Pre-cooling of air by water spray evaporation to improve thermal performance of lithium battery pack

Pre-cooling of air by water spray evaporation to improve thermal performance of lithium battery pack

Applied Thermal Engineering 163 (2019) 114401 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.c...

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Applied Thermal Engineering 163 (2019) 114401

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Pre-cooling of air by water spray evaporation to improve thermal performance of lithium battery pack

T



Yue Yang, Lijun Yang , Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

H I GH L IG H T S

spray cooling is effective to reduce maximum temperature. • The temperature difference of batteries gets large due to spray cooling. • Maximum optimum water flow rate is related to the air velocity. • The velocity dominates the residence time and diffusion behavior of droplets. • Air • High ambient temperature results in increased maximum temperature of batteries.

A R T I C LE I N FO

A B S T R A C T

Keywords: Battery pack Cooling performance Water spray cooling Mass flow rate Water droplet size Ambient temperature

The performance of battery pack is sensitive to the working temperature and often hindered by overheating, so the high efficiency cooling technology is of significant benefit to the battery performance. In this work, the air pre-cooling by water spray evaporation is applied to the battery pack thermal management. The influences of water flow rate, water droplet size, air velocity and ambient temperature on the battery performance are investigated by computational fluid dynamics. The results show that the water spray cooling can greatly reduce the maximum temperature but increase the temperature difference compared to the dry cooling. A high water flow rate leads to the reduced maximum temperature, but plays the adverse role in the maximum temperature difference. The water droplet optimal size depends on the air velocity due to its dominant roles in the residence time and diffusion behavior of droplets. When the ambient temperature is below 308.15 K and the air velocity exceeds 2 m/s, the water flow rate of 0.0002 kg/s can meet the cooling demands of battery pack.

1. Introduction

battery thermal management system (BTMS), including air cooling, liquid cooling, phase change material (PCM) cooling [4], heat pipe cooling [5–7] and cold plate cooling [8–11], among which air cooling is one of the most commonly used solutions thanks to its simplicity and low cost. Fan et al. [12] studied an air-cooled module in the transient thermal state by numerical simulation, and found that by lowering the gap space and increasing the air flow rate the maximum temperature is reduced. Zhang et al. [13] developed an air-cooled module with a special kind of aluminum pin fin for prismatic Li-ion cells, and studied the effects of pin fin arrangement, discharge rate, inlet air flow velocities and temperatures on the battery. Unfortunately, the air cooling performance is so poor that it cannot meet the cooling demands of batteries in the extreme environment or under heavy duty cycles [14]. For liquid cooling, Rao et al. [15] designed a novel system for the cylindrical lithium-ion battery module with variable contact surface,

The global energy and environmental issues have attracted more and more widespread attentions with the great consumption of fossil fuels in the last decades. The vehicle equipped with internal combustion engine burns much more fuels, which is accepted as one of the main pollution sources. As an ideal alternative, electric vehicles (EVs) are highly recommended for reducing the carbon and pollutant emissions in urban area and solving the energy problem. Lithium battery pack is one of the popular power sources of EVs due to its high specific energy density, no memory effect, long cycle life, and good stability [1,2]. However, the battery pack performance greatly depends on the working temperature ranging ideally from 298.15 K to 313.15 K [3], so it is often hindered by overheating. More emphases have been placed upon the cooling performance of



Corresponding author. E-mail address: [email protected] (L. Yang).

https://doi.org/10.1016/j.applthermaleng.2019.114401 Received 17 March 2019; Received in revised form 11 July 2019; Accepted 15 September 2019 Available online 16 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A C cp DAB D h k L ṁ Nu p Pr Q Re S Sc Sh t T u V

Y

mass fraction

Greek symbols

surface area (m2) coefficient heat capacity (J kg−1 K−1) mass diffusion coefficient (m2 s−1) diameter (m) convection heat transfer coefficient (W m−2 K−1) thermal conductivity (W m−1 K−1) latent heat (J kg−1) mass flow rate (kg s−1) Nusselt number pressure (Pa) Prandtl number heat generation rate (W m−3) Reynolds number volumetric source (W m−3) or (kg m−3 s−1) Schmidt number Sherwood number time (s) temperature (K) velocity (m s−1) volume (m3)

