Thermal Analysis of an Integrated Power Electronics Module
by
Nicholas Palumbo
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete,Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2012
© Copyright 2012
by
Nicholas Palumbo
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
NOMENCLATURE ....................................................................................................... viii
ABSTRACT ..................................................................................................................... xi
1. Introduction.................................................................................................................. 1
1.1
Cold Plate Options ............................................................................................. 2
1.1.1
Cold Plate Option One ........................................................................... 3
1.1.2
Cold Plate Option Two .......................................................................... 5
1.1.3
Cold Plate Option Three......................................................................... 7
2. Methodology ................................................................................................................ 9
2.1
Losses of Integrated Power Electronic Module Analysis .................................. 9
2.2
Pressure Drop Analysis .................................................................................... 13
2.3
Thermal Analysis ............................................................................................. 19
2.3.1
Conduction Heat Transfer .................................................................... 19
2.3.2
Forced Convection Heat Transfer ........................................................ 22
2.3.3
Fouling Effects on Heat Transfer ......................................................... 26
3. Results........................................................................................................................ 29
3.1
Losses of Integrated Power Electronic Module ............................................... 29
3.2
Pressure Drop Results ...................................................................................... 32
3.3
3.2.1
Pressure Drop Results of Cold Plate Option One ................................ 32
3.2.2
Pressure Drop Results of Cold Plate Option Two................................ 35
3.2.3
Pressure Drop Results of Cold Plate Option Three .............................. 37
Thermal Results ............................................................................................... 41
3.3.1
Calculated Thermal Results of Cold Plate Option One ....................... 42
3.3.2
ANSYS Thermal Results of Cold Plate Option One ........................... 48
3.3.3
Calculated Thermal Results of Cold Plate Option Two ....................... 54
iii
3.3.4
ANSYS Thermal Results of Cold Plate Option Two ........................... 59
4. Conclusion ................................................................................................................. 70
5. References.................................................................................................................. 72
6. Appendix A: IGBT Data Sheet .................................................................................. 73
7. Appendix B: Sil Pad Data Sheet ................................................................................ 77
8. Appendix C: Thermal Grease Data Sheet .................................................................. 78
9. Appendix D: IPEM Power Losses Calculation ......................................................... 79
10. Appendix E: Pressure Drop Mathcad Calculations ................................................... 81
10.1 Cold Plate Option One Pressure Drop Calculation .......................................... 81
10.2 Cold Plate Option Two Pressure Drop Calculation ......................................... 82
10.3 Cold Plate Option Three Pressure Drop Calculation ....................................... 84
11. Appendix F: Pressure Drop Excel Data ..................................................................... 86
11.1 Cold Plate Option One ..................................................................................... 86
11.2 Cold Plate Option One ..................................................................................... 88
11.3 Cold Plate Option 3 .......................................................................................... 90
12. Appendix G: Thermal Calculations ........................................................................... 91
12.1 Cold Plate Option One Thermal Calculation ................................................... 91
12.2 Cold Plate Option Two Thermal Calculation .................................................. 96
iv
LIST OF TABLES
Table 1 Cold Plate Design Requirements .......................................................................... 2
Table 2 Cold Plate Option One Information...................................................................... 3
Table 3 Cold Plate Option Two Information ..................................................................... 6
Table 4 Cold Plate Option Three Information ................................................................... 7
Table 5Loss Coefficients[5] .............................................................................................. 16
Table 6 Material Thermal Conductivities[6] ..................................................................... 19
Table 7 Nusselt Number Equation n Value[6] .................................................................. 25
Table 8 Nusselt Equation Applicable Ranges[6] .............................................................. 25
Table 9 Common Fouling Factors[6] ................................................................................ 27
Table 10 Cold Plate Options One, Two & Three Pressure Drops ................................... 32
Table 11 Cold Plate Option One Head Losses ................................................................ 32
Table 12 Cold Plate Option One Requirement Review ................................................... 34
Table 13 Cold Plate Option Two Head Loss ................................................................... 35
Table 14 Cold Plate Option Two Requirement Review .................................................. 37
Table 15 Cold Plate Option Three Head Losses .............................................................. 38
Table 16 Cold Plate Option Three Requirement Review ................................................ 40
Table 17 Thermal Requirements of Cold Plate Option One & Two ............................... 41
Table 18 Final Thermal Results for Cold Plate Options One & Two ............................. 42
Table 19 Cold Plate Option One Resistance & Associated Temperature Changes ......... 44
Table 20 Cold Plate Option One IGBT Temperature ...................................................... 47
Table 21 Cold Plate Option One Thermal Results vs. Requirements.............................. 53
Table 22 Cold Plate Option Two Resistance & Associated Temperature Changes ........ 55
Table 23 Cold Plate Option Two IGBT Temperature ..................................................... 58
Table 24 Cold Plate Option Two Thermal Results vs. Requirements ............................. 66
Table 25 Cold Plate Option Comparison ......................................................................... 71
v
LIST OF FIGURES
Figure 1 Cold Plate Option One - Series Top View .......................................................... 3
Figure 2 Cold Plate Option One – Series Elevation View................................................. 4
Figure 3 Cold Plate Option Two -Parallel Top View ........................................................ 5
Figure 4 Cold Plate Option Two - Parallel Elevation View .............................................. 6
Figure 5 Cold Plate Option Three - Parallel/Series Top View .......................................... 7
Figure 6 Cold Plate Option Three - Parallel/Series Elevation View ................................. 8
Figure 7Circuit Diagram of Integrated Power Electronic Module .................................. 10
Figure 8 Switching Losses, Turn-on & Turn-off Losses[3] .............................................. 11
Figure 9Sudden Expansion[5] ........................................................................................... 16
Figure 10Sudden Contraction[5] ....................................................................................... 17
Figure 11 Losses of Transistor & Diode.......................................................................... 29
Figure 12 Total Switching Losses vs. Total Conduction Losses ..................................... 30
Figure 13 IPEM Power Losses ........................................................................................ 31
Figure 14 Pressure Drop of Cold Plate Option One ........................................................ 33
Figure 15ANSYS Pressure Drop Results Cold Plate Option One ................................... 34
Figure 16 Pressure Drop of Cold Plate Option Two........................................................ 36
Figure 17ANSYS Pressure Drop Results Cold Plate Option Two .................................. 37
Figure 18 Pressure Drop of Cold Plate Option Three...................................................... 39
Figure 19 Basis of Thermal Resistance Circuit ............................................................... 42
Figure 20 Cold Plate Option One Thermal Circuit .......................................................... 43
Figure 21 Temperature Difference along Cold Plate Option One ................................... 45
Figure 22 Temperature Difference along Cold Plate Option One Pipe ........................... 46
Figure 23 Meshing of Cold Plate Option One ................................................................. 48
Figure 24 Meshing of Cold Plate Option One Piping...................................................... 49
Figure 25 Meshing of Cold Plate Option One Inflation Boundary ................................. 50
Figure 26 Temperature Results of Cold Plate Option One .............................................. 51
Figure 27 Temperature Results of Cold Plate Option One Mid-Plane ............................ 52
Figure 28 Temperature Results of Cold Plate Option One Piping .................................. 53
Figure 29 Cold Plate Option Two Thermal Circuit ......................................................... 54
Figure 30 Temperature Difference along Cold Plate Option Two .................................. 56
vi
Figure 31 Temperature Difference along Cold Plate Option Two Pipe .......................... 57
Figure 32 Meshing of Cold Plate Option Two Pipe Entrance ......................................... 59
Figure 33 Meshing of Cold Plate Option Two ................................................................ 60
Figure 34 Meshing of Cold Plate Option Two Pipe ........................................................ 61
Figure 35 Meshing of Cold Plate Option Two Pipe Inflation Boundary ......................... 61
Figure 36 Meshing of Cold Plate Option Two Pipe Inflation Boundary......................... 62
Figure 37 Temperature Results of Cold Plate Option Two ............................................. 63
Figure 38 Temperature Results of Cold Plate Option Two Mid-Plane ........................... 64
Figure 39 Temperature Results of Cold Plate Option Two Pipe ..................................... 65
Figure 40 Temperature Results of Cold Plate Option Two IGBT Junction .................... 65
Figure 41 Cold Plate Option Two Modified Inlet and Outlet Directions ........................ 67
Figure 42 Temperature Results of Modified Cold Plate Option Two Mid-Plane ........... 68
Figure 43 Temperature Results of Modified Cold Plate Option Two Pipe ..................... 68
Figure 44 Temperature Results of Modified Cold Plate Option Two IGBT Junction .... 69
vii
NOMENCLATURE
Variable
Description
Units (SI)
μ
ρ
Є
𝛾
𝑚̇
µ
Dynamic Viscosity
Density
Surface Roughness
Specific Weight of Water
Mass Flow Rate
Dynamic Viscosity of Water
Dynamic Viscosity of Water Wall
Temperature
Dynamic Viscosity of Water Bulk
Temperature
Area
Specific Heat of Water
Diameter
Hydraulic Diameter
De-rating Factor
Voltage
Turn on Energy of the Diode
IGBT's Turn-off Switching Energy per Pulse
IGBT‘s Turn-on Switching Energy per Pulse
Pipe Friction Factor
Switching Frequency
Gravity
Coefficient of Heat Transfer
Heat Transfer Coefficient w/ Fouling
Heat Transfer Coefficient w/ Fouling
Head Loss
Major Head Loss
Minor Head Loss
Minor Head Loss of Contraction
Head Loss Total
Current
Rated Current
De-rated Current
Diode Peak Recovery Current
Thermal Conductivity
(Pa-s)
(kg/m3)
(m)
(N/m3)
(kg/s)
(kg/m s)
Units
(English)
(lb/ft-s)
(lb/in3)
(in)
(lbf/in3)
(lb/s)
(lb/in s)
(kg/m s)
(lb/in s)
(kg/m s)
(lb/in s)
(m2)
(J/g·K)
(m)
(m)
(V)
(mJ)/P
(mJ/Pulse)
(mJ/Pulse)
(Hz)
(m/s2)
(W/m2K)
(W/m2K)
(W/m2K)
(m)
(m)
(m)
(m)
(m)
(A)
(A)
(A)
(A)
(W/m-oC)
(in2)
(Cal/lb oF)
(in)
(in)
(V)
(lb ft2/s2)/P
(lb ft2/s2)/P
(lb ft2/s2)/P
(cycles/s)
(in/s2)
(W/in2oF)
(W/in2oF)
(W/in2oF)
(in)
(in)
(in)
(in)
(in)
(A)
(A)
(A)
(A)
Btu/(ft.hr.oF)
µb
µw
A
Cp
D
Dh
DRfactor
E
EonD
ESWoff
ESWon
ƒ
fsw
g
hc
hclean
hdirty
hL
hLmajor
hLminor
hLminorcon
hLTotal
I
Io
Io de-rated
IRR
k
viii
Kcon
Kexp
KL
KL90
KLReturnBend
KTbranch
KTeeLine
L
l
M
Nu
P
PCD
PCT
PD
PF
Pr
PswD
PswM
PT
PTD
PTD w/ SF
Pw
q
Qf
QRR
r
R
RC
RD
Re
Rf
ri
ro
Rth
SF
T
Tb
Tin
Loss Coefficient of Contraction
Loss Coefficient of Expansion
Loss Coefficient
Loss Coefficient of 90o Bend
Loss Coefficient of Return Bend
Loss Coefficient of Tee Branch
Loss Coefficient of Tee Line
Length
Pipe Length
Modulation Index
Nusselt Number
Pressure
Diode Conduction Losses
IGBT Conduction Losses
Diode Total Losses
Power Factor
Prandlt Number
Recovery Loss Per Diode
IGBT Switching Losses
IGBT Total Losses
IGBT Module Total Losses
IGBT Module Total Losses w/ Safety Factor
Wetted Perimeter
Heat Transfer
Flow Rate
Diode Reverse Recovery Charge
Radius
Electrical Resistance
Collector Emitter on-state Resistance
Diode on State Resistance
Reynolds Number
Thermal Resistance of Fouling
Inner Radius
Outer Radius
Thermal Resistance
Safety Factor
Temperature
Bulk Temperature
Temperature In
ix
(m)
(m)
(Pa)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(m)
(W)
(m3/s)
(C)
(m)
(Ω)
(Ω)
(Ω)
o
( C m2/W)
(m)
(m)
o
( C m2/W)
o
( C)
(oC)
(oC)
(in)
(in)
(psi)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(lb ft2/s3)
(in)
((lb ft2/s3)
(gpm)
(A s)
(in)
(lb ft2/s3 A2)
(lb ft2/s3 A2)
(Ω)
2
(m K/W)
(in)
(in)
2
(m K/W)
o
( F)
(oF)
(oF)
Toverall
tRR
Tw
UCEO
UClean
UDirty
UDO
V
VCE
VCE de-rated
x
z
Z
Thermal Potential Difference
Diode Reverse Recovery Time
Temperature Wall
On State Collector Emitter Voltage
Overall Heat Transfer Coefficient No Fouling
Overall Heat Transfer Coefficient Fouled
On State Zero Current Diode Voltage
Velocity
Emitter-Collector Voltage
De-rated Emitter Collector Voltage
Distance Long Pipe
Height of Fluid
Height
x
(oC)
(S)
(oC)
(V)
(W/m2K)
(W/m2K)
(V)
(m/s)
(V)
(V)
(m)
(m)
(m)
(oF)
(S)
(oF)
(V)
(W/in2oF)
(W/in2oF)
(V)
(in/s)
(V)
(V)
(in)
(in)
(in)
ABSTRACT
Integrated power electronics such as IGBT’s are widely used to efficiently deliver
electrical power in electrical drive systems in transportation, home electronics, and
electrical grid applications. Applying integrated power electronics to electric drive
systems is causing the need to improve volumetric requirements, ruggedness, weight,
reliability, noise levels, and thermal heat dissipation. Modern integrated power
electronics have a much higher power density compared to past technologies and
companies continue to innovate. The limiting factor in these electronic components is
heat removal. In order to achieve adequate cooling at current power densities, design
engineers are forced to look beyond standard forced-convection air cooling. Liquid
cooling has become an accepted and necessary form of heat dissipation for integrated
power electronic modules. A notable cooling technology that has evolved into an
efficient and reliable means to dissipate heat is cold plates. In this project three cold
plate designs were analyzed. A pressure drop calculation was completed on all three
designs and cold plate option one and two passed based off set requirements. A thermal
analysis was then completed on cold plate option one and two. Cold plate option two out
performed cold plate option one based off of a 95.38oC and 100.45oC IGBT operating
temperature. It was determined that neither cold plate option produced a uniform
temperature along the IGBT junction location. Therefore, cold plate option two’s design
was modified to improve upon a symmetric temperature profile at the IGBT junction
location. The modification implemented to cold plate option two was alternating inlet
and outlet locations; water flow paths were reversed for every other pipe. This
modification resulted in a more uniform IGBT junction temperature and a decreased
IGBT operating temperature of 94.38oC. All results were first self-calculated and then
verified through an analysis using ANSYS.
xi
1. Introduction
Integrated power electronic modules consist of components such as insulated gate
bipolar transistors (IGBTs), rectifying diodes, snubber capacitors, direct current (DC)
link capacitors, resistors, gate driver boards and many other components based on the
application. However, IGBTs are the main source of waste heat loads. The IGBT is a
semiconductor power conversion device which can achieve a high power density while
performing its fundamental role of electrical power processing, known as switching, at
high frequencies. IGBT power losses are divided into three groups: conduction losses,
switching losses and blocking losses (which are normally disregarded). Conduction
losses deal with a series connection of DC voltage source of the on-state zero current of
the collector-emitter voltage and resistance. Switching losses deal with turn-on energy
losses in the IGBT taking into account the switch-on energy and the switch-off energy
caused by the reverse-recovery of the free-wheeling diode; switching losses in the IGBT
are the product of switching energies and the switching frequency.
