Thermal performance of lithium-ion battery thermal management system by using mini-channel cooling

Thermal performance of lithium-ion battery thermal management system by using mini-channel cooling

Energy Conversion and Management 126 (2016) 622–631 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www...

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Energy Conversion and Management 126 (2016) 622–631

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Thermal performance of lithium-ion battery thermal management system by using mini-channel cooling Zhen Qian, Yimin Li, Zhonghao Rao ⇑ School of Electric Power Engineering, China University of Mining and Technology, XuZhou 221116, China

a r t i c l e

i n f o

Article history: Received 15 May 2016 Received in revised form 19 August 2016 Accepted 21 August 2016

Keywords: Mini-channel Cold-plate Battery thermal management Lithium-ion battery pack

a b s t r a c t Thermal management is indispensable to lithium-ion battery pack especially within high power energy storage device and system. To investigate the thermal performance of lithium-ion battery pack, a type of liquid cooling method based on mini-channel cold-plate is used and the three-dimensional numerical model was established in this paper. The effects of number of channels, inlet mass flow rate, flow direction and width of channels on the thermal behaviors of the battery pack were analyzed. The results showed that the mini-channel cold-plate thermal management system provided good cooling efficiency in controlling the battery temperature at 5C discharge. A 5-channel cold-plate was enough and the temperature could be evidently reduced by increasing the inlet mass flow rate. Additionally, for the bad temperature uniformity in the design 1, design 2 was proposed and compared with the design 1. The maximum temperature and temperature difference decreased 13.3% and 43.3%, respectively. Temperature uniformity was significantly improved. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The issues of energy shortage and environment pollution have provided opportunities for the development of pure electric vehicles (EVs) and hybrid electric vehicles (HEVs) [1]. Compared to conventional vehicles, EVs have the advantages of less noise, higher energy utilization and environment protection [2]. Power battery is the key to electric vehicles development. Various kinds of battery such as lead-acid battery, nickel-metal hydride (Ni-MH) battery and lithium-ion battery are available for electric vehicles [3]. Compared with other batteries, lithium-ion batteries have significant advantages such as higher power density, longer cycle life and lower self-discharge rate. Therefore, they are the advisable candidates for electric vehicles [4]. However, lithium-ion batteries are very sensitive to temperature. Temperature affects the cycle life, efficiency, reliability and safety of the battery [5]. During charge and discharge process, a large amount of heat is generated inside the battery due to electrochemical reaction and resistance, which will increase the temperature of the battery. Thermal runway, electrolyte fire and explosions can occur when the temperature is too high [6]. Lithium-ion batteries operate best at temperature between 25 °C and 40 °C. The desirable temperature distribution is less than 5 °C in a battery or from module to module ⇑ Corresponding author. E-mail address: [email protected] (Z. Rao). http://dx.doi.org/10.1016/j.enconman.2016.08.063 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

[7]. As a result, efficient thermal management systems are highly necessary for lithium-ion batteries. At present, battery thermal management system can be divided into three types: air cooling system, liquid cooling system and phase change material (PCM) based cooling system. The first two types can be further divided as active system and passive system. PCM based cooling system is usually passive [8]. PCM based cooling system is a new type of battery thermal management. It was first proposed to apply in battery thermal management by Al-Hallaj and Selman [9]. Javani et al. [10] investigated the effects of PCMs on square lithium-ion battery. They found PCMs could bring more uniform temperature distribution and keep battery in safe temperature range. In our previous work [11], PCM was employed to cool the ageing lithium iron phosphate (LiFePO4) power battery. It was shown that the higher thermal conductivity and lower melting point of PCM was very beneficial to decrease the battery temperature. However, they still cannot be widely used limited by their very lower thermal conductivity [12]. In the aspect of air cooling, it is one of the widely used cooling system in electric vehicles due to its simple structure, low cost and easy maintenance. Air cooling system was employed in the Toyota Prius and Honda Insight, Nissan and GM also used forced air cooling system to cool batteries [13]. Zolot et al. [14] studied the temperature control performance of a forced air cooling system in Ni-MH batteries, it was shown that the maximum temperature was effectively reduced and temperature distribution was uniform.

