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S1359-4311(17)32484-5 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.060 ATE 10371

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Applied Thermal Engineering

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Please cite this article as: K. Chen, S. Wang, M. Song, L. Chen, Configuration optimization of battery pack in parallel air-cooled battery thermal management system using an optimization strategy, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.05.060

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Configuration optimization of battery pack in parallel air-cooled battery thermal management system using an optimization strategy Kai Chena*, Shuangfeng Wanga*, Mengxuan Songb, Lin Chenc a

Key Laboratory of Enhanced Heat Transfer and Energy Conservation of the Ministry of Education, School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, Guangdong, P. R. China b Department of Control Science and Engineering, Tongji University, Shanghai 201804, P. R. China c Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, P. R. China

* Corresponding author. Tel.:020-22236929 E-mail address: [email protected] (Kai Chen), [email protected] (Shuangfeng Wang) 1

3

Configuration optimization of battery pack in parallel air-cooled battery thermal management system using an optimization strategy

4

Kai Chen*a , Shuangfeng Wang*a , Mengxuan Songb , Lin Chenc

1

2

5 6 7 8 9 10 11

12

a Key

Laboratory of Enhanced Heat Transfer and Energy Conservation of the Ministry of Education, School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, Guangdong, PR China b Department of Control Science and Engineering, Tongji University, Shanghai 201804, PR China c Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, PR China

Abstract

13

Battery thermal management system (BTMS) is essential for heat dissipa-

14

tion of the battery pack to guarantee the safety of electric vehicles. Among the

15

various BTMSs, the parallel air-cooled system is one of the most commonly used

16

solutions. In this paper, the conﬁguration of the battery pack in parallel air-

17

cooled BTMS is optimized through arranging the spacings among the battery

18

cells for cooling performance improvement. The ﬂow resistance network model

19

is introduced to calculate the velocities of the cooling channels. The heat trans-

20

fer model is used to calculate the battery cell temperature. Combining these

21

two models, an optimization strategy is proposed to optimize the conﬁguration

22

of the battery pack under the constant cell heat generation rate. The numeri-

23

cal results of typical cases show that the optimization strategy can obtain the

24

ﬁnal solution in only several times of adjustments of cell spacings. The cooling

25

performance of the BTMS is improved remarkably after optimization. The max-

26

imum temperature diﬀerence is reduced by 42% and the maximum temperature

27

of the battery pack is reduced slightly after optimization, with no increment on

28

the total pressure drop of the system. Furthermore, the optimized BTMS still

Email addresses: [email protected] (Kai Chen*), [email protected] (Shuangfeng Wang*) Preprint submitted to Elsevier May 11, 2017

29

performs much better than the original one for various inlet ﬂow rates and for

30

the situation of unsteady heat generation rate.

31

Keywords: battery thermal management, air cooling, conﬁguration

32

optimization, ﬂow resistance network model, heat transfer model

33

1. Introduction

34

In recent years, electric vehicles (EVs) and hybrid electric vehicles (HEVs)

35

have attracted worldwide attention, which are treated as one of the eﬀective

36

ways to relieve the energy shortage and environmental pollution problems. In

37

EVs and HEVs, battery pack is one of the most critical components for power

38

supply. A large amount of heat is generated by the battery pack when the

39

vehicles are working. If the heat cannot be ejected fast, the temperature of the

40

system will increase rapidly, ﬁnally damaging the battery pack or even causing

41

explosion of the system. Furthermore, the local high temperature increases the

42

temperature diﬀerence of the battery pack, which will shorten the service life of

43

the battery pack. Therefore, thermal management is needed to guarantee that

44

the battery pack works under the situation of the appropriate temperature.

45

Many thermal management technologies have been developed to control the

46

temperature of the battery pack in EVs and HEVs, including air cooling, liquid

47

cooling, phase change material cooling [1], heat pipes cooling [2–4] and cold plate

48

cooling [5–8], where air cooling is one of the most commonly used methods due

49

to the low cost and simple structure of the cooling system.

50

In the air-cooled battery thermal management system (BTMS), the cooling

51

air is pumped into the system and removes the heat generated by the battery

52

cells. The cooling performance of the BTMS depends on the airﬂow distribution,

53

which is inﬂuenced by the structure of the system. Many scholars have tried to

54

improve the cooling performance of the system through changing the structure

2

55

of the BTMS. Pesaran et al. [9] designed an air-cooled BTMS with single-

56

wide subsections and double-wide subsections. The proposed system helped to

57

deliver the airﬂow uniformly to each battery module for uniform temperature

58

distribution. Subsequently, Pesaran et al. [10] used the ﬁnite element method to

59

study the performance of the BTMS with serial ventilation cooling and parallel

60

ventilation cooling, respectively. It is found that the parallel ventilation cooling

61

system performed better than the serial one due to the more uniform airﬂow

62

around the battery cells. The maximum temperature of the battery packs was

63

reduced by 4 ◦ C and the temperature diﬀerence was reduced by 10 ◦ C after

64

adopting the parallel air cooling. Mahamud et al. [11] used the reciprocating

65

airﬂow to improve the cooling performance of the BTMS. The reciprocating ﬂow

66

reduced the temperature diﬀerence of the battery pack by about 4% and the

67

maximum cell temperature by 1.5% for a reciprocation period of 120 s when

68

compared with the uni-directional ﬂow situation. Yu et al. [12] reduced the

69

temperature and the temperature diﬀerence of the system through combining

70

the serial ventilation cooling with the parallel ventilation cooling. Wang et al.

71

[13] compared the cooling performances of the battery modules with various cell

72

arrangement structures, including the rectangular arrangement, the hexagonal

73

arrangement and the circular arrangement. The inﬂuence of the location of the

74

fans on the system performance was also investigated. Sun et al. [14] studied the

75

performance of the BTMS with U-type ﬂow, the inlet and outlet of which were

76

at the same side. The simulation result showed that the maximum temperature

77

variation of the battery cells in the battery pack can be improved by about

78

70% through using a tapered upper cooling duct. Subsequently, Sun et al. [15]

79

explored the performance of the BTMS with Z-type ﬂow, the inlet and outlet

80

of which were at the opposed side. The temperature variation of the battery

81

cells can be signiﬁcantly reduced through using tapered inlet and outlet ducts.

