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Journal of Power Sources 272 (2014) 404e414

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Journal of Power Sources

journal homepage: www.elsevier .com/locate/ jpowsour

Development of cooling strategy for an air cooled lithium-ion batterypack

Hongguang Sun*, Regan DixonCanadian Regional Engineering Centre, GM of Canada Ltd. e General Motors Company, 1908 Colonel Sam Drive, Oshawa, ON L1H 8P7, Canada

h i g h l i g h t s

� A transient battery thermal model is developed to predict battery thermal behavior.� A design of experiments approach is developed to identify battery cooling strategy.� An optimal design concept of air-cooled battery pack has been proposed.� The cooling strategy to improve battery temperature uniformity has been studied.

a r t i c l e i n f o

Article history:Received 28 April 2014Received in revised form7 August 2014Accepted 25 August 2014Available online 2 September 2014

Keywords:Battery packThermal behaviorThermal modelDesign of experiments (DOE)

* Corresponding author. Tel.: þ1 905 6442624; faxE-mail address: hongguang.sun@gm.com (H. Sun)

http://dx.doi.org/10.1016/j.jpowsour.2014.08.1070378-7753/© 2014 Published by Elsevier B.V.

a b s t r a c t

This paper describes a cooling strategy development method for an air cooled battery pack with lithium-ion pouch cells used in a hybrid electric vehicle (HEV). The challenges associated with the temperatureuniformity across the battery pack, the temperature uniformity within each individual lithium-ion pouchcell, and the cooling efficiency of the battery pack are addressed. Initially, a three-dimensional batterypack thermal model developed based on simplified electrode theory is correlated to physical test data. Ananalytical design of experiments (DOE) approach using Optimal Latin-hypercube technique is thendeveloped by incorporating a DOE design model, the correlated battery pack thermal model, and amorphing model. Analytical DOE studies are performed to examine the effects of cooling strategiesincluding geometries of the cooling duct, cooling channel, cooling plate, and corrugation on battery packthermal behavior and to identify the design concept of an air cooled battery pack to maximize itsdurability and its driving range.

© 2014 Published by Elsevier B.V.

1. Introduction

The rechargeable lithium-ion battery pack continues to beconsidered an efficient and reliable power source for a HEV/PHEVpropulsion system. It is known that battery cell internal ohmicresistance and charge transfer resistance at electrode/electrolyteinterface can generate heat during charge or discharge cycle ofoperation. Overheating of the battery cells may undesirably affectthe operation and durability/lifetime of the battery assembly.Accordingly, a cooling system is typically employed with the bat-tery cells in the battery pack.

A typical air cooled battery pack includes single or multiplestrings of battery cells, a plurality of spaced apart battery coolingplates, cooling ducts, and control modules. Prior art air cooling

: þ1 905 6444932..

systemwith cooling ducts and spaced apart cooling plates may leadto major thermal concerns for the battery pack such as battery celloverheating and uneven heating within each individual battery celland across the entire battery pack during charge/discharge cycles.This can cause accelerated battery degradation and capacityreduction of battery cells. It is desirable to identify an air coolingsystem to ensure battery cells in the pack operate in a controlledtemperature range and uniform temperature within and acrosscells to maximize battery pack capacity and durability. Mathe-matical modeling of battery thermal behavior in terms of coolingstrategy has proven to be an efficient and cost effective tool toextend battery pack durability and driving range.

In this study, a transient three-dimensional battery pack ther-mal model is developed by incorporating a three-dimensionalbattery pack flow sub-model, one-dimensional battery packnetwork sub-model, and battery cell/module thermal sub-model inwhich the battery cell heat generation rate due to the chargetransfer at the battery cell electrode/electrolyte interface and the

Fig. 2. Schematic of battery cell and its cooling channel.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414 405

gradient of potentials are expressed in the form of User DefinedFunctions (UDFs). After the battery pack thermal model is corre-lated to physical tests, analytical DOE studies are performed toeffectively identify the cooling strategy to minimize battery celllumped temperature, battery cell temperature variation across thepack, and total pressure drop of the pack. This is achieved byincorporating a DOE design model developed using iSight software,a morphing model developed using DEP (Detroit EngineeredProducts Inc.) Morpher software, the three-dimensional batterypack flow sub-model, and the one-dimensional battery packnetwork sub-model. Finally, the cooling strategy to reduce tem-perature variationwithin each individual battery cell is studied anddiscussed using the three-dimensional battery pack thermal model.

2. Simulation approach

2.1. Battery pack thermal model

In order to efficiently predict battery pack thermal behaviorunder simulated vehicle drive schedules (e.g., US06 schedule that isa driving pattern with high battery loads) using current computinghardware, a de-coupled transient three-dimensional battery packthermal model has been developed by incorporating a steady statethree-dimensional battery pack flow sub-model, one-dimensionalbattery pack network sub-model, and transient three-dimensionalbattery cell/module thermal sub-model. The description of thesimulation process is shown in Fig.1. In particular, the total pressuredrop of battery pack, the lumped convection heat transfer coeffi-cient of each individual cooling plate, and velocity and pressureprofiles at the inlet and outlet of individual cooling channels (Fig. 2)at different battery pack flow rates are calculated in the steady statethree-dimensional battery pack flow sub-model. Using lumpedconvection heat transfer coefficients of individual cooling plates asinput parameters, individual battery cell transient lumped tem-peratures including lumped cell temperature variation across the

Fig. 1. Description of three-dimensional battery pack thermal model.

pack under various battery charge/discharge cycles are calculatedin the one-dimensional battery pack network sub-model. Finallythe temperature distribution within battery cells are predicted inthe three-dimensional battery cell/module thermal sub-model us-ing the transient battery cell heat generation rate expressed basedon electrode potentials and the relation between electrode poten-tials and current density that is estimated in the one-dimensionalnetwork sub-model. The flow boundary conditions in battery cell/module thermal sub-model are established using the velocity andpressure profiles of the cooling channels obtained from the three-dimensional battery pack flow sub-model.

