotive
industry continues to electrify, the highly compact nature of double-sided and stacked liquid
cooling may lead this to be a standard practice in years to come.
2.5 Design Optimization
Despite all the new technologies and methods presented in this section thus far, a major aspect of
electronic cooling design that cannot be ignored is that of performance and system optimization.
In a mass -production industry, such as automotive manufacturing, small improvements in size,
weight and performance can translate to major reductions in processing costs [109]. Many
optimization methods have been practiced over the years and are tailored to a specific
optimization goal. Common focus include: the physical design variables of heat exchangers, the
layout of heat sink geometries and fin/channel ratios, or the influence of controlled system
variables, such as the mass flow of coolant and the associated incoming fluid temperatures [110]
33
2.5.1 Practical Techniques
Early work in field of heat sink optimization relied on the governing equations of fluid dynamics
as well as the principles of conduction and convection heat transfer. Analytical modeling
provided functional relationships between design variables and performance variables. Like the
major work of Knight et al., who developed dimensionless, generalized equations relating the
geometrical aspects of microchannel heat sinks to their thermal resistance values. This
methodology was applied to several existing designs and found to have significant improvements
on cooling performance [111]. Ritzer and Lau utilized thermal modelling and experimental
variations to optimize the performance of a laboratory chiller responsible for managing transient
heat loads. The basis of this optimization process was set on economic feasibility of the heat sink
under review. It was found that the bulky nature of passive air cooled heat sinks made them an
unsuitable option while high fin density heat sinks were found to be price competitive with low
density models while out performing all competitors with regards to thermal performance [112].
In a similar fashion, Lee developed analytical simulation models base on parametric analysis,
capable of predicting and optimizing the heat transfer capability of bi-directional heat sinks
within a confined configuration [113].
The optimization of thermal systems saw a major shift with the rise CFD analysis. These high
performing, reasonably reliable software packages allowed for the complete modeling and
numerical simulation of Multiphysics systems. This tool was quickly adapted into optimization
procedures. An early example is that of Lee, who was able to reduce the operating temperatures
of the IGBT devices to below 100°C associated with a given power module by simulating
various pin fin arrangements within the liquid cooling design [114]. A more advanced technique
was implemented by Li and Peterson, utilizing numerical simulations to attain a simplified three
dimensional conjugate heat transfer model capable of optimizing the geometric structure of
microchannel heat sinks [115]. Husain and Kim relied on FEA simulations to solve 3-D Navier-
Stokes and conjugate heat transfer equations for rectangular micro-channel heat sinks. The size
of the designs was then optimized for a constant heat source by a variety of surrogate models
which included: Response Surface Approximation, Kriging and Radial Basis Neural Network
methods. Although these models were found to provide slightly different geometric designs they
all predicted similar objective function values [116]. Thermal FEA analysis was also used by
Wang, Hung and Chen to model the heat transfer of a finned air-cooled heat sink working in
34
tandem with a thermos-electric generator. A two-stage optimization process was carried out on
the design, first utilizing an analytical approach to determine the optimal fin-to-fin spacing, then
applying a compromised programming method to determine the maximum generator
performance at the cost of the heat sink performance when the heat sink volume was fixed. Final
results showed an 88.7% increase in the generators power density at the cost of a 20.93%
decrease in the heat sink efficiency [117].
2.5.2 Topology Optimization
With the increasing capabilities of advanced manufacturing techniques, such as CNC machining
and 3D printing an area of growing popularity within the field of automotive design is Topology
Optimization. This method seeks to move beyond simple size variables but instead optimize the
structural layout of a product or model within a predefined design space [118]. A common
application for this method is the volume or mass minimization of material within an object
while satisfying load or force requirements. This is useful when dealing with automotive
structural problems, such as vehicle chassis design as was the case with Mantovani et. al. Using
a two-stage lattice approach a system of truss structures was used to represent the automotive
chassis and achieve an admissible stress level of 50MPa [119]. A more complex approach,
introduced by Yang et al. utilized a multi-step topology optimization frame work with adaptive
and varying design domains to automate the layout of spot welds within complex automotive
structures [120].
Topology optimization has also been utilized in the field of electronic cooling. Improvements to
the topology of fin density, as shown in Figure 22, keep electronic heat sources more isothermal
while decreasing total heat sink mass [121].
35
Figure 22: Heat Sink with Increased Fin Density Topology. - [121]
One of the more radical works conducted by Alexander et al., demonstrated the application of
density-based topology optimization to the design of three-dimensional heat sinks under natural
convection [122]. The Multiphysics system coupled to this procedure was solved using stabilized
trilinear equal-order finite elements with an order of 20-330 million state degrees of freedom.
This allowed for the optimization of large scare problems and the generation of custom, novel
design iterations as depicted in Figure 23.
Figure 23:Optimized Heat Sink Designs with Constant Gr Value and Mesh Size of 329 x 640 x
320 Elements. - [122]
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2.5.3 Genetic Algorithms
As the computation tools for modeling and predicting the behavior of hydraulic-thermal systems
improve, so to do the optimization techniques involved with the design process. Of these
techniques, Genetic Algorithms (GA) are being established as one of the more advanced and
promising methods. GAs are a powerful tool, utilizing stochastic search and optimization
procedures to provide optimal solutions across a wide variety of applications [123]. This
optimization process follows the principles of organic evolution and does not require the rate of
objective functions to be determined, which can be a major benefit when dealing with
computational simulations [124]. The general procedure of this optimization method, as shown
in Figure 24 starts with the randomized generation of an initial population. After the performance
of population is evaluated based on the designated objective function and the high and low
performing models are identified. A ‘Survival of the Fittest’ approach is then implemented as the
poor performing members of the initial population are then discarded and new models are
formed by applying variations or ‘Mutations’ to the surviving models. A new population is then
generated for evaluation and this process is iteratively continued until an optimal model is
produced.
Figure 24: Basic Genetic Optimization Workflow. - [125]
This procedure has already begun to be implemented in the design optimization of electrical
cooling systems. An early evaluation of this method was conducted by Fonseca and Fleming
found that GAs ability to cope with discontinuous and noisy functions made them an ideal tool
for multi-objective optimization, predicting a promising future with engineering applications
[126]. Husain and Kim utilized a Response Surface approximation surrogate analysis working in
conjunction with an evolutionary algorithm to optimize the channel depth and fin width of their
37
heat sink design with the objective functions related to require pressure and resulting heat
transfer. This achieve low thermal resistances of 0.09 – 0.08°C/W [127]. A different approach
was taken by Xie, Sunden and Wang, by employing a GA procedure to optimize the structure of
a compact plate-finned heat exchanger on the basis of minimizing total volume and annual cost.
When ignoring pressure drop constraint a 49% volume reduction was achieved, however when
pressure was a accounted only a 30% reduction was produced [128]. A non-dominated sorting
GA was applied by Sanate and Hajabdollahi for the multi-objective optimization of a common
plate fin heat exchanger. Several design variables, fin pitch, height, offset length, cold stream
flow length, no-flow length and hot stream flow length were used to provide an optimal thermal
performance at minimal annual cost. Further sensitivity analysis on the resulting, or Pareto,
models provided more insight into the functional relationship between the design parameters and
the multi-objective function through the optimization process [129].
More recent work has begun to pair the structure of Gas to not just size variable optimization but
to the more complex task of topology optimization. Wu, Ozpineci and Ayers sought to achieve
an optimized liquid cooled heat sink through a two stage GA based design process with FEA
simulations via COMSOL. The first stage, shown in Figure 25, implemented the conventional:
Initialization, Evaluation, Selection, Mutation and Reproduction iterative process, while the
second stage applied more refined perturbation mutations, as shown in Figure 26. With a 15%
improvement in heat transfer, it should be noted that findings of the study indicated designs
achieved through this method may only be attainable through 3D printing procedures due to their
complex nature [125].
Figure 25: First Stage Conventional Genetic Optimization.
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Figure 26: Second Stage Perturbation Genetic Optimization. - [125]
An innovative design process achieved by Bornoff et. al incorporated the fin topology layout
into a generative optimization procedure for an automotive audio amplifier. Mass reductions of
18% were achieve while maintaining thermal performance [130]. Wu et al. also utilized the
principles of genetic algorithms, coupled with FEA simulations to produce a complex 3-D
printed heat sink model, shown in Figure 27, specifically optimized for air cooling a 50kW
inverter [131].
Figure 27: Two Stage Genetically Optimized Air-Cooled Heat Sink. - [132]
39
It is clear that GAs can provide a computationally effective solution to both single and multi-
objective optimization procedures. The automatic nature in which they operate makes them an
ideal design tool in the continual effort to improve the cost, size and performance of integrated
cooling structures.
40
Chapter 3
Methodology and Construction of Optimization Program for Liquid Heat Sink Topologies
As discussed in Chapters 1 and 2, the growing thermal requirements of power electronics are
beginning to push to bounds of conventional heat sink technologies. If automotive designers
wish to keep up with the rapid increases in power density and electrical performance more
modern approaches need to be taken in order to achieve innovative solutions to the issue of
electronics cooling. With the availability of advanced production techniques, like additive
manufacturing, topology optimization is an ideal area of focus for those looking to achieve the
highest level of heat transfer within a heavily constrained design space, as is the case with on-
board EV applications.
In this chapter we present the creation of a novel design approach, utilizing the optimization
techniques of genetic algorithms, to develop compact high performing heat sink structures. Code
generated in MATLAB is used to form an iterative design loop, using arrays of binary data
points to represent heat sink geometries. Using the Ansys AAS toolbox, the MATALB code
uploads generated designs into the ANSYS workspace, taking advantage of its powerful
simulation capabilities, to evaluate potential heat sink geometries. This iterative optimization
process learns as it cycles through groups of design candidates, producing a final heat sink
geometry, specifically tailored to the thermal profile of the associated electrical system.
The layout of this chapter, depicted in Figure 28, is as follows: Section 3.1 discusses the
formation of the Genetic Optimization Logic and its associated functions, constructed in
MATLAB and implemented on simple two-dimensional flow geometries simulated in ANSYS
Fluent. Section 3.2 provides an overview of ANSYS Icepak and its unique abilities to model and
simulated electronic thermal assemblies and goes on to detail the integration of ANSYS Icepak
into the programming structure and the required changes to optimization procedure to account
for three-dimension liquid heat sinks topologies. Section 3.3 concludes this chapter with an
overview of the final genetic optimization process and the potential of this custom procedure.
41
Figure 28: Content Breakdown for Chapter 3.
3.1 Stage I: Genetic Optimization Logic
The optimal heat sink topologies discussed in this chapter are attained via binary genetic
optimization [133], [134]. By applying this method to principles of topology optimization,
design of a structure can be broken down into a set of 2D pixels or 3D voxels, which are
represented by bit arrays of equal size [135]. The binary values within these arrays are assigned
to different materials, such that any alteration, manipulation or morphology carried out on the
data matrix directly controls the allocation of said materials throughout the physical design.
While the majority the of functions and operations responsible for this custom procedure, laid
out in shown in Figure 29, are implemented in MATLAB, ANSYS is used to simulate each heat
sink design and evaluate the corresponding cooling performance for an applied heat load.
42
Figure 29: Structure of Genetic Optimization Process.
The following sections detail how each stage of the proposed genetic optimization loop were
formulated into MATALB functions and brought together to construct the foundational genetic
logic of the optimization program. This initial version of the program, largely drawn from [136],
dealt only with two-dimensional matrices (MB), representing the workspace of simple planar
43
flow geometries. This approach kept simulation run times low and simplified geometry
visualization, as shown in Figure 30, allowing for better characterization of the initial logic.
Figure 30: Visualization of Structural Bit Array.
3.1.1 Constructing Model and Defining Workspace
When first defining the model for optimization, reducing the complexity of the overall system
and simplifying the associated geometry is the key to achieving simulation efficiency without
sacrificing system accuracy [137]. In this stage, designers must attempt to simplify the heat sink
model into the components that have direct influence on the performance variables in question.
As with conventional topology optimization [135], the physical bounds of the heat sink must be
defined within the simulation space as well as the “active” and “reserved” regions in relation to
the design process, as depicted in Figure 31a. In the case of planar geometries, the reserved
regions commonly take the form of inlet and outlet regions as well as heat sources acting as
pseudo devices or electronic ‘chips’. However, when dealing with more complex systems and
three-dimensional models the formation of this workspace and the allocation of these active and
passive design regions becomes more complex, as will be discussed in a later section.
Once these regions are defined, the optimization workspace are subdivided into a grid of
structural pixel elements much like Figure 31b. The size and shape of these elements are
controlled by the designer, however in this work, only square elements are used to discretize the
active workspace. This is done to simplify the grid indexing, as described in the following
section. It is important to note that the geometric nature of the workspace elements may be
constrained by both computational cost and manufacturability [17]. Increased discretization leads
44
to smaller element size, which in turn can increase the cost or complexity of the manufacturing
techniques associated with creating the generated features [138].
