Designing Thermal Management Systems For Lithium-Ion Battery Modules Using COMSOL

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Designing Thermal

Management Systems For

Lithium-Ion Battery

Modules Using COMSOL

Emma Bergman

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Abstract

In this thesis, a section of a lithium ion battery module, including five cells and an indirect liquid cooling system, was modelled in COMSOL Multiphysics 5.3a. The purpose of this study was to investigate the thermal properties of such a model, including heat generation per cell and temperature distribution. Additionally, the irreversible and reversible heat generation, the cell voltage and the internal resistance were investigated. The study also includes the relation between heat generation and C-‐rates, and an evaluation of COMSOL Multiphysics 5.3a as a software.

It was found that having liquid cooling is beneficial for the thermal management, as the coolant flow helps to transfer away the heat generated within the battery. The results also show that it is important to not go below a set cell voltage at which the cell is considered fully discharged. If a control mechanism to stop the battery is not implemented, the generated heat, and consequently the temperature, increase drastically. COMSOL

Multiphysics 5.3a was considered a suitable software for the modelling. For future research it is of interest to expand the model to a full scale module to fully investigate the

temperature distribution where more cells are being cooled by the same coolant loop.

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Acknowledgements

First I would like to thank my supervisor at Northvolt Ehsan Haghighi for all the help and guidance during the project. I want to thank my supervisor at KTH Göran Lindbergh for valuable help during the project. I would also like to thank Henrik Ekström at KTH and

COMSOL for all the help and explanations regarding the construction of the battery model in COMSOL. I would also like to thank Per Backlund and Daniel Ericsson at COMSOL for

additional help with the model. Finally I would like to thank everyone at Northvolt who helped me out in various ways during the project.

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Appendix 4: Lithium ion cell variables used in COMSOL model 59 Appendix 5: Coolant heat capacity interpolation used in COMSOL model 60 Appendix 6: Coolant density interpolation used in COMSOL model 61 Appendix 7: Coolant dynamic viscosity interpolation used in COMSOL model 62 Appendix 8: Coolant thermal conductivity interpolation used in COMSOL model 63

Appendix 9: Modelling Instructions 64

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Introduction and Project Description

Lithium ion batteries are lightweight energy-‐dense batteries ideal for both portable and stationary uses. The interest in lithium ion batteries is high both from the appliance and the vehicle industries. However, one issue with lithium ion batteries is that they are badly affected by high temperatures. A prolonged exposure to high temperatures can decrease the life time of the battery. If the battery is exposed to high enough temperatures, a thermal runaway might occur, which can cause the battery to explode. Consequently, the area of thermal control is of high interest for battery system producers.

The goal of this project is to determine the effectiveness of liquid cooling system for a set of five 21700 lithium ion batteries, which are a part of a bigger module. This will be

investigated through simulations in COMSOL Multiphysics 5.3a. A model is constructed, which will calculate the heat generation from the electrochemistry given certain input parameters. To analyse the system, some parameters such as fluid velocity, current, and driving cycle are varied to investigate the effect of temperature distribution and heat generation.

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Background

Li(Ni1/3Mn1/3Co1/3)O2 (NMC) Li-‐Ion Batteries

Lithium ion batteries are relatively new on the market, and the demand for them have grown rapidly. They have high energy density, which make them ideal for portable devices requiring small and lightweight batteries. The interest in Li-‐ion batteries is also large from the automobile industry. The properties of the energy dense Li-‐ion batteries are desired for electric and hybrid vehicles.

Most lithium ion batteries typically utilize a graphite material for the negative electrode. The positive electrode consists of the lithium in a metal oxide form, usually mixed with other metals. One such positive electrode material is NMC, or Li(Ni1/3Mn1/3Co1/3)O2. It is showing promising properties in regards to being used for electric vehicle, as it has a high energy density and a large rechargeable capability. The combinations of metals in the positive electrode adds stability to the cell, in addition to making the electrode high performing and cost-‐effective [1]. The recommended electrolyte for Li-‐ion cells is 1M LiPF6 3:7 EC-‐EMC [2].

Cylindrical lithium-‐ion batteries consist of a can containing a jellyroll of the cathode, anode, and separator, in addition to terminals, current collectors, insulation plates, and safety features. This is illustrated in Fig.1 [3]. The jellyroll is constructed by alternating cathode and anode sheets, with separator sheets between them. It has been given its nickname by how it is rolled up to fit the cylindrical cell, similar to the jelly roll pastry. The current generated by the batteries is collected through the current collectors, the positive and negative ends [4].

