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Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs
Accepted Manuscript Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs Yiran Zheng, Yu Shi, Yunhui Huang PII: DOI: Reference:
S1359-4311(18)33632-9 https://doi.org/10.1016/j.applthermaleng.2018.10.090 ATE 12834
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
10 June 2018 16 August 2018 21 October 2018
Please cite this article as: Y. Zheng, Y. Shi, Y. Huang, Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.10.090
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Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs
Yiran Zhenga, Yu Shib, Yunhui Huanga,c* a
Institute of New Energy for Vehicles, School of Automotive Studies, Tongji University, Shanghai 201804, China State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China c School of Materials Science and Engineering, Tongji University, Shanghai 201804, China b
Abstract
We propose a thermal management system for fast charging Li-ion battery pack combining liquid cooling and phase change material cooling. The main heat dissipating approach is liquid cooling, while composite phase change material wipes out the thermal-opaque area in the battery pack and provides relatively small amount of heat absorption. Alternated flow of coolant is required to guarantee temperature uniformity in the battery pack but is found detrimental to the holistic thermal dissipation. A method to address that issue, adding polyurethane adiabatic interlayers between cooling tubes, is proven to be an effective answer. Via analysing the heat transfer mechanism of the designed thermal management system, the influencing factors on its performance are found and a heat dissipation balancing coefficient is defined to quantify the temperature balancing performance of the system. The simulation for the system under an 8 C rate charging condition is conducted, as well as compare tests concerning coolant flowing directions, coolant flowing speeds, filling materials, and the interlayers. Simulation results show that the system in question well controls the temperature of an 8 C rate charging battery pack, with the maximum temperature at 38.69 ℃ and the temperature difference at 2.23 ℃.
Highlights
A cooling strategy is devised for fast charging battery packs. A balancing coefficient for the temperature balancing performance is defined. Detrimental impacts of alternated flow are found in hyper-thermogenic situations. Page 1 of 24
Adiabatic interlayers eliminate one flaw of the alternated flow. Simulations in COMSOL Multiphysics confirm the ability of the cooling method.
Keywords
Li-ion battery pack Fast charging Liquid-dominated cooling method Adiabatic interlayer Balancing coefficient Simulation
1. Introduction
Clean and energy-saving electric vehicles (EVs) have been researched and developed in hoping to substitute, if not all of, the major part of conventional vehicles [1]. Yet the confessed reality is that EVs take a small share in vehicles globally, resulting from untreated inconveniences. Two concerned issues are driving distance range and battery charging rate [2]. The demand for long driving range and fast charging spawns safety issues about applying hundreds, or even thousands of Li-ion battery (LIB) cells on EVs [3]. To assuage the “range anxiety”, large amount of LIBs are schematically modularised and packed, and systematically managed to be applied in electric vehicles [4, 5]. To tackle the other issue of too long charging time, the answer lies in fast charging technology, with 3 C or higher rates charging, which in theory reduces the full charging time to 20 minutes or less [6]. However, fast charging to LIBs actuates vast heat generation. Ye et al. [7] reported the vast heat generation of charging a sort of prismatic LIBs, which at 8 C rate charging have a volumetric heat generating rate of 797.1 kW m-3. It implies the perils in fast charging: the batteries mentioned above, in 8 C rate full charge, if not well cooled, would heat themselves up from atmospheric temperature (20 ℃) to averagely 154.4 ℃, according to Eq. (1), which is based on energy conservation principle. (1)
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The assumption accords with several studies involving the heat generation of LIBs, which is among 21.3–800 kW m-3 under fast charging or discharging, and potential dangers lie in them if the heat is not well dissipated [8–13]. Cells at such high temperature are in inappropriate working condition, leading to irreversible damage, or worse, combustion or even explosion [14, 15]. Therefore, the requirement abounds for an efficient battery thermal management system (BTMS), which, via taking away the heat, maintains the average temperature and maximum temperature difference within their safe ranges. Looking for an answer from existing and conventional cooling methods, including air cooling, liquid cooling, and phase change material (PCM) cooling, the most hopeful for vast heat dissipation must be liquid cooling due to liquid’s high specific heat capacity and fluidity. Fuller et al. [16] compared air cooling and liquid cooling applied in LIB pack, and observed that the peak temperatures of the pack under air cooling and liquid cooling were 50.65 ℃ and 35.60 ℃ respectively, while the temperature differences were 1.31 ℃ and 3.76 ℃ respectively. Chen et al. [11] compared air cooling, direct and indirect liquid cooling and fin cooling, and eventually deemed liquid cooling as the most practical method, while air cooling should consume 2 to 3 times more energy and fin cooling should add 40% more weight. Both illustrate liquid cooling’s potential to handle hyper-thermogenic situations, albeit with larger temperature difference. PCM alone can not handle the thermal management for such hyper-thermogenic situations. One problem is the inadequate latent heat capacity, 200－220 kJ kg-1. The volume cost should rise by 1.50–1.62 times of that of battery cells (considering 8 C rate charging), and mass cost should soar as well, based on the energy conservation principle as specified in Eq. (2). The other problem is the poor heat conductivity of paraffin, lower than 0.30 W m-1 K-1, hampering the diffusion and the dissipation of the generated heat. (2)
By the same token, composite PCM alone does not have that potential. Combining paraffin wax with Al, Cu, graphite, graphene, or hexagonal boron-nitride, can enhance thermal conductivity from 0.1–0.3 to 3–16 W m-1 K-1 [17– 21], at the sacrifice of a part of the latent heat capacity. Its lower latent heat capacity is not what fast charging LIBs are looking for, but the thermal conductivity of 3–16 W m-1 K-1 allows composite PCM the method combination with some efficient others, for instance, with heat pipe [22–24], with semiconductor thermoelectric device [25], with water cooling [26], or with fin structures [27]. All demonstrate that the combination methods have the edge over their original counterparts. Liquid cooling can handle the heat generation of LIBs under a wide range of charging rates. Panchal et al. [28] utilised cold plates with liquid cooling to control the temperature of a 4 C rate discharging LIB. Using cascade cooling method, Zhang et al. [29] reduced the temperature difference of an LIB pack from 7 ℃ observed in liquid cooling plate
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method to 2 ℃. Li et al. [30] deemed their designed water cooling method an effective one in dealing with the battery pack at cycling rates lower than 3 C. On a smaller scale, Mini-channel liquid cooling is convenient to be integrated with a single cell and deal with the heat generation under a 2 C discharging rate [31]. And mini-channel cooling is found capable of preventing battery fratricide when the thermal runaway within a single cell occurs, by Ma et al. [32]. Also found in the mini-channel liquid cooling method [31] is a detrimental effect brought by alternative flows, but the reason remains unfathomed. Besides, we believe the water cooling design conducted by Li et al. [30] can deal with higher cycling rates if the thermal conduction between cells and cooling tubes is raised. Liquid cooling needs delicate design methods for it to exert the best function. This work focuses on a thermal management method that combines liquid cooling with PCM cooling. It intends, with less space and mass costs, to achieve the effect observed in one cooling method that combines water cooling with heat pipes studied by Ye et al. [33]. Vast heat needs to spread from the internal to the surface of cells with a thermal conductivity not high, so that a considerable temperature difference will be formed between the internal and the external to power the heat transfer. And thus, it would be inappropriate to focus on the temperature variation by position in one cell, instead, the average temperature of a single cell should be worth the attention, and used to evaluate the maximum temperature and the temperature difference of the battery pack, and their criteria should be regarded as respectively not exceeding 40 ℃ and 5 ℃ [34]. Initially for flowing field design, this study applies several cooling tubes in parallel running through one large-scale battery module. Via theoretical analysis and the simulations, additionally, the issue of temperature inconformity in the battery pack is analysed and dealt with by adopting alternative flowing method in cooling tubes, which, unfortunately, induces unwanted “heat recovery”, which is later addressed by the insertion of adiabatic interlayers between the cooling tubes. The use of the adiabatic interlayers in liquid-dominated cooling system is an innovative concept. The adiabatic bars with low thermal conductivity can block heat transfer between cooling tubes. It is a solution for the problem that the large heat generation of fast charging batteries has made the alternated coolant flowing method deficient. Eventually, the effects of those designs including the coolant flowing directions, coolant flowing speeds, the insertion of the adiabatic interlayers, the filling for the composite PCM, etc., are studied in numerical simulations, searching for enhancement on the designed composite PCM and liquid cooling system.
