Performance improvement of thermal management system of lithium-ion battery module on purely electric AUVs

Accepted Manuscript Performance Improvement of Thermal Management System of Lithium-ion Battery Module on Purely electric AUVs Yan-Feng Wang, Jiang-Tao Wu PII: DOI: Reference:

S1359-4311(18)34639-8 https://doi.org/10.1016/j.applthermaleng.2018.09.108 ATE 12717

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

26 July 2018 28 August 2018 24 September 2018

Please cite this article as: Y-F. Wang, J-T. Wu, Performance Improvement of Thermal Management System of Lithium-ion Battery Module on Purely electric AUVs, Applied Thermal Engineering (2018), doi: https://doi.org/ 10.1016/j.applthermaleng.2018.09.108

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Performance Improvement of Thermal Management System of Lithium-ion Battery Module on Purely electric AUVs Yan-Feng Wang*, Jiang-Tao Wu MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China

Highlights A paraffin-dominated BTMS is developed to optimize the output performance of the battery module for purely electric AUV. Modeling heat generation and diffusion for the battery module with paraffin-dominated BTMS is implemented. Numerical calculations expose the potential mechanism and critical conditions on thermal runaway. Some new insights are incorporated into capturing the excellent performance of the battery module.

Abstract A paraffin-dominated battery thermal management system (BTMS) is developed in this work, to protect the Li-ion battery (LIB) module from thermal runaway and improve the output performance of autonomous underwater vehicles (AUVs). First, a physical model is established for analyzing the transient heat transfer process and corresponding thermal behavior, occurring in the AUV’s battery module during its charge/discharge cycles. Second, numerical calculations are performed by using a pressure-velocity coupled algorithm based on a finite volume solver, to reveal heat dissipation and temperature distribution on the battery module cooled by the paraffin-dominated BTMS. Third, the calculation results are verified comparing with the open literature data. It indicates that air-dependent thermal resistance in the battery module causes an inevitable temperature rise and nonuniformity accounting for potential thermal runaway. Also, the

* Corresponding author. E-mail address: [email protected] (Y. F. Wang). 1 / 39

customized RT48 paraffin mixture with a melting temperature range from 321.0 K to 325.0 K is high-efficiency to maintain the optimal working temperature and temperature difference for the battery module. In conclusion, a well-controlled phase change temperature range and equivalent thermal conductivity combined with the optimized charge/discharge strategy is exceedingly crucial for guaranteeing thermal safety and high performance regarding the AUVs. Besides, the research findings are in good agreement with the open literature data.

Keywords Battery module; phase change material; battery thermal management system; thermal runaway; user-defined function

Nomenclature A Heat transfer area ( m 2 )

Bi The Biot number c p Specific heat capacity ( kJkg -1K -1 )

Da Thermal diffusivity ( m2s-1 )

E Voltage ( V ) F Faraday constant, 96485 Cmol-1

g Gravitational acceleration ( ms-2 ) -1 -1 h Heat transfer coefficient ( Wm K ), specific sensible enthalpy ( kJkg -1 )

href Specific reference sensible enthalpy ( kJkg -1 ) -1 H Specific enthalpy ( kJkg )

I Discharge current ( A ) -1 L Specific latent heat of fusion ( kJkg )

m Mass ( kg ) n Number of moles of electrons ( mol )

N Number of batteries, modules p Pressure ( Pa )

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Q Heat energy ( J )

Q Volumetric heat source ( Wm-3 )

r Cylindrical-coordinate ( m ) R Electric resistance (  ), radius of battery ( mm )

S Entropy ( JK -1 ) T Temperature ( K )

U Velocity vector ( ms-1 ) V Voltage ( V ) x, y, z Cartesian coordinates ( m ) H The change in specific enthalpy ( kJkg -1 )

S The change in entropy ( JK -1 ) T The change in temperature ( K )

Greek letters  Thermal expansion coefficient ( K -1 )

 Volumetric fraction  Volume expansion rate for the paraffin mixture

 Thermal conductivity ( Wm-1K-1 )  Kinematic viscosity ( m2s-1 )

 Density ( kgm-3 )  Discharge time ( s )

Subscripts a Air b Battery

conv Convective heat transfer cond Conductive heat transfer eff

Effective

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j Joule effect

i Initial, the ith iteration l Liquidus

ocv Open circuit voltage

p Phase change material, i.e. RT48 paraffin, electrochemical polarization

r Electrochemical reactions ref

Reference

s Solidus, side reactions

Abbreviations AUV Autonomous underwater vehicle ABS Acrylonitrile butadiene styrene engineering plastic BTMS Battery thermal management system EV Electric vehicle HEV Hybrid electric vehicle LIB Li-ion battery PCM Phase change material PPS Polyphenylene sulfide engineering plastic ROV Remotely operated vehicle UUV Unmanned underwater vehicle

1. Introduction An autonomous underwater vehicle, as an intelligent underwater robot, usually travels in the sea without any operator controlling. In general, AUVs constitute an essential part of a larger group of unmanned underwater vehicles (UUVs), which also consist of non-autonomous remotely operated underwater vehicles (ROVs) controlled and powered from the surface by an operator via a cable or using remote techniques. Autonomous underwater gliders (AUGs) are known as a subclass belonging to AUVs. With the development of advanced controlling technologies and high-performance power supplies, purely electric AUVs are now being extended to perform more and more complex, hazardous tasks, e.g., shallow-water hydrographic and hazard surveys,

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geophysical mapping and positioning, deepwater pipeline and flowline inspections, marine construction surveys, offshore oil and gas exploration, etc. For instance, the Bluefin-21 AUV has been utilized to search for Malaysia Airlines Flight 370 (MH370/MAS370) in 2014 [1]. When it refers to some essential technologies relevant to AUVs, undoubtedly, the power supply is especially indispensable and very urgent. Until now, two kinds of power supplies have been successfully applied in the AUVs, i.e., the batteries including primary, rechargeable types, even fuel cells, and environmental energy conversions, such as solar energy, ocean thermal energy, wave energy and so on [2]. Take fuel cells for example, Li et al. [3-6] have been exploring the potential performance of the proton membrane fuel cells for a long time, as well as they have already made a great contribution for promoting the PEMFCs’ commercialization in the fields of EVs/HEVs/AUVs. Comparing with other electrochemical conversions, the LIB is more advantageous for either civil or military AUVs due to its significantly high energy density and charge/discharge efficiency, little memory effect, low self-discharge, etc. [7]. Given many successful applications incorporating Li-ion batteries (LIBs) as well as relevant battery thermal management systems (BTMSs) [8-12] into electric vehicles (EVs) and hybrid electric vehicles (HEVs), it is increasingly feasible to develop purely electric AUVs. The purely electric AUVs propelled by lithium-ion batteries have a huge potential market for ocean surveys. However, relevant research can hardly be found especially on the reliable battery thermal management system. No matter how the AUVs obtain the power supply, they are severely dependent on the proper battery pack working well in the ocean, just as the common EVs/HEVs, e.g., electric cars, buses, trucks, etc., according to the extensive open literature data [13-15]. According to the open literature data [12, 16], either high operating temperature or big temperature difference can cause irreversible damage to any LIB type. Pesaran [17] has found that the optimal operating temperatures for most LIBs are ranging from 298.0 K to 328.0 K, and also the acceptable temperature difference on the battery module is no more than 5.0 K. Meanwhile, Sato et al. [18] have also pointed out the battery module’s temperature above 323.0 K will naturally diminish its charge/discharge efficiency as well as endurance. In theory, the LIB will be permanently destroyed at the operating temperatures over 373.0 K, especially when it exceeds 403.0 K, hazardous thermal runaway, and even explosion is almost bound to happen due to