Cold plates have matured into a common cooling technique for high power density
integrated power electronic modules.[1] Unless properly designed, high rates of heat
generation result in high operating temperatures for electronic equipment, which then
jeopardizes its safety and reliability. In order to promote the needed heat transfer and
improve temperature distribution within the power devices cold plates must be designed
with the correct attributes for efficient heat transfer and dissipation. Cold plates act as an
indirect cooling system where there is no contact between the cooling medium and the
component. The heat generated by the IGBT is transferred from the case to the heat sink
block which has imbedded piping containing a circulating cooling medium. The heated
liquid is then cooled by an external heat exchanger. Desirable characteristics of cooling
liquids include high thermal conductivity, high specific heat, low viscosity, high surface
tension, and high dielectric strength.[2] Required heat removal rates can be achieved by
varying inlet temperature, flow rate, flow type (laminar or turbulent), thermal contact
boundaries, and materials used pipe, heat sink and junctions. References 8 – 15 of this
analysis were used in obtaining an understanding of the technology under test.
1
A high level set of specification requirements were compiled for each cold plate design.
The requirements are listed in Table 1 below.
Table 1 Cold Plate Design Requirements
Requirement
Value
Liquid Cooling Medium
De-ionized Water
Inlet Water Temperature
40oC
Maximum Flow Rate
10 gpm
Maximum Liquid Velocity
15 ft/s
Maximum Pressure Drop
5 psi
Maximum Temperature Change of Liquid
10oC
Pipe Material
Corrosion Resistant Steel
1.1 Cold Plate Options
For this analysis three different cold plate options were designed. Each design has a
specific set of attributes that cause varying pressure drop and temperature results. The
three options analyzed are: Option One – Series Piping, Option Two - Parallel Piping,
and Option Three - Parallel/Series Piping. Each design is constructed by manufacturing
the cold plate in two sections: the top and bottom half’s. This is known as a clam shell
design. The inner piping is then placed within a machined groove of both top and bottom
sections. The piping is metallurgically bonded to the top and bottom sections with
(63/37) solder and the top and bottom sections are bolted together. Extreme build
tolerances must be followed during the manufacturing process in order to maintain
acceptable surface roughness and flatness to create an effective heat transfer path.
Materials chosen for each cold plate were kept relatively constant in order to determine
which cold plate design was most effective of removing heat.
2
1.1.1
Cold Plate Option One
IGBT
IGBT
IGBT
Series
Pipe
Path
IGBT
Outlet
Inlet
Figure 1 Cold Plate Option One - Series Top View
Figure 1 Cold Plate Option One - Series Top View shows a top view of cold plate option
one. The IGBTs are spaced vertically with their greater dimension perpendicular to pipe
flow. Cold plate option one makes use of a series piping system; the water has only one
path throughout the entire cold plate. It is a serpentine design which allows the one water
path to pass over each IGBT four times. Specific information for cold plate option one is
listed below in Table 2.
Table 2 Cold Plate Option One Information
Cold Plate Option One Information
Plate Material
Aluminum
Plate & Pipe Interface Material
(63/37) Solder
Pipe Material
Corrosion Resistant Steel
Pipe Flow Path
Series
Pipe Layout
Serpentine
Pipe Diameter
.57 inches
Pipe Thickness
.09 inches
3
Plate & Pipe Interface Material Thickness .05 inches
IGBT & Cold Plate Junction Material A
Sil-Pad 2000
IGBT & Cold Plate Junction Material B
Dow-Corning TC-5022
Figure 2shows an elevation view of cold plate option one. The four pipe passes are
visible as well as the two different materials for the pipe and interface. Junction material
between the IGBT and cold plate material is no visible due to their extremely minimal
thickness.
Figure 2 Cold Plate Option One – Series Elevation View
4
1.1.2
Cold Plate Option Two
Left
Manifold
IGBT
Right
Manifold
IGBT
Parallel
Pipe
Paths
IGBT
IGBT
Inlet
Outlet
Figure 3 Cold Plate Option Two -Parallel Top View
Figure 3 shows a top view of cold plate option two. The IGBTs are spaced vertically
with their greater dimension perpendicular to pipe flow. Cold plate option two makes
use of a parallel piping system; the water has 40 paths to flow through when under
IGBTs. This design allows for a total of 10 flow paths in parallel for each IGBT.
Compared to option one, the diameter of cold plate option two piping is much smaller in
order to fit the parallel paths. The left and right side of the piping consists of an inlet
manifold and an outlet manifold. These two manifolds act as a supply and return for
each individual parallel pipe. Specific information for cold plate option one is listed
below in Table 3.
5
Table 3 Cold Plate Option Two Information
Cold Plate Option Two Information
Plate Material
Aluminum
Plate & Pipe Interface Material
(63/37) Solder
Pipe Material
Corrosion Resistant Steel
Pipe Flow Path
Parallel
Pipe Layout
40 Parallel Pass
Pipe Diameter
.188 inches
Pipe Thickness
.024 inches
Plate & Pipe Interface Material Thickness .05 inches
IGBT & Cold Plate Junction Material A
Sil-Pad 2000
IGBT & Cold Plate Junction Material B
Dow-Corning TC-5022
Figure 4 shows an elevation view of cold plate option two. The 40 pipe paths are visible
and they are broken up equally for each IGBT. Pipes were placed partially outside of
each cold plate outer dimensions based on the assumption of heat spreading occurring in
the aluminum plate. Pipe and interface material are not visible in Figure 4, along with
the junction material between the IGBT and the cold plate.
Figure 4 Cold Plate Option Two - Parallel Elevation View
6
1.1.3 Cold Plate Option Three
IGBT
IGBT
Parallel
Pipe
Paths
IGBT
IGBT
Inlet
Outlet
Figure 5 Cold Plate Option Three - Parallel/Series Top View
Figure 5 shows a top view of cold plate option three. The IGBTs are spaced horizontally
with their smaller dimension perpendicular to pipe paths. Cold plate option three is a
hybrid design of both cold plate option one and two. Cold plate option three pipe path is
a parallel and series combination. Parallel paths pass under the first two IGBTs and are
in series with the parallel paths for the remaining IGBTs. For cold plate option three, the
plate shape was modified to allow the analysis to determine if there are potential benefits
or detrimental effects to both pressure drop and heat transfer. Specific information for
cold plate option three is listed in Table 4.
Table 4 Cold Plate Option Three Information
Cold Plate Option Three Information
Plate Material
Aluminum
Plate & Pipe Interface Material
(63/37) Solder
Pipe Material
Corrosion Resistant Steel
Pipe Flow Path
Parallel / Series
Pipe Layout
10 Parallel Pass
Pipe Diameter
.57 inches
Pipe Thickness
.09 inches
Plate & Pipe Interface Material Thickness .05 inches
7
IGBT & Cold Plate Junction Material A
Sil-Pad 2000
IGBT & Cold Plate Junction Material B
Dow-Corning TC-5022
Figure 6 shows an elevation view of cold plate option three. Fourteen parallel paths are
visible; however the cold plate has a total of 28 between both parallel sections in series.
Pipes were placed directly under each IGBT. IGBT and plate junction material is not
visible in Figure 6 again due to the small thickness.
Figure 6 Cold Plate Option Three - Parallel/Series Elevation View
8
2.
Methodology
The first objective was to determine the operating voltages and currents for the IGBTs
within the integrated power electronic module. Once the operating conditions were
known, a calculation was completed to determine the total losses associated with the
IGBTs contained within the IPEM. Once losses were determined, the design of three
separate cold plates were completed, all having slightly different attributes. Analysis of
each cold plate began with determining pressure drop. Pressure drop calculations
allowed for a down selection to two cold plates to continue on with the thermal analysis.
Materials, flow rate, and cold plate attributes were addressed during the analysis phase.
Calculations were completed to determine heat spreading, temperature changes and the
effectiveness of force convection fluid cooling to develop an understanding of
performance based attributes. Once standard calculations were completed, an ANSYS
CFX analysis of the cold plate design was performed to compare with calculated results
and obtain a better understanding of cold plate operation. Modifications were then
performed to the cold plate which performed best during analysis to obtain an improved
design.
2.1 Losses of Integrated Power Electronic Module Analysis
Integrated power electronic modules contain many heat producing electronic devices,
however IGBTs are the cause of the majority of the module’s losses. In this analysis, for
simplification, the IPEM contains four IGBTs and all other components have been
disregarded. A circuit diagram shown by Figure 7 depicts the four IGBTs and their
associated circuitry.
9
Figure 7Circuit Diagram of Integrated Power Electronic Module
IGBTs 1-4 are Powerex’s CM1800HCB-34N model and rated for 1800A and 1700 volts.
Each IGBT device consists of three IGBTs in parallel as shown in Figure 7 at the bottom
right. This circuit configuration is known as an H-bridge and is commonly used in many
IPEM applications. Each IGBT consists of two power devices, a transistor and a diode.
Both power devices will have conduction and switching power losses. Heat is generated
as a result of these losses and must be conducted away from the power chips via the
available cold plate designs.
Switching losses are a resultant of the power dissipated during the turn-on and turn-off
switching transitions. To accurately determine switching losses, both current and voltage
waveforms must be plotted during the switching transition. The area under the power
waveform is the switching energy. Powerex’s data sheet of the IGBT used in the current
analysis contain both the turn-on energy ESW(on) and the turn-off energy ESW(off). A
typical wave form of switching is shown below in Figure 8, depicting both the turn-on
and turn off energy. [3]
10
Figure 8 Switching Losses, Turn-on & Turn-off Losses[3]
The main concern with these power pulses is they’re summed together when the device
is repetitively switching on and off. For this analysis the current and voltage are
considered constant therefore ESW(on) and ESW(off) are the same for every turn-on and turnoff. Therefore, the formula for the average switching power loss of the transistor is:
𝑃𝑠𝑤𝑀 = (𝐸𝑆𝑊𝑜𝑛 + 𝐸𝑆𝑊𝑜𝑓𝑓 )𝑓𝑠𝑤
Equation 1[3]
The variable fsw is the switching frequency, which allows the equation to sum up all
turn-on and turn-off occurrences. For the diode’s calculation of the switching losses,
EonD must be determined first by the following equation:
𝐸𝑜𝑛𝐷 = .125𝐼𝑅𝑅 𝑡𝑅𝑅 𝑉𝐶𝐸
Equation 2[4]
Variable IRR is the peak reverse recovery current, tRR is the diode reverse recovery time
and VCE is the emitter-collector voltage. Once EonD is obtained the formula for the
average switching power loss of the diode is:
𝑃𝑠𝑤𝐷 = 𝐸𝑜𝑛𝐷 𝑓𝑠𝑤
11
Equation 3[3]
Steady state losses or conduction losses occur while the IGBT is on and conducting
current. To obtain the total power dissipated due to conduction, the on-state saturation
voltage must be multiplied by the on-state current.[3] In addition, the collector-emitter
on-state resistance Rc must be taken into account. The equation for the transistor’s
conduction losses is as follows:
1 𝑀 𝑃𝐹
1 𝑀 𝑃𝐹
𝑃𝐶𝑇 = 𝑈𝐶𝐸𝑂 𝐼𝑜 ( +
) + 𝑅𝐶 𝐼𝑜2 ( −
)
2𝜋
8
8
3𝜋
Equation 4[3]
Variable UCEO is the on-state zero current collector-emitter voltage, Io is the current, M is
the modulation index which is assumed to be at 50% and PF is the power factor assumed
to be 98%.The equation for the diode’s conduction losses is similar and is as follows:
𝑃𝐶𝐷 = 𝑈𝐷𝑂 𝐼𝑜 (
1 𝑀 𝑃𝐹
1 𝑀 𝑃𝐹
+
) + 𝑅𝐷 𝐼𝑜2 ( −
)
2𝜋
8
8
3𝜋
Equation 5[3]
Variable UDO is the on-state zero current collector-emitter voltage of the diode and RD is
the collector-emitter on-state resistance of the diode. To obtain the total power loss of
the IGBT from both switching and conducting losses, PswM and PCT must be added as
shown below by Equation 6:
𝑃𝑇 = 𝑃𝑠𝑤𝑀 + 𝑃𝐶𝑇
Equation 6
Similarly for the diode, the conduction and switching losses must be added as shown by
Equation 7:
𝑃𝐷 = 𝑃𝑠𝑤𝐷 + 𝑃𝐶𝐷
Equation 7
Lastly, total transistor losses and total diode losses must be summed to obtain the final
losses the cold plate must remove for safe and efficient operation of the IPEM. The total
power loss of an IGBT device is formulated to be:
𝑃𝑇𝐷 = 𝑃𝑇 + 𝑃𝐷
12
Equation 8
2.2 Pressure Drop Analysis
An important characteristic when designing cold plates are their overall pressure drop.
The larger the pressure drop of the cold plate the more energy must be used to maintain
constant flow rates for the system. A cold plate’s main function is to remove heat from
the heat source, in this case a integrated power electronic module. The system designer
must take into account the cooling system as a whole; therefore cold plate design must
adhere to system level requirements and limitations. In this case, system level limitations
stem from the cooling system’s external heat exchanger and pump. Pumps are rated to
supply a specific flow rate to the cooling system. Cold plate designers must develop the
internal piping of a cold plate for a specific flow rate and must abide to strict pressure
drop limitations.
The cold plate designer must perform a pressure drop calculation to understand all losses
endured by the cooling system. In order to perform this calculation we must assume that
the system is a steady flow in a pressure conduit. It is assumed that the cooling medium
is an incompressible fluid with a relatively constant density (𝜌). In order to understand
the type of flow within our system we must determine if the flow is turbulent or laminar.
Turbulent flow is desired in forced convective heat transfer but causes large pressure
drops. The Reynolds number can be calculated to determine the type of flow the system
has. In the flow of a fluid through a completely filled conduit, gravity will not affect the
flow pattern. Therefore the significant forces are inertia and fluid friction due to
viscosity. For the ratio of inertia forces to viscous forces, we call the resulting parameter
the Reynolds number (Re). The Reynolds number is a dimensionless number which
helps compare different flows. The Reynolds number formula is:
𝑅𝑒 =
𝜌𝐷𝑉
𝜇
Equation 9
This takes into account the pipe hydraulic diameter Dh, the velocity of the fluid V, the
density 𝜌 and the dynamic viscosity𝜇. To determine the type of flow one must take into
account the laminar, transitional, and turbulent flow ranges. For laminar flow, the
Reynolds number falls into the range of 0-2000. The transition range is from 2000-4000.
13
The turbulent flow regime ranges from 4000 and on.[5]The Reynolds number ranges
vary based on equations used during the analysis and from reference to reference;
however throughout this analysis the above ranges will be used for determining all flow
characteristics.
The flow rate, Qf is an important characteristic of fluid flow. If the cross sectional area
of the pipe/channel is known, the flow rate formula will allow for the calculation of fluid
velocity. The flow rate formula is:
𝑄𝑓 = 𝑉𝐴
Equation 10
Hydraulic diameter is used when determining the Reynolds number, mainly to handle
non-circular conduits. When used to determine circular pipe hydraulic diameters the
equation simplifies to the diameter of the pipe. The hydraulic diameter’s formula is:
𝐷ℎ =
4𝐴
𝑃𝑤
Equation 11
A is the cross-sectional area and P is the wetted perimeter.
Pipe friction head loss is the major cause of pressure loss in a pipe system. The pipe
friction (Darcy Weisbach) equation is:
ℎ𝐿𝑚𝑎𝑗𝑜𝑟
𝑉 2𝑙
=𝑓
2𝑔𝐷ℎ
Equation 12[5]
The friction factor ƒ is based on the Reynolds number and pipe smoothness, L is the pipe
length, Dh is the hydraulic diameter, V is the velocity and g is the gravity constant. The
important variable within the pipe friction equation is ƒ the friction factor. Assuming
that the flow is turbulent, the friction factor must be determined by determining the
relative roughness of the pipe. The relative roughness equation is:
𝑅𝑜𝑢𝑔ℎ𝑛𝑒𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 =
14
∈
𝐷
Equation 13
The variable∈ is the absolute roughness of the pipe wall and is based on the different
sizes of material surface grains which can act as projections piercing the viscous sub
layer. The roughness equation is valuable when determining the pipe friction by use of
the Moody Chart for Pipe Friction Factor. However, there are equations which can be
used to obtain pipe friction factors which follow the Moody chart; the equation for pipe
friction factor used is shown below:
𝑓 = 0.0055 [1+(2000𝜀 +
106 1
)3 ]
𝑅𝑒
Equation 14[5]
The Darcy Weisbach equation is characterized as the major pipe loss equation which
takes into account pipe friction. Major pipe losses do not incorporate minor losses, such
as those caused by changes in cross section, elbows, valves, etc. Minor losses are
normally insignificant in comparison to losses due to pipe friction. However, in the
analysis of cold plate pressure losses one must take into account the minor losses
because their values may be just as significant to the major losses. The minor loss
equation is:
ℎ𝐿𝑚𝑖𝑛𝑜𝑟 = 𝐾𝐿
𝑉2
2𝑔
Equation 15
For the current analysis, the cold plate designs have multiple minor losses throughout
each pipe channel. Therefore in order to obtain the total minor head losses, all minor
losses must be summed as shown by Equation 16 below.