2. Design of the thermal management system
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Prismatic LIBs same as those studied by Ye et al. [7], sized as 140 mm
65 mm
15 mm, with a capacity of 10
Ah, and a heat generation of 797.1 kW m-3 at 8 C rate charging, are involved to demonstrate the capability of the designed liquid/PCM cooling method. Fig. 1 shows the concept design of liquid and PCM cooling method in such prismatic battery pack. The pack contains 110 prismatic LIBs in a 10 tubes with a sectional size of 6 mm size of 10 mm
11 arrangement; 8 Aluminium (Al) cooling
13 mm; 7 adiabatic interlayers inserted between 8 cooling tubes with a sectional
2 mm; and PCM or composite PCM that fills up all the clearance of a 843 mm
235 mm
145 mm
cubic box (see Fig. 1c).
Fig. 1. The concept design of liquid and PCM cooling method. The method (a) with adiabatic interlayers and (b) without adiabatic interlayers, and (c) PCM filling.
Flows of coolant in cooling tubes are in alternated directions, which means that a flow direction of coolant in one tube is opposite to an adjacent counterpart. The coolant is 50% water-ethylene glycol mixture. Its physical property parameters, including heat capacity, heat conductivity, dynamic viscosity, and density, are variable by temperature. Algebraic equations were built between those physical property parameters and temperature (see Table 1). Composite PCM is applied in the designed BTMS, filling up all of the clearance in the battery module. The applied composite PCM consists of paraffin and EGM, already reported by other researchers [8], boasting a heat conductivity of 3.95 W m-1 K-1, and a latent heat absorption of 132.6 kJ kg-1 at a phase change temperature range of 21.6–25.5 ℃ (simulations involve the other phase change ranges).
Table 1 Thermo-physical properties of coolant symbols
definitions
units
temperature
℃
heat capacity
kJ kg-1 K-1
density
kg m-3
dynamic viscosity heat conductivity
variation with temperature
Pa s W m-1 K-1
Inserting adiabatic interlayers between cooling tubes is an optimising scheme in this study, while the original models without adiabatic interlayers are put here for comparison (shown in Fig. 1b). Those adiabatic interlayers cut off the heat transfer between cooling tubes. In our original design (shown in Fig. 1b), the application of the alternated flow is found performing an detrimental “heat recovery” — a high thermal conductivity of Al causes vast heat transfer
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between cooling tubes so that the coolant entering the battery pack would absorb, from coolant in the adjacent cooling tubes, heat that would have otherwise been taken out. The ultimate target for the designed BTMS that combines liquid cooling with composite PCM cooling is to maintain the maximum temperature of single cells, at 8 C rate charging condition, below 40 ℃ and the temperature difference of the battery pack below 5 ℃, meanwhile to reveal the interplay between the performance of the system and its variable factors. Besides, we intend to explicit the potential lying in liquid and PCM cooling system, by achieving the same effect brought by heat pipe thermal management system (HPTMS) applied on battery cells of same type and amount [33], but with lower costs of volume and mass.
3. Theoretical analyses
3.1 On the heat transfer
The heat transfer
1
between cell and cooling tube is calculated from the coolant to a cell wall with following
equations: (3) (4)
(5) (6) (7) 𝑏
is the average temperature of a battery cell, variating with 𝑠 , the flowing distance of coolant. Eq. (5) is a
Sieder-Tate empirical equation of the laminar flow heat transfer under constant wall temperature condition. the Reynolds number, and
is
, fluent’s equivalent diameter, expressed respectively in Eqs. (6) and (7).
3.2 On the temperature uniformity
To understand the temperature distribution in cooling tubes, the heat transfer between the cooling tubes and cells are calculated along the 6 straight ways of the cooling pipes, which are numbered from S1 to S6 shown in Fig. 2a, while the
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heat transfer at the U turns, including from U1 to U5, is neglected in the analysis. Vertically downwards, cooling tubes are numbered from 1 to 8 (see Fig. 2b), the alternated flowing directions are according with those shown in Fig. 1.
Fig. 2. The analyses on (a) the top view, (b) the bilateral view.
The heat absorption amount on an infinitesimal length
𝑠
of some coolant in Tube 1 can be expressed with
following equation: 𝑠
(8)
Via absorbing the quantity of the heat of
1
in some time of 𝜏 , this infinitesimal coolant gets a heat-up, and the
temperature rise can be expressed with following equation: (9)
From the inlet to the current position 𝑥 , conduct an integral operation: 𝑠
(10)
Then the temperature distribution on cooling Tube 1 can be expressed with the function of 𝑠 : (11)
with const 𝐶
1
and const 𝐶
2
𝐶
:
(12)
𝐶
(13)
Considering the symmetry of the designed model, the average temperature
𝑠
of 8 cooling tubes at 𝑠
position can be calculated with a function of 𝑠 , expressed in following equations: 𝑠
(14)
The variable part g(y) Elicited from Eq. (14) decides the fluctuation of temperatures of both coolant and batteries: (15)
with variable
and const 𝐶
3
defined as:
(16) 𝐶
𝐶
(17)
Indicated in the functional image of and 3.0, is that the value of 𝐶
3
in Fig. 3, while 𝐶
3
respectively equals to 0.1, 0.3, 0.6, 1.0, 1.5, 2.0
has got a correlativity with the fluctuation of
fluctuation by the flowing distance of coolant.
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, and hence with the temperature
, when 𝐶 equals respectively to 0.1, 0.3, 0.6, 1.0, 1.5, 2.0 and
Fig. 3. The function image of 3.0.
And the higher value of 𝐶
3
causes a worse temperature uniformity. Therefore, 𝐵
, the reciprocal of 𝐶
3
, is
defined in this study as thermal dissipation balancing coefficient: 𝐵
Coincidentally, 𝐵
(18)
or 𝐶
3
is a dimensionless factor. Higher value of 𝐵
depicts a better temperature
uniformity. Using the parameters in the control test (see section 5.1), where the maximum temperature difference in the end is 2.23 ℃, the value of the 𝐵 increases the value of 𝐵
is worked out to be 2.824 (𝐶
3
= 0.354). Raising the coolant flowing speed
, and indeed would narrow the temperature difference (see section 5.3). Nonetheless, this at
first could give suggestions on how to design a liquid-dominated BTMS for battery packs with better temperature conformity. The results of these analyses and particularly the definition of 𝐵
to some extent directed the design of
the BTMS in our work.
4. Simulations
Numerical simulations have been conducted in COMSOL Multiphysics, dedicated in different scenarios. The geometries for simulations were imported 3D-models mentioned before, including 134 parts, respectively 110 parts for the prismatic cells, 8 parts for the coolant, 8 parts for the cooling tubes and 7 parts for the adiabatic interlayers, and meshed in COMSOL Multiphysics generating 11,481,028 tetrahedral domain units, 1,631,129 boundary units and 159,450 edge units (shown in Fig. 4).
Fig. 4. The designed model meshing in COMSOL Multiphysics.
The bottom boundary is regarded as heat-convective to a stationary charging environment where constantly the temperature is 293.15 K or 20 ℃, the relative fluidity is 85%, and the wind speed is 0 m s-1, while the other boundaries are heat-insulated to the ambient. The starting temperature for the entire system is set as 293.15 K or 20 ℃. The heat generation rate is 797.1 kW m-3 as mentioned before, set to be evenly distributed in battery cells, and be a constant, which does not conflict with the intention of the simulations to assess the cooling ability of the designed system. This method is also applied in other researches using the same batteries [7, 33]. Page 8 of 24
The physical fields applied in all the simulations include heat transfer in pipes and heat transfer in solids. The values of Reynolds number for the coolant flow are among 497.8–2489.1, calculated with Eq. (6), with the coolant flowing speeds of respectively 0.2 m s-1 and 1.0 m s-1, the minimum value and the maximum value used in simulations (see section 5.3). And thus the coolant flow in cooling tubes is considered laminar flow, controlled by Eqs. (19) and (20), respectively the momentum equation and the mass conservation equation. (19) (20)
Besides, normal inflow velocity is set for coolant inlet, whilst 0-pressure condition and the suppressed back flow are set for coolant outlet. Heat Transfer in fluid is governed by Eq. (21); in PCM, Eq. (22); and in cells, Eq. (23). (21) (22) (23)
In Eq. (21), the first term on the left side denotes the time-unit heat variation via sensible heat exchange, the second denotes the heat transport caused by fluid flow, and the third, the heat conduction. Since no fluidity is set in battery and PCM, the item concerning heat transport is missed in Eqs. (22) and (23). The phase changing process of the composite PCM functions with the mechanism that is expressed in the following equations: (24) (25) (26) (27)
where
denotes the fraction of the phase before transition, and equals to 1 before transition and 0 after transition;
is the mass fraction of that, and equals to -0.5 before transition and +0.5 after transition. Generally 5 groups of simulations are conducted, and their purposes and details are listed below: The first is the control test containing our optimisation methods, applying alternated flowing directions in cooling tubes, setting the flowing speed of coolant 0.5 m s-1, inserting adiabatic interlayers with a thermal conductivity of 0.024 W m-1 K-1 (a theoretical value for polyurethanes with 30% blowing agent), and filling clearances with PCM boasting a thermal conductivity of 3.95 W m-1 K-1 and a latent heat of 132.6 kJ kg-1.
