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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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Table of Contents

Abstract 1

Acknowledgements 2

Table of Contents 3

Introduction and Project Description 4

Background 5Li(Ni1/3Mn1/3Co1/3)O2 (NMC) Li-‐Ion Batteries 5Generated Heat 6Cooling systems 11

Methodology 15Model 15Study 16

Results and Discussion 20Inlet Flow Rate 20Driving Cycle 23Current 41

Conclusions and future work 42

Nomenclature and Abbreviations 44Abbreviations 44Nomenclature 44

References 46

Appendix 48Appendix 0: Calculations complement 48Appendix 1: Scale adjusted plots and 3D temperature model for Driving 2 cycle 1 51Appendix 2: Plots for the C-‐Rate Measurements 54Appendix 3: Parameter values used in COMSOL model 57Appendix 4: Lithium ion cell variables used in COMSOL model 59Appendix 5: Coolant heat capacity interpolation used in COMSOL model 60Appendix 6: Coolant density interpolation used in COMSOL model 61Appendix 7: Coolant dynamic viscosity interpolation used in COMSOL model 62Appendix 8: Coolant thermal conductivity interpolation used in COMSOL model 63Appendix 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 ∙ 3

4 (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]:

<=<>= 𝛻 ∙ (𝐷𝐿𝑖𝛻𝑐𝑒) (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 = 𝑐E 𝑎𝑡 𝑡 = 0

𝐷I:<=<J= 0 𝑎𝑡 𝑟 = 0

𝐷I:𝜕𝑐𝜕𝑟 =

𝑖M𝐹 𝑎𝑡 𝑟 = 𝑟E

COMSOL’s battery module also utilizes the Bruggeman model, tF = ep-‐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]:

𝜀P<<>𝑐P − ∇ ∙ 𝐷I:∇𝑐P − :R∇ST

4+ 𝑎V𝑗M 1 − 𝑡YE = 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:

𝜕𝑐P𝜕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 = 𝑖E expa𝑎𝐹h𝑠𝑅𝑇 − exp

−a𝑐𝐹h𝑠𝑅𝑇 (Eq.5)

where i is the current density, i0 is the exchange current density, aa anode transfer

coefficient, F is the Faraday constant, hs is the surface overpotential, R is the overpotential

resistance, and T is the temperature.

The exchange current density, i0, is defined:

𝑖E = 𝐹𝑘𝑎a𝑐𝑘𝑐

a𝑎 𝑐𝑠𝑚𝑎𝑥 − 𝑐𝑠 a𝑐𝑐𝑒a𝑎 (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, hs, is defined:

hV = ØV − ØP − 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]:

𝑖P + 𝑘PccÑØP −.de,fRgg

41 + <hMc±

<hM=R1 − 𝑡YE Ñ𝑙𝑛𝑐P = 0 (Eq.8)

where ie is the current density in the electrolyte phase, keff 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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𝜕ØP 𝜕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]:

𝑖V = −sPccÑØV (Eq.9)

where is is the solid phase current density, seff 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]:

−sPcc𝜕ØV 𝜕𝑥 =

𝐼𝐴 𝑎𝑡 𝑥 = 0 𝑎𝑛𝑑 𝑥 = 𝐿

𝜕ØV 𝜕𝑥 = 0 𝑎𝑡 𝑥 = 𝐿M 𝑎𝑛𝑑 𝑥 = 𝐿M + 𝐿VP7

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 =𝐸𝑂𝐶𝑉79V − 𝐸𝑂𝐶𝑉MPm − 𝐸=Phh

𝐼n77

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.

20

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

21

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

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

22

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

23

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

24



25


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

26

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

27



28


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

29

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


30



31

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

32

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

33



34


Fig. 33: Temperature over time for Driving 3

35

Fig. 34: Temperature distribution for Driving 1 cycle 1


36


Fig. 37: Temperature distribution for Driving 3

37

Fig. 38: Temperature distribution in a cut section in the xy plane for Driving 3

Fig. 39: Temperature distribution in a cut section in the yz plane for Driving 3

Fig. 40: Temperature distribution in a cut section in the xz plane for Driving 3

38

Here Driving 2 cycle 1 (Fig. 31) has the lowest temperature. It is also the shortest cycle. The

longest regular cycle is Driving 3 (Fig.33), which also reaches the highest temperatures. High

heat production over longer time gives higher temperatures. Consequently, the shorter

cycles, Driving 1 cycle 1 (Fig. 29) and Driving 2 cycle 1, also results in lower temperatures

than the other cycles. The temperature rises with the heat production when the battery is in

use. When the battery is not in use the temperature is decreasing, as more heat is

transferred away by the coolant than what is being produced by the cells. In fig.38-‐40 the

dissipation of heat is clearly shown. The heat spreads faster along the jellyroll, which causes

the temperature to be higher in the middle of the cylindrical cell, and cooler towards the

surface. The jellyroll also causes the heat to dissipate uniformly along the vertical axis.

Internal Resistance The internal resistance for the different cycles are shown in Fig. 41-‐45. All cycles have been

put on the same y-‐axes for simplified comparison.

Fig. 41: Internal resistance over time for Driving 1 cycle 1

39



40


Fig. 45: Internal resistance over time for Driving 3

The internal resistance is generally quite low for the different driving cycles. The exception is

timestamps where the internal resistance appears to run sky high. These are likely due to an

error for low currents in the equation. The equation only works well for reasonable high

currents, and when the current gets too low the internal resistance does not appear

correctly. A case where the internal resistance is increasing which is not explained by this

error is Driving 1 cycle 2 (Fig. 39). In the figure the internal resistance increases rapidly while

41

the discharge current is high. This is related to that the battery is effectively fully discharged

at this point and the internal resistance is increasing due to the cell voltage drop.

Current The model was run for several different C-‐Rates, where 1 C is 3.2 A, 0.5 C is 1.6 A, etc. The

discharging models are set to start at a different state of charge than the charging models.

For these models, the factors investigated were the time until fully charge/discharged, the

maximum heat production during the cycle, and the heat production at half the total cycle

time. This result is given in Table 4. Plotted individual cycles for the different C-‐rates can be

found in Appendix 2.

Test Time until 3V/4.2V

Max heat production

Heat production at time halfway point

0.1C Charge 29100s 0.1W 0.02W Discharge 30400s 0.03W 0.00W

0.3 C Charge 9590s 0.28W 0.10W Discharge 10000s 0.14W 0.03W



1C Charge 2600s 1.3W 0.91W Discharge 2800s 1.2W 0.61W




Table 4: Charge and discharge data for different C-‐rates

In Table 4 it can be seen that charging the battery produces more heat and goes generally

faster than discharging the battery. Higher C-‐Rates requires higher currents and

consequently drains or charges the battery faster, with a higher heat production.

42

Conclusions and future work

A model for the module section with the five cells and liquid cooling system was successfully

constructed and tested in COMSOL Multiphysics 5.3a. The input parameter data consists of

both data obtained from Northvolt, as well as literature data provided by the built-‐in

functions of the COMSOL Multiphysics 5.3a suite. With this in mind, it is possible to further

improve the accuracy of the model by replacing the literature data by experimental data

from the exact cell. However, for the analyzed cases, the current parameter data is

considered sufficiently accurate.

COMSOL Multiphysics 5.3a proved to be a suitable software to construct a battery model in

to analyze heat generation and temperature distribution, with and without cooling. It was

also possible to analyze the other properties of interest. The model constructed is quite

advanced to include several input data and for requested output data to be obtained.