2.1.1. Battery pack flow sub-modelA steady state three-dimensional battery pack flow sub-model

has initially been developed using FLUENT to calculate the totalpressure drop, convection coefficient of the cooling plate surface ofeach individual battery unit [3], and velocity and pressure profilesof each cooling channel at different flow rates in a battery pack(Fig. 2). In order to significantly reduce the model size andcomputing memory requirements, the detail of battery cells are notcaptured and the battery charge/discharge behavior and thermalbehavior thereof are not described in this sub-model. The Reynoldsnumber of the cooling flow in the flow duct and cooling channelformed between the battery cooling plates is in the range of400e6000 at desired flow rates, so the shear-stress transport (SST)k-omega viscous model [4] with the function of Low ReynoldsNumber Correlations is used to calculate the transitional flowproperties, i.e., the robust and accurate formulation of the k-omegamodel is applied in the near-wall region without the need of anydamping functions. K-omega formulation switches to k-epsilonbehavior in the far field to avoid the dependence of the free-streamvalue of omega. Since the shear-stress transport k-omega viscousmodel requires mesh resolution near the wall to ensure the solu-tion accuracy, three layers of prism elements with equal height areapplied in the region near wall surfaces (battery cooling platesurfaces). The height of prism layer is chosen so that the values ofwall function yþ (yþ ¼ utyp/n) are in the range of 0.4e0.8. Thelumped convection heat transfer coefficient of each individualbattery cooling plate surface is calculated based on the predictedlumped temperature of the cooling plate surface, inlet flow tem-perature, and constant heat flux that is applied on the cooling platesurface as an input boundary condition. Since the temperaturechange of cooling air in the battery pack is under 10 �C duringnormal charge/discharge cycles, the lumped convection heattransfer coefficient defined based on the inlet flow temperature isapproximately independent of the cooling plate temperature,

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414406

which in turn can be used as an input parameter to calculate thelumped convection heat transfer rate of the cooling plate in batterypack network sub-models. In addition, the velocity and pressure atinlet and outlet of cooling flow channels are saved as profiles andused as the flow boundary conditions in the three-dimensionalbattery cell/module thermal sub-model.

2.1.2. Battery pack network sub-modelThis study focuses on a typical air cooled HEV battery pack that

includes a single string of battery cells. At given battery pack powereach individual battery cell current, I, and voltage, Vi, can beexpressed using an equivalent circuit model [5,6] as follows

P ¼ IXni¼1

Vi (1)

d�Vi � Voc;i

�dt

¼ ��Vi � Voc;i

�CiR2;i

þ R1;idIdt

þ ICi

1þ R1;i

R2;i

!(2)

where subscript i represents the number of the battery cell in apack. By default battery cell 1 is at the flow inlet side of the packwhile cell n is at the opposite side in themodel. The symbol withoutsubscript i means the value is the same for each cell in the batterypack. Each individual battery cell ohmic resistances, R1,i, chargetransfer resistance at the electrode/electrolyte interface, R2,i,capacitance, Ci, and open circuit voltage, Voc,i, shown in Fig. 3 arefunctions of battery cell temperature, Tc,i, and SOC (state of charge).These parameters are determined using interpolation and leastsquares fitting techniques in terms of HPPC (Hybrid Pulse PowerCharacterization) test data [3].

The lumped temperature of each individual battery cell, Tc,i, in apack under various charge/discharge cycles is calculated usinggoverning equations as follows�Tc;i � Tpt;i

�Rcon

� have;iApt�Tpt;i � Tin

� ¼ mptCp;ptdTpt;idt

(3)

"I�Vi � Voc;i

�þ ITc;idVoc;i

dTc;i

#��Tc;i � Tpt;i

�Rcon

�Xni¼1

ktAt

�Tc;i � Tadj;i

�Lt

¼ mcCp;cdTc;idt

(4)

Here, the first term of the left-hand side of Eq. (3) is the con-duction heat transfer rate between a battery cell and its coolingplate or holder (Fig. 2). The thermal contact resistance between abattery cell and its cooling plate, Rcon, is estimated based onphysical test data. The second term of the left-hand side of Eq. (3) is

Fig. 3. Description of equivalent circuit model.

the convection heat transfer rate between a battery cooling plateand its surrounding cooling fluid. Since the lumped convection heattransfer coefficient of battery cooling plate surface, have,i, is esti-mated based on the flow temperature at the battery pack inlet inthe three-dimensional battery pack flow sub-model, the flowreference temperature in the second term of Eq. (3) should also bethe pack inlet flow temperature, Tin. Each battery cell heat gener-ation rate during charge/discharge cycles is expressed as the firstterm of the left-hand side of Eq. (4). The cell heat generation rateinvolves an irreversible part due to electro-chemical polarizationand a reversible part due to entropy change [1,7,8]. The conductionheat transfer rate between a battery cell unit and its connecting cellunits (Fig. 2) is also considered in the model and presented as thethird term of the left-hand side of Eq. (4). Since battery cell voltages,Vi and Voc,i, and temperature, Tc,i, depend on each other, Eqs. (1)e(4)are simultaneously solved using 4th order RungeeKutta method.

