Transient thermal analysis of a lithium-ion battery pack comparing different cooling solutions for automotive applications

Transient thermal analysis of a lithium-ion battery pack comparing different cooling solutions for automotive applications

Applied Energy 206 (2017) 101–112 Contents lists available at ScienceDirect Applied Energy journal homepage: Trans...

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Applied Energy 206 (2017) 101–112

Contents lists available at ScienceDirect

Applied Energy journal homepage:

Transient thermal analysis of a lithium-ion battery pack comparing different cooling solutions for automotive applications


Armando De Vitaa, , Arpit Maheshwaria, Matteo Destroc, Massimo Santarellia, Massimiliana Carellob a b c

Department of Energy (DENERG), Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy Department of Mechanical and Aerospace Engineering (DIMEAS), Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy Lithops S.r.l., Strada Del Portone 61, Torino 10137, Italy

H I G H L I G H T S experimental set-up is designed and developed for thermal characterization of a Li-ion battery. • An generation and internal resistance profile at various C-rates (1C, 2C, 5C and 8C) are studied. • Heat entropic coefficient and internal resistance determination with temperature dependence were performed. • Heat • A battery thermal model is developed and used in a CFD-3D software for cooling methods analysis.



Keywords: CFD Air/liquid cooling battery pack Entropy heat coefficient Internal resistance determination

This paper presents a computational modeling approach to characterize the internal temperature distribution within a Li-Ion battery pack. In the mathematical formulation both entropy-based and irreversible-based heat generation have been considered; combined with CFD software in order to simulate the temperature distribution and evolution in a battery pack. A prismatic Li-ion phosphate battery is tested under constant current discharge/charge rates of 1C, 2C, 5C and 8C. Model parameters (in particular, the entropic heat coefficient and the internal resistance) needed for the calibration of the model are determined using experimentation. The model is then used to simulate two different strategies for the thermal control of a battery pack in case of car application: an air-cooling and a liquid-cooling strategy. The simulation has highlighted the pros and cons of the two strategies, allowing a good understanding of the needs during the process of battery pack design and production.

1. Introduction Since the performance, life, safety and reliability of Li-Ion batteries are quite dependent on the operating temperature, great interest has been devoted to study cooling solutions and control algorithms for thermal management. Temperature affects battery in many ways: operation of the electrochemical system, round trip efficiency, power and energy available, safety and reliability, life and life-cycle cost. There are different approaches to study thermal behavior in the battery. These approaches can be broadly categorized into computational and experimental approaches. Detailed studies of the temperature distribution within Li-Ion battery cells during charging and

discharging conditions have been proposed by several authors [1–4]. Computational approaches mostly consist of studies conducted utilizing FEM (Finite Element Method) thermal simulations and are often coupled with detailed models that characterize the electrochemical reactions and transport phenomena that take place inside a battery pack. Such simulations are extremely useful to gain understanding on how the temperature distribution affects the performance of a battery cell. Moreover, they also provide important information for cell modeling and design; for instance, they can help in identifying hot spots. However such tools are too complex to be applied to studies oriented to the characterization of the electro-thermal performance of modules and battery packs, or to the design of battery cooling systems and control algorithms, especially developed for on-board applications due to the

Corresponding author. E-mail address: [email protected] (A. De Vita). Received 18 March 2017; Received in revised form 17 August 2017; Accepted 19 August 2017 Available online 24 August 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