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thermal accumulation relevant to SEI film decomposition [11, 19]. Wherein, thermal runaway is mostly noticeable for the battery pack’s research and development, primarily referring to either high discharge rates or long endurance. Besides, the temperature nonuniformity due to poor heat diffusion effectiveness within the battery pack will severely affect its overall output performance as well as charge/discharge efficiency. Above potential risks immensely restrict incorporation of the LIB into the AUV applications, as well as invariably indicate that the BTMS plays an indispensable role in maintaining the optimal working temperature for the battery, improving the temperature uniformity within the battery pack, and protecting the large-scale battery pack from potential thermal runaway [20]. Frankly speaking, the application of LIBs in the AUVs’ field is still in its infancy compared with conventional power sources. Some restrictions are highlighted here to account for this bottleneck. Relatively narrow geometric structures corresponding to the AUVs are not suited for high battery pack density, which impacts both the cruising speed and endurance. Also, the unexpected complexity in technology seems to be inevitable due to low seawater temperature as well as heat accumulation inside the LIBs, which means how to maintain the optimal working temperature within the LIBs requires comprehensive consideration on heat preservation outside the AUV and heat dissipation inside the AUV. To overcome those technical bottlenecks on the LIB utilization in the AUV’s field, on the one hand, it is necessary to optimize the charge/discharge strategy against the battery pack to minimize heat generation due to the Joule effect, electrochemical reactions, polarization reactions, etc. [21]. On the other hand, it is also practicable to develop high-performance battery thermal management systems (BTMSs) based on high-efficiency heat exchanger array, microscale heat pipes, phase change materials, etc. [22-24], improving heat transfer efficiency relevant to the whole battery pack. In general, the common BTMSs can be classified into three main categories regarding different application backgrounds [25, 26], i.e., active cooling systems, passive cooling systems as well as hybrid cooling systems. On the one hand, active cooling systems, such as the air cooling or liquid cooling technique, usually are composed of complicated flow management, which increases the technical difficulty for the system and also presents a risk of fluid leakage. Also, system components such as a fan/pump are also required for driving the wording fluid. Besides, the

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cooling must be well distributed in order to obtain relatively uniform temperature distribution within the whole battery pack. Rao et al. [27] have introduced a liquid cooling BTMS for the cylindrical LIB module. Liu et al. [28] have also demonstrated that the liquid cooling method is more efficient to mitigate the temperature rise in the battery compared with the PCM cooling method. In contrast with the air cooling BTMS, the liquid cooling BTMS is increasingly widespread owing to its high heat transfer efficiency [29], especially for the large-scale battery module operating at high charge/discharge rates. On the other hand, the passive cooling systems depend mainly on the phase change phenomenon. Therefore, all of the cooling techniques based on phase change materials and heat pipes belong to this kind of category. Regarding these phase change cooling BTMSs, the phase shift for solid/liquid or liquid/gas can readily occur within the utilized phase change materials (PCMs) and experience a relatively narrow temperature fluctuation. Simultaneously, molecular structures of the PCMs are reconstructed quickly, as well as tremendous heat energy is also absorbed or released. The elevated PCMs draw relevant researchers’ and manufacturers’ attention on account of their non-toxicity, non-corrosion, chemical stability, low-cost, high-efficiency, etc. Al-Hallaj and Selman [30] have first introduced and demonstrated better performance compared with other BTMSs. As one of the competitive PCMs, paraffin is usually featured as high compatibility with conventional materials of construction, non-undercooling and non-reactive apart from those advantages described previously [31, 32]. Greco et al. [33, 34] have explored the effects of the PCM cooling solution through thermal and electrochemical modeling. They have found that the paraffin material/compressed extended natural graphite exhibits more advantages for controlling both temperature rise and uniformity within the battery module in contrast with forced convection cooling. Besides, Van Gils et al. [35] have immersed Sony 18650 LIB into the dielectric liquid (Novec 7000), as well as have observed the temperature difference within the battery less than 1 K under a non-boiling condition. Besides, the temperature difference has almost been eliminated when the dielectric coolant is boiled. As mentioned above, considerable efforts have been making to explore the high-performance and cost-effective BTMSs for EVs/HEVs in the past decades. In general, the active cooling BTMSs are relatively complicated, but they are usually famous for better heat diffusion

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effectiveness. So far, only a few of extremely mature liquid cooling configurations are suitable for the mass-produced battery packs. It is undoubtedly paradoxical between sophisticated technology and high reliability. Also, either the air or liquid cooling approach is encountering a significant challenge due to seawater pressure, seal and electric insulation. Therefore, the active cooling BTMSs are not properly utilized in AUV applications after weighing the pros and cons. In contrast, the passive cooling BTMSs exhibit significant advantages for creating more homogenous temperature distribution within the battery pack, which coincides with the primary purpose of this work. However, all of the pioneering explorations are basically concentrated on the EV/HEV utilizations according to the literature review. Those findings cannot be directly transplanted to the AUVs due to their more complicated heat convection environments and higher thrust-weight ratios. As we all know, the heat diffusion effectiveness of seawater is better than that of air, so that temperature nonuniformity will be more apparent in defect of a high-efficient BMTS. So far, the relevant researches incorporating the PCM cooling BTMS into the purely electric AUV applications are still extremely scarce, especially full-scale modeling powered by the large-scale LIBs, although it exhibits significant advantages for predicting a whole heat transfer phenomenon and the 3D temperature distribution. Thus, the purely electric AUVs powered by LIBs call for much more efforts after considering all those factors emphasized above. This study aims to develop a state-of-the-art, pollution-free, high-efficiency, high-performance battery module based on a kind of customized cylindrical lithium-ion battery, to provide sufficient propulsion power for commercial AUV, which is mainly applied to survey offshore oil and gas resources in the South China Sea. For this purpose, a PCM cooling BTMS is mainly designed for this purely electric AUV based on the customized RT48 paraffin mixture, to suppress sharp temperature rise in the batteries and improve the temperature uniformity within the battery pack combining with the optimal charge/discharge strategy addressed in previous work. Concurrently, this study is oriented at the practical application, the authors have accurately measured thermal and electrochemical properties for the utilized PCM and lithium-ion battery, e.g., bulk density, specific heat capacity, anisotropic thermal conductivity, internal electric resistance and so on, depending or not, on the SOC and transient temperature. All of these parameters adding computation-related ones have been programmed as different user-defined functions (UDFs) using