The parameter, Zi, used to describe the relation between currentdensity and electrode potentials in the three-dimensional batterycell/module thermal sub-model is also estimated in battery packnetwork sub-model, i.e.,

Zi ¼ NAe

�Vi � Voc;i

I� Rt

�(5)

Since the electrical resistance of aluminum or copper is notsensitive to slight temperature change, the battery cell tab resis-tance, Rt, is set to the same value for each individual battery cell inthe pack.

2.1.3. Battery cell/module thermal sub-modelBy incorporating the parameter, Zi, calculated in one-

dimensional battery pack network sub-model, positive electrodepotential, Vp,i, negative electrode potential, Vn,i, and current density,Ji, can be solved using following governing equations

V2Vp;i ¼ �rpJi (6)

V2Vp;i ¼ �rpJi (7)

Ji ¼�Vp;i � Vn;i � Voc;i

��Zi (8)

Here, the governing equations of electrode potentials (6) and (7)in the three-dimensional battery cell/module thermal model areadopted from Shin et al.'s two-dimensional approach [1,2]. In orderto accurately predict the battery cell behavior during transientcharge/discharge cycles, the relationship between current densityand potential difference in Eq. (8) is expressed using the parameter,Zi, that is determined based on an equivalent circuit model as dis-cussed in Eq. (2).

The transient heat generation rate of the battery active materialregion, q

00a;i, due to gradients of potentials and the charge transfer

[1e3,9] is given as

q00a;i ¼

VV2p;i

LerpþVV2

n;i

Lernþ Cq;i

LeJi

"Vp;i � Vn;i � Voc;i � T

dVoc;i

dTc;i

#(9)

where Le is the distance including the thicknesses of one-half ofpositive electrode current collector, one side of cathode, oneseparator, one side of anode, and one-half of negative electrodecurrent collector for a battery cell with double-sided electrodes.The first and second terms of the right-hand side of Eq. (9) are theheat rates generated due to the gradient of positive potential andthe gradient of negative potential, respectively. The parameter, Cq,i,expressed as

Cq;i ¼

ZvL

JiLe

"Vp;i � Vn;i � Voc;i � T

dVoc;i

dTc;i

#!dvL �

ZvL

VV2

p;i

LerpþVV2

n;i

Lern

!dvL

ZvL

JiLe

"Vp;i � Vn;i � Voc;i � T

dVoc;i

dTc;i

#!dvL

(10)

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414 407

is introduced at the third term of the right-hand side of Eq. (7) tooffset the portion due to the gradients of electrode potentials fromthe total heat generation rate. The heat rate generated at the batterytabs, q

00t , is given as

q00t ¼

I2RtAtLt

(11)

User Defined Functions (UDFs) are used to incorporate govern-ing Eqs. (6)e(11) into FLUENT solver in which above governingequations are simultaneously solved with energy equation inFLUENT solver. In particular, governing Eqs. (6) and (7) are definedas scalar transport equations while Eq. (8) is defined as a globalfunction. Eqs. (9) and (11) are used as heat source terms in UDFs.The boundary conditions for User Defined Scalars, positive elec-trode potential, Vp,i, and negative electrode potential, Vn,i, at theinterface between negative tab and cell activematerial region are asfollows: both the specified flux of scalar, Vp,i, and the specified valueof scalar, Vn,i, are equal to zero. At the interface between positive taband cell active material region the specified flux of scalar, Vp,i, isdefined as rpI/(WtN) and the specified flux of scalar, Vn,i, is set tozero.

Similar to the battery pack flow sub-model the shear-stresstransport (SST) k-omega viscous model [3] with the function ofLow Reynolds Number Correlations has been used to calculate thetransitional flow properties in the three-dimensional battery cell/module thermal sub-model. The flow boundary conditions in themodel are the velocity and pressure profiles at inlet of coolingchannel and the pressure profile at outlet of cooling channel thatare calculated in battery pack flow sub-model.

