Dynamic thermal characteristics of heat pipe via segmented thermal resistance model for electric vehicle battery cooling

Dynamic thermal characteristics of heat pipe via segmented thermal resistance model for electric vehicle battery cooling

Journal of Power Sources 321 (2016) 57e70 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/loca...

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Journal of Power Sources 321 (2016) 57e70

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Dynamic thermal characteristics of heat pipe via segmented thermal resistance model for electric vehicle battery cooling Feifei Liu a, b, Fengchong Lan a, b, Jiqing Chen a, b, * a b

School of Mechanical &Automotive Engineering, South China University of Technology, Guangzhou 510641, China Guangdong Key Laboratory of Automotive Engineering, Guangzhou 510641, China

h i g h l i g h t s  A “segmented” thermal resistance model of a heat pipe is proposed.  Accuracy of “segmented” model is verified by comparing with “non-segmented” model.  Ultra-thin micro heat pipe(UMHP) is compact and effective for EV battery cooling.  The cooling effect of an UMHP pack with natural/forced convection is evaluated.  The thermal performance of an UMHP pack with different arrangements is compared.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 February 2016 Received in revised form 20 April 2016 Accepted 22 April 2016

Heat pipe cooling for battery thermal management systems (BTMSs) in electric vehicles (EVs) is growing due to its advantages of high cooling efficiency, compact structure and flexible geometry. Considering the transient conduction, phase change and uncertain thermal conditions in a heat pipe, it is challenging to obtain the dynamic thermal characteristics accurately in such complex heat and mass transfer process. In this paper, a “segmented” thermal resistance model of a heat pipe is proposed based on thermal circuit method. The equivalent conductivities of different segments, viz. the evaporator and condenser of pipe, are used to determine their own thermal parameters and conditions integrated into the thermal model of battery for a complete three-dimensional (3D) computational fluid dynamics (CFD) simulation. The proposed “segmented” model shows more precise than the “non-segmented” model by the comparison of simulated and experimental temperature distribution and variation of an ultra-thin micro heat pipe (UMHP) battery pack, and has less calculation error to obtain dynamic thermal behavior for exact thermal design, management and control of heat pipe BTMSs. Using the “segmented” model, the cooling effect of the UMHP pack with different natural/forced convection and arrangements is predicted, and the results correspond well to the tests. © 2016 Elsevier B.V. All rights reserved.

Keywords: Electric vehicle battery Heat pipe “Segmented” thermal resistance model Dynamic thermal characteristic Cooling

1. Introduction The issues of the serious energy shortage and environment pollution all over the world have induced the growing opportunity of some alternative energy to fossil fuel as the power for clean vehicles recently [1,2]. For instance, hydrogen could act as a fuel for internal combustion engines (ICEs) and for fuel cells used in fuel

* Corresponding author. Room 1301, Building of Automotive Engineering Institute, No.381, Wushan Road, Tianhe District, Guangzhou City, Guangdong Province, China. E-mail addresses: [email protected] (F. Liu), [email protected] (F. Lan), [email protected], [email protected] (J. Chen). http://dx.doi.org/10.1016/j.jpowsour.2016.04.108 0378-7753/© 2016 Elsevier B.V. All rights reserved.

cell electric vehicles (FCEVs), or the battery as a power source for electric vehicles (EVs) is attractive [3e6]. Among them, the battery is significantly concerned by designers, manufacturers and EVusers about its performance characteristics to satisfy the requirements of an EV, such as good dynamic charging/discharging performance for long driving range, fast acceleration, adequate idle-stop, motor assisting and regenerative braking, and good adaptability to thermal environment from extreme hot summer to cold winter and reliable running safety [7,8]. Therefore, reliable, efficient and safe operation, good cycle lifespan, and superior State of Charge (SOC) and State of Health (SOH) of the battery system especially under highly dynamic driving conditions, have become the key factors for the determination of power, reliability, safety,

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cost and broad application of EVs [9,10]. Among various power batteries, Lithium-ion (Li-ion) batteries are taking an increasing market share for EVs' application because of their outstanding characteristics in higher energy density, longer life-time and lower self-discharge rate [11]. Generally, to achieve sufficient voltages and capacities to power an EV, even hundreds to thousands of cells must be connected in series/parallel to form a large-scale battery module/pack usually working at high frequency charge/discharge rate, which will cause large heat generation with various chemical and electrochemical reactions. However, the performance of Li-ion cells is sensitive to extremely high or low temperature and uneven temperature distribution caused by such reactions. According to the Arrhenius law, the reaction rate increases exponentially with the rising cell temperature; the higher the temperature, the faster the rate of aging [12,13]. As a result, hotter cells degrade more quickly than colder ones, and shorten the lifetime of entire battery pack. Additionally, overheating and nonuniform temperature gradient commonly caused by high currents or internal short-circuiting without rapid and sufficient cooling will trigger the thermal runaway (combustion or even explosion) and failure of cells [14]. Chiu et al. [15] expressed that under 45  C ambient temperature, after 1322 cycles with 0.5C charge/discharge, the capacity of a 26650 Li-ion cell (2.3 Ah) decayed by 17%; while at 60  C, it faded by almost 20% through only 754 cycles. Additionally, at low temperature, electric polarization of the graphite electrode caused by the low diffusivity of Li-ions will cause the loss of power and lifetime of cells [16]. A common phenomenon is that the thermal performance of Li-ion cells deteriorate drastically below 10  C [17]. Consequently, for Li-ion batteries, the optimal operating temperature range is 25  Ce40  C, and the maximum temperature difference is less than 5  C [18,19]. The above issues including thermal safety, stability and uniformity have been crucially considered for a well-designed and highefficient battery thermal management system (BTMS) to ensure the batteries working under their desired temperature range and uniform temperature distribution. Thus, the BTMSs should provide reliable thermal regulation to keep the batteries best performing, and also satisfy the requirements for EVs, such as compactness, lightweight, convenient maintenance, electrical insulation, low power consumption and low cost. Up to now, many researches [20,21] have reported various types of BTMSs for EVs, in which the selection of cooling mediums, the thermal design of cooling systems and the assessment of cooling effect became focused. In general, air, liquid and phase change materials (PCMs) as coolants were more considered; occasionally two or more mediums were combined to improve the cooling effect. Among the above methods, air cooling can be passive/active, parallel/series or natural/forced, and most widely used due to its low cost, availability and easy installation (e.g. Toyota Prius and RAV-4) [22,23]. In fact, even using air forced cooling still cause the non-uniform temperature distribution especially for a large-scale battery pack in EVs [24]. Liquid cooling (e.g. GM Volt and Tesla Model S) usually uses water, glycol or insulated oil as the common coolants, has higher heat transfer coefficient and offers greater cooling capacity than air cooling [25,26]. However, some additional equipment such as pumps, tanks, heat exchangers and valves have to be installed in EVs to cause more occupied space, weight and requirements for leakage protection and complicated maintenance. Furthermore, the relatively high pressure drop across the liquidcooled heat exchangers will lead to significant increased energy consumption and cost of the system [27]. PCMs (e.g. paraffin wax or capric acid) have high thermal energy storage capacity because of the large latent heat in the phase change process with small temperature variations [28]. Therefore, the PCM cooling systems can maintain uniform temperature distribution among the cells closing