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complexity of the model. In EV/HEV applications, a thermal model that could predict battery temperature under various charging and discharging conditions is necessary for developing thermal management algorithms and cooling strategies. To achieve these objectives, the model must be both sufficiently simple to be executed quickly, and accurate enough to provide a reasonable estimation of thermal dynamics inside the cell. Computationally efficient models that can provide a reasonable estimate of the cell thermal profile can be useful tools for battery pack designers and integrators. Experimental approaches to study thermal behavior have also been attempted. Some researchers have installed thermocouples insides the battery (or on the battery surface [5]) to measure internal temperature [6,7]. It should be noted that thermocouples inserted into cells increase manufacturing costs (especially for large battery capacity) and represent a potential safety threat. Moreover, the surface measured temperature can only describe the trends of core temperature changes rather than the real time changes because the heat conduction between the heat source and battery surface is not instantaneous [8]. This means that a thermal runaway cannot be detected only with surface temperature monitoring. For some applications, this can be critical especially with high C-Rates [9]. Hence, the core temperature estimation is not an appropriate method for industrial applications. In these applications constructing a thermal model to predict the internal temperature with a Computational Fluid Dynamic CFD simulation is a promising approach to estimate a battery’s thermal state. Ye and his team [10], designed and analyzed the thermal behavior of a cylindrical Li-ion battery pack using a computational fluid dynamic analysis to investigate the air cooling system for a 38,120 cell battery pack. The Heat generated by the cell during charging was measured using an accelerating rate calorimeter. This method provides a simple way to estimate thermal performance of the battery pack when the battery pack is large and full transient simulation is not viable. Lin [11] designed an adaptive observer method based on a two-state thermal model to estimate the core temperature. However, Lin’s model ignored the effect of heat generation caused by entropy changes. Although this contribution is relatively small compared with the overpotential heat generation, it can influences the thermal behavior significantly. Especially, the contribution from entropy changes can be high for some battery chemistries [12]. Forgez’s [13] thermal model considers the entropy change, but it lacks a quantitative analysis of the influence of heat generation. This work aims at developing a thermal model taking into account the entropy change. This model is also used in Lin’s [11], Forgez’s [13] and Zhu’s [5] model research works. What differs is that the entropy change is considered in the heat generation formulation through experimental tests to get the entropy coefficients, showing its influence in the CFD simulations. Furthermore, empirical relationship between the internal resistance (the irreversible heat) and the temperature of the cells is found. Hence, the model is combined with a CFD code in order to make predictions about the cooling power needed to operate the battery pack under safety conditions. The simulation has highlighted the pros and cons of the two strategies (air and liquid cooling), allowing a good understanding of the needs during the process of battery design and production. These indications are now used for a re-design of the battery pack that will be tested allowing a second step of validation of the model in a subsequent paper.

Fig. 1. Lithops pouch-type cell.

throughout the battery and changes in temperature over time are assumed to be determined by the following processes: reactions, changes in the heat capacity of the system, phase changes, mixing, electrical work and heat transfer with the surroundings. However, not all the processes contribute equally to the heat generation within the cell. For electrochemical systems with good transport properties, the heat from mixing can usually be neglected [15]. In addition, if all species taking part in the electrochemical reactions within the cell are in the same phase, the phase change terms are zero. Therefore, a simplified form of the equation proposed by Bernardi [14] can be used as the expression for the heat source in the lithium-ion cell tested in this paper:

qṪ = I ·(V −U avg ) + I ·T ·

∂U avg ∂T


where: I is the current delivered by the Li-ion cell, the difference between V and Uavg is the cell overpotential, and it is indicative of the irreversibility such as ohmic losses in the cell, charge transfer overpotentials at the interface, and mass transfer limitations. The first term on the right side of the Eq. (1), the overpotential multiplied by the current, is known as the polarization heat and is composed of the Joule heating within the battery as well as the energy dissipated in electrode overpotential. This term is always positive (the sign convention adopted here makes the current positive during charge). This equation takes the form of the heat source that is most commonly encountered in literature [16–19]. The overpotential heat can be described using the equation:

qṖ = I ·(V −U avg ) = I 2·Rint


In this way, the overpotential heat can be determined from the internal resistance, Rint. This yields the equation for the heat source:

qṪ = I 2·Rint + I ·T ·

∂U avg ∂T


The second term on the right side of the Eq. (3) is the reversible entropic heat, which is related to the entropy change, and the potential derivative with respect to temperature is often referred to as the entropic heat coefficient or temperature coefficient. This term can be either positive or negative. In order to avoid confusion, from now on the term ∂Uavg / ∂T will be represented by dV/dT. Positive (negative) values indicate that the effect of entropic heat is exothermic (endothermic) during discharging/charging processes.

2. Thermal modeling The thermodynamic energy balance for Li-ion batteries has been discussed in detail by Bernardi et al. [14]. In the derivation of the energy balance, the temperature of the battery is assumed uniform 102

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Fig. 2. Voltage relaxation method applied at constant temperature (45 °C) during charging process.

Fig. 3. OCP curves for discharging and charging process at 25 °C.

Fig. 4. Entropy coefficient for SOC = 20% referred to the 1st cell during charging process.