Z. Qian et al. / Energy Conversion and Management 126 (2016) 622–631

Nomenclature Q gen Qr Qj

q

k Cp I n F DS E V T

Subscripts b battery c cold-plate j joule r reaction w water gen generation

heat generation of the battery (W) electrochemical reaction heat (W) joule heat (W) density (kg/m3) thermal conductivity (W/m K) heat capacity (J/kg K) discharge current (A) number of electrons (mol) Faraday constant, 96485 C/mol entropy change open circuit voltage (V) operating voltage (V) temperature (K)

Acronyms EVs electric vehicles HEVs hybrid electric vehicles PCM phase change materials UDF user defined function SOC state of charge

Y-direction rake

Symmetry

Cell3 Cell2

Cold-plate

Cell1

(a)

Active volume

Positive electrode Negtive electrode

(b)

(c)

Unit: mm

Fig. 1. Schematic of the cooling system: (a) design 1. (b) Single battery cell. (c) Half of cold-plate.

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In practical applications, batteries are usually used in the form of pack. Fig. 1(a) illustrates the schematic of the cooling system, each cold-plate is sandwiched by two battery cells. The battery is rectangular in shape. Heat generated from the cell transfers into the cold-plate through contact surface, then into the cooling liquid which flows through the mini-channel. There are totally five battery cells in this pack. Only half of the pack is considered because of the application of symmetry boundary condition to reduce computation load. These battery cells are named as cell1, cell 2, cell 3 in

Material

q (kg m3)

C P (J kg1 k1)

k (W m1 k1)

l (Pa s)

Aluminum Water Battery

2719 998.2 2500

871 4128 1000

202.4 0.6 3

– 1.003  103 –

8.0 7.8 7.6 7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0 0

2000000

4000000

6000000

8000000

Grid number Fig. 2. Independent test of grid number.

turn. Fig. 1(b) and (c) describes the structure of the battery and mini-channel cold-plate, respectively. The non-uniformity of coolant distribution in cold-plate is considered. Inlet and outlet are distributed on both sides of the cold-plate. Cooling liquid flows into the cold-plate, then are divided into several branches. Therefore, mass flow rate in each branch is different. Considering higher temperature in the near-electrode area, the main stream is placed near electrodes of batteries. The gap d1 between each channel is the same and d1 is equal to d2. The width of channel along Y direction d3 and the width of inlet and outlet d4 are 3 mm. Also, the width of channel along X direction is 3 mm. The cold-plate is made of aluminum and water is employed as cooling medium. The thermal properties of the cold-plate, water and battery used in this paper are summarized in Table 1. 2.1. Numerical solution The model was meshed in ICEM CFD and the numerical calculation was conducted in FLUENT 14.0. Laminar model was employed because the maximum Reynolds number was less than 2300 in this 100

5 Experimental Simulation

90

4 80 70

3

60 2

50

Relative error (%)

2. Model and methodology

Table 1 The thermo-physical parameters of the cold-plate, water and battery [19].

Heat transfer rate (W)