Figure 31: Defining the Design Optimization Workspace.
This initial Partitioned Workspace (MP), model acts as a form of blank geometry for the
optimization to work with. Being a part of the programs Initialization Stage, this step is only
executed once and ideally is carried out in a modelling software prior to the activation of the
optimization program.
3.1.2 Grid Indexing
The geometric information of a candidate heat sink geometry must be input to Ansys. This is
achieved as follows. Once the designer constructs the initial heat sink model, the Genetic Logic
extracts the geometric information of the structural elements (ΔxPixel, ΔyPixel) as well as the
optimization workspace (XWS, YWS) to create an array of equal size, as shown in Figure 32. The
dimensions of the array are dictated by via (Eq. 3.1) and (Eq. 3.2). The cells within this array are
sequentially indexed, forming a Global Array (MG) of values, each representing an element
within physical model.
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Figure 32: Created Global Array.
𝒏 = 𝒀𝒘𝒔
𝜟𝒚𝑷𝒊𝒙𝒆𝒍
(3. 1)
𝒎 = 𝑿𝒘𝒔
𝜟𝒙𝑷𝒊𝒙𝒆𝒍
(3. 2)
The partitioned workspace (MP), developed in the previous section, is also indexed in a similar
fashion as shown in Figure 33. This is done by first counting the number of active elements to
form a size vector (xS) and then mapping that vector back to the positioning of the elements
within MP. This process assigns an element label to each of the structural cells within MP based
on their associated coordinates and positioning within the physical workspace.
Figure 33: Assigning Element Labels to Partitioned Workspace.
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The formation of the Global Array (MG) and the indexing of the Partitioned Workspace (MP)
allows the program to tie the element label of the structural cells to a value within MG as depicted
in Figure 34. This is a vital step moving forward with the genetic design process. It allows the
solution vectors generated by the Genetic Logic to be easily converted to Bit Matrices (MB)
consistent with the MP structure.
Figure 34: Linking Element Labels to Global Array.
3.1.3 Mutate Seed Design
Before the automated design process can start, an initial group of ‘Seed Designs’ must be
generated. The designer must input an initial geometric heat sink design for the program to
build from. This first model may, for example, represent the best engineering design, achieve by
the user and the desired structure to be optimized. For example, in the case of electronic heat
sinks, this could take the form of micro channeled heat exchangers [79], [80]. This base Seed
Design acts as a good ‘starting point’ for the optimization process and gives an initial
measurement of performance for future comparison.
The program then creates an initial group or ‘Population’ of design candidates, by inducing
random changes in the Seed Design as shown in Figure 35. Both the quality of the starting design
and the size of the genetic Population can have significant influence on the performance of the
overall optimization process.
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Figure 35: Seed Mutation.
These design candidates, or ‘Individuals’ take the form of solution vectors (xFE) containing the
values of elements within the workspace to be allocated as ‘Fluid Blocks’. By relating xFE back
to MG, as shown in Figure 36, these vectors are converted to the structural bit arrays presented
earlier.
Figure 36: Utilizing Solution Vector and Global Array to Form Structural Bit Matrix for New
Individual.
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3.1.4 Validation
Due to the randomized nature of this genetic inspired optimization process, it is important to
verify the geometric feasibility of generated Individuals and refine them if necessary. Each
design generated by this Seed Mutation stage undergoes a validation check, to ensure that the
generated structure is a feasible solution for the given topology problem. For the case of liquid
heat exchangers an ‘Invalid’ design may take the form of candidates with blocked flow channels,
unconnected to the defined Inlet and Outlet boundaries, as demonstrated by the design shown in
Figure 37. Treating each MB as a binary image, these bodies are easily identified via ‘Blob
Analysis’ and with extensive image processing capabilities within MATLAB, many options exist
for modifying these invalid designs.
Figure 37: Validating New Design Candidate with Blob Analysis and Image Morphology.
Once a blocked channel is identified, the designated functions deal with the Invalid aspects of the
designs. For this initial study the program first identifies isolated liquid bodies causing design
issues and applies the following conditions:
1. If the body is found to connect to only one boundary (either the Inlet or Outlet), it is dilated
horizontally until it either meets the missing boundary, forming a full channel, or connects
to an existing channel network.
2. If the body is found to have no boundary connections, the ‘Floating Body’ is removed from
the binary structure.
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This Initialization loop of Seed Design Mutation and Validation continues to produce design
candidate until an initial Population of Seed Designs is created, similar to the one demonstrated
in Figure 38. This set of design options marks the end of the programs initialization function and
move into the main optimization process, as discussed in the following sections.
Figure 38: 2D Example Population of Initial Design Candidates.
3.1.5 Evaluation
Once a full population of initial design candidates is established, each Individual is sequentially
evaluated. To test the performance of each potential heat sink design stored in the xFE solution
vectors, this program utilizes the modeling and simulation capabilities of the ANSYS
Workbench software suite. Specifically, the CFD based program Fluent is used to model the flow
and heat transfer associated with these active cooling systems. Establishing valid CAD
geometries and accurately predicting the temperature gradients of each design within a
generation is essential for identifying candidates with optimal design characteristics. By relating
the fluid elements stored in the solution vectors to the layout of the physical workspace, the
program can associate the resulting thermal performance to the data structures within the genetic
logic.
To accomplish this, the optimization program creates a Script File for each potential design
candidate, based on the topology information provided by the associated xFE vector and updates
50
the corresponding structural model in ANSYS Design Modeler (DM). A Simulate function,
executed through the AAS Toolbox, sets the boundary conditions and materials properties to
Fluent. This file structure is demonstrated in Figure 39.
Figure 39: File Structure of Evaluation Stage.
Once the model and simulate space is set for the given design, ANSYS calculates the device
temperatures (TD) along with the pressure drop across the inlet and outlet flow faces (ΔPInlet-Outlet)
through CFD Multiphysics simulation, as shown in Figure 40.
Figure 40: Evaluation Stages. a) Candidate Solution Vector. b) Representative Bit Array.
c) ANSYS CFD Model.
The results obtained from Fluent are used to assign a Fitness Score to each Individual,
represented by (Eq. 3.3). The Fitness scoring is controlled by user defined weighting factors a
51
and b, dictating the importance of minimizing the device temperatures to that of the pressure
drop.
𝑭𝒊𝒕𝒏𝒆𝒔𝒔 = 𝒂(𝑻𝑫𝒆𝒗𝒊𝒄𝒆𝒔) + 𝒃(∆𝑷𝒊𝒏𝒍𝒆𝒕−𝒐𝒖𝒕𝒍𝒆𝒕) (3. 3)
The population is then reorganized, ranking the Individuals from best (lowest fitness) to worst
(highest fitness). A ‘Breeding Probability’ is assigned to each candidate based on their rank as
demonstrated in Figure 40. This percentage value dictates how likely each candidate is to be
chosen as a ‘Parent’ for the new generation of designs, as discussed in the following section.
Figure 41: Evaluation Process. a) Generated Bit Arrays. b) Converted to ANSYS CAD
Structures and Simulated in FLUENT. c) Ranked and Assigned Breeding Probability.
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3.1.6 Selection, Crossover and Mutation
Here we discuss the operation of the Genetic Algorithm to generate new solutions from previous
simulation results and candidate heat sink designs. In order to continually improve the genetic
pool of design candidates, ranked solutions are ‘Bred’ together in order to generate new
Individuals or ‘Child’ designs. Parents are randomly selected for Breeding, such that the higher
performing solutions are more likely to be chosen, as discussed in the previous section. Here,
designers can specify the desired ratio of Parents to a Child. Each Parent is split into a series of
‘Chromosomes’ which consist of a specified number of adjacent pixels. These strings of pixels
or ‘Genes’ from the associate design matrix, MB carry binary values of the Parent design,
indicating either a ‘fluid’ or ‘solid’ element being transferred to the new Child design. Each
parent has an equal probability of passing along a Chromosome string to the Child. This
Breeding process is repeated until a full Binary Design Matrix (MB) is constructed for the Child.
Once all Genes have been allocated and a new design is formed, the Child undergoes
“Mutation”. For this process, each element in the new design matrix has a small probability of
changing state. The role of this random Mutation stage is to induce a certain level of randomness
and “Genetic Diversity” throughout the duration of the design process. However, due to the
randomized nature of this gene-splitting process, each Child also undergoes the same validation
process as outlined in Section 3.1.4. This avoids the creation of blocked flow channels and
invalid geometric regions that may be formed by this breeding process. The entire formation,
mutation and validation of these Child designs is represented in Figure 42 below
Figure 42: Generating Child Design.
This process of Selection, Crossover, Mutation and Validation repeats until a new Population of
design candidates, similar to the one shown in Figure 38 is formed. In order to avoid objective
regression, the highest-ranking design from the evaluated group, or the ‘Elite Individual’ is
53
carried over into the next Population. The designer can also choose to include a percentage of
completely randomized designs into each new Population. This can further increase the Genetic
Diversity of the design gene pool, but at the cost of computational efficiency [139]. Once a new
Population if formed the program then cycles back to the Evaluation Stage, repeating all the
functions within the Optimization Loop continuously until an optimal design is achieved, as
discussed in the following section.
3.1.7 Convergence and End Process
The Evaluation, Crossover and Reproduction stages are repeated until the convergence
conditions of the GA algorithm are met. Here the designer specifies both a maximum number of
iterations and a convergence condition. Figure 43 shows a typical convergence plot for an
optimization process, providing the designer with the best fitness evaluated during each
generational iteration and the corresponding pressure and temperature values of the design.
Figure 43: Convergence Window with Objective Tracking.
Many options exist for convergence criteria and are easily interchangeable. Designers decide
which suits the desired goals of the specific design optimization. Common end conditions can
include targeting desired temperatures or setting minimum changes in design improvements
between iterations [16]. Some designers may choose to assign a maximum computation cost to
the process (maximum iterations) with no stop condition in order to avoid a premature
convergence with a local optimal instead of a global [25]. Once the parameters defined in this
54
stage are met, the highest-ranking Individual in the final generation is output as the optimized
heat sink design.
3.1.8 Preliminary Results
In order to assess the functionality of the initial Genetic Optimization Logic outlined in the
previous sections, several preliminary optimization trails were run on a 60mm by 60mm
aluminum heat sink design space, similar to Figure 31 . The corresponding physical layout and
operating conditions are as follows: left side inlet, right side outlet, 0.1 m/s flow rate and a single
centralized SiC heat load or ‘Chip ‘dissipating ~50 Watts. The mutation rate was set to 5%, with
two parents per child each donating full width chromosome strings. Figure 44 presents the
evolution of the constructed design process applied to a mini channel starting model.
55
Figure 44: Genetic Optimization Process on a 2mm Grid Mini-Channel Design. a) Convergence
Plot. b) Intermediate Designs. c) Final Thermal-Flow Contours.
56
This example demonstrates an improved performance score from 472 to 325 over the course of
70 genetic iterations, with the final design achieving a maximum device temperature of ~322 K
with a corresponding pressure drop of 15 Pa. Analyzing the progression of the design evolution,
the Genetic Logic appears to first eliminate central fluid channels in close proximity to the heat
source. In turn this surrounds the chip with a large area of aluminum, allowing the heat to spread
away from the load due to the higher conductivity of the metal. This initial transformation leads
to significantly lower operating temperatures. The program then proceeds to slowly grow the
outer fluid channels back inwards, altering the structure of the central aluminum body. This
shape morphing is seen to gradually allow more fluid flow, reducing the system pressure yet
creating higher velocity channels that quickly remove heat from the outside edges of the
aluminum.
The allocation of solid pixels around the heat load and the formation of this central aluminum
heat spreader is found to be a reoccurring trend with the genetic design process. Figure 45
depicts how a different starting design, with similar physics yet a finer grid and larger population
size arrives to a comparable solution. The shape and volume of the metal structure tends to vary,
but the principle design traits remain the same. A central aluminum block is formed around the
chip with surrounding coolant channels.
57
Figure 45:Genetic Optimization Process on 1mm Grid Central Channel Design. a) Convergence
Plot. b) Intermediate Designs. c) Final Thermal-Flow Contours.
58
The continual reappearance through various trials indicates that this arrangement represents a
Parento-optimal solution for the given design problem. Another point of interest is that this
centralize metal heat sink shape is comparable to other genetically inspired designs found in
literature [140], like the ones depicted in Figure 46.
Figure 46: Additive Topologically Optimized Heat Sink. a) Smoothed 3D View. b) 2D Profile. -
[140]
It is also noted that final designs provided by the program can be somewhat unstructured. Post
processing contours can also be useful to clearly indicate critical bodies within the design
structure in the event that user refinements are required to achieve a more simplified,
manufacturable final product.