µ ρ τ

dynamic viscosity (kg m−1 s−1) density (kg m−3) shear stress (Pa)

Subscripts a ave b db D e m max p v wb 0

air average battery dry bulb drag energy mass maximum droplet vapor wet bulb initial

battery thermal management is rarely reported. The feasibility of spray cooling for the thermal management of Lithium-ion battery pack was proved by Saw et al. [31], but the influences of inlet temperature and velocity of air, water spraying rate and droplet size are not analyzed in detail. In this work, the pre-cooling of air by water spray is applied to battery thermal management system to ensure the desired maximum temperature and temperature difference, and compared with dry cooling. Besides, the effects of operating parameters on the cooling performance of BTMS are studied by three-dimensional numerical simulations, which can contribute to the energy-efficient and safe operation of lithium battery pack.

which could effectively reduce the maximum temperature and temperature difference. Lan et al. [16] proposed the aluminum minichannel tubes for a single lithium-ion cell, with the maximum temperature at a discharge rate of 1C less than 300.95 K and the temperature difference across the cell less than 0.80 K at a small expense of pumping power. As well known, the liquid cooling basically works with the high investment cost, large space occupation and great power consumption [17], etc. For solving the aforementioned problems, PCM has been widely adopted in BTMS. Wang et al. [18] concluded that paraffin/aluminum foam composite PCM can improve the cooling performance of Li-ion battery. Li et al. [19] proposed a compact sandwiched BTMS with copper foam-paraffin, and experimentally analyzed its thermal performance. As another popular method, heat pipe is also applied to the BTMS. Yan et al. [20] proposed a new composite board based BTMS which contains a heat conduction shell, an insulation panel and PCM. Wu et al. [21] investigated the temperature distribution in the lithium-ion battery with the heat pipe inserted. Rao et al. [22] concluded that the BTMS with heat pipe can reduce the energy consumption when applying to the EVs/HEVs. However, the complex structure and strict operating environment requirements of heat pipe limit its extensive applications [23]. All the aforementioned cooling methods are widely used but still with unexpected setbacks, which have stimulated the development of more efficient and yet cost effective thermal management system of battery pack, such as the emerging technology of evaporative cooling. In evaporation cooling, water is injected to the inlet air and then gets evaporated to reduce the air temperature prior to reaching the heat surface. Alkhedhair et al. [24] and Xiao et al. [25] employed the spray cooling for air-cooled condenser to improve the thermal performance in hot days. Montazeri et al. [26] analyzed the effect of physical parameters on the performance of mist spray system. Tissot et al. [27] found that the droplet injection opposite to the incoming air is beneficial to the droplet diffusion, heat exchanger wetting area enlargement and cooling efficiency improvement. Yang et al. [28] verified the performance improvement of air-cooled chillers with water mist system by experiment. Bandhauer et al. [29] adopted the method of microscale liquid–vapor phase to cool the batteries. Wei et al. [30] proposed a hybrid cooling method with PCM cooling, convection and conduction for battery thermal management. Despite of many studies on the spray cooling, the application to the

2. Modeling and solutions 2.1. Physical model The air cooling with water spray evaporation for a battery pack with six battery cells is taken into account in this study. According to the battery box size of electric bus, which is generally 1.065 m (x) × 0.63 m (y) × (0.215–0.245) m (z), a 3D numerical model is developed with a channel size of 1 m long and 0.4 × 0.28 m2 cross section, in which several nozzles (zero, two, or four) in the solid cone form are located at the position of 0.3 m away from the inlet and 0.2 m above the floor. In order to enlarge the diffusion zone of droplets ejected from the nozzles, the spray direction is set opposite to the air flow [27]. The battery cell has the dimensions of 173 mm (z) × 168 mm (x) × 39 mm (y). Due to the symmetry of the physical model, only half of the system is considered to reduce the calculation cost as shown in Fig. 1(a) and (b) with the case of four nozzles as examples, and Fig. 1(c) for the configuration of two nozzles. The heat generation in the battery is assumed uniform, but the thermal conductivity is anisotropic, and other physical properties of the battery are considered homogenous. The Boron Nitride is coated on the battery bodies to enhance the heat transfer and avoid the short circuits and corrosion issue [32], with the material parameters listed in Table 1 [33,34]. 2.2. Mathematical model For the complicated transport process in cooling system, some assumptions are made as follows: 2

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Fig. 1. Schematics of half system with water spray cooling. (a) Geometry and boundary conditions for four nozzles, (b) vertical view for four nozzles, (c) vertical view for two nozzles.