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The second is to demonstrate the effect of the alternated flow design, by comparing the method with parallel coolant flow, which means the flow directions of coolant in cooling tubes are the same, and the method in first group. Parallel coolant flow is set in the simulation in the second group. The third seeks to reveal the interplay between the coolant flowing speed and the performance of the BTMS. Based on the control test, several simulations have been conducted with different flowing speeds, respectively 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 m s-1. The fourth is to prove the influence brought by inserting the adiabatic interlayers between the cooling tubes. A compare test is conducted by replacing the adiabatic interlayers with the heat-conductive interlayers, and in handling of the simulation, the thermal conductivity of the interlayers is changed from 0.024 W m-1 K-1, as well as the other thermophysical properties, to that of Al, 237 W m-1 K-1. The last is to study the functions of the composite PCM that fills up all the clearance in the battery pack. To find out which parameter exerts most impact on the performance of the BTMS, 4 cases were studied including the first replacing the composite PCM with pure paraffin, the second assuming the phase change range to be 28.0–31.9 ℃, the third, 34.0– 37.9 ℃, and the fourth, 52.0–55.9 ℃ (COMSOL Multiphysics has direct access for setting the phase change range). The thermal conductivity of pure paraffin is 0.3 W m-1 K-1. Thus a comparison between the first case and the control test would explicate the function of thermal conductivity, if there is some. Likewise, between the control test and the second or the third case, comparisons would indicate the influence of differentiated phase change ranges. The fourth case applies an unexperienced phase change range to cancel the involvement of the latent heat, to see how the latent heat of PCM would matter to this system. All the simulations are processed in time-dependent studies, in which the time ends are set at 450s when LIBs theoretically get fully charged from 0% under 8 C rate charging. Data are stored per second. All the simulations are computed by the segregated time-dependent solver. The maximum number of iterations are set 10, the absolute tolerances are set 10-6 for velocity field, temperature and pressure, and at each time stepping, the event tolerances are all set 10-3.
5. Results and discussion
5.1 The capability of the designed thermal management system
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Fig. 5a shows the temperature distribution of the control test (PCM part is hidden) at 450s, where the inspected highest temperature is at the centre of the battery pack, about 46 ℃, while the lowest is at the inlets of coolant, 10 ℃. Fig. 5b shows the slice view of the temperature distribution in an XY-plane which evenly divides Tube 1. The similarity of the temperature distribution in every cell marks a good performance.
Fig. 5. The simulation results for the control test. (a) The volume view and (b) the slice view of the temperature distribution at 450s, (c) temperature rise of cells in an 8 C rate full charge.
To better reveal the temperature distributions, this study focuses on several special values: shown in Fig. 5c, the maximum, minimum, and quantiles. A p quantile value of temperature t indicates that the cell temperatures which are lower than or equal to t take a proportion p of the data cluster in one time point. From the temperature curves in Fig. 5c: the temperatures in cells rocket up when the charging begins; at about 20s, the phase change stage of PCM is activated and it starts to absorb heat, stored as latent heat, so that the temperature rise tends to decelerate from soaring to ratcheting up; at about 70s, PCM is gradually depleting its latent heat storage, causing the temperature curves returning to steepen; later as the temperature rises, temperature differences between cells and coolant expand, which accelerates the heat dissipation; in the end the trend for the temperatures to rise is wearing thin. The max value of the average temperatures of each cell at 450s is 38.69 ℃, while the lowest is 36.46 ℃ (according to the calculating mechanism of singular temperature), fostering a temperature difference of 2.23 ℃. The curves for quantiles over 0.9 seem dense, while the curves for quantiles under 0.1 are scattered, meaning that most temperatures of cells concentrate closely to the maximum temperature. Compared with HPTMS in the study of Ye et al. [33], which has the same amount of the identical cells and similar results (the maximum temperature in the end is also less than 40 ℃) when dealing with the 8 C rate charging condition, the liquid and composite PCM cooling system saves a large space cost by the evaporator in the HPTMS.
5.2 The effect of the alternated flowing design
The alternated flow design is intended for better temperature distribution in the battery pack, to eliminate the issue in the parallel flow that the cells near the inlet would have far lower temperature than the cells near the outlet. Simulation in that case, when the parallel flow is applied, results congruously to the expectation. From Fig. 6a, higher temperature distribution is observed in the parallel flow method than the equivalent in the alternated flow one, and the outlets of the coolant gathered at same side have obviously higher temperature than the inlets, causing the cells near the outlet obviously hotter than that near the inlet. Page 11 of 24
Fig. 6. The simulation results for the parallel-flow method. (a) The contour view of the compare test at 450s, (b) temperature rise of cells in parallel-flow method.
Fig. 6b shows the hot temperature and temperature inconformity brought by the involvement of the parallel flow. The maximum of the average temperatures of single cells at 450s is 42.69 ℃, while the minimum is 31.47 ℃, forming a temperature difference of 11.22 ℃. The other quantiles further indicate the temperatures of cells have a disperse distribution. For comparison, the corresponding temperatures in the alternated flow method are respectively 38.69 ℃ and 36.46 ℃ (temperature difference 2.23 ℃), demonstrating the indispensability of the alternated flow design in this TMS.
5.3 The influences of the coolant flowing speed
It was assumed that altering the flowing speed would have influences both on the bulk temperature and the temperature difference in the battery pack. Based on the deducted equation of 𝐵
(see Eq. (18)), raising the flowing
speed can improve the temperature uniformity in the battery pack. From Fig. 7a a sensitivity the temperature distribution has on the flowing speed is observed. Temperature variates by flowing speeds largely among low speedings (from 0.2 m s-1 to 0.5 m s-1). When the flowing speed is higher than 0.5 m s-1, the influences on the temperature distribution by raising the flowing speed wear thin. For safety concern that those temperatures should be under 40 ℃, the requisite flowing speed should be over 0.4 m s-1.
Fig. 7. The simulation results for different flowing speeds. (a) The curves of maximum temperatures, (b) the curves of temperature differences.
Their temperature difference curves among cells of various flowing speeds of coolant are shown in Fig. 7b. When the flowing speed is below 0.5 m s-1, lower flowing speed leads to obviously larger temperature difference, while at higher flowing speeds, that influence diminishes. In the initial 200 seconds, temperature differences experience similar fluctuations, due to the interference of phase change process. Temperature differences are all maintained under 5 ℃, which is largely because of the alternated flowing design. Temperature curves in Fig. 7 show that when the flowing speed is already 0.5 m s-1, to further raise the flowing speed has limited effects.
5.4 The effects of the adiabatic interlayers Page 12 of 24
It was presumed that cutting off the heat recovery caused by the heat transfer between cooling tubes would boost the cooling rate of the entire battery pack, and therefore lower the bulk temperature. Indeed this compare test (without the adiabatic interlayers) has confirmed that thought. There are mainly 3 differences between the compare test and the control test. First is a higher temperature, shown in the temperature contour view at the end of 8 C charging, in Fig. 8a; and in the maximum temperature curves in Fig. 8b display the difference — the compare test ends up with a maximum temperature of 44.52 ℃, while the corresponding value in the control test is 38.69 ℃. Second is a large temperature inconformity of cells observed in the contour view in Fig. 8a, also quantified in Fig. 8b, a temperature difference of 10.81 ℃ at 450s, compared to 2.23 ℃, the counterpart in the control test. Third is a visualised difference that, shown in Fig. 8a, the temperature distribution in Tube 1 becomes transparently different, especially at the second U-turn of the cooling circuit, with Tube 3, 5 and 7, where the flowing directions are the same with Tube 1. The phenomenon is observed in Tube 8 compared to Tube 2, 4 and 6 by the same token. Fig. 8c shows the temperature distribution in tubes. Because of geometrical symmetry, only the data of Tube 1 and Tube 3 are required to reveal their temperature distribution at 450s. Fig. 8d further illustrates the narrowed in-outlet temperature difference in the compare test compared to the control test. From Fig. 8c it is also observed that in control test the coolant temperature distribution is nearly an linearity rise over the flowing distance. And in compare test the coolant temperature starts to drop from S5 in Tube 3 or S6 in Tube 1, demonstrating the detrimental influence the heat transfer between adjacent cooling tubes brings. Further proving that is the difference shown between Tube 1 and Tube 3 that the coolant temperature in Tube 3 starts to drop earlier than that in Tube 1 as a result of their different adjacent conditions. Due to the geometrical symmetry of the design, a better linearity in the coolant temperature distribution depicts a better temperature uniformity in cells. So that the temperature difference of cells in the control test is smaller than that in the compare test (see Fig. 8b). To interpret the shake-up of the temperature distribution of the coolant in the compare test (see Fig. 8c), the nonuse of the adiabatic interlayers has turned the entry and exit parts of cooling pipe into two “heat recovery units”. The massive heat transfer between cold ingoing coolant and hot outgoing coolant has realised the recovering of the heat that would have otherwise been dissipated. The in-outlet temperature differences are proportional to the overall dissipated heat. And a comparison between the overall mean values of the them, 8.28 ℃ and 9.44 ℃ respectively in the compare test and the control test, shown in Fig. 8d, can well explicate the necessity of the adiabatic interlayers.
