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Numerical Simulation toAccelerate (H)EV BatteryDevelopmentThe lithium-ion battery is a preferred candidate as a power source for hybrid electric vehicle (HEV) andelectric vehicle (EV) due to its outstanding characteristics such as high energy density, high voltage, low self-discharge rate, and good stability. However, the HEV and EV market requires much larger lithium-ionbatteries than those available in the market for consumer electronics. The possibility of significanttemperature increases in large batteries during high power extraction, or even the risk of thermal runaway, is currently one of the major concerns confronting development of lithium batteries for electric vehicles. So, electric engineers need an accurate and yet simple to use thermal model that couples with their batteryelectric circuit model. Xiao Hu, Lead Engineer, ANSYS Inc., Canonsburg, USA

A properly designed thermalmanagement system is crucial to preventoverheating and uneven heating across alarge battery pack, which can lead todegradation, mismatch in cell capacity andpotentially thermal runaway. Design of thethermal management system thereforerequires knowledge about the coolingsystem as well as the amount of heat thatwill be generated by cells within thebattery pack.

How simulation can helpSimulation can help on two levels, celllevel and system level. Cell level refers tosingle battery cell, and system level couldbe either a battery module or a complete

battery pack. At a battery cell level, the focus is on

detailed heat generation and temperaturedistribution within a battery cell. This typeof study is pursued mainly by batterymanufacturers and battery researchers.Experimental data reveals that the rate ofheat generation varies substantially overtime throughout the course of chargingand discharging. Heat can be generatedfrom internal losses of Joule heating andlocal electrode over-potentials, the entropyof the cell reaction, heat of mixing, andside reactions. If only the most importanteffects of Joule heating and local electrodeover-potentials are considered, heatgeneration can be expressed by open

Figure 1: Schematic of a lithium-ion cellFigure 2: Typical results from models a) packand b) detail generated in ANSYS® FLUENT®

a)

b)

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circuit potential and potential differencebetween the positive and negativeelectrodes. Figure 1 shows the schematicof a lithium-ion cell.Models based on this area can be used

to predict the potential and current densitydistribution on the electrodes of a lithium-ion battery as a function of discharge time.Then, based on the results of the modelingof potential and current densitydistributions, the temperature distributionsof the lithium-ion battery are calculated.The results can then be used to examinethe effect of the configuration of theelectrodes, such as the aspect ratio of the

electrodes and the placing of currentcollecting tabs as well as the dischargerates on the thermal behaviour of thebattery. Figures 2a and 2b show typicalresults from such models generated inANSYS® FLUENT®. The temperaturedistributions from the modeling wereshown to be in good agreement withthose from the experimentalmeasurement.While this type of model is simple to

use and gives detailed information abouttemperature and current densitydistribution, it needs experimental testingdata as input. As a result, this type of

model cannot predict the impact of designchanges on the battery thermalperformance without re-conducting thetesting. Physics based electrochemistrymodels, on the other hand, can be used toinvestigate the impact of battery designparameters on battery performance, whichincludes the geometry parameters,properties, and most importantlytemperature. Physics based models canalso provide inputs that would otherwiseneed experimental testing to obtain. The most famous physics based model

was originally proposed by professor JohnNewman from UC Berkeley. Such a modelhas been implemented in Simplorer®.Figure 3 shows charge and discharge cycleresults from John Newman’selectrochemistry model. Figure 4 showsthe concentration profiles during discharge.One optimisation problem that isimmediately apparent when examiningFigure 4 is the determination of the initialconcentration of electrolyte in the cell. Theconcentration used in Figure 4 ispresumably determined due to theconductivity maximum that occurs atapproximately this concentration.However, Figure 4 shows that the bulk ofthe composite cathode is at a significantlylower concentration, where theconductivity is also much lower as a result.This leads to severe transport limitations inthe depth of the electrode, suggesting thata higher initial concentration leads to asomewhat lower conductivity in theseparator, but a much larger conductivity inthe composite cathode, where this is ofprime importance. Figure 5 shows theconcentration profiles under differenttemperatures. The information containedin such data tells battery designers whenthe limiting current occurs, and thus canhelp specify the temperature range thatthe cooling system has to maintain toavoid hitting the limiting current.