3

82

Without increasing the battery pack height, the temperature uniformity of the

83

battery pack can be further improved by adding two secondary outlet ducts that

84

were placed on opposite sides of the major outlet duct. Park [16] also compared

85

the cooling performance of the BTMSs with U-type ﬂow to the one with Z-type

86

ﬂow.

87

For the ﬁxed cell arrangement structure, the inter-cell spacing distribution

88

among battery cells (conﬁguration of the battery pack) is a critical factor that

89

inﬂuences the uniformity of the velocities in the cooling channels, and ﬁnally

90

determines the cell temperature and cell temperature diﬀerence of the battery

91

pack. Therefore, the inﬂuence of the cell spacing on the cooling performance

92

of the BTMS is also studied widely. Xun et al. [17] found that increasing

93

the cooling channel size improved the cooling energy eﬃciency but led to more

94

unevenly distributed temperature. Yong et al. [18] developed a lumped thermal

95

model to study the inﬂuence of the cell spacing on the performance of the

96

cuboid lithium-ion battery system. The result showed that the cell temperature

97

increased as the cell spacing increased when ﬁxing the airﬂow rate. Fan et

98

al. [19] studied the inﬂuence of the uneven gap spacing among the battery

99

cells. The results indicated that uneven gap spacing aﬀected the temperature

100

distribution remarkably, but it did not impact the maximum temperature of

101

the battery pack. Zhao et al. [20] studied the inﬂuence of the ratio of spacing

102

distance between neighbor cells and cell diameter on the cooling performance

103

using numerical method. The result indicated that suitable value of this ratio

104

was reduced along as the cell diameter increased.

105

The existing studies have shown that the cooling performance of BTMS is

106

strongly inﬂuenced by the conﬁguration of the battery pack. In this paper, the

107

conﬁguration optimization of battery pack in the parallel air-cooled BTMS is

108

conducted through arranging the spacings among the battery cells to improve

4

109

the cooling performance. The ﬂow resistance network model is introduced to

110

calculate the velocity in the cooling channel. The heat transfer model is used

111

to calculate the battery cell temperature. Based on the analysis of the char-

112

acteristic of the BTMS, an optimization strategy is proposed for conﬁguration

113

optimization of the battery pack when combined with the two simpliﬁed mod-

114

els, with the objective of reducing the maximum cell temperature. A typical

115

case is used to test the eﬀectiveness of the proposed optimization strategy for

116

conﬁguration optimization of battery pack in parallel air-cooled BTMS. The

117

performance of the optimized BTMS is evaluated by three-dimensional Com-

118

putational Fluid Dynamics calculation, and is compared to the performance of

119

the original BTMS.

120

2. Calculation models

121

2.1. Illustration of configuration optimization of parallel air-cooled BTMS

122

The parallel air-cooled BTMS is one of the most commonly used BTMSs.

123

Figure 1 depicts the structure of the parallel air-cooled BTMS. The system

124

contains the large battery pack with N × M cuboid battery cells. Figure 2

125

shows the schematics of the battery cell and the battery pack. When the system

126

works, the battery pack provides power to the vehicle and generates a large

127

amount of heat. Meanwhile, the cooling air ﬂows into the system from the inlet,

128

and is distributed into the cooling channels (CCs) by the divergence plenum

129

(DP). Then the heat generated by the battery cells is removed by the airﬂow

130

in the cooling channels. At the end of the CCs, the air is converged by the

131

convergence plenum (CP), and is ejected through the outlet. The temperature

132

distribution of the battery pack mainly depends on the airﬂow distribution in

133

the cooling channels. An appropriate airﬂow distribution will lead to a low

134

maximum temperature of the battery pack. Note that the conﬁguration of

5

135

the battery pack, especially the spacings among the battery cells will strongly

136

determine the pressure loss of the cooling channels, ﬁnally aﬀecting the airﬂow

137

distribution in the cooling channels. Therefore, it is expected to reduce the

138

temperature of the battery pack and improve the cooling performance of the

139

BTMS through arranging the conﬁguration of the battery pack.

Ċ

Ċ

Convergence plenum Convergence plenum

M

⍱䚃

N wout

y

z

Ċ

Ċ

Ċ

Ċ

Lout

x

y

Ċ

z

Lin

Air

Air

Ċ

win

Ċ

Divergence plenum

N

Divergence plenum

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

(a) Orthographic view of the BTMS

(b) Side view of the BTMS

Figure 1: Schematic of the parallel air-cooled BTMS

Ċ

Ċ

Cooling channel

N

Ċ

Ċ

Ċ Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ

Ċ M

hb

Ċ b

Ċ Ċ

wb

lb

(a) Battery cell

(b) Battery pack

Figure 2: Schematic of the battery pack

140

In this paper, the conﬁguration of the parallel air-cooled BTMS is opti-

141

mized through choosing appropriate spacings among the battery cells, with the

142

objective of reducing the maximum temperature of the battery pack. The opti-

143

mization problem is described as follows 6

Ċ

Objective = min (Tmax ) 144

(1)

s.t. N +1 ∑

di = const, di > 0

(2)

i=1 145

where Tmax is the maximum temperature of the battery pack and di is the

146

spacing between the (i − 1)th row and ith row of the battery pack. Usually, the

147

total volume of the BTMS is limited according to the design of the vehicle. The

148

constraint that the sum of di is a constant can guarantee that the BTMS after

149

optimization will occupy no more space than the original one.

