2007-01-4117

Experimental and Analytical Characterization of Copper Fin Patterns for Heat Sinks in Liquid Cooling Loops for Motor Drives Ralph Remsburg Amulaire Thermal Technology

Joe Hager Amulaire Thermal Technology Copyright © 2007 SAE International

ABSTRACT A numerical and experimental study of heat transfer and fluid flow in heat sinks that may be used for cooling loops for motor drives is presented. An experimental study of 4 heat sinks was completed: a serpentine 4pass copper tube in an aluminum plate, a design having folded aluminum fins brazed in an aluminum housing, a minichannel aluminum extrusion, and two molded copper fin designs. In addition, using the results from the experimental analysis, a CFD and similarity study was performed on models of a serpentine 4-pass copper tube in a copper plate, a design having corrugated copper fins brazed in a copper housing, and a minichannel copper heat sink. Temperature, pressure drop, flow rate, and other pertinent data were recorded during the experiments and compared to the computational models. Nondimensional numbers and dimensional values were calculated from the results. o The data was then normalized for thermal resistivity ( C2 2 cm /W) and normalized for flow rate (l/min-cm ) to allow comparison of different size cold plates, with different size heat sources at different flow rates. Finally, the data was used in CFD simulations to improve the baseline thermal performance of the IGBT/cold plate assembly of a 2004 Toyota Prius. Compared to the stock cold plate, size of the IPEM was reduced by 50%, total weight was reduced by 59%, and junction temperature was reduced by 2.7oC,

INTRODUCTION IGBT (Insulated Gate Bipolar Transistor) power modules are now commonly used in both military converter and inverter circuits. The primary application of the IGBT is for use as a switching component in inverter circuits which are used in both power supply and motor drive applications. Although very efficient, these modules suffer from conduction and switching power losses. The heat generated by these losses must be conducted away from the power chips and into the environment

using a heat sink. Air-cooled aluminum heat sinks and even liquid-cooled aluminum cold plates were once 1 widely used ( ), but as some military and commercial applications have arrived at multi-megawatt requirements, liquid cooling using copper cold plates has become more common In an effort to use engine coolant to cool the die instead of using a dedicated cooling loop, much of the recent attention directed toward power electronics is aimed at lowering the temperature differential between the die and the coolant. Even though IGBTs typically operate with 98% efficiency, the 2kW of waste heat from a 100kW converter will overwhelm most cooling solutions. The advent of 3D multi-layered packaging of these modules can help achieve better reliability, lower electrical noise and lower costs. However, as the electronic chips are placed closer together, heat flux (W/cm2) and heat density (W/cm3) problems become more pronounced. Because the desired junction temperature of an IGBT module should not normally exceed 125oC, current heat fluxes of 300W/cm2 are challenging to even most liquid cooling solutions. This paper examines the thermal resistance of two types of IGBT/cold plate mounting schemes, bolt-on and direct attachment, and details the primary thermal resistance, which is wholly inside the cold plate, from the IGBT/cold plate mounting surface to the coolant media. The primary thermal resistance is mostly a function of coldplate fin surface area and the heat transfer coefficient that is achieved with specific fin array configurations. The findings of this paper were simulated on the IGBT/ cold plate assembly of a 2004 Toyota Prius, where advantages in junction temperature, size, and weight were realized.

THERMAL RESISTANCE STACK Power electronics dies must usually be mounted to a cold plate surface to aid heat dissipation. However, several requirements must be met in order to attach the die. The interface between the power die and the cold plate must have: low thermal resistance (usually measured in oC/W); electrical losses such as resistance, inductance, and capacitance must be kept to a minimum; thermal stresses due to the differing rates of expansion of the die (silicon = 4.2 × 10-6) and the cold plate (copper = 17.6 × 10-6) must be minimized; and electrical isolation (dielectric strength) must be maximized (2). Currently, most power electronics circuits use a direct bonded copper (DBC) technique using a power electronics module with an integral copper heat spreader. The module/heat spreader assembly is bolted to an aluminum cold plate using a thermal grease interface as shown in Fig. 1.

Silicon Die 5% Aluminum Coldplate 24%

Solder 15%

Copper 2% AlN 7% Copper 2% Solder 5% Thermal Grease 29%

Copper Baseplate 11%

Figure 2 Bolt-on power electronics thermal resistance stack – 0.037oC/W Layer 1 2 3 4 5 6 7 8 9

Material Silicon Solder Copper AlN Copper Solder Copper Grease Cast Alum

x (mm) y (mm) z (mm) 13 30 0.090 13 30 0.127 32 40 0.310 32 40 0.640 32 40 0.310 32 40 0.127 32 40 2.000 32 40 0.050 32 40 2.000

R, θ (oC/W) 0.0019 0.0054 0.0006 0.0025 0.0006 0.0017 0.0040 0.0112 0.0087 0.0366

Table 2 Geometry of bolt-on power electronics thermal resistance stack – 0.037oC/W

Figure 1 Bolt-on electronics thermal resistance stack – 0.037oC/W

Thermal resistance from the die to the inner surface of the cold plate, θj-c, is found by:

θ j −c = However, when examining these layers in detail, it becomes apparent that some layers drastically impede the flow of heat. The pie chart of Fig. 2 shows the contribution to thermal resistance of each layer in the bolt-on DBC technique, when using the material property values of Table 1 and the geometry detailed in Table 2. Material Silicon Solder (Sn60/Pb40) Copper (C11000) Aluminum Nitride Thermal Grease (Dow TC-5022) Cast Aluminum (A356)

ρ 3 (kg/ m ) 2300 8500 8913 3200 3230 2685

cp (J/kg K) 664 176 383 711 1100 935

k (W/m K) 120 60 390 200 4 159

Table 1 Properties of bolt-on power electronics thermal resistance stack

L kAc

Where L is the thickness of the material layer, k is the thermal conductivity of the material and Ac is the cross sectional area, perpendicular to the path of heat transfer. Fig. 3 shows a cross section of an assembly using the direct attach technique wherein the bottom layer of the DBC is soldered directly to a copper cold plate. When comparing the material stack construction technique of Fig. 1, bolt-on, to Fig. 3, direct attach, a substantial penalty in thermal resistance is noted, primarily due to the thermal grease layer of Fig. 1. In the model shown, thermal resistance drops from about 0.037 in Fig. 1, bolton technique to about 0.017oC/W in Fig. 3, direct attach. In this model, thermal resistance can be reduced by about 55% by attaching the DBC stack directly to a copper cold plate through a solder layer.