Fan et al. [15] analyzed the influence of gap spacing and air flow rate on lithium-ion battery module. The results showed that the lower gap spacing and higher flow rate of the fan could decrease the maximum temperature rise. However, the temperature gradients along the air flow direction were unavoidable. In general, air cooling system is adequate in many cases. However, air cooling system cannot meet the requirements under severe operation conditions such as fast charge or discharge. Compared with air, liquid has higher thermal conductivity which leads to higher cooling performance and is more suitable for cooling large-scale battery pack. Chen et al. [16]compared different cooling system for lithium-ion batteries. The results showed that an indirect liquid cooling system had the lowest maximum temperature rise, and was more practical than direct liquid cooling. Huo and Rao [17] employed alumina(Al2O3)-water nanofluid in a 5-battery system. The results showed that adding the nanoparticles could enhance the cooling performance and decrease the average temperature. Compared to water, the average temperature was decreased by 7% with volume fraction as 0.04. Heat pipe is another form of liquid cooling system. Due to its best advantage-super thermal conductivity, it is very popular in thermal management. In our previous work [18], a kind of oscillating heat pipe had been studied. The results showed that its start-up temperature was decided by the desired and the acceptable maximum temperature difference of the battery. Higher heat transfer coefficient attainable by the application of mini-channels enables cold-plate to effectively remove a large amount of heat from the batteries in the liquid cooling system. Huo et al. [19] designed a mini-channel cold-plate based battery thermal management. The results showed that the maximum temperature of the battery decreased with the increase of the channel number and inlet mass flow rate. Zhao et al. [20] designed a minichannel liquid cooled cylinder. They found that the maximum temperature could be controlled under 40 °C when the number of mini-channel was no less than four and the inlet mass flow rate was 1  103 kg/s. In our previous work [21], a phase change material/mini-channel coupled battery thermal management system was designed. Compared with the PCM based system, this system presented more effective thermal performance and the maximum temperature could be reduced 14.8 °C. Jin et al. [22] designed an oblique liquid cold plate. The results showed that the oblique mini-channel could get higher heat transfer coefficient than conventional straight mini-channel. In this paper, a type of liquid cooling system based on minichannel cold plate was introduced to manage the temperature of lithium-ion battery pack. The numerical method was employed and three-dimensional liquid-cooled model was established on the consideration of the non-uniform coolant distribution in cold-plate. The effects of number of mini-channel, inlet liquid mass flow rate, flow direction and width of mini-channel on battery pack were investigated. The object of this study aimed to provide guidance for the design of the battery thermal management system in electric vehicles.

Maximum temperature (°C)

624

40 1 30 20

0

100

200

300

400

500

600

700

800

0 900

Time (s) Fig. 3. Comparison between experimental and simulated results of single battery.

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study. Mass flow inlet and outflow were chosen as the inlet and outlet boundary conditions, respectively. The side surface of the whole pack was defined as free convection boundary condition with the heat transfer coefficient of 5 W/(m K). The inlet water temperature was equal to ambient temperature which was set as 25 °C. Independent test of grid number was carried out to ensure accuracy of the calculation. The result is shown in Fig. 2, so the grid number 5.7  106 was chosen. The discharge rate of the battery is 5C and discharge time last 720 s. The UDF (user defined function) was used to define heat source. Fig. 3 shows the comparison

between experimental (experimental result [23]) and simulate results. It could be seen that the relative error did not exceed 2.7%. 2.2. Governing equations The temperature of a single battery can be calculated by the energy conservation equation [24]:

@ ðq C pb TÞ ¼ r  ðkb rTÞ þ Q gen @t b

45

20

(a)

(d) 40°C

40

15

ΔΤ (°C)

Maximum temperature ( °C)

ð1Þ

35

3channels 5channels 7channels

2channels 4channels 6channels

30

13.8°C

10

2channels 4channels 6channels

5

0

25 0

120

240

360

480

600

0

720

120

240

45

360

600

720

20

(b)

(e)

B

A 40

15

ΔT (°C)

Maximum temperature (°C)

480

Time (s)

Time (s)

35

2 channels 4 channels 6 channels

30

10

2 channels 4 channels 6 channels

5

0

25 0

120

240

360

480

600

0

720

120

240

360

480

600

720

Time (s)

Time (s) 20

45

(c)

(f) B

A 15

40

ΔT ( °C)

Maximum temperature (°C)

3channels 5channels 7channels

35

3 channels 5 channels 7 channels

30

10

3 channels 5 channels 7 channels

5

0

25 0

120

240

360

Time (s)

480

600

720

0

120

240

360

480

Time (s)

Fig. 4. Maximum temperature (a)–(c) and temperature difference (d)–(f) in the pack under different cooling channels.