150

When optimizing the spacings among the battery cells, the velocity distri-

151

bution and the temperature distribution of the BTMS should be calculated to

152

evaluate the maximum temperature of the battery cells. Computational Fluid

153

Dynamics (CFD) method is an eﬀective method to calculate the velocity dis-

154

tribution and temperature distribution. For the CFD method, the calculation

155

domain is divided into ﬁne meshes and the detailed information of each mesh can

156

be obtained. However, the CFD calculation costs a large amount of calculation

157

time. During the conﬁguration optimization process, the calculation needs to

158

be conducted for many times and the calculation domain should be re-divided

159

into meshes for each calculation. The operation is tedious and the total com-

160

putational cost is unacceptable. Therefore, the simpliﬁed models that calculate

161

fast with enough accuracy are needed for airﬂow and temperature calculation

162

of the parallel air-cooled BTMS.

163

2.2. Flow resistance network model

164

In the present study, the ﬂow resistance network model developed by Liu

165

et al. [21] is introduced for airﬂow calculation of the BTMS. When the air

7

166

ﬂows along the channel, there exists the pressure loss caused by the friction

167

between the air and the channel wall along the channel. This kind of pressure

168

loss is named friction pressure loss. When the air encounters the curved channel,

169

there exists the pressure loss caused by shape change of the cross section of the

170

channel. This kind of pressure loss is named local pressure loss. The basic idea

171

of the ﬂow resistance network model is to treat the pressure loss as the ﬂow

172

resistance. Thus, the three-dimensional air-cooled BTMS can be equivalent to

173

the two-dimensional ﬂow resistance network, shown as Figure 3. In Figure 3,

174

the blocks represent the total pressure of each segment, including the friction

175

pressure loss and the local pressure loss. According to the analysis based on

176

Bernoulli equation in the study of Liu et al., for a loop shown as the dotted-line

177

frame in Figure 3, the pressure loss equation is obtained as [21]

∆Ploss,DP,i+1 + ∆Ploss,CC,i+1 − ∆Ploss,CP,i − ∆Ploss,CC,i = 0

(3)

178

where Ploss is the total pressure loss. DP, CC and CP represent the divergence

179

plenum, the cooling channel and the convergence plenum, respectively. i rep-

180

resents the ith segment. The total pressure loss includes the local loss and the

181

friction loss, expressed as

∆Ploss = ∆Plocal + ∆Pfriction 182

(4)

where

∆Plocal,DP,i =

ξDP,i 2 2 ρUDP,i−1

∆Plocal,CP,i =

ξCP,i 2 2 ρUCP,i+1

∆Plocal,CC,i =

ξDP→CC,i 2 ρUDP,i 2

8

(5) +

ξCC→CP,i 2 ρUCP,i 2

l

2 ∆Pfriction,DP,i = λDP,i 2DDP,i ρUDP,i DP,i

∆Pfriction,CP,i =

l 2 λCP,i 2DCP,i ρUCP,i CP,i

(6)

l

2 ∆Pfriction,CC,i = λCC,i 2DCC,i ρUCC,i CC,i

183

where U is the cross-sectional average velocity of the channel, which is called

184

velocity for short in the following content. ξ and λ are the local loss coeﬃcient

185

and the dimensionless friction factor, respectively. ρ is the air density. l and D

186

are the length and the equivalent diameter of the segment, respectively.

1

2

n

i

CP

2

CC 1

3

i + 1

i

n + 1

n

DP 2

i+1

3

n+1

Figure 3: Schematic of the flow resistance network model

187

The local loss coeﬃcient (ξ) depends on the local geometry and the local

188

ﬂow status in the system. According to the study of Bassett et al. [22], ξ can

189

be calculated by 3 2 1 2 ξDP,i = qDP,i − qDP,i + 2 2 ( ξDP→CC,i =

2 2 qDP→CC,i ψDP,i

− 2 cos

) 3 π qDP→CC,i ψDP,i + 1 8

2 ξCP,i = 1 − qCP,i

9

(7)

(8)

(9)

2 2 2 ξCC→CP,i = qCC→CP,i ψCP,i + 2qCC→CP,i −1

(10)

190

where q is the ratio of airﬂow in the branch channel to the one in the main chan-

191

nel. ψ is the cross-sectional area ratio of the plenums to the cooling channels.

192

The friction factor (λ) depends on the status of the airﬂow, expressed as F 64 , Re ≤ 3 × 103 Re λ= 0.3164 , 3 × 103 < Re < 105 Re0.25

(11)

193

where F is the shape factor, which equals 0.89 for rectangular cross-sectional

194

channel. Re is the local Reynolds number, expressed as Re = ρDU/µ, where µ

195

is the dynamics viscosity of the air.

196

In the air-cooled BTMS, the velocity of the airﬂow is much smaller than

197

the acoustic speed, so the air is assumed to be incompressible ﬂuid and the

198

airﬂow rates at each divergence point and each convergence point are conserved.

199

According to law of mass conservation, it obtains the following expressions.

Q0 = UDP,1 ADP,1

(12)

UDP,i ADP,i = UDP,i+1 ADP,i+1 + UCC,i ACC,i

(13)

UCP,i ACP,i = UCP,i−1 ACP,i−1 + UCC,i ACC,i

(14)

200

where Q0 is the inlet airﬂow rate. A is the average cross-sectional area of the

201

channel. In the ﬂow resistance network model, there are 3 × (N + 1) unknown

202

variables (UDP,i , UCC,i and UCP,i , i = 1, 2, · · · , N + 1). Equations (3) provide

203

(N + 1) independent equations, and Equations (12) ∼ (14) provide 2 × (N + 1)

10

204

independent equations. Therefore, when the structure parameters of the BTMS

205

and the inlet airﬂow rate are given, the airﬂow velocities in the cooling channels

206

can be calculated through solving the ﬂow resistance network model.