to the melting point of PCMs [29]. But suffering from the inherent limitation of low thermal conductivity, PCMs have insufficient long term thermal stability even if adding copper/aluminum foam or carbon fibre [30]. Furthermore, the high cost and the possible liquid leakage caused by the volume expansion after melting have limited the PCM systems widely applied for EVs. The weakness of the above BTMS cooling systems makes it very difficult to meet the thermal requirements for power batteries working at various complex driving conditions. Thus, in demanding for high efficient and low-energy consumption BTMSs, heat pipes have been intensively concerned by researches [31,32]. They make use of phase change heat transfer, evaporate at a heat source (evaporator) and condense at a heat sink (condenser). Furthermore, they possess excellent characteristics such as high thermal conductivity, compact structure, flexible geometry, bidirectional heat transfer characteristics, long service life and convenient maintenance. Therefore, heat pipes have been widely used for cooling and thermal management of various electrical and electronic equipments [33e36]. Recently, heat pipe cooling has been garnering more attention in BTMSs. Rao et al. [37,38] investigated the cooling performance of an oscillating heat pipe (OHP) BTMS by experiments, and concluded that the maximum temperature of battery could be controlled below 50  C when the heat generation was lower than 50 W. Wang et al. [39] provided an experimental characterization of a heat pipe BTMS coupled with liquid cooling, and pointed out that the battery temperature could be kept below 40  C if the heat generation was less than 10 W/cell, and reduced down to 70  C under uncommon thermal conditions (e.g. 20e40 W/cell). Tran et al. [40,41] indicated that adding heat pipe to a battery module would reduce the thermal resistance of a common heat sink by 30% under natural convection and 20% under low air velocity cooling. Also, they compared the measured temperature of battery under adiabatic and forced convections with the simulated data from an AMESim model, in which the temperature within each cell was assumed being homogeneous. Greco et al. [42] proposed a simplified onedimensional (1D) transient computational model of battery using the thermal circuit method in conjunction with the thermal model of heat pipe to analyze the thermal behavior of a heat pipe BTMS. They predicted the maximum temperature of 27.6  C by heat pipes compared with 51.5  C by forced convection, which is in agreement with both the analytical solution and the corresponding threedimensional (3D) computational fluid dynamics (CFD) results. But there are no details about CFD modeling and relevant experimental validation. Ye et al. [43] confirmed an optimized BTMS with heat pipe cold plates (HPCPs) to be feasible on different cooling strategies even during 8C charging by experiments. Also, a simple numerical model was conducted to predict the thermal behavior of the heat pipe BTMS, in which the effective heat transfer coefficient at the surfaces in contact with HPCPs, was estimated from steadystate experimental data. Considering the space and weight constrains of EVs, a heat pipe BTMS needs to be more compact, lighter and of easier installation. Among various heat pipes, micro heat pipes (MHPs) and miniature heat pipes (mHPs) are small scale devices with hydraulic diameter on the order of 10e500 mm and 2~4 mm respectively [44,45]. Zhao et al. [46] demonstrated an experimental study on excellent cooling effect of two different ultra-thin aluminum heat pipe BTMSs with wet cooling by comparing with other four cooling methods (i.e. in ambient, by horizontal/vertical fans and thermostat bath). The above relevant investigations revealed the superior aspects of thermal performance of heat pipe BTMSs compared to other cooling systems mainly based on experiment methods. As known, some different heat transfer phenomena occur within the complicated constitution of a heat pipe, such as thermal conduction, phase

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change, fluid dynamics and the unpredictable thermal boundary conditions. This makes it much difficult to obtain complete and accurate numerical temperature distribution and variation in the heat pipes' heat and mass transfer process in addition to the batteries' transient and high frequency charging/discharging. The computational thermal model of heat pipe BTMSs becomes very complex in CFD simulation including thermal parameters acquirement and thermal boundaries determination. Meanwhile, the compactness and miniaturization of the cooling device for meeting the requirements in optimal geometrical structure and layout for EVs also make it even harder. Thus, our work was motivated by the need to investigate and develop more accurate computational methods to analyze in depth the dynamic thermal characteristics especially in complex heat transfer in and between heat pipes and batteries for optimizing a heat pipe BTMS. A thermal resistance (R) network model using thermal circuit method was developed by Faghri [47] and Zuo et al. [48] to describe the thermal behavior of a heat pipe, where the equivalent thermal conductivity (k f (1/R)) is calculated as the thermal parameter for CFD simulation. In this situation, the pipe is usually simply treated as one conductor (here denoted as “non-segmented” model). In this case, a single parameter (i.e., total equivalent thermal conductivity) is used to reflect the overall thermal performance of the heat pipe. As a result, the variation in heat transfer between evaporator and condenser of the pipe caused by different phase changes is ignored. This will result in dynamic calculation error which affects the exact thermal design, management and control for BTMSs. In this paper, a “segmented” thermal resistance model of a heat pipe was proposed based on the thermal circuit method. The equivalent conductivities of different segments (the evaporator and condenser of pipe), are used to determine their own thermal parameters and conditions integrated into the thermal model of battery for a complete 3D CFD simulation to predict temperature distribution and variation of heat pipe BTMSs. The main contributions of this study are the development of such a computational model and its application to thermal management of a battery pack with heat pipe cooling, and thus to serve as a guide to thermal design and control of heat pipe BTMSs. The remained of this paper is organized as follows: Section 2 describes a Li-ion battery pack with ultra-thin micro heat pipe (UMHP) cooling for EVs; Section 3 proposes a “segmented” thermal model and details the comparison with the “non-segmented” model; the 3D transient thermal model of battery cell is established in Section 4; experimental investigation on the thermal performance of the UMHP pack is carried out in Section 5; then the temperature predictions from the “segmented” model are validated by comparing with the “non-segmented” model, and the cooling effect of the UMHP pack with different natural/forced convection and arrangements are discussed in Section 6; finally, some conclusions are drawn in Section 7. 2. Description of UMHP cooling system In this work, we considered the use of UMHPs to mitigate the temperature rising of a prismatic 3.2 V50 Ah Li-ion battery pack consisting of 5 cells in parallel for EVs. The initial design of the UMHP battery cooling system is shown in Fig. 1(a). Each cell in the pack is numbered from cell 1 to cell 5 along the y direction. Each UMHP (sintered copper-water) is inserted into the cavity between cells to form a sandwiched configuration. The flat UMHP can fit closely to the surface of the studied cells, and more benefit for the compact arrangement of cooling system. The geometry of the cell and UMHP group are present in Fig. 1(b)~(c). There are three groups of pipes with spacing sgp between two adjacent groups in the z direction, and each group has 4 pipes arranged in parallel with