600

720

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2 channels

3 channels

4 channels

5 channels

6 channels

7 channels

(a)

(b) Fig. 5. Temperature contours of middle section in cold-plate under different cooling channels (a) and that of the pack under 5 channels (b) (inlet mass flow rate = 0.001 kg/s).

Table 2 Pressure drop under different cooling channels.

Q j ¼ IðE  VÞ

Channel number

2

3

4

5

6

7

Pressure drop/Pa

527.7

326.4

373.3

277.8

316.4

257.4

where Q gen is the heat generation of the battery, qb is the density, kb is the thermal conductivity, C pb is the heat capacity and T is the temperature. The battery temperature is determined by the Q gen in Eq. (1). The source Q gen is mainly composed of two parts: electrochemical reaction heat Q r and joule heat Q j [25]. Reaction heat is generated during the chemical reaction process, it can be calculated as follows:

Q r ¼ T DS

I nF

ð2Þ

where I is the discharge current, n is the number of electrons, F is faraday constant, DS is the entropy change in battery reaction, T is the temperature. Current transfer across internal resistances is the main cause of the joule heat, which can be calculated as follows:

ð3Þ

where E is the open circuit voltage, V is the operating voltage. Both E and V depend on the temperature and the SOC (state of charge). Therefore, Q gen can be expressed as [25]:

Q gen ¼ IðE  VÞ  T DS

I nF

ð4Þ

The continuity and the momentum conservation equations of water are as follows: ! @ qw þ r  ðqw t Þ ¼ 0 @t

ð5Þ

! ! ! @ ðq t Þ þ r  ðqw t t Þ ¼ rP @t w

ð6Þ

The energy conservation equations of water and the liquid cold plate are as follows: ! @ ðq cpw T w Þ þ r  ðqw cpw t T w Þ ¼ r  ðkw rT w Þ @t w

ð7Þ

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@ ðq cpc T c Þ ¼ r  ðkc rT c Þ @t c

70

ð8Þ

!

3. Results and discussion The channel number, mass flow rate, flow direction and channel width in mini-channel cold plate have significant effects on the thermal performance of lithium-ion battery pack. So these four variables are investigated. Besides, two different designs are compared. The cooling performance is measured by maximum temperature and temperature difference which represents temperature uniformity.

60

Maximum temperature (°C)

where qw , cpw , kw , T w , t are the density, heat capacity, thermal conductivity, temperature and velocity vector of water. qc , cpc , kc , T c are the density, heat capacity, thermal conductivity and temperature of cold plate.

(a)

65

55 50 45 40 35 30

1 × 10 kg/s

3 × 10 kg/s

5 ×10 kg/s

7 × 10 kg/s

9 × 10 kg/s

1 × 10 kg/s

1.5 × 10 kg/s

2 × 10 kg/s

-4

25

-4

-4

-3

-4

-4

-3

-3

20 0

120

240

360

480

600

720

Time (s) 25

(b)

3.1. Effects of channel number

ΔT (°C)

20

15

10

1×10 kg/s

3×10 kg/s

5×10 kg/s

7×10 kg/s

9×10 kg/s

1×10 kg/s

1.5×10 kg/s

2×10 kg/s

-4

5

-4

-4

-3

-4

-4

-3

-3

0 0

120

240

360

480

600

720

Time (s) Fig. 6. Maximum temperature (a) and temperature difference (b) in the pack under different inlet mass flow rates.