207

2.3. Heat transfer model

208

Based on the airﬂow velocity through solving the ﬂow resistance network

209

model, Liu et al. [21] proposed a transient heat transfer model to calculate

210

the cylindrical battery cell temperature which changes with time. Similar to

211

the study of Liu et al., a heat transfer model is developed to calculate the

212

cuboid battery cell temperature with constant heat generation rate. As an

213

approximation, the details inside the battery cells are neglected, so the volume

214

average temperature is used to describe the battery cell temperature. The

215

details of the air in the cross-section are also neglected, so the cross-section

216

average temperature is used to describe the temperature of the air. Consider

217

the ith battery cell, the heat generated is removed by the air in the ith cooling

218

channel and in the (i + 1)th cooling channel, shown as Figure 4. For the ith

219

cooling channel, the air is heated by the (i − 1)th battery cell and ith battery

220

cell. According to the energy conservation law, it obtains

Φi − hi A∆Tleft,i − hi+1 A∆Tright,i =0

(15)

ρair Cp,air ucc,,i Acc,,i (Tair,i − T0 ) = hi A∆Tleft,i + hi A∆Tright,i−1

(16)

221

where Φi is the heat generated by the ith battery cell. A is the equivalent heat

222

transfer area between the cell surface and the airﬂow, which includes the area in

223

the cooling channel and the one in the main channels. hi is the convective heat

224

transfer coeﬃcients between the air in the ith cooling channel and the battery

225

cell surface. ρair and Cp,air are the density and the heat capacity of the air,

11

226

respectively. (ucc,,i Acc,,i ) is the airﬂow rate in the ith cooling channel. T0 is

227

the initial temperature of the air, and Tair,i is the air temperature at the end of

228

the ith cooling channel. ∆Tleft,i is the temperature diﬀerence between the ith

229

battery cell and the airﬂow in the cooling channel on the left side, and ∆Tright,i

230

is the temperature diﬀerence between the ith battery cell and the airﬂow in

231

the cooling channel on the right side. These two temperature diﬀerences are

232

calculated by ( ∆Tleft,i = (Tair,i − T0 ) / ln

Tb,i − T0 Tb,i − Tair,i

( ∆Tright,i = (Tair,i+1 − T0 ) / ln

)

Tb,i − T0 Tb,i − Tair,i+1

(17) ) (18)

233

where Tb,i is the temperature of the ith battery cell. In the model, the con-

234

vective heat transfer coeﬃcient (h) is a critical parameter that determines the

235

performance of the model. For the parallel air-cooled BTMS, the shape of the

236

cooling channel is rectangular. Usually the width of the cooling channel is small

237

and the Reynolds number is less than 2000. Therefore, it is laminar ﬂow in

238

the cooling channel. Considering the heat convective inlet eﬀective, h can be

239

calculated by the following expression [23]. (

(

h = 8.23 1 +

D l

)0.7 )

D kair

(19)

240

where kair is the thermal conductivity of the air. l and D are the length and

241

the equivalent diameter of the cooling channel, respectively.

242

In this heat transfer model, there are (2 × N + 1) unknown variables (Tb,i ,

243

Tair,i and Tair,N+1 i = 1, 2, · · · , N ). Equations (15) ∼ (19) provide (2 × N + 1)

244

independent equations. Therefore, when the structure parameters of the BTMS

245

and the inlet airﬂow rate are given, the velocities in the cooling channel (ucc,,i )

12

246

can be calculated using the ﬂow resistance network model, and the temperature

247

of each battery cell (Tb,i ) can be calculated using the heat transfer model.

airi+1

airi

hiAΔTleft,i

hi+1AΔtright,i

batteryi Figure 4: Schematic of the heat transfer on the surface of a battery cell and air

248

3. Optimization procedure

249

In the present study, the cooling performance of the parallel air-cooled BTMS

250

is improved through arranging the spacings among the battery cells. The spac-

251

ings among the battery cells inﬂuence the cross-sectional areas of the cooling

252

channels, ﬁnally determining the velocity distribution and the heat transfer

253

performance of the cooling channels. For a speciﬁed cooling channel, when the

254

cross-sectional area is increased, the pressure loss along this channel will be re-

255

duced. Then more air will ﬂow through this channel, which improves the heat

256

transfer performance and reduces the temperatures of the battery cells on both

257

sides of the channel. Conversely, when the cross-sectional area of the cooling

258

channel is reduced, the pressure loss along this channel will be increased and

259

the air ﬂow rate of this channel will be reduced, leading to higher temperatures

260

of the battery cells on both sides of the channel. Therefore, in order to reduce

261

the temperature of the battery pack, the spacing around the battery cell with

262

the highest temperature should be increased while the one around the battery 13

263

cell with the lowest temperature should be reduced. Note that this strategy is

264

expected to reduce the maximum cell temperature and improve the cooling per-

265

formance of the BTMS, with no increment on the volume of the system. Based

266

on this optimization strategy, an optimization process is developed to optimize

267

the conﬁguration of the battery pack. For convenience, a variable W is deﬁned

268

to describe the spacings among the battery cells, shown as

W = [d1 , d2 , · · · , di , · · · , dN +1 ]

(20)

269

where di is the width of the ith cooling channel. N is the row number of

270

the battery cells. The detailed steps of the optimization process are shown as

271

follows.

272

1. Set the initial values of the cell spacings as W0 , the number of the spacing

273

adjustments as Nadjust and the step of the spacing adjustment as ∆d. Let

274

the values of the cell spacings W = W0 .

275

2. For the BTMS with W, calculate the temperatures of the battery cells us-

276

ing the ﬂow resistance network model and the heat transfer model. Record

277

the maximum cell temperature and the relevant spacing variable, denoted

278

as Tmax and Wopt .

279

3. For the latest conﬁguration of the system, determine the spacing of which

280

cooling channel to be increased. Find the index of the battery cell with

281

the maximum temperature, denoted as nmax .