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Fig. 8. The simulation results for the method without the adiabatic interlayers and its comparison with the method with the adiabatic interlayers. (a) The contour view of the compare test at 450s, (b) the comparison on the maximum temperature and the temperature difference, (c) the comparison on the temperature distribution in cooling tubes at 450s, and (d) the comparison on the temperature difference variating over time.
5.5 The simulations for the composite PCM
From previous temperature curves (see Fig. 5, 6, 7 and 8), the composite PCM has slowed down the temperature rise during its phase change temperature range during some certain time. Yet as discussed before, the really useful quality of the composite PCM could be its large thermal conductivity. The results of simulations concerning the question are shown in Fig. 9. From Fig. 9a, with paraffin filling, the maximum temperature ends up at 62.03 ℃, while the others maintain the maximum temperature under 40 ℃. Whereas in case 4 the assumed composite PCM with a phase change range of 52– 55.9 ℃ is not able to perform the phase change function, it controls the temperature well. From Fig. 9b, those fluctuations are similar to the counterparts in Fig. 7b, at different timings according fitly with their respective phase change ranges. But no clear interplay, can be found in the curves, between those temperature differences and the thermal conductivity or other properties of the filling materials. The in-outlet temperature difference shown in Fig. 9c and the coolant temperature distribution in Fig. 9d confirms that if the composite PCM of same thermal conductivity is applied, no matter whether there is a phase change process, or when, the results resemble with each other.
Fig. 9. The simulation results comparison among the methods with case 1, altered to pure paraffin; case 2, phase change range 28– 31.9 ℃; case 3, phase change range 34–37.9 ℃; case 4, phase change range 52–55.9 ℃; and control test (see section 5.1). The curves of (a) maximum temperatures, (b) temperature differences and (c) coolant temperature differences, (d) the coolant temperature distribution at 450s, (e) the statistics for heat taken out, latent or sensible.
The quantities of heat including those dissipated by liquid cooling, absorbed by the composite PCM and remaining for temperature rise, denoted respectively as heat “taken-out”, “latent” and “sensible” are collected and shown in Fig. 9e. The statistics for each case are calculated in light of heat conservation principles, including that in this battery pack the heat generated equals to the sum of 3 mentioned constituents. Among the holistic 5.39 MJ heat generated by LIBs under 8 C charging for 450s, the majorities are taken out by coolant in all cases. In control test, some 4.49 MJ heat is dissipated by liquid cooling, accounting for 83.3% of the generated heat, while the corresponding percentage for the heat absorbed by the composite PCM is only 8.5%. Sensible heat remains in the battery pack to cause the temperature rise. Some 1.31 MJ sensible heat abounds in case 1, wherein leading to the maximum temperature reaching 62 ℃ (see Fig. 9a). For contrast, the equivalents in other cases and the control test range between 0.35 MJ and 0.46 MJ, and their
Page 14 of 24
thermal performances reveal the connotation that a high heat conductivity of the filling material functions in a great difference with a low one.
6. Conclusions
We propose a thermal management method that combines liquid cooling and composite PCM cooling for the large heat generation of LIBs during fast charging. The factors that dominate the performance of the system, concerning both liquid cooling and PCM cooling, are investigated. For liquid cooling, theoretical analysis is conducted on the heat transfer mechanism between the coolant and the cells, and the heat dissipating uniformity is found related to several design parameters so that 𝐵
is defined and
expressed with those parameters to quantify the heat dissipating uniformity. Alternated flowing design is needed for better temperature uniformity, but has brought a problem — the heat transfer between cooling tubes returns the heat from the outgoing coolant into the incoming coolant, forming a detrimental “heat recovery” — which is addressed by the adiabatic interlayers inserted between cooling tubes. The adiabatic interlayers cut out the massive heat transfer, and maintain both the cooling ability and the temperature uniformity of the system. Simulations on the filling materials have confirmed the designed BTMS as a liquid-dominated cooling system. Whereas the composite PCM is applied, the heat absorption it supplies only accounts for less than 10% of the generated heat, while liquid cooling takes 80% by the same token. The system still shows acceptable performance when the phase change of the material is not involved, and the real usefulness found out of the composite PCM seems to be its boost for the heat conduction between the coolant and the cells. Therefore, the composite PCM functions well, but could be better being replaced by some other materials with higher thermal conductivity and better feasibility. A high thermal conductivity of the filling material is extremely important in a fast charging battery pack, since it impacts largely on the heat transfer between the coolant and the cells. As a conventional cooling method, liquid cooling is authenticated powerful to deal with hyper-thermogenic situations. Space and mass costs are critical to an electrical vehicle, and the designed BTMS can lower the cost. It is advisable to develop a BTMS that combines liquid and composite PCM cooling achieving such good temperature distribution in a fast charging Li-ion battery pack.
Acknowledgement Page 15 of 24
This work was financially sponsored by the National Natural Science Foundation of China (No. 51632001)
Nomenclature coolant flowing area in Tube 1 [m2] cooling tube’s sectional width [m] 𝐵 𝑏
thermal dissipation balancing coefficient cooling tube’s sectional height [m]
𝐶
constant 1
𝐶
constant 2
𝐶
constant 3 battery’s specific heat capacity [kJ kg-1 K-1]
𝑏
coolant’s specific heat capacity [kJ kg-1 K-1] PCM’s specific heat capacity [kJ kg-1 K-1] PCM’s specific heat capacity in phase 1 [kJ kg-1 K-1] PCM’s specific heat capacity in phase 2 [kJ kg-1 K-1] Al wall’s thickness [m] fluent’s equivalent diameter [m] PCM’s thickness [m] unite matrix Euler’s number fluid volume force [N] heat transfer coefficient [W m-2 K-1] cooling pipe’s height [m] convective heat transfer coefficient [W m-2 K-1] charging rate [C] coolant full flowing distance [m] 𝑏
battery’s mass [kg] PCM’s mass [kg] Prandtl number Pressure [Pa] heat dissipation rate by liquid cooling [W] heat dissipation rate by natural cooling [W] heat flux density [W m-2]
𝑏
cell’s volumetric heat variation [kW m-3] coolant’s volumetric heat variation [kW m-3] PCM’s volumetric heat variation [kW m-3] cell’s volumetric heat generating rate [kW m-3] heat transferred to Tube 1 [J] Reynolds number PCM’s latent heat [kJ kg-1]
𝑠 𝑏
coolant’s flowing distance [m] battery’s temperature [℃] coolant’s temperature [℃] Page 16 of 24
PCM’s temperature [℃] coolant’s flowing speed [m s-1] 𝑏
battery’s volume [m3] PCM’s volume [m3]
𝑥, ,
Cartesian coordinates [m]
difference operator nabla operator PCM’s mass related phase position PCM’s volumetric related phase position Al’s thermal conductivity [W m-1 K-1] coolant’s thermal conductivity [W m-1 K-1] PCM’s thermal conductivity [W m-1 K-1] PCM’s thermal conductivity in phase 1 [W m-1 K-1] PCM’s thermal conductivity in phase 2 [W m-1 K-1] dynamic viscosity of coolant [Pa s] 𝑏
battery’s density [kg m-3] coolant’s density [kg m-3] PCM’s density [kg m-3] PCM’s density in phase 1 [kg m-3] PCM’s density in phase 2 [kg m-3]
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S1359-4311(18)33632-9 https://doi.org/10.1016/j.applthermaleng.2018.10.090 ATE 12834
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
10 June 2018 16 August 2018 21 October 2018
Please cite this article as: Y. Zheng, Y. Shi, Y. Huang, Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.10.090
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Optimisation with adiabatic interlayers for liquid-dominated cooling system on fast charging battery packs
Yiran Zhenga, Yu Shib, Yunhui Huanga,c* a
Institute of New Energy for Vehicles, School of Automotive Studies, Tongji University, Shanghai 201804, China State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China c School of Materials Science and Engineering, Tongji University, Shanghai 201804, China b
Abstract
We propose a thermal management system for fast charging Li-ion battery pack combining liquid cooling and phase change material cooling. The main heat dissipating approach is liquid cooling, while composite phase change material wipes out the thermal-opaque area in the battery pack and provides relatively small amount of heat absorption. Alternated flow of coolant is required to guarantee temperature uniformity in the battery pack but is found detrimental to the holistic thermal dissipation. A method to address that issue, adding polyurethane adiabatic interlayers between cooling tubes, is proven to be an effective answer. Via analysing the heat transfer mechanism of the designed thermal management system, the influencing factors on its performance are found and a heat dissipation balancing coefficient is defined to quantify the temperature balancing performance of the system. The simulation for the system under an 8 C rate charging condition is conducted, as well as compare tests concerning coolant flowing directions, coolant flowing speeds, filling materials, and the interlayers. Simulation results show that the system in question well controls the temperature of an 8 C rate charging battery pack, with the maximum temperature at 38.69 ℃ and the temperature difference at 2.23 ℃.