However, it is also possible to construct simpler battery cell models which will not require as

much data power or input information as the constructed model. COMSOL Multiphysics 5.3a

proved its versatility in that it was possible to run on old laptops as well as on state-‐of-‐art

stationary computers. However, even with this versatility it is advised to run the program on

computers with better specs, as the calculation time was severely prolonged on the old

laptop. In one case tested, the calculation time increased from 3 hours on a good stationary

computer to 28 hours on an old laptop. However, the software to still worked well on the

old laptop without being slowed down in other areas than calculations.

The model shows that the addition of the cooling system is beneficial, and also what

temperatures the system may reach and what heat is being generated. However, it is still

important to stay within the battery limits and having an additional system that shut down

the battery when it reaches the defined maximum discharge and that stops charging it when

it reaches the defined fully charged state.

It should be noted that the temperatures here are quite low. This is due to the small scale of

the model. The section of five cells is only a small part of the full module which will be

cooled by the same coolant loop. In a larger system with more cells, the coolant

temperature will pass through more than five cells before it is looped through a heat

exchanger. With more cells to pass through, the coolant temperature will increase more

43

than for the five cell section, reducing the cooling effect. Consequently, while the difference

between the 0.5 liter per minute flowrate and the 1.5 liter per minute flowrate is not large

here, it might be of higher importance in a full module with more cells.

It is of interest to expand the system in future work to test the temperature effects and if

the coolant still is sufficient. It is also of interest to compare the calculated data with

experimental data from performing tests and measurements on a physical battery module

under the same conditions. Additionally, analyzing temperatures distribution in the cell over

time for the different C-‐rates is a point of interest. To make the model even clearer, adding a

SOC, state of charge, distribution plot would be of interest for the future.

44

Nomenclature and Abbreviations

Abbreviations NMC = Nickel Manganese Cobalt, batteries with a Li(Ni1/3Mn1/3Co1/3)O2 Electrode OCV = Open Cell Voltage P2D = Pseudo-‐Two Dimensional PCM = Phase Change Material SOC = State of Charge TIM = Thermal Interface Material Nomenclature Greek letters an = Anode transfer coefficient [-‐] a= = Cathode transfer coefficient [-‐] ee = Volume fraction/porosity of electrolyte [-‐] hs = Surface overpotential [V] Øe = Electrolyte phase potential [V] Øs = Solid phase potential [V] seff = Effective electronic conductivity of the solid phase [S/m] Alphabetic letters as = Specific interfacial area of solid phase [m2/m3] A = Surface area of active material [m2] c = Concentration of Li ions [mol/m3] ce = Concentration of Li ions in electrolyte phase [mol/m3] cs = Concentration of Li ions in solid phase [mol/m3] Cp = Specific heat capacity [J/(kg × K) DLi = Diffusion coefficient of Li [m2/s] dU/dT = Entropic heat coefficient [-‐] Ecell = Cell voltage [V] EOCPneg = Open cell potential, negative electrode [V] EOCPpos = Open cell potential, positive electrode [V] f± = molecular salt activity coefficient [-‐] F = Faraday constant, 96.485 [C/mol] ie = Current density in electrolyte phase [A/m2] i0 = Exchange current density [A/m2] in = Reaction current density at particle surface [A/m2] is = Current density in solid phase [A/m2] I = Current [A] Iapp = Applied current [A] jn = Pore-‐wall flux across interface [mol/(m2×s)] 𝑘n = Anodic reaction rate constant [m3/s] 𝑘= = Cathodic reaction rate constant [m3/s] 𝑘Pcc = Effective ionic conductivity [S/m]

45

𝐿 = Total thickness of cell [m] 𝐿M = Thickness of negative electrode [m] 𝐿VP7 = Thickness of separator [m] 𝑚 = Mass flow rate of coolant [kg/s] 𝑄 = Heat generation [W] r0 = NMC particle radius [m] R = Overpotential resistance [W] Rg = Universal gas constant, 8.3145 [J/(mol×K)] ∆S = Entropy change [J/(mol×K)] t = Time [s] t+0 = Transfer number of the lithium ions with respect to the velocity of solvent [s] T = Temperature [K] To = Outlet temperature [K] Ti = Inlet temperature [K] U = Open-‐circuit potential [V] V = Cell voltage [V]

46

References

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[2] S. S. Zhang, T. R. Jow, K. Amine and G. L. Henriksen, "LiPF6±EC±EMC electrolyte for Li-ion battery," Journal of Power Sources , vol. 107, pp. 18-23, 2003.

[3] S. Kim, Y. S. Lee, H. S. Lee and H. L. Jin, "A study on the behavior of a cylindrical type Li-Ion secondarybattery under abnormal conditions," Materials Science & Engineering Technology, vol. 41, pp. 378-385, 2010.

[4] H. Liu, Z. Wei, W. He and J. Zhao, "Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: A review," Energy Conversion and Management, vol. 150, pp. 304-330, 2017.

[5] C. G. Motloch, J. P. Christophersen, J. R. Belt, R. B. Wright, G. L. Hunt, R. A. Sutula, T. Duong, T. J. Tartamella, H. J. Haskins and T. J. Miller, "High-Power Battery Testing Procedures and Analytical Methodologies for HEV’s," in Proceedings of the 2002 Future Car Congress , Arlington, 2002.

[6] D. Bernardi, E. Pawlikowski and J. Newman, "A General Energy Balance for Battery Systems," Journal of the Electrochemical Society, vol. 132, pp. 5-12, 1985.

[7] T. M. Bandhauer, S. Garimella and T. F. Fuller, "A Critical Review of Thermal Issues in Lithium-Ion Batteries," Journal of The Electrochemical Society,, vol. 158, no. 3, pp. R1-R25, 2011.

[8] K. Onda, H. Kameyama, T. Hanamoto and K. Ito, "Experimental Study on Heat Generation Behavior of Small Lithium-Ion Secondary Batteries," Journal of The Electrochemical Society, vol. 150, pp. A285-A291, 2003.

[9] G. Karimi and X. Li, "Thermal management of lithium-ion batteries for electric vehicles," International Journal of Energy Research, vol. 37, pp. 13-24, 2013.

[10] S. Panchal, I. Dincer, M. Agelin-Chaab, R. Fraser and M. Fowler, "Experimental and theoretical investigations of heat generation rates for a water cooled LiFePO4 battery," International Journal of Heat and Mass Transfer, vol. 101, pp. 1093-1102, 2016.

[11] COMSOL, "Understand, Predict, and Optimize Engineering Designs with the COMSOL Multiphysics® Software," COMSOL, [Online]. Available: https://www.comsol.com/comsol-multiphysics. [Accessed 02 01 2018].

[12] COMSOL, Batteries & Fuel Cells Module: v.5.3 User’s Guide, 2017. [13] M. Doyle, T. F. Fuller and J. Newman, "Modeling of Galvanostatic Charge and

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[14] T. F. Fuller, M. Doyle and J. Newman, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society, vol. 141, pp. 1-10, 1994.

[15] Q. Wang, B. Jiang, B. Li and Y. Yan, "A critical review of thermal management models and solutions of lithium-ion batteries for the development of pure electric vehicles," Renewable and Sustainable Energy Reviews, vol. 64, pp. 106-128, 2016.

47

[16] V. Ramadesigan, P. W. C. Northrop, S. De, S. Santhanagopalan, R. D. Braatz and V. R. Subramanian, "Modeling and Simulation of Lithium-Ion Batteries from a Systems Engineering Perspective," vol. 159, pp. R31-R45, 2012.