282

If nmax = 1,

283

284

285

286

287

let d2 = d2 + ∆d. else if nmax = N , let dN = dN + ∆d. else if Tb,nmax −1 ≥ Tb,nmax +1 , 14

let dnmax = dnmax + ∆d.

288

289

else let dnmax +1 = dnmax +1 + ∆d.

290

291

4. Determine the spacing of which cooling channel to be reduced. Find the

292

index of the battery cell with the minimum temperature, denoted as nmin .

293

If nmin = 1,

294

295

296

297

298

299

300

301

302

let d1 = d1 − ∆d. else if nmin = N , let dN +1 = dN +1 − ∆d. else if Tb,nmin −1 ≤ Tb,nmin +1 , let dnmin = dnmin − ∆d. else let dnmin +1 = dnmin +1 − ∆d. 5. A new spacing W′ is obtained through steps 3 and 4. Evaluate the max-

303

′ imum cell temperature with the cell spacings as W′ , denoted as Tmax . If

304

′ ′ Tmax < Tmax , let Tmax = Tmax and Wopt = W′ .

305

6. Let W = W′ , return to Step 3 and continue the process. If the number of

306

the spacing adjustment reaches the speciﬁc number (Nadjust ), the process

307

is stopped.

308

When the optimization process is completed, the values of Wopt is the ﬁnal

309

optimal solution.

310

4. Numerical cases

311

4.1. Parameters of the cases

312

In this section, numerical cases are used to test the eﬀectiveness of the pro-

313

posed optimization strategy for conﬁguration optimization of the battery pack 15

314

in the parallel air-cooled BTMS shown as Figure 1. The inlet width (win ) and

315

the outlet width (wout ) are set as 20 mm. The battery cell in Ref. [16] is intro-

316

duced in the present study. The detailed properties of the battery cell and the

317

air are listed in Table 1. The battery pack with 2 × 12 battery cells are included

318

in the BTMS. The original spacings among the battery cells are set as 2 mm.

319

The ﬂow rate of the cooling air (Q0 ) is 0.012 m3 /s, with the initial temperature

320

at 300 K. Table 1: Properties of battery cell and air

Property Density (kg/m3 ) Speciﬁc heat (J/(kg · K)) Dynamic viscosity (kg/(m · s)) Thermal conductivity (W/(m · K)) Intensity of heat generated (W/m3 ) Initial temperature (K)

321

Air 1.165 1005 1.86 × 10−5 0.0267 300

Battery cell [16] 2700 900 240 41408 300

4.2. Validation of the numerical models

322

First, the eﬀectiveness of the ﬂow resistance network model and the heat

323

transfer model is validated through comparison with the Computational Fluid

324

Dynamics (CFD) method. Three-dimensional CFD calculation with k − ε tur-

325

bulence model is conducted. Mass ﬂow inlet is chosen as the inlet condition

326

and pressure outlet as the outlet condition. The walls of the BTMS are set as

327

non-slip boundaries, among where the surrounding wall is adiabatic. The heat

328

can only exchange between the battery cells and the airﬂow. The calculation

329

domain and the boundary conditions are symmetric with the plane at x = 0,

330

so half of the domain with 12 battery cells are set as the calculation domain,

331

which is discretised by cuboid grid system. The grids around the walls are re-

332

ﬁned and the size of the ﬁrst layer grid is set around 0.1 mm. The governing

333

equations including the Navier-Stokes (N-S) equations and the energy conser-

334

vation equation are discretised by ﬁnite volume method, where the diﬀusive 16

terms and the convective terms in the equations are discretised by the central-

336

diﬀerencing scheme and the second-order upwind scheme, respectively. SIMPLE

337

algorithm is used to solve the discretised equations. The iteration is considered

338

to be converged when the residuals of the equations all fall below 10−6 . Grid

339

dependence analysis is conducted to determine the appropriate grid sizes for

340

the CFD calculation. Figure 5 shows the maximum temperature and maximum

341

temperature diﬀerence of the battery pack for various numbers of grid cells for

342

the case with d = 2 mm and Q0 = 0.012 m3 /s. The results indicate that the

343

maximum temperature and the maximum temperature diﬀerence both change

344

smaller than 0.05 K when the number of the grid cells is larger than 1.8 × 106 .

345

Therefore, the grid cell number of 1.8 × 106 is suﬃcient for the case with d = 2

346

mm and Q0 = 0.012 m3 /s. The similar grid size is used for the following test

347

cases. 314.7

Tmax of battery pack

Maximum temperature (K)

314.6

5.2

∆Tmax of battery pack

314.5 314.4

5.1

314.3 314.2 314.1

5

314 313.9 313.8 0.5

1

1.5

2

2.5

Number of grid cells

3

Maximum temperature difference (K)

335

4.9 3.5 6 x 10

Figure 5: Grid dependence analysis result (d = 2 mm, Q0 = 0.012 m3 /s)

348

In order to test the eﬀectiveness of the CFD method used in the present

349

study, the result of the present study is compared to the one in Park’s study

350

[16]. The parallel air-cooled BTMS with 2 × 36 battery cells is introduced, the

17

351

schematic and the relevant structure parameters of the system are shown in

352

Figure 6. The spacings among the battery cells are 3 mm and the inlet ﬂow rate

353

is 0.045 m3 /s. Figure 7 shows the comparison of the ﬂow rates in the cooling

354

channels by the present CFD method and the one of Park’s study [16]. In the

355

ﬁgure, the horizontal coordinate represents the index of the cooling channels

356

and the vertical one represents the ﬂow rate in the cooling channels. It can be

357

observed that the numerical result in the present study is in good agreement

358

with the one in Park’s study. The average relative error between the two results

359

is only 2%, validating the eﬀectiveness of the present CFD method. 225

20 20

37.5 65

37.5 65

(a) Sectional view 20

10 100

687 100

10

20

(b) Side view Figure 6: Schematic of the calculation domain for the test case (Unit: mm)