Highlights
A cooling strategy is devised for fast charging battery packs. A balancing coefficient for the temperature balancing performance is defined. Detrimental impacts of alternated flow are found in hyper-thermogenic situations. Page 1 of 24
Adiabatic interlayers eliminate one flaw of the alternated flow. Simulations in COMSOL Multiphysics confirm the ability of the cooling method.
Keywords
Li-ion battery pack Fast charging Liquid-dominated cooling method Adiabatic interlayer Balancing coefficient Simulation
1. Introduction
Clean and energy-saving electric vehicles (EVs) have been researched and developed in hoping to substitute, if not all of, the major part of conventional vehicles [1]. Yet the confessed reality is that EVs take a small share in vehicles globally, resulting from untreated inconveniences. Two concerned issues are driving distance range and battery charging rate [2]. The demand for long driving range and fast charging spawns safety issues about applying hundreds, or even thousands of Li-ion battery (LIB) cells on EVs [3]. To assuage the “range anxiety”, large amount of LIBs are schematically modularised and packed, and systematically managed to be applied in electric vehicles [4, 5]. To tackle the other issue of too long charging time, the answer lies in fast charging technology, with 3 C or higher rates charging, which in theory reduces the full charging time to 20 minutes or less [6]. However, fast charging to LIBs actuates vast heat generation. Ye et al. [7] reported the vast heat generation of charging a sort of prismatic LIBs, which at 8 C rate charging have a volumetric heat generating rate of 797.1 kW m-3. It implies the perils in fast charging: the batteries mentioned above, in 8 C rate full charge, if not well cooled, would heat themselves up from atmospheric temperature (20 ℃) to averagely 154.4 ℃, according to Eq. (1), which is based on energy conservation principle. (1)
Page 2 of 24
The assumption accords with several studies involving the heat generation of LIBs, which is among 21.3–800 kW m-3 under fast charging or discharging, and potential dangers lie in them if the heat is not well dissipated [8–13]. Cells at such high temperature are in inappropriate working condition, leading to irreversible damage, or worse, combustion or even explosion [14, 15]. Therefore, the requirement abounds for an efficient battery thermal management system (BTMS), which, via taking away the heat, maintains the average temperature and maximum temperature difference within their safe ranges. Looking for an answer from existing and conventional cooling methods, including air cooling, liquid cooling, and phase change material (PCM) cooling, the most hopeful for vast heat dissipation must be liquid cooling due to liquid’s high specific heat capacity and fluidity. Fuller et al. [16] compared air cooling and liquid cooling applied in LIB pack, and observed that the peak temperatures of the pack under air cooling and liquid cooling were 50.65 ℃ and 35.60 ℃ respectively, while the temperature differences were 1.31 ℃ and 3.76 ℃ respectively. Chen et al. [11] compared air cooling, direct and indirect liquid cooling and fin cooling, and eventually deemed liquid cooling as the most practical method, while air cooling should consume 2 to 3 times more energy and fin cooling should add 40% more weight. Both illustrate liquid cooling’s potential to handle hyper-thermogenic situations, albeit with larger temperature difference. PCM alone can not handle the thermal management for such hyper-thermogenic situations. One problem is the inadequate latent heat capacity, 200－220 kJ kg-1. The volume cost should rise by 1.50–1.62 times of that of battery cells (considering 8 C rate charging), and mass cost should soar as well, based on the energy conservation principle as specified in Eq. (2). The other problem is the poor heat conductivity of paraffin, lower than 0.30 W m-1 K-1, hampering the diffusion and the dissipation of the generated heat. (2)
By the same token, composite PCM alone does not have that potential. Combining paraffin wax with Al, Cu, graphite, graphene, or hexagonal boron-nitride, can enhance thermal conductivity from 0.1–0.3 to 3–16 W m-1 K-1 [17– 21], at the sacrifice of a part of the latent heat capacity. Its lower latent heat capacity is not what fast charging LIBs are looking for, but the thermal conductivity of 3–16 W m-1 K-1 allows composite PCM the method combination with some efficient others, for instance, with heat pipe [22–24], with semiconductor thermoelectric device [25], with water cooling [26], or with fin structures [27]. All demonstrate that the combination methods have the edge over their original counterparts. Liquid cooling can handle the heat generation of LIBs under a wide range of charging rates. Panchal et al. [28] utilised cold plates with liquid cooling to control the temperature of a 4 C rate discharging LIB. Using cascade cooling method, Zhang et al. [29] reduced the temperature difference of an LIB pack from 7 ℃ observed in liquid cooling plate
Page 3 of 24
method to 2 ℃. Li et al. [30] deemed their designed water cooling method an effective one in dealing with the battery pack at cycling rates lower than 3 C. On a smaller scale, Mini-channel liquid cooling is convenient to be integrated with a single cell and deal with the heat generation under a 2 C discharging rate [31]. And mini-channel cooling is found capable of preventing battery fratricide when the thermal runaway within a single cell occurs, by Ma et al. [32]. Also found in the mini-channel liquid cooling method [31] is a detrimental effect brought by alternative flows, but the reason remains unfathomed. Besides, we believe the water cooling design conducted by Li et al. [30] can deal with higher cycling rates if the thermal conduction between cells and cooling tubes is raised. Liquid cooling needs delicate design methods for it to exert the best function. This work focuses on a thermal management method that combines liquid cooling with PCM cooling. It intends, with less space and mass costs, to achieve the effect observed in one cooling method that combines water cooling with heat pipes studied by Ye et al. [33]. Vast heat needs to spread from the internal to the surface of cells with a thermal conductivity not high, so that a considerable temperature difference will be formed between the internal and the external to power the heat transfer. And thus, it would be inappropriate to focus on the temperature variation by position in one cell, instead, the average temperature of a single cell should be worth the attention, and used to evaluate the maximum temperature and the temperature difference of the battery pack, and their criteria should be regarded as respectively not exceeding 40 ℃ and 5 ℃ [34]. Initially for flowing field design, this study applies several cooling tubes in parallel running through one large-scale battery module. Via theoretical analysis and the simulations, additionally, the issue of temperature inconformity in the battery pack is analysed and dealt with by adopting alternative flowing method in cooling tubes, which, unfortunately, induces unwanted “heat recovery”, which is later addressed by the insertion of adiabatic interlayers between the cooling tubes. The use of the adiabatic interlayers in liquid-dominated cooling system is an innovative concept. The adiabatic bars with low thermal conductivity can block heat transfer between cooling tubes. It is a solution for the problem that the large heat generation of fast charging batteries has made the alternated coolant flowing method deficient. Eventually, the effects of those designs including the coolant flowing directions, coolant flowing speeds, the insertion of the adiabatic interlayers, the filling for the composite PCM, etc., are studied in numerical simulations, searching for enhancement on the designed composite PCM and liquid cooling system.