Fig. 1. UMHP battery cooling system: (a) demonstration of the UMHP battery cooling system; (b) geometry of the battery cell; (c) geometry of the UMHP group.

spacing shp in the y direction. To conduct the heat generated by cells more effectively, the evaporator (leva) of each pipe is directly attached to the surface of cells using thermal conductive silicone. The cooling system is combined with air convection on the condenser (lcon1 þ lcon2) of each pipe, and aluminum fins with spacing sfin between two adjacent fins in the x direction are

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combined with the condensers of each group using the thermal conductive silicone. The initial specifications of the UMHP pack are listed in Table 1. 3. “Segmented” thermal modeling of heat pipe 3.1. “Segmented” thermal resistance model proposed In general, the thermal behavior of a heat pipe can be represented by a thermal resistance (R) network model using thermal circuit method [49,50]. The thermal resistance network model of a heat pipe is shown in Fig. 2(a). The heat pipe is a sealed tube filled with working fluid in a saturated state. When the evaporator is heated by cells with the heat transferred from the wall to the wick of evaporator, the vapor is generated on phase change process and carries the heat to the condenser with small pressure difference; then the heat is transferred from the wick to the wall on the condenser dissipated with air convection. The condensed liquid in the condenser is brought back to the evaporator due to the capillary forced of the wick. Thus the process works continuously. In this model, Retac is the contact resistance between the cell and evaporator; Rewall , Rawall , Rcwall (or Rewick, Rawick , Rcwick ) are the thermal resistances due to the wall (or wick) of evaporator, adiabatic section and condenser respectively; the thermal resistances Reva and Rcon are due to the phase change; the thermal resistance Rvap is due to the vapor flow. In the above model, the pipe is usually simply treated as one conductor using “non-segmented” model to calculate the total thermal resistant (Rt) and the total equivalent conductivity (kt f (1/ Rt)) of the pipe as the thermal parameter for CFD calculation. This method was conducted by research [42] to analyze the thermal behavior of a heat pipe BTMS. This simulation calculation uses a single thermal parameter and neglect the influence of the transient heat transfer between evaporator and condenser caused due to different phase changes. It can only reflect the overall thermal performance of a heat pipe, and will result in dynamic calculation error especially when used in BTMSs to get accurate transient thermal behavior, so as to affect the thermal design, management and control. To analyze in depth the dynamic thermal characteristics in and between evaporator and condenser, an accurate computational method is indispensable. In this paper, a “segmented” thermal resistance model of a heat pipe is proposed based on the above network model. For the adiabatic section, Rvap is considerably small and can be neglected from the thermal network without causing significant errors; Rawall and Rawick can be neglected due to the small thickness and length of both the wall and wick. Therefore, the heat pipe is segmented into the evaporator and condenser in the “segmented” thermal resistance model (shown in Fig. 2(b)). For the condenser, the heat within the pipe can be dissipated through two parts: bald pipe (part 1: consisting ofRcon1,Rcwick1 and Rcwall1 in series) and pipe with fins (part 2: consisting of Rcon2, Rcwick2 , Rcwall2 , Rctac and Rfin in series). For the part 2, Rctac is the contact resistance Fig. 2. Thermal resistance models of a heat pipe: (a) thermal network model, (b) “segmented” model and (c) “non-segmented” model.

Table 1 Initial specifications of the UMHP pack. Size

Initial value

Cell(lbat  bbat  dbat) Terminal(ltem  btem  dtem) UMHP(lhp  bhp  dhp) Fin(lfin  hfin  dfin) sgp shp sfin

155 mm  102 mm  10 mm 15 mm  5 mm  1 mm 168 mm  10 mm  1 mm 55 mm  35 mm  0.5 mm 35 mm 10 mm 3 mm

between the condenser and the fins; Rfin is the thermal resistance due to the heat transfer between the fins and the surrounding air flow. Additionally, Retac and Rctac can be neglected because of good thermal conduction using the thermal conductive silicone. Thus, the thermal resistances of different segments (the evaporator and condenser) calculated by thermal circuit method can be used to

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

respectively express their own complex heat and mass transfer performance, and the equivalent thermal conductivity of each segment is obtained to determine the thermal parameters and conditions for 3D CFD simulation.