2.2.1. Governing equations For the two-phase flow in BTMS with spray cooling, the thermalflow behavior of water spray evaporation is characterized by the Eulerian-Lagrangian approach. The air flow is assumed as continuous phase by using the Eulerian framework, while the water droplets are

(1) The natural convection and radiation is negligible [35]. (2) The fluid flow is incompressible with constant thermo-physical properties. (3) The heat generation in the battery is uniform.

3

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Table 1 Material properties [13,17].

Table 2 Heat generation rate of 55Ah lithium-ion battery monomer at different discharge rates [16].

Item

Parameter

Value

Sizes of battery Capacity of battery Specific heat of battery Specific heat of BN Density of battery Density of BN Thermal conductivity of battery in X/Ydirection Thermal conductivity of battery in Zdirection Thermal conductivity of BN in X/Ydirection Thermal conductivity of BN in Zdirection Initial temperature

(mm) (Ah) cb (J kg−1 K−1) cB (J kg−1 K−1) ρb (kg m−3) ρB (kg m−3) kb-X/Y (W m−1 K−1)

168 × 39 × 173 55 830 1610 1700 1900 3.4

kb-Z (W m−1 K−1)

34

Only the drag and gravity effects are involved in the force analysis of droplets, and the force balance equation can be expressed as:

kB-X/Y (W m−1 K−1)

30

⎯u d ⎯→ p

kB-Z (W m−1 K−1)

33

dt

(K)

300

(1)

mp0 ΔV

18μCpRep

(5)

∫T

TP

ref

ṁ p0 cP, v dT ⎞ ⎤ ⎠⎥ ⎦ dV ⎟

(6)

The transport equation for water vapor is expressed as,

∂Y ∂ ∂ ⎛ (ρui Yv ) = ρDAB v ⎞ + Sm ∂x i ⎠ ∂x i ∂x i ⎝ ⎟

(7)

The liquid droplet evaporation is calculated by:

= −hm (ρv, s − ρv ) Ap

(8)

where hm is defined as:

hm DP = 2.0 + 0.6Rep0.5 Sc1/3 DAB

(9)

The energy balance equation of the single droplet is expressed by:

dmp dTP = hAp (T − Tp) + Lp dt dt

(12)

(13)

dTc = ∇ (kc ∇Tc ) + Qgen dt

(14)

(15)

(16)

(17)

2.2.2. Numerical approaches and boundary conditions It’s more practical to investigate the thermal performance of battery module by three-dimensional transient simulation. However, this type of CFD simulation will take a large amount of time and require extensive computational resources for various working conditions. Therefore, a steady state three dimensional conjugate heat transfer simulation is adopted to study the flow field and thermal response to the cells. At last, the cell thermal performances at different current discharge rates under typical conditions are studied by three-dimensional transient simulation to justify the steady state assumption. The boundary conditions of cooling system and battery cells are shown in Fig. 1(a). The velocity boundary is set at the inlet of cooling system with the air used for dry cooling. At the outlet of cooling system, the pressure outlet boundary condition with the atmospheric pressure is assigned. The outer surface of tube and cells is specified as non-slip and adiabatic wall boundary. The spray media consist of cooling air, water vapor and distilled water. The droplets with the uniform size are injected by spray nozzles in a solid cone with the angle of 60° and uniform temperature of 300 K. Each spray nozzle has the same flow rate for a specified total water flow rate. The wall boundary is set as “escape” with the droplets terminated and excluded from the further calculation once impacting the walls. The commercial software FLUENT 15.0 is utilized to simulate the performance of the battery. The SIMPLE algorithm is employed for the coupling of pressure and velocity, and the second order upwind differencing scheme is adopted to discretize the governing equations, turbulent kinetic energy and dissipation rate equations.