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the C++ language, which have subsequently been compiled with the ANSYS package for pursuing high-accuracy numerical calculations. Also, given an approximately periodic distribution along the symmetric axis (Z-axis) direction consistent with realistic AUV configuration, only one of the battery modules is selected from the whole battery pack for high calculation efficiency. In addition, each battery module consists of 60 individual batteries fixed through ABS or PPS engineering plastic frameworks. Heat diffusion occurring in the battery module is numerically studied combining the RT48 paraffin-dominated BTMS in the cubic space and single discharge cycle. Relevant studying results are clearly illustrated via time-dependent temperature contours and velocity curves, isotherm plots, as well as the trend of heat transfer coefficients regarding quantitative amounts of heat energy generated by the batteries. The present modeling provides extensive information about transient temperature rise and distribution characteristics within the AUV’s battery module/pack throughout the charge/discharge cycles [36], which is beneficial to both achieve high propulsion power and prevent potential thermal runaway, as well as give guidelines for design and manufacturing of the BTMS. Last but not the least, a prototype of 50 kg class lightweight AUV has been trial-manufactured and tested in the South China Sea based on the numerical simulations from this work. The close agreement can be obtained between computational results with the open literature data and experimental data. Unfortunately, the experimental data cannot be published at present due to a confidentiality agreement with the collaborative company.

2. Modeling development Decreasing air volume fraction of the battery module as much as possible contributes to elevate the power density, as well as to improve heat transfer efficiency theoretically, due to much lower equivalent thermal resistance on the whole battery module. According to this guideline, a hexagonal close-packing battery module with around 30% in air volume fraction had already been designed very well consistent with the AUV’s tubular shell, approximately increasing by 20% in output propulsion power in contrast to the conventional cylindrical close-packing battery module [37, 38]. According to measurements carried out by the authors, the utilized lithium-ion battery can almost achieve the optimal power performance at 322.7 K roughly, as well as the assembled battery pack/module exhibits the optimal consistency when temperature difference within it keeps 9 / 39

less than 5.0 K. Therefore, an RT48 paraffin-dominated BTMS is developed in this work for the AUV’s battery module, to maintain the optimal working temperature for all lithium-ion batteries as well as prevent thermal failure relevant to the battery module. A three-dimensional, time-dependent physical model comprehensively considering mass, momentum, energy conservation on a combination of batteries, RT48 paraffin phase change material, ABS/PPS engineering plastic frameworks, aluminum interconnectors, air layer, etc., is constituted to describe coupled conduction, convection, and phase change process. The details are presented as follows.

2.1. Heat generation in Li-ion batteries When mentioning the heat transfer process, it is crucial to first understand the potential mechanism of heat generation, with the series-parallel LIBs discharging, especially at either high operating temperatures or discharge rates. In theory, heat energy due to LIB’s charge/discharge cycles may derive from normal electrochemical reactions between active anode material and active cathode material, solid electrolyte interface film, electrolyte and anode decomposition, uncontrollable electrochemical reactions between cathode and electrolyte or cathode with adhesive, etc. The processes mentioned above relevant to electrode decomposition and electrochemical reactions are unexpected complex, although abundant research work has been carrying out to seek their mechanisms in the past decades. Huang et al. [39] have reported that the heat energy produced at the cathode is roughly four times of that donated by the other domains from the single battery. Comprehensively considering the other open literature data [40-42], it can be reasonably assumed that the temperature distribution near the electrodes including both the anode and the cathode ought to be significantly higher than the other place far from the electrodes. However, the primary purpose of the BTMS is aimed to not only control the temperature distribution over the single battery and the assembled battery module or pack within an appropriate range but also keep the temperature difference in the whole unit as even as possible. In general, transportation of chemical species due to electrochemical reactions are usually characterized by Fick’s law of diffusion inside the single battery. The Nernst equation is often used to describe a complicated relationship among open-circuit voltage, output voltage, operating temperature and concentration of electrodes’ active materials. The classical Butler-Volmer 10 / 39

equation theoretically expresses the current densities over both electrodes. The Arrhenius equation approximately represents the activation energy, the diffusion coefficient, the electric conductivity, etc., varying with the operating temperature. Whereas, the methodology in this work is formulated regarding thermal characteristics of the LIB, as well as temporarily not considered the further simulations for those complex electrochemical reactions, although which are closely related to the heat generation and consumption processes. The law of conservation of energy expresses the heat generation due to the Joule effect, electrochemical reactions, polarization reactions and side reactions. First, the heat generation due to the Joule effect during the battery’s discharge cycle is approximately described according to Bernardi equation [43, 44] as follows. Q j  Ib  Eoc  E   Ib 2 Rb

(1)

where Q j is the heat energy due to the Joule effect in the single battery, I b is the discharge current, Eoc is the open-circuit voltage, E is the output voltage, Rb is the battery’s electric resistance,  is the discharge duration. G  H  T S  H  Qr

(2)

where G indicates the Gibbs free energy, primarily representing the potential maximum electric work outputted by battery, H is the enthalpy change occurring in the battery during the discharge process, S is the entropy change, Qr is the heat energy relevant to the entropy change due to reversible electrochemical reactions in the battery. During the reversible electrochemical reaction, the following equations involving the Gibbs free energy hold. Qr  T S  T

G T

G  nFEe

(3) (4)

Substituting equations 3, 4 into equation 2, it obtains the final form for heat energy due to the electrochemical reactions as follows. Qr  nFT

dEe dEe  I bT  dT dT

(5)

where n is the mole number of electrons transferred in the electrochemical reactions, F is the Faraday constant with a value of 96485 C/mol , T is the nominal battery temperature, Ee is 11 / 39

equilibrium electromotive force (EMF) of the battery, dE dT is usually known as the e temperature coefficient. The electrochemical polarization occurring in the charge/discharge cycles over the battery is prone to cause a deviation between actual electromotive force and EMF as usual, in which it also releases a little part of heat energy. Qp  nF  E f  Ee 

(6)

Qb  Q j  Qr  Qp  Qs

(7)

where Q p is heat energy due to the electrochemical polarization, E f is the actual electromotive force, Qb is total heat energy in the discharge process of the battery, Qs is the heat energy due to undesired side reactions. Therein, in the early stage during the charge/discharge cycles regarding the battery, Q j is dominantly accounting for total heat energy, especially at high discharge rates. However, in the late stage, especially being close to the end, this phenomenon will be reversed, and then Qs will contribute much higher proportion for heat generation. In most cases, Qs is usually produced due to electrolyte decomposition and other accompanied side reactions.