Looking further into the zones of thermal resistance, the thermal resistance from the inner surface of the cold plate to the coolant, θc-a, is applicable to either bolt-on or direct attach power electronics, and is added to the prior resistance, θj-c, of Table 1 or Table 2 (die to inner cold plate surface. The temperature rise from the coolant to the inner surface of the cold plate is found by the equation:

ΔT = Figure 3 Direct attach power electronics thermal resistance stack – 0.017oC/W When comparing the pie chart of Fig. 2, bolt-on, to the pie chart of Fig. 4, direct attach, it is noted that without the thermal grease resistance, the solder layer attaching the die to the DBC becomes the largest contributor to thermal resistance. As modeled, the heat flow is onedimensional and does not spread to a larger cross sectional area, which would reduce the thermal resistance of this solder layer.

Q hc As

Where hc is the heat transfer coefficient and As is the surface area in contact with the coolant. This value can be expressed as thermal resistance from the inner surface of the cold plate to the coolant by:

θ c −a =

1 hc As

Using a heat transfer coefficient of 1847W/m2 K and a surface area of 0.0208m2, which is typical of a cold plate comprised of a copper tube swaged to an aluminum plate having a water flow rate of roughly 11.0 l/min, thermal resistance, θj-c, can be seen in Fig. 5 in the context of the other resistances for direct attachment.

Silicon Die, 11%

Copper Coldplate, 24%

Silicon Die 4%

Solder 13% Copper 1% AlN 6%

Solder, 32%

Solder, 10%

Surface to Coolant 62%

Copper, 4% Copper, 4%

Figure 4 Direct attach power electronics thermal resistance stack – 0.017oC/W Material Silicon Solder Copper AlN Copper Solder Cu Plate

Solder 4% Copper Coldplate 9%

AlN, 15%

Layer 1 2 3 4 5 6 7

Copper 1%

x (mm) y (mm) z (mm) 13 30 0.10 13 30 0.13 32 40 0.30 32 40 0.64 32 40 0.31 32 40 0.20 32 40 2.00

R, θ (oC/W) 0.0019 0.0055 0.0006 0.0025 0.0006 0.0017 0.0040 0.0168

Table 3 Geometry of direct attach power electronics thermal resistance stack – 0.017oC/W

Figure 5 Direct attach resistance from die to coolant As shown in Fig. 5, in this model the direct attachment technique represents 38% of the resistance from the die to the coolant, while the resistance from the cold plate surface to the coolant is 62% of the total resistance. Clearly, although attachment methods have lowered the thermal resistance from the die to the inside surface of the cold plate, and therefore the die temperature, cold plate technology, in terms of increased heat transfer coefficient and increased internal surface area, should be an area of at least equal concern. In addition to heat transfer, the efficiency of a fin pattern such as pressure drop versus thermal performance has often been neglected in the literature and therefore rarely pertains 3 to actual flow conditions ( ).

EXPERIMENTATION An experimental setup to study the flow rate, pressure drop, and heat transfer in: a serpentine 4-pass copper tube in an aluminum plate; a design having folded aluminum fins brazed in an aluminum housing; a minichannel aluminum extrusion; and two molded copper fin designs was developed. The experimental setup as shown in Fig. 6 consisted of a heat source mounted to the cold plate test specimen, and the cold plate test specimen placed in a recirculating coolant loop. Motive force and temperature control for the coolant loop was provided by a commercial recirculating chiller having an R-134a refrigerant system with a cooling capacity of 2400W, an 8-liter reservoir, and a 16liter/minute pump. Each cold plate specimen was tested in a volumetric flow range of 1.9 l/min to 11.4 l/min of water. Clear flexible tubing having a 9.5mm inner diameter and a 12.7mm outer diameter was used in all experiments. All experiments used a thin layer of roughly 0.0025mm thick Dow Corning TC-5022 thermal grease as an interface material between the heat source and the cold plate. The experiments were conducted using various heat loads within the flow range to determine the operating characteristics of each of the five cold plate test specimens.

interface to the cold plate test specimen. Three slots were cut into the copper block, between each heater, on the interface surface between the heater block and the cold plate mounting surface, measuring 1.0mm wide and 1.0mm deep. One thermocouple was mounted in each slot. The slots were then filled with a thermal epoxy and sanded flush with the surrounding copper block surface. An insulator body completely covers the copper block on 4 sides, partially covers the block on one side to allow room for wires, and leaves one side open for heat transfer.

Figure 7 Heat source “A” is similar to an IGBT baseplate Heat source B replicates the heat spreading found in an Intel CPU. The copper heat spreader was 2.9cm x 2.9cm. A single slot was cut into the copper block on the interface surface between the heat block and the cold plate mounting surface, measuring 1.0mm wide and 1.0mm deep. One thermocouple was mounted in the slot. The slot was then filled with a thermal epoxy and sanded flush with the surrounding copper block surface. An insulator body completely covers the copper block on 5 sides, and allows one side open for heat transfer.