3. Experimental

if kept at high voltage for a prolonged time. As a trade-off, its lower nominal voltage of 3.3 V/cell reduces the specific energy below that of cobalt-blended lithium-ion. With most batteries, cold temperature reduces performance and elevated storage temperature shortens the service life, and Li-phosphate is no exception. Li-phosphate has a higher self-discharge than other Li-ion batteries, which can cause balancing issues with aging. This can be mitigated by buying high quality cells and/or using sophisticated control electronics, both of which increase

Prototype lithium-ion cells produced by Lithops were used as sample cells to validate our model. Li-phosphate offers good electrochemical performance with low resistance. The key benefits are high current rating and long cycle life, besides good thermal stability, enhanced safety and tolerance if abused. Li-phosphate is more tolerant to full charge conditions and is less stressed than other lithium-ion systems 103

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Fig. 5. Entropy Coefficient Curves (ECC) with the change of SOC.

the cost of the pack. Cleanliness in manufacturing is of importance for longevity. The experimental results here described were obtained directly through cell testing at the facilities present in Lithops, the first Italian Li-Ion technology developer and provider. Prototype pouch cells under study were assembled in Lithops with LiFePO4 and graphite based electrodes and 1 M LiPF6 in EC: DEC (2:3 w/w) + 1% VC as liquid electrolyte. In this paper, the study was conducted on Lithium iron phosphate (LFP) – Graphite prototype pouch cells produced by Lithops.

Table 1 Polynomial parameters for charging/discharging process.

1 2 3 4 5



1.7071e−10 −1.7798e−7 2.9653e−5 2.3538e−3 −3.410e−1

−3.5439e−9 1.9636e−6 −3.9161e−4 2.8576e−2 −2.499e−2

Fig. 6. Vterminal for charging (top) and discharging (bottom) processes at constant temperature (25 °C) for 1C and 2C rates.


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Fig. 7. Vterminal for charging (top) and discharging (bottom) processes at constant temperature (25 °C) for 5C and 8C rates.

and a C/2-rate would be 2.75 A. In these conditions, the measured capacity was around 5.5 Ah, corresponding to the expected nominal capacity. Starting from a discharged cell (2.5 V cut-off), the cells were charged/discharged repeatedly using CC-CV procedure till 3.6 V and the current cut-off of 10 mA.

For this particular prototype cell the electrolyte was selected and designed for sub-ambient temperature operation. The active materials (LFP/graphite) are commonly used in batteries market, especially graphite that is the most common choice for anodic electrodes. LFP was selected in Lithops because of its thermal stability, for the absence of heavy metals and for its low production cost. The dimensions of this pouch-type cells are: 4 mm thick, 164 mm wide and 296 mm long (see Fig. 1). Nominal cell voltage is 3.3 V and the nominal capacity is 5.5 Ah. Depending on the conditions of discharge (current-rate, temperature, and discharge protocol, etc.) and the cells operational history (previous conditions of charge and discharge), the nominal capacity may be different or could have changed in relation to the initial value. In order to validate the results obtained from the sample cell evaluated here and to exclude any dependence of the previous testing conditions, four similar pouch-type cells were tested. The electrochemical response of the tested cells was investigated by the use of a Solith Fomation Unit (model MFC96). This instrument allows charging/discharging cells up to 5 V–50 A, offering the possibility to control three different cell testing ambient with a temperature range from 10 °C to 55 °C ± 1 °C. Cells were placed in Plexiglas custom-made holders (150 mm thickness). These maintained a comparable pressure in all cells and prevented the current collectors from being pulled apart or bended. Nominal capacity values were confirmed by the average values obtained during preliminary test consisting of 3 charge/discharge cycles at 1C-rate and 25 °C. C-rate is here adopted as a measure of the currentrate at which the cell is discharged relative to its nominal capacity. A 1C rate means that the discharge current will discharge the entire cell in 1 h. In this case, for cells with a nominal capacity of 5.5 Ah, this equates to a discharge current of 5.5 A. An 8C-rate for this cell would be 44 A,