2.2. Heat transfer in RT48 paraffin mixture It is usually complicated to explain a heat transfer problem due to phase change, mainly because a gradually developing solid-liquid boundary as a function of time must be dealt with simultaneously except for regular heat transfer component. This moving boundary explains a phenomenon that the principle of linear superposition on solutions is no longer applicable. Thus, all subdomains referring to a solid phase, liquid phase, and transition phase have to be considered, respectively. Also, convective heat transfer coupling with volume change due to the phase change process makes the heat transfer problem more complex further. Combining the previous research work, a kind of unique paraffin phase change material, named as RT48, is customized in this study according to thermal features of the utilized LIB and the optimal charge/discharge strategy. Because its thermophysical properties are uncommon in the open literature data. Therefore, the authors have measured some essential thermophysical

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properties as shown in Table 1, mainly including bulk density, specific heat capacity, thermal conductivity, phase change temperatures and so on, using different measurement methods for pursuing high-accuracy numerical calculations. The RT48 paraffin is filled into each battery submodule, as well as in direct touch with the batteries due to its reliably electric insulation and homogeneous thermal conductivity. Therefore, the RT48 paraffin-dominated BTMS can control the optimal operating temperature for the battery module due to its sponge-like heat absorption and heat conduction, when the AUV works in the South China Sea. Table 1 Thermophysical properties of the RT48 paraffin phase change material Thermophysical property

Solid

Averaged molecular weight

Liquid 377.0

Temperature of phase change ( K )

<321.0

>325.0

Latent heat of fusion ( kJkg -1 )

-179.0

179.0

Specific heat capacity ( kJkg-1K -1 )

1.18

2.14

Density ( kgm-3 )

900.0

760.0

Thermal conductivity ( Wm-1K-1 )

0.558

0.335

Table 1 shows the equivalent thermophysical properties of the RT48 paraffin mixture customized regarding the AUV’s requirements in this study. According to measurements on the current-voltage characteristics for the utilized lithium-ion battery, the authors have found that the battery’s optimal working temperature is around 322.7 K. Meanwhile, a temperature difference of less than 5.0 K is always recommended for the lithium-ion battery pack according to the open literature data. Hence, the biggest motivation for this study is to maintain the optimal working temperature range for the battery module/pack instead of reducing it as much as possible, although a viewpoint that the lower the working temperature of battery module/pack, the better the output performance of battery module/pack, seems to be more popular for most of the research literature. For this purpose, a kind of unique paraffin mixture has been customized through adjusting different chemical compositions for matching above optimal working temperature range from 321.0 K to 325.0 K subject to the utilized battery module in this research. It means that the RT48 paraffin begins to melt at 321.0 K, and then wholly becomes liquid above 325.0 K. Meanwhile,

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both solid and liquid paraffin components co-exist between 321.0 K and 325.0 K. During the phase change process, a significant rise in temperature does not appear for the whole AUV’s battery module until all the paraffin is transformed into the liquid phase. Substituting relevant thermophysical properties of the customized RT48 paraffin phase change material as shown in Table 1 into the energy conservation equation subject to the whole battery pack, one can reasonably estimate the total amount of solid-state paraffin consistent with the heat generation due to the batteries discharging. N m Nb



i 1 j 1

0

N m Nb Qb    mb c p ,b T (i, j )    ha ATd  m p c p , p Tp ,l  Tp , s 

mp 

N m Nb



i 1 j 1

0

N m Nb Qb    mb c p ,b T  i, j     ha ATd c p , p  Tp , l  Tp , s 

(8)

(9)

where N m is the number of battery module composing the AUV’s battery pack, N b is the number of single batteries composing each battery module, mb , c p ,b are the battery’s mass, specific heat capacity, respectively, m p is the total mass of RT48 paraffin filled into the complete battery pack, ha is convection heat transfer coefficient of the air, A is the heat exchange area due to natural convection, Tp , s , Tp ,l is the solidus, liquidus temperature of the paraffin, respectively. Only a small portion of paraffin melts slightly during the charge/discharge cycles in the AUV application. An enthalpy-porosity technique is used in this study for modeling the melting process [45, 46]. In this technique, the melt interface is not tracked explicitly. Instead, a quantity called the liquid fraction, which indicates the fraction of the cell volume that is in liquid form, is associated with each cell in the domain. The liquid fraction is computed at each iteration, based on an enthalpy balance. The liquid-solid mushy zone is a region in which the liquid fraction lies between 0 and 1. The mushy zone is modeled as a “pseudo” porous medium with porosity equal to the liquid fraction, in which the porosity increases from 0 to 1 as the material melts. When the material has fully melted in a cell, the porosity becomes one, and hence the local temperature also rises. Besides, appropriate momentum source terms are added to the momentum equations to account for the change in pressure caused by the presence of the liquid material. Therefore, the

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phase change problem related to the RT48 paraffin mixture becomes much more straightforward since the governing equations are the same for both solid and liquid phases by introducing the enthalpy-porosity method. Also, interface conditions are automatically achieved and create a mushy zone between the two phases. Enthalpy function, defined as a function of transient temperature, is given by Voller et al. [46] H p 

   p  T  

(10)

where H p is total specific enthalpy of the paraffin, which is computed as the sum of the specific sensible enthalpy and the latent heat of fusion as follows.  is heat transfer time, T is time-dependent temperature of the paraffin,  p , s ,  p ,l is the thermal conductivity relevant to solidus and liquidus paraffin, respectively. H p  hp  H p

(11)

T

hp  href , p 

c

p, p

dT

(12)

Tref

H p   p ,l Lp

 p ,l

0,  T  T p,s  T  T p,s  p ,l 1

(13)

T  Tp , s Tp , s  T  Tp , l

(14)

T  Tp , l

where  p ,l is volume fraction of the liquid paraffin, h p is specific sensible enthalpy, H p is latent heat of fusion corresponding to the melted paraffin, href , p is reference specific sensible enthalpy, Tref is reference temperature, c p , p is specific heat capacity of the paraffin, L p is specific latent heat of liquefaction, Tp , s , Tp ,l is the solidus and liquidus temperature, respectively. For the phase change problem in this study, the energy conservation equation is written as    p H p       p vH p      pT   S 

(15)

where  p is density of the RT48 paraffin, v is velocity of the liquid paraffin, S is source term of total specific enthalpy on the paraffin.

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The solution for temperature is essentially an iteration between the energy conservation equation and the liquid fraction equation. Directly using equation 14 to update the liquid fraction usually results in a poor convergence of the energy equation. Thus, the method suggested by Voller et al. as shown in equation 10 is utilized to update the liquid fraction instead. Besides, slight volume expansion usually takes place accompanying with the paraffin mixture melting, which can be described as follows.



Vi  V0 V0

(16)

where  is the volume expansion rate due to the paraffin melt, V0 ,Vi indicate an initial volume of the paraffin mixture and the total volume at the ith iteration, respectively. mp , s ,0  V0  p , s

(17)

mp, s ,i  1   Vi  p , s

(18)

m p,l ,i  Vi  p ,l

(19)

where mp, s ,0 , mp, s ,i , mp,l ,i are an initial mass of solid paraffin mixture, the mass of solid paraffin component and mass of liquid paraffin component at the ith iteration, respectively. According to the law of conservation of mass, the total amount of paraffin mixture is conservative at each iteration, so that equations 17, 18, 19 can be rearranged in the below form. V0  p, s  1   Vi  p, s  Vi  p,l

(20)

Substituting equation 20 into 16, the volume expansion rate can be rewritten as follows. 

   p , s   p ,l 

 p , s     p , s   p ,l 

(21)

Until now, it is not difficult to find that the volume change due to paraffin melt is directly related to the liquid fraction and further explained by the enthalpy change in the domain.