60

50

Temperature ( °C)

The number of channel was changed from 2 to 7 in this section. The inlet mass flow rate was set as 0.001 kg/s. Fig. 4 shows the maximum temperature and temperature difference in the pack under different channel number at 5C discharge rate. Fig. 4(a) is divided into Fig. 4(b) and (c) for the convenience of analysis, so is Fig. 4(d). It can be seen that the maximum temperature increases evidently in the first 240 s, then decreases until about 540 s, during which heat generation rate decreases and is lower than cooling rate. The time range of temperature decrease is slightly different when the number of channel is different. The maximum temperature is 41.6 °C during the discharge when the number of channel is 2, which is acceptable. Meanwhile, the maximum temperature is kept under 40 °C at 65% of the discharge time. Fig. 4(b) and (c) show that with the increase of channel number in even and odd forms, respectively, the maximum temperatures of the pack are both reduced. The more channels are, the lower the degree of maximum temperature decrease is. When the number of channel was changed from 2 to 7, the maximum temperature is reduced about 2.4 °C. Higher heat transfer rate is available, because the heat transfer area is increased caused by more channels. On the other hand, channel distribution cannot be ignored when channel number increases. In the 5-channel case, the maximum temperature is even higher than that in the 4-channel case at some time. The same phenomenon appears in the 7-channel case. As shown in Fig. 1(c), when the number of channel is odd, the middle channel which is far from electrodes is rightly opposite to the inlet, more than half of water flows along the middle channel. Thus, the cooling effect of water on the near-electrode area where heat generation is more serious is worse. The maximum temperature appears rightly in the near-electrode area. It can be seen in Fig. 5(b). However, when the number of channel was changed from 5 to 7, the temperature reduction is less than 1 °C, which is not evident. At the same time, there is a large temperature difference in the pack due to the uneven heat generation. The temperature increases along the liquid flow direction. As shown in Fig. 4(d) –(f), the change rule of temperature difference is the same as maximum temperature. In region A, more channels have higher temperature difference, but in region B, more channels have smaller temperature difference on the contrary. In the 7-channel case, temperature difference can be up to 13.8 °C. Only in the first 20 s, the temperature difference is below 5 °C. Therefore, temperature uniformity is not good. The pressure drop is shown in Table 2. The result indicates that with the increase of channel number in even and odd forms, respectively, the pressure drop both decreases. When the number

40

30

10

-4

3 ×10 kg/s

-4

1 ×10 kg/s

1 ×10 kg/s

20

9 ×10 kg/s

0

20

40

-4

5 ×10 kg/s

-3

1.5 ×10 kg/s

60

-4

-3

80

-4

7 ×10 kg/s -3

2 ×10 kg/s

100

Position in Y-direction rake (mm) Fig. 7. Temperature distribution along the Y-direction rake in the pack.

of channels is odd, the pressure drop is usually smaller, the reason has been explained in the above. More channels will lead to more cost [20]. However, fewer channels will cause higher pressure drop and worse cooling performance. Take the above three factors, a 5-channel cold-plate is enough. So, in the following study, the 5-channel case was chosen.

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0.0001kg/s

0.0002kg/s

0.001kg/s

0.002kg/s

Fig. 8. Temperature contours of the slice under different inlet mass flow rates.

electrodes

Maximum temperature (°C)

45

cell

Cold-plate

40

35

case1 case2 case3 case4

30

25 0

120

240

360

480

600

720

Time (s)

Case1

Case2

Case3

Case4

Fig. 10. Maximum temperature in the pack under different flow direction.

Fig. 9. Schematic of different flow direction.

3.2. Effects of mass flow rate In this section, eight types of inlet mass flow rate which were changed from 1  104kg/s to 2  103kg/s and a 5-channel coldplate were chosen to study its influence on cooling performance. The maximum temperature and temperature difference are shown in Fig. 6(a) and (b). At the end of 5C discharge, the maximum temperature is 61.4 °C when inlet mass flow rate is 1  104kg/s, and the maximum temperature is 36.1 °C when inlet mass flow rate is 2  103kg/s, the temperature decreases about 25.3 °C. When inlet mass flow rate is higher than 5  104kg/s, the maximum temperature can be decreased below 45 °C, while that is higher than 1.5  103kg/s, the temperature can be reduced below 40 °C. The higher the inlet mass flow rate is, the more maximum temperature decreases. However, the decrease trend gets slow with the increase of inlet mass flow rate. It is not necessary to use the high inlet mass flow rate. In Fig. 6(b), when inlet mass flow rate is 1  104kg/s, the trend of temperature difference is significantly different from others as it keeps increasing during the whole time. The result indicates that it is very difficult to reduce the temperature difference in the pack under 5 °C. Fig. 7 shows the temperature distribution along the Y-direction rake.