Se is defined as:



(11)

The convective heat transfer is provided by:





18μ CDRep ρp dp2 24

Qconv = hb A (Tb − Ta)

(4)

∂ ∂P ⎛ ∂T ⎞ (ρcp ui t ) = ki + Se ∂x i ∂x i ⎝ ∂x i ⎠

¯ ΔmP ⎛ m Se = ⎡ P CP , P ΔTp + − Lp + ⎢ mP 0 ⎝ ⎣ mP 0

→ ⎯u − ⎯→ ⎯u ) + g (ρp − ρa ) = FD ( ⎯→ a p ρp

Qtotal = Qconv

(3)

(up, i − ui ) ṁ p Δt



hDP = 2.0 + 0.6Rep0.5 Pr 1/3 k

The radiation heat of the battery module is neglected [31], so the heat transfer equation can be reduced as:

Energy equation:

mp cP, ρ

23.89

Qtotal = Qrad + Qconv

Fi stands for the momentum transfer from droplets to air with the following form,

Sh =

15.60

where Qgen is obtained from the work of Lan et al. [16] at different discharge rates of a single battery cell, as listed in Table 2. The heat transfer between cooling air and the batteries can be expressed as:

(2)

∂τij ∂p ∂ (ρui uj ) = + Fi + ∂x j ∂x i ∂x i

dt

7.60

where the drag coefficient CD can be obtained in [36]. The transient energy equation of the battery is expressed by:

Momentum equation:

dmp

Heat generation rate Qb (W)

FD =

Δmp ṁ p0

24ρP DP2

3C

FD represents the drag force per unit droplet mass with the following form.

Sm accounts for the mass transfer from droplets to air with the following formula expressed:



2C

mCp

∂ (ρui ) = Sm ∂x i

Fi =

1C

Nu =

treated as discrete phase in the Lagrangian framework. The influence of water droplets on the air flow is treated by introducing source terms to the air governing equations. The continuity, momentum and energy equations used for spray cooling are provided as follows. Continuity equation:

Sm =

Discharge rate

(10)

where h is defined as: 4

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2.3. Mesh approach and independence test

4.1. Comparison between dry cooling and spray cooling

For capturing the flow and heat transfer details, the battery cells and their adjacent zones in the flow channel are meshed with very small grids, while for the extended regions the gradually increased grids are generated to save the computational resources. The grid independence is tested to make sure of the simulation accuracy. Three different grids are generated, Mesh-1 with 2411288 cells, Mesh-2 with 3616932 cells and Mesh-3 with 5425398 cells. The grid sensitivity is checked under the condition at the air velocity of 2 m/s and water flow rate of 0.0004 kg/s for four nozzles, with the simulation results listed in Table 3. It can be seen that the maximum relative deviations in the maximum temperature and maximum temperature difference between Mesh-2 and Mesh-3 are both less than 0.5%, so the medium level Mesh-2 scheme is finally adopted to guarantee the acceptable results at a small calculation cost.