2.2. Analytical DOE approach

By incorporating iSight design model, a morphing model, bat-tery pack flow sub-model, and battery pack network sub-model, ananalytical design of experiments (DOE) approach is developed toeffectively identify a design concept of a battery pack, inwhich eachindividual battery cell temperature, battery cell lumped tempera-ture variation across a battery pack, and total pressure drop areminimized. The process flow diagram is shown in Fig. 4. OptimalLatin-hypercube technique, a modified Latin-hypercube method, isapplied to allow more design factor levels and combinations to bestudied for each design factor. In particular, the design space foreach design factor is divided uniformly and randomly combined togenerate a preliminary design matrix using Latin-hypercube tech-nique. An optimization process is then applied to the preliminaryLatin-hypercube matrix to design an optimal matrix in which thecombined deign points are spread as evenly as possible within thedesign space [10]. The morphing model, developed using DEPMorpher software [11], is used to modify the battery pack flow sub-model based on each combined design point. After running modi-fied battery pack flow sub-model and one-dimensional batterypack network sub-model, each individual battery cell temperatureincluding lumped cell temperature variation across the pack and

total pressure drop of the battery pack are saved into output arrays.The modification of battery pack flow sub-model and simulationsof battery pack thermal behavior are then repeated based on nextcombination of design factors until completing all of the simula-tions for the design matrix. Since the computing time limits thenumber of design points, the optimal design point to ensure thebest battery pack thermal behavior (e.g., lowest maximum batterycell temperature in the pack, lowest lumped cell temperaturevariation across the pack, and acceptable total pressure drop) maynot be included in the design matrix. Thus, Response SurfaceApproximation, the technique based on a fourth order polynomialfit via the least squares regression of outputs in iSight designmodel,is used to approximate the battery pack thermal behavior of addi-tional design points in terms of output arrays and then to identifyoptimal design concept of a battery pack. It should be noted that thetransient three-dimensional battery cell/module thermal sub-model that is used to predict the temperature distribution withinindividual battery cells is not included in the DOE approach due tounacceptable computing time.

2.3. Correlation to physical test data

Physical tests have been conducted on a baseline battery pack tovalidate the battery pack thermal model. The baseline battery packincludes single string of 80 battery cells, battery cell cooling plates,and lower and upper cooling ducts. As shown in Fig. 5, the coolingair from the pack inlet enters the lower cooling duct and passesthrough the cooling channels between two adjacent battery coolingplates to facilitate heat transfer from the battery cells to the fluid.The hot air exits from the upper cooling duct through the packoutlet. The pack inlet and outlet are located at the same side to form“U-type” flow in the pack. Appropriate pressure is applied on bat-tery cell during assembly by aligning and pressing punched stepson the cooling plates. Considering the viability of installationthermocouples are attached on planar surfaces of battery cells andthe cooling plates in the pack as shown in Fig. 6.

Initially the battery pack is charged or discharged to achieve thestate of charge (SOC) to be approximately 50%. The cut-off voltagesare set to 200.0 V during discharge and 336.0 V during charge,respectively. The cooling fan of the battery pack is operated atconstant flow rate of 0.0283 m3 s�1 (60 CFM) and constant inlettemperature of 29 �C. After the temperature of the battery cellreturns to approximately the same temperature as the inlet air, theformal test is then performed based on aggressive charge/dischargecycles to address the worst battery pack thermal behavior. The timeperiod of formal testing is over 4 h during which the heat transferrate and heat generation rate tends to be approximately balancedand the cell temperature fluctuates around a certain value.

By choosing appropriate height of boundary layer elements inbattery pack flow sub-model to ensure the values of wall functionyþ (yþ ¼ utyp/n) to be in the range of 0.4e0.8, the predicted tem-peratures of battery cells and cooling plates are in good agreementwith the experimental data. As examples, the comparisons ofanalytical and experimental transient temperatures of the hottest

Fig. 5. Schematic of a baseline “U-type” flow battery pack.

Fig. 6. Schematic of a battery cell and its cooling plate.

Fig. 4. Analytical DOE study flow diagram.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414408

battery cell unit in the pack are shown in Fig. 7(a) and (b), and thetemperatures of the coldest battery cell unit in the pack are shownin Fig. 8(a) and (b), respectively. It should be noted that the data arethe transient average temperatures at four measurement positionsof the battery cell unit. As can be seen, the maximum deviation ofthe predicted transient temperature between the simulation andphysical test is less than 0.5 �C. The predicted maximum lumpedcell temperature variation across the baseline pack is 4.4 �C that isin agreement with physical test data, 4.2 �C. It is also found that the

battery pack reaches the equilibrium state after 6000 s and themaximum or peak temperature of battery cell or cooling plate re-peats approximately every 600 s with the same value. Table 1 liststhe peak temperatures of a cooling plate and battery cell at mea-surement positions. Simulation results indicate the maximumtemperature variation of the cooling plate at measuring positions is1.8 �C, which is also in agreement with physical test data, 1.9 �C.

3. Results and discussions

As discussed in Section 2.3 the fan and exhaust pipe are at thesame side in the baseline “U-type” flow battery pack. However, the

Fig. 7. Transient temperatures of (a) hottest cooling plate and (b) hottest battery cell ina baseline “U-type” flow battery pack.

Fig. 8. Transient temperatures of (a) coldest cooling plate and (b) coldest battery cell ina baseline “U-type” flow battery pack.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414 409

available space for battery pack(s) in vehicles may be in favor of the“Z-type” flow pack where the inlet and outlet are located on theopposite sides. Fig. 9 shows a baseline “Z-type” flow pack that alsoincludes 80 pouch battery cells. The sizes of lower and upper flatcooling ducts are approximately the same. As defined in Section2.1.2 battery cell 1 is adjacent to the pack inlet and battery cell 80 islocated at the outlet end. Simulations are performed based onsixteen repeated US06 drive cycles for a certain hybrid electricvehicle. The period of each simulated US06 drive cycle is 600 s. Itshould be noted that this simulated US06 drive cycle is slightlydifferent from the aggressive charge/discharge cycle used for cor-relation study in a “U-type” pack. The inlet air temperature is set tostandard state, i.e., 25 �C.