[17] J. Yang, X. Wei, H. Dai, J. Zhu and X. Xu, "Lithium-ion Battery Internal Resistance Model Based on the Porous Electrode Theory," in Vehicle Power and Propulsion Conference (VPPC), Coimbra, 2014.

[18] J. Newman and W. Tiedemann, "Porous-Electrode Theory With Battery Applications," American Institute of Chemical Engineers Journal, Vols. LBL-3117, pp. 1-81, 1974.

[19] D. Chen, J. Jiang, G.-H. Kim, C. Yang and A. Pesaran, "Comparison of different cooling methods for lithium ion battery cells," Applied Thermal Engineering, vol. 94, pp. 846-854, 2016.

[20] G. Xia, C. Lei and G. Bi, "A review on battery thermal management in electric vehicle application," Journal of Power Sources, vol. 367, pp. 90-105, 2017.

[21] A. Faass and E. Clough, "Battery module with integrated thermal management system". USA Patent US 20130196184 A1, 01 08 2013.

[22] P. T. Tennessen, J. C. Weintraub and W. A. Hermann, "Battery Coolant Jacket". USA Patent US 20130004820 A1, 03 01 2013.

[23] A. J. McNamara, Y. Joshi and Z. M. Zhang, "Characterization of nanostructured thermal interface materials e A review," International Journal of Thermal Sciences, vol. 62, pp. 2-11, 2012.

[24] M. Singh, J. Kaiser and H. Hahn, "Thick Electrodes for High Energy Lithium Ion Batteries," Journal of The Electrochemical Society, vol. 162, pp. A1196-A1201, 2015.

[25] H. Kang, C. Lim, T. Li, Y. Fu, B. Yan, N. Houston, V. De Andrade, F. De Carlo and L. Zhu, "Geometric and Electrochemical Characteristics of LiNi1/3Mn1/3Co1/3O2 Electrode with Different Calendering Conditions," Electrochimica Acta, vol. 232, pp. 431-438, 2017.

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48

Appendix

Appendix 0: Calculations complement Appendix 0.1: Calculations to support the probability of the coolant temperature increase for

three different non-‐zero flow rates.

Properties of interest: Property Value Unit Inlet temperature 20 °C Coolant heat capacity 3400 J/(kg*K) Coolant density 1,4 kg/L Approximated heat energy production in joule for Driving1cycle1: Time Extent Energy produced (J) 270 s 202,5 180 s 9 350 s 245 20 s 0,4 Total energy: 456,9 The temperature increase is calculated:

𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 =𝐻𝑒𝑎𝑡 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 (𝐽)

𝑀𝑎𝑠𝑠 𝑜𝑓 𝑐𝑜𝑜𝑙𝑎𝑛𝑡 𝑘𝑔 ∙ 𝐻𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑐𝑜𝑜𝑙𝑎𝑛𝑡( 𝐽𝑘𝑔 ∗ 𝐾)

The mass of coolant is dependent on flowrate, and is calculated:

𝑀𝑎𝑠𝑠 𝑜𝑓 𝐶𝑜𝑜𝑙𝑎𝑛𝑡 = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑐𝑜𝑜𝑙𝑎𝑛𝑡 𝑖𝑛 𝑠𝑦𝑠𝑡𝑒𝑚 + 𝐹𝑙𝑜𝑤𝑟𝑎𝑡𝑒 ∙ 𝑡𝑖𝑚𝑒 Flow Rate (L/min) Mass of coolant (kg) 0,5 8,3 1 16,1 1,5 23,9

This results in the following temperatures: Flow Rate (L/min) Outflow temperature (°C) 0,5 20,08 1 20,04 1,5 20,03

This heat increase is similar to that which was calculated by COMSOL.

49

Appendix 0.2: Comparing the thermic and electric effects

Graphs showing the required electrical power from each battery cell has been constructed based on given data. These can be compared to the heat power generated by the cells. The electric power and the heat power for Driving 1 cycle 1 is compared in Fig. 46 and 47.

Fig. 46: Electric power required by Driving 1 cycle 1

Fig. 47: Heat power generated by Driving 1 cycle 1 The electric power for the remaining drive cycles are shown in Fig. 48-‐51. These can be compared with Fig. 20-‐23.

-‐15

-‐10

-‐5

0

5

10

15

20

0 100 200 300 400 500 600 700 800 900

Power re

quire

d (W

)

Time (s)

Electric Power Required, Driving 1 Cycle 1

50




-‐10

-‐5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Power re

quire

d (W

)

Time (s)


0,0

1,0

2,0

3,0

4,0

5,0

6,0

0 50 100 150 200 250 300 350 400 450

Power re

quire

d (W

)

Time (s)


-‐10

-‐5

0

5

10

15

0 1000 2000 3000 4000 5000 6000

Power re

quire

d (W

)

Time (s)


51

Fig. 51: Electric power required by Driving 3 When comparing the generated heat with the electric power required, it can be seen that the generated heat is about a tenth the size of the required power. Appendix 1: Scale adjusted plots and 3D temperature model for Driving 2 cycle 1 Driving 2 cycle 1 is a short cycle with relatively low C-‐rates. This causes the values to not be as high as for the other cycles and therefore difficult to read on the scale all of them are placed on. In this appendix, all figures are given on scales adjusted for the values of Driving 2 cycle 1.

Fig. 52: Adjusted scare cell voltage over time for Driving 2 cycle 1

-‐15

-‐10

-‐5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500

Power re

quire

d (W

)

Time (s)

Electric Power Required, Driving 3

52

Fig. 53: Adjusted scale heat production over time for Driving 2 cycle 1

Fig. 54: Adjusted scale reversible and irreversible heat production over time for Driving 2 cycle 1

53

Fig. 55: Adjusted scale temperature over time for Driving 2 cycle 1


54

Appendix 2: Plots for the C-‐Rate Measurements This appendix gives the plots of heat production over time for the different charge and discharge C-‐rates.

Fig. 57: Charge heat production for 0.1C Fig. 58: Discharge heat production for 0.1C



55


Fig. 65: Charge heat production for 1C Fig. 66: Discharge heat production for 1C



56


57

Appendix 3: Parameter values used in COMSOL model This list includes all parameter data used in the COMSOL model. Please see notes for the origin of each parameter. This is the file “5_Cell_NMC_Battery_Parameter.txt” mentioned in the modelling instructions in Appendix 9.

1 Value given by Northvolt 2 Calculated from given data 3 Value obtained from COMSOL model and deemed comparable

Parameter name Value Description rp_neg 18.5e-‐6[m]1 Particle radius negative electrode rp_pos 12e-‐6[m]1 Particle radius positive electrode epss_pos (1-‐epsl_pos-‐0.170)*3.2/3.65232 Solid phase volume fraction positive electrode

epsl_pos 0.251 Electrolyte phase volume fraction positive electrode

epss_neg (1-‐epsl_neg-‐0.172)*3.2/3.65232 Solid phase volume fraction negative electrode

epsl_neg 0.421 Electrolyte phase volume fraction negative electrode

epsl_sep 0.3501 Electrolyte phase volume fraction separator k_neg 2e-‐11[m/s]3 Reaction rate coefficient negative electrode k_pos 5e-‐10[m/s]3 Reaction rate coefficient positive electrode cl_0 1200[mol/m^3]3 Initial electrolyte salt concentration i_1C_c 3.2[A]1 1C current L_neg 218.8e-‐6[m]1 Length of negative electrode L_sep 16e-‐6[m]1 Length of separator L_pos 158.7e-‐6[m]1 Length of positive electrode d_can 0.25[mm]3 Thickness of battery canister r_batt 10.5 [mm]1 Battery radius h_batt 70 [mm]1 Battery height L_neg_cc 10[um]1 Negative current collector thickness L_pos_cc 10[um]1 Positive current collector thickness L_batt L_neg+L_neg_cc+L_sep+L_pos+L_pos_cc2 Cell thickness kT_batt_ang 25 [W/(m*K)]1 Battery thermal conductivity, angular and axial kT_batt_r 1 [W/(m*K)]1 Battery thermal conductivity, radial rho_batt 68[g]/(r_batt^2*pi*h_batt)1 Battery density Cp_batt 1000 [J/(kg*K)]1 Battery heat capacity T_inlet 293.15[K]1 Inlet temperature T_init T_inlet2 Initial temperature h_tube1 5.95[mm]1 Height tube type 1, geometry