360

The ﬂow resistance network model and the heat transfer model are validated

361

through comparison with the CFD calculation. Figure 8(a) shows the compari-

362

son of the velocities by the ﬂow resistance network model and those by the CFD

363

method for 2 mm cell spacing and various inlet ﬂow rates (Q0 ). In Figure 8(a),

364

the horizontal coordinate represents the index of the cooling channels and the

18

x 10

−3

Result in the study of Park CFD result in the present study

1.5

3

Flow rate (m /s)

2

1

0.5

0 0

10

20

30

Index of cooling channel

40

Figure 7: Comparison of the numerical results of the present study and the reference

365

vertical one represents the average velocity in the cooling channels. It can be

366

seen that the velocities by the ﬂow resistance network model agree well with the

367

ones by the CFD calculation. The relative errors of the velocity for the four inlet

368

ﬂow rates are 4.6%, 4.4%, 3.9% and 3.3%, respectively. Figure 8(b) depicts the

369

comparison of the cell temperatures by the heat transfer model and by the CFD

370

model for various Q0 s. In Figure 8(b), the horizontal coordinate represents the

371

index of the battery cells and the vertical one represents the volume average

372

temperature of the battery cell. It can be observed that the heat transfer model

373

can obtain the cell temperature curves similar to the ones by the CFD method.

374

The average errors of the cell temperature for the four inlet ﬂow rates are 0.4 K,

375

0.4 K, 0.6 K and 1.0 K, which indicate that the proposed model can predict the

376

cell temperature better when the air ﬂow rate is small. The results show that

377

the heat transfer model can predict the maximum cell temperature well for var-

378

ious ﬂow rates. The errors of the maximum cell temperature for the four inlet

379

ﬂow rates are 0.7 K, 0.4 K, 0.6 K and 0.5 K, respectively. Moreover, the ﬂow

380

resistance network model and the heat transfer model calculate the velocity and

19

381

the temperature through using algebraic equations instead of using the partial

382

diﬀerential CFD equations. Thus, CFD method needs hours to obtain the ﬂow

383

ﬁeld and temperature ﬁeld for one case, while the ﬂow resistance network model

384

and the heat transfer model only need several seconds to calculate the velocities

385

in the cooling channels and the cell temperatures. The simpliﬁed numerical

386

models can save much calculation time. In summary, the ﬂow resistance net-

387

work model is eﬀective for calculation of the velocity in the cooling channels in

388

the parallel air-cooled BTMS. Also, the heat transfer model is eﬀective for cell

389

temperature calculation, especially for maximum cell temperature prediction. CFD(Q =0.015)

Model(Q =0.01) 0

Model(Q =0.015)

CFD(Q =0.012) 00

CFD(Q =0.018)

Model(Q =0.012) 0

Model(Q =0.018)

0

0

00

u (m/s)

8

325

CFD(Q0=0.01) 0

Average temperature (K)

10

0

0

0

00

0

6

4

2 0

2

4

6

8

10

Index of cooling channel

12

CFD(Q =0.015)

Model(Q =0.01)

Model(Q =0.015)

CFD(Q0=0.012)

CFD(Q0=0.018)

Model(Q =0.012)

Model(Q =0.018)

0

0

0

320

0

0

315

310

305 0

14

CFD(Q0=0.01)

2

4

6

8

10

12

Index of battery

(a) Velocity

(b) Cell temperature

Figure 8: Comparison of the results of the simplified models and CFD methods for various inlet flow rates (d = 2 mm)

390

4.3. Configuration optimization result Consider the situation that the inlet ﬂow rate Q0 = 0.012 m3 /s and the cell spacing d = 2 mm. The cell spacings of the original BTMS are described as

W0 = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] mm

(21)

391

The adjustment step is set as 0.1 mm and the number of spacing adjustments is

392

15. Then the conﬁguration of the battery pack is optimized using the proposed

393

optimization process described in Section 4, with the objective of minimizing 20

394

the maximum cell temperature. Figure 9 depicts the maximum cell temperature

395

with the number of spacing adjustments. The solution with the minimum maxi-

396

mum cell temperature is the ﬁnal solution. The curve in Figure 9 indicates that

397

it only needs 12 cell spacing adjustments to obtain the ﬁnal optimized BTMS.

398

The cell spacings of the optimized BTMS are

Wopt = [1.7, 2, 2.3, 2.3, 2.1, 2.1, 2.1, 2.1, 2, 2, 2, 2, 1.3] mm

(22)

399

It can be seen from Figure 8(b) that the battery cells near the airﬂow inlet

400

have higher temperatures than the ones near the outlet for the original BTMS.

401

Therefore, the cell spacings near the airﬂow inlet are enlarged after optimiza-

402

tion, which can help to reduce the maximum temperature of the battery pack.

403

Moreover, the airﬂow in the ﬁrst and the last cooling channels only needs to

404

cool one battery, so the spacings of these two channels can be reduced for the

405

optimized BTMS.

Maximum temperature (K)

313.8 313.6 313.4 313.2 313 312.8 312.6 0

5

10

Adjustment number

15

Figure 9: Maximum temperature with the adjustment number during the optimization process(Q0 = 0.012 m3 /s)

406

In order to evaluate the improvement of the cooling performance of the

407

optimized BTMS, the cell temperatures of optimized BTMS by the CFD method 21

408

are compared to the ones of the original BTMS, shown in Figure 10. It indicates

409

that the cell temperatures of the system are more uniform after optimization.

410

The maximum temperature diﬀerences of the battery pack are 5.0 K for the

411

original BTMS and 2.9 K for the optimized BTMS. The maximum temperature

412

diﬀerence is reduced by 42% after optimization. Furthermore, the maximum

413

temperature of the battery pack is also reduced by 0.8 K after optimization.