2. Design of the thermal management system
Page 4 of 24
Prismatic LIBs same as those studied by Ye et al. [7], sized as 140 mm
65 mm
15 mm, with a capacity of 10
Ah, and a heat generation of 797.1 kW m-3 at 8 C rate charging, are involved to demonstrate the capability of the designed liquid/PCM cooling method. Fig. 1 shows the concept design of liquid and PCM cooling method in such prismatic battery pack. The pack contains 110 prismatic LIBs in a 10 tubes with a sectional size of 6 mm size of 10 mm
11 arrangement; 8 Aluminium (Al) cooling
13 mm; 7 adiabatic interlayers inserted between 8 cooling tubes with a sectional
2 mm; and PCM or composite PCM that fills up all the clearance of a 843 mm
235 mm
145 mm
cubic box (see Fig. 1c).
Fig. 1. The concept design of liquid and PCM cooling method. The method (a) with adiabatic interlayers and (b) without adiabatic interlayers, and (c) PCM filling.
Flows of coolant in cooling tubes are in alternated directions, which means that a flow direction of coolant in one tube is opposite to an adjacent counterpart. The coolant is 50% water-ethylene glycol mixture. Its physical property parameters, including heat capacity, heat conductivity, dynamic viscosity, and density, are variable by temperature. Algebraic equations were built between those physical property parameters and temperature (see Table 1). Composite PCM is applied in the designed BTMS, filling up all of the clearance in the battery module. The applied composite PCM consists of paraffin and EGM, already reported by other researchers [8], boasting a heat conductivity of 3.95 W m-1 K-1, and a latent heat absorption of 132.6 kJ kg-1 at a phase change temperature range of 21.6–25.5 ℃ (simulations involve the other phase change ranges).
Table 1 Thermo-physical properties of coolant symbols
definitions
units
temperature
℃
heat capacity
kJ kg-1 K-1
density
kg m-3
dynamic viscosity heat conductivity
variation with temperature
Pa s W m-1 K-1
Inserting adiabatic interlayers between cooling tubes is an optimising scheme in this study, while the original models without adiabatic interlayers are put here for comparison (shown in Fig. 1b). Those adiabatic interlayers cut off the heat transfer between cooling tubes. In our original design (shown in Fig. 1b), the application of the alternated flow is found performing an detrimental “heat recovery” — a high thermal conductivity of Al causes vast heat transfer
Page 5 of 24
between cooling tubes so that the coolant entering the battery pack would absorb, from coolant in the adjacent cooling tubes, heat that would have otherwise been taken out. The ultimate target for the designed BTMS that combines liquid cooling with composite PCM cooling is to maintain the maximum temperature of single cells, at 8 C rate charging condition, below 40 ℃ and the temperature difference of the battery pack below 5 ℃, meanwhile to reveal the interplay between the performance of the system and its variable factors. Besides, we intend to explicit the potential lying in liquid and PCM cooling system, by achieving the same effect brought by heat pipe thermal management system (HPTMS) applied on battery cells of same type and amount [33], but with lower costs of volume and mass.
3. Theoretical analyses
3.1 On the heat transfer
The heat transfer
1
between cell and cooling tube is calculated from the coolant to a cell wall with following
equations: (3) (4)
(5) (6) (7) 𝑏
is the average temperature of a battery cell, variating with 𝑠 , the flowing distance of coolant. Eq. (5) is a
Sieder-Tate empirical equation of the laminar flow heat transfer under constant wall temperature condition. the Reynolds number, and
is
, fluent’s equivalent diameter, expressed respectively in Eqs. (6) and (7).
3.2 On the temperature uniformity
To understand the temperature distribution in cooling tubes, the heat transfer between the cooling tubes and cells are calculated along the 6 straight ways of the cooling pipes, which are numbered from S1 to S6 shown in Fig. 2a, while the
Page 6 of 24
heat transfer at the U turns, including from U1 to U5, is neglected in the analysis. Vertically downwards, cooling tubes are numbered from 1 to 8 (see Fig. 2b), the alternated flowing directions are according with those shown in Fig. 1.
Fig. 2. The analyses on (a) the top view, (b) the bilateral view.
The heat absorption amount on an infinitesimal length
𝑠
of some coolant in Tube 1 can be expressed with
following equation: 𝑠
(8)
Via absorbing the quantity of the heat of
1
in some time of 𝜏 , this infinitesimal coolant gets a heat-up, and the
temperature rise can be expressed with following equation: (9)
From the inlet to the current position 𝑥 , conduct an integral operation: 𝑠
(10)
Then the temperature distribution on cooling Tube 1 can be expressed with the function of 𝑠 : (11)
with const 𝐶
1
and const 𝐶
2
𝐶
:
(12)
𝐶
(13)
Considering the symmetry of the designed model, the average temperature
𝑠
of 8 cooling tubes at 𝑠
position can be calculated with a function of 𝑠 , expressed in following equations: 𝑠
(14)
The variable part g(y) Elicited from Eq. (14) decides the fluctuation of temperatures of both coolant and batteries: (15)
with variable
and const 𝐶
3
defined as:
(16) 𝐶
𝐶
(17)
Indicated in the functional image of and 3.0, is that the value of 𝐶
3
in Fig. 3, while 𝐶
3
respectively equals to 0.1, 0.3, 0.6, 1.0, 1.5, 2.0
has got a correlativity with the fluctuation of
fluctuation by the flowing distance of coolant.
Page 7 of 24
, and hence with the temperature
, when 𝐶 equals respectively to 0.1, 0.3, 0.6, 1.0, 1.5, 2.0 and
Fig. 3. The function image of 3.0.
And the higher value of 𝐶
3
causes a worse temperature uniformity. Therefore, 𝐵
, the reciprocal of 𝐶
3
, is
defined in this study as thermal dissipation balancing coefficient: 𝐵
Coincidentally, 𝐵
(18)
or 𝐶
3
is a dimensionless factor. Higher value of 𝐵
depicts a better temperature
uniformity. Using the parameters in the control test (see section 5.1), where the maximum temperature difference in the end is 2.23 ℃, the value of the 𝐵 increases the value of 𝐵
is worked out to be 2.824 (𝐶
3
= 0.354). Raising the coolant flowing speed
, and indeed would narrow the temperature difference (see section 5.3). Nonetheless, this at
first could give suggestions on how to design a liquid-dominated BTMS for battery packs with better temperature conformity. The results of these analyses and particularly the definition of 𝐵
to some extent directed the design of
the BTMS in our work.
4. Simulations
Numerical simulations have been conducted in COMSOL Multiphysics, dedicated in different scenarios. The geometries for simulations were imported 3D-models mentioned before, including 134 parts, respectively 110 parts for the prismatic cells, 8 parts for the coolant, 8 parts for the cooling tubes and 7 parts for the adiabatic interlayers, and meshed in COMSOL Multiphysics generating 11,481,028 tetrahedral domain units, 1,631,129 boundary units and 159,450 edge units (shown in Fig. 4).
Fig. 4. The designed model meshing in COMSOL Multiphysics.
The bottom boundary is regarded as heat-convective to a stationary charging environment where constantly the temperature is 293.15 K or 20 ℃, the relative fluidity is 85%, and the wind speed is 0 m s-1, while the other boundaries are heat-insulated to the ambient. The starting temperature for the entire system is set as 293.15 K or 20 ℃. The heat generation rate is 797.1 kW m-3 as mentioned before, set to be evenly distributed in battery cells, and be a constant, which does not conflict with the intention of the simulations to assess the cooling ability of the designed system. This method is also applied in other researches using the same batteries [7, 33]. Page 8 of 24
The physical fields applied in all the simulations include heat transfer in pipes and heat transfer in solids. The values of Reynolds number for the coolant flow are among 497.8–2489.1, calculated with Eq. (6), with the coolant flowing speeds of respectively 0.2 m s-1 and 1.0 m s-1, the minimum value and the maximum value used in simulations (see section 5.3). And thus the coolant flow in cooling tubes is considered laminar flow, controlled by Eqs. (19) and (20), respectively the momentum equation and the mass conservation equation. (19) (20)
Besides, normal inflow velocity is set for coolant inlet, whilst 0-pressure condition and the suppressed back flow are set for coolant outlet. Heat Transfer in fluid is governed by Eq. (21); in PCM, Eq. (22); and in cells, Eq. (23). (21) (22) (23)
In Eq. (21), the first term on the left side denotes the time-unit heat variation via sensible heat exchange, the second denotes the heat transport caused by fluid flow, and the third, the heat conduction. Since no fluidity is set in battery and PCM, the item concerning heat transport is missed in Eqs. (22) and (23). The phase changing process of the composite PCM functions with the mechanism that is expressed in the following equations: (24) (25) (26) (27)
where
denotes the fraction of the phase before transition, and equals to 1 before transition and 0 after transition;
is the mass fraction of that, and equals to -0.5 before transition and +0.5 after transition. Generally 5 groups of simulations are conducted, and their purposes and details are listed below: The first is the control test containing our optimisation methods, applying alternated flowing directions in cooling tubes, setting the flowing speed of coolant 0.5 m s-1, inserting adiabatic interlayers with a thermal conductivity of 0.024 W m-1 K-1 (a theoretical value for polyurethanes with 30% blowing agent), and filling clearances with PCM boasting a thermal conductivity of 3.95 W m-1 K-1 and a latent heat of 132.6 kJ kg-1.