The preliminary optimization trials also indicate certain system variables have a noticeable
impact on the performance of the genetic optimization procedure. Smaller cell sizes applied to
the workspace section of the model were found to lead to faster convergence and better fitness.
This is assumed to be a result of the increased discretization allowing for a wider variety of
potential design solutions and the finer grid formation producing thinner channels to increase the
rate of heat removal. The user specified population size was seen to represent a clear
fundamental trade-off between performance and computational efficiency. Faster convergence
and better fitness result from larger populations of design candidates at the cost of processing
time. Increasing the size of design options for each iteration raises the chance a Parento-optimal
result will be generated during a given generation. However, this comes at a high computational
cost, drastically increasing the potential of ‘inferior designs’ being generated and evaluated
during each iteration, which add little benefit to the optimization process. These traits help
characterize the constructed design process and identify key parameters that can be fine-tuned in
order to achieve the maximum design improvements.
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3.2 Stage II: Integrating Three-Dimensional Liquid Heat Sink Topologies
The coding developed in the previous section laid the framework for a novel optimization
process base on the principles of Genetic Algorithms. However, the initial models used to
represent potential heat sinks designs do not accurately capture the complexities of three-
dimensional flow or the intricacies of advance electronic systems. In order to develop a program
better suited to the design of real electronic heat sinks, a more powerful simulation tool was
needed to pair with the existing genetic loop. The AAS Toolbox and scripting communication
established by the existing code bridged the gap from ANSYS to MATLAB, allowing automated
access to any application within the Workbench. This allows the Genetic Logic to access a
variety of FEM and CFD based simulations tools, including those more equipped to handle
electronic systems.
This move towards more advanced, real world models, lead to the integration of ANSYS Icepak,
a software application specific to the thermal and fluid flow analysis of electronic assemblies. A
variety of new modeling techniques and unique design capabilities were made possible by the
inclusion of this new simulation tool, discussed in the following section. However, moving the
optimization process from simple two-dimensional geometries to more complex three-
dimensional structures required several alterations to the existing code, which is detailed in
Section 3.2.2.
3.2.1 ANSYS Icepak
Modern power electronic devices have compact packaging and rigid temperature constraints that
require the design of superior thermal management systems to ensure reliable performance and
avoid product degradation or failure. Accurate computational modeling is the key to achieving
and validating these thermal designs without the costly process of repeated experimental
prototyping.
ANSYS Icepak is a CFD based simulation tool within the ANSYS workbench, specific to
electronic devices and electromechanical systems. Usually tied to a CAD modeling tool, as seen
in Figure 47, Icepak allows for the thermal and flow analysis of complex design characteristics,
unique to compact electronics.
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Figure 47: Typical Icepak Workflow.
Utilizing a FLUENT based CFD solver, Icepak calculates Conduction, Convection and Radiation
heat transfer with efficient accuracy. The automatic Unstructured Hex-Dominant meshing allows
the software to capture small geometric details such as thin solder layers, devices packages and
other small components. Non-conformal meshing tools allow designers to separately mesh and
store critical areas within system designs, making it ideal for design optimization and running
iterative simulations. Due to the unique features it offers, Icepak is becoming an increasingly
populator tool for thermal and electrical engineers for design validation [141], [142]. A typical
progression of an Icepak design analysis is present in Figure 48 with a simple half bridge
converted constructed on a ceramic DBC module and a ruffled fin heat sink.
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Figure 48: Example Icepak Project on Half-Bridge DBC Converter Module.
Icepak also contains more advanced modelling capabilities for complex objects such as
semiconductor packaging [Figure 49], or ECAD importing for trace layers and copper vias
[Figure 50]. Key design components, such as these, can heavily influence the thermal profile of
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the respective system. Accurately capturing the heat transfer throughout the design structure is
essential for the genetic algorithm to optimally allocate liquid channels. For these reasons,
ANSYS Icepak was chosen as a simulation tool for evaluation of the heat sink topologies
generated by the genetic optimization process.
Figure 49: Icepak Semiconductor Package Design.
Figure 50: Icepak ECAD Import Structure.
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3.2.2 Changes to Modeling Procedure and Genetic Functions
While much of the code established in Section 3.1 remained valid, several key areas of the
genetic logic had to be adjusted in order to compensate for the three-dimensional models and the
incorporation of Icepak evaluations into the programming structure.
3.2.2.1 Initial Modeling
The main area of focus for the new process centers on the initial stage of Model Construction
and Workspace Initialization, presented earlier in Section 3.1.1. With the move towards more
complex geometries, the modeling procedure in turn is more complex:
1. Starting with an existing Electrical Layout , the users adds three main additional regions:
Optimization Workspace, Heat Sink Shell and Inlet/Outlet Bodies [Figure 51].
Figure 51: Workflow of Model Construction.
2. The Optimization Workspace is then partitioned into a series of three-dimensional voxels
[Figure 52], with user defined dimensions corresponding the desired height, width, and
depth of the liquid channels
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Figure 52: Partitioning of Optimization Workspace with Three-Dimensional Voxels.
3. Each voxel is assigned a sequential label, dictated by its positioning within the
Workspace [Figure 53].
Figure 53: Indexing Workspace Elements.
4. Design Modeler Scripts are used to active Boolean functions [Figure 54a], which select
the ‘Liquid’ voxels to be combined with the Inlet/Outlet bodies to form the fluid domain
[Figure 54b], while the remaining voxels are combined with the Heat Sink Shell to form
the solid domain [Figure 54c]
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Figure 54: Formation of Heat Sink Topology. a) Allocation of Structural Elements via Design
Modeler Boolean Functions. b) Forming Fluid Domain. c) Forming Solid Domain. d) Initial Seed
Model.
5. The user then transfers the CAD structure into an Icepak project, setting the desired
operating conditions, material properties and meshing parameters in the local GUI
[Figure 55]
Figure 55: Setting Simulation Conditions in Icepak GUI
6. Lastly, the user selects the desired performance values in Icepak they are seeking to
optimization [Figure 56a], defining them as Output Variables, with the final Workbench
structure taking the form of Figure 56b.
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Figure 56: Defining Output Parameters. a) Icepak GUI. b) Variables Exported from Workbench
Project as CSV File.
Unlike the Stage I program, this modeling procedure is carried out ahead of the optimization
process. This allows designers the flexibility to carry out intricate studies on the initial model,
such as mesh independency, sensitivity analysis or even experimental validation. Once a suitable
architecture is achieved, it is exported and saved as a Workbench (.WBPZ) file.
3.2.2.2 Grid Indexing
Upon activation, the genetic programming launches ANSYS in server mode and loads the
corresponding Workbench Project file, constructed in the previous section. The voxel and
workspace data is extracted in a similar fashion as demonstrated in Section 3.1.2, to construct a
three-dimensional Global Array of indexed values, depicted in Figure 57.
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Figure 57: Formation of Three-Dimensional Global Array.
3.2.2.3 Mutate Seed Design
The Seed Mutation process, outlined in Section 3.1.3, is carried out on the 3D model. Binary
voxel values within the optimization workspace are randomly altered at a low probability to form
a starting Population of Design Candidates, like the one shown in Figure 58.
Figure 58: Mutating the Three-Dimensional Workspace to Achieve New Fluid Domain.
3.2.2.4 Validation
The same binary validation methods presented in Section 3.1.4 are applied to the new three-
dimension liquid topologies to ensure that no blocked flow channels or floating solid/liquid
bodies are generated by the mutation process.
3.2.2.5 Evaluation
With the integration of Icepak into the design Evaluation, small alterations were made to the file
structure of this stage. As was the case in Section 3.1.5, new design candidates generated by the
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Genetic Logic take the form of solution vectors (xFE) containing the element values to be
allocated as fluid blocks. When evaluating a new Individual, the MATLAB code uses the
information within the solution vector to write a corresponding DM script. The script structure
first clears the previous topology by deleting the existing Boolean functions [Figure 59a,b],
mentioned in Section 3.2.2.1, responsible for forming the Fluid and Solid Domains. The file then
implements a new set of Boolean functions, selecting the fluid elements provided by xFE [Figure
59c] and combining then with the Inlet and Outlet bodies to form the new Fluid Domain. As
before, a second Boolean combines the remaining voxels with the Heat Sink Shell to form the
Solid Domain [Figure 59d].
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Figure 59: Operations for Generating New ANSYS Models. a) Starting with Previous Design. b)
Clearing Liquid and Solid Boolean Functions. c) Selecting New Fluid Elements. d) Reapplies
Boolean Functions to Generate New Design Topology.
Since the Workbench project and Icepak conditions are defined prior to the start of the genetic
program [Section 3.2.2.1] and activated during the Indexing Stage [Section 3.2.2.2] there is no
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need to resend the simulation parameters to ANSYS. Once the new topology is successfully
uploaded and formed in DM, the MATLAB code simply sends a command to update the entire
workbench process, with new heat sink geometry. With the Icepak parameters already set, each
Design Candidate will be automatically meshed and evaluated under the same conditions.
Once Simulated, the output parameters set during the Initial Modeling Stage [Section 3.2.2.1] are
exported in a CSV document and read into the MATALB coding structure. The performance of
each design is evaluated on the basis of a new Fitness Function, defined by (Eq. 3.4).
𝑭𝒊𝒕𝒏𝒆𝒔𝒔 = 𝒂 (𝑻𝑫𝒆𝒗𝒊𝒄𝒆𝒔
𝑻𝑫,𝑩𝒂𝒔𝒆) + 𝒃 (
∆𝑷𝒊𝒏𝒍𝒆𝒕−𝒐𝒖𝒕𝒍𝒆𝒕
∆𝑷𝑩𝒂𝒔𝒆) (3. 4)
The Temperature and Pressure values of the initial seed design (TD,Base, ΔPBase) are integrated into
the exiting Fitness Function (Eq 1.3) to normalize the output variables of each Design Candidate.
This allows the program to measure and track the design improvements induced by the genetic
process using the starting model as a base reference.
3.2.2.6 Selection, Crossover and Mutation
Once an entire Population of Design Candidates is evaluated and ranked, a new Generation of
Child designs is formed, following the procedure laid out previously in Section 3.1.6.
3.2.2.7 Convergence and End Process
Criteria for convergence of the new optimization program follow the same principles previously
described in Section 3.1.7. With the changes to the fitness scoring [Section 3.2.2.5], the new
convergence tracking window takes the form of Figure 60. Both pressure and temperature values
for the highest performing design in each Generation are still displayed for user convenience.
However, the fitness scores are presented as a factional value in comparison with the starting
design performance score of 1.
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Figure 60: Stage II Convergence Window with Objective Tracking.
Unlike the Stage I program, once optimization convergence is met, the Stage II program outputs
a full three-dimensional model in STEP format. This allows designers to continue analysis or
refinements on the resulting geometry, which make for easy prototyping and experimental
validation of the optimized structure.
3.3 Overview of Genetic Optimization Process for Three-Dimensional Liquid Heat Sinks
By combining the custom GA structure, presented in Section 3.1, with the computational power
of ANSYS Icepak, detailed in Section 3.2.1 and the changes presented in Section 3.2.2, a final
optimization program was achieved, capable of analyzing three-dimension liquid cooled power
electronic systems and intelligently generating optimal design solutions. Dividing the
Optimization Workspace of the heat sink model into an array of voxels and tying these structural
elements to representative bit arrays allows the MATLAB code to quantify the improvements
made by the genetic process, learning the optimal layout of liquid and solid materials, specific to
a given electrical design. The general workflow of this process, demonstrated in Figure 61,
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targets the topologically structure of the main heat transfer area within electronic-thermal
systems.
Figure 61: Design Progression of Genetic Optimization Process.
The nature of the GA program allows binary strings associated with high ranking designs to
carry on through the iterative process, building on the design improvements of the previous
Generation. By cycling through Populations of Design Candidates, the coding structure produces
novel heat sink topologies that adapt to the specific thermal profile of the designated electrical
load, including any trace layers, thermal vias or bonding materials. In addition, the performance
of the three-dimension models should account for the materials of the associated simulations,
capturing any important physical occurrences, such as areas of induced turbulence, thermal
spreading through conductive metals or convective heat dissipation. A complete overview of the
main program code, constructed in MATLAB R2018a, and all associated functions responsible
for the various stages of the genetic optimization process are presented in the Appendix.
Further analysis on the influence of environmental parameters on the optimization procedure is
presented in the following chapter. Another important aspect to consider is the impact of genetic
variables, such as population size, breeding parameters or fitness scoring, on the performance
nature of the GA code.