Three cases with no nozzles (case 1), two nozzles (case 2) and four nozzles (case 3) are investigated. The cooling performances are discussed at the same air velocity of 2 m/s, and the water mass flow rates of 0.0002 kg/s for both case 2 and 3. When the number of nozzles is changed, the total water flow rate remains constant, namely, the water flow rate of each nozzle is 0.0001 kg/s for case 2 and 0.00005 kg/s for case 3. Fig. 5 shows the air temperature distributions at the cross section of 0.5175 m away from the inlet. For case 1, the air temperature is maintained at 300 K. Fortunately, the low air temperature regions can be observed for both case 2 and case 3 thanks to the water droplet evaporation, with the minimum temperature of about 296 K. Compared with case 2, the low temperature region for case 3 is extended because more nozzles lead to more uniform droplet evaporation inside the channel, which can effectively enhance the heat transfer. Fig. 6 shows the variations of maximum temperature and maximum temperature difference of batteries with the air velocity at the water flow rate of 0.0002 kg/s. In Fig. 6(a), the maximum temperature decreases as the air velocity increases for all cases. Moreover, the maximum temperature is always highest for case 1, while lowest for case 3 due to the air pre-cooling by water spray evaporation. The difference for the maximum temperatures of these three cases is less than 0.5 K when the air velocity exceeds 2 m/s because at high air velocities, the residence time of droplets is reduced and the dry air plays a dominant role in the thermal performance of battery. As can be seen in Fig. 6(b), the maximum temperature difference always appears in case 2. For case 1 in Fig. 5(a), the air temperature is maximum but uniform. For case 2 however, the air temperature at the center of cross section is lower than other parts, resulting in the high temperature difference of batteries. The air temperature is more uniformly distributed for case 3, so the maximum temperature difference is lower than case 2. The spray cooling can effectively reduce the maximum temperature, but gets difficult in reducing the maximum temperature difference, showing that a tradeoff between the maximum temperature and maximum temperature difference of batteries should be taken. The uniformity of battery temperature is mainly affected by air temperature and velocity distributions. The water spray evaporation plays a dominant role in the temperature distribution of air, but has little effect on the velocity distribution. In case 1, the temperature difference of batteries depends on the uneven velocity distribution. In case 2 and case 3, the non-uniform air temperature caused by spray evaporation and uneven velocity together result in the temperature difference of batteries. For case 3, the maximum temperature is always lowest at various air velocities, and the maximum temperature difference is under 5 K when the air velocity exceeds 1.6 m/s, which can meet the requirement for the battery operation. Moreover, the comparison between case 2 and case 3 shows that the number and position of nozzles are of great concern for the spray cooling. Besides, the position of nozzles is related to the battery module spacing, so the cooling performance of batteries can be further improved by optimizing the arrangement of nozzles and

3. Validation of numerical simulation The experiments of battery pack with water spray cooling are rarely involved, so the CFD methods used in this study to simulate the water spray cooling and battery system are tested respectively. The model with the same size as the Alkhedhair’s experiment is developed as shown in Fig. 2. The computational results are compared to Alkhedhair’s data [37], and Table 4 lists the facet average temperatures of the 4.7 m away from the nozzle in the Alkhedhair’s experiment and present simulation, with the average relative error between them less than 10%, justifying the CFD methods used in the water spray cooling in this study. The experiment results from Ye et al. [38] are used to validate the numerical solution of battery system in this study. The average temperature variation of one certain battery cell is shown in Fig. 3, from which can be seen that the simulation results are quite coincide with the experimental data from 0 to 4000 s. Although a deviation between these two results from 4000 s to 7200 s exists, the largest relative error at 7200 s is less than 2%, which is acceptable in practical engineering. These two validation works together prove that the modeling and numerical approaches in this work are reliable enough to predict the cooling performance of lithium battery pack with or without water spray evaporation.

4. Results and discussion When the water is ejected from the nozzle, it breaks up into a large number of small droplets, which greatly increase the contact area between water and the surrounding air. Subsequently, the droplets move together with the air and get evaporated, so the air temperature decreases significantly, and the temperature difference between the battery and air increases. The convective heat transfer is conspicuously enhanced, thus the thermal performance of battery pack gets improved. In order to show the behavior of droplets, the spray streamline colored by residence time and air temperature distribution across the channel for the droplet size of 40 µm at the air velocity of 2 m/s and water flow rate of 0.0002 kg/s are shown in Fig. 4. It can be seen that under the strong drag force of airflow in the opposite direction, the droplets move to the battery with air, which are almost perpendicular to the outlet due to the high velocity of air and short flow path of channel. As a result, the temperature of the battery gets uniformly distributed in the vertical direction. Thanks to the droplet evaporation, the air temperature is clearly reduced as shown in Fig. 4(b). Besides, the low temperature exists at the central part of spray zone with the droplets highly concentrated. The nearly symmetric distribution of air temperature about the horizontal central plane can be observed.

Table 3 Results of grid independent test.