Figure 6 Experimental test setup HEAT SOURCE Because the tested cold plates were not all the same size, two different sizes of heat sources were used. Heat source A is shown in Fig 7. Heat source B is shown in Fig. 8. Heat source A replicates the heat spreading found in a typical IGBT module. The heat transfer surface is 11cm x 8cm. Four blind holes were drilled into a solid copper C11000 block. One McMaster-Carr model 4877K22 heater cartridge was mounted in each blind hole. The cylindrical heater cartridges were 9.5mm diameter and 50.8mm long, resulting in a heat flux of approximately 12.2W/cm2 at the interface between the cartridge and the wall of the copper block and 8.4W/cm2 at the

Figure 8 Heat Source “B” is similar to an Intel microprocessor package INSTRUMENTATION An Omega FTB-4805 paddle wheel flowmeter was used to measure the volumetric flow rate in the coolant loop. This flowmeter is rated for use within the range of 0.38 l/min to 37.8 l/min. To calculate flow resistance, inlet and outlet pressure of each cold pate test specimen was measured using two Omega PX209 solid state pressure

transducers rated for use within the range of 101.1kPa to 206.8kPa. Coolant temperature was measured at three points in the system: coolant into the cold plate test specimen, coolant out of the cold plate test specimen, and chiller reservoir. The heat source temperature was measured at three points on the heater/cold plate surface interface. In addition, ambient air temperature was also measured. All temperatures were measured using Omega T-type (copper/ constantan) thermocouples. Power to the heat source was controlled by a Staco Energy Products 3PN1010B variable transformer. This device is rated up to 1,400W (10A @ 140V). Power was measured using an Omega HHM290 multimeter. All measured data was routed to an Agilent 34970A data acquisition switch unit. UNCERTAINTY ANALYSIS All temperatures were measured using Omega T-type thermocouples with a standard limit error of ±1.0°C or 0.75% whichever is greater for temperatures above 0°C. Power dissipation was calculated from voltage and current measurements made with an Omega HHM290 multimeter with a typical voltage error of 0.25% and a typical current error of 2.0%. Flow rate was measured using an Omega FTB-4805 flowmeter with an error of 1.0% FS. Thermal resistance values were calculated using the average of three heater baseplate temperatures, the average of two water inlet temperatures, and the calculated power dissipation. The uncertainty analysis was conducted using the root mean 4 5 square method described by Moffat ( ) and Holman ( ). The rms error of thermal resistance is ±3.5%. DATA ANALYSIS The measured rate of heat transfer and flow resistance data obtained at each volumetric flow rate point was reduced to nondimensional form. Since the cold plate test specimens used a variety of fin types; the Reynolds number, Re; Nusselt number, Nu; Colburn factor, j; and Darcy friction factor, f, were calculated based on the hydraulic diameter, DH, for each fin type. The hydraulic diameter was based on the space between fins. Velocity is taken as the approach velocity, which uses the cavity cross sectional area without fins. Where: DH =

2bh b+h

Re =

ρUDH μ

Nu =

hc DH k

⎛ Nu ⎞ 2 3 ⎟ Pr ⎝ Re Pr ⎠

j= ⎜

f=

ΔP ⎛ L ⎞⎛ ρ U 2 ⎞ ⎟⎟ ⎟⎟⎜⎜ ⎜⎜ D 2 g c ⎠ ⎝ H ⎠⎝

NUMERICAL SIMULATION Simulations were run on the different cold plate fin configurations. Because some of the commercial cold plates had a disadvantage due to use of aluminum instead of copper, the simulations examined the difference between each copper/aluminum cold plate and an identical cold plate manufactured entirely from copper The simulations were run using COSMOSFloworks. This software is a commercial, detailed, validated, finiteelement simulator of 3D heat flow. It calculates both flow patterns and heat transfers for systems of various geometries, combinations of materials, fluid flows, boundary conditions, and heat sources. MATHEMATICAL MODELS COSMOSFloWorks solves the traditional Navier-Stokes equations for mass, momentum, and energy conservation laws for fluid flows. The formulations are supplemented by fluid state equations defining the nature of the fluid, and by empirical dependencies of fluid viscosity and thermal conductivity based on temperature. The code was mainly developed to study turbulent flows, but is also used for laminar flow simulations. To predict turbulent flows, the software uses the Favre-averaged Navier-Stokes equations, where time-averaged effects of the flow turbulence on the flow parameters are considered. Other, i.e. large-scale, time-dependent phenomena are taken into account directly (6). Briefly, FloWorks solves the governing equations using the finite volume method on a spatially rectangular computational mesh designed in the Cartesian coordinate system. Planes are configured orthogonally to its axes and refined locally at the solid/fluid interface and additionally in specified fluid regions, at the solid/solid surfaces, and in the fluid region during calculation. Values of all the physical variables are stored at the mesh cell centers. Due to the finite volume method, the governing equations are discretized in a conservative form. The spatial derivatives are approximated with implicit difference operators of second-order accuracy. Time derivatives are approximated with an implicit first-order Euler scheme 7 ( ). The numerical scheme’s viscosity is negligible with respect to the fluid viscosity. The second-order upwind approximations of fluxes in the finite volume technique are automatically based on the implicitly treated modified Leonard's QUICK approximations (8) and the Total Variation Diminishing (TVD) method (9).

Through this procedure, extra terms such as the Reynolds stresses appear in the equations for which additional information must be provided. To close this system of equations, FloWorks employs transport equations for the turbulent kinetic energy and its dissipation rate, the so-called k-ε model. FloWorks employs one system of equations to describe both laminar and turbulent flows. Moreover, transition from a laminar to turbulent state and/or vice versa is possible.

Note that μt and k are zero for laminar flows. In the frame of the k-ε turbulence model, μt is defined using two basic turbulence properties, namely, the turbulent kinetic energy k and the turbulent dissipation ε, such that:

The mass, momentum, and energy conservation laws in a Cartesian coordinate system rotating at the Ω angular velocity about an axis passing through the coordinate system's origin can be written in the conservation form as follows:

Here, fμ is a turbulent viscosity factor and is defined by the expression:

∂ρ ∂ (ρ U i ) = 0 + ∂t ∂xi

(

)

∂ρH ∂ρU i H ∂ ∂p ∂U i + = U j τ ij + τ ijR + qi + − τ ijR + ρε + SiU i + QH , ∂t ∂xi ∂xi ∂t ∂x j

( (

) )

U2 2

Where: Si is a mass-distributed external force per unit mass due to media resistance and a buoyancy force (gravity), h is the thermal enthalpy, QH, is a heat source or sink per unit volume, τik is the viscous shear stress tensor, qi is the diffusive heat flux, and the subscripts are an expression to denote summation over the three coordinate directions. Because the simulations and experiments in this paper were performed using pure water, the viscous shear stress tensor is given as:

⎛ ∂U i ∂U j 2 ∂ U k ⎞⎟ + − δ ij τ ij = μ ⎜⎜ ∂xi ∂ x k ⎟⎠ 3 ⎝ ∂x j Following Boussinesq's assumption, the Reynoldsstress tensor has the following form:

⎛ ∂U i

τ ijR = μ t ⎜⎜

⎝ ∂x j

+

∂U j ∂xi

−

∂ U k ⎞⎟ 2 2 − ρ kδ ij δ ij 3 ∂ x k ⎟⎠ 3

C μ ρk 2

ε

) ] ⋅ ⎛⎜⎜1 + 20,5 ⎞⎟⎟,

[

f μ = 1 − exp ( − 0.025Ry

Where

∂ρU i ∂ ( ρ U iU j ) + ∂p = ∂ τ ij + τ ijR + Si i = 1,2,3 + ∂t ∂x j ∂xi ∂x j

H =h+

μt = f μ

2

RT ⎠

⎝

ρk 2 ρ ky RT = , Ry = με μ

and y is the distance from the wall. This function allows the laminar-turbulent transition. Two additional transport equations are used to describe the turbulent kinetic energy and dissipation:

⎛⎛ ∂ρk ∂ ( ρ U i k ) = ∂ ⎜⎜ ⎜⎜ μ + μ t + ∂t ∂xi ∂xi ⎝ ⎝ σk

⎞ ∂k ⎟⎟ ⎠ ∂xi

⎞ ⎟ + Sk ⎟ ⎠

⎛⎛ ∂ ρε ∂ ( ρ U i ε ) = ∂ ⎜⎜ ⎜⎜ μ + μ t + ∂t ∂xi ∂xi ⎝ ⎝ σε

⎞ ∂ε ⎟⎟ ⎠ ∂xi

⎞ ⎟ + Sε ⎟ ⎠

Where the source terms Sk and Sε are defined as:

S k = τ ijR

∂U i − ρε + μt PB ∂x j

Sε = Cε 1

ε ⎛⎜ k ⎜⎝

f 1τ ijR

⎞ ∂U i ρε 2 + μ t C B PB ⎟ − C ε 2 f 2 ⎟ ∂x j k ⎠

In the preceding terms, PB represents the turbulent generation due to buoyancy forces and can be written as B

PB = −

g i 1 ∂ρ σ B ρ ∂xi

Where gi is the component of gravitational acceleration in the xi direction. The constant σB = 0.9. Constant CB is defined as: CB = 1 when PB > 0, and CB = 0. In all other cases; B

In this case, τij is the Kronecker delta function (it is equal to unity when i = j, and zero otherwise), μ is the dynamic viscosity coefficient, μt is the turbulent eddy viscosity coefficient, and k is the turbulent kinetic energy.

B

B

B

3

B

⎛ 0.05 ⎞ ⎟ , f 2 = 1 − exp − RT2 f1 = 1 + ⎜ ⎜ f ⎟ ⎝ μ ⎠

(

)

The constants Cμ, Cε1, Cε2, σk, and σε are defined empirically. In FloWorks the following typical values were used: Cμ = 0.09 Cε1 = 1.44 Cε2 = 1.92 σk = 1.0 σε = 1.3 When the Lewis number, Le is equal to 1, the diffusive heat flux is defined as:

⎛ μ μ ⎞ ∂h , i = 1, 2, 3. qi = ⎜⎜ + t ⎟⎟ Pr σ ∂ x c ⎠ i ⎝ Here, the constant σc = 0.9. It should be noted that these equations describe both laminar and turbulent flow so that transitions from one flow regime to another and back are possible. In laminar flow, k and μt are zero. The software allows predictions of simultaneous heat transfer in solid and fluid media with energy exchange between them. Heat transfer in fluids is described by the energy conservation equation where the heat flux is defined by qi. The phenomenon of anisotropic heat conductivity in solid media is described by the following equation

∂ρe ∂ ⎛ ∂T ⎞ ⎟ + QH ⎜ λi = ∂t ∂xi ⎜⎝ ∂xi ⎟⎠ where e is the specific internal energy, e = cT, c is specific heat, QH is specific heat release per unit volume, and λi is the eigenvalues of the thermal conductivity tensor. It is supposed that the heat conductivity tensor is diagonal in the considered coordinate system. For isotropic medium λ1 = λ2 = λ3 = λ. If a composite solid consists of several solids attached one to another, then the thermal contact resistances between them (on the related contact surfaces), in the form of contact conductance, is accounted for when calculating the heat conduction in solids. As a result, a solid temperature step appears on the contact surfaces. In the same manner, a thin layer of interstitial material between solids or on a solid in contact with fluid can be accounted for when calculating the heat conduction in solids, but is specified by the interstitial layer material and thickness. When predicting conjugate heat transfer, the continuity of energy flux is enforced at the interface of fluid and solid media. To solve the asymmetric systems of linear equations that arise from approximations of momentum, temperature and species equations, a preconditioned generalized conjugate gradient method (9) is used. Incomplete LU factorization is used for reconditioning.

The multigrid method was used to decrease the solution time. Basic features of the multigrid algorithm are as follows. Based on the given mesh, a sequence of grids (grid levels) are constructed, with a decreasing number of nodes. On every such grid, the residual of the associated system of algebraic equations is restricted onto the coarser grid level, forming the right hand side of the system on that grid. When the solution on the coarse grid is computed, it is interpolated to the finer grid and used there as a correction to the result of the previous iteration. After that, several smoothing iterations are performed. This procedure was repeated four times on every grid level until the corresponding iteration met the stopping criteria, which were allowed to be set automatically by the software. The coefficients of the linear algebraic systems associated with the grid are therefore only computed once and stored.