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Chapter 4
Simulation Results & Discussion
The Binary Genetic Optimization Process, constructed in Chapter 3, was found to provided novel
designs when applied to the topological optimization of liquid channels within electronic heat
sinks. As populations of potential designs are evaluated following this “Survival of Fittest”
methodology, engineering designs run through the program can only be improved upon. This
coding structure follows a simple learning process, associating binary patterns with high fitness
scores as good design structures within the simulation environment. However, the nature of this
learning process is heavily influenced by user-controlled factors, such as fitness scoring,
mutation rates and ranking procedures. Furthermore, environmental conditions defined in the
simulation space, such as applied materials, ambient settings or inlet parameters, can have
considerable impact on the nature of the automated design process.
In this chapter we seek to investigate the influence of several key operating factors on the
effectiveness of the Genetic Optimization Process. Section 4.1 introduces a compact, electrical
Half-Bridge (HB) converter design, that acts as the base test model for the simulation test carried
out in this chapter. Section 4.2 presents a ‘Case Study’ example of the optimization process,
detailing each stage associated with initializing and optimizing the base model through the
genetic design procedure. Building on the results of the Case Study, Section 4.3 investigates the
influence of key fitness values and environmental inlet conditions on the design procedure and
resulting optimized structures.
4.1 Introducing the Test Model
In order to characterize the genetic programming, a base model is used to standardize the
geometric layout associated with the various simulation-based assessments. This is done to
ensure a constant structure is utilized across all the various conditions being tested. Moreover, by
applying a consistent electrical heat load and thermal profile, both the qualitative and
quantitative adaptations induced by different tests variables can be compared and analyzed
accordingly.
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The base model, shown in Figure 62. focused around a compact, Half-bridge (HB) converter
design that utilizes two GaN power transistors along with corresponding drivers and a variety of
other passive components. The chosen converter scheme was as a suitable electrical model due
to its flexibility and versatility within power electronic applications. HB modules can be
arranged as both buck or boost converters, or replicated to create full-bridge or three-phase
systems [143].
Figure 62: Base Model for Simulation Testing.
The electrical layout was tailored to a DBC design structure [Figure 63], employing AlN as a
thermal conductive dielectric layer with top copper traces, for electrical routing and a bottom
copper layer for heat spreading.
Figure 63: Electrical DBC Design.
The heat sink geometry is comprised of thin copper layers directly integrated into the DBC
structure [Figure 64a]. This style of design is meant to mimic highly conductive 3D printer heat
sinks or advanced integrated coolers, similar in style to those presented in Section 2.4.4. With
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bottom side inlet and outlet manifolds [Figure 64b] the resulting thermal management system
maximizes the active heat transfer area while maintaining a compact overall design.
Figure 64: Compact HB Heat Sink Design. a) Integrated Cooler Approach. b) Inlet/Outlet
Manifold Design.
The main area heat sources or HDD for this base model take the form of two GaN power
transistors, shown in Figure 65a. These 650V devices from GaN Systems allow for high
switching frequencies resulting in better power conversion efficiencies and lower thermal losses
in comparison to other integrated circuit technologies. The compact packaging allows for high
rate of heat removal from the bottom trace layouts, seen in Figure 65b. Manufacturer provided
data specifies the junction-to-case thermal resistance values of the internal semiconductor
packaging [Table 3] providing accurate temperature modelling for these heat loads.
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Figure 65: GaN Power Transistors. a) GaN Systems GS66508B Schematic. b) Corresponding
CAD Model.
Table 3: GaN Transistors Manufacturer Provided Thermal Characteristics.
Parameter Value Units
Thermal Resistance (junction-to-case) - Bottom Side 0.5 °C/W
Thermal Resistance (junction-to-top) 8.5 °C/W
Thermal Resistance (junction-to-ambient) 24 °C/W
Maximum Soldering Temperatures (MSL3 rated) 260 °C
Another important aspect of this base model is the nature of the heat flux pattern from the
transistors to the integrated heat sink system. The footprint of the GaN devices on the ceramic
PCB, as shown in Figure 66, creates an irregular pattern for heat flow. This nonuniform
arrangement is an ideal candidate for the genetic optimization process, providing an unorthodox
thermal profile for program to capture and adapt to.
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Figure 66: Footprint of Heat Sources on PCB.
Furthermore, the positioning and orientation of these devices on the PCB, along with the layout
of the copper traces makes it difficult to reduce the model with conventional methods, such as
symmetry reduction or shape simplification. Thus, Icepak is the practical tool for this design,
encompassing important physical aspects, which would otherwise be difficult or infeasible to
incorporate.
4.2 Case Study
With the base model established in the previous section, the functionality of the genetic program
is demonstrated, under constant conditions, on a standardized geometry in order to better
quantify its behavior and effectiveness as a design optimization tool. This section presents a
detailed description of the genetic optimization process constructed in Chapter 3, applied to the
cooling structure of the integrated HB converter module presented in Section 4.1. All user
defined steps associated with preparing the model, defining the simulation environment and
initializing the optimization process are described. Intermediate designs generated by the
iterative program are presented, along with detailed comparisons of the improvements introduced
between the starting and ending geometries.
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4.2.1 Preparing the Seed Model
Before any testing can be carried out on an electrical cooling structure, designers must attempt to
reduce the complexity of the given model down to the main components responsible for design
performance. Removing trivial components, simplifying flow regimes or decreasing the overall
geometric size of an electronic thermal system can significantly reduce the computational cost
associated with the simulation portion of the optimization process. For this purpose, several
important changes were made to the base converter module, shown in Figure 62, in order to
create a design more suited to the optimization process:
1. Passive components, off-board connectors and unnecessary signal traces were eliminated
from the electrical design to avoid meshing objects with little to no impact on thermal
performance [Figure 67].
Figure 67: Electrical Simplification of HB Converter System.
2. The lower half of the integrated cooling structure, which included the inlet/outlet
connections and associated manifolds shown in Figure 64, was removed from the overall
design structure Figure 68. This action greatly reduced the complexity of the fluid
domain without sacrificing the accuracy of the pressure drop calculations across the heat
sink.
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Figure 68: Simplification of Fluid Domain. a) Elimination of Manifold Sections. b) Comparison
of Old vs New Inlet/Outlet Connections.
Once the design simplifications were carried out on the base model, an active workspace was
defined for the program to optimize. For the given system, this took the form of the main area for
active heat transfer [Figure 69a] within the integrated cooling structure. By partitioning this
region into a series of voxels with predetermined physical dimensions [Figure 69b] a three-
dimensional array of structural elements was formed, representing the optimization workspace
[Figure 69c]. The dimension of these voxels were chosen to correspond with reasonable copper
etching techniques as well as ensure minimal channel dimensions were suitably sized to avoided
blockages cause by debris particles [76].
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Figure 69: Generating Optimization Workspace for HB Convert Model. a) Defining Active and
Passive Regions. b) Sizing Structural Voxel Elements. c) Partitioning Active Region into Array
of Workspace Elements.
The final step in preparing the optimization model was to generate a starting seed design for
initializing the genetic process. This was done by forming the optimization workspace into a
standard crossflow channel arrangement, shown in Figure 70.
Figure 70: Forming Base Optimization Model into Starting Seed Design.
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4.2.2 Defining the Simulation Environment
With a defined optimization model and a starting seed design [Section 4.2.1] the initial structure
could be brought into the Icepak simulation space in order to set the meshing parameters and
operating characteristics of the simplified HB system [Figure 71]. Standard flow rate conditions
were applied to the inlet boundary, assuming an insulated environment with no natural
convection to the local surroundings. The GaN power transistors were modeled as Icepak
network blocks, integrating the junction-to-case thermal resistances detailed in Table 3.
Assuming an operating point of 2kW and a conversion efficiency of 98% the junction power of
each device was set to dissipate 40 Watts of thermal energy. A 0.1mm thick layer of Pb-50/Sn-50
Solder was applied as a bonding layer between the GaN devices and the corresponding power
traces. The remaining materials properties associated with the major components of the
integrated HB system applied in Icepak and can be seen in Table 4.
Figure 71: Icepak Modeling Environment & Example Surface Mesh.
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Table 4: Icepak Material Assignments.
Icepak Component/Body
Description Applied Material
Density (ρ)
Thermal Conductivity
(kth)
Specific Heat
Capacity (cp)
Transistor Semiconductor Packaging
Transistor elements, dissipating heat to simulate electrical losses in energy conversion
Gallium Nitride
(Modelled as
Network Block)
6150 kg/m3 130 W/mK 490 J/kgK
Transistor Pads Source, Drain and Gate pads located on backside of transistors. Main path for heat transfer between semiconductor junction and integrated PCB cooling structure
Copper (Pure) 8933 kg/m3 387.6 W/mK 385 J/kgK
Device Bonding Material Layer of electrically conductive metal used to bond transistor pads to top power/signal traces
Solder -
Pb50/Sn50
8890 kg/m3 46 W/mK 213 J/kgK
DBC Traces (Top & Bottom)
Thin layers of conductive material representing the power & signal traces of the electrical design
Copper (Pure) 8933 kg/m3 387.6 W/mK 385 J/kgK
Ceramic Substrate Dielectric body within the PBC used to isolate the energized components from the liquid cooling structure
Aluminum
Nitride
3300 kg/m3 200 W/mK 712 J/kgK
Heat Sink Body Solid elements associated with the generated cooling structure
Copper 8933 kg/m3 360 W/mK 385 J/kgK
Fluid Domain Fluid elements associated with the generated cooling structure
Water (@ 320K) 989 kg/m3 0.637 W/mK 4177 J/kgK
Cabinet Fluid filled cavity surrounding the structural model. Represents the ambient environment of the given system.
Air 1.1616 kg/m3 0.0261 W/mK 1005 J/KgK
Once the simulate environment for the convert module was fully defined, the entire ANSYS
project, along with the associated optimization model, mesh data and operating parameters, was
stored as a .wbpj file. This allows the full project to be archived and activated when called by the
optimization program for design evaluations.
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4.2.3 Initializing Genetic Logic
Having defined the parameters of the optimization model within the simulation environment, the
main genetic program is then activated. The primary code, constructed in MATLAB, controls the
progression of the GA workflow [Figure 29] and utilizes a variety of functions that
corresponding to for different stages of the optimization process [See Appendix].
There are a number of user defined factors that must be specified before the program can begin
the iterative design process, the most important of which, is the objective fitness function. This
equation, represented in (3.4), represents the programs interpretation of the designer’s
optimization goals. Objective weighting values, integrating different performance variables or
applying exponential scoring techniques are just some ways users can control the nature of the
genetic program. It is important to properly communicate the purpose of the given design
process for it to produce suitable optimized topologies. In the case of this trial the given fitness
function is represented by (4.1), putting more emphasis on the reduction of transistor junction
temperatures and less on the resulting hydraulic system pressure.
𝑭𝒊𝒕𝒏𝒆𝒔𝒔 = 𝟎. 𝟕 (𝑻𝑫𝒆𝒗𝒊𝒄𝒆𝒔
𝑻𝑫,𝑩𝒂𝒔𝒆) + 𝟎. 𝟑 (
∆𝑷𝒊𝒏𝒍𝒆𝒕−𝒐𝒖𝒕𝒍𝒆𝒕
∆𝑷𝑩𝒂𝒔𝒆) (4. 1)
Once a scoring mechanism is implemented the next important aspect to consider is optimization
convergence. These user defined conditions dictate when the program will classify the iterative
process as complete and provide a final optimized heat sink design. In order to avoid premature
convergence and set a standardized stop condition for further comparisons, the convergence was
defined by a maximum iterative value of 15. This indicates the GA program will evaluate 15
generations of design candidates, at which time it will provide the highest performing model as
the final optimized design.
Another significant variable to consider when initializing the program is the desired Population
size associated with the genetic logic. This specifies the number of design candidates the
program will evaluate and reproduce during each iteration. Increasing this value can have a
significant impact on the computational cost of the evaluation stage, as the program must
simulated each individual design. However, the greater the pool of design candidates the better
chance the program will generate an improved model. Given the mesh size associated with the
HB converter model, a Population size of 10 designs per Generation was chosen.
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Once the central parameters of the genetic logic were established the remaining genetic
variables, shown in Table 5,were applied and the optimization process was initiated.
Table 5: Genetic Variables for Case Study Trial.