5

Item

Value

Tmax of Mesh-1, K Tmax of Mesh-2, K Tmax of Mesh-3, K ΔTmax of Mesh-1, K ΔTmax of Mesh-2, K ΔTmax of Mesh-3, K Deviation of Tmax between Mesh-1 and Mesh-2 Deviation of Tmax between Mesh-2 and Mesh-3 Deviation of ΔTmax between Mesh-1 and Mesh-2 Deviation of ΔTmax between Mesh-2 and Mesh-3

310.12 310.77 310.94 4.86295 4.80495 4.79519 1.76% 0.45% 1.2% 0.2%

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Fig. 2. Schematics of experimental system in Alkhedhair’s study [37]. Table 4 Comparison between numerical results in this study and experimental data of Alkhedhair [37]. ua (m/s)

Inlet air (°C) Tdb,i Twb,i RH %

1.3 2.5 3.5

34 26.7 29

21.6 18.8 17.8

34.6 48 45

Facet average temperature in Alkhedhair’s study (°C)

Facet average temperature in this study (°C)

28.89 23.6 27.08

30.21 24.94 27.17

Fig. 4. Droplets trajectories and air temperature distribution in channel. (a) Droplets trajectories, (b) air temperature.

Fig. 3. Comparison of numerical results with experimental data of battery.

0.0004 kg/s, which is 5 K higher than that at 0.0001 kg/s as shown in Fig. 7(a) and (d). Moreover, the water spray affected surface areas get enlarged with increasing the water flow rate. The maximum temperature and maximum temperature difference of batteries with four nozzles are obtained at various air velocities of 1.5, 2, 2.5, 3 m/s, and the water flow rates are set 0.0001, 0.0002, 0.0003, 0.0004 kg/s based on the work of Saw et al. [31]. As well known, a suitable temperature range is needed for the battery efficient operation [3], the selection of minimum water flow rate should ensure that the cell temperature does not exceed the upper limit of 40 °C for the normal working of battery. The influence of water flow rate on the

battery spacing. 4.2. Effect of water flow rate The air temperature fields at the cross section of 0.5175 m from the inlet for case 3 at the air velocity of 2 m/s are shown in Fig. 7. When the water mass flow rate increases, the air temperature decreases but the temperature difference gets larger. For example, the air temperature at the mass flow rate of 0.0004 kg/s is lower than that at 0.0001 kg/s, but the maximum air temperature difference is 7 K at the water flow rate of 6