3.1. Uniformity of flow rates of cooling channels

The analytical results of transient lumped or average tempera-tures of battery cells 1, 40, and 80 at flow rate of 0.0283 m3 s�1 (60CFM) are shown in Fig. 10(a), respectively. As can be seen, afterseveral repeated US06 cycles the heat transfer rate and the heatgeneration rate of each individual cell tend to be approximatelybalanced such that the transient lumped cell temperature reachesthe equilibrium state and fluctuates around a certain value. Forexample, after 1800 s or 3 repeated US06 cycles the transient

lumped temperature of cell 80 approximately repeats the fluctua-tion pattern once every US06 cycle. It is also found that the tran-sient lumped temperatures of the cells adjacent to the pack inletside reach the equilibrium state much slower than those near theoutlet side. As a result, the lumped temperature variation amongcells in the battery pack initially increase with time. After thetransient lumped temperature of cell 1 reaches the equilibriumstate, the cell temperature variation across the baseline pack ap-proaches the maximum value and tends to be independent of time.

Since the transient lumped temperatures of individual cellssimultaneously reach their maximum or peak values during eachUS06 cycle at the equilibrium state (Fig. 10(a)), the cell temperaturevariation across the pack can be evaluated by examining the lum-ped peak temperatures of individual cells. The lumped peak tem-peratures of individual cells in baseline “Z-type” flow pack at flowrate of 0.0283 m3 s�1 are shown in Fig. 10(b). It is found that thelumped peak temperatures of battery cells at inlet side (left side)are much higher than those at the outlet side (right side), e.g., thetemperature of cell 1 is 10.8 �C higher than that of cell 80. The rootcause of large lumped cell temperature variation and high lumpedpeak cell temperature in the baseline “Z-type” flow pack is the largevariation of flow rates of cooling channels across entire pack. If oneignores the head loss (energy loss) due to frictional effect, Ber-noulli's equation dictates that pressures and flow velocities in

Table 1Peak temperatures at measurement positions.

Cooling plate Battery cell

Position 1 2 3 4 5 6 7 8

Physical test (�C) 36.1 38.0 37.5 37.5 38.7 37.8 39.1 38.2Simulation (�C) 36.6 38.4 37.9 37.8 38.6 37.9 38.6 37.9Difference (�C) �0.5 �0.4 �0.4 �0.3 0.1 �0.1 0.5 0.3

Fig. 10. (a) Transient lumped temperatures of battery cells, and (b) lumped peaktemperatures of individual cells in baseline “Z-type” flow battery pack.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414410

baseline upper cooling duct and lower cooling duct are inverselyrelated:

p1rþ v21

2¼ p2

rþ v22

2(12)

p3rþ v23

2¼ p4

rþ v24

2(13)

As the cooling air is supplied from a fan to the inlet of the uppercooling duct, the fluid is circulated downstream through the uppercooling duct and flows downward into the cooling channels formedbetween battery cell cooling plates. Since the upper cooling ducthas the constant cross-sectional area, the flow velocity decreasesdownstream causing the pressure of the upper cooling duct nearthe inlet end, p1, to be less than the pressure of upper duct near itsclosed end, p2 (Fig. 9), though aforementioned friction loss tends toreduce the magnitude of pressure difference. Conversely, as thefluid flows into the lower cooling duct with a constant cross-sectional area and ultimately discharges from the outlet of thepack, the gradual increase in flow velocity towards the outlet oflower duct gives rise to lower pressure of lower duct near the outletend, p4, and higher pressure of lower duct near the closed end, p3. Insuch circumstance, the pressure difference (p2ep4) at the outletside is much greater than the pressure difference (p1ep3) at theinlet side. In that case, themass flow rates of cooling channels at theinlet side are much lower than the mass flow rates of coolingchannels at the outlet side. Such disparity tends to result in smallerheat transfer rates of cooling channels at the pack inlet side than atthe outlet side, which in turn causes the lumped temperatures ofthe battery cells in the baseline pack gradually to be decreasedtowards the outlet side in general.

Fig. 9. Schematic of a baseline “Z-type” flow battery pack.

Thus, both lumped cell temperature variation across the batterypack and lumped peak cell temperature in the pack can be reducedby improving uniformity of the flow rates of cooling channels as aresult of reducing the discrepancy between (p2ep4) and (p1ep3).Since the velocities and pressures of upper duct and lower duct canbe altered by changing the cross-sectional areas, the analytical DOEstudy is performed using heights of the inlet end, the closed ends ofupper and lower ducts, and the outlet end (Fig. 9) as design factors.In design matrix the minimum height of each design factor isdefined to consider the assembly tolerance and flow noise. Themaximum height of the battery pack concept is constrained to notexceed the size of baseline battery pack due to available batterypack space in the vehicle. DOE study indicates the lumped tem-perature variation across the pack can be reduced by increasing theheights of the inlet end of upper duct and the outlet end of thelower duct and reducing the heights of the closed ends of bothupper duct and lower duct as appropriate (Fig. 11). The increase inheight or cross-sectional area of the inlet end of upper duct tends todecrease the fluid velocity, v1, and thus, increase the pressure ofupper duct near the inlet end, p1. Conversely, as the fluid flowstowards the closed end of upper duct with the reduction of heightor cross-sectional area, the fluid velocity downstream of upperduct, v2, should be higher than the velocity of the baseline upperduct with large cross-sectional area near the closed end. In thatcase, the pressure of upper duct near the closed end, p2, tends to be

Fig. 11. Schematic of “Z-type” flow battery pack with tapered cooling ducts.