Fig 1: Configuration of a cylindrical lithium ion battery cell [4].

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Generated Heat

Being able to measure the generated heat is an important step of battery system modelling.

If the generated heat is too high, it may cause damage to the system, and possibly even cause the system to explode in the event of a rapid thermal runaway. A thermal runaway is caused by high temperatures in the battery allowing for undesired exothermic reactions to occur. This in turn causes even higher temperatures, which allow for even more undesired reactions. At high enough temperatures, this phenomenon is irreparable and might even cause an explosion due to heat and phase shift to combustable gas. It is initiated by the melting of the protective solid electrolyte interface layer at 90 °C. Once the layer is gone, the electrolyte and the negative electrode are able to react with each other, causing the first exothermic reaction at a temperature of 100 °C [4]. However, already before that level, the battery calendar life is estimated to decrease significantly for temperatures at 40 °C and higher [5].

Consequently, battery developers are looking into methods of measuring the general heat, in order to produce sufficient cooling systems.

Measuring the heat directly

The first method uses an equation developed by Bernardi et. al. [6], which separates the generated heat into reversible and irreversible heating. In its simplified form the equation is:

𝑄 = 𝐼 𝑈_%&− 𝑉 − 𝐼𝑇^*+_*, = 𝐼^.𝑅 − 𝑇 ∙ ∆𝑆 ∙₄³ ^(Eq.1)

Where 𝑄 is the heat generation, I is the current, UOC is the open-‐circuit potential, V is the cell potential, T is the temperature, R is the overpotential resistance, dU/dT is the entropic heat coefficient, ∆S is the entropy change, I is the current, and F is the Faraday constant. The first half of the equation represents the irreversible heating, or Joule heating. The second part of the equation represents the reversible heating, which is due to entropy changes. To use this equation, it is necessary to assume no heat generation from mixing or phase changes, no spatial variations in temperature or SOC, only one electrochemical reaction occurring at each electrode, and that the Joule heating in the current collectors is negligible [7].

The method is quite accurate, but difficult and time consuming to measure in practice. Onda et. al. [8] gives four methods of how to perform experimental measurements of the

overpotential resistance, R. These are to measure the resistance by V-‐I characteristics, by

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difference between OCV and cell voltage, by intermittent discharge, and by an ac meter.

Measuring the difference between OCV and cell voltage is the most common method, however, it can take a long time to conduct the experiment, since the OCV needs to stabilize after the change in SOC. Onda et. al. also report inconsistencies for the last two measuring methods. To measure the entropy Onda et. al. list two suggested methods. The first method measures the entropy change by temperature gradient of OCV, and the second method measures entropy change by heat production. This measurement is another time consuming operation, as the OCP must stabilize again. Karimi and Li [9] performs a computational study using Eq.1 as an alternative.

Cooling medium heat removal

Another method looks instead to the heat removed by the cooling system. Calculating the heat transported away by the system requires a simpler measurement, but neglect heat remaining in the battery, and it is needed to be calculated separately [10]. An equation for the cooling medium heat removal is:

𝑄 = 𝑚𝐶₇(𝑇₉− 𝑇_:) (Eq.2)

Where 𝑄 is rate of heat generation, 𝑚 is the mass flow rate of coolant, Cp is the specific heat capacity of coolant, To is the outlet temperature, and Ti is the Inlet temperature. The

advantage of this method is the simple measurement. All that is needed is to measure the inlet and outlet temperatures of the cooling medium. However, the system disregards losses and heat remaining in the battery.

Computational Modelling

The methods mentioned are the main experimental methods to calculate the battery heat generation. However, since the experimental methods are complex and can be inefficient battery developers often look into computational models.

COMSOL Multiphysics is an engineering simulations software. It allows the user to define a geometry and set material properties and physics to describe a process. COMSOL then solves the system through built in or defined equations [11]. In addition to the base package, the add-‐on modules Heat Transfer in Solids and Fluids and Batteries & Fuel Cells are useful when modelling battery heat management.