Rfin ¼

Qpc ¼ 3.2. Algorithm comparison

R ¼

Rewall

þ

Rewick

þ Reva

Le leva and k ¼ e e ¼ e e R A R A

1 Z06

0

4ð1  εÞ

(1)

1

dðxÞ

8 > Lc1 l c > > ¼ ¼ con1 k > c 1 < R1 Ac1 Rc1 Ac1

Rc1 ¼ Rcon1 þ Rcwick1 þ Rcwall1 and Rc2 ¼ Rcon2 þ Rcwick2 þ Rcwall2 þ Rfin > Lc2 lcon2 > c > > : k2 ¼ c c ¼ c c R2 A2 R2 A2

Rcon2 ¼

lcon2 Rcon lcon1 þ lcon2

Rcon ¼

Tv  Tc Qpc Npc

The calculations of Rcwall1 (orRcwall2 ) and Rcwick1 (orRcwick2 ) is similar to those of Rewall and Rewick respectively. hfin is the efficiency of fins; Afin1 is the surface area of heat pipes between fins; Afin2 is the surface area of fins. Cp,l is the specific heat capacity of the working liquid; hfg is the latent heat of the working liquid; (TvTc) is the condensing temperature difference.

lhp Rc1 Rc2 Lt and kt ¼ t t ¼ t t þ Rc2 RA RA

Rc1

(3)

Thus, compared to the “non-segmented” model, the “segmented” model considers the influence of multiple parameters and conditions of a pipe, and can be used to obtain accurate heat transfer variation of the evaporator and condenser caused due to different phase changes. It will be more beneficial to analyze in depth the dynamic thermal characteristics of heat pipes for optimal design of high efficient thermal management system. For the studied UMHP pack in this paper, the calculated results are then obtainedke ¼ 1.06  104 Wm1 K1, kc1 ¼ 8.53  103 Wm1 K1, kc2 ¼ 7.94  103 Wm1 K1 and kt ¼ 5.39  103 Wm1 K1. ke,kc1 and kc2 are set as thermal parameters of the evaporator and condenser for “segmented” model, and kt for the “non-segmented” model in 3D CFD simulation. 4. Thermal modeling of battery cell

(2)

lcon1 Rcon lcon1 þ lcon2

#1=4

m1 ðT v  T c Þdp

Rt ¼ Re þ Rc ¼ Re þ

Aeva

Rcon1 ¼

0

gr1 ðr1  rv Þk31 hfg

dx

pd2p

where,

" hsp ¼ 0:826

3.2.2. “Non-segmented” model For the “non-segmented” model, the heat pipe is simply treated as one conductor. As shown in Fig. 2(c), Rt consists of Re and Rc including Rc1 and Rc2 (presented in Section 3.2.1.). Among them, Rc1 and Rc2 are connected in parallel to formRc, then Re and Rc are connected in series. Finally, Rt is calculated using thermal circuit method, and kt is obtained for CFD simulation, and expressed as

In the above equations, ε is the porosity of wick; dp is the diameter of copper powder particle; (TeTv) is the temperature difference between evaporator (copper powder) and vapor; d(x) is the thickness of liquid film, which is the function of wall distancex; q is the angle of the liquid film evaporation zone on the spherical surface of copper powder. For the condenser, Rc is divided into Rc1 (part 1) and Rc2 (part 2), and expressed as:



dc ¼ k1 hsp

0

ks ½2ks þ k1  2εðks  k1 Þ 2ks þ k1 þ εðks  k1 Þ

Qpe ¼ pdp sinqk1 ðT e  T v Þ

Npe ¼

dc

hfg ¼ hfg þ 0:68Cp;l ðT v  T c Þ

where,

2=3

k1 Acp ðT v  T c Þ

e

8 Lewall > e > > > Rwall ¼ k e > > wall Awall > > > > < LV LH wick wick Rewick ¼ þ v > 2kwick Awick 4kwick Ah > wick > > > > e v > > T  T > > : Reva ¼ Qpe Npe

kwick ¼

1   kf Afin1 þ hfin Afin2



3.2.1. “Segmented” model For the evaporator, Re consists ofRewall , Rewick and Reva in series, and expressed as: e

61

4.1. Thermal model of battery cell The thermal behavior of battery cell is complex because of the heat generation with various chemical and electrochemical reactions varying with charge/discharge rates, temperature and SOC/ SOH [39]. Various mathematical/numerical thermal models from 1D to 3D were developed for temperature prediction of both single cell and multi-cell battery pack. Al Hallaj et al. [51] and Forgez et al. [52] developed a 1D thermal model with lumped parameters to estimate the temperature response of Li-ion batteries. Karimi and Li [53,54] presented a 2D mathematical model to perform detailed temperature simulations of a battery pack cooled by natural and forced convection. Taheri et al. [55] developed a 3D thermal model using global thermo-physical properties to represent the characteristics of the cell to predict the transient thermal behavior of a Li-

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ion battery cell, and thus to be well-suited for the cell design. Additionally, when the capacity and power increases in Li-ion batteries, safety comes to the fore and is necessary in design stage [56]. A thermal-runaway model was developed to study the battery performance in extreme cases based on resistive heat generation reflecting electrochemical phenomena and chemical exothermic reaction heat. Some safety analysis on battery thermalrunaway was focused, including thermal exposure, over charge, electrical short, nail penetration, impact, crush and drop [57,58]. Lee et al. [56] improved the thermal runaway model of a Li-ion battery by combining an additional short circuit model with preexisting electrochemical and exothermic reaction model. They analyzed the influence of each design variable using this integrated model, and concluded some cell design concepts to delay the thermal-runaway. In this study, the transient 3D thermal mathematical model of the studied Li-ion cell is established, and described as [42]:

rCp

vT ¼ V,ðki VTÞ þ q vt

(4)

Based on the geometrical characteristics and thermo-physical properties of the cell multi-layer structure given in Table 2, the thermal parameters can be calculated as follows [42]:

rCp ¼

i k bx 1 i Sr C m ; kx ¼ S i i ; ky ¼ mbat i i i bbat

dbat

i k hz ; k ¼S i i;   z hbat S dyi ki i



imental internal resistances and entropy coefficients to investigate the influence of temperature on cell capacity in a mixed chargedischarge cycle. Damay et al. [63] developed a thermal and heatgeneration coupled model to estimate the temperature variation of a LiFePO4/graphite battery. In this model, the thermal parameters were identified using a thermal network through analytical and experimental methods, and the heat generation is modeled considering entropic heat and electrical losses. In this work, we focused primarily on the thermal behavior of cell during discharge; the heat generation is considered to be the sum of the resistive and entropic heat based on the Bernardi model. But for each cell, the components that can generate heat not only include the core but also the positive and negative terminals due to the Joule heat. The thermal influence of terminals on the cell cannot be ignored. Thus, the heat generation rate of each cell including three internal sources, viz. the core, the positive and negative terminals, can be determined by

qbat ¼

 Qbat 1 dU0 I2 Rd  IT ¼ Vbat Vbat dT

(6)

qpz ¼

Qpz I 2 Rpz ¼ Vpz Vpz

(7)

qnz ¼

Qnz I 2 Rnz ¼ Vnz Vnz

(8)