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The second is to demonstrate the effect of the alternated flow design, by comparing the method with parallel coolant flow, which means the flow directions of coolant in cooling tubes are the same, and the method in first group. Parallel coolant flow is set in the simulation in the second group. The third seeks to reveal the interplay between the coolant flowing speed and the performance of the BTMS. Based on the control test, several simulations have been conducted with different flowing speeds, respectively 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 m s-1. The fourth is to prove the influence brought by inserting the adiabatic interlayers between the cooling tubes. A compare test is conducted by replacing the adiabatic interlayers with the heat-conductive interlayers, and in handling of the simulation, the thermal conductivity of the interlayers is changed from 0.024 W m-1 K-1, as well as the other thermophysical properties, to that of Al, 237 W m-1 K-1. The last is to study the functions of the composite PCM that fills up all the clearance in the battery pack. To find out which parameter exerts most impact on the performance of the BTMS, 4 cases were studied including the first replacing the composite PCM with pure paraffin, the second assuming the phase change range to be 28.0–31.9 ℃, the third, 34.0– 37.9 ℃, and the fourth, 52.0–55.9 ℃ (COMSOL Multiphysics has direct access for setting the phase change range). The thermal conductivity of pure paraffin is 0.3 W m-1 K-1. Thus a comparison between the first case and the control test would explicate the function of thermal conductivity, if there is some. Likewise, between the control test and the second or the third case, comparisons would indicate the influence of differentiated phase change ranges. The fourth case applies an unexperienced phase change range to cancel the involvement of the latent heat, to see how the latent heat of PCM would matter to this system. All the simulations are processed in time-dependent studies, in which the time ends are set at 450s when LIBs theoretically get fully charged from 0% under 8 C rate charging. Data are stored per second. All the simulations are computed by the segregated time-dependent solver. The maximum number of iterations are set 10, the absolute tolerances are set 10-6 for velocity field, temperature and pressure, and at each time stepping, the event tolerances are all set 10-3.
5. Results and discussion
5.1 The capability of the designed thermal management system
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Fig. 5a shows the temperature distribution of the control test (PCM part is hidden) at 450s, where the inspected highest temperature is at the centre of the battery pack, about 46 ℃, while the lowest is at the inlets of coolant, 10 ℃. Fig. 5b shows the slice view of the temperature distribution in an XY-plane which evenly divides Tube 1. The similarity of the temperature distribution in every cell marks a good performance.
Fig. 5. The simulation results for the control test. (a) The volume view and (b) the slice view of the temperature distribution at 450s, (c) temperature rise of cells in an 8 C rate full charge.
To better reveal the temperature distributions, this study focuses on several special values: shown in Fig. 5c, the maximum, minimum, and quantiles. A p quantile value of temperature t indicates that the cell temperatures which are lower than or equal to t take a proportion p of the data cluster in one time point. From the temperature curves in Fig. 5c: the temperatures in cells rocket up when the charging begins; at about 20s, the phase change stage of PCM is activated and it starts to absorb heat, stored as latent heat, so that the temperature rise tends to decelerate from soaring to ratcheting up; at about 70s, PCM is gradually depleting its latent heat storage, causing the temperature curves returning to steepen; later as the temperature rises, temperature differences between cells and coolant expand, which accelerates the heat dissipation; in the end the trend for the temperatures to rise is wearing thin. The max value of the average temperatures of each cell at 450s is 38.69 ℃, while the lowest is 36.46 ℃ (according to the calculating mechanism of singular temperature), fostering a temperature difference of 2.23 ℃. The curves for quantiles over 0.9 seem dense, while the curves for quantiles under 0.1 are scattered, meaning that most temperatures of cells concentrate closely to the maximum temperature. Compared with HPTMS in the study of Ye et al. [33], which has the same amount of the identical cells and similar results (the maximum temperature in the end is also less than 40 ℃) when dealing with the 8 C rate charging condition, the liquid and composite PCM cooling system saves a large space cost by the evaporator in the HPTMS.
5.2 The effect of the alternated flowing design
The alternated flow design is intended for better temperature distribution in the battery pack, to eliminate the issue in the parallel flow that the cells near the inlet would have far lower temperature than the cells near the outlet. Simulation in that case, when the parallel flow is applied, results congruously to the expectation. From Fig. 6a, higher temperature distribution is observed in the parallel flow method than the equivalent in the alternated flow one, and the outlets of the coolant gathered at same side have obviously higher temperature than the inlets, causing the cells near the outlet obviously hotter than that near the inlet. Page 11 of 24
Fig. 6. The simulation results for the parallel-flow method. (a) The contour view of the compare test at 450s, (b) temperature rise of cells in parallel-flow method.
Fig. 6b shows the hot temperature and temperature inconformity brought by the involvement of the parallel flow. The maximum of the average temperatures of single cells at 450s is 42.69 ℃, while the minimum is 31.47 ℃, forming a temperature difference of 11.22 ℃. The other quantiles further indicate the temperatures of cells have a disperse distribution. For comparison, the corresponding temperatures in the alternated flow method are respectively 38.69 ℃ and 36.46 ℃ (temperature difference 2.23 ℃), demonstrating the indispensability of the alternated flow design in this TMS.
5.3 The influences of the coolant flowing speed
It was assumed that altering the flowing speed would have influences both on the bulk temperature and the temperature difference in the battery pack. Based on the deducted equation of 𝐵
(see Eq. (18)), raising the flowing
speed can improve the temperature uniformity in the battery pack. From Fig. 7a a sensitivity the temperature distribution has on the flowing speed is observed. Temperature variates by flowing speeds largely among low speedings (from 0.2 m s-1 to 0.5 m s-1). When the flowing speed is higher than 0.5 m s-1, the influences on the temperature distribution by raising the flowing speed wear thin. For safety concern that those temperatures should be under 40 ℃, the requisite flowing speed should be over 0.4 m s-1.
Fig. 7. The simulation results for different flowing speeds. (a) The curves of maximum temperatures, (b) the curves of temperature differences.
Their temperature difference curves among cells of various flowing speeds of coolant are shown in Fig. 7b. When the flowing speed is below 0.5 m s-1, lower flowing speed leads to obviously larger temperature difference, while at higher flowing speeds, that influence diminishes. In the initial 200 seconds, temperature differences experience similar fluctuations, due to the interference of phase change process. Temperature differences are all maintained under 5 ℃, which is largely because of the alternated flowing design. Temperature curves in Fig. 7 show that when the flowing speed is already 0.5 m s-1, to further raise the flowing speed has limited effects.
5.4 The effects of the adiabatic interlayers Page 12 of 24
It was presumed that cutting off the heat recovery caused by the heat transfer between cooling tubes would boost the cooling rate of the entire battery pack, and therefore lower the bulk temperature. Indeed this compare test (without the adiabatic interlayers) has confirmed that thought. There are mainly 3 differences between the compare test and the control test. First is a higher temperature, shown in the temperature contour view at the end of 8 C charging, in Fig. 8a; and in the maximum temperature curves in Fig. 8b display the difference — the compare test ends up with a maximum temperature of 44.52 ℃, while the corresponding value in the control test is 38.69 ℃. Second is a large temperature inconformity of cells observed in the contour view in Fig. 8a, also quantified in Fig. 8b, a temperature difference of 10.81 ℃ at 450s, compared to 2.23 ℃, the counterpart in the control test. Third is a visualised difference that, shown in Fig. 8a, the temperature distribution in Tube 1 becomes transparently different, especially at the second U-turn of the cooling circuit, with Tube 3, 5 and 7, where the flowing directions are the same with Tube 1. The phenomenon is observed in Tube 8 compared to Tube 2, 4 and 6 by the same token. Fig. 8c shows the temperature distribution in tubes. Because of geometrical symmetry, only the data of Tube 1 and Tube 3 are required to reveal their temperature distribution at 450s. Fig. 8d further illustrates the narrowed in-outlet temperature difference in the compare test compared to the control test. From Fig. 8c it is also observed that in control test the coolant temperature distribution is nearly an linearity rise over the flowing distance. And in compare test the coolant temperature starts to drop from S5 in Tube 3 or S6 in Tube 1, demonstrating the detrimental influence the heat transfer between adjacent cooling tubes brings. Further proving that is the difference shown between Tube 1 and Tube 3 that the coolant temperature in Tube 3 starts to drop earlier than that in Tube 1 as a result of their different adjacent conditions. Due to the geometrical symmetry of the design, a better linearity in the coolant temperature distribution depicts a better temperature uniformity in cells. So that the temperature difference of cells in the control test is smaller than that in the compare test (see Fig. 8b). To interpret the shake-up of the temperature distribution of the coolant in the compare test (see Fig. 8c), the nonuse of the adiabatic interlayers has turned the entry and exit parts of cooling pipe into two “heat recovery units”. The massive heat transfer between cold ingoing coolant and hot outgoing coolant has realised the recovering of the heat that would have otherwise been dissipated. The in-outlet temperature differences are proportional to the overall dissipated heat. And a comparison between the overall mean values of the them, 8.28 ℃ and 9.44 ℃ respectively in the compare test and the control test, shown in Fig. 8d, can well explicate the necessity of the adiabatic interlayers.