Cell temperature (K)

315

Before optimization (CFD) After optimization (CFD)

314 313 312 311 310 0

5

Index of battery

10

Figure 10: Comparison of the cell temperatures of the original BTMS and the optimized BTMS (Q0 = 0.012 m3 /s)

414

In order to further evaluate the heat transfer performance of the optimized

415

BTMS, the numerical results for various inlet ﬂow rates are compared and sum-

416

marized in Table 2. Though the optimize BTMS is obtained based on the inlet

417

ﬂow rate of 0.012 m3 /s, the maximum temperatures and the temperature diﬀer-

418

ences of the battery pack for the optimized system are also better than the ones

419

of the original system under the situations of other inlet ﬂow rates. Especially

420

for the maximum temperature diﬀerences, the improved ratios for the four inlet

421

ﬂow rates are 49%, 42%, 35% and 29% after optimization, respectively. It indi-

422

cates that the cooling performance of the BTMS for various inlet ﬂow rates is

423

improved after optimization. In Table 2, the total pressure drops (∆p) between

22

424

the inlet and the outlet for the four situations are also listed. The results show

425

that the total pressure drops of the optimized system for various inlet ﬂow rates

426

are similar to the ones of the original one. In the present study, the sum of the

427

cell spacings is a constant, so the adjustment of the spacings among the cooling

428

channels actually re-distributes the pressure loss among the cooling channels.

429

Thus, it changes the total pressure drops slightly after optimization. In sum-

430

mary, the BTMS after optimized using the proposed optimization strategy has

431

both the maximum temperature and the maximum temperature diﬀerence of

432

the battery pack reduced remarkably with little pressure drop increase. Table 2: The Comparison of performances of the original BTMS and optimized BTMS for various inlet flow rates

Q0 (m3 /s) 0.010 0.012 0.015 0.018

433

Original BTMS Tmax (K) ∆Tmax (K) 316.8 5.7 314.5 5.0 312.0 4.3 310.3 3.8

∆p 46.4 61.8 89.2 121.8

Optimized BTMS Tmax (K) ∆Tmax (K) 315.8 2.9 313.7 2.9 311.6 2.8 310.1 2.7

∆p 46.2 61.4 88.2 119.8

4.4. Performance under unsteady heat generation rate

434

For the realistic battery packs used in electric vehicles, the generated heat by

435

the battery cells changes with time, which depends on the cell temperature and

436

the state of charge (SOC) of the battery cell. In this section, the performance

437

of the optimized BTMS under unsteady heat generation rate is tested using

438

numerical cases. When the current discharge rate is high, the generated heat

439

by the battery pack is large, leading to high cell temperature and large cell

440

temperature diﬀerence. Therefore, high current discharge rate is considered. In

441

this situation, the reaction heat of the battery cell can be neglected and the

442

Joule heat dominates [24]. Thus, the heat source intensity of the battery cell is

443

calculated by

23

S = I 2 R/Vcell

(23)

444

where I is the discharge current. R and Vcell are the equivalent resistance and

445

the volume of the battery cell, respectively. The equivalent resistance depends

446

on the cell temperature and SOC. In the present study, the equivalent resistance

447

for a 2.2 Ah LiPePO4 battery determined by experiment is used, expressed as

448

[21] R = 27.54 − 27.68 × exp (−1.91/Tcell ) + −225.06 ×

exp(−1.91/Tcell ) 1+21.61×SOC

223.71 1+21.61×SOC

(24)

449

where Tcell is the cell temperature and SOC is calculated by the following ex-

450

pression

SOC = (Ci − I × t) /C0

(25)

451

where I is the discharge current and t is the discharge time. Ci and C0 are

452

the initial electric capacity and the total electric capacity of the battery cell,

453

respectively.

454

The constant discharge process from 95% SOC to 5% SOC is considered with

455

4-current (4C) discharge rate and 5-current (5C) discharge rate, respectively.

456

The cooling performance of the original BTMS and the optimized BTMS are

457

evaluated using the transient CFD calculation. The numerical results for the

458

inlet ﬂow rate at 0.012 m3 /s are shown in Figure 11. Figure 11(a) depicts the

459

maximum temperature and the minimum temperature of the battery cell with

460

discharge time for the 4C discharge process. It can be seen that the maximum

461

temperature curve of the optimized BTMS is always below the one of the original

462

BTMS. Meanwhile, the minimum temperature curve of the optimized system is

463

above the one of the original system. Thus, the maximum temperature diﬀerence 24

464

of the battery pack for the optimized system is smaller than the one before

465

optimization, which can be observed in Figure 11(b). The similar conclusion can

466

be obtained from the results of 5C discharge process, which are shown in Figures

467

11(c) and (d). For 4C discharge process, the maximum temperature diﬀerence

468

of the optimized BTMS is 1.5 K lower than the one of the original BTMS at the

469

end of the discharge process. The temperature diﬀerence is reduced by 39% after

470

optimization. For 5C discharge process, the maximum temperature diﬀerence

471

of the optimized BTMS is 1.8 K lower than the one of the original BTMS at

472

the end of the discharge process. The temperature diﬀerence is reduced by 37%

473

after optimization. Moreover, the maximum temperature of the battery pack is

474

slightly lower after optimization. Though the conﬁguration optimization of the

475

battery pack is conducted under the situation of the constant heat generation

476

rate, the cooling performance of the air-cooled BTMS after optimization is also

477

improved remarkably when the heat generation rate is unsteady.