(5) The following results are then obtained:Cp ¼ 1356.72 J kg1 K1;ky ¼ 0.89 Wm1 K1; kx ¼ kz ¼ 38.63 Wm1 K1 An efficient BTMS requires an optimal thermal design, which relies on a good understanding of the heat generation within the cells. For any thermal model of cells, the highly non-linear heat sources are one of the most difficult to represent. Two approaches are concluded in numerical thermal modeling of heat generation. One is based on an electrochemical model [59], and another is a simplified lumped mass model proposed by Bernardi et al. [60] and frequently used by researches [61]. Recently, Lin et al. [62] presented a thermal model of a 40 Ah Li-ion battery based on exper-

Rd ¼

qcore ¼

Qcore Qbat  Qpz  Qnz ¼ ¼ Vcore Vcore

0 I 2 Rd  IT dU  R  R pz nz dT Vcore (9)

The discharge resistance (Rd) and the open circuit voltage (U0) of the cell are influenced by many factors especially the ambient temperature (T∞) and the value of SOC (S), which can be measured by Hybrid Pulse Power Characterization (HPPC) test [64]. From the analysis on the test results under different T∞ (20e50  C) and S (0.0e1.0) during discharging, Rd and U0 are strongly dependent on T∞ and S, and calculated as: When 0  S  0.5 and 20  C  T∞  50  C,

2 þ 3:18524  104 S  T 0:00567 þ 0:01748S  1:62397  104 T∞ þ 4:4822  106 T∞ ∞ 2 þ 0:07559S  T 1 þ 4:23812S  0:02504T∞ þ 0:2688S2 þ 6:844  104 T∞ ∞

(10)

Table 2 Thermo-physical properties of the battery cell. Battery cell component

Material

Number of layers

Thickness d/m

Density r/(kgm-3)

Heat capacity C/(Jkg1 K1)

Positive terminal Negative terminal Aluminum foil Copper foil Positive electrode Negative electrode Separator sheet Shell

Al Ni Al Cu LiFePO4 Graphite PP/PE/PP Al-plastic film

1 1 17 18 34 36 36 5

1.0E-03 1.0E-03 2.5E-05 1.8E-05 6.8E-05 7.2E-05 2.3E-05 3.5E-04

2719 8900 2719 8933 2910 1550 492 921

871 461 871 385 1339 1320 1978 2300

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

63

4.2. Boundary conditions 4.2.1. Initial conditions The temperature distribution of both cells and UMHPs is the function of space and time, and the initial conditions are written as

Tðx; y:z; tÞjt¼0 ¼ T0

(13)

T0 ¼ T∞ Where T0 is the initial temperature.

4.2.2. Boundary conditions between cells and pipes There are two different boundary conditions between cells and pipes on the heat exchange process: (1) case 1: one side of the cell is cooled by air convection and the other side is cooled by UMHPs; (2) case 2: both two sides of the cell are cooled by UMHPs. Fig. 3. Heat generation rate of the cell core (qcore) during discharging.

Case1: The boundary conditions are presented as:

When 0.5  S  1 and20

C

 T∞  50

 C,

2

Rd ¼ 0:03073 þ 0:26909S  0:80267S þ 1:16833S 4

5

5

 0:83333S þ 0:23333S  1:05538  10

2 3 þ 4:38068  107 T∞  3:48485  109 T∞

T∞

vðTðx; y; z; tÞÞ ke ¼ e ðTðx; y; z; tÞ  T v Þ vy L y ¼ dbat ; ðn1  1Þdbat þ n2 dhp  ky

3

(11)

4 5  6:25  1011 T∞ þ 8:33333  1013 T∞

8 > > vðTðx; y; z; tÞÞ > > ¼0 > > vy > > > > > > < > > > > vðTðx; y; z; tÞÞ ke > > > ¼ e ðTðx; y; z; tÞ  T v Þ ky > > vy L > > > :

Case2:



(14)

1 þ i dbat þ jdhp 2

8 ði þ 1Þdbat þ dhp > > > > < y ¼ ði þ 1Þdbat þ 2dhp > > > > : ði þ 1Þdbat þ 3dhp

8 < i ¼ 1  ðn1  2Þ :

j ¼ 1  ðn2  1Þ

i ¼ 0; 1

(15)

i ¼ 1; 2 i ¼ 2; 3

For a givenT∞, U0 can be expressed as the following format: Where n1 and n2 are the numbers of cells and UMHPs respectively.

U0 ¼ a0 þ a1 S þ a2 S2 þ a3 S3 þ a4 S4 þ a5 S5

(12)

wherea0, a1, a2, a3, a4 and a5 are the constant coefficients. In this work, the initial temperature of the pack is 30  C, which is equal to T∞. From Fig. 3, qcore increases with the decrease of S especially obviously at high discharge rate and the end of discharging (S < 0.2), it ranges from 25.2  103 Wm3 to 34.9  103 Wm3 at 3C rate. Since the materials of positive and negative terminals are different, the values can be obtained: Rpz ¼ 0.128 mU, Rnz ¼ 0.052 mU. In CFD simulation, the function form (i.e., qcore is expressed as the function of T∞ andS) is adopted as the input for the variable internal heat source of the cell core; qpz and qnz are set as the constant internal sources of the positive and negative terminals respectively.

4.2.3. Boundary conditions of cells The heat exchange between cells and the environment depended on convection and radiation. The surface heat transfer coefficient ht is expressed as:

ht ¼ hc þ hr hc ¼ 0:332

kf Re1=2 Pr 1=3 leva



hr ¼

(16)

4  T4 s T∞



T∞  T

Where hc and hr are the heat transfer coefficients of convection and

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radiation respectively. s ¼ 5.67  108 Wm2 K4. 4.2.4. Boundary conditions of UMHPs 4.2.4.1. “Segmented” model. For the evaporator, the heat exchange is mainly through convection and radiation, thus the surface heat transfer coefficient is given asheva ¼ ht. For the condenser, the convection heat transfer takes place when air sweeps the pipe groups horizontally. The surface heat transfer coefficients hcon1(part 1) and hcon2(part 2) can be calculated as follows. Part 1: In this situation, hcon1 is influenced by the feature size, the spacing, the group number and the arrangement of UMHPs, and expressed as

hcon1 ¼ c

kf

lcon1



n Rem f;max Prf

Prf Prw

p1

shp sgp

p2 c4 cz

(17)