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The Pseudo-‐Two-‐Dimensional model (P2D)

COMSOL [12] looks at the electrochemical reactions directly, based on the model developed by Newman’s team [13, 14]. The model is the most widely used for the purpose and

approaches the cell from a homogeneous and isothermal point of view [15]. It considers the one-‐dimensional transport from the negative electrode to the positive electrode, through the separator, according to Ohm’s law. The model is based on concentrated solution theory and porous electrode theory. The concentrated solution theory works in the way that it treats the electrolyte as a binary salt with polymer solvent. This theory describes the mass-‐

and charge transport in the electrolyte phase. The porous cathode theory works in that the composite negative electrode can be modelled looking at both resistance to the solid state transport considering both kinetic and diffusional effects. It adds an extra dimension to the model to describe the lithium transport according to Fick’s law. Furthermore, the use of Butler-‐Volmer kinetics to describe the reversible process allows for an effective method of describing both the discharge and the charge processes. Following these theories, the model can look at the major features of the system, without making it too complex [12, 13].

Although it is not stated by Newman’s team in their reports, this model is generally referred to as the P2D, or Pseudo-‐Two-‐Dimensional, model in literature [4, 16]. The pseudo-‐

dimension part of the name refers to how the equation for lithium conservation is solved in the particle r-‐dimension.

Diffusion in Porous Media

Fick’s second law is one of the governing equations for the P2D model [4]. It describes diffusion with a linear equation that assumes a constant diffusion coefficient, D. In Li-‐ion batteries this equation describes the transport of solid Li in the solid electrode phase. Fick’s second law is written [1]:

<=

<> = 𝛻 ∙ (𝐷_𝐿𝑖𝛻𝑐_𝑒) (Eq.3)

Where c is the lithium ion concentration, t is the time, DLi is the lithium diffusion coefficient, and ce is the lithium ion concentration in the electrolyte phase. To accurately describe the

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lithium ion diffusion, Fick’s law also requires a set of boundary and initial conditions for the time, and location relative to the radius. These are as follows:

𝑐 = 𝑐_E 𝑎𝑡 𝑡 = 0 𝐷_I:^<=

<J= 0 𝑎𝑡 𝑟 = 0

𝐷_I:𝜕𝑐

𝜕𝑟=𝑖_M

𝐹 𝑎𝑡 𝑟 = 𝑟_E

COMSOL’s battery module also utilizes the Bruggeman model, tF = ep-‐1/2, as a correction factor for the porous media mass transfer [12].

Lithium material balance

The lithium material balance in the polymer and salt phases is another of the governing equations [13]. It uses the transport equation for concentrated solutions.

It is given by [4]:

𝜀_P_<>^< 𝑐_P− ∇ ∙ 𝐷_I:∇𝑐_P −^:^R^∇₄^ST+ 𝑎_V𝑗_M 1 − 𝑡_Y^E = 0 ^(Eq.4) Where e is the electrode porosity, ce is the lithium ion concentration in the electrolyte phase, DLi is the lithium diffusion coefficient, ie is the electrolyte phase current density, t+ is the transfer number of lithium ions, F is the Faraday constant, as is the solid phase specific interfacial area, and jn is the pore-‐wall flux across interface. The boundary conditions are dependent on the location in the phase, and are as follows:

𝜕𝑐_P

𝜕𝑥 = 0 𝑎𝑡 𝑥 = 0 𝑎𝑛𝑑 𝑥 = 𝐿

Butler-‐Volmer kinetics

Butler-‐Volmer kinetics are included in the P2D model. They describe the charge transfer kinetics process at the interface between the solid electrode and the electrolyte. Using Butler-‐Volmer’s equation requires setting up a set of boundary conditions. The expression assumes no potential gradients at the interface between the current collector and the electrolyte, for the electrolyte, or at the interface between the separator and the electrode, for the solid. The electrolyte does not have a concentration gradient in the interface either.

The concentration gradient at the surface of the solid particle is proportional to the lithium pore wall flux, and there is a symmetry for the Li-‐ion concentration in the middle of the

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particles. The boundary conditions also assume that the applied current discharge is constant [7].

The Butler-‐Volmer equation is written [4]:

𝑖 = 𝑖_E exp ^a^𝑎_𝑅𝑇^𝐹^h^𝑠 − exp ⁻^a_𝑅𝑇^𝑐^𝐹^h^𝑠 (Eq.5)

where i is the current density, i0 is the exchange current density, aa anode transfer

coefficient, F is the Faraday constant, hs is the surface overpotential, R is the overpotential resistance, and T is the temperature.