478

5. Conclusions

479

In the present study, the cooling performance of the parallel air-cooled BTMS

480

is improved through optimizing the conﬁguration of the battery pack. The ﬂow

481

resistance network model is introduced to calculate the velocities in the cooling

482

channels. Combining this model, the heat transfer model is used to calculate

483

the battery cell temperature under constant heat generation rate. Based on

484

the ﬂow resistance network model and the heat transfer model, an optimization

485

strategy is proposed to optimize the conﬁguration of the battery pack, with

486

the objective of minimizing the maximum cell temperature. A typical case is

487

introduced to test the eﬀectiveness of the proposed optimization strategy. The

488

ﬂow ﬁelds of the original BTMS and the optimized BTMS are calculated using

489

the CFD method. The cooling performance of both systems are compared under

25

4.5

Temperature difference (K)

318 316

Temperature (K)

314 312 310 308 306 304

Tmax for original BTMS, 4C discharge

302

Tmin for original BTMS, 4C discharge Tmax for optimized BTMS, 4C discharge

300

T

min

298 0

100

200

300

for optimized BTMS, 4C discharge 400

500

600

700

800

4

∆ Tmax for original BTMS, 4C discharge ∆ Tmax for optimized BTMS, 4C discharge

3.5 3 2.5 2 1.5 1 0.5 0 0

900

100

200

(a) Tmax , 4C discharge Temperature difference (K)

325

Temperature (K)

320

315

310 Tmax for original BTMS, 5C discharge Tmin for original BTMS, 5C discharge Tmax for optimized BTMS, 5C discharge 300 0

T

min

100

200

400

500

600

700

800

900

(b) ∆Tmax , 4C discharge 5

305

300

Time(s)

Time(s)

4

∆ Tmax for original BTMS, 5C discharge ∆ Tmax for optimized BTMS, 5C discharge

3

2

1

for optimized BTMS, 5C discharge

300

400

500

600

0 0

700

100

200

300

400

500

600

700

Time(s)

Time(s)

(c) Tmax , 5C discharge

(d) ∆Tmax , 5C discharge

Figure 11: Comparison of the performance of the optimized BTMS and the original BTMS for unsteady heat generation rate (Q0 = 0.012 m3 /s)

26

490

the situations of steady and unsteady heat generation rates of the battery pack.

491

The following conclusions can be obtained.

492

1. Numerical results of various inlet ﬂow rates show that the velocities in the

493

cooling channels by the ﬂow resistance network model agree well with the

494

ones by the CFD method, and the heat transfer model can also predict the

495

maximum cell temperature well. Furthermore, the models only consist of

496

algebraic equations, so they save much computational cost to obtain the

497

velocity and the cell temperature comparing to using the CFD method.

498

Therefore, the ﬂow resistance network model and the heat transfer model

499

are applicable to calculate the cell temperature during the conﬁguration

500

optimization of BTMS.

501

2. Through analyzing the characteristic of the parallel air-cooled BTMS, an

502

optimization strategy is proposed, which suggests that the spacing around

503

the battery cell with the highest temperature should be increased while

504

the one around the battery cell with the lowest temperature should be

505

reduced. This optimization strategy is combined with the ﬂow resistance

506

network model and the heat transfer model for conﬁguration optimization

507

of the battery pack. The result of the typical numerical case shows that

508

the optimization strategy can obtain the ﬁnal solution in just several times

509

of cell spacing adjustments, and the maximum temperature diﬀerence of

510

the battery pack is reduced by more than 29% after optimization for var-

511

ious inlet ﬂow rates for the situation of constant heat generation rate.

512

Moreover, the maximum temperature of the battery pack is also reduced

513

slightly.

514

3. Though the optimization solution is obtained under the constant heat

515

generation rate, the cooling performance of the optimized BTMS is also

516

improved when the heat generation rate is unsteady. The numerical results

27

517

of the unsteady heat generation situation indicate that the temperature

518

diﬀerences of the optimized BTMS are 1.5 K and 1.8 K lower than the

519

ones of the original BTMS for the 4C and 5C discharge processes, respec-

520

tively. The ratios of the improvements are 39% and 37%, respectively.

521

Moreover, the maximum temperatures of the system are reduced slightly

522

after optimization.

523

Note that the proposed optimization strategy is based on the actual tem-

524

perature distribution of the battery cells, and is independent of the operating

525

parameters and the design parameters of the BTMS, including the number of

526

the battery cells, the size of the battery cell, the heat generation rate of the bat-

527

tery cell, the size of the BTMS, the initial air temperature and the inlet airﬂow

528

rate. Therefore, the proposed optimization strategy combined with the ﬂow

529

resistance network model and the heat transfer model is an eﬀective method to

530

optimize the conﬁguration of the battery pack in the parallel air-cooled BTMS

531

for cooling performance improvement.

532

Acknowledgements

533

This research is supported by National Natural Science Foundation of China

534

(Grant Nos. 51506056 and 51536003) and the Fundamental Research Funds for

535

the Central Universities (Grant No. 2016YQ03).

536

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31

604

Captions of tables and figures

605

Table 1 Properties of battery cell and air

606

Table 2 The Comparison of performances of the original BTMS and optimized

607

BTMS for various inlet ﬂow rates

608

Figure 1 Schematic of the battery pack

609

Figure 2 Schematic of the parallel air-cooled BTMS

610

Figure 3 Schematic of the battery pack

611

Figure 4 Schematic of the ﬂow resistance network model

612

Figure 5 Grid dependence analysis result (d = 2 mm, Q0 = 0.012 m3 /s)

613

Figure 6 Schematic of the calculation domain for the test case (Unit: mm)

614

Figure 7 Comparison of the numerical results of the present study and the

615

reference

616

Figure 8 Comparison of the results of the simpliﬁed models and CFD methods

617

for various inlet ﬂow rates (d = 2 mm)

618

Figure 9 Maximum temperature with the adjustment number during the opti-

619

mization process (Q0 = 0.012 m3 /s)

620

Figure 10 Comparison of the cell temperature of the original BTMS and the

621

optimized BTMS (Q0 = 0.012 m3 /s)

622

Figure 11 Comparison of the performance of the optimized BTMS and the

623

original BTMS for unsteady heat generation rate (Q0 = 0.012 m3 /s)

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Highlights > Configuration optimization of battery pack in air-cooled BTMS is conducted. > Simplified models are used to calculate the battery cell temperature. > An optimization strategy is proposed to optimize the battery cell spacings. > Temperature difference of battery pack is reduced remarkably after optimization.