Fig. 13. Schematic of optimal “Z-type” flow battery pack.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414 411

decreased. In parallel to the pressure change in upper duct, thepressure of lower duct near the closed end, p3, can be reduced bydecreasing the height or cross-sectional area of lower duct at theclosed end as appropriate. Conversely, by increasing the height oflower duct at the outlet end the pressure of lower duct near theoutlet end, p4, can be slightly increased. Thus, by employing atapered upper duct and a tapered lower duct (rather than theconstant cross-sectional area version as shown in Fig. 9), thediscrepancy between (p2ep4) and (p1ep3) can be significantlyreduced, which in turn promotes more uniform cooling fluid flowrates through all of the channels in the pack. It should be noticedthat the taper of lower cooling duct should be substantially lessthan the taper of upper duct due to the flow impinging effect.Simulation result indicates that the optimal height of the closedend of the lower duct is 5e7 times of the gap of the cooling channel,which is slightly higher than the length of the flow potential corethat is approximately 5 times the channel gap [12,13]. Since theflow velocity of the potential core is as high as the flow velocity atthe exit of the cooling channel, further reduction in the height of

Fig. 12. Lumped peak temperatures of individual battery cells in “Z-type” flow batterypack with optimal tapered cooling ducts.

the closed end of the lower duct, e.g., to be less than length of theflow potential core, tends to increase the pressure at this flow zonedue to the effect of the flow impinging on the bottom wall of thelower duct, which in turn causes the flow rates of the coolingchannels at inlet side (left side) to decrease.

The lumped peak temperatures of individual battery cells acrossthe pack with optimal tapered upper and lower ducts (Fig. 11) at aflow rate of 0.0283 m3 s�1 are shown in Fig. 12. As can be seen, themaximum lumped cell temperature variation across the modifiedbattery pack is reduced from 10.8 �C to 3.6 �C and the maximumlumped peak cell temperature in the battery pack is reduced by6.3 �C. In addition, the improvement of the uniformity of the flowrates of cooling channels can also reduce the maximum flow ve-locity, and thus, reduce themaximumpressure drop. As a result, the

Fig. 14. Lumped peak temperatures of individual cells in optimal “Z-type” flow batterypack.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414412

pressure loss of the entire battery pack can be reduced. As anexample, the total pressure drop of modified battery pack at theflow rate of 0.0283 m3 s�1 is reduced to approximately 24% lessthan that of baseline “Z-type” flow battery pack.

The available battery pack space in the vehicle prohibits furtherreduction of both lumped cell temperature variation across thebattery pack and the maximum lumped peak cell temperature inthe pack from increasing both the inlet height and the outlet height.Since the lumped temperatures of battery cells at inlet side are stillabout 3 �C higher than those of battery cells at the opposite side(Fig. 12), the temperature non-uniformity of the modified batterypack can be improved by further reducing the pressure of the lowerduct near the closed end. This is achieved by adding two secondarylower ducts to the battery pack with the same optimal taperedupper and lower ducts as illustrated in Fig. 11. Two secondary lowerducts are placed on opposite sides of the major lower duct (or theoptimal tapered lower duct shown in Fig. 11) and between thevehicle floor and control modules in the battery pack as shown inFig. 13 [14]. Three orifices are formed in each sidewall of the majorlower duct to facilitate the flow from major lower duct to twosecondary ducts. Since a significant portion of fluid near the closedend of lower duct is exhausted to relatively spacious secondaryducts through orifices, the pressure loss of this portion of fluid isminimized, and therefore, the pressure of lower duct near theclosed end is reduced. Accordingly, the flow rates and surfaceconvection rates of cooling channels at the inlet side are substan-tially equal to those of cooling channels at the outlet side. As an

Fig. 15. Schematic of cooling channel with corrugation.

example, the lumped peak temperatures of individual battery cellsin the pack with secondary ducts at flow rate of 0.0283 m3 s�1 areshown in Fig. 14. As expected, the maximum lumped cell temper-ature variation across the pack is further minimized to about 1.1 �Cand the maximum lumped peak cell temperature in the pack isminimized to approximately 8.0 �C less than that of baseline “Z-type” flowbattery pack. The substantial uniformity of the flow ratesof cooling channels and secondary exhaust ducts also facilitatefurther reduction of total pressure drop of battery pack, e.g., thetotal pressure drop of this optimized battery pack is minimized toabout 43% less than that of baseline “Z-type” flow battery pack atflow rate of 0.0283 m3 s�1.

3.2. Cooling efficiency of battery cell

As discussed in Section 3.1, the maximum lumped peak celltemperature in the battery pack can be minimized by reducing the

Fig. 16. Temperature contours on pouch surface of a battery cell with (a) baselinealuminum cooling plate, (b) copper cooling plate, and (c) thicker aluminum coolingplate.