Figure 4:Concentrationprofiles duringdischarge

Figure 3: Charge anddischarge cycleresults from JohnNewman’selectrochemistrymodel

Figure 5:Concentrationprofiles underdifferenttemperatures

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Another implication of Figure 5 is thatbattery run-time is a strong function oftime, and battery life is longer with higheroperating temperature. This is alsoconfirmed in Figure 6 from the physicsbased electrochemistry model. Of coursehigher temperatures bring safety concerns,and thus this becomes anotheroptimisation problem in battery design.System level design engineers working

at a module or pack level have a differentset of requirements. Typically, theseengineers cannot afford to simulate asmany details as engineers working at thecell level can, and they also have adifferent set of simulation goals. Forinstance, Computational Fluid Dynamics(CFD) engineers working in batterythermal management are interested inmaintaining the desired temperature range,reducing pressure drop, and maintainingtemperature uniformity. And for them,detailed heat generation mechanisms andbattery cell structure are not of primaryinterest. CFD has been widely used forpredicting flow and heat transfer, and thusbattery thermal management CFDsimulation is just another application.ANSYS has been working to make the

process easier for the user. Rather thanhaving to use different tools for geometry,meshing, post-processing, andoptimisation, which are all integratedcomponents of a CFD analysis, ANSYSWorkbenchTM creates all the aspects of thesimulation under one umbrella.Geometries built within workbench tools orimported from other CAD packages are allparameterised. An update of results due to a change of

geometric parameters can be achieved injust one click. Data transfer betweendifferent simulation tools are handledseamlessly. With the help of ANSYSWorkbench, a complete battery thermalCFD analysis, including optimization, canbe done entirely within this environment.Figures 7 and 8 show such a CFD exampleperformed by a major automotive OEM.While CFD can give detailed thermal

information about a battery thermalmanagement system, it is time consumingto perform many transient simulationsunder different drive cycles. Model orderreduction techniques exist to extract amodel from CFD results, and the extractmodel, called Foster network model, givesthe same solution as that from the full CFDmodel. However it runs much fastercompared with CFD. For the model shown in Figures 7 and

8, it takes a couple of hours to simulateone drive cycle under one single CPU. Butfor the extracted Foster network model, thesimulation time is reduced toapproximately 20 seconds, a time

Figure 6: Cell voltagevs capacity at varioustemperatures

Figure 7: Simple CFD example

Figure 8: Complex CFD example

Figure 9: Comparisonbetween Fosternetwork model andfull CFD

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reduction of more than two orders ofmagnitude. And yet, the Foster networkmodel gives the same results as theoriginal full CFD model. Figure 9 showssuch a comparison. The model orderreduction process is handled automaticallyby ANSYS Simplorer, which uses CFDresults as inputs. This model order

reduction technology opens the door forsimulations that would otherwise havebeen impractical. For instance, batterythermal control system analysis wouldbenefit from such a fast model.

ConclusionsThe primary concern of electric engineers,

is the electric performance of the batteryrather than the thermal performance.However, as mentioned before, batteryelectric performance is a strong function oftemperature. So, electric engineers needan accurate and yet simple to use thermalmodel that couples with their batteryelectric circuit model. Figure 10 showssuch a complete dynamic model. The complete electric circuit model of a

lithium ion battery accounts for non-linearequilibrium potentials, rate andtemperature dependencies, thermal effectsand response to transient power demand.Traditional thermal network models canalso be used to couple with electric circuitmodels. With the help of VHDL-AMS,which is an IEEE standard hardwaresimulation language supported bySimplorer, a traditional thermal networkmodel can be generated easily. As amatter of fact, VHDL-AMS can be used formuch more complex multiphysics andmulti-domain problems, and the JohnNewman electrochemistry modelmentioned above was generated usingVHDL-AMS in Simplorer.

Figure 10: Complete dynamic battery model