58

Table 5: Parameter data used in model

4 Varied parameter. This value represents the flow 1 L/min and has been calculated. 5 Value obtained from other program, can be assumed to be given

h_tube2 5.60[mm]1 Height tube type 2, geometry V_in 0.12214 Inlet Velocity t 0 Initial time A_cell 808[mm]*65[mm]2 Area of active battery material sheet csmax_neg 31507[mol/m^3]5 Maximal state-‐of-‐charge negative electrode csmax_pos 49000[mol/m^3]5 Maximal state-‐of-‐charge positive electrode cs0_pos 25814[mol/m^3]5 Initial state-‐of-‐charge positive electrode cs0_neg 23907[mol/m^3]5 Initial state-‐of-‐charge negative electrode cptim 2.1[MJ/(m^3*K)]/2300[kg/m^3]1 Heat capacity of TIM material

59

Appendix 4: Lithium ion cell variables used in COMSOL model These variables are set up in the lithium ion battery part of the COMSOL model. This is the file “Variables1liion.txt” mentioned in the modelling instructions in Appendix 9.

i_app i_1C_c*driving(t) Applied Current Density T_init 293.15[K] Initial Temperature T nojac(comp2.aveop1(comp2.T)) Battery Cell Temperature Ecell pos_cc(phis) Cell Voltage

EOCPpos mat3.elpot.Eeq_int1(liion.soc_average_pce2) Open cell potential, positive electrode

EOCPneg mat1.elpot.Eeq_int1(liion.soc_average_pce1) Open cell potential, negative electrode

Total_polarization (EOCPpos-‐EOCPneg)-‐Ecell Total Polarization Table 6: Lithium ion cell variables used in model

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Appendix 5: Coolant heat capacity interpolation used in COMSOL model

This is the coolant heat capacity data for the model. The data was given by Northvolt. This is

the file “Coolant_Heat_Capacity.txt” mentioned in the modelling instructions in Appendix 9.

Temperature [K] Heat Capacity [J/(kg*K)] 255.4 3.27 277.6 3.33 299.9 3.41 322.1 3.48 344.3 3.56 Table 7: Coolant heat capacity interpolation used in model

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Appendix 6: Coolant density interpolation used in COMSOL model


the file “Coolant_Density.txt” mentioned in the modelling instructions in Appendix 9.

Temperature [K] Density [kg/m3] 255.4 1160.6 277.6 1150.2 299.9 1138.3 322.1 1126.3 344.3 1114.6 Table 8: Coolant density interpolation used in model

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Appendix 7: Coolant dynamic viscosity interpolation used in COMSOL model


the file “Coolant_Dynamic_Viscosity.txt” mentioned in the modelling instructions in

Appendix 9.

Temperature [K] Dynamic Viscosity [Pa*s] 255.4 0.075906 277.6 0.017407 299.9 0.0064288 322.1 0.0031513 344.3 0.0018442 Table 9: Coolant dynamic viscosity interpolation used in model

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Appendix 8: Coolant thermal conductivity interpolation used in COMSOL model


the file “Coolant_Thermal_Condictivity.txt” mentioned in the modelling instructions in

Appendix 9.

Temperature [K] Thermal Conductivity [W/(m*K)] 255.4 0.339 277.6 0.356 299.9 0.373 322.1 0.39 344.3 0.407 Table 10: Coolant thermal conductivity interpolation used in model

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Appendix 9: Modelling Instructions These instructions are heavily based on 1D Lithium-‐Ion Battery for Thermal Models and Thermal Modeling of a Cylindrical Lithium-‐ion Battery in 3D, and will therefore bear several similarities to them. This is due to the model also being based on these two examples. For the sake of clarity, steps that were conducted identical to those described by the guides were also described identical to the guides. From the File menu, choose New. NEW In the New window, click Model Wizard. MODEL WIZARD

1. In the Model Wizard window, click 1D 2. In the Select Physics tree, select Electrochemistry>Battery Interface>Lithium-‐Ion

Battery (liion). 3. Click Add. 4. Click Done.

GLOBAL DEFINITIONS Parameters

1. On the Home toolbar, click Parameters 2. In the Settings window for Parameters, locate the Parameters section. 3. Click Load from File. 4. Find the file named “5_Cell_NMC_Battery_Parameters.txt” and double-‐click it.

Interpolation 1

1. On the Home toolbar, click to create Interpolation 1 2. In the Settings window for Interpolation 1, click to change Function Name to

“driving”. 3. Locate the Data Source selection. 4. Select File. 5. Click Browse and find the file named “Drive_cycle_1.txt” and double-‐click it.

Interpolation 2


“cpcoolant”. 3. Locate the Data Source selection. 4. Select File. 5. Click Browse and find the file named “Coolant_Heat_Capacity.txt” and double-‐

click it.

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Interpolation 3 1. On the Home toolbar, click to create Interpolation 3 2. In the Settings window for Interpolation 3, click to change Function Name to

“rhocoolant”. 3. Locate the Data Source selection. 4. Select File. 5. Click Browse and find the file named “Coolant_Density.txt” and double-‐click it.

Interpolation 4


“mucoolant”. 3. Locate the Data Source selection. 4. Select File. 5. Click Browse and find the file named “Coolant_Dynamic_Viscosity.txt” and

double-‐click it. Interpolation 5


“kcoolant”. 3. Locate the Data Source selection. 4. Select File. 5. Click Browse and find the file named “Coolant_Thermal_Conductivity.txt” and

double-‐click it. GEOMETRY 1 Interval 1 (i1))

1. On the Geometry toolbar, click Interval. 2. In the Settings window for Interval, locate the Interval section. 3. From the Number of intervals list, choose Many. 4. In the Points text field, type 0,L_neg,L_neg+L_sep,L_neg+L_sep+L_pos. 5. Click Build All Objects. 6. Click the Zoom Extents button on the Graphics toolbar.

DEFINITIONS Explicit 1

1. On the Definitions toolbar, click Explicit. 2. Select Domain 1 only. 3. Right-‐click Explicit 1 and choose Rename. 4. In the Rename Explicit dialog box, type Negative Electrode in the New label text

field.

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5. Click OK.

Explicit 2 1. On the Definitions toolbar, click Explicit. 2. Select Domain 2 only. 3. Right-‐click Explicit 2 and choose Rename. 4. In the Rename Explicit dialog box, type Separator in the New label text field. 5. Click OK.

Explicit 3 1. On the Definitions toolbar, click Explicit. 2. Select Domain 3 only. 3. Right-‐click Explicit 3 and choose Rename. 4. In the Rename Explicit dialog box, type Positive Electrode in the New label text

field. 5. Click OK.