The exchange current density, i0, is defined:

𝑖_E =𝐹𝑘_𝑎â^𝑐𝑘_𝑐â^𝑎 𝑐^𝑚𝑎𝑥_𝑠 − 𝑐_𝑠 â^𝑐𝑐_𝑒â^𝑎 (Eq.6) where F is the Faraday constant, ka is the anodic reaction rate constant, kc is the cathodic reaction rate constant, csmax is the maximal concentration of lithium ions in solid phase, cs is the concentration of lithium ions in solid phase, and ce is the concentration of lithium ion in the electrolyte phase.

The overpotential, hs, is defined:

h_V = Ø_V− Ø_P− 𝑈_%& ^(Eq.7)

where Øs is the solid phase potential, Øe is the electrolyte phase potential, and UOC is the open-‐circuit potential.

Concentrated solution theory

Concentrated solution theory describes another of the governing equations for the P2D model. The equation predicts the potential variation in the separator from the material balance of the lithium salt. With the assumption that solvent concentration is independent of electrolyte concentration, the equation can be derived [13].

The equation read [4]:

𝑖_P+ 𝑘^PccÑØ_P−^.d^e^,f₄ ^Rgg 1 +_<hM=^<hMc^±

R 1 − 𝑡_Y^E Ñ𝑙𝑛𝑐_P = 0 ^(Eq.8)

where ie is the current density in the electrolyte phase, k^eff is the effective ionic conductivity, Øe is the electrolyte phase potential, Rg is the universal gas constant, T is the temperature, F is the Faraday constant, f± is the molecular salt activity coefficient, ce is the concentration of lithium ion in the electrolyte phase, and t+ is the transfer number of lithium ions.

It is controlled by the following location dependent boundary condition [4]:

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𝜕Ø_P

𝜕𝑥 = 0 𝑎𝑡 𝑥 = 0 𝑎𝑛𝑑 𝑥 = 𝐿

Porous electrode theory

The porous electrode theory describes the Li-‐ion battery’s internal changes and status, depending on its electrodes and electrolytes, as well as the battery’s structure [17]. The theory consists of Ohm’s law, which administers the movement of electrons [4, 18]:

𝑖_V = −s^PccÑØ_V ^(Eq.9)

where is is the solid phase current density, s^eff is the solid phase effective electronic conductivity, and Øs is the solid phase potential.

It is regulated by a set of location dependent boundary conditions [4]:

−s^Pcc𝜕Ø_V

𝜕𝑥 = 𝐼

𝐴 𝑎𝑡 𝑥 = 0 𝑎𝑛𝑑 𝑥 = 𝐿

𝜕Ø_V

𝜕𝑥 = 0 𝑎𝑡 𝑥 = 𝐿_M 𝑎𝑛𝑑 𝑥 = 𝐿_M+ 𝐿_VP7

Cooling systems

To dissipate the heat generation out, cooling systems are widely used. Passive systems that let ambient air reach the battery are the simplest, while liquid and combined phase change cooling systems can be quite complex. The desired temperature range is usually between 25°C and 35°C, as too high or low temperatures can reduce the effectiveness of the battery [15]. For air and liquid cooling, the thermal management system could also heat up the battery cells in events of low temperatures.

Air Cooling

Cooling with air is a traditional and widely used thermal regulation approach. Most systems are passively air cooled if they have at least one interface in contact with surrounding ambient air. Besides passive air cooling, systems can also be cooled actively with the use of fans and methods to cool the air to lower than ambient. This is due to passive air cooling having a lower convective heat transfer coefficient than active air cooling. Since the passive air cooling convective heat transfer is so low, it is only effective for really small systems that do not produce large amounts of heat [4]. However, a huge advantage of air is its light weight, and ease to circulate [19]. Active air cooling was adapted early by the first electric

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hybrid vehicles, 2000 Honda Insight and 2001 Toyota Prius. They take advantage of the car’s available air conditioning system to take the cooled air from the cabin to cool the battery before it is exhausted. A blower that can operate at various speeds is utilised to draw air from the cabin to the battery. The two cars use slightly different systems to ensure even heat distribution [7]. However, for a fully electric vehicle there is doubt that an air cooling system would be sufficient [15].

Liquid Cooling

Cooling the battery with liquid is an area of interest. Liquids have higher thermal

conductivities than air and can cool more effectively and uniformly. It is also possible to decrease the size of the battery pack as the cells can be placed closer to each other.