User Defined Variable Associated Stage Description Applied Value
Mutation Probability Selection, Crossover & Mutation
Probability that a binary value within a newly generated design candidate will invert
5%
Seed Mutation Probability Mutating Seed Design Probability that a binary value within the initial seed design will invert when generating the initial population of design candidates
50%
Number of Breeding Parents
Selection, Crossover & Mutation
Number of parent designs, randomly chose from the previous generation, to be bred together in order to form a new child design
2 Parents Per Child
Gene String Size (Crossover Point)
Selection, Crossover & Mutation
Number of binary values to pull from a randomly chose parent design to donate to a newly forming child design
17 Genes Per Parent
Elite Individuals Repopulation Number of highest performing design candidates within an evaluated generation to be retained and brought into the next population of candidates
1 Individuals Per Generation
Random Individuals Repopulation Number of randomly generated design candidates to include in each new generation
2 Individuals Per Generation
The optimization process begins by launching ANSYS Workbench in server mode, activating the
MATLAB AAS toolbox to enable communication and then uploading the previously established
project file, containing the starting design structure, the Icepak simulation environment and the
defined output performance variables. The program then pauses, allowing the user to inspect the
contents of the project file and make any necessary modifications. After reviewing all geometric
and simulation-based conditions are properly defined, the user then triggers the main GA
process, allowing the program to iteratively optimize the given geometry on the basis of the
provided simulation environment and the desired design objectives.
4.2.4 Design Optimization
The HB integrated converter module, presented in Section 4.1 and simulated under the
conditions detailed in Section 4.2.2, was put through the genetic optimization process for 15
design iterations. Although this program was implemented on a 14 core Dell Precision 5820
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Tower with an Intel Xeon 2.5GHz CPU and 32 GB of installed RAM, ANSYS only allows 4
cores to be freely utilized with their Icepak products. Utilizing additional cores would improve
computational speed by require the purchasing of additional licenses from ANSYS Inc. The
result was a total computational run time of 31 hours 18 minutes, generating four increasingly
improved heat sinks designs before reaching the maximum iteration count. The final model
produced by the optimization program achieved a 13.2% improvement in overall fitness
performance as compared to the starting design.
The progression of the design improvements can be seen in the associated objective tracking
window, shown in Figure 72. From the presented data, it can be seen that the genetic
optimization program was responsible for a 138 Pa drop in system pressure with a junction
temperature reduction of ~1.3°C for the GaN power transistors. The random nature of the GA
breeding process significantly reduced both temperature and pressure values within the first
generations. Between the 2nd and 4th iterations, the program began to balance the two objectives,
arriving at a Parento-Optimal solution by the 5th generation of the design process.
Figure 72: Objective Tracking Window for HB Converter Case Study.
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The progression of the physical design structure is depicted in Figure 73, representing each new
heat sink topology by its corresponding fluid domain. The genetic process appears to retain the
general structure of the original crossflow channel arrangement. However, by integrating more
liquid channels into the multi-level workspace and inducing small changes in the top-level flow
layout, the program is able to significantly reduce system pressure while increasing the spread of
thermal energy throughout the heat sink structure.
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Figure 73: Design Progression of Case Study Optimization Process.
The unique footprint of the transistor pads results in the formation of several hotspots on the
PCB. As seen in Figure 76a, these areas experience concentrated heat flux as thermal energy
transfers from the GaN devices into the integrated cooling structure. The optimization process
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appears to target these areas, enhancing heat transfer and significantly reducing the local
temperature gradients on the PCB, as seen in Figure 74b.
Figure 74: Comparing PCB Temperatures Contours. a) Starting Seed Design. b) Final Optimized
Design.
The noticeable reduction in lateral heat spreading within the PCB structure is believed to be a
result of the increased liquid channel density generated by the optimization program. By
allocating layers of fluid channels throughout the three-dimensional workspace the pressure
experienced by the inlet region [Figure 75a] as well as the corresponding gradients across the
flow regime are greatly improved [Figure 75b].
Figure 75: Comparing Fluid Domain Pressure Contours. a) Starting Seed Design. b) Final
Optimized Design.
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Furthermore, comparing the cross-sections of the HB system [Figure 76] shows how the
arrangement of these liquid channels, generated by the GA program, enhance the thermal
dissipation throughout the heat sink structure. Utilizing the high conductivity of the metal heat
sink material, the fluid network is distributed throughout the body of the integrated system,
targeting hotspots and reducing temperature gradients. The end result is a much more uniform
thermal distribution throughout the designated cooling structure.
Figure 76: Comparing Cross-Sectional Temperature Contours of Heat Sink Cooling Structure.
a) Starting Seed Design. b) Final Optimized Design.
The random nature of the genetic design process combined with the thermal modeling
capabilities of ANSYS Icepak and freedom of a three-dimensional optimization workspace
proves to be an innovative approach to electronic heat sink design. Applying the principles of
topology optimization to the layout of fluid channels within pressurized cooling structures, the
GA can adapt to the specific needs of a given electrical system, improving on traditional
engineering designs and producing unconventional geometric solutions.
4.3 Optimization Testing
The functionality of the proposed optimization process, demonstrated through the initial case
study [Section 4.2], proves its ability to adapt the flow structure within the defined workspace, to
improve heat sink performance for the designated thermal load. However, there are a large range
of variables associated with these simulation environments as well as the underlying genetic
logic that can influence the operation of the design process as well as the corresponding
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generated structures. In order to investigate these parameters, several design comparison studies
were carried out, isolating specific variables within the optimization process.
4.3.1 Weighting Fitness Function
The scoring function presented in (Eq. 3.3) represents the programs interpretation of the thermal
performance associated with each simulated geometry. Moreover, this formula governs the
ranking procedure for each population of potential design candidates, dictating the logics
understanding of ‘Good’ and ‘Bad’ performing designs. Thus, the weighting values applied to
each design objective can directly influence the intelligence of the genetic optimization process.
In order to study the impact of these variables, two different optimization procedures were run
with the same starting seed model and simulation conditions presented in the Section 4.2 case
study. However, each design procedure was performed with varying objective weightings, such
that the resulting topologies generated by each optimization trial could be compared. The
parameters of the fitness testing were as follows:
• Design 1: Optimized with objective weightings of a = 1.0, b = 0.0 such that no
considerations were given to the pressure drop of the heat sink liquid domain and fitness
scoring was only on the basis of reduced device temperatures
• Design 2: Optimized with objective weightings of a = 0.7, b = 0.3 such that the scoring
was biased to the reduction of device temperatures while some consideration was given
to the corresponding system pressure
The design progression and final structures generated by each optimization trial is presented in
Figure 77.
91
Figure 77: Convergence and Optimized Fluid Topologies for Fitness Testing. a) Temperature
Dependent Fitness Scoring (a=1, b=0). b) Temperature Biased Fitness Scoring (a=0.7, b=0.3).
Each optimal model produced by the designated genetic optimization trails were tested under
constant conditions to investigate the impact of these fitness weighted values on the performance
characteristics of the resulting geometries. Device temperatures and system pressure for each
design was assessed and compared to that of the starting seed model as depicted by the graph in
Figure 78.
92
Figure 78: Performance Comparisons of Fitness Testing Models.
From the resulting data it is clear that the weighted fitness values can control the nature of the
proposed optimization process. By applying a completely temperature-based scoring system, the
Design 1 process [Figure 77a] achieves small improvements in the flow geometry over the
course of its design cycle, reducing final device temperatures by approximately 3°C, while the
Design 2 model is found better balance the pressure and temperature improvements over the
course of its design cycle [Figure 77b]. The allocation of solid metal elements in the Design 1
heat sink, centered around the transistor pads creates a chaotic fluid regime with high
corresponding pressure requirements when compared to the starting seed model. The more
balanced fitness equation applied to the Design 2 process better ingrates the pressure aspects of
the design performance. The resulting Design 2 model, shown in Figure 77b, utilizes a more
uniform, multilevel, crossflow arrangement, allowing for improved pressure gradients across the
fluid domain while still achieving significant reductions in the device temperatures.
The results presented in Figure 77 clearly indicate that the fitness scoring can be an effect means
of altering the nature of the genetic optimization process and resulting geometries. Designers
can utilize the objective weighting values and tailor the programs evaluation scoring to either
target specific design goals or aim to produce more balanced, optimized models.
0
500
1000
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51
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Pre
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Pa)
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Fitness Function Weighting
Device Temperature System Pressure
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4.3.2 Inlet Temperature Variation
The inlet conditions of the fluid domain, especially that of the available coolant temperature
TFluid,In, can vary depending on the systems location and function within an EV cooling loop.
However, designers have to apply constant values when assessing their thermal models and
commonly assume higher inlet temperatures to simulate ‘worst case’ conditions. Thus, it is
important to investigate the potential impact of designer specified conditions, such as TFluid,In on
the functionality of the genetic optimization program. Similar to the fitness tests of Section 4.3.1,
three different optimization procedures were run with the same standardized seed model and
simulation conditions. Each trial employed a different temperature with respect to the fluid inlet
boundary so that the resulting designs could be analyzed. The applied conditions were as
follows:
• Design I: Optimized with an applied inlet temperature of 0°C
• Design II: Optimized with an applied inlet temperature of 15°C
• Design III: Optimized with an applied inlet temperature of 50°C
The design progression and final structures generated by each optimization trial is presented in
Figure 79.
94
Figure 79: Convergence and Optimized Fluid Topologies for Inlet Temperature Testing. a) 0°C
Inlet Fluid. b) 15°C Inlet Fluid. c) 50°C Inlet Fluid.
95
Following the comparative nature of Section 4.3.1, each optimal model produced by the inlet
temperature optimization trails were tested under constant conditions to investigate the impact of
this environmental condition on the performance of the genetic program. Device temperatures
and system pressure were calculated and compared to the starting seed model as depicted by the
graph in Figure 80.
Figure 80: Performance Comparisons of Inlet Temperature Testing Models.
Altering the physics of the fluid domain associated with these optimization trials had noticeable
influence on the resulting structures. From Figure 79, it appears that the trials run with lower
inlet temperatures allocated more solid elements into the fluid domain, specifically in proximity
to the area of high heat flux. It is assumed that this is a result of the program utilizing the high
temperature differentials offered by the inlet fluid, to easily achieve design improvements when
combined with the heat spreading induced by the thermal conductive metal elements. However,
when comparing the results of the Design I and II models to the Design III model [Figure 80], it
is clear that the optimization trials associated with higher TFluid,In conditions produced better
performing overall designs. It is assumed that the lower thermal gradients offered by the high
inlet temperature environments cause the genetic program to target the convective heat transfer
offered by the fluid regime as a means of achieving better design improvements and higher
fitness scores. By spreading the flow area across the defined workspace and increasing the
0
50
100
150
200
250
300
350
400
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50.8
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Seed Design I Design II Design III
Pre
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Pa)
Tem
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°C)
Inlet Temperature Testing
Device Temperature System Pressure
96
surface area of the fluid domain the program was able to attain higher rates of heat removal.
Moreover, comparing the fluid domains of the respective optimized models, Design I [Figure
79a] is found to have significantly less flow blockages that the Design II and Design III
structures [Figure 79b-c], allowing it to achieve the lowest comparative pressure drop.
The results of this testing indicate a motivation for designers to continue the practice of applying
‘worst case’ conditions to the inlet boundaries, even in the case of the proposed optimization
process. This forces the genetic logic to better identify patterns that increase relative convective
heat transfer and not rely on thermal spreading techniques which fall short when high liquid
temperatures area applied.
4.3.3 Flow Rate Variation
Some environmental conditions associated with the simulations of these liquid heat sinks are
predefined by the desired application. A common example of this is the coolant flow rate QFluid,
which is applied to the inlet boundary of the fluid domain. This rate is usually a predetermined
value, dictated by the pumping conditions of the associated automotive cooling system.
However, the available flow rate of the fluid domain is a significate system parameter that can
impact the thermal performance of any heat sink design. Thus, it is important to assess the
impact of this variable on the programs ability to a generate optimal heat sink topologies. The
standard conditions of Section 4.2 were once again applied to three different optimization trials,
each defined with a different coolant flow rate as follows:
• Design A: Optimized with an applied inlet flow rate of 0.25 LPM
• Design B: Optimized with an applied inlet flow rate of 0.5 LPM
• Design C: Optimized with an applied inlet flow rate of 1 LPM
The design progression and final structures generated by each optimization trial is presented in
Figure 81.
97
Figure 81: Convergence and Optimized Fluid Topologies for Flowrate Testing a) Inlet Flow 0.25
LPM. b) Inlet Flow 0.5 LPM. c) Inlet Flow 1.0 LPM.
Once again, each optimized model was simulated under constant conditions to compare their
corresponding design characteristics in relation to the starting seed design model Figure 82.
98
Figure 82: Performance Comparisons for Flowrate Testing Models.
The results of the flow rate testing appear to reinforce the findings of the Section 4.3.2, such that
the models produced under the lower flow rate environments outperform those optimized with
higher flow rates [Figure 82]. The resulting structures, shown in Figure 81, exhibit similar design
traits to those produced during the inlet temperature testing. The low levels of convective heat
transfer offered by the Design A flow rate, cause the optimization program to spread the fluid
domain throughout the workspace, increasing surface area and heat removal while
simultaneously reducing system pressure. The higher flow rates, applied to the Design B and
Design C simulation environments offered better initial heat remove, such that the optimization
program positioned more solid elements close to the transistors source areas, as a means of
thermal conductive heat spreading. Moreover, it is assumed that applying high coolant flow rates
to the simulation environments result in high initial system pressures, such that the optimization
program can attain more dramatic improvements in fitness scoring by focusing on reducing
pressure gradients across corresponding heat sink designs in leu of improving waste heat
removal.