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evaporation ratio is obtained as listed in Table 5, showing that the evaporation ratio decreases as the water flow rate increases. The maximum evaporation ratio reaches 54% of the injected water at the water flow rate of 0.0001 kg/s, but the minimum evaporation ratio is only 47% at 0.0004 kg/s. Fig. 8(a) shows that the maximum temperature is reduced as the water flow rate increases due to the increased flow rate ratio of water to air, but this trend gets weaker. The maximum temperature at the water flow rate of 0.0002 kg/s is reduced by 1 K compared with that at 0.0001 kg/s. However, the maximum temperature varies by only 0.25 K between the water flow rate of 0.0003 kg/s and 0.0004 kg/s. In sum, the excessive increase of water flow rate cannot always take effect to reduce the maximum temperature, because the ability of air to absorb moisture is limited, not all droplets can evaporate completely. Accordingly, the cooling performance is not conspicuously improved due to the constrained evaporation capacity at low air velocities. The maximum temperature difference increases with increasing the water flow rate due to the large air temperature difference, as seen in Fig. 8(b). It shows that too much spray water in practical cooling system is not recommended with the adverse effect on the temperature difference. At the air velocity higher than 2 m/s, the maximum temperature difference is less than 5 K at the water mass flow rate of 0.0003 kg/s. In such a case, the optimal water flow rate is 0.0003 kg/s instead of 0.0004 kg/s. Conclusively, the optimal water flow rate should be determined based on the air velocity. 4.3. Effect of droplet size Fig. 9 shows the air temperature distribution at the air velocity of 2 m/s and water flow rate 0f 0.0002 kg/s with various droplet sizes. It can be seen that the air minimum temperature at the droplet size of 20 µm is about 289 K, which is 11 K lower than ambient temperature as shown in Fig. 9(a). The comparison between Fig. 9(b) and (c) shows that the drop of air temperature gets weakened as the droplet size increases. For the droplet size of 80 µm in Fig. 9(d), the air temperature across the entire section becomes high with the minimum temperature of about 299.2 K, which is close to the ambient temperature. The maximum temperature and maximum temperature difference of batteries at various air velocities and different water droplet sizes are shown in Fig. 10, from which it can be seen that the influence of droplet size on the cooling performance is related to the air velocity. Fig. 10(a) shows that the maximum temperature of batteries decreases with increasing the air velocity. At low air velocities, the small droplets get easy to evaporate and the cooling is enhanced consequently due to the large contact areas. For instance, the evaporation ratio at the droplet size of 20 µm is approximately 92%, while it is only 21% for the droplets of 80 µm at the air velocity of 2 m/s, as listed in Table 5. Moreover, the growth rate of area affected by small droplets is larger than that of large droplets. However, the drop trend of maximum temperature gets weak as the air velocity increases, because the high air velocity results in the short residence time for small droplets, which will be concentrated in a small area due to their low inertia compared with the airflow. For large droplets, they tend to penetrate the flow due to high inertia to drag force ratio, and a great plume is produced at the high air velocity. The effect of droplet size on evaporation is balanced by the effect of penetration. As a result, the maximum temperatures at the droplet sizes of 60 µm and 80 µm decrease slowly at low air velocities but sharply at high air velocities as shown in Fig. 10(a), because the diffusion area becomes enlarged with increasing the air velocity for large size droplets. Fig. 10(b) shows the variations of maximum temperature difference with air velocity at various droplet sizes. The maximum temperature difference at the droplet size of 20 µm is highest while that at the droplet size of 80 µm is lowest. The non-uniform air temperature due to water spray cooling causes the badly distributed temperature of batteries. As shown in Fig. 9(d), the air temperature is highest at the droplet size of 80 µm but shows uniform. The reduced droplet size is effective to reduce the maximum temperature, but

Fig. 5. Air temperature fields at the cross section of 0.5175 m away from inlet at air velocity of 2 m/s and water flow rate of 0.0002 kg/s. (a) No nozzle, (b) two nozzles, (c) four nozzles.

7

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Fig. 6. Comparison of battery performances with different nozzles. (a) Maximum temperature, (b) maximum temperature difference.

unfavorable for the maximum temperature difference. The optimal water droplet size depends on the air velocity. To meet the requirements that the maximum temperature and maximum temperature

difference should be less than 333.15 K and 5 K respectively [3], it is recommended to select the droplet size of 60 µm instead of other sizes when the air velocity is below 2 m/s, however, the droplet size of 40 µm

Fig. 7. Air temperature fields at the cross section of 0.5175 m away from inlet with four nozzles at air velocity of 2 m/s. (a) Water flow rate of 0.0001 kg/s, (b) water flow rate of 0.0002 kg/s, (c) water flow rate of 0.0003 kg/s, (d) water flow rate of 0.0004 kg/s. 8

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batteries can be controlled within 313.15 K and 5 K at the water flow rate of 0.0002 kg/s.

Table 5 Evaporation ratio of water droplets in various cases. Droplet size (µm)

Mass flow rate (kg/s)

Ambient temperature (K)

% of water evaporated

20 40 40 40 40 60 80 40 40 40 40

0.0002 0.0001 0.0002 0.0003 0.0004 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002

298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 308.15 313.15 318.15

94 54 50 49 47 30 21 55 61 66 72

4.5. Unsteady state situation During the fast charging, the battery may not reach the thermal equilibrium state. Therefore, it is more practical to investigate the thermal response of battery cell under various conditions by means of transient simulation. In this work, the cooling performance of BTMS with water spray cooling is compared to that with dry cooling in the transient state to verify the reliability of steady state results. The discharge process takes place at the 2-current (2C) discharge rate, the air velocity of 2 m/s and water flow rate of 0.0002 kg/s. Fig. 12(a) shows the variation of maximum temperature of battery cell with discharge time, from which can be seen that the maximum temperature for spray cooling is always lower than dry cooling. The equilibrium of maximum temperature for spray cooling is about 310.33 K, with the relative error of only 0.046% to the steady simulation. The maximum temperature difference for the spray cooling is larger than that for the dry cooling, as shown in Fig. 12(b). The final equilibrium of maximum temperature difference for spray cooling is about 4.14 K, with the relative deviation of about 3.9% to the steady case. The comparison between the steady and unsteady results shows that the steady state simulation can well predict the BMTS performance with and without spray cooling.