However, liquids can be less flexible than air and it is of high importance that they do not leak out onto the battery [19]. There are three major liquid cooling methods. The first is direct submersion into the liquid. The second is indirect cooling through placing the battery modules on a cooling plate that cools the batteries from the bottom up. The third method is also indirect, where cooling tubes or jackets are placed around the batteries [15]. All three of the methods have their own advantages and disadvantages.

Direct Submersion

Direct submersion of the battery in the cooling liquid is the most straightforward liquid cooling method. The battery unit surfaces are directly in contact with the coolant, which minimizes the thermal resistance between battery and coolant. However, a disadvantage of using direct submersion is that it requires the coolants to be dielectric. Consequently, highly viscous fluids are common. These viscous coolants cause a higher power consumption for circulating the fluid [4]. The reason dielectric fluids are needed is to avoid short circuit. Since these fluids often are oil based, it is also important to consider other properties, such as toxicity and flammability, to not switch one problem for another. There are coolants available that can reduce the maximum temperature if thermal runaway occurs. Although for these fluids, economical factors might also play in, as the fluid cost can greatly increase the cost of the entire system [20]. When considering direct submersion cooling for batteries to be used in electrical vehicles, the risk of short circuit is still significant since the cells are in direct contact with the fluid. Having direct submersion also makes it more difficult to replace

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faulty cells. With this in mind, direct submersion cooling, although effective, is not ideal for batteries to be used in electrical vehicles.

Indirect cooling with cooling plates

With indirect cooling, an extra factor arises in form of a layer between the coolant and the battery cell. It is important to consider convection heat transfer and thermal contact

resistance here, as those properties affect the effectiveness of the cooling system more than the extra thermal resistance itself [20]. Cooling plates are placed under the battery cells. The plates are thin, with a cooling media transported between the plates [15]. The cooling channels in between the cooling plates can be of various styles, ranging from straight channels to complex structures. The batteries are cooled from the bottom up, causing a temperature difference between top and bottom. Adding an additional heat plate at the top can prevent this. A further step to obtain more uniform cooling is to add fins, which are additional plates going between the cells. However, these measures add weight to the cooling system [20].

Indirect cooling with cooling tubes or jackets

Cooling tubes and cooling jackets are two indirect methods of cooling the battery. Cooling tubes usually consists of a series of wavy tubes placed alongside the battery cells, so that they have a contact area on one side. Cooling jackets usually form casings around the battery, and then allows the coolant to flow through the compartment surrounding the casings. Cooling jacket can thus cover the entire battery, while cooling tubes have a smaller contact area. However, a great advantage of cooling tubes over cooling jackets is that the safety increase, as the possibility of liquid leaking out is smaller. With cooling tubes, it is possible to have all fluid connections to the tube outside of the battery model. Cooling tubes also have fewer welding spots. Another advantage of cooling tubes is that they have a smaller volume and the total weight is less, which is advantageous for mobile uses [20].

However, it should be noted that the risk of leakage is still smaller for a heating jacket than many other solutions [19]. Electric vehicle producer Tesla has patented both cooling tubes and cooling jackets for use in their vehicles [21, 22]. The Tesla solutions are shown in fig. 2 and fig. 3. To improve thermal conductivity while electrically insolating the transfer, a thermal interface material, TIM, is added between the cell and cooling container [23].

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Fig 2: Tesla cooling case patent [22] Fig 3: Tesla cooling tubes patent [21]

Phase Change Material (PCM) Cooling

Cooling through phase change materials utilizes the PCM as a heat sink during battery discharge. The PCM collects the heat and goes through a phase change, from a less energy dense phase to a phase with more free energy, such as solid to liquid or liquid to gas. PCM cooling is a passive, rather than active, cooling method. The PCM cycles through the phases between battery discharge and standby. A disadvantage of PCM cooling systems are that they do not function well in extreme weather. If it is too hot, the PCM might melt completely and stop working as a heat sink. In too cold weather the PCM will be difficult to melt, adding a large thermal inertia which requires significant energy to warm up [20]. It is extremely important to consider the melting point of the PCM. The ideal melting point should be within the temperature range the battery operates. The ideal PCM has the perfect balance of thermal conductivity. Low thermal conductivities cause uneven melting, which can lower the effective PCM cooling. Too high thermal conductivities cause the entire PCM to melt, which renders it unable to function properly. Other properties such as toxicity, stability, and flammability are important to consider for safety aspects [15]. PCM systems are not used in commercial electric vehicle battery systems today, as research within the area still have some grounds to cover.