ℎ𝐿𝑚𝑖𝑛𝑜𝑟 = ∑ 𝐾𝐿𝑖
𝑖
𝑉2
2𝑔
Equation 16[5]
The resistance coefficient K, is determined for each particular case and most fluid
sources contain specific values for all possible components which cause minor losses.
The minor losses taken into account for the three cold plate designs included loss of head
due to 90o elbows, 180oreturns, tee flow through, tee branch flow, contraction in pipe
15
diameter, and expansion in pipe diameter. Below is a table consisting of the assumed
loss coefficients for each situation.
Table 5Loss Coefficients[5]
Type
Loss Coefficient K
90o Elbow
.3
180o Return
.2
Tee Line Flow
.2
Tee Branch Flow
1
Contraction Pipe Diameter
Dx&Vx Dependent
Expansion Pipe Diameter
Dx&Vx Dependent
Minor head loss for contraction of pipe diameter and expansion of pipe diameter must be
determined by comparing entrance and exit pipe diameters and their associated
velocities. For expansion or sudden enlargement in pipe diameter the minor head loss
equation is:
ℎ𝐿𝑚𝑖𝑛𝑜𝑟𝑒𝑥𝑝 = 𝐾𝐿
𝑉12
2𝑔
Equation 17[5]
To determine KL, a comparison of D2/D1 must be completed and then referenced from
the Resistance Coefficient of Expansion Table. Velocities and diameters are dependent
on the following figure:
Figure 9Sudden Expansion[5]
Similarly with sudden contraction in pipe diameter the minor head loss equation is:
16
ℎ𝐿𝑚𝑖𝑛𝑜𝑟𝑐𝑜𝑛
𝑉22
= 𝐾𝐿
2𝑔
Equation 18
To determine KL, a comparison of D1/D2 must be completed and then referenced from
the Resistance Coefficient of Contraction Table. Velocities and diameters are dependent
on the following figure:
Figure 10Sudden Contraction[5]
Total head loss is determined by first determining the major losses and sum all combined
minor losses. Total head loss equation is:
ℎ𝐿𝑇𝑜𝑡𝑎𝑙 = 𝑓
𝑉 2𝑙
𝑉2
+ ∑ 𝐾𝐿𝑖
2𝑔𝐷ℎ
2𝑔
Equation 19
𝑖
In order to incorporate both major and minor head losses correctly, it must be
determined whether the losses are in series or parallel flow paths. Pipe flow paths in
series allow their head losses to be additive and their flow rates are equal, shown by the
equation below:
𝑄𝑓 = 𝑄𝑓1 = 𝑄𝑓2 = 𝑄𝑓3 = 𝑄𝑓𝑛
Equation 20[5]
ℎ𝐿 = ℎ𝐿1 + ℎ𝐿2 + ℎ𝐿3 + ℎ𝐿𝑛
Equation 21[5]
Pipes in parallel satisfy continuity and energy equations by having the flow rates of each
pipe additive but the head losses of each pipe are equal to one another. Equation 22 and
Equation 23below better describe these principles.
17
𝑄𝑓 = 𝑄𝑓1 + 𝑄𝑓2 + 𝑄𝑓3 + ⋯ 𝑄𝑓𝑛
Equation 22[5]
ℎ𝐿 = ℎ𝐿1 = ℎ𝐿2 = ℎ𝐿3 = ℎ𝐿𝑛
Equation 23[5]
In order to determine pressure drop from head loss calculations, the energy balance
equation must be formulated. The Bernoulli energy equation is:
𝑃1
𝑉12
𝑃2 𝑉2 2
+
+ 𝑧1 − ℎ𝐿𝑚𝑎𝑗𝑜𝑟 − ∑ ℎ𝐿𝑚𝑖𝑛𝑜𝑟 = +
+ 𝑧2
𝛾
2𝑔
𝛾
2𝑔
Equation 24[5]
Variable P1 and P2 are pressures. In this case P2 was assumed to be zero to obtain the
pressure drop along the pipe length. V1 and V2 are velocities at the start and finish of the
pipe length. Z1 and Z2 are the height values of both the pipe start and finish. Both head
loss major and head loss minor are incorporated within the equation. Lastly, 𝛾 is specific
weight of water which is determined by multiplying the gravity constant by the density
of the water.
18
2.3 Thermal Analysis
Thermal analysis of the integrated power electronics module involves two major forms
of heat transfer: both conduction and forced convection. Radiation heat transfer and
natural convection are assumed to be small enough where the analysis does not need to
incorporate such modes of heat transfer. The assumption is that the IPEM is a closed
system which does not factor in radiated and natural convection heat transfer. The only
opportunity for energy transfer is via the de-ionized water.
2.3.1
Conduction Heat Transfer
The first major method of heat transfer this analysis takes into account is conduction
heat transfer. When temperature gradients exist in a solid body, there is energy transfer
from the high-temperature region to the low -temperature region. The energy transfer is
by conduction and the heat transfer rate is based on the unit area in proportion to the
temperature gradient. This relationship can be better understood by the following
equation for heat transfer rate:
𝑞 = −𝑘A
∂T
∂𝑥
Equation 25[6]
𝜕𝑇
q is known as the heat-transfer rate, 𝜕x is the temperature gradient in the direction of heat
flow, k is a constant, known as the thermal conductivity of the material and A is the
cross sectional area of the heat transfer. A negative sign is inserted prior to the thermal
conductivity constant due to the 2nd principle of thermodynamics which states that heat
must flow downhill on the temperature scale, which is known as Fourier's law of heat
conduction. The thermal conductivities used within this analysis are depicted in Table
6below.
Table 6 Material Thermal Conductivities[6]
Material
Thermal Conductivity (W/m-oC)
Corrosion Resistant Steel
25.9
Solder (63/37) SnPb
50
19
Aluminum
204
Copper-Nickel (70/30)
29
Copper-Nickel (90/10)
50
Thermal Grease (Dow Corning TC-5022)
4
Sil Pad
3.5
It is important to understand steady-state conduction, one dimension, which is used to
develop conduction heat transfer equations. Using Fourier's law, stated above, with
integration it yields Equation 26 based on the thermal conductivity considered constant.
𝑞=−
𝑘A
(T − T1 )
∆𝑥 2
Equation 26
Variable ∆x is the material thickness and T2 and T1 are the face temperatures. If there is
conduction through multiple materials, the heat flow equation is the following
𝑞 = −𝑘𝐴 𝐴
𝑇2 − 𝑇1
𝑇3 − 𝑇2
𝑇4 − 𝑇3
= −𝑘𝐵 𝐴
= −𝑘𝐶 𝐴
∆𝑥𝐴
∆𝑥𝐵
∆𝑥𝐶
Equation 27[6]
The equation shows that heat flow must be the same through all sections. When the
equations are solved simultaneously, heat flow can be rewritten as:
𝑞=
𝑇1 − 𝑇4
∆𝑥𝐶
∆𝑥𝐴
∆𝑥
⁄𝑘 𝐴 + 𝐵⁄𝑘 𝐴 +
⁄𝑘 𝐴
𝐴
𝐵
𝐶
Equation 28[6]
This equation introduces a slightly different concept which allows the heat transfer rate
to develop into a flow and the resistance to the heat flow is based on the combination of
thermal conductivity, thickness of material and area of heat transfer. Therefore, the heat
flow function can be written as
𝐻𝑒𝑎𝑡 𝐹𝑙𝑜𝑤 =
𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑞=
∆𝑇𝑜𝑣𝑒𝑟𝑎𝑙𝑙
∑ 𝑅𝑡ℎ
20
Equation 29
Equation 30
Rth is known as the thermal resistance of a material and has the units of oC/W or oF
h/Btu. Heat resistance, just as electrical resistance, may flow through different paths in
parallel and/or in series, each having different thermal resistances. Thermal networks
developed in this fashion provide a tool to determine an equivalent resistance which
leads to the ability to determine a temperature difference.
Thermal resistance, which is similar to electrical resistance to current flow, is dependent
on the material and how it resists heat flow. In electrical analysis the relationship
between the electric potential and resistance is defined as
∆𝐸 = 𝐼𝑅
Equation 31
whereI is the electrical current. Therefore, a similar relationship can be developed for
temperature; the thermal resistance and heat flow equations are shown below:
∆𝑇 = 𝑄𝑅
Equation 32
𝐿
𝑘𝐴
Equation 33
𝑅𝑡ℎ =
Series resistance is when the conduction path causes an increase of the overall thermal
resistance. Series resistance’s basic equation is:
𝑅𝑡ℎ𝑡𝑜𝑡𝑎𝑙 = 𝑅𝑡ℎ1 + 𝑅𝑡ℎ2 + 𝑅𝑡ℎ3 +. . . +𝑅𝑡ℎ𝑛
Equation 34[6]
Therefore in a series resistance network the thermal resistances will simply add to
develop the overall thermal resistance. The parallel rule is present when the conduction
path is varied through multiple materials with varying thermal conductivity. Therefore
the thermal resistance of such a network will decrease due to the formulation below
1
𝑅𝑡ℎ𝑡𝑜𝑡𝑎𝑙
=
1
1
1
1
+
+
+. . . +
𝑅𝑡ℎ1 𝑅𝑡ℎ2 𝑅𝑡ℎ3
𝑅𝑡ℎ𝑛
Equation 35[6]
Heat flow for cylinders must be understood for this application because of the internal
pipes routed throughout the cold plate. When a cylinder is exposed to a temperature
differential there will be a radial heat flow. It is assumed that the cylinder length is very
21
large compared to its diameter, which fits our application. Fourier's law is used again by
developing the proper area relation. The area of a cylinder is
𝐴 = 2𝜋𝑟𝐿
Equation 36
Therefore when the cylindrical area is implemented into Fourier's equation heat flow is
𝑞 = −2𝜋𝑘𝑟𝐿
𝑑𝑇
𝑑𝑟
Equation 37
𝑑𝑇
Boundary conditions must be determined for 𝑑𝑟 and are determined to be:
T=Tiat r=ri[6]
T=To at r=ro[6]
Therefore the final equation for radial heat flow and cylindrical resistance is:
𝑞=
𝑅𝑡ℎ
2𝜋𝐿(𝑇𝑖 − 𝑇0 )
r
ln( o⁄ri )
Equation 38[6]
ln(𝑟𝑜 ⁄𝑟𝑖 )
=
2𝜋𝑘𝐿
Equation 39[6]
2.3.2 Forced Convection Heat Transfer
Convective heat transfer is the second form of heat transfer that must be analyzed within
the integrated power electronic module analysis. The cold plate internal piping uses deionized water as the cooling transport medium. This method of cooling is better known
as forced convection cooling. This is an indirect method; therefore no fluid comes into
contact with the electrical equipment within the IPEM. Convection takes place in liquids
and gases and relies on the relative motion of viscous media. The basic equation for
convection is
𝑄 = ℎ𝑐 𝐴Δ𝑇
22
Equation 40
The new variable introduced for convective heat transfer is hc which is the coefficient of
heat transfer. The temperature gradient ∆T is confined to a very thin fluid layer
immediately adjacent to the surface of the pipe. This fluid layer is known as the
boundary layer and exists due to the mixing motion of the de-ionized water. Boundary
layer thickness is dependent on the de-ionized coolant velocity and the two conditions
that must be taken into account for are laminar and turbulent flow. Turbulent flows are
broken up into eddies and cross currents; all which affect the boundary layer
effectiveness to absorb heat flow. Therefore, in this analysis, a turbulent flow condition
is desired to obtain the highest heat transfer rate into the de-ionized fluid; though careful
consideration must be taken to control the excessive pressure drop related with turbulent
flow, which is better described in the pressure drop section of this analysis.
Nondimensional groups were used within the analysis while determining flow
characteristics. Results of engineering research and works in fluid flow and heat transfer
are expressed in terms of nondimensional numbers. As seen in the prior section of the
initial pressure drop calculations, the Reynolds number gives a nondimensional
relationship between inertia and viscous forces and its equation is:
𝑅𝑒 =
𝜌𝑉𝐿
𝜇
Equation 41
The Nusselt number shows the relationship between a fluid's capacity to convect heat
versus its capacity to conduct heat. The formula is as follows:
𝑁𝑢 =
ℎ𝐿
𝑘
Equation 42
The last nondimensional number used within this analysis is the Prandtl Number. The
Prandtl number shows the relationship between the capacity of a fluid to store heat
versus its conductive capacity. The formula is as follows:
𝑃𝑟 =
23
𝐶𝑝 𝜇
𝑘
Equation 43
The current analysis equations must be developed to handle heat transfer in a fully
developed turbulent tube flow. Analysis of turbulent flow systems is a far more
complicated process compared to laminar flow; however turbulent flow is an extremely
important aspect of cold plate and associated heat transfer equipment. The bulk
temperature is an important factor which must be considered in heat transfer involving
flow within a pipe or channel. Bulk temperature represents an energy average condition.
For tube flow of the cold plate the total energy added can be expressed in terms of bulk
temperature difference by the following formula:
𝑞 = 𝔪̇𝐶𝑝 (𝑇𝑏2 − 𝑇𝑏1 )
Equation 44
For this expression to correctly relate to the problem at hand, Cp, the specific heat of
water, must be considered constant over the length of the pipe. However, once initially
calculated, iterations will be completed to better accurately calculate all non-constant
properties or those that are affected by temperature change. Along the pipe, a differential
length dx is considered to determine the heat added dq which can be expressed in bulk
temperature difference with the heat transfer coefficient h which is shown below:
𝑑𝑞 = 𝔪̇𝐶𝑝 𝑑𝑇𝑏 = ℎ(2𝜋𝑟)𝑑𝑥(𝑇𝑤 − 𝑇𝑏 )
Equation 45[6]
The total heat transfer can also be expressed as the following formula:
𝑞 = ℎ𝐴(𝑇𝑤− 𝑇𝑏 )𝑎𝑣𝑔
Equation 46
Tw and Tb are the wall and bulk temperatures at a particular length location of the pipe.
With the assumption that our piping within the cold plate is smooth pipe, it is possible to
use a traditional expression for the calculation of heat transfer in fully developed
turbulent flow, which is recommended by Dittus and Boelter:
𝑁𝑢 = 0.023𝑅𝑒 0.8 𝑃𝑟 𝑛
Equation 47[6]
However, it has been determined that the accuracy of this formula could range from +/25%. Petukhov has developed a more accurate, yet complicated expression for fully
developed turbulent flow in smooth pipes:
24
𝑁𝑢 =
(𝑓 ⁄8)𝑅𝑒𝑃𝑟
𝜇𝑏 𝑛
)
1⁄
2⁄
𝜇
2
𝑤
3
⁄
1.07 + 12.7(𝑓 8) (𝑃𝑟 − 1)
(
Equation 48[6]
Variable n is dependent on temperature differences between the wall temperature and the
bulk temperature and is dependent on the type of heat flux. Table 7 shows what value n
is depending on various situations.
Table 7 Nusselt Number Equation n Value[6]
Situation
Value of n
Tw> Tb
0.11
Tw< Tb
0.25
Constant Heat Flux
0.0
Gas Medium
0.0
All fluid properties are evaluated at Tf =(Tw+Tb). The friction factor has been
determined earlier in the pressure drop section, however there is an equation that is
related to the Nusselt number equation which is:
𝑓 = (1.82 log10 𝑅𝑒 − 1.64)−2
Equation 49[6]
Equation 48 is applicable for the following ranges listed in Table 8 below.
Table 8 Nusselt Equation Applicable Ranges[6]
Range
Accuracy Percentage
0.5 <Pr< 200
For 6% Accuracy
0.5 <Pr< 2000
For 10% Accuracy
104< Red< 5x106
N/A
.8 < µb/µw< 40
N/A
In the case that the flow condition is determined to be laminar the specific Nusselt
number equation is needed for fully developed flow in pipe. The formula is as follows:
𝑁𝑢 = 3.66 +
0.0668(𝐷⁄𝐿)𝑅𝑒𝑃𝑟
Equation 50[6]
2⁄
3
1 + 0.04[(𝐷⁄𝐿)𝑅𝑒𝑃𝑟]
25
This formulation of the Nusselt number is calculated from an average value of the heat
transfer coefficient over the entire length of the pipe. The Nusselt number will approach
a constant value of 3.66 if the pipe length is sufficiently long.