ADD MATERIAL 1. On the Home toolbar, click Add Material to open the Add Material window. 2. Go to the Add Material window. 3. In the tree, select Batteries and Fuel Cells>Electrodes>Graphite Electrode, LixC6

MCMB (Negative, Li-‐ion Battery). 4. Click Add to Component in the window toolbar. 5. In the tree, select Batteries and Fuel Cells>Electrolytes> LiPF6 in 3:7 EC:EMC

(Liquid electrolyte, Li-‐ion Battery). 6. Click Add to Component in the window toolbar. 7. In the tree, select Batteries and Fuel Cells>Electrodes>NMC Electrode,

LiNi1/3Mn1/3Co1/3O2 (Positive, Li-‐ion Battery). 8. Click Add to Component in the window toolbar. 9. On the Home toolbar, click Add Material to close the Add Material window.

MATERIALS Graphite Electrode, LixC6 MCMB (Negative, Li-‐ion Battery) (mat1)

1. In the Model Builder window, under Component 1 (comp1)>Materials click Graphite Electrode, LixC6 MCMB (Negative, Li-‐ion Battery) (mat1).

2. In the Settings window for Material, locate the Geometric Entity Selection section.

3. From the Selection list, choose Negative Electrode. LiPF6 in 3:7 EC:EMC (Liquid electrolyte, Li-‐ion Battery) (mat2)

1. In the Model Builder window, under Component 1 (comp1)>Materials click LiPF6 in 3:7 EC:EMC (Liquid electrolyte, Li-‐ion Battery) (mat2).

2. In the Settings window for Material, locate the Geometric Entity Selection

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section. 3. From the Selection list, choose Separator. NMC Electrode, LiNi1/3Mn1/3Co1/3O2 (Positive, Li-‐ion Battery) (mat3) 1. In the Model Builder window, under Component1(comp1)>Materials click NMC

Electrode, LiNi1/3Mn1/3Co1/3O2 (Positive, Li-‐ion Battery) (mat3). 2. In the Settings window for Material, locate the Geometric Entity Selection

section. 3. From the Selection list, choose Positive Electrode.

LITHIUM-‐ION BATTERY (LIION) Porous Electrode 1

1. In the Model Builder window, under Component 1 (comp1) right-‐click Lithium-‐ Ion Battery (liion) and choose Porous Electrode.

2. In the Settings window for Porous Electrode, locate the Domain Selection section.

3. From the Selection list, choose Negative Electrode. 4. Locate the Model Inputs section. In the T text field, type T. 5. From the c list, choose Electrolyte salt concentration (liion). 6. Locate the Electrolyte Properties section. From the Electrolyte material list,

choose LiPF6 in 3:7 EC:EMC (Liquid electrolyte, Li-‐ion Battery) (mat2). 7. Locate the Volume Fractions section. In the εs text field, type epss_neg. 8. In the εl text field, type epsl_neg.

Particle Intercalation 1 1. In the Model Builder window, expand the Porous Electrode 1 node, then click

Particle Intercalation 1. 2. In the Settings window for Particle Intercalation, locate the Species Settings

section. 3. In the cs, init text field, type cs0_neg. 4. Locate the Particle Transport Properties section. In the rp text field, type rp_neg. 5. Locate the Model Input section. In the T text field, type T.

Porous Electrode Reaction 1 1. In the Model Builder window, under Component 1 (comp1)>Lithium-‐Ion Battery

(liion)> Porous Electrode 1 click Porous Electrode Reaction 1. 2. In the Settings window for Porous Electrode Reaction, locate the Equilibrium

Potential section. 3. From the Eeq list, choose From material. 4. From the dEeq/dT list, choose From material. 5. Locate the Electrode Kinetics section. In the ka text field, type k_neg. 6. In the kc text field, type k_neg.

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7. Locate the Model Input section. In the T text field, type T. 8. From the c list, choose Insertion particle concentration, surface (liion).

Porous Electrode 2 1. In the Model Builder window, under Component 1 (comp1)>Lithium-‐Ion Battery

(liion) right-‐click Porous Electrode 1 and choose Porous Matrix Double Layer Capacitance.

2. Right-‐click Lithium-‐Ion Battery (liion) and choose Porous Electrode. 3. In the Settings window for Porous Electrode, locate the Domain Selection section. 4. From the Selection list, choose Positive Electrode. 5. Locate the Model Inputs section. In the T text field, type T. 6. From the c list, choose Electrolyte salt concentration (liion). 7. Locate the Electrolyte Properties section. From the Electrolyte material list,

choose LiPF6 in 3:7 EC:EMC (Liquid electrolyte, Li-‐ion Battery) (mat2). 8. Locate the Volume Fractions section. In the εs text field, type epss_pos. 9. In the εl text field, type epsl_pos.

Particle Intercalation 1

1. In the Model Builder window, expand the Porous Electrode 2 node, then click Particle Intercalation 1.

2. In the Settings window for Particle Intercalation, locate the Species Settings section.

3. In the cs, init text field, type cs0_pos. 4. Locate the Particle Transport Properties section. In the rp text field, type rp_pos. 5. Locate the Model Input section. In the T text field, type T.

Porous Electrode Reaction 1 1. In the Model Builder window, under Component 1 (comp1)>Lithium-‐Ion Battery

(liion)> Porous Electrode 2 click Porous Electrode Reaction 1. 2. In the Settings window for Porous Electrode Reaction, locate the Equilibrium

Potential section. 3. From the Eeq list, choose From material. 4. From the dEeq/dT list, choose From material. 5. Locate the Electrode Kinetics section. In the ka text field, type k_pos. 6. In the kc text field, type k_pos. 7. Locate the Model Input section. In the T text field, type T. 8. From the c list, choose Insertion particle concentration, surface (liion).

Separator 1 1. In the Model Builder window, under Component 1 (comp1)>Lithium-‐Ion Battery

(liion) right-‐click Porous Electrode 2 and choose Porous Matrix Double Layer Capacitance.

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2. Right-‐click Lithium-‐Ion Battery (liion) and choose Separator. 3. In the Settings window for Separator, locate the Domain Selection section. 4. From the Selection list, choose Separator. 5. Locate the Model Input section. In the T text field, type T. 6. From the c list, choose Electrolyte salt concentration (liion). 7. Locate the Electrolyte Properties section. From the Electrolyte material list,

choose LiPF6 in 3:7 EC:EMC (Liquid electrolyte, Li-‐ion Battery) (mat2). 8. Locate the Electrolyte Volume Fraction section. In the εl text field, type epsl_sep.

Electric Ground 1

1. Right-‐click Lithium-‐Ion Battery (liion) and choose Electrode>Electric Ground. 2. Select Boundary 1 only.

Electrode Current 1 1. Right-‐click Lithium-‐Ion Battery (liion) and choose Electrode>Electrode Current. 2. Select Boundary 4 only. 3. In the Settings window for Electrode Current Density, locate the Electrode Current

section. 4. In the is, total text field, type i_app.

Initial Values 2 1. Right-‐click Lithium-‐Ion Battery (liion) and choose Initial Values. 2. In the Settings window for Initial Values, locate the Domain Selection section. 3. From the Selection list, choose Positive Electrode. 4. Locate the Initial Values section. In the phil text field, type -‐

mat1.elpot.Eeq_int1(cs0_neg/mat1.elpot.cEeqref). 5. In the cl text field, type cl_0. 6. In the phis text field, type mat3.elpot.Eeq_int1(cs0_pos/mat3.elpot.cEeqref)-‐

mat1.elpot.Eeq_int1(cs0_neg/mat1.elpot.cEeqref).

Initial Values 1 1. In the Model Builder window, under Component 1 (comp1)>Lithium-‐Ion Battery

(liion) click Initial Values 1. 2. In the Settings window for Initial Values, locate the Initial Values section. 3. In the phil text field, type -‐mat1.elpot.Eeq_int1(cs0_neg/mat3.elpot.cEeqref). 4. In the cl text field, type cl_0.