2.3. Heat transfer in Lithium-ion batteries In the sections mentioned above, the total volumetric heat source inside the whole battery module has been derived from the dominant Joule effect, normal electrochemical reactions between anode and cathode active materials, the unavoidable electrochemical polarization and undesired side reactions due to electrodes, electrolyte decomposition in equations 1, 5, 6 and 7.

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Theoretically, it accounts for the potential mechanisms of common thermal behavior occurring in the batteries’ charge/discharge cycles, mainly including rapid temperature rise, uneven temperature distribution, even potential thermal failure, etc. Besides, the equation 10 describes heat dissipation as well as temperature variation corresponding to the expected RT48 paraffin phase change process. For computing the paraffin mass for the proposed BTMS in this study, the entire heat transfer equation has already been presented in equation 8, totally considering individual batteries, referred RT48 paraffin, engineering plastic frameworks, interconnectors and other the AUV battery pack’s components. Meanwhile, it is also applicable for the global energy conservation on the whole battery module. As complementary, the heat transfer process regarding the batteries is described as follows. b c p , b

 1   T   2T  T  b  r   2   Qb   r r  r  z 

Qb 

Qb Vb

(22)

(23)

  0,T  T0

(24)

where r is cylindrical coordinate, Qb is the volumetric heat source of the single battery, Vb is the volume of the single battery, T0 is initial temperature of the battery. The RT48 paraffin, batteries, interconnectors, frameworks, etc., are in direct touch with each other inside the whole battery module, even spreading to the AUV’s shell and outer seawater. Thus, continuous boundary conditions are also defined herein, supposing that the paraffin flow is nearly negligible at the same time. Finally, the equation set on the continuous boundary conditions are expressed below.  T  TII , I   I  TI  TII , I  

T r T z

T r T  II z  II

I

I

II

(25)

II

where I , II represents heat transfer medium 1 and 2, respectively, z is Cartesian coordinate index along the symmetric axis of the battery. Also, the equation 24 is not only on-site boundary conditions but also global boundary conditions subject to the governing equation 8. Until now, combining energy conservation equations 8, 15 and 10 with the initial condition in

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equation 24 and boundary conditions in equation set 25, one can calculate time-dependent temperature within the whole computing domain including from the individual batteries to the outside seawater.

3. Results and discussion In the previous sections, thermal behavior relevant to the charge/discharge cycles is analyzed in theory, as well as an integrated physical model describing energy conservation regarding the battery module has already been established step by step. Although those conduce to understand not only underlying mechanisms of thermal behavior but also inducing factors accounting for the possible thermal runaway, there is still far off visualization on the heat diffusion and temperature distribution occurring in the battery module. In general, the visualization expression is more direct and

significant

for

determining

the

transient

process

with

temperature

increasing

comprehensively. In this case, numerical calculations based on the ANSYS package have been implemented in a three-dimensional space and at a full discharge cycle. In the beginning, the hybrid meshing technique was introduced to discrete the whole geometry; the size function was used to refine the boundary layers as well. The mesh and time step size independence have been examined for pursuing high accuracy. By comparing the changes in maximum temperature, it found that the total 1.29 million grid elements and 30 second time step size were optimal. Moreover, because this study is closely associated with the practical application, the authors have accurately measured thermal and electrochemical properties for the utilized PCM and lithium-ion battery, e.g., bulk density, specific heat capacity, anisotropic thermal conductivity, internal electric resistance and so on, depending or not, on the SOC and transient temperature. All of these parameters adding computation-related ones have been written as different user-defined functions (UDFs) using the C++ language, which have subsequently been compiled with the ANSYS package. In another word, the basic features built in the ANSYS package cannot support satisfactory numerical simulations for this work. Also, the laminar model was selected since the Reynolds number within the battery module was no more than 2300 in this study; a pressure-based, incompressible, transient solver was utilized for numerical calculations; the flow problem was solved by using a pressure-velocity coupled scheme, which is high-efficiency when the mesh quality is poor, or if large time step size is used; the coupled algorithm solved the energy, 18 / 39

momentum and pressure-based continuity equations together in the second-order upwind scheme. The last but not the least, the absolute convergence criterion was the residuals of both energy and continuity equations, which were set as 106 and 1012 , respectively. Herein, a full discharge cycle equals the battery’s capacity divided by the discharge rate. Considering big thermal resistance between the battery can and surrounding media due to extremely low thermal conductivity of polyimide film, all customized lithium-ion batteries are therefore naked without any plastic outer film. However, a significant problem of electric insulation must be paid more attention to during the utilization subsequently. Two kinds of insulating battery frameworks have been chosen, i.e., ABS (Acrylonitrile Butadiene Styrene), PPS (Polyphenylene Sulfide) engineering plastic frameworks. In contrast to the ABS framework, the -1 -1 PPS framework presents a higher thermal conductivity, up to 3.0 Wm K , which is

approximately 12 times the ABS’s, but worse tenacity, unfortunately. Two prototypes of the AUV’s battery module have been designed based on the ABS and PPS frameworks, respectively, but excluding any other heat transfer enhancement solutions. It insists that to conduct numerical studies first on the prototype mentioned above contributes to comprehensively explore the essential characteristics of the battery module as well as the optimal performance combining the state-of-the-art heat transfer enhancement solutions.

3.1. Characteristics of temperature and velocity The rechargeable LIB used in this research work has a capacity of 30 Ah, and also the maximum permissible discharge rate is 1 C, i.e., 3 A. The batteries are usually assembled in series for higher output voltage as well as in parallel for more output current. Either series or parallel assembly is highly dependent on the technical requirements of the AUVs, especially their output power and allowable temperature. In general, the whole battery pack consists of several battery modules, and then each module further contains many series-parallel batteries. Due to a periodic approximation along Z-axis direction of the AUV (Z-axis direction is the same with the AUV’s cruising velocity, Y-axis direction is the same with the gravitational acceleration, and the right-hand rule can readily determine the X-axis direction.), only one module has been selected to represent the whole battery pack, so as to improve the computational efficiency. Thus, the

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numerical calculations have been carried out towards one battery module, which can continuously discharge ten hours at a discharge rate of 1 C. Also, a layer of seawater with a thickness of 50 mm has been added due to water forced convection heat transfer. In theory, the maximum temperature inside the battery module under the regular charge/discharge cycles can be captured very well.