4. Determination of model parameters In order to calculate the heat generation from the simplified energy balance formulated in the Eq. (3), two parameters need to be determined: the entropic heat coefficient, dUavg/dT, and the internal resistance, Rin. 4.1. Entropic heat coefficient, dV/dT The entropic heat coefficient has to be determined in order to calculate the heat generation within the cell. Several methods are used to estimate this coefficient, though potentiometry is the most common method [18] and it is the method used also in this work. Open Circuit Potential (OCP) experiments were performed in order to determine the entropic heat coefficient as a function of State of Charge (SOC). The prototype pouch-cells were charged and/or discharged up to a defined SOC (%) and then allowed to relax at constant temperature for a certain time. This procedure was repeated for several different temperatures values. Thomas et al. [20] reported that it is more convenient to vary the SOC for a given temperature in order to reduce the error from self-discharge when measuring the entropy of reaction potentiometrically. The temperature range in the thermal cycle was defined based on the temperature range in which cells operate 105

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Fig. 8. Internal resistance values for various Crates and different temperatures (discharging process).

enough long to ensure the cell reaches the equilibrium potential. In this work it was selected to be 90′ by mean of a batch of measurements where the resting time was increased from 15′ to 120′ and the open circuit potential was monitored. We found out that 90′ was a good compromise between the testing time and the equilibrium potential. The cell potential measured after this resting period was taken as the OCP value at the target SOC. The cells were then discharged by a further 15% of the nominal capacity at the same current rate. The procedure above has been made repeatedly to obtain the OCP-SOC curve until the cutoff voltage is reached. Similar test was also performed during charging from 20% to 80% of SOC range (Fig. 2). The charge and discharge OCP-SOC curves do not coincide, because of the hysteresis effect as shown in Fig. 3, hence two different OCP curves will be considered. Taking 20% SOC as example, the entropy coefficient for the cell one is obtained from the slope of the curve as a function of temperature, as shown in Fig. 4. The final entropy coefficient used was calculated as an average value of that obtained from the test performed over the four sample cells. The same process has been carried out at different SOC (%) with an interval of 15%; the resulting fit curve is shown in Fig. 5. If entropy increases, then dV/dT is positive, the reaction is endothermic and the cell has released heat. If dV/dT is negative the cell has absorbed heat. Checking from the dV/dT shown in Fig. 5, it is seen that in discharge, since SOC of cell decreases from 80% to 20%, dV/dT is initially negative, which suggest an exothermic reaction (negative current), the heat is released and temperature increases. Then dV/dT becomes

Table 2 Fitting parameters for the overpotential resistances interpolation. ci 1 2 3 4 5 6 7 8 9 10 11 12 13 14

di 2

5.5571e −2.8749 −5.4294 3.7742e−4 1.7831e−2 2.7755e−2 −1.9532e−5 −5.0986e−7 9.6229e−8 −8.9737e−5 −1.3901e−6 5.2566e−9 −4.9289e−9 2.8816e−9

−4.5292e3 −5.852e1 −4.505e1 09.88e−2 1.496e−1 6.113e−1 −1.656e−4 −2.0181e−5 2.4444e−6 −2.1e−3 6.635e−4 −1.11e−6 7.4074e−8 −2.0576e−8

safely according to cell specification sheets. In order to calculate the heat generation, the relationship between OCP and SOC (%) is required. The true OCP value can be reached by monitoring the cells voltage when idling the cell for a long time. To acquire the data, the test procedure was designed as follows: the cells were firstly discharged by 20% of the nominal capacity from fully charged state at 5.5 A (1C) at constant temperature, thus reaching 80% SOC. The cell potential to be taken into account for OCV value at a defined SOC (%) was measured after a proper relaxation time, that for this work was found out to be 90′. This relaxation period has to be 106

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Fig. 9. Resistance functions interpolation (top: 8C charging, bottom: 8C discharging).

where: t is the physical time, going from 0 to 225 s for 8C-rate (44 A). It corresponds to the maximum current value handled by the testing instrument for these cells (so the maximum possible heat power). The SOC (%) considered for the interpolation are between 30 and 80% (see Table 1). 4.2. Internal resistance, Rin Precise knowledge of the internal resistance of a lithium ion battery is a key factor for the battery thermal design and management [21]. The lower internal resistance the battery cell has, the lower the heat generation in the cell will be [22]. The internal resistance depends strongly on the method used for its determination. It also depends on the levels of the thermal and chemical equilibriums: it is a function of cell temperature, current and SOC [22]. The most widely used methodology for determining Rin is to apply constant current charge/discharge pulses [21,23]. The voltage response is monitored in order to determine the total overpotential resistance as a function of the state of charge (SOC) and the temperature. The pulse test is laborious and time consuming, so in this work another method to determine the internal resistance is adopted [24]. The starting equilibrium voltage of the battery is correlated to the SOC, and the internal resistance of the battery is determined according to the equation:

Fig. 10. Battery pack design for forced-air cooling solution.

positive (endothermic reaction) and subsequently negative again. So, the cell during discharge is releasing heat and consequently it increases its temperature. Instead during charge, as SOC varies from 20% to 80%, the dV/dT is negative at the beginning, suggesting endothermic reaction (the current is positive) and then it increases slowly to 0 until up to around 50% of SOC when it becomes positive (exothermic reaction). The entropy coefficients were fitted with 5 parameters (Table 1) both for charging and discharging process with the polynomial expressions:

ECC8C charging = a1


+ a2


+ a3


+ a4 t + a5

ECC8C discharging = b1 t 4 + b2 t 3 + b3 t 2 + b4 t + b5

Rin =

OCP (T )−Vterminal I


where Vterminal is the cell voltage during charging or discharging process, OCP is the open circuit voltage measured for the entropic coefficient determination and I is the current (charge/discharge). In Figs. 6 and 7 the sampling time is 1 min and 30 s for 1C and 2C rates respectively; instead it is 1 s for 5C and 8C.

(4) (5) 107

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Fig. 11. Temperature evolution during a discharging/charging process for natural/forced convection.

Fig. 12. Average heat power generated by Li-ion cells for the forced convection simulation.

Fig. 13. Temperature distribution for natural convection.

OCP is current independent and depends on temperature. However it is possible to estimate its temperature dependence by:

dV OCP (T ) = OCP (Tref )−(T −Tref )· dT

R8C charging = c1 + c2 t + c3 T + c4 t 2 + c5 T 2 + c6 Tt + c7 T 3 + c8 t 3 + c9 T 3t + c10 T 2t + c11 t 2T + c12 t 2T 2 + c13 t 3T + c14 t 4


R8C discharging = d1 + d2 t + d3 T + d4 t 2 + d5 T 2 + d6 Tt + d7 T 3 + d8 t 3


+ d 9 T 3t + d10 T 2t + d11 t 2T + d12 t 2T 2 + d13 t 3T + d14 t 4

where Tref is set to 25 °C and dV/dT is the entropic heat coefficient. Several charge/discharge cycles at different temperatures were considered (see Fig. 8) and, since the internal resistance depends both on temperature and SOC, it is necessary to fit the data in order to get an appropriate interpolating resistance functions (R (T, t)). The surfaces fitting of the resistances yields the following equations:

(9) where T and t represent the temperature and the time respectively. The SOC considered for the interpolation are between 30 and 80% and t is the time, going from 0 to 225 s for 8C-rate. In the Table 2 the fitting parameters for the resistances interpolation have been reported. 108

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Fig. 14. Temperature distribution for forced convection with the flow direction streamlines.

Fig. 15. Battery pack render for liquid cooling solution (on the right) and the cross-section view for the cooling channels.

Fig. 16. Temperature evolution during a discharging/charging process for liquid cooling simulation.

total groups). This particular structure is a compromise between space constraint and cooling requirements. Two different air-cooling configurations are considered: natural and forced. The first case considers air in stagnation condition (natural convection) inside the case. A forced convection on the Li-ion cells case is also studied. Forced convection occurs when the fluid flow (air) is introduced in the domain (internal battery pack) by an external force, such as a blower or fan. The mass flow rate for the forced convection solution is equal to 0.0695 kg/s/m2, of air (the value is normalized considering the total surface of the cells which is actually cooled by the air). The maximum final cell temperature (after one discharging/charging process (8C rate)) for natural and forced convection is increased by 10 °C and 8 °C respectively, with respect to initial conditions (25 °C). It is important to note that the initial and ambient temperatures are set to 25 °C, which means “ideal” conditions. Under the hood of a car