DEFINITIONS Variables 1

1. On the Home toolbar, click Variables and choose Local Variables. 2. In the Settings window for Variables, locate the Load From File. 3. Click it and and find the file named “Variables1liion.txt” and double-‐click it.

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Domain Point Probe 1 1. On the Definitions toolbar, click Probes and choose Domain Point Probe. 2. In the Settings window for Domain Point Probe, locate the Point Selection section. 3. In row Coordinate, set x to L_neg+L_sep+L_neg. 4. Select the Snap to closest point check box. 5. In the Model Builder window, expand the Domain Point Probe 1 node, then click

Point Probe Expression 1 (ppb1). 6. In the Settings window for Point Probe Expression, type CellVoltageProbe in the

Variable name text field. 7. Click Replace Expression in the upper-‐right corner of the Expression section. From

the menu, choose Component 1 (comp1)>Lithium-‐Ion Battery>phis -‐ Electric potential.

8. Click to expand the Table and window settings section. Locate the Table and Window Settings section. Click Plot window.

Global Variable Probe 1 1. On the Definitions toolbar, click Probes and choose Global Variable Probe. 2. In the Settings window for Global Variable Probe, type CRate in the Variable name

text field. 3. Locate the Expression section. In the Expression text field, type i_app/i_1C. 4. Click to expand the Table and window settings section. Locate the Table and

Window Settings section. From the Plot window list, choose Probe Plot 1. Global Variable Probe 2 1. On the Definitions toolbar, click Probes and choose Global Variable Probe. 2. In the Settings window for Global Variable Probe, type InternalResistance in the

Variable name text field. 3. Locate the Expression section. In the Expression text field, type -‐

(Total_polarization/i_app*(i_app>i_1C_c)+Total_polarization/i_app*(-‐i_1C_c>i_app)). 4. In the Table and plot unit text field, type Ω. 5. In the Description text field, type Internal Resistance. 6. Click to expand the Table and window settings section. Locate the Table and

Window Settings section. From the Plot window list, click plus to add Probe Plot 2.

Global Variable Probe 3 1. On the Definitions toolbar, click Probes and choose Global Variable Probe. 2. In the Settings window for Global Variable Probe, type irrevv in the Variable name

text field. 3. Locate the Expression section. In the Expression text field, type

intop2(liion.Qirrevv_per1)*A_cell. 4. In the Table and plot unit text field, type W. 5. In the Description text field, type Irreversible Heat. 6. Click to expand the Table and window settings section. Locate the Table and

Window Settings section. From the Plot window list, click plus to add Probe Plot 3.

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Global Variable Probe 4 1. On the Definitions toolbar, click Probes and choose Global Variable Probe. 2. In the Settings window for Global Variable Probe, type revv in the Variable name

text field. 3. Locate the Expression section. In the Expression text field, type

intop2(liion.Qirrevv_per1)*A_cell. 4. In the Table and plot unit text field, type W. 5. In the Description text field, type Reversible Heat. 6. Click to expand the Table and window settings section. Locate the Table and

Window Settings section. From the Plot window list, choose Probe Plot 3. Average 1 (aveop1) 1. On the Definitions toolbar, click Component Couplings and choose Average. 2. In the Settings window for Average, locate Source Selection text field. 3. Select All domains.

Integration 1 1. On the Definitions toolbar, click Component Couplings and choose Integration. 2. In the Settings window for Integration, type pos_cc in the Operator name text

field. 3. Locate Source Selection text field. 4. Change Geometric entity level to Boundary. 5. Select Boundary 4 only.

Integration 2 1. On the Definitions toolbar, click Component Couplings and choose Integration. 2. Locate Source Selection text field. 3. Select Domain 1 and 3 only.

Integration 3 1. On the Definitions toolbar, click Component Couplings and choose Integration. 2. Locate Source Selection text field. 3. Select All domains.

ROOT On the Home toolbar, click Component and choose Add Component>3D. COMPONENT 2 (COMP2) In the Model Builder window, click Component 2 (comp2). ADD PHYSICS

1. On the Home toolbar, click Add Physics to open the Add Physics window. 2. Go to the Add Physics window.

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3. In the tree, select Heat Transfer>Conjugate Heat Transfer>Laminar Flow. 4. Click Add to Component in the window toolbar. 5. On the Home toolbar, click Add Physics to close the Add Physics window.

GEOMETRY 2 Import 1

1. On the Geometry toolbar, click Import. 2. In the Settings window for Import, locate Import section. 3. From the Source list, select 3D CAD file. 4. Click Browse and select the file FiveCellsCooling.STEP 5. Click Import.

Rotate 1

1. On the Geometry toolbar, click Transforms and choose Rotate. 2. In the Settings window for Rotate, locate the Input objects section. 3. Press ctrl+A to select all objects. 4. Locate the Rotation Angle section, in the Rotation text field, type 90. 5. Locate the Axis of Rotation section, select x-‐axis from the Axis type list.

Move 1

1. On the Geometry toolbar, click Transforms and choose Move. 2. In the Settings window for Move, locate the Input objects section. 3. Press ctrl+A to select all objects. 4. Locate the Displacement section, in the x text field, type 54 5. In the y text field type 31 6. In the z text field type -‐12

Work Plane 1

1. On the Geometry toolbar, click Work Plane. 2. In the Settings window for Work Plane, locate the Plane definition section. 3. In the Plane type list, select Edge parallel. 4. In Planar curved edge, find and select mov1(23) 339, on the top right side curve

of the cooling case in the model.

Partition Domains 1 1. On the Geometry toolbar, click Booleans and Partitions and choose Partition

Domains. 2. In the Settings window for Partition Domains, locate the Partition Domains

section. 3. In the Work plane list, select Work Plane 1 (wp1). 4. In Domains to Partition, select all cylinders, so that they appear as mov1(1)-‐

mov1(5) in the field.

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Work Plane 2 1. On the Geometry toolbar, click Work Plane. 2. In the Settings window for Work Plane, locate the Plane definition section. 3. In the Plane type list, select Edge parallel. 4. In Planar curved edge, find and select mov1(23) 337, on the bottom right side

curve of the cooling case in the model.



section. 3. In the Work plane list, select Work Plane 2 (wp2). 4. In Domains to Partition, select all cylinders, so that they appear as pard1(1)-‐

pard1(5) 1 in the field.



section. 3. In the Partition with list, select Extended faces. 4. In Domains to Partition, select the bottom part of all cylinders, so that they

appear as pard2(1)-‐pard2(5) 1 in the field. 5. In Planar, cylindrical, or spherical faces, select the top surface of the bottom

right clamshell circles, so that they appear as mov1(24) 21 in the field.



section. 3. In the Partition with list, select Extended faces. 4. In Domains to Partition, select the top part of all cylinders, so that they appear

as pard3(1)-‐pard3(5) 4 in the field. 5. In Planar, cylindrical, or spherical faces, select the top surface of the top right

clamshell circles, so that they appear as mov1(25) 21 in the field.



section. 3. In the Partition with list, select Extended faces.

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4. In Domains to Partition, select the top clamshell, so that it appears as mov1(25) 1 in the field.