The results of this section support the notion that applying extreme or ‘worst case’ conditions to
the simulation environment causes the genetic optimization program to identify better design
traits within the defined workspace.
0
20
40
60
80
100
120
140
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Pa)
Tem
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ratu
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°C)
Inlet Flow Testing
Device Temperature System Pressure
99
Chapter 5
Conclusion
As stated in Section 1.2, this thesis investigates the construction of a design optimization
program, utilizing a genetic binary methodology to produce optimal three-dimensional heat sink
structures for use with high power EV electronics. Approaching the layout of the flow regimes
within these heat sink designs as a topological optimization problem, the workflow of the
genetically inspired process captures the thermal characteristics of a given electrical system to
effectively tailor the corresponding heat sink structure, maximizing waste heat removal and other
performance objectives. The resulting program is an effective tool for achieving significant
improvements in the design and prototyping of compact liquid heat exchangers for high output
power electronics.
5.1 Contributions
A review of the existing literature predicts a continued increase in the energy density
requirements of power electronics, specifically in the case of EV/HEV technologies. A variety of
innovative methods for manufacturing compact, high performing cooling systems are being
explored in attempt to address the growing issue of proper thermal management for these
electronic devices [Section 2.1 - 2.4]. With greater constraints on weight, volume, performance
and reliability, the EV industry is being to beginning experience a need for more creative
methods of design optimization [Section 2.5]. Most techniques seek to achieve design
improvements by finding optimal combinations of pre-defined heat sink variables, such as liquid
flow rates, fin density, or channel dimensions. The presented work breaks away from these
conventional methods in the following ways:
1. The prosed heat exchanger design optimization process is designed to allow for
completely unconstrained optimization of three-dimensional topologies, allowing it to
freely search the defined workspace for optimal design solutions
2. The proposed heat exchanger design optimization process utilizes the intelligence of
binary genetic optimization to systematically identify high performing design
characteristics and build on them, evolving towards unique, optimal solutions
100
3. The proposed heat exchanger design optimization process integrated a custom validation
process, employing the principles of binary image analysis and morphology, ensures the
genetic optimization produces feasible structures that are practical solutions to the desired
application
4. Utilizing the industry leading simulation capabilities of ANSYS Workbench attains
accurate performance-based evaluations in specific used-defined environmental
conditions for each potential design candidate
5. Incorporating ANSYS Icepak allows designers to capture detailed thermal models and
physical aspects of these complex, Multiphysics systems
6. The workflow of the proposed heat exchanger design optimization process integrates
seamlessly into the prototyping design process, allowing for easy post processing and
continued analysis of the resulting geometries
5.2 Prototyping Tool
The study presented in Section 4.2, for the optimization of a liquid cooled half-bridge converter
system, demonstrates the optimization approaches capability to attain novel design
improvements on a starting, engineered seed model. By incorporating this genetic optimization
into the prototyping process, electronic-thermal designers can customize their models to meet
specific performance objectives. The results of Section 4.3.1 demonstrate the influence of the
user-defined fitness function and how weighted values can alter the evaluation scoring and
corresponding optimal designs generated by the program. Sections 4.3.2 - 4.3.3 compare the
environmental impact of the simulation conditions on the resulting optimization structures. It is
clear that the GA not only adapts to the physics of the given design problem but also captures the
influence of the boundary conditions associated with the thermal modelling and performance
evaluations.
Operating within the ANSYS simulation space, the optimized models produced by the GA can
work seamlessly with other Workbench applications, allowing for continued design analysis or
post processing. Figure 83 demonstrates the potential benefits of this aspect, applied to the scope
of the Half-Bridge model presented in Chapter 4. By re-integrating the optimized heat sink
101
geometries, such as the one in Figure 73, back into the complete system model, continued
analysis on passive device temperatures and PCB thermal expansion can be performed.
102
Figure 83: Workflow of Genetic Optimization is Prototyping Process. a) Starting Design
Temperature Profile. b) Optimized Design Temperature Profile. c) Thermal Deformation of
Optimized Design.
103
Flexible to a variety of heat sink patterns as well as adaptable to any liquid cooled PCB layout,
the presented Genetic Design Optimization program represents a powerful tool to address the
continual design challenges required to design better thermal management systems for high
output power electronics.
5.3 Closing Remarks and Future Works
The initial results of the optimization platform show great promise in the GA’s ability to adapt to
the physics and environment of automotive liquid heat sinks. An important step to strengthen the
programs validity will be to integrate this design optimization into an experimental prototyping
process. Experimentally validating and comparing both the starting seed designs and the final
optimized designs associated with this process will better verify the programs ability to induced
quantifiable design improvements for these liquid cooled components. Furthermore, applying the
proposed design optimization methodology and utilizing the genetic optimization process for
different PCB designs or cooling schemes would further establish the program as a flexibility
design tool.
Having bridged the logic gap from the GA code to ANSYS Workbench, continued work could
also seek to integrated different simulation tools into the design evaluation stages. Additional
performance variables, such as structural reliability, thermal fatigue or semiconductor efficiency
could be incorporated into the fitness scoring of each potential design. ANSYS has a large
library of powerful CFD and FEA based applications that could aid in the electronic thermal
design process, creating a more inclusive multi-objective optimization tool.
The constructed program pairs the computational abilities of ANSYS with a custom optimization
process, largely inspired by the workflow of traditional GA’s. With an abundance of existing
literature surrounding the study of genetic optimization, future works should seek to implement
more advanced principles into to the logic of the underlying code [144]–[146]. Adaptive
mutations, exponential fitness scoring and intelligent gene swapping are just some unique
improvements that could enhance the computational efficiency and overall effectiveness of the
proposed genetic optimization process.
The presented work and results clearly show that the genetically inspired optimization program
can provide effective solutions when applied to the design of compact heat sink topologies for
104
EV power electronics. By targeting multiple design objectives and allowing the program to work
with un-constrained three-dimensional geometries, this optimization program can generate
significant improvements for designers across a wide range of applications. The automatic and
intuitive nature of the customized design process makes it a useful tool in the continual effort to
improve the cost, size and performance of integrated cooling structures for automotive power
electronics.
105
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Appendix: Details of Heat Sink Design Optimization
The following MATLAB code implements the heat sink optimization methodology
outlined in Chapter 3. The applied variables correspond with the case study conditions presented
in Chapter 4. Variables share names with those defined in the chapter wherever possible.
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Main Program Code
%%%%% Launch ANSYS in Server Mode and Pause for User to Define Simulation %%%%% Generate Model WorkSpace Grid, Apply suitable Meshing parameters and %%%%% their corresponding Physics
GeometryFile = 'HB GaN Chip Optimization Model.agdb';%'Optimization Model - Indexing.SLDPRT'; WorkingDirectory = 'C:\\Users\\Andrew\\Desktop\\Thesis\\Thesis Example Simulations\\Chapter
4\\Initial Testing'; %%Define Working Directory Path
initialize(GeometryFile,WorkingDirectory); pause
tic;
%%%%% Define workspace Size
deltaX = 42; %mm deltaY = 40; %mm deltaZ = 4; %mm
%%%%% Define Mesh Pixels/Voxels
x = 2; %mm y = 2; %mm z = 1; %mm
%%%%%Define GA Parameters
PopulationSize = 10; MutationProbability = 0.05; %Percentage SeedMutationProbability = 0.5; %Percentage ParentsPerChild = 2; %Size of Breeding Group
MaxGeneration = 15; %%Define Maximum Number of Iterations for Program MaxWait = 1500; %%Define Time to Wao
EliteIndividuals = 1; %Set Number of Elite Designs to Carry over during
Repopulation SeedDesigns = 1; %Set Number of User Defined Seed Designs RandomIndividuals = round(PopulationSize/5); %Set Number of Randomly
Generated Design to arry over % during Repopulation
%%%%%Set Remaining File Paths
SeedDesignFolder = fullfile(WorkingDirectory,'SeedDesigns'); %%Create Folder for Seed Designs GeomFolder = fullfile(WorkingDirectory,'GeometryFiles'); %%Create Folder for Geometry
files of %Best Individuals ScriptPath = fullfile(WorkingDirectory,'DesignModelerScript.js'); ResultsFile = 'Output.csv';
%%%%%Set Scoring Constants
weightSum = 0;
for count = 1:1:(PopulationSize-RandomIndividuals) weightSum = weightSum + 1/count; end
for count = 1:1:(PopulationSize-RandomIndividuals)
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weight = 1/count; BreedingProbability(count,:) = weight/weightSum;
end
%%%%%Begin Automated Process
mkdir(SeedDesignFolder); %%Create Folders mkdir(GeomFolder);
X_Elements = deltaX/x; %%Determine Number of WS Elements in X Direction Y_Elements = deltaY/y; %%Determine Number of WS Elements in Y Direction Z_Elements = deltaZ/z; %%Determine Number of WS Elements in Z Direction
Horizontal_Coordinate = Y_Elements; %%Flow Direction Vertical_Coordinate = Z_Elements; %%Up-Down Lateral_Coordinate = X_Elements; %%Width
ElementCount = X_Elements*Y_Elements*Z_Elements; %%Determine Total Number of WS Elements
%%%%%Remaining User Defined/Related Factors % X = []; % % for n = 1:2:42 % X = [X,((n*:1:40)]; % end SeedDesign(1,:) =
{[(1:1:20),(41:1:60),(81:1:100),(121:1:140),(161:1:180),(201:1:220),(241:1:260),(281:1:300),(321:
1:340),(361:1:380),(401:1:420),]};%{[(1:1:9),(19:1:27),(37:1:45),(55:1:63)]};
%%Input Seed Design(s) %SeedDesign(2,:) = {[4,5,6]};
CrossoverPoint = round(0.01*ElementCount); %Input Size of Chromosone String Defined as Specific
Number % of WS Bodies or as Percentage of Total Number of WS
Bodies
WorkSpaceMatrix = zeros(Horizontal_Coordinate,Lateral_Coordinate,Vertical_Coordinate);
%%Create empty WS Matrix
for i = 1:1:ElementCount
WorkSpaceMatrix(i) = i; %%Fill WS Matrix and Ensure this Grid Indexing Aligns
with that of the % physical matrix of Design Element % within the model end
WorkSpaceMatrix2 = rot90(fliplr(WorkSpaceMatrix),1); BinaryMatrix = zeros(size(WorkSpaceMatrix2)); ReferenceMatrix = reshape((1:1:ElementCount),size(WorkSpaceMatrix2));
WorkSpace2Reference = containers.Map(WorkSpaceMatrix2,ReferenceMatrix); %%%%%Create Monitor Plots
figure(1)
TempPlot = subplot(2,2,1); title('Temperature Plot'); ylabel('Chip Temp (C)'); xlabel('Generation'); hold on
PressurePlot = subplot(2,2,2); title('Pressure Plot');
119
ylabel('Pa'); xlabel('Generation'); hold on
ConvergPlot = subplot(2,2,[3 4]); title('Convergence'); ylabel('Fitness'); xlabel('Generation'); hold on