Fig. 1. Temperature distribution over the battery module fixed by ABS frameworks, without the paraffin-dominated BTMS. Fig. 1 shows that the peak temperature inside the battery module is up to 399.0 K when it continuously works 10 h at a discharge rate of 1 C only relying on natural air convection. In reality, such a high temperature of 399.0 K is entirely beyond the upper limit of temperature regarding the LIB, and even thermal runaway seems almost inevitable. In another word, it is unallowable for the AUV to work several hours at 1 C discharge rate successively. Moreover, it is easy to find out that the temperature distribution along the positive Y-axis direction is higher than it along the negative Y-axis direction. The buoyancy-driven air flow can explain this phenomenon. a  a ,0   a a ,0 T

(26)

where  a is air density,  a ,0 is the initial density of air,  a is coefficient of thermal expansion.  U a  0

(27)

U a 1  U a U a   pa  a  2U a  g a T  a

(28)

where U a is the local velocity of a parcel of air, pa is the local pressure of air,  a is the kinematic viscosity of air.

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T  U a T  Da  2T 

(29)

where Da indicates thermal diffusivity of air. According to the Boussinesq approximation in equations 26 to 29, it ignores air density differences except where they appear in terms multiplied by g , the gravitational acceleration, which accounts for mass transportation and heat transfer of a fluid flow like air in the enclosure space. Therefore, the upper part of the battery module always presents quite higher temperature than its lower part. Herein, that usually means those batteries in red as shown in Fig. 1 are much more prone to take place thermal runaway due to long-time more massive thermal load. Also, there is a circular layer of air between the hexagonal battery module and the AUV’s shell, actually, which is divided into six subdomains by interconnectors. However, they are still relevant to the Boussinesq flow in the enclosure space. It significantly exhibits that the temperature profile of the outer air is much closer to the seawater outside the AUV, due the high thermal resistance corresponding to the air layer. The following figure will supply more evidence for this phenomenon.

Fig. 2. Velocity profile of warmed air inside the battery module supported by ABS frameworks, without the paraffin-dominated BTMS. In Fig. 2, the dark blue area indicates the stationary components inside the battery module, mainly consisting of batteries, ABS frameworks, aluminum interconnectors, and shells, even seawater there, which means it does not exist a heat-induced flow over those domains. Oppositely, the colorful area describes the Boussinesq flow regarding the warmed air. According to the

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geometry of the battery module, the air is filled into all gaps in the battery module, as well as it is divided into several smaller subdomains. In each subdomain, the natural convection takes place, -1 and subsequently, the air’s velocity is up to 0.46 ms . Although this small geometry is beneficial

for inducing turbulent flows at lower Reynolds numbers, which contributes to enhancing heat transfer naturally, unfortunately, in this case, the conductive heat transfer is still dominant for the air. Next, both the maximum velocity and heat transfer coefficient are further calculated with discharge rates or currents varying. It finds that the maximum velocity of the air flow is almost constant with the discharge current increasing from 2.0 A to 3.0 A, as well as its average heat transfer coefficient, is in good accordance with the characteristic of air natural convection heat -2 -1 transfer, roughly ranging from 3.0 to 8.0 Wm K . Also, a variation in the average heat transfer

coefficient displays a positive correlation with the discharge current, especially it being close to 3.0 A. Bi 

Rb ha

b

(30)

where Bi is the Biot number, herein characterizing the ratio of the heat transfer resistances inside and at the surface of the batteries, Rb is a radius of the battery, ha is the air’s heat transfer coefficient outside the batteries, b is the equivalent thermal conductivity over the individual battery. According to equation 30, it is not difficult to calculate the Biot number is no more than 0.03, which means the relatively uniform temperature distribution exists inside the batteries, although higher temperature field. This phenomenon is in good agreement with the open literature data [47]. Evolution of maximum temperature with the depth of discharge at different discharge conditions has also been calculated over the battery module. As mentioned above, the prototype of the battery module is only supported via the ABS frameworks without any other enhanced heat transfer solutions, which have excellently electric insulation and mechanical performance, but low -1 -1 thermal conductivity, i.e., 0.26 Wm K roughly. In general, the proper utilization about

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large-scale series-parallel LIBs is a far complicated issue, as well as one of the most important as abuses of them, can cause thermal runaway even an explosion [48-51]. According to measurements of the current-voltage characteristics for the utilized lithium-ion battery, its output performance is relatively optimal when the battery works at 322.7 K roughly. Nevertheless, from the calculation results, the maximum temperature within the battery module can easily break through 322.7 K after two hours due to thermal accumulation, although it is lower than that at the beginning. In this section, thermal behavior relevant to mass transportation, momentum transfer, and heat dissipation, happening in a repeated battery module unit, has been analyzed sufficiently on the basis of the standard ABS frameworks. Despite excellent electric insulation and mechanical stability due to the ABS engineering plastic utilization, a terrible temperature rise is always inseparable if no enhanced heat transfer solution has been considered in proper ways. In recent years, the industries related to LIBs have been undergoing the rapid development, so that how to figure out the paradox due to high-performance output as well as the thermal runaway is becoming more and more urgent. Therefore, a paraffin-dominated BTMS has been incorporated into the battery module, expecting to maintain both a moderate temperature environment and temperature gradient, which usually accounts for ultimate thermal stability and durability.

3.2. Enhanced heat transfer solutions Before the paraffin-dominated BTMS, a simple approach against temperature rise is attempted using another conventional engineering plastic, i.e., the PPS engineering plastic. It is famous for higher thermal conductivity, generally more than ten times of the ABS’s. However, its mechanical strength is not satisfactory compared with the ABS’s.

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Fig. 3. Temperature distribution over the battery module fixed by PPS frameworks, without the paraffin-dominated BTMS. Fig. 3 shows the temperature contour distributed inside the battery module supported via the PPS frameworks, when it has worked for ten hours at 1 C. Its maximum temperature reached 391.0 K, reducing by 8.0 K in comparison with the module supported through the ABS frameworks. Also, the similar temperature pattern appears again. The main reason accounting for this phenomenon is that the PPS frameworks enhance the batteries’ heat conduction along the Z-axis direction due to the higher thermal diffusivity comparing with the ABS frameworks. Comparing with the battery module fixed by the ABS engineering plastic frameworks in Fig. 2, -1 the local air velocity reaches 0.51 ms , slightly higher than the ABS’s. Two possible reasons

should be considered to describe the velocity distribution herein. On the one hand, due to higher thermal conductivity and diffusivity, a temperature rise occurs much faster, as well as the depth of thermal penetration is much more in-depth in the PPS frameworks. On the other hand, heat exchange efficiency at the surface of the PPS frameworks keeps higher in contrast with the ABS from the mathematical research. They result in both slightly higher temperature distribution in the air and a velocity increase according to equations 26 and 28. In above sections, neither the ABS nor the PPS configuration can satisfy practical applications for the AUV. Therefore, it is still crucial to seek high-efficiency enhanced heat transfer solutions. In this work, the state-of-the-art BTMS based on phase change material is proposed to suppress thermal behavior taking place in the AUV’s battery module. A particular kind of phase change material, known as RT48 paraffin mixture, is customized for the utilized LIBs in the AUV. This

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RT48 paraffin is an excellent medium for storing heat and also, it is solid at room temperature, but begins to melt up to 321.0 K, finally becomes liquid beyond 325.0 K. Thermal conductivity of the solid paraffin mixture is around 0.558 Wm-1K-1 , as 21 times as the air’s roughly, and also a little bit higher than thermal conductivity of conventional paraffin phase change materials. According to equation 14, the proper amount of RT48 paraffin is filled as well as is in direct touch with the batteries inside the module due to its inspiringly electric insulation.