Since the UMHPs are arranged in rows, the empirical valuesp1 ¼ 0.25, p2 ¼ 0, c4 ¼ 1.0, cz ¼ 0.9 are adopted. c, m and n are decided by Reynolds number Ref ;max ¼ ðv0 shp =shp  lcon1 Þ lcon1 =mf :Pr ¼ hcp =k. Part 2: For this section, hcon2 is influenced by the geometry and arrangement of the fins in the heat transfer between the fins and the surrounding air flow, and is described as

hcon2

k  0:681 1=3 sfin ¼ 0:134 f Ref Prf lcon2 hfin

!0:2

sfin

dfin

!0:1134 (18)

±2  C, is used to capture surface temperature distribution and also to check the accuracy of the thermocouples. To test the cooling effect of the pack with air convection, three helicoidal fans (80  80 mm of dimension) are installed to blow air in parallel toward the condensers of three pipe groups, which can be driven by the power control with different fan speeds. A programmable temperature & humidity chamber ranged from 70 to 150  C with an accuracy of ±0.5  C helps to change the working (ambient) temperature of the UMHP pack for testing, and to ensure accurate temperature regulation and good thermal insulation performance. Considering the symmetry of temperature distribution in the pack, the thermocouples are arranged from cell 1 to cell 3, shown in Fig. 4(c). Among them, Tb1 ~ Tb14 are used to measure the temperatures of the pack (Tb1 ~ Tb4, Tb5 ~ Tb8 and Tb9 ~ Tb14 for the temperature uniformity of cells 1e3 respectively), and Tp1 ~ Tp6 are used to test the temperatures of UMHPs (Tp1 ~ Tp3 and Tp4 ~ Tp6 for the temperatures of evaporators and condensers respectively). Through the comparison of the measured temperatures, the maximum/minimum temperatures and the temperature gradients in pack and cell levels can be obtained. In this study, under the ambient temperature of 30  C, the UMHP pack with S ¼ 0.0 was firstly charged at 0.5C constant rate until S ¼ 1.0 (with 3.65 ± 0.03 V charge cut-off voltage); then the temperature variation of the pack was tested at 1 ~ 3C constant discharge rates until S ¼ 0.0 (with 2.5 V discharge cut-off voltage) with different natural/forced convection and different arrangements between cells and pipes. Each test condition was experimented three times. For all the tests, the temperature deviation measured at the same location of the UMHP pack was lower than 1.5  C. Hence, the mean measured temperature was reported in this paper. 6. Results and discussions 6.1. Model verification

4.2.4.2. “Non-segmented” model. In this situation, the heat transfer between UMHPs and the environment can be interpreted as the average effect of convection and radiation on evaporator (heva) and forced convection on condenser (hcon1 andhcon2). Thus, a total convection heat transfer coefficient (ht) is set as the boundary condition of UMHPs, and is calculated as

ht ¼ ðheva þ hcon1 þ hcon2 Þ=3

(19)

5. Experimental set-up A 3.2 V50 Ah, prismatic Li-ion battery pack (5 cells in parallel) with UMHP cooling is taken as a sample for test, shown in Fig. 4(a). Each cell in the pack is numbered from cell 1 to cell 5, which is consistent with the initial model as presented in Fig. 1(a). Fig. 4(b) describes the test rig for experimental evaluation. A Digatron battery test system (BTS-600) is used to control the charging/discharging for the pack with different rates. In order to obtain the detail temperature distribution of the UMHP pack during operation, 20 K-type thermocouples with an uncertainty of ±1.5  C are arranged, including 4 thermocouples on the surface cell, 10 embedded into the pack and 6 on the UMHPs, shown in Fig. 4(c). Temperatures at different locations of the pack are measured by DHDAS dynamic signal analyzer, and recorded every 10 s by the control computer. Also, a FLUKE Ti25 infrared thermal imaging camera with a spectral range of 7.5e14 mm, a test temperature range of 20e350  C, a resolution of 0.01  C and an accuracy of

There are some main indexes to assess the thermal performance of the UMHP pack: the maximum temperature of the pack Tmax, the maximum temperature difference of the pack DTmax,pack (defined as the difference between Tmax and the minimum temperature of the pack), the maximum temperature rising of the pack DTmax (defined as the difference between Tmax andT∞) and the maximum temperature difference of the cell DTmax,cell (defined as the difference between the maximum and the minimum temperatures of each cell). The predicted temperature distribution of the UMHP pack with the “segmented” model compared to the “non-segmented” model at the end of 1~3C discharge under natural convection is shown in Fig. 5(a)e(b). The temperature of the pack is increased with the rising discharge rate, the temperature distribution shows similar for the both models. The maximum temperature region concentrates at the center of the pack towards the positive terminal. Tmax appears on the positive terminal of the cell 3 (measured byTb9). Moreover, the temperature is reduced gradually from the center cell to the outside cell. The minimum temperature region appears on the edge of the outside cell described byTb4. Tmax and DTmax,pack can reach 51.8  C and 7.8  C with “segmented” model, and 54.6  C and 9.0  C with “non-segmented” model respectively at 3C rate. The temperature distribution of the UMHP pack at the end of 1~3C discharging was visualized through the infrared thermal imaging camera, as presented in Fig. 5(c). The maximum temperature region from tests also appears in the center of the pack towards the positive terminals, this finding agrees with our assumption that the thermal influence of the terminals on the cell cannot be ignored; Tmax and DTmax,pack are 52.6  C and 8.4  C at the end of 3C discharge

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

65

Fig. 4. Demonstration of (a) the battery pack with UMHP cooling, (b) the test rig and (c) arrangement of thermocouples.

respectively. The test temperature distribution is in better agreement with the simulation from “segmented” model than that from “non-segmented” model. Moreover, the temperature profiles obtained from model simulations and experimental measurements through K-type thermocouples are shown in Fig. 6. Fig. 6(a) illustrates a comparison ofDTmax, DTmax,pack and DTmax,cell at 3C rate. The transient variations of the simulated DTmax from the two models show much different.

