kirk t. lowe and rao v. arimilli - comsol multiphysics · 1. application of solution mapping to...
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Application of Solution Mapping to Reduce Computational Time
in Actively Cooled Power Electronics
Kirk T. Lowe and Rao V. Arimilli
Mechanical, Aerospace, and Biomedical EngineeringUniversity of Tennessee - Knoxville
October 9, 2008
Presented at the COMSOL Conference 2008 Boston
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AcknowledgementsProject Sponsored by:
Oak Ridge National LaboratoryWork in support of Direct-Cooled Power Electronics Substrate Project funded by DOE FreedomCar Program
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Problem DescriptionTypical packaging has many layersThermal resistance is largeCommercial applications can require a coolant temperature over 100°C Thermal resistance must be reduced
PE ChipSolder
DBC Substrate
Copper Base Plate TIM
Heat Sink
Typical PE Module Package
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Proposed Solution
Front View Top View
Flow ChannelChip
Copper
Ceramic Substrate
A
B●
●
Provision Patent 61/037,129
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Proposed Solution (ii)Embeds heat sink into ceramicEliminates TIM, copper base plate, one solder layer, and aluminum heat sinkThermal performance of coolant channel design is modeled to compare to design limitations.
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Model SetupFluid Dynamics
Incompressible Navier-StokesContinuity
Heat TransferConduction and Convection
Constant PropertiesSteady State to predict worst-case-scenarioMaximum Temperatures
Fluid – 130°CInterface – 150°C
( )( )[ ]Tuupuu vvvv ∇+∇+Ι−⋅∇=∇⋅ ηρ
0=⋅∇ uv
TkQTuCp
2''' ∇+=∇⋅vvρ
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Solution StrategySolve 2-D axisymmetric flow fieldMap solution to 3-D cylinders (Extrusion Coupling Variables)Apply thermal boundary conditionsSolve for temperature distribution
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Boundary ConditionsInlet Velocity, ReD,in
Outlet, Pressure, no viscous stress, p0=0Walls, no slipChip Heat Load, 1.78e9 W/m3
Inlet Temperature, 105°CAll other boundaries thermally insulated
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Solution MappingUseful for simple flow field in more complex structureSolve 2-D axisymmetric flow fieldMap solution to 3-D cylinder using Extrusion Coupling VariablesTranslate axis as necessarySeparate variables into directional componentsIncorporate into convection heat transferSolve temperature distribution
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Solution Mapping (i)
xzy
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Solution Mapping (iii)2-D axisymmetric solutionSolved parametrically to desired input velocity or Reynolds number
r,u
z,v
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Solution Mapping (iv)
rzzxx ii =−+− 22 )()(
zy =
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Solution Mapping (v)
Initial model update uses initialized (coarse) meshMesh refinement is necessary to transfer velocity data to convection regime
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Solution Mapping (vi)
Fine mesh better resembles the accuracy of the 2-D solution
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Solution Mapping (vii)
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Solution Mapping (viii)
xzy
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ResultsHigh thermal conductivity ceramics produce lower maximum interface and fluid temperaturesChip temperatures are within design limitsWorking Fluid is above its boiling point
100
110
120
130
140
150
160
170
180
190
0 20 40 60 80 100 120 140 160 180
Thermal Conductivity, W/m-K
Tem
pera
ture
, o C
Interface Fluid
Maximum Interface and Fluid Temperatures of the Four Ceramic Materials at ReD,in
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Results (ii)Increasing inlet ReD, decreases maximum temperaturesPressure drop is smallModel pressure drop coincides well with analytic calculations
105
110
115
120
125
130
135
140
145
150
0 1000 2000 3000 4000 5000 6000 7000
ReD
Tem
pera
ture
, o C
0
2000
4000
6000
8000
10000
12000
14000
Pres
sure
, Pa
Interface Temperature
Fluid Temperature
ΔP COMSOL
ΔP Analytic
Boiling Point
Variations of Maximum Interface and Fluid Temperatures and the Pressure for Ceramic 4
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Results (iii)Large core of “cold” fluid at channel exit (41.3%)Diameter at mass manufacturing limitTo improve cooling
Surface enhancement Thermal conductivity enhancement
100
105
110
115
120
125
130
0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
Position along Diameter
Tem
pera
ture
, o C
Fluid Temperature Along Diameter at Outlet of Hottest Channel in Ceramic 4
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Solution Accuracy
120
125
130
135
140
145
0 1000 2000 3000 4000 5000 6000 7000
ReD
Max
imum
Flu
id T
empe
ratu
re ,
o C
COMSOL
Analytic
Comparison of Maximum Fluid Temperature between COMSOL Solutions and Analytical Solution for a Constant Flux Tube
q''= constant
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Solution Accuracy (ii)Analytic solution within 5% of simulation for all Reynolds numbersModel results are conservative
Larger maximum temperatures
Analytic solution provides good basis for initial sizing and feasibility
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ConclusionsNew package substrate can enable the use of high temperature coolantsHigh thermal conductivity ceramics are necessary to minimize thermal resistance for this coolant path design An increase in the nominal flow rate is required to meet the design limitationsSolution mapping significantly decreases the amount of time required to solve 3-D convective flowsWork continues to improve flow channel design and thermal conductivity of working fluid
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Questions?