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414 413

flow rate variation across cooling channels. Particularly, the uni-formity of the flow rates of cooling channels facilitates an increasein fluid velocities of cooling channels adjacent the inlet end andtherefore increases the heat transfer rates. The fluid velocity of thecooling channel can also be maximized by reducing the gap of thecooling channel without changing the flow rate. However, the in-crease in fluid velocity of the cooling channel gives rise to signifi-cant increase in total pressure drop of the battery pack. In addition,physical test indicates that the pouch cell at end of life is thickerthan that at beginning of life. The expansion in thickness of pouchcell and significant change in total pressure drop prohibit theimprovement of heat transfer rate of the cooling plate fromreducing the cooling channel gap in this study.

A viable solution for improvement of heat transfer rate of thecooling plate is to increase the cooling surface area without thechange in cooling channel gap or fluid velocity. This is achieved byinserting an aluminum corrugation between cooling plates asshown in Fig. 15. It should be noted that the other major function ofthe corrugation is to provide appropriate pressure on pouch cellsurface to minimize the cell expansion during charge/dischargecycles. In order to effectively evaluate the heat transfer rate of thecooling plate, the cooling efficiency of the flow channel, h, isintroduced in terms of the average fluid temperature at the exit ofcooling channel, Tex, fluid temperature at the inlet, Tin, and themaximum cooling plate temperature, Tpt,max, i.e., h ¼ (Tex e Tin)/(Tpt,max e Tin). Since the ideal function of the cooling channel is thefluid temperature at the exit of cooling channel, Tex, to be the sameas the maximum cooling plate temperature, Tpt, max, the target ofthe design concept of the cooling channel in this study is to ensurethe cooling efficiency of flow channel, h, to be higher than 90% atthe flow rate of 0.0283 m3 s�1. Simulation results indicate thecooling efficiency of the flow channel can be increased to approx-imately 93% that is about 10% higher than that of the baselinecooling channel by adding an aluminum corrugation with appro-priate period length and thickness and applying appropriate con-tact pressure between the cooling plate and aluminum corrugation.Accordingly, the maximum lumped peak cell temperature in thepack is further reduced by about 0.4 �C, while the maximumlumped cell temperature variation across the pack is approximatelyunchanged and the total pressure of the battery pack is slightlyincreased by approximately 6 Pa at the flow rate of 0.0283 m3 s�1.

3.3. Temperature variation within a battery cell

The temperature distribution of each battery cell in the opti-mized “Z-type” flow battery pack (Fig. 13) has been predicted usingbattery pack thermal model. As an example, the contour of the peaktemperature of the hottest battery cell in the battery pack at theinlet flow rate of 0.0283 m3 s�1 under simulated US06 charge/discharge cycles is shown in Fig. 16(a). As can be seen, the cellsurface temperature variation along horizontal direction is verysmall. On the other hand, the temperature gradually increasesalong the flow direction. In particular, the temperature of the bot-tom edge is approximately 2.2 �C higher than the temperature oftop edge of battery cell. It has been shown that the cooling effi-ciency of flow channel is extremely high and the temperature of thefluid at the exit of the cooling channel is very close to the tem-perature of the bottom edge of the cooling plate. Extremely smalltemperature difference between the cooling plate and the fluid atthe exit of cooling channel facilitates the heat transfer rate to bemuch less than the heat transfer rate of the top edge of coolingplate where the fluid temperature is approximately the same asbattery pack inlet temperature. Since the heat generation rates oftop edge and bottom edge of battery cell are approximately thesame due to symmetric structure, the extreme non-uniformity of

the convection heat transfer rate of cooling plate is the major rootcause of large battery cell temperature variation particularly at highinlet flow rate.

Although a previous study [3] showed the temperature variationwithin a battery cell can be reduced by increasing the thermalconductivity of the battery cell in the in-plane direction, changes inthe properties of the battery cell materials present concerns forbattery cell performance, safety, life and cost. A viable solution toreduce the cell temperature variation without significantly chang-ing the pack design and increasing the lumped battery cell tem-perature is to reduce the heat transfer rate variation on the pouchcell surface. This is achieved by replacing the aluminum coolingplate with copper cooling plate or increasing the thickness of thealuminum cooling plate to increase the heat conduction of thecooling plate in the in-plane direction. As an example, Fig. 16(b)shows the temperature contours of the hottest battery cell with acopper cooling plate at a pack inlet flow rate of 0.0283 m3 s�1. Ascan be seen, by using a copper cooling plate the maximum tem-perature variation on the pouch cell surface is reduced to about0.3 �C less than that of the pouch cell with the baseline coolingplate.

Since available space in the vehicle allows the length of batterypack to be slightly increased, the improvement of temperatureuniformity within a cell is studied by appropriately increasing thethickness of each aluminum cooling plate. The temperature contourof the hottest battery cell with a thicker aluminum cooling plate isshown in Fig. 16(c). It is found that the maximum temperaturevariation on pouch cell surface is minimized to about 0.6 �C lessthan that of pouch cell with baseline cooling plate, though themaximum lumped peak cell temperature is increased by 0.1 �C dueto the change in thermal resistance of the cooling plate in normaldirection.