SOLUTION METHODOLOGY BOUNDARY CONDITIONS Internal Flow Boundary Conditions For each simulation an inlet volumetric flow rate and coolant temperature were applied manually. These parameters were set normal to a perpendicular plane to the flow axis. Because the turbulence intensity at the entrance is dependent on the upstream flow history, a lead-in entrance length of five times the diameter of the inlet tube was applied to allow the flow to develop and attenuate any inlet maldistributions. Turbulence intensity was specified at 2% and surface roughness was 0 rms. The inlet tube length was specified to be a nonconducting insulator. The fluid inlet port and fluid outlet port were classified as a “flow” opening, and a "pressure" opening respectively. The flow opening was given a specified volumetric flow rate. The pressure opening at the fluid outlet was given a pressure of ambient, 101325Pa. A "pressure" opening’s flow boundary condition, which can be static pressure, or total pressure, or environment pressure was imposed when the flow direction and/or magnitude at the model opening are not known a priori, so they are to be calculated as part of the solution. Which of these parameters is specified depends on which one of them is known. In this study the static pressure is not known, whereas the opening that connects the computational domain to the external space environment with known pressure, the total pressure at the opening is known. The environment pressure condition is interpreted by the software as a total pressure for incoming flows and as a static pressure for outgoing flows. A "flow" opening’s flow boundary condition is imposed when dynamic flow properties (i.e., the flow direction and mass/volume flow rate or velocity) are known at the opening. If the flow enters the model, then the inlet

temperature, fluid mixture composition and turbulence parameters were specified also. The pressure at the opening will be determined as part of the solution. Outlet conditions were set at zero gauge pressure. Again, as stated in the inlet boundary conditions, an exhaust length of 10 times the diameter of the outlet tube was applied as normal to a perpendicular plane to the flow axis to allow the flow to develop and attenuate any outlet maldistributions. Wall Boundary Conditions In COSMOSFloWorks the default velocity boundary condition at solid walls corresponds to the no-slip condition. The solid walls are also considered to be impermeable. The software also provides the "Ideal Wall" condition that corresponds to the slip condition. Thermophysical properties The fluid coolant used for all tests was filtered distilled water. The coolant was supplied at 20oC. For purposes of consistent analysis the properties of Table 4 were used at the fluid inlet. The properties of Table 5 are applicable to other materials used in the models. Tin o ( C) 20

ρ 3 (kg/m ) 998.2

cp k (J/kg K) (W/m K) 4182 0.5967

μ 2 (N s/m ) .000993

Pr (calculated) 6.960

Table 4 Coolant properties at the coolant inlet Material

ρ 3 (kg/ m ) 8930 8573 2713 3230

Copper (C11000) Molded Copper Aluminum (6061) Thermal Grease (Dow TC-5022)

cp (J/kg K) 383 383 963 1100

where: Fins = total number of fins DH = hydraulic diameter based on space between fins AFIN = active internal fin surface area APLATE = active external cold plate surface area AFIN/APLATE = ratio of active internal surface area to the active external surface area of the cold plate From Table 5 note that the ratio of fin area to the external active area is much greater for the molded copper fins than for the other configurations. The active area is defined as the overall area of the surface to which the fins are mounted. This is also the area of maximum heat transfer. For the folded fin configuration the total external area was larger than the heat source, so the active external area is the area of the heater, and the internal fin area is the fin surface area attached to an area the size of the heater. A cutaway isometric view of the swaged tube cold plate is shown in Fig. 9. The unit tested was constructed using a copper tube and an aluminum cold plate. The copper tube had an inner dimension of 8.0mm and total length was about 0.83m. Values for a copper tube and copper cold plate were found by taking the ΔT between the copper tube/aluminum cold plate and the copper tube and copper cold plate, and subtracting that value from the temperature measured by testing the copper tube/aluminum cold plate.

k (W/m K) 390 325 180 4.0

Table 5 Properties of other materials The above values represent the material properties at the beginning of the test at a water inlet temperature of 20oC, however all properties were dynamic and were allowed to change per the local environmental conditions as the model reached a steady state operating temperature. Geometry Creation and Meshing A solid model was created of each commercially available cold plate using SolidWorks software. After experimental testing each sealed cold plate was also dissected to obtain the internal fin geometry, construction, and materials used. Table 5 presents a comparison of the fin geometries tested. Type

Fins

Swaged Tube Folded Fins Minichannels Molded Fins 01 Molded Fins 02

N/A 7030 43 2026 2614

Table 6 Fin Geometry

DH (mm) 8.00 1.84 1.25 1.69 1.09

AFIN 2 (m ) 0.0153 0.0349 0.0135 0.0449 0.0445

APLATE AFIN/APLATE 2 (m ) 0.0135 1.13 0.0088 3.97 0.0031 4.36 0.0041 10.95 0.0041 10.85

Figure 9 Copper tube swaged to an aluminum plate A cutaway isometric view of the folded fin cold plate is shown in Fig. 10. The unit tested was constructed using aluminum fins brazed inside an aluminum cold plate. The folded fin arrangement resulted in a staggered fin configuration. Each fin was 3mm long and 0.2mm thick. Spacing between fins in a row averaged 0.5mm, resulting in a fin density of about 22 fins/cm2. Values for copper folded fins inside a copper cold plate were found by taking the ΔT between the aluminum fin/aluminum cold plate and the copper fin/copper cold plate, and subtracting that value from the temperature measured by testing the aluminum fin/aluminum cold plate.

Figure 10 Folded fins in a machined copper base A cutaway isometric view of the minichannel cold plate is shown in Fig. 11. The unit tested was constructed using aluminum tubes welded to an extrusion of aluminum fins which formed the mounting surface. This design had 43 internal fins that were 0.35mm thick and 61mm long. Spacing between the fins averaged 0.8mm. Values for copper tubes welded to an extrusion of copper fins were found by taking the ΔT between the aluminum tube/ aluminum cold plate and the copper tube/copper cold plate, and subtracting that value from the temperature measured by testing the aluminum tube/aluminum cold plate.