Fig. 4. Temperature distribution over the battery module fixed by ABS frameworks, with the paraffin-dominated BTMS. In Fig. 4, numerical calculations have been expanded into the battery module supported by the ABS frameworks as well as cooled with the RT48 paraffin-dominated BTMS. It shows that the maximum temperature is no more than 325.0 K, i.e., the upper melting temperature limit, and much more uniform temperature distribution is also displayed. Meanwhile, the air layer between the module and the AUV’s shell reaches higher temperature due to relatively higher equivalent thermal conductivity and diffusivity of the overall module. This phenomenon benefits from heat absorption due to the RT48 paraffin’s phase change process, which usually occurs at the temperature range from 321.0 K to 325.0 K, accompanying with unobvious temperature rise inside the whole battery module simultaneously, because of the customized paraffin mixture without a specific melting point. Also, it finds that the battery temperature gradually decreases from the innermost to the outermost, as well as a 3.4 K temperature difference among all the batteries arrives after continuous ten hours release at a discharge rate of 1 C. Obviously, this small temperature

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difference is quite inspiring to gain the highest output performance towards the module and also not to worry about the potential thermal runaway. In another word, it is quite advantageous for guaranteeing all batteries to conduct the charge/discharge cycles safely and reliably throughout their entire lifespan. Herein, the paraffin, like a warm water bath, plays an essential role in balancing the temperature distribution of all batteries. Because the RT48 paraffin substitutes on-site air inside the battery module with this configuration, the air as a heat transfer medium with high thermal resistance occupies a smaller volumetric fraction compared with the previous situations. Therefore, natural convection heat transfer is probably suppressed due to a narrow space. The calculation results on velocity field inside the battery module, which is fixed by the ABS frameworks and cooled with the paraffin-dominated BTMS, show a maximum velocity of 0.34 ms-1 and that the narrowest sites along X-axis direction obtain the highest velocity. Also, the velocity profile exhibits an approximate symmetry distribution along the Y-axis direction due to the Boussinesq flow. That means the paraffin almost wholly absorbs the heat energy released by all batteries instead of diffusing to the outside seawater. In another word, a sharp temperature rise will be presented once the paraffin gets saturated. To some extent, this phenomenon never appears in this study thanks to finite battery capacity. Before all the RT48 paraffin melts totally, the batteries have already released all electric quantity. Next, it turns to the phase change phenomenon existing in the paraffin as shown in Fig. 5.

Fig. 5. The liquid fraction of paraffin filled in the battery module fixed by ABS frameworks during the phase change proceeding.

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Fig. 5 indicates liquid fraction of the RT48 paraffin relevant to the phase change proceeding, when the batteries continuously discharge ten hours at a rate of 1 C. Only a little paraffin begins to melt due to the customized RT48 paraffin mixture that thermophysical properties, i.e., density, latent heat of fusion, specific heat capacity, thermal conductivity, etc., are consistent with the thermal characteristics of those utilized LIBs in this study. Hence, the sealing requirements are relatively flexible. Combining Fig. 1, the batteries along the positive Y-axis direction always undergo the peak temperature during the whole discharging process, so that phase change first starts in the local paraffin nearby those high-temperature batteries while the other portion still keeps solid.

Fig. 6. Illustration of maximum temperature versus time at the different discharge currents inside the battery module cooled with the ABS frameworks plus paraffin BTMS. In Fig. 6, numerical calculations have been extended to different discharge currents from 2.0 A to 3.0 A. Although the battery can theoretically work for 10 hours at a current of 3.0 A due to a total 30 Ah electric capacity, it is not recommended to run out of the battery during practical applications, mainly considering low output performance and potential damage to the battery at the end of discharge. Herein, the early 7 hours discharge corresponding to 46.7% to 70% depth of discharge (DOD) dependent on the discharge currents, is conducted uniformly. When the DOD reaches 46.7% (7 hours) at the lower discharge current of 2.0 A, the paraffin starts to soften without apparent phase change. Whereas, the phase change occurs under approximate 25% DOD (around 2.5 hours) at the upper discharge current of 3.0 A. In general, the initial phase change is in a positive correlation to the discharge current. During the phase change process, the system

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temperature including individual batteries and other components of the battery module is not beyond the upper melting temperature of the RT48 paraffin mixture, i.e., 325.0 K, which is in good agreement with the optimal operating temperature subject to the utilized batteries herein [32, 52]. As the ABS frameworks plus paraffin BTMS, the time-dependent maximum temperatures under the different discharge currents have also been researched regarding the battery module cooled with the PPS frameworks plus paraffin BTMS. The calculation shows the further suppression of temperature rise inside the battery module based on a combination of the PPS frameworks and RT48 paraffin mixture. The primary variation tendencies keep similar with those exhibited in Fig. 6, but a contribution due to the PPS frameworks is also significant. Comparing with the configuration of ABS frameworks plus RT48 paraffin mixture mentioned above, about 30% DOD can trigger phase change inside the paraffin at 3.0 A discharge current, which is delayed by around 5% DOD. Meanwhile, maximum 51.3% in DOD is not enough to induce phase change at discharge currents less than 2.2 A. In this section, three kinds of enhanced heat transfer solutions are proposed gradually, i.e., the PPS frameworks alone, the ABS frameworks plus RT48 paraffin, and the PPS frameworks plus RT48 paraffin, respectively. As was expected, around 8.0 K temperature decrease can be gained by taking advantage of the PPS substitution. Moreover, based on a combination of the ABS and RT48 paraffin, the top temperature and temperature difference inside the module is no more than 325.0 K and 3.4 K, separately. Also, the similar tendencies appear regarding the PPS plus RT48 paraffin BTMS, except that the initial phase change is postponed by maximum 5% DOD corresponding to the PPS donated enhancement of heat transfer.

3.3. Thermal behavior of the battery module Next, thermal behavior related to the temperature rise as well as temperature difference over the whole battery module are evaluated regarding the ABS, PPS, ABS plus RT48 paraffin and PPS plus RT48 paraffin BTMSs, respectively.