%%%%%Create Initial Population of Seed Designs
for SD = 1:1:PopulationSize
if SD<=SeedDesigns SolutionVector = SeedDesign{SD,1}; ValidIndividual = ismember(WorkSpaceMatrix2,SolutionVector); else [NewIndividual] =
GenerateSeedDesign(WorkSpace2Reference,BinaryMatrix,ElementCount,SeedMutationProbability); [ValidIndividual,SolutionVector] =
ValidateSeedDesign(NewIndividual,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_
Coordinate,Lateral_Coordinate,ElementCount); %%Function to take in Generated Designs and Validate
them for Physics end
%Individual_Label = sprintf('%s/Individual_%d',GeomFolder,SD);
InitialPopulation(SD,:) = {SolutionVector}; %%Store Solution Vectors to Population
Vector
end
%%%%%Initialize Numerics and Population
NewPopulation = InitialPopulation; GenerationCount = 1;
%%%%% Begin Main GA Loop %%%%%%
while GenerationCount<=MaxGeneration
%%%% Evaluate Each Individual in Current Population for PopulationCount = 1:1:PopulationSize
CurrentIndividual = NewPopulation{PopulationCount};
callout = sprintf('Current Individual = %d Current Generation =
%d',PopulationCount,GenerationCount); disp(callout); %%Callout Status of Evaluation Process
[ScriptFile] = GenerateScriptFile(CurrentIndividual,ElementCount); %%Write DM Scipt
File Corresponding to Current %%Individuals
Solution Vector
if PopulationCount==1 NewFileLabel =
sprintf('%s/Design_%d_%d.js',GeomFolder,PopulationCount,GenerationCount); copyfile(ScriptFile,NewFileLabel); % Store Geometry Script File end
if GenerationCount==1 NewFileLabel =
sprintf('%s/Design_%d_%d.js',SeedDesignFolder,PopulationCount,GenerationCount); copyfile(ScriptFile,NewFileLabel); % Store Geometry Script File
120
end
[Temperature,Pressure] = Simulate(ScriptPath,ResultsFile,MaxWait);
if (GenerationCount==1)&&(PopulationCount==1) Base_Temp = Temperature; Base_Press = Pressure; end
[FitnessValue] = FitnessFunction(Temperature,Pressure,Base_Temp,Base_Press); %%Fitness
Function
%%%%% Store Performance Values, Fitness Score and Solution Vectors of Each Individual in
current Population EvaluatedPopulation(PopulationCount,:) = [FitnessValue, {CurrentIndividual},
PopulationCount, Temperature, Pressure];
execwbcommand('setup1.Exit()'); %%Close/Reset Icepak Window
end
%%%%% Rank Population, Graph & Store Best Performing Design of Generation %%%%%
RankedPopulation = sortrows(EvaluatedPopulation,1); %%ReOrder from Lowest-to-Highest Based
on Fitness Score TrimmedPopulation = RankedPopulation([1:(PopulationSize-RandomIndividuals)],:); %%Remove
Lostest Performing Individuals
BestFitness = RankedPopulation{1,1};%%Check these values BestTemp = RankedPopulation{1,4};%%Check these indexed values BestPress = RankedPopulation{1,5};%%Check these indexed values
TopPerformers(GenerationCount,:) = BestFitness; TopTemp(GenerationCount,:) = BestTemp; TopPress(GenerationCount,:) = BestPress;
callout = sprintf('Top Fitness of Generation = %f At Individual =
%d',BestFitness,RankedPopulation{1,3}); disp(callout);
subplot(2,2,1) scatter(GenerationCount,BestTemp,'filled','b')
subplot(2,2,2) scatter(GenerationCount,BestPress,'filled','m')
subplot(2,2,[3 4]) scatter(GenerationCount,BestFitness,'filled','k')
%%%%% Repopulate %%%%%
for RepopulateCount = 1:1:PopulationSize
if RepopulateCount<=EliteIndividuals
SolutionVector = RankedPopulation{RepopulateCount,2};
elseif RepopulateCount>(PopulationSize-RandomIndividuals)
[NewIndividual] =
GenerateRandomDesign(WorkSpace2Reference,BinaryMatrix,ElementCount,MutationProbability); [ValidIndividual,SolutionVector] =
ValidateRandomDesign(NewChild,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_Coo
rdinate,Lateral_Coordinate,ElementCount);
121
else [NewChild,BreedingGroup] =
CreateChild(TrimmedPopulation,ParentsPerChild,CrossoverPoint,BreedingProbability,MutationProbabil
ity,ElementCount); [ValidIndividual,SolutionVector] =
ValidateChildDesign(NewChild,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_Coor
dinate,Lateral_Coordinate,ElementCount); end
NewPopulation(RepopulateCount,:) = {SolutionVector}; %%Store Solution Vectors of
Newly Formed Childern to New Population Group
end
GenerationCount = GenerationCount+1;
end
Elapsed_Time = toc; toc;
%%%%% End Process and Callout Final Info
clear('orb'); %% Cant Save this Object - causes Errors save('Workspace Variables.mat'); %% Save All Variables saveas(gcf,'Convergence Plot.fig'); %% Save Convergence Plot
BestFitnessCount = length(unique(TopPerformers)); callout = sprintf('Number Of Different Top Performing Designs = %2d',BestFitnessCount); disp(callout);
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Initialization Function
function [] = initialize(GeometryFile,WorkingDirectory)
Command = '"C:\Program Files\ANSYS Inc\v192\Framework\bin\Win64\runwb2.exe" -I -E "with
open(''aaS_WbId.txt'',''w'') as file:file.write(Server.StartServer(''localhost'',0,9000,9200))"
&';
status = system(Command);
pause(30);
orb=initialize_orb(); %% Only need to be executed once per session
load_ansys_aas();
actwbserver('C:/Users/Andrew/aaS_WbID.txt');
execwbcommand('Open(FilePath="C:/Users/Andrew/Desktop/Thesis/Thesis Example Simulations/Chapter
4/Temp_Simulate.wbpj")');
execwbcommand('system1 = GetSystem(Name="Geom")');
execwbcommand('geometry1 = system1.GetContainer(ComponentName="Geometry")');
execwbcommand('geometry1.Edit()');
execwbcommand('system2 = GetSystem(Name="IPK")');
execwbcommand('setup1 = system2.GetContainer(ComponentName="Setup")');
execwbcommand('setup1.Edit(SystemCoordinate="B")');
123
Seed Design Generation Function
function [NewIndividual] =
GenerateSeedDesign(WorkSpace2Reference,BinaryMatrix,ElementCount,MutationProbability)
NewBinary = BinaryMatrix;
for element = 1:1:ElementCount
x =rand;
if x<=MutationProbability
NewBinary(WorkSpace2Reference(element))=~NewBinary(WorkSpace2Reference(element));
end
end
NewIndividual = NewBinary;
124
Seed Design Validation Function
function [ValidIndividual,SolutionVector] =
ValidateSeedDesign(NewIndividual,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_
Coordinate,Lateral_Coordinate,ElementCount)
IsValid = 0;
FluidElements = [];
while ~(IsValid == 1)
IsValid = 1;
IdentifyBlobs = bwconncomp(NewIndividual,6);
BlobNum = IdentifyBlobs.NumObjects;
BlobsROI = regionprops(IdentifyBlobs,'BoundingBox');
for num = 1:1:BlobNum
BlobBox = BlobsROI(num);
XBound = BlobBox.BoundingBox(1); %%Right-to-Left in Binary Matrix
YBound = BlobBox.BoundingBox(2); %%Up-Down in Binary Matrix
ZBound = BlobBox.BoundingBox(3); %%Across the Matrice Levels
BoundWidth = BlobBox.BoundingBox(4); %%Number of Pixels Across
BoundHeight = BlobBox.BoundingBox(5); %%Number of Pixels Up-Down
BoundDepth = BlobBox.BoundingBox(6); %%Number of Pixels Deep
if (BoundWidth~=Horizontal_Coordinate)
IsValid = 0;
SE_line = strel('line',3,180);
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
BlobBinary = imdilate(BlobBinary,SE_line);
NewIndividual = NewIndividual|BlobBinary;
end
end
end
ValidIndividual = NewIndividual;
WorkSpace2Individual = containers.Map(WorkSpaceMatrix2,NewIndividual);
FCount = 1;
for element = 1:1:ElementCount
if (WorkSpace2Individual(element)== 1)
FluidElements(FCount,:) = element;
FCount = FCount+1;
end
end
SolutionVector = FluidElements;
125
Write Design Modeler Script Function
function [ScriptFile] = GenerateScriptFile(SolutionVector, ElementCount)
A = (1:1:ElementCount);
B = ismember(A,SolutionVector);
SolidVector = A(~B);
ScriptFile = sprintf('%s.js','DesignModelerScript');
ScriptWrite = fopen(ScriptFile,'w');
DocumentStart = '////This Document Clears Previous BOOLEAN Functions, \n ////then Selects Bodies
for Fluid and HeatSink BOOLEAN Combine';
fprintf(ScriptWrite,'%s\n\n' ,DocumentStart);
%%%%%Delete Pre-Existing Booleans
fprintf(ScriptWrite,'ag.selectedFeature = ag.gui.TreeviewFeature("FluidCombine", 0);\n');
fprintf(ScriptWrite,'ag.selectedFeature = ag.gui.TreeviewFeature("SolidCombine", 0);\n');
fprintf(ScriptWrite,'ag.gui.FeatureSuppression (701 - 700);\n\n');
fprintf(ScriptWrite,'ag.selectedFeature = ag.gui.TreeviewFeature("FluidCombine", 0);\n');
fprintf(ScriptWrite,'ag.gui.Delete(0);\n\n');
fprintf(ScriptWrite,'ag.selectedFeature = ag.gui.TreeviewFeature("SolidCombine", 0);\n');
fprintf(ScriptWrite,'ag.gui.Delete(0);\n\n');
%%%%%Combine Fluid Bodies With Boolean
FluidBoolean1 = 'var F_Boolean= ag.gui.CreateBoolean();';
FluidBoolean2 = 'F_Boolean.Name = "FluidCombine";';
FluidBoolean3 = 'F_Boolean.Operation = 0; ';
FluidBoolean4 = 'ag.listview.ActivateItem("Tool Bodies"); ';
FluidBoolean5 = 'agb.ClearSelections(); ';
fprintf(ScriptWrite,'%s\n%s\n%s\n%s\n%s\n\n',FluidBoolean1,FluidBoolean2,FluidBoolean3,FluidBoole
an4,FluidBoolean5);
fprintf(ScriptWrite,'F1 = selectNode("Fluid.1");\n');
fprintf(ScriptWrite,'ag.bodyPick;\n');
fprintf(ScriptWrite,'agb.AddSelect(agc.TypeBody, F1);\n\n');
fprintf(ScriptWrite,'F2 = selectNode("Fluid.2");\n');
fprintf(ScriptWrite,'ag.bodyPick;\n');
fprintf(ScriptWrite,'agb.AddSelect(agc.TypeBody, F2);\n\n');
for block = 1:1:(length(SolutionVector))
VarLabel = sprintf('FBlock%d',block);
BodyLabel = sprintf('Body.%d',SolutionVector(block));
fprintf(ScriptWrite,'%s = selectNode("%s");\n',VarLabel,BodyLabel);
fprintf(ScriptWrite,'ag.bodyPick;\n');
fprintf(ScriptWrite,'agb.AddSelect(agc.TypeBody, %s);\n\n',VarLabel);
end
fprintf(ScriptWrite,'ag.listview.ItemValue = "Apply";\n\nag.b.Regen();\n');
%%%%%Combine Solid Bodies with Boolean
SolidBoolean1 = 'var S_Boolean= ag.gui.CreateBoolean();';
SolidBoolean2 = 'S_Boolean.Name = "SolidCombine";';
SolidBoolean3 = 'S_Boolean.Operation = 0; ';
SolidBoolean4 = 'ag.listview.ActivateItem("Tool Bodies"); ';
SolidBoolean5 = 'agb.ClearSelections(); ';
fprintf(ScriptWrite,'%s\n%s\n%s\n%s\n%s\n\n',SolidBoolean1,SolidBoolean2,SolidBoolean3,SolidBoole
an4,SolidBoolean5);
126
fprintf(ScriptWrite,'HS = selectNode("Heat Sink");\n');
fprintf(ScriptWrite,'ag.bodyPick;\n');
fprintf(ScriptWrite,'agb.AddSelect(agc.TypeBody, HS);\n\n');
for block = 1:1:(length(SolidVector))
VarLabel = sprintf('SBlock%d',block);
BodyLabel = sprintf('Body.%d',SolidVector(block));
fprintf(ScriptWrite,'%s = selectNode("%s");\n',VarLabel,BodyLabel);
fprintf(ScriptWrite,'ag.bodyPick;\n');
fprintf(ScriptWrite,'agb.AddSelect(agc.TypeBody, %s);\n\n',VarLabel);
end
fprintf(ScriptWrite,'ag.listview.ItemValue = "Apply";\n\nag.b.Regen();\n\n');
%%%%%Define 'Select Node Function'
fprintf(ScriptWrite, 'function selectNode (target)\n{\n var DM = ag.wb.AppletList.Applet(
"AGApplet" ).App;\n var Nodes = DM.Script.ag.tree.Nodes;\n var count = Nodes.Count;\n
var name, current;\n for (var i =1; i <= count; i++)\n {\n current = Nodes(i);\n
name = current.Text.toLowerCase();\n if (name == target.toLowerCase())\n {\n
DM.Script.agTree_LeftClick(current, false);\n var obj = ag.listviewSelectedObject;\n
return obj;\n }\n }\n}');
127
ANSYS Simulation Function
function [Temperature,Pressure] = Simulate(ScriptPath,ResultsFile,MaxWait)
WaitCount = 0;
execwbcommand('geometry1.SendCommand(Command
="(ag.wb.ScriptEngine.RunScript(''C:/Users/Andrew/Desktop/Thesis/Thesis Example
Simulations/Chapter 4/Initial Testing/DesignModelerScript.js''))")');
execwbcommand('boolean1 = CheckPartialUpdateAndRetainPartialUpdatePropertiesSetConsistently()');
execwbcommand('designPoint1 = Parameters.GetDesignPoint(Name="0")');
execwbcommand('backgroundSession1 = UpdateAllDesignPoints(DesignPoints=[designPoint1])');
execwbcommand('Parameters.ExportAllDesignPointsData(FilePath="C:/Users/Andrew/Desktop/Thesis/Thes
is Example Simulations/Chapter 4/Initial Testing/Output.csv")');
while exist(ResultsFile)==0
pause(1);
WaitCount = WaitCount+1;
if WaitCount>=MaxWait
disp('No Output File Created in Allowed Time, Suspectyed Simulation Error');
break;
end
end
%%%%% Check and Read Results File From WB
if isfile(ResultsFile)
[Temperature,Pressure] = CFD_Results(ResultsFile); %%Function to Read Contents of WB Results
File
if Pressure<=0 %% Check if Results are Currupt
Pressure = NaN; %% If so apply 'BAD' values to Performance Variables
Temperature = NaN;
end
fclose('all');
delete(ResultsFile);
else
Pressure = NaN;
Temperature = NaN;
end
128
Read ANSYS Results Function
function [Temperature,Pressure] = CFD_Results(filename, startRow, endRow)
%IMPORTFILE Import numeric data from a text file as a matrix.