Figure 12 Molded copper pins

RESULTS DIMENSIONAL VALUES Heat transfer coefficient (hc) The heat transfer coefficient was calculated using the total wetted surface area inside each cold plate and is shown compared to Reynolds number in Fig. 13 and compared to measured volumetric flow rate in Fig. 14. The swaged tube cold plate is clearly in the turbulent flow regime because of the large hydraulic diameter of the tube and therefore has the highest heat transfer coefficient. The folded fin cold plate has the lowest heat transfer coefficient. 2000 1800

2

Heat Transfer Coefficient (W/m K)

1600

Figure 11 Minichannel copper heat sink

Swaged Tube

1400

Patch 02 Patch 01

1200

Minichannel Folded Fins

1000 800 600 400

A cutaway isometric view of a molded pin fin cold plate is shown in Fig. 12. Two units were tested, Model 01 had 1.0mm fins and Model 02 had 0.5mm pins. The units tested were constructed using a machined copper tub to which two molded pin copper cold plates were brazed. Unique about this design is the size and spacing of the pins. Model 01 had pins approximately 1.0mm in diameter having a spacing of 1.0mm between pins in a row. The pins were molded in a staggered pattern which results in a total of 2026 individual pins, having a pin density of about 47 pins/cm2. The pins molded for the Model 02 cold plate are approximately 0.5mm in diameter and have a spacing of 0.5mm between pins in a row. The pins are molded in a staggered pattern which results in a total of 2614 individual pins, having a pin density of about 62 pins/cm2.

200 0 100

1000

10000 Reynolds Number

Figure 13 Calculated heat transfer coefficient versus Reynolds number

100000

14.0

2000 Swaged Tube

1800

Patch 02

Folded Fins Swaged Tube Minichannel Patch 01 Patch 02

12.0

Patch 01 1600

Minichannel 10.0

1200

Pumping Power (w)

2

Heat Transfet Coefficient (W/m K)

Folded Fins 1400

1000 800

8.0

6.0

600 4.0

400 200

2.0

0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

Volumetric Flow Rate (l/min)

0.0 100

Figure 14 Calculated heat transfer coefficient versus flow rate

1000

10000

100000

Reynolds Number

Figure 16 Calculated Pumping power versus Reynolds number

Pumping Power (PP) The pumping power required to move the coolant at a given flow rate is shown in Fig. 15. Pumping power versus Reynolds number is shown in Fig. 16. Pumping power is calculated as the product of the measured pressure drop and the measured flow rate. The pumping power required to move the coolant through the folded fin cold plate is considerably higher than the other designs. The low-cost commercial design of the folded fin cold plate suffers from a restrictive flow path that includes four 90-degree turns through small diameter holes. 14.0 Folded Fins Swaged Tube

12.0

Minichannel Patch 01 Patch 02

Pumping Power (W)

10.0

Thermal Resistance (θ) The thermal resistance was calculated using the measured average temperature difference from: a thermocouple in the reservoir and the coolant temperature near the inlet to the cold plate; to the average temperature of the three thermocouples located at the heat source/cold plate interface surface. Thermal resistance compared to flow rate is shown in Fig. 17, and thermal resistance versus Reynolds number is shown in Fig. 18. Due to the small heat transfer area of the minichannel cold plate, the thermal resistance was higher at any flow rate versus the other cold plates. Again, as seen in Fig. 18, the swaged tube cold plate was operating in the turbulent region, and even with a disadvantage in fin area, performed well. The best performance in the measured envelope was seen in the patch 02 molded copper cold plate.

8.0 0.12

Minichannel Swaged Tube

6.0

Folded Fins Patch 01

0.10

Patch 02

0.08

o

2.0

Thermal Resistance ( C/W)

4.0

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

Flow Rate (l/min)

0.06

0.04

Figure 15 Calculated Pumping power versus flow rate 0.02

0.00 0.0

2.0

4.0

6.0

8.0

10.0

Volumetric Flow Rate (l/min)

Figure 17 Thermal resistance versus flow rate

12.0

0.50

0.120 Minichannel

0.45

Swaged Tube 0.100

Patch 01 Patch 02 Minichannel Swaged Tube Folded Fins

Folded Fins 0.40

Patch 01 Patch 02

Colburn Factor

Thermal Resistance (oC/W)

0.35 0.080

0.060

0.30

0.25

0.20

0.040 0.15

0.10 0.020 0.05

0.000 100

1000

10000

0.00 100

100000

1000

10000

100000

Reynolds Number

Reynolds Number

Figure 18 Thermal resistance versus Reynolds number

Figure 20 Colburn Factor versus the Reynolds number Nusselt number (Nu)

Pressure Drop (ΔP) The pressure at the inlet and outlet ports was measured directly. The differential pressure is compared to the flow rate in Fig. 19 and is similar to the pumping power graph of Fig. 15. Again, the low-cost commercial design of the folded fin cold plate suffers from a restrictive flow path that includes four 90-degree turns through small diameter holes which results in a high ΔP without aiding heat transfer.

The Nusselt number is a dimensionless value that indicates the ratio between convective heat transfer and conductive heat transfer, and therefore shows the benefit that surface enhancement has on the heat transfer. Fig. 21 shows that the swaged tube cold plate has the highest Nusselt number for the cold plates tested. The Nusselt number was determined from the calculated heat transfer coefficient for the entire cold plate and the measured hydraulic diameter. 25.0

80 Folded Fins Swaged Tube

70

Minichannel 20.0

Patch 01 Patch 02

60

Swaged Tube Patch 01 Nusselt Number

Pressure (kPa)

50

40

30

Patch 02

15.0

Minichannel Folded Fins

10.0

20 5.0 10

0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 100

1000

Figure 19 Pressure drop versus flow rate

10000

100000

Reynolds Number

Volumetric Flow Rate (l/min)

Figure 21 Nusselt number versus the Reynolds number Darcy Friction Factor (f)

NONDIMENSIONAL NUMBERS Colburn Factor (j) The Colburn factor is a dimensionless value that indicates the relationship between heat transfer and fluid friction. Fig. 20 shows a comparison of the Colburn factor for the tested configurations versus the Reynolds number. This figure clearly shows that the two molded copper cold plates have better performance for the amount of fluid friction they contribute.

The Darcy friction factor versus the Reynolds number is shown in Fig. 22. The friction factor was calculated using the measured hydraulic diameter, the measured ΔP, and the calculated approach velocity.

7

6.0

Folded Fins Patch 01 Patch 02 Minichannel Swaged Tube

6

5.0

4

Thermal Resistivity (oC cm2/W)

Darcy Friction Factor

5

3

2

1

0 100

1000

10000

4.0

3.0

2.0

100000

Reynolds Number

10

Figure 22 Darcy friction factor versus the Reynolds number

Figure 24 Thermal resistivity versus normalized flow rate Thermal Resistivity (R') to Pressure Drop

NORMALIZED DATA Thermal Resistivity (R') to Flow Rate Fig. 23 shows the thermal resistivity versus the flow rate. Thermal resistivity is calculated as the thermal resistance per unit area of the cold plate. In this manner, different sized cold plates can be compared. Fig. 23 shows that the molded copper cold plates are the most efficient in terms of cooling a given surface area.