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Fig. 7. Comparisons of maximum temperature and temperature difference corresponding to the battery modules supported by the ABS, PPS frameworks, respectively (MT indicates max temperature, as well as TD, is temperature difference.). Herein, more comparisons have been incorporated into the PPS as well as ABS frameworks. According to Fig. 7, the black lines, corresponding to the left Y-axis, indicate maximum temperatures occurring inside the battery module with the discharge current varying. Similarly, the red lines based on the right Y-axis, describe temperature differences over the module due to the ABS, PPS frameworks utilization. Therein, the black line with solid blocks presents the maximum temperature variation of the battery module due to the discharge current consistent with the ABS frameworks. Meanwhile, the black line with solid circles illustrates the peak temperature variation owing to the PPS frameworks. Also, the solid red line with hollow blocks explains temperature difference of the batteries, corresponding to the module with ABS frameworks, as well as the solid red line with hollow circles exhibits temperature difference due to the PPS frameworks, appearing a bit lower than the former. Both the maximum temperature and temperature difference occurring in the battery module, are significantly dependent on the batteries’ discharge current, in the form of a positive correlation, which can be explained due to the dominant Joule heat especially at high discharge currents from the equation 1. This variation tendency is in good agreement with the open literature data [40-42]. The last but not the least, to note that both flat red lines marked with regular triangles and inverted triangles demonstrate the differences of maximum temperature and the temperature difference between the ABS and PPS configuration, respectively. Also, the average values of 6.0 and 3.4 K expose the PPS frameworks’ benefit in respect of temperature rise

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and uniformity, although it is not entirely satisfying.

Fig. 8. Comparisons of maximum temperature and temperature difference corresponding to the battery modules with varying BTMSs (ABS frameworks alone, ABS frameworks plus RT48 paraffin, PPS frameworks alone, PPS frameworks plus RT48 paraffin. MT indicates max temperature, as well as TD, is temperature difference.). In Fig. 8, the effect of RT48 paraffin is considered as well. The left and right Y axes are related to temperature rise as well as temperature difference after 7 hours discharge, respectively. First seeing the left Y-axis, the black line marked with solid diamonds describes the maximum temperature variation under the ABS plus RT48 paraffin BTMS, which is almost proportional to the discharge current and keeps lower than the upper melting temperature of 325.0 K. Also, a similar variation due to the PPS plus RT48 paraffin BTMS appears, but the discharge current less than 2.2 A is insufficient for latent heat of phase change related to the RT48 paraffin. Now turn to the right Y-axis, the red line with hollow squares denotes the improvement of temperature rise taking advantage of the ABS plus RT48 paraffin BTMS, which is in a positive correlation to the discharge current, as well as obtains the maximum 78.0 K decrease in contrast with the primary ABS BTMS. Also, an entirely similar improvement seeing the red line with hollow triangles due to the PPS plus RT48 paraffin BTMS can be observed compared to the PPS BTMS, by which around 70.0 K temperature suppression is observed. In addition, there is no apparent distinction regarding the temperature suppression between the ABS plus RT48 paraffin BTMS and PPS plus paraffin RT48 BTMS relevant to the lowest red line with hollow diamonds, especially discharging at those currents more than 2.2 A. However, PPS engineering plastic is usually more expensive

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and brittler comparing with ABS engineering plastic. Although the heat dissipation is more apparent due to PPS heat conduction in contrast with ABS heat conduction, this advantage is primarily offset when combining with RT48 paraffin mixture. The heat absorption due to the paraffin phase change like a sponge accounts for this phenomenon. In general, either the ABS plus RT48 paraffin BTMS or PPS plus RT48 paraffin BTMS can perfectly meet the practical requirements on temperature rise and uniformity, proceeding the maximum 70% depth of discharge. If both material cost and mechanical strength is also considered together with the thermal performance of the battery module when designing the BTMS, the former is undoubtedly preferred. Besides, although the PPS-based BTMS contributes maximum 8.0 K temperature improvement towards the battery module, it still fails to protect the whole battery module from thermal runaway like the ABS-based BTMS.

3.4. Verification of the results In this study, calculations on thermal behavior occurring in the battery module have been carried out computationally. Meanwhile, the experimental research has also been implemented in the South China Sea for a prototype of 50 kg class lightweight AUV, which has been trial-manufactured according to the numerical research in this work. Although the experimental study can present direct and reliable advantages for validation as well as close agreement is indeed obtained between experimental data and computational results, unfortunately, the experimental data cannot be published at present due to a confidentiality agreement with the collaborative company. Hence, the computational results in this work is primarily verified against the open literature data as follows. Table 2 Comparison of calculated maximum temperature and temperature difference in this work with the open literature data. References

Cooling method

Maximum

Temperature

temperature

difference

1C

303.6 K

10.5 K

1C

315.0 K

5.0 K

Discharge rate

Forced air Ref. [53] convection Ref. [54]

Forced air

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convection Ref. [52]

RT35 paraffin

1C

320.0 K

4.0 K

Ref. [32]

RT58 paraffin

1C

333.0 K

8.0 K

This work

RT48 paraffin

1C

325.0 K

3.4 K

According to previous sections, the calculated maximum temperatures and temperature differences inside the battery module cooling with the RT48 paraffin-dominated BTMS are in good agreement with the open literature data [32, 52-54], as shown in Table 2. Based on Table 2, the calculation results are validated against the open literature data as well as presented here to give a detailed insight into the temperature rise and difference. It finds the customized RT48 paraffin mixture can also control operating temperature of the battery module at the optimal range using heat conduction and heat adsorption comparing with references [32, 52], but it is more efficient to reduce temperature difference with no more than 3.4 K due to higher thermal conductivity. In contrast, the forced air convection method is much more advantageous to suppress the maximum temperature in the battery module but being offset by poor temperature distribution subsequently [53, 54]. Besides, the liquid cooling technology is generally more complicated as well as it is not that the lower the operating temperature in the battery module, the better the output performance on the battery module.

4. Conclusions With the shortage of natural resources and environmental pollution becoming worse and worse, extensive investigations on clean and high-efficiency electrochemical energy conversion have been paying more and more attention in recent years. On the basis of this background, the LIBs are incorporated into the AUV applications. However, some problems relevant to temperature rise and nonuniformity must be figured out in advance. In this study, the temperature distribution and velocity field have been explored first based on the primary ABS BTMS, as well as contributions to heat transfer enhancement have also been studied corresponding to PPS, ABS plus RT48 paraffin, and PPS plus RT48 paraffin BTMSs, respectively. In summary, thermal runaway is more prone to occur in those batteries along the positive Y-axis direction due to the Boussinesq flow. Meanwhile, neither the ABS BTMS nor the PPS BTMS can meet the requirements in the AUV application on both the temperature limit and temperature uniformity because of air-dependent 32 / 39

thermal resistance. Also, the RT48 paraffin-dominated BTMS can excellently maintain the optimal temperature range from 321.0 K to 325.0 K, as well as control the temperature difference in the battery module less than 3.4 K due to heat absorption relevant to the paraffin phase change, no matter the RT48 paraffin is combined with either the ABS frameworks or PPS frameworks. Last but not the least, the ABS plus RT48 paraffin BTMS will be recommended for the AUV applications comprehensively considering mechanical, dynamic, thermophysical, reliability and even economic performance.

Acknowledgment The calculations were performed on the resources provided by the Institute of Autonomous Underwater Vehicle (IAUV) affiliated with Northwestern Polytechnical University (NPU).

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