The determination of temperature variance along pipe length is an important factor cold
plate design engineers must understand to size the necessary heat exchangers for the
overall system. The water temperature will be increasing along the pipe length; this will
cause a temperature variation amongst the IGBT modules being cooled on the cold plate.
In order to determine relative hot spots temperature variations in the water must be taken
into account when determining the necessary properties which are used within the heat
transfer analysis. To determine the change in temperature along the pipe length of the
cold plate the following formula was used:
𝑞 ′ (𝑥) = 𝑚̇𝐶𝑝 (𝑇(𝑥) − 𝑇𝑖𝑛 )
Equation 51[7]
This formula was rearranged on obtain T(x), the temperature at distance x along the
pipe, resulting in the following formula:
𝑇(𝑥) = 𝑇𝑖𝑛 +
𝑞
𝑥
𝑚̇𝐶𝑝
Equation 52[7]
With a constant heat flux, this formula equates to a linear function of temperature along
the cold plate pipe length.
2.3.3
Fouling Effects on Heat Transfer
Design engineers must be aware of fouling affects which could diminish the cold plate’s
ability to remove the necessary added heat to keep the electrical equipment at an
acceptable temperature rise. A certain design margin must be added to account for
fouling over long periods of system operation. After a period of operation the heat
transfer surfaces of a heat exchanger (the cold plate) may become coated with various
deposits present in the flow system. These deposits can be left over material from
26
construction or an accumulation of corroded material. This coating, in relation to heat
transfer, represents an additional resistance to the heat flow, and thus results in a
decreased performance of the cold plate. The fouling factor represents the overall affect
and is also known as the fouling resistance Rf. The fouling resistance must be
incorporated with the overall heat transfer coefficient.
Fouling factors are obtained experimentally by determining both the clean and dirty
(fouled) conditions of the cold plate piping. The fouling factor is defined as follows:
𝑅𝑓 =
1
𝑈𝐷𝑖𝑟𝑡𝑦
−
1
Equation 53[6]
𝑈𝐶𝑙𝑒𝑎𝑛
Table 9 contains the recommended values of the fouling factor for various cooling
mediums.
Table 9 Common Fouling Factors[6]
Fouling Factor
Type of Fluid
m2 o C/W
Sea Water (below 125 oF)
0.00009
Refrigerating Liquid
0.0002
De-ionized Water
0.00009
Using the above recommended values for the fouling factor gives the ability to
determine the influence it has on the heat transfer coefficient. The following formula
depicts this ability:
𝑅𝑓 =
1
ℎ𝑑𝑖𝑟𝑡𝑦
+
1
Equation 54[6]
ℎ𝑐𝑙𝑒𝑎𝑛
Other common ways to determine the effect of fouling on the heat transfer coefficient is
to design the exchanger, in this case the cold plate, with a fouling factor percentage. A
common military fouling factor percentage is that of 10%. Therefore, to obtain the heat
transfer coefficient based on a 10% fouling factor the following equation must be used:
27
ℎ𝑑𝑖𝑟𝑡𝑦 = ℎ𝑐𝑙𝑒𝑎𝑛 + [ℎ𝑐𝑙𝑒𝑎𝑛 ∗ 10%]
Equation 55
The added fouling factor of a heat exchange process is an extremely important
characteristic that design engineers must incorporate into their overall system design.
28
3. Results
3.1 Losses of Integrated Power Electronic Module
Losses of the integrated power electronic module were calculated to be 4125 watts per
IGBT. A total of 16500 watts per IPEM must be removed by each cold plate option. The
IGBT under analysis was a Powerex CM1800HCB-34N and the manufacturer rated the
power device for 1800 A and 1700 volts. In order to extend the life of the power
electronic devices within the IPEM, a de-rating factor of 25% was used based on rated
power. Therefore each IGBT used within this analysis is de-rated to 1350 A and 1275 V.
Losses were calculated for both the transistor and diode of the IGBT. Both switching
losses and conduction losses were accounted for. Figure 11 breaks down the losses
calculated for each power device based on conduction and switching. It is understood
that the transistors switching losses are far greater than all other losses found in the
IGBT. The transistor losses totaled to 2494.65 W and the diode losses were 1093 W. The
transistor losses make up 60% of the IGBTs total losses.
Losses of Transistor & Diode
487.69 W
522.65 W
605.62 W
1972.00 W
0.00
500.00
1000.00
1500.00
2000.00
Diode Recovery Losses
Transistor Conduction Losses
Diode Conduction Losses
Transistor Switching Losses
Figure 11 Losses of Transistor & Diode
29
It is important to understand that the IGBT's switching losses are 68% of the losses
compared to conduction losses. Figure 12 displays how much greater the switching
losses of the IGBT are compared to its conduction losses.
Switching Losses vs. Conduction Losses
1297.52 W
2828.64 W
0.00
500.00
1000.00
1500.00
2000.00
Conduction Losses
2500.00
3000.00
Switching Losses
Figure 12 Total Switching Losses vs. Total Conduction Losses
The IGBT's switching frequency is a major concern to IPEM design engineers. There are
many benefits to a high switching frequency, mainly better output power quality.
Various switching frequencies were analyzed to understand their relation to IGBT
losses. The switching frequency has a direct relationship with the IGBT power losses.
Figure 13 shows the relationship between switching frequency and total power losses.
Two de-rating cases were graphed two shows the relationship between de-rating factors
and losses based on various frequencies. Losses calculated to 4125 W for each IGBT
was chosen because it is the middle value of the losses range calculated. A factor of
safety of 15% was applied to the calculation because the calculation uses average values
of turn-on and turn off energies of the IGBT.
30
IPEM Power Losses
6500
6000
Losses (Watts)
5500
5000
4500
Losses
(.25
Derating)
4000
3500
3000
2500
500
1000
1500
2000
Switching Frequency (Hz)
2500
3000
Figure 13 IPEM Power Losses
The calculated losses from the IGBTs located on the cold plate will generate 16500
watts. The heat flux into the cold plate is determined to be 155132.7 W/m2or 15.51
W/cm2.
31
3.2 Pressure Drop Results
Pressure drop calculations were completed for each cold plate option. In order to
compare each cold plate's pressure drop, water properties were kept constant as well as
flow rates. To correctly develop each cold plate option, specific pipe sizes and pipe
routing was implemented. Table 10 below displays the calculated pressure drop values
for each cold plate option. The pressure drops due to the major and minor losses are
irreversible. Cold plate option two provided the lowest pressure drop while cold plate
option three produced the largest.
Table 10 Cold Plate Options One, Two & Three Pressure Drops
Pressure Drop
(psi)
4.96
Cold Plate Option
Option 1- Series
Option 2- Parallel
2.67
Option 3- Parallel/Series
6.0
A more in depth discussion of calculated pressure drops occurs in the following sections.
3.2.1
Pressure Drop Results of Cold Plate Option One
Cold plate option one was designed with a series pipe flow path. Calculations were
completed with an inner pipe diameter of .57 inches. The total length of pipe imbedded
within the cold plate totaled to 147.6 inches. Flow rate was kept constant at 10 gallons
per minute. The flow rate and pipe cross sectional area produced a 12.57 ft/s water
velocity. The flow condition was determined to be turbulent. Both major and minor head
loss was calculated and Table 11 shows associated calculated values.
Table 11 Cold Plate Option One Head Losses
Type of Head Loss Head Loss (m)
Major Head Loss
3.37
Minor Head Loss
.45
32
Major head loss consisted of 88% of total head loss for cold plate option one. Minor
head loss was minimal for cold plate option one's design due to the limited bends and
lack of flow contractions. The only minor loss considered was that of the three 180o
return bends.
Figure 14 depicts the pressure distribution along cold plate option one's piping. This
graph displays all major and minor head losses the piping system forces upon the fluid.
Slopes within the data are representative of losses due to pipe friction (major head
losses) and sharp declines are due to component losses; in this analysis the three 180 o
return piping bends are clearly visible in Figure 14.
Pressure Drop of Cold Plate Option One
6.0
5.0
Pressure Drop (psi)
4.0
Pressure
Drop
(psi)
3.0
2.0
1.0
0.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
Length (in)
Figure 14 Pressure Drop of Cold Plate Option One
An ANSYS pressure drop analysis was completed for cold plate option one. Results
came in fairly similar to the self-calculated pressure drop. The self-calculated pressure
drop totaled to 5.36 psi and the ANSYS analysis determined a 4.96 psi pressure drop.
33
Self-calculated versus ANSYS analysis results, resulted in a percent error of 8%.Figure
15 below depicts the pressure contours of cold plate option one. It was assumed that the
static pressure at the outlet was equal to zero to obtain the pressure drop.
Figure 15ANSYS Pressure Drop Results Cold Plate Option One
Cold plate option one met all fluid related design requirements as shown in Table 12
below.
Table 12 Cold Plate Option One Requirement Review
Requirement
Requirement Calculated/Actual
Value
Value
Maximum Flow Rate
10 gpm
10 gpm
Maximum Liquid Velocity
15 ft/s
12.57 ft/s
Maximum Pressure Drop
6 psi
4.96 psi
34
3.2.2
Pressure Drop Results of Cold Plate Option Two
Cold plate option two was designed with a supply and a return manifold connecting a
total of 40 parallel pipe flow paths. Calculations were completed with an inner pipe
diameter of .14 inches. One pipe run under the IGBTs totaled 7.98 inches and the total
length of pipe imbedded under each IGBT is 79.8 inches. The manifold supply and
return piping inner diameter was sized at .57 inches. Flow rate was kept constant at 10
gallons per minute for the pressure drop calculation. Velocity of the water within the
manifolds was calculated to be 12.58 ft/s and the velocity of the parallel pipe section was
calculated to be 5.21 ft/s. Both flows were determined to be turbulent. Both major and
minor head loss was calculated and Table 13 shows their associated values.
Table 13 Cold Plate Option Two Head Loss
Type of Head Loss
Head Loss (m)
Major Head Loss of Manifolds
1.38
Minor Head Loss of Manifolds
.2855
Major Head Loss of Parallel Section .23
Minor Head Loss of Parallel Section 0
Major head loss was again the majority of head loss experienced by the fluid of cold
plate option two. However, minor head loss did contribute to a sizeable head loss. Minor
head loss was attributed to sudden contraction, sudden expansion and flow through a tee
branch.
Figure 16 depicts the pressure distribution along cold plate option two piping. This graph
displays all major and minor head losses the piping system forces upon the fluid. Slopes
within the data are representative of losses due to pipe friction (major head losses) and
sharp declines are due to the sudden contraction of flow coupled with tee branch flow
and sudden expansion coupled with tee branch flow.
35
Pressure Drop of Cold Plate Option Two)
3.000
Pressure Drop (psi)
2.500
2.000
1.500
Pressure
Drop (psi)
1.000
0.500
0.000
0
10
20
30
40
50
60
70
Coldplate Distance (in)
Figure 16 Pressure Drop of Cold Plate Option Two
An ANSYS pressure drop analysis was completed for cold plate option two. Results
were more complicated to compare based on a simplification made to the pipe geometry
of both the supply and return manifold. However, the pressure drop results from ANSYS
of the parallel section of pipe to relate closely to the self-calculated pressure drop. The
self-calculated pressure drop for the parallel section totaled to .91 psi and the ANSYS
analysis determined a .87 psi pressure drop. Self-calculated versus ANSYS analyses
resulted in a percent error of 4.4%. Figure 15 below depicts two pipe sections of the
pressure contours of cold plate option two and their steady pressure decline. It was
assumed that the static pressure at the outlet was equal to zero to obtain the pressure
drop.
36
Figure 17ANSYS Pressure Drop Results Cold Plate Option Two
Cold plate option two met all fluid related design requirements as shown in Table 14
below.
Table 14 Cold Plate Option Two Requirement Review
Requirement
Requirement Calculated/Actual
Value
Value
Maximum Flow Rate
10 gpm
10 gpm
Maximum Liquid Velocity
15 ft/s
Maximum Pressure Drop
6 psi
3.2.3
12.58 ft/s
5.2 ft/s
2.7 psi
Pressure Drop Results of Cold Plate Option Three
Cold plate option three is a hybrid design which incorporated both parallel and series
pipe flow paths. The pipe flow path is symmetrical for both sets of two IGBTs. Each
symmetrical section consists of a supply and return manifold connecting seven smaller
37
parallel piping located under each IGBT. Calculations were completed with the parallel
section inner pipe diameter of .31 inches. One pipe run under the IGBTs totaled 7.98
inches and the total length of pipe imbedded under each IGBT is 55.9 inches. The
manifold supply and return piping inner diameter was sized at .57 inches. Flow rate was
kept constant at 10 gallons per minute for the pressure drop calculation. Velocity of the
water within the manifolds was calculated to be 12.58 ft/s and the velocity of the parallel
pipe section was calculated to be 6 ft/s. Both flows were determined to be turbulent.
Both major and minor head loss was calculated and Table 15 shows their associated
values.
Table 15 Cold Plate Option Three Head Losses
Type of Head Loss
Head Loss (m)
Major Head Loss of Manifolds
1.03
Minor Head Loss of Manifolds
2.85
Major Head Loss of Parallel Section .366
Minor Head Loss of Parallel Section .99
Major head loss is not the majority of head loss experienced by the fluid of cold plate
option three. Minor head loss contributed to a sizeable head loss for cold plate option
three. Minor head loss was attributed to sudden contraction, sudden expansion, 90o bend
and flow through a tee branch.
Figure 18depicts the pressure distribution along cold plate option three piping. This
graph displays all major and minor head losses the piping system forces upon the fluid.
Slopes within the data are representative of losses due to pipe friction (major head
losses) and sharp declines are due to flow through a tee branch, sudden contraction,
again flow through a tee branch, sudden expansion, and a 90o elbow and that series of
losses repeated again for the other symmetrical section.
38
Pressure Drop of Cold Plate Option Three
8.0
7.0
6.0
Pressure Drop (psi)
5.0
4.0
Pressure
Drop
(psi)
3.0
2.0
1.0
0.0
0
20
40
60
80
100
Cold Plate Pipe Distance (in)
Figure 18 Pressure Drop of Cold Plate Option Three
An ANSYS analysis was not completed for cold plate option three based on the selfcalculated pressure drop being over the required limit of pressure drop. The selfcalculated pressure drop totaled to 7.4 psi. Cold plate option three was disregarded for
the remainder of the analysis based on a 20% overage of pressure drop compared to the
required limit. A percent error of 15% was taken into account and the result was still
above the required limit. The requirement comparison is shown in Table 16.
39
Table 16 Cold Plate Option Three Requirement Review
Requirement
Requirement Calculated/Actual
Value
Value
Maximum Flow Rate
10 gpm
10 gpm
Maximum Liquid Velocity
15 ft/s
Maximum Pressure Drop
6 psi
40
12.58 ft/s
6.07 ft/s
7.4 psi
3.3
Thermal Results
Each cold plate design is geared to remove the calculated heat flux of 155,132.69 W/m2.
The cold plate designs were developed with certain varying parameters to understand
their effects on the heat transfer of the cold plate. Both cold plate options were designed
based on meeting certain component specification requirements which are listed in Table
17 below. These requirements are directly associated with the thermal analysis of each
cold plate.
Table 17 Thermal Requirements of Cold Plate Option One & Two
Requirement
Value
Pipe Material
Corrosion Resistant Steel
Pipe and Plate Interface
(63/37) Solder
Fluid
De-ionized Water
Inlet Temperature
40oC
Temperature Change of Fluid Limit
10oC
IGBT Maximum Temperature
120oC
Maximum Flow Rate
10 gpm
The driving requirement of each design is the IGBT maximum temperature of 120oC
which totals to a 20% maximum temperature de-rating. Each IGBT is rated to run at
150oC; however to obtain a safe and reliable IPEM the de-rated temperature of 120oC
must be met.
Thermal results of cold plate option one and cold plate option two were self-calculated
and compared to ANSYS computer analyses. For both cold plates a thermal resistance
circuit was developed. Each cold plate thermal resistance circuit is based off Figure 19;
however each cold plate design’s thermal resistance circuit varied slightly based on
number of pipe passes.