Finally, the thermal resistance per unit area is compared to the pressure drop in Fig. 25. This comparison shows that molded copper cold plates are more efficient in terms of converting flow resistance to cooling power per unit area of the cold plate surface. 6.0

5.0 6.0 Swaged Tube

Thermal Resistivity (oC cm2/W)

Minichannel Folded Fins

5.0

Patch 01

4.0

o

2

Thermal Resistivity ( C cm /W)

Patch 02

3.0

4.0

3.0

2.0

2.0

Figure 25 Thermal resistivity versus pressure drop

1.0

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

Volumetric Flow Rate (l/min)

Figure 23 Thermal Resistivity versus flow rate Thermal Resistivity (R') to Normalized Flow Rate (Q') Fig. 24 shows the thermal resistivity versus the normalized flow rate. While thermal resistivity describes the efficiency of the cold plate surface, the normalized flow rate expresses the flow rate per unit area of the cold plate and is a more valid comparison of the performance of each cold plate to the total cooling surface area (10). Normalizing the flow rate allows the comparison of different sized cold plates using different flow rates. Fig. 24 shows that, the molded copper cold plates are the most efficient in terms of cooling a given surface area with a given volume of coolant.

CONCLUSION A numerical and experimental study of heat transfer and fluid flow in heat sinks that may be used for cooling loops for motor drives has been presented in this paper. An experimental study of five heat sinks was completed: a serpentine 4-pass copper tube in an aluminum plate, a design having folded aluminum fins brazed in an aluminum housing, a minichannel aluminum extrusion, and two molded copper fin designs. In addition, using the results from the experimental analysis, a CFD and similarity study was performed on models of a serpentine 4-pass copper tube in a copper plate, a design having folded copper fins brazed in a copper housing, and a minichannel copper heat sink. Temperature, pressure drop, flow rate, and other pertinent data were recorded during the experiments and compared to the computational models. Nondimensional numbers and dimensional values were calculated from the results. The data was then o 2 normalized for thermal resistivity ( C cm /W) and 2 normalized for flow rate (l/min-cm ) to allow comparison

of different size cold plates, with different size heat sources at different flow rates.

heat from this assembly is stipulated to be 1kW, which represents an IPEM efficiency of 98%. The mounting arrangement is shown in Fig.1.

Of the tested cold plate configurations a molded copper heat sink having round 0.5mm diameter pins and 0.5mm spacing between pins in a staggered configuration had better performance than other fin configurations in terms of thermal resistivity (oC cm2/W) versus normalized flow rate (l/min-cm2), and thermal resistivity (oC cm2/W) versus pressure drop (kPa). Table 7 and Table 8 provide the numerical values to compare thermal resistivity (oC cm2/W) versus normalized flow rate (l/min-cm2), and thermal resistivity (oC cm2/W) versus pressure drop (kPa) for each configuration, respectively. Values in italics are extrapolated from the data. Type Swaged Tube MiniChannel Folded Fins Molded Fins 01 Molded Fins 02

Normalized Flow Rate (l/min cm2) 0.025 0.05 0.10 0.15 0.20 0.25 4.84 3.93 3.41 3.80 3.42 3.19 3.03 2.92 2.20 1.75 1.43 1.35 0.71 0.58 0.53 0.50 0.48 0.71

0.56

0.51

0.48

0.47

Table 7 Comparison of thermal resistivity to normalized flow rate Type Swaged Tube MiniChannel Folded Fins Molded Fins 01 Molded Fins 02

2.5 5.83 3.62 2.40 0.64

Pressure Drop (kPa) 5 10 20 30 4.78 4.20 3.81 3.63 3.37 3.10 2.90 2.77 2.21 1.94 1.70 1.59 0.57 0.53 0.49 0.48

0.64

0.55

0.50

0.47

The Prius has two separate ethylene glycol/water cooling systems, one for the gasoline engine and one for the electric motor. The flow rate through the cold plate that cools the IPEM assembly is roughly 3.0 l/min. In this analysis, the fluid inlet temperature is 75oC, but after absorbing 1kW the actual fluid temperature and properties are consistent with 80oC propylene glycol in a 50/50 mixture with water. Fluid properties are shown in Table 9. Tin o ( C) 80

ρ 3 (kg/m ) 1002.8

cp k (J/kg K) (W/m K) 3763 0.3518

Pr μ 2 (N s/m ) (calculated) 0.001215 13.0

Table 9 Properties of propylene glycol and water coolant Fig. 26 shows a model of a single IGBT module. The dimensions of the 2mm thick copper base plate are 35mm x 45mm, resulting in a total height of 3.60mm. For this analysis the IGBT silicon dissipates 45.5W and the diode dissipates 10W, for a total power of 55.5W. Because there are 18 IGBTs in an IPEM, the IPEM dissipates about 1kW.

40 3.52 2.69 1.53

0.45

Table 8 Comparison of thermal resistivity to pressure drop

DISSCUSSION and APPLICATIONS Because the thermal resistance and pressure drop of molded copper fins is much lower than many other cooling surfaces, it can be argued that the thermal performance and lowered pressure drop inherent in this technology can be used to leverage reductions in weight and size of products that are sensitive to these parameters. To this end, a comparative simulation was made on the IGBT/cold plate assembly of a 2004 Toyota Prius comparing the stock cast aluminum fins and a configuration using the Patch 02 fin array of the current analysis. The 2004 Toyota Prius is a hybrid vehicle that uses both a gasoline-powered internal combustion engine capable of delivering a peak-power output of 57 kW and a battery-powered electric motor capable of delivering a peak-power output of 50 kW as motive power sources. The inverter assembly is comprised of a single integrated power electronics module (IPEM) having 18 IGBTs. The IPEM is mounted to a cast aluminum housing which contains simple fins. For this analysis, the

Fig. 26 A single Prius IGBT showing coolant channels Fig. 27 shows a model of the full Prius cold plate depicting the flow channels. Fig 28 shows the cold plate with the IPEM attached. Overall dimensions are approximately 25cm x 15.5cm resulting in a heat flux of approximately 2.58W/cm2. The internal fins are estimated to be 10mm high and 1mm thick. Total surface area inside the cold plate is estimated to be 0.0972m2, and weight with the IPEM attached is roughly 1.80kg. Normalized flow rate is only about 0.008 l/mcm2. Using a 2mm thick aluminum wall on each side of the fluid passages results in a coldplate z-axis dimension of 17.65mm, which includes a 0.05mm thick thermal grease layer.