% OUTPUT = IMPORTFILE(FILENAME) Reads data from text file FILENAME for
% the default selection.
%
% OUTPUT = IMPORTFILE(FILENAME, STARTROW, ENDROW) Reads data from rows
% STARTROW through ENDROW of text file FILENAME.
%
% Example:
% Output = importfile('Output.csv', 8, 8);
%
% See also TEXTSCAN.
% Auto-generated by MATLAB on 2019/05/03 17:44:38
%% Initialize variables.
delimiter = ',';
if nargin<=2
startRow = 8;
endRow = inf;
end
%% Format for each line of text:
% column2: double (%f)
% column3: double (%f)
% For more information, see the TEXTSCAN documentation.
formatSpec = '%*s%f%f%[^\n\r]';
%% Open the text file.
fileID = fopen(filename,'r','n','UTF-8');
% Skip the BOM (Byte Order Mark).
fseek(fileID, 3, 'bof');
%% Read columns of data according to the format.
% This call is based on the structure of the file used to generate this
% code. If an error occurs for a different file, try regenerating the code
% from the Import Tool.
dataArray = textscan(fileID, formatSpec, endRow(1)-startRow(1)+1, 'Delimiter', delimiter,
'TextType', 'string', 'HeaderLines', startRow(1)-1, 'ReturnOnError', false, 'EndOfLine', '\r\n');
for block=2:length(startRow)
frewind(fileID);
dataArrayBlock = textscan(fileID, formatSpec, endRow(block)-startRow(block)+1, 'Delimiter',
delimiter, 'TextType', 'string', 'HeaderLines', startRow(block)-1, 'ReturnOnError', false,
'EndOfLine', '\r\n');
for col=1:length(dataArray)
dataArray{col} = [dataArray{col};dataArrayBlock{col}];
end
end
%% Close the text file.
fclose(fileID);
%% Post processing for unimportable data.
% No unimportable data rules were applied during the import, so no post
% processing code is included. To generate code which works for
% unimportable data, select unimportable cells in a file and regenerate the
% script.
%% Create output variable
Output = table(dataArray{1:end-1}, 'VariableNames', {'P1','P2'});
Temperature = table2array(Output(1,1));
Pressure = table2array(Output(1,2));
129
ANSYS Simulation Function
function [FitnessScore] = FitnessFunction(Temperature,Pressure,Base_Temp,Base_Press)
a = 0.70;
b = 1-a;
FitnessScore = (a*(Temperature/Base_Temp)) + (b*(Pressure/Base_Press));
130
Generate Child Design Function
function [NewChild,BreedingGroup] =
CreateChild(TrimmedPopulation,ParentsPerChild,CrossoverPoint,BreedingProbability,MutationProbabil
ity, ElementCount)
BreedingGroup = []; %%Create Empty Array for Breeding Group
BreedingParents = {};
ChildVector = [];
GeneStringCount = 1;
ChildGeneCount = 1;
Parent = 1;
while Parent<=ParentsPerChild
x = rand;
while x>BreedingProbability(1)
x = rand;
end
for count = 1:1:size(TrimmedPopulation,1)
if BreedingProbability(count) > x
Prob = BreedingProbability(count);
CurrentParent = (TrimmedPopulation(count,2));
end
end
if ~ismember(Prob,BreedingGroup)
BreedingGroup = [BreedingGroup Prob];
BreedingParents(Parent,:) = CurrentParent;
Parent = Parent+1;
else
Parent=Parent;
end
end
ChooseParent = randi(ParentsPerChild);
SelectedParent = cell2mat(BreedingParents(ChooseParent));
for CurrentGene = 1:1:ElementCount
if GeneStringCount>=CrossoverPoint
GeneStringCount = 1;
ChooseParent = randi(ParentsPerChild);
SelectedParent = cell2mat(BreedingParents(ChooseParent));
end
if ismember(CurrentGene,SelectedParent)
ChildVector(ChildGeneCount,:) = CurrentGene;
ChildGeneCount = ChildGeneCount+1;
end
end
%%%%% Mutate Child Design Genes
for element = 1:1:ElementCount
x = rand;
if x<=MutationProbability
if ismember(element,ChildVector)
NewChild(element,:) = NaN;
else
NewChild(element,:) = element;
end
else
131
if ismember(element,ChildVector)
NewChild(element,:) = element;
else
NewChild(element,:) = NaN;
end
end
end
132
Validate Child Design Function
function [ValidIndividual,SolutionVector] =
ValidateChildDesign(NewChild,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_Coor
dinate,Lateral_Coordinate,ElementCount)
FluidValid = 0;
SolidValid = 0;
FluidElements = [];
NewIndividual = ismember(WorkSpaceMatrix2,NewChild);
while ~(FluidValid == 1)
FluidValid = 1;
IdentifyBlobs = bwconncomp(NewIndividual,6);
BlobNum = IdentifyBlobs.NumObjects;
BlobsROI = regionprops(IdentifyBlobs,'BoundingBox');
for num = 1:1:BlobNum
BlobBox = BlobsROI(num);
XBound = BlobBox.BoundingBox(1); %%Right-to-Left in Binary Matrix
YBound = BlobBox.BoundingBox(2); %%Up-Down in Binary Matrix
ZBound = BlobBox.BoundingBox(3); %%Across the Matrice Levels
BoundWidth = BlobBox.BoundingBox(4); %%Number of Pixels Across
BoundHeight = BlobBox.BoundingBox(5); %%Number of Pixels Up-Down
BoundDepth = BlobBox.BoundingBox(6); %%Number of Pixels Deep
Xe = XBound-0.5+BoundWidth;
if (BoundWidth~=Horizontal_Coordinate)
FluidValid = 0;
if (XBound==0.5)||(Xe==Horizontal_Coordinate)
SE_line = strel('line',3,180);
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
BlobBinary = imdilate(BlobBinary,SE_line);
NewIndividual = NewIndividual|BlobBinary;
else
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
NewIndividual = NewIndividual - BlobBinary;
end
end
end
end
NewIndividual = not(NewIndividual); %%Invert Values of Logical array such that 1'
= Solid Elements and 0's = Fluid
while ~(SolidValid == 1)
SolidValid = 1;
IdentifyBlobs = bwconncomp(NewIndividual,6);
BlobNum = IdentifyBlobs.NumObjects;
BlobsROI = regionprops(IdentifyBlobs,'BoundingBox');
for num = 1:1:BlobNum
BlobBox = BlobsROI(num);
Xs = BlobBox.BoundingBox(1); %%Right-to-Left in Binary Matrix
Ys = BlobBox.BoundingBox(2)+0.5; %%Up-Down in Binary Matrix
133
Zs = BlobBox.BoundingBox(3); %%Across the Matrice Levels
X_Width = BlobBox.BoundingBox(4); %%Number of Pixels Across
Y_Width = BlobBox.BoundingBox(5); %%Number of Pixels Up-Down
Z_Width = BlobBox.BoundingBox(6); %%Number of Pixels Deep
Ye = Ys-0.5+Y_Width;
Ze = Zs-0.5+Z_Width;
if ((Ys~=0.5)&&(Zs~=0.5)&&(Ye~=Lateral_Coordinate)&&(Ze~=Vertical_Coordinate))
SolidValid = 0;
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
NewIndividual = NewIndividual - BlobBinary;
end
end
end
NewIndividual = ~(NewIndividual);
ValidIndividual = NewIndividual;
WorkSpace2Individual = containers.Map(WorkSpaceMatrix2,NewIndividual);
FCount = 1;
for element = 1:1:ElementCount
if (WorkSpace2Individual(element)== 1)
FluidElements(FCount,:) = element;
FCount = FCount+1;
end
end
SolutionVector = FluidElements;
134
Generate Random Design Candidate Function
function [NewIndividual] =
GenerateRandomDesign(WorkSpace2Reference,BinaryMatrix,ElementCount,MutationProbability)
NewBinary = BinaryMatrix;
for element = 1:1:ElementCount
x =rand;
if x<=MutationProbability
NewBinary(WorkSpace2Reference(element))=~NewBinary(WorkSpace2Reference(element));
end
end
NewIndividual = NewBinary;
135
Validate Random Design Candidate Function
function [ValidIndividual,SolutionVector] =
ValidateRandomDesign(NewChild,WorkSpaceMatrix2,ReferenceMatrix,Horizontal_Coordinate,Vertical_Coo
rdinate,Lateral_Coordinate,ElementCount)
FluidValid = 0;
SolidValid = 0;
FluidElements = [];
NewIndividual = ismember(WorkSpaceMatrix2,NewChild);
while ~(FluidValid == 1)
FluidValid = 1;
IdentifyBlobs = bwconncomp(NewIndividual,6);
BlobNum = IdentifyBlobs.NumObjects;
BlobsROI = regionprops(IdentifyBlobs,'BoundingBox');
for num = 1:1:BlobNum
BlobBox = BlobsROI(num);
XBound = BlobBox.BoundingBox(1); %%Right-to-Left in Binary Matrix
YBound = BlobBox.BoundingBox(2); %%Up-Down in Binary Matrix
ZBound = BlobBox.BoundingBox(3); %%Across the Matrice Levels
BoundWidth = BlobBox.BoundingBox(4); %%Number of Pixels Across
BoundHeight = BlobBox.BoundingBox(5); %%Number of Pixels Up-Down
BoundDepth = BlobBox.BoundingBox(6); %%Number of Pixels Deep
if (BoundWidth~=Horizontal_Coordinate)
FluidValid = 0;
SE_line = strel('line',3,180);
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
BlobBinary = imdilate(BlobBinary,SE_line);
NewIndividual = NewIndividual|BlobBinary;
end
end
end
NewIndividual = not(NewIndividual); %%Invert Values of Logical array such that 1'
= Solid Elements and 0's = Fluid
while ~(SolidValid == 1)
SolidValid = 1;
IdentifyBlobs = bwconncomp(NewIndividual,6);
BlobNum = IdentifyBlobs.NumObjects;
BlobsROI = regionprops(IdentifyBlobs,'BoundingBox');
for num = 1:1:BlobNum
BlobBox = BlobsROI(num);
Xs = BlobBox.BoundingBox(1); %%Right-to-Left in Binary Matrix
Ys = BlobBox.BoundingBox(2)+0.5; %%Up-Down in Binary Matrix
Zs = BlobBox.BoundingBox(3); %%Across the Matrice Levels
X_Width = BlobBox.BoundingBox(4); %%Number of Pixels Across
Y_Width = BlobBox.BoundingBox(5); %%Number of Pixels Up-Down
Z_Width = BlobBox.BoundingBox(6); %%Number of Pixels Deep
Ye = Ys-0.5+Y_Width;
Ze = Zs-0.5+Z_Width;
136
if (Ys~=0.5)&&(Zs~=0.5)&&(Ye~=Lateral_Coordinate)&&(Ze~=Vertical_Coordinate)
SolidValid = 0;
BlobBinary = ismember(ReferenceMatrix,IdentifyBlobs.PixelIdxList{num});
NewIndividual = NewIndividual - BlobBinary;
end
end
end
NewIndividual = ~(NewIndividual);
ValidIndividual = NewIndividual;
WorkSpace2Individual = containers.Map(WorkSpaceMatrix2,NewIndividual);
FCount = 1;
for element = 1:1:ElementCount
if (WorkSpace2Individual(element)== 1)
FluidElements(FCount,:) = element;
FCount = FCount+1;
end
end
SolutionVector = FluidElements;