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Methodology

Model

The study was conducted through creating a model of a five-‐cell battery and cooling tube thermal system in COMSOL Multiphysics 5.3a. The model includes electrochemistry, heat transfer, and liquid flow physics. The electrochemistry is based on the P2D model, through COMSOL’s Lithium-‐Ion Battery interface. The model uses a coupling function to pair the 1D electrochemical model with a 3D thermal model. Interpolations are set up to describe the temperature affected properties of the coolant. For the studied effects, equations utilizing COMSOL’s built in equations where formulated where they could not be collected directly.

The equation to describe the internal resistance of the model is written:

𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝐸𝑂𝐶𝑉_79V− 𝐸𝑂𝐶𝑉_MPm − 𝐸_=Phh

𝐼_n77

This equation is derived over time to plot the time dependent internal resistance for set parameters and drive cycle. EOCVpos and EOCVneg are variables calculated from the

equilibrium potential for the current state of charge for that electrode. Ecell is calculated by integrating the cell voltage over the positive current collector.

The reversible heat production is calculated by integrating the reversible heat source in W/m³ over the two electrodes, and then multiplying it with the area of the jellyroll.

The irreversible heat is all heat that is not reversible, so it was calculated by subtracting the reversible heat from the total heat production.

The model assumes that heat transfer only occurs between contact surfaces in the model.

No heat is being transferred to the air or between batteries separated by air. Heat is defined as being produced uniformly in the battery cylinders. However, heat is being transferred with different heat transfer coefficient depending on direction in the battery cell. The heat transfer vertically, or along the jellyroll layers is higher than the radial heat transfer that crosses the jellyroll layers.

Parameter data used in the model were obtained from fact sheets, through in-‐person communication, through calculations, and through built-‐in COMSOL data when it was deemed comparable.

The 3D model for thermal modelling was created in the CAD software SolidWorks and imported to COMSOL. This model is shown in Fig. 4.

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A full description to re-‐create the model and a list of constant parameters can be found in Appendix 9.

Fig. 4: Geometrical model of 5-‐cell battery module section

Study

To conduct the study of the cooling tube cooling system’s effectiveness, two areas of interest were identified. These are the inlet flow rate and the driving cycle. In addition to those, it was also investigated what effect the current has on the heat generation.

Inlet Flow Rate

The suggested normal flow rate for the system is 1 liter per minute of coolant entering the inlet. Flow rates of 0.5 liter per minute higher and lower than the suggested flow rate were tested to determine the effect of changing the velocity. A simulation was also run with an extremely low flowrate to illustrate the situation at no flow. All of these were run for the specific driving cycle Driving 1 Cycle 1, which is described in the Driving Cycle section.

For each flowrate, the maximum temperature reached and minimum temperature in a battery cell at the same time was obtained.

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Driving Cycle

For the set flowrate of 1 liter per minute, the effect of five different driving cycles was simulated. The simulations included temperature, cell voltage, internal resistance, total heat production, and how the total heat is split into reversible and irreversible heat. This is to see how different uses affect the battery system. The five driving cycles are pictured in Fig. 5-‐9 with the y-‐axis as C-‐rate, and the exact data is given in Table 1.

Fig. 5: Driving 1 Cycle 1 Fig. 6: Driving 1 Cycle 2

Fig. 7: Driving 2 Cycle 1 Fig. 8: Driving 2 Cycle 2

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Fig. 9: Driving 3

Table 1: Driving cycle data

Current

An area of additional interest is the effect of current on heat production. To analyze this effect, simulations were run for various C-‐rates. A 1C C-‐rate is set to 3.2 A. With this as a base, eight different C-‐rates were run for both a charge and discharge process, until they were either fully charged of fully discharged. This was defined as reached the cell voltage limits of 3.0 V as fully discharged and 4.2 V for fully charged.

The C-‐rates included in the study are listed in Table 2.