As shown in Fig. 30, note that the mounting configuration for the IGBT is based on Fig. 3. In this manner, a window is sectioned from the 2mm thick cold plate cover and the 2mm thick copper baseplate containing the pins is sealed in place.

Fig. 27 The 2004 Prius cold plate showing the internal flow channels which are 10mm high and velocity contours.

Fig. 30 Shows a detail of the construction of the molded copper pins. It can be argued that the stock heat flux at the die level, approximately 6W/cm2 is very low. Many other IGBTs with similar performance have chip-level heat fluxes of over 100W/cm2. If the heat flux of each IGBT could be doubled to 12W/cm2 at the die level, and if the heat dissipation of the IPEM remained constant at 1kW, then the IPEM heat flux would double, from 2.58W/cm2 up to 5.16W/cm2, and the area for the IPEM would be reduced from the stock 25cm x 15.5cm down to 12.5cm x 7.75cm. In order to reduce the computational time for such a large CFD model, only a single IGBT will be evaluated using a section of 35mm x 45mm.

Fig. 28 2004 Prius coldplate showing the IPEM, composed of 18 IGBT modules Fig. 29 shows a cold plate using similar fluid passages, but having molded copper pins in the configuration of the Patch 02, 0.5mm diameter round pins spaced 1.0mm center to center. Because the pins have such a small diameter, maintaining the stock fin height of 10mm would not produce a thermal benefit, so the pin height has been reduced to 5mm.

Fig 29 A cold plate similar to the stock Prius, except having molded copper pins 5mm high.

Table 10 lists some of the important performance parameters for the stock configuration, molded copper pin configuration, and the molded pins having doubled heat flux. The parameters are for the last IGBT module in the flow series, which represents the highest temperatures. Parameter TJUNCTION (oC) Total Weight (kg) Module Weight IGBT+Fins (kg) Power (W) Die Heat Flux (W/cm2) Plate Heat Flux (W/cm2) Temperature Rise ΔT (oC) Pressure Drop ΔP (Pa) Heat Transfer Area AS (m2) Hydraulic Diameter DH (mm) Reynolds Number Re 2 Heat Transfer Coeff hc (W/m K) Nusselt Number Nu Colburn Factor j Pumping Power PP (W) Thermal Resistance θ (oC/W) Thermal Resistivity R (oC cm2/W)

Stock Prius 104.2 1.796 0.0998 55.5 5.83 2.58 29.2 956 0.0054 6.67 1376 426

Molded Pins 90.7 1.449 0.0805 55.5 5.83 2.58 15.7 14373 0.0114 0.909 715 456

2X Heat Flux 101.5 0.725 0.0805 111 11.7 5.16 26.5 14435 0.0114 0.909 715 456

8.06 0.0025 0.0478 0.435 6.85

1.18 0.0007 0.719 0.193 3.04

1.18 0.0007 0.722 0.193 3.04

Table 10 Important module parameters

As shown in Table 10, compared to a stock Prius cold plate, the size of the IPEM was reduced by 50%, total weight was reduced by 1.07kg, and junction temperature was reduced by 2.7oC, by using the Model 02 molded copper fin configuration and by doubling the IGBT die heat flux. The efficiency of this heat transfer surface, when used in this mounting configuration, is more than double the efficiency of the stock Prius cold plate, as shown by the thermal resistivity value.

REFERENCES 1. Moores, K., Joshi, Y., and Schiroky, G., "Thermal Characterization of a Liquid Cooled AlSiC Baseplate with Integrated Pin Fins," IEEE Transactions on Components and Packaging Technologies, Vol. 24, June 2001, pp. 213 - 219. 2. Valenzuela, J., Jasinski, T., and Sheikh, Z., "Liquid Cooling for High Power Electronics Technology," Power Electronics Technology, February 2005, pp. 50 - 56. 3. Khan, W. A., Culham, J. R., and Yovanovich, M. M., “The Role of Fin Geometry in Heat Sink Performance,” Journal of Electronic Packaging, Volume 128, Number 4, December 2006, pp. 324 – 330. 4. Moffat, R. J., “Describing the Uncertainties in Experimental Results,” Experimental Thermal Fluid Science, 1, 1988, pp. 3 – 17. 5. Holman, J. P., Experimental Methods for Engineers, 6th Ed., New York, 1994 6. Fundamentals of COSMOSMFloworks, Structural Research and Analysis Corporation, 2002, pp.182 - 208. 7. Roache, P.J., Fundamentals of Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM 1998. 8. Hirsch, C., Numerical computation of internal and external flows. John Wiley and Sons, Chichester, 1988. 9. Saad, Y. Iterative methods for sparse linear systems, PWS Publishing Company, Boston, 1996. 10. Leslie, G. Scott, “Cooling Options And Challenges Of High Power Semiconductor Modules,” Electronics Cooling Magazine, Volume 12, Number 4, November 2006, pp. 20 - 27. 11. Staunton, R.H., Ayers, C.W., Marlino, L.D., et al, "Evaluation of 2004 Toyota Prius Hybrid Electric Drive System," ORNL/TM-2006/423, UT-Battelle, Oak Ridge National Laboratory, Oak Ridge, Tennessee, May 2006. 12. Hsu, J.S., Nelson, S.C., Jallouk, P.A. et al., "Report on Toyota Prius Motor Thermal Management," ORNL/TM-2005/33, UT-Battelle, LLC, Oak Ridge National Laboratory, Oak Ridge, Tennessee, February 2005.