The R-square values for the Eqs. (4), (5), (8), (9) are respectively equal to 0.9952, 0.9895, 0.9923 and 0.9963. As an example, Fig. 9 shows fitting surfaces of the resistance functions, in particular conditions of charging and discharging. In order to correctly calculate the internal resistance, the resistance of the hoods (4 m ∊) for the data acquisition system were also considered. The functions for internal resistance are used along with the entropic heat coefficient in STAR CCM+ software in order to calculate the total heat generated in a battery. This is then used to simulate the battery pack thermal behavior in different cooling conditions over time. 5. CFD simulation for air-cooling battery pack The first case study is the air cooling solution, thus the heat generated is exchanged by convection process. Fig. 10 shows the battery pack with 48 total cells with a distance of 2 cm between each 6 cells (8 109

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Fig. 17. Average heat power generated by Li-ion cells for the liquid-cooling case.

Fig. 18. Temperature distribution for the cold plates (down) and the Li-ion cells (up) considering the liquid cooling simulation.

It is advisable to avoid deep discharging process in order to limit the heat generation as well as to increase the life of Li-ion cells. In applications such as Electric Vehicle or Hybrid Electric Vehicle, if the heat is not taken away from the battery efficiently, the accumulated heat may cause a thermal runaway, which threatens the operational safety. The temperature distribution for the two cases of natural and forced convection is different. The natural convection approach presents a more homogeneous temperature distribution at the end of the discharging-charging process (Fig. 13). The temperature distribution for the forced convection is seen in Fig. 14. The average temperature in case of forced convection is 3 °C less than the average temperature in natural cooling case.

(considering a hot summer’s day) the temperature is higher than 25 °C. The temperature evolution is quite similar for each cell for the natural convection simulation as shown in Fig. 11. The discharging process (charging process) at 8C rate goes from t = 0 s to t = 225 s (t = 225 s to 450 s), which explains the change of slope in the Fig. 11. The maximum (minimum) trend, mentioned in Fig. 11, is referred to the highest (lowest) average temperatures assumed by the most heatstressed cell. As discussed in the Section 2, the overpotential heat generation is always positive which means that the effect of this part is exothermic. For entropy change heat generation, whether it is exothermic or endothermic depends on the sign of the current (negative in discharging process and positive in charging process) and of the entropy coefficient. As is observed in Fig. 12, the amplitude of the overpotential heat generation is large, due to the high resistance. During the final stage of the discharging process, the total heat dramatically increases and this is most likely due to entropy change.

6. CFD simulation for liquid-cooling battery pack Coleman’s research work [25] analyzes two failure mode simulations to investigate block performance during a slow and a fast 110

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Fig. 19. Average total heat power produced by cells at two different initial temperature.

which is actually in contact with the battery cells). Also in this case, the maximum (minimum) trend is referred to the highest (lowest) average temperatures assumed by the most (least) heat-stressed cell. In Fig. 16 the difference between the maximum and minimum average temperatures seems to rise over time. This is the reason why a cooling system is equipped with a Thermal Management System (TMS). Different temperature sensors are located inside the battery pack and connected directly with the TMS, which decides the water flow rate (or air flow rate). The goal of a properly designed TMS is not only to decrease the average temperature of the stack but also to decrease the pack temperature gradient. However, the difference between the temperature of the cells and the liquid cooling fluid especially depends on the heat transfer, hence on the pipes and cold plates material. The total heat produced by the battery in the liquid cooling case (Fig. 17) is lower than air cooling solution (especially when the state of charge is less than 40%). This aspect is related to the cell temperature and the SOC. During the discharging process (from 80% to 30% of SOC), the entropic heat coefficient is multiplied by the current (negative in the discharging process and constant over time) and the average temperatures of the cells, which is lower than air cooling approach. Fig. 18 shows the temperature distribution of the 48 cells that make up the battery stack. In the Fig. 19 is shown the different heat power produced by the cells with different initial conditions showing that the total power slightly increases if the initial temperature is increased. The total heat power is the sum of the entropic contribution and the irreversible heat. Both solutions (air and liquid cooling) give the normalized mass flow rate. For the real applications this is the most important parameters to size the auxiliaries cooling equipment. All procedures (from experimental data execution to CFD results) require about 1 weeks’ time which is practical from an industry point of view [27]. The developed model is simple and fast enough to be implemented for battery pack simulations and semi empirical approach for the input parameters determination allows good accuracy. However, the methodology described for the charge of entropy in this paper could be further improved using the electrothermal impedance spectroscopy, clearly at the expense of the equipment costs. Recently, Schmidt developed an electrothermal impedance spectroscopy method to determine the change of entropy, in which the measurement times can be 100 times shorter than in a potentiometric method [28]. The accuracy of this method is similar to that of a potentiometric method. In the Table 3 there are the pro and con for the two cooling approaches.