5. In Planar, cylindrical, or spherical faces, select the inside surface of the top clamshell, so that it appears as mov1(25) 3 in the field.



section. 3. In the Partition with list, select Extended faces. 4. In Domains to Partition, select the bottom clamshell, so that it appears as

mov1(24) 1 in the field. 5. In Planar, cylindrical, or spherical faces, select the inside surface of the bottom

clamshell, so that it appears as mov1(24) 4 in the field. Ignore Faces 1

1. On the Geometry toolbar, click Virtual Operations and choose Remove Details. 2. On the Geometry toolbar, click Virtual Operations and choose Ignore Faces. 3. In the Settings window for Ignore Faces, locate the Input section. 4. Click Paste Selection and add the following faces: 200, 204, 208, 212, 216, 220,

224, 228, 700, 704, 708, 712, 716, 720, 724, 728. DEFINITIONS Explicit 4

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 4 and choose Rename. 3. In the Rename Explicit dialog box, type Flow Compartment in the New label text

field. 4. Click OK. 5. Select Domains 17-‐24.

Explicit 5

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 5 and choose Rename. 3. In the Rename Explicit dialog box, type Active Battery Material in the New label

text field. 4. Click OK. 5. Select Domains 5-‐14, 27-‐41.

Explicit 6

1. On the Definitions toolbar, click Explicit.

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2. In the Model Builder window, right-‐click Explicit 6 and choose Rename. 3. In the Rename Explicit dialog box, type TIM in the New label text field. 4. Click OK. 5. Select Domain 15 only.

Explicit 7

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 7 and choose Rename. 3. In the Rename Explicit dialog box, type Cooling Tube in the New label text field. 4. Click OK. 5. Select Domain 16 only.

Explicit 8

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 8 and choose Rename. 3. In the Rename Explicit dialog box, type Inlet in the New label text field. 4. Click OK. 5. In the Settings window for Explicit, locate the Input Entities section. 6. From the Geometric entity level list, choose Boundary. 7. Select Boundaries 223-‐230.

Explicit 9

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 8 and choose Rename. 3. In the Rename Explicit dialog box, type Outlet in the New label text field. 4. Click OK. 5. In the Settings window for Explicit, locate the Input Entities section. 6. From the Geometric entity level list, choose Boundary. 7. Select Boundaries 596, 600, 604, 608, 612, 616, 620, 624.

Explicit 10

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 10 and choose Rename. 3. In the Rename Explicit dialog box, type Clamshells in the New label text field. 4. Click OK. 5. Select Domains 1-‐4, 25-‐26.

Explicit 11

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 11 and choose Rename. 3. In the Rename Explicit dialog box, type Cell 1 in the New label text field. 4. Click OK.

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5. Select Domains 35-‐38, 41. Explicit 12

1. On the Definitions toolbar, click Explicit. 2. In the Model Builder window, right-‐click Explicit 12 and choose Rename. 3. In the Rename Explicit dialog box, type Cell 2 in the New label text field. 4. Click OK. 5. Select Domains 9-‐12, 14.

Explicit 13


Explicit 14


Explicit 15


Average 2 (aveop2) Define a component coupling operator for the average temperature in the active battery material of the 3D thermal model to use in the 1D battery model.

1. On the Definitions toolbar, click Component Couplings and choose Average. 2. In the Settings window for Average, locate the Source Selection section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Active Battery Material.

Variables 2

1. On the Definitions toolbar, click Local Variables. 2. In the Settings window for Variables, locate the Variables section. 3. In the table, enter the following settings:

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Name Expression Unit Description Qh nojac(comp1.aveop2(comp1

.liion.Qh))*(L_neg+ L_sep+L_pos)/L_batt* ((r_batt-‐d_can)^2-‐ r_mandrel^2)*(h_batt-‐ d_can*2)/((r_batt^2-‐ r_mandrel^2)*h_batt)

W/m3

Average heat source from 1d battery model

r sqrt(x^2+y^2) m radius Domain Probe 1 (dom1) 1. On the Definitions toolbar, click Probes and choose Domain Probe. 2. In the Settings window for Domain Probe, type MeanT in the Variable name text

field. 3. Locate the Source Selection section. From the Selection list, choose Active Battery

Material. 4. Locate the Expression section. In the Expression text field, type T-‐T_inlet. 5. Click to expand the Table and window settings section. Locate the Table and

Window Settings section. From the Plot window list, click plus to add Probe Plot 4. Domain Probe 1 (dom1) 1. On the Definitions toolbar, click Probes and choose Domain Probe. 2. In the Settings window for Domain Probe, locate the Probe Type section. 3. From the Type list, choose Maximum 4. In the Variable name text field, type MaxT 5. Locate the Source Selection section. From the Selection list, choose Active Battery


Window Settings section. From the Plot window list, choose Probe Plot 4. Domain Probe 1 (dom1) 1. On the Definitions toolbar, click Probes and choose Domain Probe. 2. In the Settings window for Domain Probe, locate the Probe Type section. 3. From the Type list, choose Minimum 4. In the Variable name text field, type MinT 5. Locate the Source Selection section. From the Selection list, choose Active Battery


Window Settings section. From the Plot window list, choose Probe Plot 4.

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ADD MATERIAL

1. On the Home toolbar, Click Blank Material. Repeat so that you have three blank materials.

2. On the Home toolbar, click Add Material to open the Add Material window. 3. Go to the Add Material window. 4. In the tree, select Material Library >Miscellaneous

Polymers>Polycarbomate>Polycarbonate [solid]. 5. Click Add to Component in the window toolbar. 6. On the Home toolbar, click Add Material to close the Add Material window.

MATERIALS Material 4 (mat4)

1. In the Model Builder window, under Component 2 (comp2)>Materials click Material 4 (mat4).

2. In the Settings window for Material, type TIM in the Label field. 3. Locate the Geometric Entity Selection section. 4. From the Selection list, choose TIM. 5. Locate the Material Contents section. 6. For Heat capacity at constant pressure, input cptim as value. 7. For Density, input 2300[kg/m^3] as value. 8. For Thermal condictivity, input 1.2 [W/(m*K)] as value.

Material 5 (mat5) 1. In the Model Builder window, under Component 2 (comp2)>Materials click

Material 5 (mat5). 2. In the Settings window for Material, type Cooling Tube Material (A3102) in the

Label field. 3. Locate the Geometric Entity Selection section. 4. From the Selection list, choose Cooling Tube. 5. Locate the Material Contents section. 6. For Heat capacity at constant pressure, input 900[J/(kg*K)] as value. 7. For Density, input 2710[kg/m^3] as value. 8. For Thermal condictivity, input 238 [W/(m*K)] as value.

Material 6 (mat6)

1. In the Model Builder window, under Component 2 (comp2)>Materials click Material 6 (mat6).

2. In the Settings window for Material, type Coolant in the Label field. 3. Locate the Geometric Entity Selection section. 4. From the Selection list, choose Flow Compartment. 5. Locate the Material Contents section. 6. For Heat capacity at constant pressure, input cpcoolant as value.

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7. For Density, input rhocoolant as value. 8. For Thermal condictivity, input kcoolant as value. 9. For Dynamic Viscosity, input mucoolant as value. 10. For Ratio of specific heats, input 1 as value.