41
Figure 19 Basis of Thermal Resistance Circuit
The final thermal results for each cold plate are depicted in Table 18 below. Results are
based off an ambient temperature of 40oC, thermal grease applied between IGBT
junction and cold plate, 10% fouling, 10 gpm flow rate and an inlet temperature of 40oC.
Table 18 Final Thermal Results for Cold Plate Options One & Two
Cold Plate Design IGBT Calculated Temperature
Option One
92.53 oC
Option Two
85.63 oC
All results are further discussed in the following sections.
3.3.1
Calculated Thermal Results of Cold Plate Option One
The calculation of the thermal results of cold plate option one can be found in section
12.1 of Appendix G. The calculation was based off a thermal resistance circuit as shown
in Figure 20 below.
42
Figure 20 Cold Plate Option One Thermal Circuit
The thermal resistant circuit was developed by placing the IGBT junction resistance,
thermal grease resistance and aluminum plate resistance in series. The equivalent series
resistance was then added to a set of four equivalent resistances of the pipe interface
which are in parallel. Each pass of the piping interface consisted of the solder interface,
corrosion resistant steel, and water convection resistance. The piping interface was
added because they're in series; however the four piping interfaces are run parallel to
each other, causing them to follow the parallel rule shown in Equation 35. It was
assumed that all material properties remained constant for the self-calculated results.
Thermal conduction paths rely heavily on geometric properties of the material the heat is
passing through. With the formulation of all geometric properties of each resistance
43
shown in Figure 20, resistance values were determined along with the temperature
change their associated temperature change. The water resistive property is the major
varying attribute to each cold plate option. To obtain the water resistive value, the heat
transfer coefficient was calculated by using Equation 48 which determined the Nusselt
number leading to the calculation of the heat transfer coefficient. Cold plate option one’s
design allowed for a very effective heat transfer coefficient of 19509 W/m 2 K. Using the
water's heat transfer coefficient, the water's thermal resistance and temperature was then
determined. Table 19 shows the breakdown of material resistance and its associated
temperature change.
Table 19 Cold Plate Option One Resistance & Associated Temperature Changes
Section
Calculated Resistance Calculated Temperature
(oC m2/W)
Change (oC)
IGBT Junction to Case
.00175
28.75
Sil Pad
.00068
11.26
Thermal Grease
.00007
1.16
Cold Plate
.00052
8.62
Solder Interface
.000101
1.62
Corrosion Resistant Steel Pipe
.000426
7.04
De-ionized Water Convection
.000285
4.7
.000313
5.17
De-ionized Water Convection
w/ Fouling
By obtaining the above temperature changes and having an ambient temperature of
40oC, the IGBT's operating temperature can be determined. Figure 21displays the
temperature profile of cold plate option one. Temperatures were based off a cold plate
design using thermal grease or sil pads. It is very important to understand the application
of thermal grease versus a sil pad. Thermal greases main function in to fill tiny
imperfections of the plate material that comes into contact with the base of the IGBT.
For this analysis, Dow Corning TC-5022 thermal grease was used. TC-5022 has a
thermal conductivity of 4 W/m-oC. A negative quality of thermal grease for electrical
44
applications is that it will not provide electrical isolation. For this calculation the thermal
grease thickness was assumed to be .00003 m thick. During construction of the cold
plate, the manufacturer must adhere to extreme tolerances of thermal grease thickness. If
the manufacture places too much thermal grease the cold plate could easily fail at
successfully removing the heat required for safe and reliable operation. Sil pads were
also analyzed to understand their effectiveness of creating an adequate thermal
conduction path. Unlike thermal grease, sil pads provide electrical isolation; however
their thermal properties are much weaker than thermal grease. The sil pad used in the
design of cold plate option one was Sil Pad 2000. This sil pad was chosen based on its
high thermal conductivity of 3.5W/m-oC. Both the thermal grease and sil pad analyzed
have similar thermal conductivity values. The main reason why the sil pad is a poor heat
conductor is due to its thickness compared to thermal greases'. For sil pads, the
manufacture must adhere to a stringent uniform pressure placed upon the junction
material. If the IGBT is mounted with an inconsistent pressure placed upon the sil pad,
its thermal conductivity could cause major heat transfer problems.
Temperature (oC)
Temperature Difference of Cold Plate Option One
110.00
105.00
100.00
95.00
90.00
85.00
80.00
75.00
70.00
65.00
60.00
55.00
50.00
45.00
40.00
35.00
30.00
Delta T w/
Thermal
Grease
Delta T w/ Sil
Pad
0
0.005
0.01
0.015
0.02
0.025
Distance Along Cold Plate (m)
Figure 21 Temperature Difference along Cold Plate Option One
45
Figure 21depicts the temperature difference based on cold plate option one being
constructed with thermal grease or sil pads. Sil pads add an additional 10oC to the IGBT
operating temperature.
An important assumption taken into account for the self-calculated analysis is that
temperature change of the water was disregarded in the overall temperature calculation.
The water temperature change can be accounted for to better understand the temperature
hotspots on the cold plate under analysis. It was determined that the outlet water
temperature would increase by 6.3 oC. Figure 22shows the temperature increase of the
de-ionized water as it travels through the cold plate piping. The temperature increase is a
linear function based on the water's flow rate and specific heat.
Temperature Difference Cold Plate Option One Pipe
320.00
319.00
Temperature (K)
318.00
317.00
316.00
Temperature
Difference
Along Pipe
315.00
314.00
313.00
312.00
0
0.5
1
1.5
2
2.5
3
3.5
4
Distance Along Pipe (m)
Figure 22 Temperature Difference along Cold Plate Option One Pipe
To better understand hotspots and the varying temperature of the water as it travels
through the cold plate pipe; the temperature change of the water can be added to the
calculated IGBT temperature. This should adjust the calculated IGBT temperature to
better match actual IGBT temperature rise. Table 20 breaks down all related temperature
increases of the IGBTs based on varying junction material and with/without fouling.
46
Table 20 Cold Plate Option One IGBT Temperature
With Out Fouling & Thermal Grease
Total Resistance w/ out Fouling 0.00316
o
C m2/W
Temperature Delta of IGBT
52.06
o
Ambient Temperature
40
o
Total IGBT Temperature
92.06
o
Total Resistance w/ Fouling
0.00318
o
Temperature Delta of IGBT
52.53
o
Ambient Temperature
40
o
Total IGBT Temperature
92.53
o
C
C
C
With Fouling & Thermal Grease
C m2/W
C
C
C
With Out Fouling & Sil Pad
Total Resistance w/ out Fouling 0.003767
o
C m2/W
Temperature Delta of IGBT
62.15
o
Ambient Temperature
40
o
Total IGBT Temperature
102.15
o
Total Resistance w/ Fouling
0.003795
o
Temperature Delta of IGBT
62.62
o
Ambient Temperature
40
o
Total IGBT Temperature
102.62
o
C
C
C
With Fouling & Sil Pad
C m2/W
C
C
C
Cold plate option one combined with thermal grease performed the best thermally. The
incorporation of thermal grease and the effects of fouling resulted in a 92.53oC IGBT
temperature, an increase of 52.53oC. Taking into account the water temperature increase
as it travels within the pipe, the actual IGBT temperature is calculated to be 98.85 oC.
The IGBT operating temperature is well below the de-rated temperature of 120oC. A
difference of 21.15oC which allows for a 17.6% temperature margin of error.
47
3.3.2
ANSYS Thermal Results of Cold Plate Option One
A self-calculated analysis of cold plate option one was completed followed by a
comparison analysis with ANSYS. Result validation through computer analysis allowed
for a successful thermal analysis comparison of the cold plate design. ANSYS is an
extremely powerful computational tool which gave the ability to geometrically develop
the cold plate model and incorporate all associated boundary conditions and system
inputs. ANSYS allows for model importing through the development of the model in
another solid modeling program by the use of an IGES file format; however all geometry
for this analysis was created in ANSYS. Following model construction, meshing of the
geometry was completed. Different meshing techniques were implemented for varying
sections of cold plate option one. Lastly, all boundary conditions, material properties,
and necessary inputs were programed into ANSYS.
3.3.2.1
ANSYS Meshing of Cold Plate Option One
Meshing of cold plate option one was completed by two different meshing techniques.
Meshing sections were broken into piping and plate sections. The plate section was
meshed using ANSYS automatic method. ANSYS allowed the user to select minimum
mesh sizes which was necessary to keep computation time to a minimum. Figure 23is an
image of cold plate option one’s plate mesh in ANSYS.
Figure 23 Meshing of Cold Plate Option One
48
The more complicated meshing process occurred when developing a mesh for the fluid
section of the cold plate. The finer the mesh the more accurate the results ANSYS can
compute; however the finer mesh models required much more computing time. In order
to obtain successful results and minimize computing time, ANSYS allows for multiple
meshing techniques. Meshing of the face of the piping model was the first meshing
technique used. Face spacing is a specific mesh length scale on a face, in this case the
outer surface area of the pipe model. Limitations were placed on face spacing lengths
which included: minimum edge length, maximum edge length, and expansion factor.
Length restrictions were determined by trial and error until expected results were
obtained.
Figure 24 Meshing of Cold Plate Option One Piping
The last and most important meshing technique used within the analysis was that of
inflation. Boundary inflation was necessary because when developing geometry with a
near-wall region, a boundary level effect will give rise to velocity gradients which are
greatest normal to the pipe wall. In order to develop a computationally-efficient mesh
this region required that the elements have a high aspect ratio. The CFX-mesh program
uses prisms to create the mesh which is normal to the wall but then coarse meshing of all
parallel to it. ANSYS recommend 10 inflated boundary layers for turbulent fluid
49
modeling. Figure 25 below is an image of the completed inflated boundary layers of the
pipe within cold plate option one.
Figure 25 Meshing of Cold Plate Option One Inflation Boundary
Once meshing of the model was completed, all necessary boundary inputs and any
related material properties can be inputted.
3.3.2.2
ANSYS Temperature Results of Cold Plate Option One
After cold plate option one's meshing was completed, all remaining input parameters
were inputted into ANSYS. For cold plate option one, inlet and outlet locations were
specified. Water boundary conditions consisted of a 40oC inlet temperature, 0 Pa static
outlet pressure and including an energy system with the ability for thermal heat flux. All
material interfaces were either understood by ANSYS or manually inputted. The
corrosion resistant steel interface and the solder interface were chosen to be a thin
conductive interface.
Adiabatic boundary conditions were assumed for the plate material of cold plate option
one. This allows the analysis to understand that the cold plate is a closed system and the
only way for energy to be removed from the system is via the cooling medium. On top
of the cold plate, imprinted faces were created to allow for a localized injection of heat
50
flux from the IGBTs. Uniform heat flux of 155,132 W/m2 was placed over the surface of
the cold plate based on the actual location of the IGBTs.
Figure 26 depicts the temperature contours of cold plate option one. It is visible that the
IGBT hotspots occur biased to the right side of the cold plate. The water passing beneath
the right side of the IGBTs has already absorbed energy from the first and second passes.
The temperature profile under each IGBT is not uniform.
Figure 26 Temperature Results of Cold Plate Option One
The maximum temperature reaches 71.7oC. This temperature does not include the IGBT
junction resistance temperature rise since this was a given value by the IGBT
manufacturer. To obtain a true temperature of the IGBT, a 28.88oC value was added to
the ANSYS result. Therefore, knowing the ambient to be 40oC the IGBT temperature
rise was calculated to be 60.45oC. The IGBT hotspot operating temperature was
determined to be 100.45oC. The self-calculated results without fouling were calculated to
be 98.38oC. A difference of 2.07oC comparing self-calculated to ANSYS analysis and a
percent error of 2.06%. It is noted that the ANSYS calculation did not incorporate
51
fouling effects. Figure 27below depicts the temperature contours of cold plate option one
mid plane. A plane was inserted into the center of the model to where an elevation view
of the cold plate temperature difference could be viewed. The inlet location is located to
the far left and the outlet pipe path is on the far right. The water temperature variation is
visible as it enters and exits the cold plate. The water temperature change from inlet to
outlet was calculated in ANSYS to be 6.18oC and 6.37oC for the self-calculated method.
Variation of results was minimal but is assumed to be from the ANSYS convergence
method chosen. In order to minimize computation time, a less conservative convergence
method was chosen.
Figure 27 Temperature Results of Cold Plate Option One Mid-Plane
Figure 28below depicts the temperature values of the corrosion resistant steel. There are
visible hot spots on the surface of the pipes which are directly under each IGBT. It is
again visible that the hotspots are biased towards the right side of the cold plate, again
due to increase water temperature from the earlier passes.
52
Figure 28 Temperature Results of Cold Plate Option One Piping
Cold plate option one meets all necessary thermal requirements as shown below in Table
21.
Table 21 Cold Plate Option One Thermal Results vs. Requirements
Requirement
Pipe Material
Requirement Value
Corrosion Resistant
Steel
Calculated/Actual
Value
Corrosion Resistant Steel
Pipe and Plate Interface
(63/37) Solder
(63/37) Solder
Fluid
De-ionized Water
De-ionized Water
Inlet Temperature
40oC
40oC
10oC
6.32oC
IGBT Maximum Temperature
120oC
100.45oC
Maximum Flow Rate
10 gpm
10 gpm
Temperature Change of Fluid
Limit
53
3.3.3
Calculated Thermal Results of Cold Plate Option Two
The calculation of the thermal results of cold plate option one can be found in Section
12.2 of Appendix G. The self-calculation was based off the thermal resistance circuit as
shown in Figure 29 below.
Figure 29 Cold Plate Option Two Thermal Circuit
The thermal resistance circuit was developed in a similar manner of cold plate option
one’s thermal circuit. The resistance values of the IGBT junction to plate, thermal
grease, and aluminum plate were summed as a series resistance. The equivalent
resistance was then added to a set of 40 equivalent resistances of the pipe interface
which are in parallel with one another. Each pass of the piping interface consisted of the
following resistances: solder interface, corrosion resistant steel pipe, and water
convection. Each pipe interface paths equivalent series resistance was than summed
following the parallel rule shown in Equation 35. For cold plate option two analysis, all
material properties were assumed to be constant in order to perform a more manageable
calculation.
The geometric properties of cold plate option two was determined and then the
calculation of each material’s resistance followed. Resistances and temperature changes
were determined for cold plate option two and are shown in Table 22.
54
Table 22 Cold Plate Option Two Resistance & Associated Temperature Changes
Section
Calculated Resistance Calculated Temperature
(oC m2/W)
Change (oC)
IGBT Junction to Case
.001750
28.75
Sil Pad
.000682
11.26
Thermal Grease
.000070
1.16
Cold Plate
.000520
8.62
Solder Interface
.000167
2.76
Corrosion Resistant Steel Pipe
.000223
3.69
De-ionized Water Convection
.000090
1.48
.000099
1.63
De-ionized Water Convection
w/ Fouling
The water resistive property is the major varying attribute to each cold plate option. The
resistive value was calculated by obtaining the heat transfer coefficient. Equation 48 was
used to determine the specific Nusselt number which led to the calculation of the heat
transfer coefficient. It was determined that cold plate option two had a lower heat
transfer coefficient compared to cold plate option one. The heat transfer coefficient for
cold plate option two was calculated to be 12301 W/m2K. It is understood that based on
the lower mass flow rate flowing through each parallel tube of cold plate option two
caused a lower velocity thus reducing the Reynolds number which directly affects both
calculated values of the Prandlt number and Nusselt number. Similar to solid materials,
waters thermal resistance was calculated and the associated temperature change was
determined.
The resistance values of the IGBT junction to plate, thermal grease and cold plate values
match those of cold plate option one. These resistances were left constant between each
cold plate option. Determining how water flow and pipe construction was an important
aspect to this analysis. Cold plate option one’s pipe interface section fared much better
as providing a successful heat removal path. Resistances and their associated
temperature changes were significantly lower.
Figure 30 displays the temperature
profile of cold plate option two. These temperatures were obtained with matching
55
junction materials as describe earlier; both Dow Corning TC-5022 and Sil Pad 2000 was
used within the analysis. Again, the sil pad junction material caused a 10oC temperature
difference.