4. Conclusions

A correlated three-dimensional battery pack thermal model andan analytical DOE approach have been used to identify a designconcept of a “Z-type” flow battery pack with optimal thermalbehavior. Simulations indicate the geometries of inlet and outletflow ducts play a major role in the uniformity of flow rates ofcooling channels, which in turn can significantly affect the lumpedcell temperature in the “Z-type” flow pack, lumped cell tempera-ture variation across entire pack, and total pressure drop of thepack. The variation of flow rates of cooling channels can besignificantly reduced by using tapered inlet and outlet ducts. Inparticular, the taper of lower (outlet) duct is substantially less thanthe taper of upper (inlet) duct due to the flow impinging effect.Without increasing the battery pack height the uniformity of flowrates of individual cooling channels can be further improved byadding two secondary outlet ducts that are placed on opposite sidesof major outlet duct. Three orifices are formed in each of thesidewalls of the major outlet duct to facilitate the flow from majoroutlet duct to two secondary ducts. As a result, the maximumlumped cell temperature variation across the pack is reduced toabout 1.1 �C and themaximum lumped peak cell temperature in thepack is minimized to approximately 8.0 �C less than that of baseline“Z-type” flow pack under US06 drive cycles. In addition, totalpressure drop of the battery pack is minimized to about 43% lessthan that of baseline battery pack at flow rate of 0.0283 m3 s�1.

The lumped battery cell temperature can be further reduced byinserting corrugations between cooling plates in the pack to in-crease the cooling surface area and cooling efficiency of each in-dividual flow channel. For example, the cooling efficiency of theflow channel can be increased to approximately 93% and themaximum lumped peak cell temperature in the pack is further

H. Sun, R. Dixon / Journal of Power Sources 272 (2014) 404e414414

reduced by about 0.4 �C by using aluminum corrugation withappropriate period length and thickness and applying appropriatecontact pressure between cooling plate and aluminum corrugation.

Simulations also indicate the temperature uniformity within acell can be improved by increasing heat conduction of the coolingplate in the in-plane direction. In particular, by using a coppercooling plate the maximum temperature variation on pouch cellsurface is reduced to 1.9 �C which is about 0.3 less than that ofpouch cell with baseline aluminum cooling plate. By slightlyincreasing the thickness of aluminum cooling plate the maximumtemperature variation on pouch cell surface can be minimized toabout 0.6 �C less than that using baseline cooling plate.

Acknowledgments

The authors would like to thank Brian Tossan, Mary Fortier,Anthony Modafferi, Joseph Lograsso, Daniel Brouns, Jasmine Wang,and Andrew Oury for their support on this study. Special thanks goto Christopher Ciaramitaro, Eric Losiewicz, Ramona Ying, Christo-pher Mousseau, and Andrew Herman for their valuable help andproviding the physical test data.

Nomenclature

Ae area of cell active material surface, m2

Apt area of battery cooling plate surface, m2

At cross section area of battery cell terminal tab, m2

C capacitance at battery equivalent circuit model, FCp,c specific heat of battery cell, J kg�1 K�1

Cp,pt specific heat of battery cooling plate, J kg�1 K�1

Cq coefficient of heat generation rate (dimensionless)DOD depth of discharge (dimensionless)have lumped heat transfer coefficient of cooling plate,

W m�2 K�1

I battery pack current, AJ current density, A m�2

kt heat conductivity of battery cell terminal tab, W m�1 K�1

Le distance between centerlines of positive and negativeelectrode current collectors, m

Lt length of battery cell terminal tab, mmc mass of a battery cell, kgmpt mass of cooling plate of a cell, kgN number of separators in a cell (dimensionless)P power input/output of a battery pack, Wp1 pressure of upper duct near the inlet end, Pap2 pressure of upper duct near the closed end, Pap3 pressure of lower duct near the closed end, Pap4 pressure of lower duct near the outlet end, Paq

00a heat generation rate of battery active material, W m�3

R1 battery cell internal ohmic resistance, UR2 battery cell internal charge transfer resistance, URcon contact thermal resistance between cell and cooling plate,

K W�1

Rt resistance of battery tabs of a cell, Urp positive electrode resistance, USOC state of charge (dimensionless)t time, STadj,i adjacent battery cell temperature, �CTc lumped battery cell temperature, �CTex average fluid temperature at exit of cooling channel, �CTin temperature of cooling fluid at battery pack inlet, �CTpt lumped cooling plate temperature, �Cut friction velocity or shear velocity, m s�1

V battery voltage, VVoc battery open circuit voltage, VVp positive electrode potential, VVn negative electrode potential, VvL volume of active material, m3

v1 fluid velocity in upper duct near the inlet end, ms�1

v2 fluid velocity in upper duct near the closed end, ms�1

v3 fluid velocity in lower duct near the closed end, ms�1

v4 fluid velocity in lower duct near the outlet end, ms�1

yp distance between wall surface and the center of prismlayer adjacent to the wall surface, m

yþ wall function value (dimensionless)Z parameter describing battery current density and

potential, V m2 A�1

r fluid density, kg m�3

n fluid kinetic viscosity, m2 s�1

Subscripti battery cell number in battery pack(dimensionless)n number of cells in battery pack (dimensionless)

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