There are evidently temperature gradients along the liquid flow directions which are inevitable but can be reduced by increasing the inlet mass flow rate. It can be controlled within 2 °C. As shown in Fig. 8, the maximum temperature of the battery pack appears in cell1. The maximum temperature of cell 1 is 12% higher than that of cell 2 and 3 at 0.002 kg/s inlet mass flow rate. This situation must be improved for temperature uniformity. 3.3. Effects of flow direction Flow direction has important influence on the temperature and its distribution. In this section, four cases of different flow directions were considered and simulated (Fig. 9). The inlet mass flow rate is 1  103kg/s, and the number of channel is 5. The maximum temperature is shown in Fig. 10 and temperature contours are shown in Fig. 11. The maximum temperature has little difference between case1 and case 3, which is the same between case 2 and case 4. However, the maximum temperatures in case 1 and case 3 are about 8% lower than those in case 2 and case 4 at the end of 5C discharge. In case 1 and case 3, high temperatures appear at the bottom and the near-electrode area in cell1. In case 2 and case 4, high temperatures only appear at near-electrode area. Take the case 1 as reference, in case 3, flow direction in the inner coldplate is changed. Though near-electrode area has more serious heat

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Case1

Case2

Case3

Case4

Fig. 11. Temperature contours of the slice under different flow direction.

42

45

40.6°C

(a)

Maximum temperature (°C)

Maximum temperature (°C)

39

40

37

35

0.6°C

36

3mm 4mm 5mm 6mm

35

30

34 33 40

60

80

100

120

36

35.2°C

33 30 Design 1 Design 2

27 24 0

25 0

120

240

360

480

600

120

240

720

360

480

600

720

Time (s)

Time (s) Fig. 12. Maximum temperature in the pack under different channel width.

15

13.7°C

(b) 12

Channel width (mm)

3

4

5

6

Pressure drop (Pa)

277.8

196.5

151.7

124.2

9°C

9

ΔΤ (°C)

Table 3 Pressure drop under different channel width.

6

Design 1

3

Z-direction rake

Design 2

Symmetry 0 0

120

240

360

480

600

720

Time (s) Cell3

Fig. 14. Maximum temperature (a) and temperature difference (b) comparison in the two designs when inlet mass flow rate = 0.001 kg/s.

Cell2 Cell1 Cold-plate

Fig. 13. The schematic of design 2.

generation than other area, this change has no significant effect on maximum temperature due to cell 3 is cooled by two cold-plates. In case 4, flow direction in the outer cold-plate is changed, that leads to worse cooling performance in cell1. So, case 2 and case 4 are clearly inadvisable.

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and d4 is equal to d3. Their cooling performance was analyzed and compared. The inlet mass flow rate 1  103kg/s and a 5-channel cold-plate were chosen. The maximum temperature is shown in Fig. 12. The maximum temperature only decreased by 0.6 °C during whole discharge time when d3 was changed from 3 mm to 6 mm. With the d3 increases, the velocity in every channel decreases. The cooling performance is determined by heat transfer coefficient and heat transfer area. So heat transfer rate is not obviously increased. Pressure drops under different channel width are listed in Table 3. When d3 was changed from 3 mm to 6 mm, pressure drop decreases 55%. A wider channel leads to lower pressure drop which is favorable to save energy consumption.