Temperature (oC)
Temperature Difference of Cold Plate Option Two
100.00
95.00
90.00
85.00
80.00
75.00
70.00
65.00
60.00
55.00
50.00
45.00
40.00
35.00
30.00
Delta T w/
Thermal Grease
Delta T w/ Sil Pad
0
0.005
0.01
0.015
0.02
0.025
Distance Along Cold Plate (m)
Figure 30 Temperature Difference along Cold Plate Option Two
To obtain the true temperature rise of the IGBT, the assumption of constant material
properties needed to be addressed. Therefore the water temperature increase was
determined. The water temperature increase resulted in a 6.3oC rise which is identical to
cold plate option one. The reason this occurred is based on each analysis using a flow
rate of 10 gallons per minute. The main difference for cold plate option one occurred
with cold plate option two’s ability to absorb heat at a greater rate; each water pass
created an equal temperature rise compared to cold plate option one’s entire length. It is
understood that the heat absorption rate increase is due to a more efficient use of the
turbulent flow within cold plate option two’s piping. Cold plate option two’s piping
diameter was much smaller than cold plate option one’s. This allowed a greater effective
heating of the entire fluid flow from the boundary layer temperature increase. Cold plate
option two’s water boundary layer temperature increase is better averaged over the entire
56
cross section of the pipe fluid. Figure 31 displays the temperature increase along cold
plate option two’s pipe.
320.00
Temperature Difference Along Pipe
319.00
Temperature (oC)
318.00
317.00
316.00
Temperature
Difference
Along Pipe
315.00
314.00
313.00
312.00
0.000
0.050
0.100
Distance Along Pipe (m)
0.150
0.200
Figure 31 Temperature Difference along Cold Plate Option Two Pipe
The calculated value of water temperature increase was then added to the calculated
IGBT temperature rise. Table 23 breaks down all IGBT temperatures prior to the
addition of the water temperature increase.
57
Table 23 Cold Plate Option Two IGBT Temperature
With Out Fouling & Thermal Grease
Total Resistance w/ out Fouling
Temperature Delta of IGBT
0.00277
oC
45.63
oC
40
oC
85.63
oC
Ambient Temperature
Total IGBT Temperature
m2/W
With Fouling & Thermal Grease
Total Resistance w/ Fouling
0.00277
oC
Temperature Delta of IGBT
45.78
oC
40
oC
85.78
oC
Ambient Temperature
Total IGBT Temperature
m2/W
With Out Fouling & Sil Pad
Total Resistance w/ out Fouling 0.003377
oC
Temperature Delta of IGBT
55.73
oC
40
oC
95.73
oC
Ambient Temperature
Total IGBT Temperature
m2/W
With Fouling & Sil Pad
Total Resistance w/ Fouling
0.003386
oC
Temperature Delta of IGBT
55.87
oC
40
oC
95.87
oC
Ambient Temperature
Total IGBT Temperature
m2/W
Cold plate option two combined with thermal grease performed the best thermally. The
incorporation of thermal grease and the effects of fouling resulted in a 85.78oC IGBT
operating temperature; a temperature increase of 45.78oC. Taking into account the water
temperature increase as it travels within the pipe, the actual IGBT operating temperature
was calculated to be 92.08oC; a temperature increase totaling to 52.08oC. The calculated
IGBT operating temperature is well below the de-rated temperature of 120oC. There is
an available 27.92oC temperature margin to the de-rated maximum temperature. It is
noted that the IGBT operating temperature when mounted to cold plate option two
58
provides a cooler operating temperature. An analysis through ANSYS will allow the
self-calculated findings to be validated.
3.3.4
ANSYS Thermal Results of Cold Plate Option Two
Upon completion of the self-calculated analysis of cold plate option two, a comparison
analysis of the cold plate was performed in ANSYS. Result validation through ANSYS
computer analysis proved to validate the self-calculated findings.
3.3.4.1
ANSYS Meshing of Cold Plate Option Two
Similarly to cold plate option one, the analysis of cold plate option two in ANSYS
required two different meshing techniques. For cold plate option two, meshing
techniques were differentiated for the piping and plate sections. The automatic meshing
method was used again for the plate material; however mesh computing time took a
significantly greater amount of time. It is suspected that the meshing around each of the
small cylindrical pipe paths forced a much high mesh density around each path. The high
mesh density can be seen in Figure 32.
Figure 32 Meshing of Cold Plate Option Two Pipe Entrance
59
A full view of the plate meshing is displayed in Figure 33. Finer mesh densities are
located in areas where the corrosion resistant pipes are placed. In Figure 33, the less
dense mesh sections are visible in areas where pipe paths are not located, such as the far
left and right sides along with the center.
Figure 33 Meshing of Cold Plate Option Two
It can be seen that cold plate option two’s geometry was not completely modeled.
Originally a model of the entire cold plate was created; however it was determined that
the mesh was far too detailed. Therefore a symmetric function of ANSYS was taken
advantage of. The new function required only half of cold plate option two to be
modeled and meshed.
Figure 34 below displays the face meshing of the piping of cold plate option two. A
similar technique was completed on cold plate option two as was done on cold plate
option one. The main difference in meshing cold plate option two’s piping was a much
smaller face spacing which forced a highly regulated minimum edge length, maximum
60
edge length and expansion factor. The cause of a much denser meshing of the piping for
cold plate option two was due to the smaller pipe diameter size.
Figure 34 Meshing of Cold Plate Option Two Pipe
Figure 35 displays the boundary inflation of cold plate option two’s piping. Again, a
finer boundary inflation was required in order to match the plates finer meshing. The
interface of two meshes must have edge lengths sizes relative to one another. Ten
inflated boundary layers were used again; however their thickness was greatly reduced.
Figure 35 Meshing of Cold Plate Option Two Pipe Inflation Boundary
61
Figure 36 better displays the extremely finer mesh and boundary inflation of cold plate
option two’s piping.
Figure 36 Meshing of Cold Plate Option Two Pipe Inflation Boundary
Once meshing of cold plate option two’s model was completed, all necessary boundary
inputs and any related material properties were inputted.
3.3.4.2
ANSYS Temperature Results of Cold Plate Option Two
Once meshing was completed, all necessary parameters of cold plate option two were
inputted. Cold plate option two was modeled without both supply and return manifolds;
therefore inlet and outlet locations were specified for all twenty pipes. The manifolds
would not directly affect the heat transfer path therefore it was assumed modeling
without both manifolds would not negatively alter results. The water boundary
conditions consisted of a 40oC inlet temperature, 0 Pa static pressure at the outlet and
allowed for energy transfer based upon thermal heat flux. The corrosion resistant steel
interface and solder interface were chosen to be a thin conductive interface.
Adiabatic boundary conditions were assumed for the plate material, except for the heat
flux areas. An adiabatic boundary condition was assumed based on the cold plate being a
62
closed system and the only way to transfer energy in or out is through the cooling
medium. On top of the cold plate, imprinted faces were created to allow for a localized
injection of heat flux from the operating IGBTs. Uniform heat flux of 155,132 W/m2was
placed over the surface of the cold plate based on actual locations of the IGBTs.
Figure 37 displays the temperature contours of cold plate option two. IGBT hotspots are
visible at the rear end of the cold plate. These hotspots are due to the increase in water
temperature as it absorbs energy transferred along the pipe flow path. The temperature
profile is again not uniform.
Figure 37 Temperature Results of Cold Plate Option Two
The maximum junction temperature reaches 66.5oC for cold plate option two. This
temperature does not include the IGBT junction resistance temperature rise since it is a
given value by the IGBT manufacturer. To calculate the true operating temperature of
the IGBT, a 28.88oC value was added to the ANSYS hotspot temperature. Therefore,
with a 40oC ambient temperature, the IGBT temperature rise was calculated to be
55.38oC. The IGBT hotspot operating temperature was determined to be 95.38oC. The
self-calculated results without fouling were calculated to be 91.93oC. A difference of
3.45oC comparing self-calculated results to ANSYS results; a 3.6 percent error.
63
Figure 38 below displays the temperature contours of cold plate option two mid-plane. A
plane was inserted into the center of the model to where an elevation view of the cold
plate temperature distribution could be viewed. Water temperatures are constant in this
view because they’re all inlet locations.
Figure 38 Temperature Results of Cold Plate Option Two Mid-Plane
Pipe temperature variations can be seen in Figure 39; however they are not water
temperature contours, they’re corrosion resistant steel temperature contours. The
temperature increase over each pipe length is visible, based on the water temperature
increase as it enters the cold plate on the front side and exits out the rear. ANSYS allows
for the calculation of average water inlet and outlet temperatures. The temperature
increase of the water was determined to be 6.54oC compared to the self-calculated
6.37oC. This inconsistency again was attributed to the less conservative convergence
method chosen to minimize computing time.
64
Figure 39 Temperature Results of Cold Plate Option Two Pipe
Figure 40 displays a more detailed temperature contour of the IGBT operating
temperature.
Figure 40 Temperature Results of Cold Plate Option Two IGBT Junction
Cold plate option two met all necessary thermal requirements as shown by Table 24.
65
Table 24 Cold Plate Option Two Thermal Results vs. Requirements
Requirement
Pipe Material
Requirement Value
Corrosion Resistant
Steel
Calculated/Actual
Value
Corrosion Resistant Steel
Pipe and Plate Interface
(63/37) Solder
(63/37) Solder
Fluid
De-ionized Water
De-ionized Water
Inlet Temperature
40oC
40oC
10oC
6.32oC
IGBT Maximum Temperature
120oC
95.38oC
Maximum Flow Rate
10 gpm
10 gpm
Temperature Change of Fluid
Limit
3.3.4.3
ANSYS Temperature Results of Modified Cold Plate Option Two
It was recognized that both cold plate options met the requirements placed upon their
ability to remove heat generated by the IGBTs; however the IGBTs were not operating
at a uniform temperature. The uneven heat dissipation is due to the increasing water
temperature long a singular direction. It was theorized that if two paths of opposite flow
were utilized, a more uniform IGBT temperature could be obtained. Cold plate option
two out performed cold plate option one and its piping geometry allowed for a simpler
opportunity for the cold plate to be modified for alternating water flow. Figure 41 better
displays the alternating inlet and outlet directions. Blue arrows indicate an inlet direction
flow and black arrows indicate an outlet direction flow. All existing meshing was reused
and simple boundary conditions of alternating inlet and outlets were reversed. This
allowed for each pipe path to alternate flow direction. If the modified cold plate were to
be constructed, a much more complicated supply and return manifold would need to be
created.
66
Figure 41 Cold Plate Option Two Modified Inlet and Outlet Directions
Figure 41 also displays the temperature contours of modified cold plate option two with
alternating inlet and outlet flows. A much more uniform temperature distribution is
visible along the IGBT junction locations. In addition to a uniform temperature
distribution, the IGBT hotspot decreased 1oC.
Figure 42 displays a mid-plane view of the modified cold plate option two. A much
more uniform temperature distribution is seen through the inner section of the cold plate.
67
Figure 42 Temperature Results of Modified Cold Plate Option Two Mid-Plane
Figure 43 displays the temperature distribution along the corrosion resistant steel. It is
visible that the alternating flow temperatures average out better compared to the
unmodified version where outlet temperatures were much greater than at the inlet area.
Figure 43 Temperature Results of Modified Cold Plate Option Two Pipe
68
Figure 44 displays a more detailed view of the IGBT junction hotspot temperatures.
There is still a slight uneven heat dissipation, however less drastic than the unmodified
version of cold plate option two.
Figure 44 Temperature Results of Modified Cold Plate Option Two IGBT Junction
69
4.
Conclusion
Three cold plate designs were analyzed for use within the integrated power electronic
module. The IPEM losses were calculated to be 16,500 watts which were generated by
four Powerex IGBT CM1800HCB-34N switching at a frequency of 1700 Hz. Cold plate
option one met all requirements and allowed for an IGBT operating temperature of
100.45oC. Cold plate option two met all requirements and allowed for an IGBT operating
temperature of 95.38oC. Cold plate option three did not meet pressure drop requirements
and was eliminated from the analysis prior to a thermal results were conducted. Modified
cold plate option two was only thermally tested and allowed for an IGBT operating
temperature of 94.38oC.
Pressure drops of both cold plate option one and two met the required limit. However,
cold plate option two out performed cold plate option one. Cold plate option two caused a
2.67 psi pressure drop while cold plate one produced a 4.96 psi pressure drop. Cold plate
option two excelled in the pressure drop analysis due to its parallel flow paths. Cold plate
option one was based on a series pipe flow path, while cold plate option two utilized a
parallel pipe flow path.
The heat transfer coefficient of cold plate one was far better than cold plate option two’s
heat transfer coefficient. However, due to the larger pipe size, cold plate option one was
unable to utilize its superior heat transfer coefficient to the best of its ability. Table 25
displays a breakdown of important results of the cold plate options analyzed. The main
reason behind the decreased IGBT operating temperature of cold plate option two was
based on a lower resistance of the combined solder interface, corrosion resistant steel
pipe, and water convection sections. A 13.36oC temperature rise was attributed to the
piping interface of cold plate option one, while a 7.93oC temperature rise was attributed
to cold plate option two’s piping interface.
To obtain a uniform IGBT operating temperature, a modified version of cold plate option
two was analyzed. Alternating the water flow direction of every other pipe produced a far
more uniform junction temperature on the cold plate surface. The modified version of
cold plate option two also produced a lower IGBT operating temperature of 94.38oC.
Each cold plate option had specific operating benefits, however construction is an
important aspect to any design and cold plate option one could be constructed with
70
moderate difficulty. The modified version of cold plate option two performed the best
thermally based on this analysis.
Table 25 Cold Plate Option Comparison
Cold Plate
Cold Plate
Cold Plate
Option One
Option Two
4.96
2.67
-
IGBT Operating Temperature (oC)
100.45
95.38
94.38
Heat Transfer Coefficient (W/m2K)
19509
12301
-
.000071
.000071
-
Sil Pad Resistance (oC m2/W)
.000682
.000682
-
Al Plate Resistance (oC m2/W)
.000052
.000464
-
Solder Interface Resistance (oC m2/W)
.000101
.000167
-
.000426
.000223
-
.000285
.000090
-
.000313
.000099
-
Thermal Grease Temperature Change (oC)
1.16
1.16
-
Sil Pad Temperature Change (oC)
11.26
11.26
-
Al Plate Temperature Change ( C)
8.62
7.66
-
Solder Interface Temperature Change (oC)
1.62
2.76
-
7.04
3.69
-
4.7
1.48
-
5.17
1.63
-
Moderate
High
Elevated High
Condition
Pressure Drop (psi)
Thermal Grease Resistance
(oC m2/W)
Corrosion Resistant Steel Pipe Resistance
(oC m2/W)
De-ionized Water Convective Resistance (oC
m2/W)
De-ionized Water Convective Resistance w/
Fouling (oC m2/W)
o
Corrosion Resistant Steel Pipe Temperature
Change (oC)
De-ionized Water Convective Temperature
Change (oC)
De-ionized Water Convective Temperature
Change w/ Fouling (oC)
Construction Difficulty
71
Option Two
Modified
5. References
Below is a list of the technical references for this project:
1. Jamnia, Ali. Practical Guide to the Packaging of Electronics 2nd Edition. Boca
Raton, FL: CRC Press Taylor 7 Francis Group, LLC., 2009.
2. A. Soule, Christopher. Cooling High-density Electronics with Liquid-cooled Cold
Plates.Powertechnics Magazine, August 1988, (pp: 21-27). Laconia, NH:
Thermshield, LLC.
3. IGBT/Intelligent Power Modules. http://www.pwrx.com/pwrx/app/IGBT-IntelligentPwrMods.pdf . Youngwood, Pennsylvania: Powerex, Inc.
4. Draovac, Dr. John and Purschel, Marco. IGBT Power Losses Calculation Using
Data-Sheet Parameters V1.1.Neubiberg, Germany: Infineon Technologies AG, Am
Campeon, 2009-01-29.
5. Finnemore, John and Franzini, Joseph. Fluid Mechanics with Engineering
Applications, 10th Edition. NY, New York: Mc-Graw Hill Companies, Inc., 2002.
6. Holman, Jack P. Heat Transfer 9th Edition. NY, New York: McGraw-Hill
Companies, Inc., 2002.
7. H. Lienhard IV, John and H. Lienhard V, John. A Heat Transfer Textbook, 4th
Edition. Cambridge, MA: Phlogiston Press, 2012.