For the “non-segmented” model, since Rt is equivalent to be increased by 63.8%, 31.6% and 22.2% more than Re, Rc1 and Rc2 with “segmented” model respectively, DTmax is increased sharply at the initial discharge (aboutS > 0.7), then flattens gradually until the end of discharge; the error between simulation and tests appears great when 0.2 < S < 0.9, the maximum value can reach 11.6  C at S z 0.56. For the “segmented” model, the initial rising rate of DTmax is increased slowly due to ke > kt, then quickly when S < 0.65

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F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

Fig. 5. Temperature distribution of the UMHP pack at the end of 1~3C discharge rates with (a) “segmented” model, (b) “non-segmented” model and (c) through thermal imaging.

because of the increased heat generation of cells and time accumulation at the end of discharging; these simulation results correspond well to the experimental data (DTmax, DTmax,pack and DTmax,cell are 22.4  C, 8.1  C and 5.2  C from tests at the end of discharge). Fig. 6(b) presents the temperature variation of UMHPs at 3C rate. The heat generated from cells can be conducted to the evaporators immediately as the UMHPs directly pasted on the surface of cells. This causes the temperature of the evaporator (Tp1) varying in a similar way with the cells for the two simulation models. The temperature of condenser (Tp4) is lower than the correspondingTp1; the difference between Tp1 and Tp4 is increased gradually with the discharge time, but the maximum value is no more than 1.5  C. At the end of discharge, Tp1 and Tp4 can up to 47.1  C and 45.9  C

respectively with “segmented” model and 49.8  C and 48.3  C respectively with “non-segmented” model. From the tests, these values are 47.3  C and 46.1  C. Consequently, the validation of the 3D CFD model showed that the proposed “segmented” thermal resistance model of a heat pipe integrated into the cell's thermal model is of higher precision than the “non-segmented” model. Hence, the proposed model can be used for an accurate temperature estimation of the UMHP pack. 6.2. Influence discussion 6.2.1. Natural/forced convection To improve the cooling effect of the UMHP pack, the forced convection is applied on the condensers by adding fans. The

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

67

Fig. 7. Comparison between calculated and measured temperature (Tb12) at 2C rate with different cooling conditions.

Fig. 6. Temperature variations of (a) the UMHP pack and (b) the UMHPs from simulations and measurements through thermocouples at 3C rate.

simulatedTmax, DTmax,pack and DTmax,cell at the end of 1~3C discharge with different cooling systems (methods: 1) ambient without

UMHPs; 2) forced convection without UMHPs; 3) UMHPs with natural convection; 4) UMHPs with forced convection) are listed in Table 3. The results indicate that there is more excellent dissipation performance for the pack equipped with UMHPs than that without pipes. Especially for the method 4, Tmax is found to be lower than 40  C below 2C rate at 4 ms1 fan speed, DTmax,pack and DTmax,cell are all below 5  C under 1~3C rates. Even at the end of 3C discharge, DTmax,pack is only 4.3  C, but 7.8  C with method 3 and 8.9  C with method 1. The improved temperature distribution inside the pack is mainly due to the involvement of UMHPs with forced convection, which has higher heat transfer coefficient and can conduct the heat from the center region of the pack to the ambient more efficiently than that with natural convection. Additionally, the cooling effect of the pack with method 4 is obviously better than that with method 2 under the same power consumption of fan. Fig. 7 describes the comparison between calculated and measured Tb12 at 2C rate with different cooling conditions. With method 1, Tb12 experiences a sharp rise with the proceeding of discharge (or the decreasing ofS). With method 2, the rising of Tb12 can be decreased slightly. For method 3 and method 4, adding UMHPs can make Tb12 decrease from the beginning of discharge (S z 0.95). This indicates that pipes have started work at that instant, here, Tb12 is about 31.1  C. But for method 3, the increasing rate of Tb12 has a rising trend whenS < 0.3

Table 3 SimulatedTmax, DTmax,pack and DTmax,cell at the end of 1~3C discharge rates under different cooling conditions. Cooling methods

C Rate

Tmax/ C

DTmax,pack/ C

DTmax,cell/ C

Method 1: Ambient without UMHPs

1C 2C 3C 1C 2C 3C 1C 2C 3C 1C 2C 3C

46.7 51.8 59.1 43.3 46.6 53.5 41.6 44.7 51.8 36.2 39.9 43.9

6.3 7.9 8.9 5.9 7.1 8.3 5.6 6.7 7.8 3.5 4.1 4.3

4.6 4.8 6.0 4.4 4.5 5.8 4.2 4.4 5.4 2.8 3.2 3.6

Method 2: Forced convection without UMHPs

Method 3: UMHPs with natural convection

Method 4: UMHPs with forced convection

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due to the possible dry-out phenomenon in UMHPs. These findings suggest that heat pipe cooling with forced convection is capable of improving the dissipation and is preferred in BTMS designs. 6.2.2. Different arrangement Considering the thermal influence of terminals on the cell, the temperature variations of two different arrangements between UMHPs and cells at 3C discharge rate are compared. The discussion is mainly based on the arrangements that the condensers are arranged closed to the positive terminals (Case 1) and the negative terminals (Case 2). The Case 2 has been analyzed in section 6.1, so the results are used to compare with that of Case 1. As shown in Fig. 8(a), the temperature rising rate of the positive terminal (Tb5) under Case 1 is obviously less than that under Case 2. However, for the negative terminal (Tb6), the opposite trend is observed whenS > 0.55. It can be concluded that, when the positive (or negative) terminal is close to the condenser, the heat which accumulated on the region of positive (or negative) terminal can be conducted rapidly through the UMHPs. Therefore, Tb5 and Tb6 can reach 48.9  C and 48.3  C under Case 1 at the end of 3C discharge, but up to 50.2  C and 49.1  C under Case 2. The variation trends of the surface temperature at the center of cell 2 (Tb7) between Case 1 and Case 2 are similar, the temperature of Case 1 is the average of 1.5  C less than that of Case 2 during discharging. WhenTb5, Tb6 and Tb7 are up to 40  C, S is 0.10, 0.05 and 0.08 respectively for Case 2 more than that for Case 1. From Fig.8(b), the temperature rising of evaporators and condensers with Case 1 are all lower than that with Case 2. But at the same temperature measurement point, the maximum temperature difference between Case 2 and Case 1 is no more than 1.5  C. As presented in Fig. 8(c), the simulatedTmax, DTmax,pack and DTmax,cell of Case 1 at the end of 3C rate are 20.2  C, 7.2  C and 4.6  C respectively, which correspond well to the measured values 20.5  C, 6.4  C and 4.1  C respectively. Therefore, the conclusion can be found that the dissipation performance of Case 1 is better than that of Case 2, but the effect is not obvious which is confined by the maximum heat transfer power of UMHPs with natural convection. 7. Conclusions As a power source of EVs, the battery usually works with transient and high frequency charging/discharging in a severe dynamic thermal environment. Its instant dissipation and thermal management becomes very important. In this work, the high efficient UMHP is adopted for effective cooling to meet the requirements of EV batteries, instead, it increases the difficulty of structure design and dynamic thermal analysis for BTMSs. This investigation focused on the solution to the complex heat and mass transfer in the complicated constitution of a heat pipe. With calculation method by proposed thermal resistance modeling, it revealed the dynamic thermal behavior in and between cells and pipes for improved thermal design, management and control of BTMSs. Based on the results obtained from the simulation and experiments, the conclusions are summarized as follows.