35.0 Design 2 Design 1

Cell 1

Temperature ( °C)

32.5

Cell 3

Cell 2

30.0

27.5

symmetry 25.0 0

10

20

30

40

3.5. Effects of different designs

Position (mm)

As it is mentioned in Section 3.2, the maximum temperature of cell 1 is 12% higher than that of cell 2 and 3, and it cannot be reduced by increasing the inlet mass rate and channel number. It illustrates that only four cold-plates cannot meet the requirements of the whole pack. Too thick battery hampers heat transfer. Therefore, another cold-plate is highly needed.

Fig. 15. Temperature distribution along the Z-direction rake in the two designs when inlet mass flow rate = 0.001 kg/s.

3.4. Effects of channel width In this section, the effects of different channel width were considered. As shown in Fig. 1(c), d3 was changed from 3 mm to 6 mm

A

0.0001kg/s

0.001kg/s

0.0005kg/s

0.002kg/s

(a)

(b) Fig. 16. Temperature contours of the design 2: (a) under four different inlet mass flow rates. (b) inlet mass flow rate = 0.001 kg/s, at the view of A.

Z. Qian et al. / Energy Conversion and Management 126 (2016) 622–631

Design 2 was proposed and compared with the design 1. As shown in Fig. 13, in this design, a cold-plate was added to cool cell1. So each battery cell is sandwiched by two cold-plates. The inlet mass flow rate were 1  103 kg/s and the number of channel is 5. Fig. 14 shows the maximum temperature and temperature difference in the two designs at the end of 5C discharge. It can be seen that the maximum temperature and temperature difference in design 2 are 35.2 °C and 9 °C, respectively, which are 5.4 °C and 4.7 °C lower than that in design 1. The maximum temperature and temperature uniformity are greatly improved in the pack. Fig. 15 shows temperature distribution along the Z-direction rake in the two designs. The temperature at Z = 0 was decreased 20%. The cold-plate added in cell 1 makes great contributions to the pack. In design 2, the intermediate temperature of the each battery is 1 °C higher than temperature in two sides. The maximum temperature of the whole pack appears in cell 3 on the contrary. Fig. 16(a) shows temperature contours of the design 2 under four different inlet mass flow rates. It can be seen in Fig. 16(b) that the temperature distribution is very uniform except the nearelectrode area whose temperature is about 3 °C higher than that of the surrounding area when inlet mass flow rate was 1  103 kg/s. 4. Conclusions To investigate the thermal performance of lithium-ion battery pack, a type of liquid cooling method based on mini-channel cold-plate is used and the three-dimensional numerical model was established in this paper. The effects of number of channels, inlet mass flow rate, flow direction and width of channels on the thermal behaviors of the battery pack were analyzed. The maximum temperature and temperature uniformity were used to measure the cooling efficiency. The main conclusions are listed as follows: (1) The mini-channel cold-plate thermal management system provides good cooling efficiency in controlling the battery pack temperature. Only a 2-channel cold-plate can keep the maximum temperature under 40 °C during more than half of the discharge time. The more channels are, the better the cooling efficiency is. Nevertheless, cold-plate whose channel number exceeds five does not have apparent advantages. (2) The maximum temperature and temperature difference can be reduced by the way of increasing inlet mass flow rate which is more efficient than other methods. However, it is at the expense of energy consumption. Increasing the channel width can reduce the energy consumption. When d3 was changed from 3 mm to 6 mm, pressure drop decreases 55%. Because of the higher heat generation rate in near-electrode area and different cooling effects on each battery, it is very difficult to decrease the temperature difference under 5 °C. (3) The design 2 is proposed to improve the temperature uniformity of the pack. The result indicates that compared to design 1, the maximum temperature and temperature difference in design 2 decreased 13.3% and 43.3%, respectively, when the inlet mass flow rate is 1  103 kg/s. The temperature uniformity is improved, which has a positive effect on safety and life of batteries.

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