Driving 1 Cycle 1 Driving 1 Cycle 2 Driving 2 Cycle 1 Driving 2 Cycle 2 Driving 3 Duration

(s) C-‐rate Duration

(s) C-‐rate 270 -‐1.381 1300 0.581 20 -‐0.306 2550 -‐0.972 480 -‐0.9 180 -‐0.025 180 -‐0.025 25 -‐0.4 2550 0.638 10 -‐1.028 350 1.078 2600 -‐1.472 20 -‐0.419 900 0.791

20 -‐0.134 20 -‐0.134 10 -‐0.122 120 0.119

20 -‐0.306 120 0.238

25 -‐0.4 120 0.475

20 -‐0.419 120 0.791

10 -‐0.122 120 0.119

20 -‐0.306 1200 -‐1.263

25 -‐0.4 10 -‐1.028

20 -‐0.419

180 -‐0.028

Total: 820 s Total: 4100 s Total: 395 s Total: 5100 s Total: 3200 s

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0.1C Charge

Discharge

0.3 C Charge

Discharge

0.5C Charge

Discharge

0.7C

Charge

Discharge

1C Charge

Discharge

1.2C

Charge

Discharge

1.4C

Charge

Discharge

1.5C

Charge

Discharge

Table 2: C-‐rates included in study

The discharging models where given initial lithium ion concentrations of 26814 mol/m³ in the negative electrode, and 22995 mol/m³ in the positive electrode, values assumed to represent the defined fully charged battery. The charging models were given initial lithium ion concentrations of 7921.3 mol/m³ in the negative electrode, and 41318 mol/m³ in the positive electrode, values assumed to represent the defined fully discharged battery. The defined battery statuses are not the same as the completely drained or charged battery, but set as limits for desired usage.

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Results and Discussion

Inlet Flow Rate

Temperature data and curves were obtained for the four flowrates. As the driving cycle remained constant Driving 1 cycle 1, temperature is the only changing factor in this

experiment. Fig. 10-‐13 show how the temperature inside the battery varies over time for the four different velocities. Table 2 summarizes the data through the maximum temperature reached at any point of time, the minimum temperature in a battery cell at that time, and the coolant outflow temperature. All figures are modelled on the same time and

temperature scale for simplified comparison.

Fig. 10: Temperature over time at flowrate 0 liter per minute

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Fig. 11: Temperature over time at flowrate 0.5 liter per minute

Fig. 12: Temperature over time at flowrate 1 liter per minute

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Fig. 13: Temperature over time at flowrate 1.5 liter per minute

Test Max temp. Min temp. Coolant Outflow Temp.

Flow Rate 0 L/min 25.4 °C 24.6 °C 24.6 °C

0.5 L/min 22.8 °C 20.8 °C 20.03 °C 1 L/min 22.7 °C 20.8 °C 20.02 °C 1.5 L/min 22.6 °C 20.7 °C 20.01 °C Table 2: Temperature data for the different flow rates.

The data shows that having no coolant flow gives a noticeable effect, where the

temperature is significantly higher than for even the lowest coolant flowrate at 0.5 liter per minute. Between the different flow rates, the difference is smaller. Between 0.5 liter per minute (fig. 11) and 1.5 liter per minute (fig. 13), the coolant flow rate has been tripled.

However, the difference in maximum temperature in the cells is only 0.2 °C. The coolant outflow temperature has decreased by 0.02 °C between the two simulations.

The temperature rises when the battery is in use, as heat is being generated. When the battery is not in no additional heat is being generated, and two different scenarios are visible from the figures. In Figure 10 with the 0 liter per minute flowrate, the temperature stabilizes

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at this time stamp. For the other three flow rates, the temperature decreases, as the coolant can transfer away more heat than what is being produced.

Driving Cycle

For the five different driving cycles, the data obtained includes cell voltage, heat generation, heat generation separated into reversible and irreversible heat, temperature, and internal resistance. They were all given a coolant flow rate of 1 liter per minute. Thus, the

temperature obtained for the Driving 1 cycle 1 cycle is the same as for the 1 liter per minute flow rate given above.

Cell Voltage

The cell voltage is shown in Fig. 14-‐18. The plots also contain the drive cycle, to illustrate how they depend on each other. A bottom limit of 3.0 V and an upper limit of 4.2 V has been defined in product sheets as the cell voltages that equals to 0 % SOC and 100 % SOC. In the cycle Driving 1 cycle 2, the drive cycle has been allowed to continue past this limit to illustrate what would happen. All cycles have been put on the same y-‐axes for simplified comparison. The Driving 1 cycle 2 cycle will be difficult to read due to the wide range of the axis, and a scale-‐adjusted version is available in Appendix 1.