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Fig. 8. The simulation results for the method without the adiabatic interlayers and its comparison with the method with the adiabatic interlayers. (a) The contour view of the compare test at 450s, (b) the comparison on the maximum temperature and the temperature difference, (c) the comparison on the temperature distribution in cooling tubes at 450s, and (d) the comparison on the temperature difference variating over time.
5.5 The simulations for the composite PCM
From previous temperature curves (see Fig. 5, 6, 7 and 8), the composite PCM has slowed down the temperature rise during its phase change temperature range during some certain time. Yet as discussed before, the really useful quality of the composite PCM could be its large thermal conductivity. The results of simulations concerning the question are shown in Fig. 9. From Fig. 9a, with paraffin filling, the maximum temperature ends up at 62.03 ℃, while the others maintain the maximum temperature under 40 ℃. Whereas in case 4 the assumed composite PCM with a phase change range of 52– 55.9 ℃ is not able to perform the phase change function, it controls the temperature well. From Fig. 9b, those fluctuations are similar to the counterparts in Fig. 7b, at different timings according fitly with their respective phase change ranges. But no clear interplay, can be found in the curves, between those temperature differences and the thermal conductivity or other properties of the filling materials. The in-outlet temperature difference shown in Fig. 9c and the coolant temperature distribution in Fig. 9d confirms that if the composite PCM of same thermal conductivity is applied, no matter whether there is a phase change process, or when, the results resemble with each other.
Fig. 9. The simulation results comparison among the methods with case 1, altered to pure paraffin; case 2, phase change range 28– 31.9 ℃; case 3, phase change range 34–37.9 ℃; case 4, phase change range 52–55.9 ℃; and control test (see section 5.1). The curves of (a) maximum temperatures, (b) temperature differences and (c) coolant temperature differences, (d) the coolant temperature distribution at 450s, (e) the statistics for heat taken out, latent or sensible.
The quantities of heat including those dissipated by liquid cooling, absorbed by the composite PCM and remaining for temperature rise, denoted respectively as heat “taken-out”, “latent” and “sensible” are collected and shown in Fig. 9e. The statistics for each case are calculated in light of heat conservation principles, including that in this battery pack the heat generated equals to the sum of 3 mentioned constituents. Among the holistic 5.39 MJ heat generated by LIBs under 8 C charging for 450s, the majorities are taken out by coolant in all cases. In control test, some 4.49 MJ heat is dissipated by liquid cooling, accounting for 83.3% of the generated heat, while the corresponding percentage for the heat absorbed by the composite PCM is only 8.5%. Sensible heat remains in the battery pack to cause the temperature rise. Some 1.31 MJ sensible heat abounds in case 1, wherein leading to the maximum temperature reaching 62 ℃ (see Fig. 9a). For contrast, the equivalents in other cases and the control test range between 0.35 MJ and 0.46 MJ, and their
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thermal performances reveal the connotation that a high heat conductivity of the filling material functions in a great difference with a low one.
6. Conclusions
We propose a thermal management method that combines liquid cooling and composite PCM cooling for the large heat generation of LIBs during fast charging. The factors that dominate the performance of the system, concerning both liquid cooling and PCM cooling, are investigated. For liquid cooling, theoretical analysis is conducted on the heat transfer mechanism between the coolant and the cells, and the heat dissipating uniformity is found related to several design parameters so that 𝐵
is defined and
expressed with those parameters to quantify the heat dissipating uniformity. Alternated flowing design is needed for better temperature uniformity, but has brought a problem — the heat transfer between cooling tubes returns the heat from the outgoing coolant into the incoming coolant, forming a detrimental “heat recovery” — which is addressed by the adiabatic interlayers inserted between cooling tubes. The adiabatic interlayers cut out the massive heat transfer, and maintain both the cooling ability and the temperature uniformity of the system. Simulations on the filling materials have confirmed the designed BTMS as a liquid-dominated cooling system. Whereas the composite PCM is applied, the heat absorption it supplies only accounts for less than 10% of the generated heat, while liquid cooling takes 80% by the same token. The system still shows acceptable performance when the phase change of the material is not involved, and the real usefulness found out of the composite PCM seems to be its boost for the heat conduction between the coolant and the cells. Therefore, the composite PCM functions well, but could be better being replaced by some other materials with higher thermal conductivity and better feasibility. A high thermal conductivity of the filling material is extremely important in a fast charging battery pack, since it impacts largely on the heat transfer between the coolant and the cells. As a conventional cooling method, liquid cooling is authenticated powerful to deal with hyper-thermogenic situations. Space and mass costs are critical to an electrical vehicle, and the designed BTMS can lower the cost. It is advisable to develop a BTMS that combines liquid and composite PCM cooling achieving such good temperature distribution in a fast charging Li-ion battery pack.
Acknowledgement Page 15 of 24
This work was financially sponsored by the National Natural Science Foundation of China (No. 51632001)
Nomenclature coolant flowing area in Tube 1 [m2] cooling tube’s sectional width [m] 𝐵 𝑏
thermal dissipation balancing coefficient cooling tube’s sectional height [m]
𝐶
constant 1
𝐶
constant 2
𝐶
constant 3 battery’s specific heat capacity [kJ kg-1 K-1]
𝑏
coolant’s specific heat capacity [kJ kg-1 K-1] PCM’s specific heat capacity [kJ kg-1 K-1] PCM’s specific heat capacity in phase 1 [kJ kg-1 K-1] PCM’s specific heat capacity in phase 2 [kJ kg-1 K-1] Al wall’s thickness [m] fluent’s equivalent diameter [m] PCM’s thickness [m] unite matrix Euler’s number fluid volume force [N] heat transfer coefficient [W m-2 K-1] cooling pipe’s height [m] convective heat transfer coefficient [W m-2 K-1] charging rate [C] coolant full flowing distance [m] 𝑏
battery’s mass [kg] PCM’s mass [kg] Prandtl number Pressure [Pa] heat dissipation rate by liquid cooling [W] heat dissipation rate by natural cooling [W] heat flux density [W m-2]
𝑏
cell’s volumetric heat variation [kW m-3] coolant’s volumetric heat variation [kW m-3] PCM’s volumetric heat variation [kW m-3] cell’s volumetric heat generating rate [kW m-3] heat transferred to Tube 1 [J] Reynolds number PCM’s latent heat [kJ kg-1]
𝑠 𝑏
coolant’s flowing distance [m] battery’s temperature [℃] coolant’s temperature [℃] Page 16 of 24
PCM’s temperature [℃] coolant’s flowing speed [m s-1] 𝑏
battery’s volume [m3] PCM’s volume [m3]
𝑥, ,
Cartesian coordinates [m]
difference operator nabla operator PCM’s mass related phase position PCM’s volumetric related phase position Al’s thermal conductivity [W m-1 K-1] coolant’s thermal conductivity [W m-1 K-1] PCM’s thermal conductivity [W m-1 K-1] PCM’s thermal conductivity in phase 1 [W m-1 K-1] PCM’s thermal conductivity in phase 2 [W m-1 K-1] dynamic viscosity of coolant [Pa s] 𝑏
battery’s density [kg m-3] coolant’s density [kg m-3] PCM’s density [kg m-3] PCM’s density in phase 1 [kg m-3] PCM’s density in phase 2 [kg m-3]
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