is more suitable when the air velocity ranges from 2 m/s to 3 m/s. 4.4. Effect of ambient temperature Taking the case at the water flow rate of 0.0002 kg/s and droplet size of 40 μm as example, the variations of maximum temperature and maximum temperature difference of batteries with ambient temperature at various air velocities are shown in Fig. 11. From Fig. 11(a), it can be seen that the maximum temperature increases as the ambient temperature increases and the air velocity decreases. The maximum temperature drop gets more conspicuous when the spray cooling operates at a higher air velocity. Moreover, the maximum temperature difference at the air velocity of 1 m/s is larger than that at other air velocities as shown in Fig. 11(b). The maximum evaporation ratio is 72% at 318.15 K as listed in Table 5. But the temperature difference between the battery and air decreases with increasing the ambient temperature, which is adverse to the cooling performance. The higher the ambient temperature is, the stronger the evaporation and consequently the more enhanced the cooling performance, so the air temperature difference gets big at high ambient temperatures, which means that the high ambient temperature results in the increased maximum temperature and maximum temperature difference of batteries. High air velocity can improve the cooling performance, but the fan power consumption increases correspondingly. When the ambient temperature is less than 308.15 K and the air velocity is higher than 2.5 m/s, the maximum temperature and maximum temperature difference of

5. Conclusions The spray cooling is effective to reduce the Tmax, but unfavorable for the ΔTmax. Moreover, the configuration of nozzles plays an important role in the cooling performance of batteries. The Tmax decreases with increasing the water flow rate, but this changing trend gets weak due to the reduced evaporation rate at large water flow rates. The increased water flow rate is unfavorable for the ΔTmax because of the large air temperature difference. The small droplets get easy to evaporate thanks to the large contact area, but the cooling capacity is limited by their low inertia and short residence time at high air velocities. For large droplets, the droplet size effect on evaporation is balanced by the effect of penetration due to their high inertia to drag ratio. As a result, the maximum temperatures at the droplet sizes of 60 µm and 80 µm decrease slowly at low air velocities but clearly at high air velocities.

Fig. 8. Battery performances at different water flow rates and air velocities. (a) Maximum temperature, (b) maximum temperature difference. 9

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Fig. 9. Air temperature fields at the cross section of 0.5175 m away from inlet at air velocity of 2 m/s and water flow rate of 0.0002 kg/s. (a) Droplet size of 20 µm, (b) droplet size of 40 µm, (c) droplet size of 60 µm, (d) droplet size of 80 µm.

Fig. 10. Battery performances at different water droplet sizes and air velocities. (a) Maximum temperature, (b) maximum temperature difference. 10

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Fig. 11. Battery performances at different air temperatures and velocities. (a) Maximum temperature, (b) maximum temperature difference.

Fig. 12. Comparison between dry cooling and spray cooling in unsteady state. (a) Maximum temperature, (b) maximum temperature difference.

The high air velocity leads to the reduced Tmax and ΔTmax. The evaporation ratio increases with increasing the ambient temperature, but the reduced temperature difference between the battery and cooling air results in the increased Tmax. When the ambient temperature is below 35 °C and the air velocity exceeds 2 m/s, the water flow rate of 0.0002 kg/s can ensure the safe operation of battery pack.

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Acknowledgments The financial supports for this research, from the National Natural Science Foundation of China (Grant No. 51776067, 51821004), and the National Basic Research Program of China (Grant No. 2015CB251503) are gratefully acknowledged. References [1] L.H. Saw, Y. Ye, M.C. Yew, W.T. Chong, M.K. Yew, T.C. Ng, Computational fluid

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