Fig. 14: Cell voltage over time for Driving 1 cycle 1

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Fig. 18: Cell voltage over time for Driving 3

In Fig. 14-‐18, it can be clearly seen how the cell voltage is related to the C-‐rate. When the C-‐

rate is negative, implying that the battery is being discharged, the cell voltage drops. When the C-‐rate is zero, implying that the battery is not in use, the cell voltage stabilizes. When the C-‐rate is positive, implying that the battery is being charged, the cell voltage increases. For all the tested driving cycles, except for Driving 1 cycle 2 (Fig.15), the cell voltage stays within the given limits. Within the limits, the cell voltage does not increase or decrease as rapidly as

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it can be seen dropping once the cell voltage goes below 3.0 V in Driving 1 cycle 2, without changing the C-‐rate.

Heat Production per battery cell, including reversible and irreversible heat

The heat production, and the heat separated reversible and irreversible heat for an individual battery cell in the model is shown in Fig. 19-‐23, respectively Fig. 24-‐28. In addition, cut sections of the cycle Driving 3 has been added to show how the heat is

dissipated from inside the battery. The total heat adds the reversible and irreversible heat. It is assumed that the cells produce equal heat. The driving cycle is included to illustrate the relation. Again, the cycle Driving 1 cycle 2 is out of the ordinary range, and will thus produce more heat than the other cycles. All cycles have been put on the same y-‐axes for simplified comparison. The Driving 1 cycle 2 cycle will be difficult to read due to the wide range of the axis, and a scale-‐adjusted version is available in Appendix 1.

Fig. 19: Total heat production over time for a single cell over Driving 1 cycle 1

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Fig. 23: Total heat production over time for a single cell over Driving 3

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Fig. 24:Reversible and irreversible heat production over time for a single cell over Driving 1 cycle1

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Fig. 28: Reversible and irreversible heat production over time for a single cell over Driving 3

In the figures it can be seen that high C-‐rates, either positive or negative, cause higher heat generation, while lower C-‐rates causes less heat production. Looking at the reversible and irreversible heat, we can see that more irreversible heat is produced when the battery is discharging. At discharge, the reversible heat generated is negative, which means that it is actually cooling the system. However, as the irreversible heat also increases during the same time period, the makes reversible heat loss is evened out when looking at the total heat generation. For the cycle Driving 1 cycle 2 (Fig.20, Fig. 25), the heat increases rapidly at the timestamp of when the potential drops below 3.0 V. The battery struggles with the situation, and more heat is produced.

Temperature

The modelled temperatures for the driving cycles are given in Table 3 and Fig. 29-‐33. Driving 1 cycle 1, Driving 2 cycle 1, Driving 2 cycle 2, and Driving 3 are also given as heat colored 3D figures in Fig. 34-‐37. The 3D figures are given at the point of time where the highest

temperature is measured and placed on the same temperature scale. Driving 1 cycle 2 is excluded to better illustrate the temperature distribution in the other 3D models. The obtained temperatures are strongly related to the heat productions for the driving cycles.

The more demanding drive cycle, the more heat is being produced. The additional heat results in higher temperatures. This is extra notable for Driving 1 Cycle 2, where heat

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production is allowed to run higher for the sake of the study. All cycles have been put on the same y-‐axes for simplified comparison. The Driving 1 cycle 2 cycle will be difficult to read due to the wide range of the axis, and a scale-‐adjusted versions are available in Appendix 1.

Test Max temp. Min temp. Coolant Outflow Temp.

Driving cycles Driving 1 cycle 1 22.7 °C 20.8 °C 20.02 °C

Driving 1 cycle 2 27.7 °C 22.1 °C 20.05 °C Driving 2 cycle 1 20.1 °C 20.04 °C 20.001 °C Driving 2 cycle 2 23.6 °C 21.0 °C 20.02 °C Driving 3 23.8 °C 21.1 °C 20.02 °C Table 3: Temperature data for the different driving cycles

Fig. 29: Temperature over time for Driving 1 cycle 1

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Fig. 33: Temperature over time for Driving 3

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Fig. 34: Temperature distribution for Driving 1 cycle 1

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Fig. 37: Temperature distribution for Driving 3

Designing Thermal Management Systems For Lithium-Ion Battery Modules Using COMSOL