8. G. Kandlikar, Satish and N. Hayner II, Clifford. Heat Transfer Engineering Volume
30, no 12, 2009. Liquid Cold Plates for Industrial High-Power Electronic Devices –
Thermal Design and Manufacturing Considerations. Taylor and Franics Group,
LLC., 2009.
9. Kutz, Myer (2006). Mechanical Engineers' Handbook - Energy and Power (3rd
Edition). (pp: 371-418). John Wiley & Sons. Online version available at:
http://www.knovel.com.colelibprxy.ewp.rpi.edu/web/portal/browse/display?_EXT_
KNOVEL_DISPLAY_bookid=1532&VerticalID=0.
10. Valenzuela, Javier; Jasinski, Thomas; Sheikh, Zahed. Power Electronics Technology,
February 2005; Liquid Cooling for High-Power Electronics (pp. 50-56).
www.powerelectronics.com.
11. 6. Cooling of Electronic Equipment (pp 15-1 – 15-69). 2005, Quark
Press.http://highered.mcgrawhill.com/sites/dl/free/0073398128/835451/Chapter15.p
df . Accessed 10/01/2012.
12. Cornell Aeronautical Laboratory. Guide Manual of Cooling Methods for Electronic
Equipment. Lewis Library, NACA Cleveland, Ohio. Feb 18, 1957.
http://www.dtic.mil/cgibin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=AD
A278747.
13. Shipboard Propulsion, Power Electronics and Ocean Energy. Chapter 6: Power
Converter Cooling. Jan 1, 2011. Taylor and Francis, LLC.
14. Kutz, Myer (2006). Mechanical Engineers' Handbook - Energy and Power (3rd
Edition). (pp: 335-361). John Wiley & Sons. Online version available at:
http://www.knovel.com.colelibprxy.ewp.rpi.edu/web/portal/browse/display?_EXT_
KNOVEL_DISPLAY_bookid=1532&VerticalID=0.
15. Yang, Bo. Chapter 3: Integrated Power Electronics Module (pp 72-93). Accessed
09/25/2012.
72
6. Appendix A: IGBT Data Sheet
73
74
75
76
7. Appendix B: Sil Pad Data Sheet
77
8.
Appendix C: Thermal Grease Data Sheet
78
9.
Appendix D: IPEM Power Losses Calculation
Description
IGBT‘s Turn-on Switching Energy per Pulse
Value
Unit
0.39 mJ/P
IGBT's Turn-off Switching Energy per Pulse
0.77 mJ/P
Switching Frequency
1700 Hz
On State Collector Emitter Voltage
1.35 Volts
De-rating Factor
0.25
Rated Current
1800 Amps
De-rated Current
Modulation Factor
Power Factor
Collector Emitter on-state Resistance
Diode Reverse Recovery Charge
1350 Amps
0.5
0.98
0.000375 ohms
0.0009 µC
Diode Reverse Recovery Time
0.0000012 s
Peak Revese Recovery Current
1500 Amps
Emitter-Collector Voltage
1700 Volts
De-rated Emitter-Collector Voltage
1275 Volts
On State Zero Current Diode Voltage
Diode on state Resistance
Transistor Losses
Transistor Switching Losses
Transistor Conduction Losses
1.7 Volts
0.00075 Ohms
1972.00 Watts
522.65 Watts
Transistor Total Losses
2494.65 Watts
Diode Losses
0.29
Diode Recovery Losses
487.69 Watts
Diode Conduction Losses
605.62 Watts
Diode Total Losses
1093.31 Watts
IPEM Losses
IGBT Module Total Losses
Safety Factor
IGBT Module Total Losses w/ Safety Factor
79
3587.96 Watts
15%
4126.16 Watts
fsw
(Hz)
1000
Losses (.25 De-Rating) Losses (.1 De-Rating)
(Watts)
(Watts)
2961.42
3347.83
1100
3127.81
3520.82
1200
3294.2
3693.81
1300
3460.59
3866.8
1400
3626.98
4039.79
1500
1600
1700
1800
3793.37
3959.76
4126.15
4292.54
4212.78
4385.77
4558.75
4731.75
1900
4458.93
4904.73
2000
4625.32
5077.72
2100
4791.72
5250.71
2200
4958.11
5423.7
2300
5124.49
5596.69
2400
5290.89
5769.7
2500
5457.28
5942.67
80
10. Appendix E: Pressure Drop Mathcad Calculations
10.1 Cold Plate Option One Pressure Drop Calculation
81
10.2 Cold Plate Option Two Pressure Drop Calculation
82
83
10.3 Cold Plate Option Three Pressure Drop Calculation
84
85
11.
Appendix F: Pressure Drop Excel Data
11.1 Cold Plate Option One
L (in)
0.000
1.969
3.937
5.906
7.874
9.843
11.811
13.780
15.748
17.717
19.685
21.654
23.622
25.591
27.559
29.528
31.496
33.465
35.433
37.402
37.402
39.370
41.339
43.307
45.276
47.244
49.213
51.181
53.150
55.118
57.087
59.055
61.024
62.992
64.961
66.929
68.898
L (m)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
Pressure Drop (Pa)
0.000
434.141
868.282
1302.423
1736.564
2170.705
2604.846
3038.987
3473.128
3907.269
4341.410
4775.551
5209.693
5643.834
6077.975
6512.116
6946.257
7380.398
7814.539
8248.680
9695.678
10129.819
10563.960
10998.101
11432.242
11866.383
12300.524
12734.665
13168.806
13602.947
14037.088
14471.229
14905.370
15339.511
15773.653
16207.794
16641.935
Pressure Drop (psi)
0.0000
0.0630
0.1259
0.1889
0.2519
0.3148
0.3778
0.4408
0.5037
0.5667
0.6297
0.6926
0.7556
0.8186
0.8815
0.9445
1.0075
1.0704
1.1334
1.1964
1.4062
1.4692
1.5322
1.5951
1.6581
1.7211
1.7840
1.8470
1.9100
1.9729
2.0359
2.0989
2.1618
2.2248
2.2878
2.3507
2.4137
86
L (m)
3.750
3.700
3.650
3.600
3.550
3.500
3.450
3.400
3.350
3.300
3.250
3.200
3.150
3.100
3.050
3.000
2.950
2.900
2.850
2.800
2.800
2.750
2.700
2.650
2.600
2.550
2.500
2.450
2.400
2.350
2.300
2.250
2.200
2.150
2.100
2.050
2.000
L (in)
147.638
145.669
143.701
141.732
139.764
137.795
135.827
133.858
131.890
129.921
127.953
125.984
124.016
122.047
120.079
118.110
116.142
114.173
112.205
110.236
110.236
108.268
106.299
104.331
102.362
100.394
98.425
96.457
94.488
92.520
90.551
88.583
86.614
84.646
82.677
80.709
78.740
70.866
72.835
72.835
74.803
76.772
78.740
80.709
82.677
84.646
86.614
88.583
90.551
92.520
94.488
96.457
98.425
100.394
102.362
104.331
106.299
108.268
108.268
110.236
112.205
114.173
116.142
118.110
120.079
122.047
124.016
125.984
127.953
129.921
131.890
133.858
135.827
137.795
139.764
141.732
143.701
145.669
1.80
1.85
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
17076.076
17510.217
18957.215
19391.356
19825.497
20259.638
20693.779
21127.920
21562.061
21996.202
22430.343
22864.484
23298.625
23732.766
24166.907
24601.048
25035.189
25469.330
25903.471
26337.612
26771.754
28218.752
28652.893
29087.034
29521.175
29955.316
30389.457
30823.598
31257.739
31691.880
32126.021
32560.162
32994.303
33428.444
33862.585
34296.726
34730.867
35165.008
35599.149
36033.290
36467.431
2.4767
2.5396
2.7495
2.8125
2.8754
2.9384
3.0014
3.0643
3.1273
3.1903
3.2532
3.3162
3.3792
3.4421
3.5051
3.5681
3.6310
3.6940
3.7570
3.8199
3.8829
4.0928
4.1557
4.2187
4.2817
4.3447
4.4076
4.4706
4.5336
4.5965
4.6595
4.7225
4.7854
4.8484
4.9114
4.9743
5.0373
5.1003
5.1632
5.2262
5.2892
87
1.950
1.900
1.900
1.850
1.800
1.750
1.700
1.650
1.600
1.550
1.500
1.450
1.400
1.350
1.300
1.250
1.200
1.150
1.100
1.050
1.000
1.000
0.950
0.900
0.850
0.800
0.750
0.700
0.650
0.600
0.550
0.500
0.450
0.400
0.350
0.300
0.250
0.200
0.150
0.100
0.050
76.772
74.803
74.803
72.835
70.866
68.898
66.929
64.961
62.992
61.024
59.055
57.087
55.118
53.150
51.181
49.213
47.244
45.276
43.307
41.339
39.370
39.370
37.402
35.433
33.465
31.496
29.528
27.559
25.591
23.622
21.654
19.685
17.717
15.748
13.780
11.811
9.843
7.874
5.906
3.937
1.969
147.638
3.75
36901.572
5.3521
0.000
0.000
11.2 Cold Plate Option One
L (in)
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
0
0.60
1.60
2.60
L (m)
0.00
0.03
0.05
0.08
0.10
0.13
0.15
0.18
0.20
0.23
0.25
0.28
0.30
0.33
0.36
0.38
0.41
0.43
0.46
0.48
0.51
0.53
0.56
0.58
0.61
0.64
0.66
0.69
0.71
0.74
0.76
0.79
0.01524
0.04064
0.06604
Pressure
Drop (Pa)
0.000
220.544
441.087
661.631
882.175
1102.718
1323.262
1543.806
1764.349
1984.893
2205.437
2425.980
2646.524
2867.067
3087.611
3308.155
3528.698
3749.242
3969.786
4190.329
4410.873
4631.417
4851.960
5072.504
5293.048
5513.591
5734.135
5954.679
6175.222
6395.766
6616.310
8385.664
8550.670
8825.680
9100.690
Pressure Drop
(psi)
0.000
0.032
0.064
0.096
0.128
0.160
0.192
0.224
0.256
0.288
0.320
0.352
0.384
0.416
0.448
0.480
0.512
0.544
0.576
0.608
0.640
0.672
0.704
0.736
0.768
0.800
0.832
0.864
0.896
0.928
0.960
1.216
1.240
1.280
1.320
88
L (m)
1.539
1.524
1.499
1.473
1.448
1.422
1.397
1.372
1.346
1.321
1.295
1.270
1.245
1.219
1.194
1.168
1.143
1.118
1.092
1.067
1.041
1.016
0.991
0.965
0.940
0.914
0.889
0.864
0.838
0.813
0.787
L (in)
60.58
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
3.60
4.60
5.60
6.60
7.60
7.98
31.000
32.000
33.000
34.000
35.000
36.000
37.000
38.000
39.000
40.000
41.000
42.000
43.000
44.000
45.000
46.000
47.000
48.000
49.000
50.000
51.000
52.000
53.000
54.000
55.000
56.000
57.000
58.000
59.000
60.000
61.000
0.09144
0.11684
0.14224
0.16764
0.19304
0.2027
0.79
0.81
0.84
0.86
0.89
0.91
0.94
0.97
0.99
1.02
1.04
1.07
1.09
1.12
1.14
1.17
1.19
1.22
1.24
1.27
1.30
1.32
1.35
1.37
1.40
1.42
1.45
1.47
1.50
1.52
1.55
9375.699
9650.709
9925.719
10200.729
10475.739
11577.148
11797.69
12018.24
12238.78
12459.32
12679.87
12900.41
13120.96
13341.50
13562.04
13782.59
14003.13
14223.68
14444.22
14664.76
14885.31
15105.85
15326.40
15546.94
15767.48
15988.03
16208.57
16429.12
16649.66
16870.20
17090.75
17311.29
17531.84
17752.38
17972.92
18193.47
18414.01
1.360
1.400
1.440
1.479
1.519
1.679
1.711
1.743
1.775
1.807
1.839
1.871
1.903
1.935
1.967
1.999
2.031
2.063
2.095
2.127
2.159
2.191
2.223
2.255
2.287
2.319
2.351
2.383
2.415
2.447
2.479
2.511
2.543
2.575
2.607
2.639
2.671
89
0.787
0.737
0.711
0.686
0.660
0.635
0.610
0.584
0.559
0.559
0.508
0.483
0.457
0.432
0.406
0.381
0.356
0.330
0.305
0.279
0.254
0.229
0.203
0.178
0.152
0.127
0.102
0.076
0.051
0.025
0.000
31
29
28
27
26
25
24
23
22
22
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
11.3 Cold Plate Option 3
L (m)
0.00
0.05
0.05
0.15
0.20
0.25
0.30
0.35
0.35
0.45
0.50
0.55
0.60
0.60
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.30
1.40
1.45
1.50
1.55
1.55
1.65
1.70
1.75
1.80
1.85
1.85
1.95
L (in)
0.000
1.969
3.000
3.937
5.906
7.874
9.843
11.287
0.000
1.969
3.937
5.906
6.760
1.969
3.937
5.906
7.874
9.843
11.811
13.595
1.969
3.937
5.115
5.906
7.874
9.843
11.811
13.595
0.000
1.969
3.937
5.906
6.760
1.969
3.000
3.937
5.906
7.874
9.843
11.287
L (m) Pressure Drop (Pa)
0.0000
0.00000
0.0500
434.14104
0.0762
5002.62511
0.1000
5870.90719
0.1500
6305.04824
0.2000
6739.18928
0.2500
7173.33033
0.2867
7491.98985
0.00
10964.78518
0.05
11222.30207
0.10
11479.81896
0.15
11737.33585
0.17
13165.50196
0.05
23005.13034
0.10
23439.27138
0.15
23873.41243
0.20
24307.55347
0.25
24741.69451
0.30
25175.83556
0.3453
25569.28022
0.05
26003.421
0.10
26396.866
0.12992
26831.007
0.15
27265.148
0.20
27699.289
0.25
27699.289
0.30
28133.430
0.3453
37973.058
0.00
39401.225
0.05
39658.741
0.10
39916.258
0.15
40173.775
0.17
43646.571
0.0500
43965.230
0.0762
44399.371
0.1000
44833.512
0.1500
45267.653
0.2000
46135.935
0.2500
50704.419
0.2867
51138.560
Difference Pressure Drop (psi)
434.141
0.000
4568.484
0.063
868.282
0.726
434.141
0.852
434.141
0.914
434.141
0.977
318.660
1.040
3472.795
1.087
257.517
1.590
257.517
1.628
257.517
1.665
1428.166
1.702
9839.628
1.909
434.141
3.337
434.141
3.400
434.141
3.463
434.141
3.526
434.141
3.588
393.445
3.651
434.141
3.709
393.445
3.771
434.141
3.829
434.141
3.892
434.141
3.954
0.000
4.017
434.141
4.017
9839.628
4.080
1428.166
5.508
257.517
5.715
257.517
5.752
257.517
5.789
3472.795
5.827
318.660
6.330
434.141
6.377
434.141
6.440
434.141
6.503
868.282
6.566
4568.484
6.691
434.141
7.354
0.000
7.417
90
L (m)
1.950
1.900
1.850
1.800
1.750
1.700
1.650
1.600
1.550
1.500
1.450
1.400
1.350
1.300
1.250
1.200
1.150
1.100
1.050
1.000
0.950
0.900
0.850
0.800
0.750
0.700
0.650
0.600
0.550
0.500
0.450
0.400
0.350
0.300
0.250
0.200
0.150
0.100
0.050
0.000
L (in)
76.77165
72.83465
72.83465
70.86614
68.89764
66.92913
64.96063
61.02362
61.02362
59.05512
57.08661
55.11811
51.1811
51.1811
49.2126
47.24409
45.27559
43.30709
41.33858
39.37008
37.40157
35.43307
33.46457
31.49606
29.52756
27.55906
23.62205
23.62205
21.65354
19.68504
17.71654
13.77953
13.77953
11.81102
9.84252
7.874016
5.905512
1.968504
1.968504
0
12.