Fig. 8. Temperature variations of (a) the cell 2 and (b) the UMHPs between Case 1 and Case 2; (c) Comparison of calculated and measuredDTmax,DTmax,pack, and DTmax,cell under Case 1 during 3C discharging.

(1) To accurately analyze the dynamic thermal characteristics of UMHP pack, the “segmented” thermal resistance model of a heat pipe is proposed to describe the heat and mass transfer performance of different segments, viz. the evaporator and condenser. The equivalent conductivity of each segment is used to determine its own thermal parameters and

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70

(2)

(3)

(4)

(5)

conditions integrated into the thermal model of battery for a complete 3D CFD simulation. The proposed “segmented” model is verified more precise than the “non-segmented” model by estimating temperature distribution and variation of the UMHP pack. UMHP combined with air convection can be a compact, effective and low-energy consumption solution to reduce the maximum temperature and mitigate the gradient of the pack under 1~3C constant discharge rate. Adding UMHPs can make Tmax decrease about 7.1  C from the beginning of discharge (S z 0.95) at 2C rate compared with that without pipes. The start temperate of the pipe is about 31.1  C (T∞ ¼ 30  C). UMHP cooling with natural convection is not sufficient to keep the pack operating within its desirable temperature range due to the possible dry-out phenomenon in heat pipes especially at the end of discharging. For better heat evacuation, the forced convection caused by fan or ventilation needs to be coupled with the heat pipe system. UMHP cooling with forced convection can handle instant increases of heat generation more efficiently than forced convection without pipes under the same power consumption of fan. Consequently, Tmax is kept below 40  C for discharge rate lower than 2C with a fan speed of 4 ms1, DTmax,pack and DTmax,cell are all below 5  C during 1 ~ 3C discharging. The thermal influence of terminals on the cell cannot be ignored to obtain accurate temperature distribution of the pack in 3D CFD simulations. Considering the thermal impact of the positive terminal is greater than the negative one, when the condenser is close to the positive terminal, the maximum temperature of the cell can be more suppressed because the heat can be conducted more rapidly through the UMHP than closing to the negative terminal.

Moreover, the liquid cooling or PCM may be considered to be coupled with the heat pipe system to enhance the dissipation performance of BTMSs. In future, the heating properties of UMHPs for battery pack at low temperature will be further researched using the bidirectional characteristics of pipes. Acknowledgements This work was supported by the National Natural Science Foundation of China (51375170) and Science and Technology Planning Project of Guangdong Province (2013B010405007/ 2013B090600024/2014B010125001). References [1] H. Fathabadi, J. Power Sources 245 (2014) 495e500. [2] C.H. Zheng, G.Q. Xu, S.W. Cha, Q. Liang, Int. J. Precis. Eng. Manuf. 16 (2015) 197e202. [3] L.Z. Ouyang, H. Zhong, Z.M. Li, Z.J. Cao, H. Wang, J.W. Liu, X.K. Zhu, M. Zhu, J. Power Sources 269 (2014) 768e772. [4] L.Z. Ouyang, X.S. Yang, M. Zhu, J.W. Liu, H.W. Dong, D.L. Sun, J. Zou, X.D. Yao, J. Phys. Chem. C 118 (2014) 7808e7820. [5] L.Z. Ouyang, Z.J. Cao, L.L. Li, H. Wang, J.W. Liu, D. Min, Y.W. Chen, F.M. Xiao, R.H. Tang, M. Zhu, Int. J. Hydrogen Energ. 39 (2014) 12765e12772. [6] Z.H. Rao, S.F. Wang, Renew. Sust. Energ. Rev. 15 (2011) 4554e4571. [7] M.R. Giuliano, S.G. Advani, A.K. Prasad, J. Power Sources 196 (2011) 6517e6524. [8] Y.L. Yang, X.S. Hu, H.X. Pei, Z.Y. Peng, Appl. Energ 168 (2016) 683e690. [9] Y. Zou, X.S. Hu, H.M. Ma, S.B. Eben Li, J. Power Sources 273 (2015) 793e803. [10] X.S. Hu, R. Xiong, B. Egardt, IEEE Trans. Industrial Inf. 10 (2014) 1948e1959. [11] Y.S. Choi, D.M. Kang, J. Power Sources 270 (2014) 273e280. [12] R. Mahamud, C. Park, J. Power Sources 196 (2011) 5685e5696. [13] Y.L. Yang, X.S. Hu, D.T. Qing, F.Y. Chen, Energies 6 (2013) 2709e2725.

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Nomenclature A: Surface area of heat transfer[m2] b: Width[m] C: Specific heat capacity[Jkg1 K1] h: convective coefficient[Wm2 K1] I: Current[A] k: thermal conductivity[Wm1K1] L: Thickness of heat transfer[m] l: Length[m]

70 m: Mass[kg] Q: Internal power[W] q: Heat generation rate[Wm3] R: thermal resistance[KW1] T: temperature[ C] t: Time[s] U0: Open circuit voltage[V] V: Volume[m3] v: Speed[ms1] Greek symbols

r: Density[kgm3] d: Thickness[m] m: Dynamic viscosity[m2s1] Superscripts c: Condenser e: Evaporator H: Horizontal V: Vertical

F. Liu et al. / Journal of Power Sources 321 (2016) 57e70 v: Vapor t: Total Subscripts bat: Battery con: Condenser core: Core of battery eva: Evaporator f: Fluid fin: Fins of heat pipe hp: Heat pipe l: Liquid(water) nz: Negative terminal p: Copper powder pz: Positive terminal s: Solid(copper) tac: Contact surface tem: Terminal of battery vap: Vapor flow wall: Wall of heat pipe wick: Wick of heat pipe