Table 3 Pro and Con evaluation for air and liquid battery cooling strategies. Pro Battery cooling using air Separate cooling loop not required All waste heat eventually has to go to air No leakage concern No electrical short due to fluid concern Simple design Lower cost Battery cooling using liquid Pack temperature is more uniform Good heat transport capacity Better thermal control Lower pumping power Lower volume and compact design


Low heat transport capacity More temperature variation inside the pack High blower power Blower noise

Additional components Weight Liquid conductivity – electrical isolation Higher maintenance Higher cost

exothermic reaction. For this purpose, a generic four-cell module was modeled using finite element analysis to determine the sensitivity of module temperatures to cell spacing. The aluminum block design performed well under all conditions, and showed that heat generated during a failure is quickly dissipated to the coolant, even under the closest cell spacing configuration. For this reason in our simulations, the cold plate is made in aluminum. It could be machined to form flow passages and then a cover is assembled to contain the flow. Fig. 15 shows the battery pack for the liquid-cooling solution and just like air-cooling solution, there are 6 cells close to each other. Between each group of 6 cells the liquid cold plate is located. During the cooling process, fluid absorbed the heat generated along the flow direction and caused the reduction of the cooling capacity. Hence, downstream temperature is always higher than the upstream temperature. Inconsistent cooling effect will lead to high variation of temperature distribution and shorten the life expectancy of the battery pack [26]. To mitigate these cooling effects, the middle pipe has a countercurrent flow with respect to the two external pipes. In this configuration, the total length of the battery pack is 201 cm (including the case). In case of water cooling approach, the temperature evolution can be seen in Fig. 16. The final cell temperature (after one discharging/ charging process) is increased by only 2.5 °C with respect to initial conditions. In order to achieve this purpose, the mass flow rate of water, which passes through the pipes, is approximately equal to 239 L/ h/m2. (The value is normalized considering the cold plates surface 111

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7. Conclusion In this paper, a complete thermal model of a Li-ion battery pack has been developed and successfully calibrated (through experimental tests) taking into account both thermodynamic-related and transportrelated heat sources. The goal of a thermal management system was to maintain all the battery pack in an optimum temperature and different simulation cases have been take into account: natural convention, forced convention and forced liquid. The first one is the least favorable solution in terms of maximum temperature, but an increase in temperature of 10 °C (for the most heat cell) is found at the end of the charge/discharge cycle while the second one is only slightly better, with the final temperature lower by a few degrees but still too high. While the last one gives good results, in fact the most heat-stressed cell increases its average temperature of 2.5 °C with respect to the initial temperature in the charge/discharge cycle. Considering that the temperature range for optimum performance/ life/reliability of a EV batteries for electric vehicles in today’s market (between 15 °C and 35 °C) and the uneven temperature distribution of the cells (< 4–5 °C) the results obtained, with the forced liquid simulation, are very interesting from the industrial point of view. Future work will involve simulations with several discharging/charging cycles in order to better clarify the temperature behavior with different mass flow rates of air and water. Acknowledgements The authors would like to thank the Lithops Batteries S.r.l. for their technical support in this research. References [1] Newman J, Pals C. Thermal modeling of the lithium/polymer battery – I discharge behavior of a single cell. J Electrochem Soc 1995;142(10). [2] Newman J, Pals C. Thermal modeling of the lithium/polymer battery – II temperature profile in a cell stack. J Electrochem Soc 1995;142(10). [3] Wan CC, Wang YY, Chen SC. Thermal analysis of lithium-ion batteries. J Power Sources 2004;140(2005):111–24. [4] Yunus A. Cengel. Heat transfer: a practical approach, 2nd ed. McGraw-Hill; 2003. [5] Jinlei S, Guo W, Lei P, Rengui L, Kai S, Chao W, Chunbo Z. Energies 2015;8:4400–15.