Appendix G: Thermal Calculations
12.1 Cold Plate Option One Thermal Calculation
Inputed Value
Calculated
Description
Heat Load Input per IGBT
Values
Units
16500.00 Watts
Density
992.30 kg/m3
o
40.00 C
Water Inlet Temperature
o
0.64 W/m- C
o
160.00 W/m- C
Water Thermal Conductivity
Aluminum Thermal Conductivity
o
25.90 W/m- C
Corrosion Resistant Steel Thermal Conductivity
Thermal Grease Thermal Conductivity
o
4.00 W/m- C
Sil Pad Thermal Conductivity
3.50 W/m- C
Solder Thermal Conductivity
50.00 W/m- C
o
4174.00 J/kg C
o
o
Specific Heat of Water
Dynamic Viscosity of Water
0.000562 kg/m s
Pipe Length for One IGBT
0.2916 m
11.48 in
3.750056 m
0.988568 m
147.64 in
38.92 in
Solder Inner Radius
0.00953 m
0.37500 in
Solder Outer Radius
0.01080 m
0.42500 in
Solder Thickness
0.00127 m
0.05000 in
Corrosion Resistant Steel Inner Radius
0.00724 m
0.28500 in
Corrosion Resistant Steel Outer Radius
0.00953 m
0.37500 in
Corrosion Resistant Steel Pipe Wall Thickness
0.00229 m
0.09000 in
Thermal Grease Thickness
0.00003 m
0.01535 in
Sil Pad Thickness
0.00025 m
0.01535 in
Aluminum Plate Length to Pipes
0.00889 m
0.35000 in
IGBT Length
0.75997 m
29.92000 in
IGBT Width
IGBT Surface Area
0.13995 m
0.10636 m2
5.51000 in
164.8592 in2
Sil Pad Surface Area
0.10636 m2
164.8592 in2
2
164.8592 in2
2
164.8592 in
Total Pipe Length
First Run Length
Thermal Grease Surface Area
0.10636 m
Aluminum Surface Area
Solder Surface Area
0.10636 m
0.25435 m2
CRES Outter Surface Area
0.22443 m2
CRES Inner Surface Area
0.04496 m2
De-ionized Water Cross Sectional Area
0.00016 m
2
91
2
Description
Thermal Resistance of IGBT Junction to Case
Calculated Values Units
0.00175 K/kW
o
2
0.00068 C m /W
Thermal Resistance of Sil Pad
o
2
0.00007 C m /W
o
2
0.00052 C m /W
Thermal Resistance of Thermal Grease
Thermal Resistance of Cold Plate
o
2
0.00040 C m /W
o
2
0.00171 C m /W
Thermal Resistance of Solder Interface
Thermal Resistance of CRES Pipe
o
2
0.00114 C m /W
o
2
0.00125 C m /W
Thermal Resistance of DI Convection
Thermal Resistance of Convection due to Fouling
Equivalent Resistance of Solder, CRES, & Conv
Equivalent Reistance of Solder, CRES & Conv w/ Fouling
Equivalent Resistance of 4 Solder,CRES, & Conv
Equivalent Resistance of 4 Solder, CRES, & Conv w/ Fouling
Equivalent Reistance of 4 Solder
Equivalent Resistance of 4 CRES
Equivalent Resistance of 4 Conv
Equivalent Resistance of 4 Conv w/ Fouling
o
2
0.00325 C m /W
o
2
0.00336 C m /W
o
2
0.00081 C m /W
0.00084
0.000101
0.000426
0.000285
0.000313
o
2
o
C m2/W
C m /W
o
2
C m /W
o
2
C m /W
o
C m2/W
o
28.875 C
o
11.26 C
Temperature Difference due to IGBT jc
Temperature Difference of Sil Pad
o
1.16 C
o
8.62 C
Temperature Difference of Thermal Grease
Temperature Difference of Cold Plate
Temperature Difference of CRES Pipe
o
6.65 C
o
28.15 C
Temperature Difference of Water
Temperature Difference of Water w/ Fouling
Temperature Difference of Equivalent Parallel Section
Temp Difference of Equiv Parallel Section w/ Fouling
Temperature Difference of Equiv Solder
Temperature Difference of CRES
Temperature Difference of Convection
Temperature Difference of Convection w/ Fouling
18.81
20.69
13.40
13.87
1.662
7.037
4.702
5.17
Temperature Difference of Solder Interface
92
o
C
C
o
C
o
C
o
C
o
C
o
C
o
C
o
Variables
Qf
Description
Calculated Values
Units
10 gpm
3
0.000631 m /s
Flow Rate
Qf
Flow Rate
m
Mass Flow Rate
0.626 kg/s
V
Velocity
3.832 m/s
V
Velocity
12.568 ft/s
Re
Reynolds Number
97954.447 Dimensionless
Flow Condition
Turbulent
f
Friction Factor
0.018 m
Pr
Prandlt Number
3.683
Nu
hm
Nusselt Number
Average Heat Trasnfer Coefficient
hm fouling
Avg Heat Transfer Coefficient with Fouling
With Out Fouling & Thermal Grease
Total Resistance w/ out Fouling
Temperature Delta of IGBT
Ambient Temperature
443.415
2
19509.278 W/(m K)
2
17558.350 W/(m K)
0.00316 oC m2/W
o
52.06 C
o
40 C
o
92.06 C
Total IGBT Temperature
With Fouling & Thermal Grease
o
2
0.00318 C m /W
o
52.53 C
Total Resistance w/ Fouling
Temperature Delta of IGBT
o
40 C
o
92.53 C
Ambient Temperature
Total IGBT Temperature
With Out Fouling & Sil Pad
Total Resistance w/ out Fouling
Temperature Delta of IGBT
Ambient Temperature
Total IGBT Temperature
With Fouling & Sil Pad
Total Resistance w/ Fouling
Temperature Delta of IGBT
Ambient Temperature
Total IGBT Temperature
93
0.003767
62.15
40
102.15
o
C m2/W
o
C
o
C
o
C
0.003795
62.62
40
102.62
o
C m2/W
o
C
o
C
o
C
With out Fouling & Thermal Grease
o
0.01972 m
44.70 C
o
0.01248 m
51.74 C
0.01019 m
0.00892 m
0.00003 m
0m
o
53.40 C
o
62.02 C
o
63.18 C
o
92.06 C
With Fouling & Thermal Grease
0.01972 m
0.01248 m
0.01019 m
0.00892 m
0.00003 m
o
45.17 C
o
52.21 C
o
53.87 C
o
62.49 C
o
63.65 C
o
0m
92.53 C
With out Fouling & Sil Pad
o
0.01972 m
44.70 C
o
0.01248 m
51.74 C
o
0.01019 m
53.40 C
0.00003 m
o
62.02 C
o
73.28 C
0m
o
102.15 C
0.00892 m
With Fouling & Sil Pad
0.01248 m
o
45.17 C
o
52.21 C
0.01019 m
53.87 C
0.00892 m
0.00003 m
0m
62.49 C
o
73.75 C
o
102.62 C
0.01972 m
o
o
94
Pipe Distance
(m)
Temperature
(K)
Pipe Distance
(m)
Temperature
(K)
0
313.00
1.900
316.20
0.050
313.08
1.950
316.28
0.100
313.17
2.000
316.36
0.150
313.25
2.050
316.45
0.200
313.34
2.100
316.53
0.250
313.42
2.150
316.62
0.300
313.50
2.200
316.70
0.350
313.59
2.250
316.78
0.400
313.67
2.300
316.87
0.450
313.76
2.350
316.95
0.500
313.84
2.400
317.04
0.550
313.93
2.450
317.12
0.600
314.01
2.500
317.21
0.650
314.09
2.550
317.29
0.700
314.18
2.600
317.37
0.750
314.26
2.650
317.46
0.800
314.35
2.700
317.55
0.850
314.43
2.750
317.63
0.900
0.950
314.51
314.60
2.800
2.850
317.72
317.80
1.000
314.68
2.900
317.89
1.050
1.100
314.77
314.85
2.950
3.000
317.97
318.05
1.150
314.93
3.050
318.14
1.200
1.250
315.02
315.10
3.100
3.150
318.22
318.31
1.300
1.350
1.400
1.450
1.500
1.550
1.600
1.650
1.700
1.750
1.800
1.850
315.19
315.27
315.36
315.44
315.52
315.61
315.69
315.78
315.86
315.94
316.03
316.11
3.200
3.250
3.300
3.350
3.400
3.450
3.500
3.550
3.600
3.650
3.700
3.750
318.39
318.48
318.56
318.64
318.73
318.81
318.90
318.98
319.06
319.15
319.23
319.32
Temperature Difference
Initial
Final
313.00
319.32
6.318
95
12.2 Cold Plate Option Two Thermal Calculation
Inputed Value
Calculated Value
Description
Heat Load Input per IGBT
Values
Units
16500.00 Watts
Density
992.30 kg/m3
o
40.00 C
Water Inlet Temperature
o
0.64 W/m- C
Water Thermal Conductivity
o
180.00 W/m- C
o
25.90 W/m- C
Aluminum Thermal Conductivity
Corrosion Resistant Steel Thermal Conductivity
Thermal Grease Thermal Conductivity
o
4.00 W/m- C
Sil Pad Thermal Conductivity
o
3.50 W/m- C
Solder Thermal Conductivity
o
50.00 W/m- C
o
4174.00 J/kg C
Specific Heat of Water
Dynamic Viscosity of Water
0.000562 kg/m s
Pipe Length for One IGBT
0.2027 m
7.98 in
Total Pipe Length
8.107680 m
319.2 in
Total Length of Pipe for One IGBT
2.026920 m
79.8 in
Solder Inner Radius
0.00239 m
0.09400 in
Solder Outer Radius
0.00366 m
0.14400 in
Solder Thickness
0.00127 m
0.05000 in
Corrosion Resistant Steel Inner Radius
0.00178 m
0.07000 in
Corrosion Resistant Steel Outer Radius
0.00239 m
0.09400 in
Corrosion Resistant Steel Pipe Wall Thickness
0.00061 m
0.02400 in
Thermal Grease Thickness
0.00003 m
0.01535 in
Sil Pad Thickness
0.00025 m
0.01535 in
Aluminum Plate Thickness to Pipe
0.00889 m
0.35000 in
IGBT Length
0.18999 m
7.48000 in
IGBT Width
0.13995 m
5.51000 in
2
0.02659 m
2
0.01930 m
41.2148 in
2
29.92 in
4 IGBT Surface Area
2
0.00355 m
2
0.10636 m
2
5.51 in
2
164.8592 in
Sil Pad Surface Area
2
0.10636 m
2
164.8592 in
Thermal Grease Surface Area
2
0.10636 m
2
164.8592 in
2
2
164.8592 in
IGBT Surface Area
4 IGBT Length
4 IGBT Width
Aluminum Surface Area
0.10636 m
Solder Surface Area
0.18633 m
2
0.12163 m
2
CRES Outter Surface Area
0.02264 m2
2
0.00001 m
CRES Inner Surface Area
De-ionized Water Cross Sectional Area
96
2
Description
Thermal Resistance of IGBT Junction to Case
Calculated Values
Units
0.001750 K/kW
o
2
0.000682 C m /W
Thermal Resistance of Sil Pad
o
2
0.000071 C m /W
o
2
0.000464 C m /W
Thermal Resistance of Thermal Grease
Thermal Resistance of Cold Plate
Thermal Resistance of (1) CRES Pipe Run
o
2
0.006698 C m /W
o
2
0.008937 C m /W
Thermal Resistance of (1) DI Convection Run
0.003590 C m /W
Thermal Resistance of (1) Convection Run due to Fouling
o
2
0.003949 C m /W
Thermal Resistance of (1) Solder Interface Run
o
Equivalent Resistance of Solder, CRES, & Conv
Equivalent Reistance of Solder, CRES & Conv w/ Fouling
Equivalent Resistance of 40 Solder,CRES, & Conv
Equivalent Resistance of 40 Solder, CRES, & Conv w/ Fouling
Equivalent Reistance of 40 Solder
Equivalent Resistance of 40 CRES
2
o
2
0.019226 C m /W
o
2
0.019585 C m /W
o
2
0.000481 C m /W
o
2
0.000490 C m /W
o
2
0.000167 C m /W
o
2
0.000223 C m /W
o
2
0.000090 C m /W
o
2
0.000099 C m /W
Equivalent Resistance of 40 Conv
Equivalent Resistance of 40 Conv w/ Fouling
o
28.875 C
o
11.26 C
Temperature Difference due to IGBT jc
Temperature Difference of Sil Pad
o
1.16 C
o
7.66 C
Temperature Difference of Thermal Grease
Temperature Difference of Cold Plate
o
2.76 C
o
3.69 C
Temperature Difference of Solder Interface
Temperature Difference of CRES Pipe
1.48 oC
o
1.63 C
o
7.93 C
Temperature Difference of Water
Temperature Difference of Water w/ Fouling
Temperature Difference of Equivalent Parallel Section
Temperature Difference of Equivalent CRES
Temperature Difference of Equivalent Convection
o
8.08 C
o
2.763 C
o
3.687 C
o
1.481 C
Temperature Difference of Equivalent Convection w/ Fouling
o
1.63 C
Temp Difference of Equiv Parallel Section w/ Fouling
Temperature Difference of Equiv Solder
97
Variables
Qf
Description
Flow Rate
Qf
Flow Rate
Qf
Flow Rate per Pipe
m
Mass Flow Rate
0.016 kg/s
V
Velocity
1.588 m/s
V
Velocity
5.209 ft/s
Re
Reynolds Number
9970.363 Dimensionless
FC
Flow Condition
Turbulent
f
Friction Factor
3
0.000016 m /s
0.031 m
Pr
Nu
Prandlt Number
Nusselt Number
hm
Average Heat Trasnfer Coefficient
hm fouling
Calculated Values
Units
10 gpm
3
0.000631 m /s
3.683
68.670
Avg Heat Transfer Coefficient with Fouling
2
12301.098 W/(m K)
2
11070.989 W/(m K)
With Out Fouling & Thermal Grease
o
2
0.00277 C m /W
o
45.63 C
Total Resistance w/ out Fouling
Temperature Delta of IGBT
o
40 C
o
85.63 C
Ambient Temperature
Total IGBT Temperature
With Fouling & Thermal Grease
o
2
0.00277 C m /W
o
45.78 C
Total Resistance w/ Fouling
Temperature Delta of IGBT
o
40 C
o
85.78 C
Ambient Temperature
Total IGBT Temperature
With Out Fouling & Sil Pad
Total Resistance w/ out Fouling
Temperature Delta of IGBT
o
2
0.003377 C m /W
o
55.73 C
o
40 C
o
95.73 C
Ambient Temperature
Total IGBT Temperature
With Fouling & Sil Pad
o
2
0.003386 C m /W
o
55.87 C
Total Resistance w/ Fouling
Temperature Delta of IGBT
o
40 C
o
95.87 C
Ambient Temperature
Total IGBT Temperature
98
With out Fouling & Thermal Grease
o
0.01972 m
41.48 C
o
0.01248 m
45.17 C
0.01019 m
0.00892 m
0.00003 m
0m
o
47.93 C
o
55.59 C
o
56.76 C
o
85.63 C
With Fouling & Thermal Grease
0.01972 m
0.01248 m
0.01019 m
0.00892 m
0.00003 m
o
41.63 C
o
45.32 C
o
48.08 C
o
55.74 C
o
56.90 C
o
0m
85.78 C
With out Fouling & Sil Pad
0.01972 m
0.01248 m
0.01019 m
0.00892 m
0.00003 m
0m
o
41.48 C
o
45.17 C
o
47.93 C
o
55.59 C
o
66.85 C
o
95.73 C
With Fouling & Sil Pad
0.01248 m
o
41.63 C
o
45.32 C
0.01019 m
o
48.08 C
0.01972 m
0.00892 m
0.00003 m
0m
55.74 oC
o
67.00 C
o
95.87 C
99
Pipe Distance
(m)
Temperature
(K)
0.000
313.00
0.005
313.17
0.010
313.33
0.015
313.50
0.020
313.67
0.025
313.83
0.030
314.00
0.035
314.17
0.040
314.33
0.045
314.50
0.050
314.67
0.055
314.84
0.060
315.00
0.065
315.17
0.070
315.34
0.075
315.50
0.080
0.085
315.67
315.84
0.090
316.00
0.095
316.17
0.100
316.34
0.105
316.50
0.110
316.67
0.115
316.84
0.120
317.00
0.125
317.17
0.130
317.34
0.135
317.51
0.140
317.67
0.145
0.150
0.155
0.160
0.165
0.170
0.175
0.180
0.185
0.189
317.84
318.01
318.17
318.34
318.51
318.67
318.84
319.01
319.17
319.31
Temperature Difference
Initial
Final
313.00
319.31
6.31
100