Polycarbonate [solid] (mat7)

1. In the Model Builder window, under Component 2 (comp2)>Materials click Polycarbonate [solid] (mat7).

2. In the Settings window for Material, locate the Geometric Entity Selection section.

3. From the Selection list, choose Clamshells. DEFINITIONS Add a cylindrical coordinate system to handle the orthotropic thermal conductivity in the active battery material. Cylindrical System 2 (sys2)

1. On the Definitions toolbar, click Coordinate Systems and choose Cylindrical System.

2. In the Settings window for Cylindrical System 2, locate the Origin section. 3. For x input 39.373[mm] 4. For y input -‐60.644[mm] 5. For z input 35.190[mm]

Cylindrical System 3 (sys3)








2. In the Settings window for Cylindrical System 5, locate the Origin section.

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3. For x input 14.830[mm] 4. For y input -‐26.925[mm] 5. For z input 35.190[mm]




HEAT TRANSFER (HT) Solid 2 1. In the Model Builder window, under Component 2 (comp2) right-‐click Heat

Transfer (ht) and choose Solid. 2. In the Settings window for Solid, locate the Domain Selection section. 3. From the Selection list, choose Cell 1. 4. Locate the Coordinate System Selection section. From the Coordinate system

list, choose Cylindrical System 2 (sys2). 5. Locate the Heat Conduction, Solid section. From the k list, choose User defined.

From the list, choose Diagonal. 6. In the k table, enter the following settings:

kT_batt_r 0 0 0 kT_batt_ang 0 0 0 kT_batt_ang

7. Locate the Thermodynamics, Solid section. From the ρ list, choose User

defined. In the associated text field, type rho_batt. 8. From the Cp list, choose User defined. In the associated text field, type Cp_batt.

Solid 3 1. In the Model Builder window, under Component 2 (comp2) right-‐click Heat




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defined. In the associated text field, type rho_batt.

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8. From the Cp list, choose User defined. In the associated text field, type Cp_batt Solid 6 1. In the Model Builder window, under Component 2 (comp2) right-‐click Heat






defined. In the associated text field, type rho_batt. 8. From the Cp list, choose User defined. In the associated text field, type Cp_batt

Heat Source 1

1. In the Model Builder window, right-‐click Heat Transfer (ht) and choose Heat Source.

2. In the Settings window for Heat Source, locate the Domain Selection section. 3. From the Selection list, choose Active Battery Material. 4. Locate the Heat Source section. In the Q0 text field, type Qh.

LAMINAR FLOW (SPF)

1. In the Model Builder window, under Component 2 (comp2) click Laminar Flow (spf).

2. In the Settings window for Laminar Flow, locate the Domain Selection section. 3. From the Selection list, choose Flow Compartment.

HEAT TRANSFER (HT) On the Physics toolbar, click Laminar Flow (spf) and choose Heat Transfer (ht). Fluid 1 1. In the Model Builder window, under Component 2 (comp2)>Heat Transfer (ht) click

Fluid 1. 2. In the Settings window for Fluid, locate the Domain Selection section. 3. From the Selection list, choose Flow Compartment.

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Temperature 1 1. In the Model Builder window, right-‐click Heat Transfer (ht) and choose

Temperature. 2. In the Settings window for Temperature, locate the Boundary Selection section. 3. From the Selection list, choose Inlet. 4. Locate the Temperature section. In the T0 text field, type T_inlet.

Outflow 1

1. Right-‐click Heat Transfer (ht) and choose Outflow. 2. In the Settings window for Outflow, locate the Boundary Selection section. 3. From the Selection list, choose Outlet.

Initial Values 1 1. In the Model Builder window, under Component 2 (comp2)>Heat Transfer (ht)

click Initial Values 1. 2. In the Settings window for Initial Values, type T_init in the T text field.

LAMINAR FLOW (SPF) Outlet 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Laminar

Flow (spf) and choose Outlet. 2. In the Settings window for Outlet, locate the Boundary Selection section. 3. From the Selection list, choose Outlet. 4. Locate the Pressure Conditions section. Select the Normal flow check box.

Inlet 1

1. In the Model Builder window, right-‐click Laminar Flow (spf) and choose Inlet. 2. In the Settings window for Inlet, locate the Boundary Selection section. 3. From the Selection list, choose Inlet. 4. Locate the Velocity section. In the U0 text field, type V_in.

MESH 2 Size 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Size. 2. In the Settings window for Size, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Flow Compartment. 5. Locate the Element Size section. From the Calibrate for list, choose Fluid

dynamics.

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6. From the Predefined list, choose Coarse. Size 2 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Size. 2. In the Settings window for Size, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Boundary. 4. Click Paste Selection and paste 151-‐222, 231-‐398, 407-‐438, 442-‐457, 460-‐493,

497-‐528, 532-‐547, 549-‐564, 566-‐581, 595, 597-‐603, 605-‐607, 609-‐611, 613-‐615, 617-‐619, 621-‐623, 625-‐650, 653-‐684, 688-‐703, 706-‐721, 724-‐739, 742-‐757, 760-‐775, 778-‐793, 796-‐811, 813-‐844, 846-‐861, 863-‐975, 1034-‐1049.

5. Locate the Element Size section. From the Calibrate for list, choose Fluid dynamics.

6. From the Predefined list, choose Fine. Corner Refinement 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Corner Refinement. 2. In the Settings window for Corner Refinement, locate the Geometric Entity

Selection section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Flow Compartment. 5. Locate the Boundary Selection section. 6. Click Paste Selection and paste 151-‐222, 231-‐398, 407-‐438, 442-‐457, 460-‐493,

497-‐528, 532-‐547, 549-‐564, 566-‐581, 595, 597-‐603, 605-‐607, 609-‐611, 613-‐615, 617-‐619, 621-‐623, 625-‐650, 653-‐684, 688-‐703, 706-‐721, 724-‐739, 742-‐757, 760-‐775, 778-‐793, 796-‐811, 813-‐844, 846-‐861, 863-‐975, 1034-‐1049.


8. From the Predefined list, choose Coarse. Free Triangular 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

under More Operations, choose Free Triangular. 2. In the Settings window for Free Triangular, locate the Geometric Entity Selection

section. 3. From the Geometric entity level list, choose Boundary. 4. From the Selection list, choose Inlet. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. From the Selection list, choose Inlet.

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10. From the Predefined list, choose Finer.

Swept 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Flow Compartment. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Distribution. 6. In the Settings window for Distribution, locate the Geometric Entity Selection

section. 7. From the Geometric entity level list, choose Domain. 8. From the Selection list, choose Flow Compartment. 9. Locate the Distribution section. In the Number of elements text field, type 140.

Free Triangular 2 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and


section. 3. From the Geometric entity level list, choose Boundary. 4. From the Selection list, click to paste 115. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection section, click to paste 115. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 0.4.


choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Cooling Tube.


under More Operations, choose Free Triangular.

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2. In the Settings window for Free Triangular, locate the Geometric Entity Selection section.

3. From the Geometric entity level list, choose Boundary. 4. In the Selection field, click to paste 90. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection field, click to paste 90. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 0.7.


choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. In the Selection field, click to paste 15.

Free Quad 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

under More Operations, choose Free Quad. 2. In the Settings window for Free Quad, locate the Geometric Entity Selection

section. 3. From the Geometric entity level list, choose Boundary. 4. In the Selection field, click to paste 47, 58, 1065, 1071, 1077. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Quad and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection field, click to paste 47, 58, 1065, 1071, 1077. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 1.


choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. In the Selection field, click to paste 13, 14, 39-‐41.


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section. 3. From the Geometric entity level list, choose Boundary. 4. In the Selection field, click to paste 13, 18, 27, 31, 37, 41, 586, 589, 981, 985,

991, 995, 1001, 1005. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection field, click to paste 13, 18, 27, 31, 37, 41, 586, 589, 981, 985,

991, 995, 1001, 1005. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 1.5.


choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. In the Selection field, click to paste 3-‐5, 7, 9, 11, 25-‐27, 29, 31, 33, 35, 37. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click


section. 7. From the Geometric entity level list, choose Domain. 8. In the Selection field, click to paste 3-‐5, 7, 9, 11, 25-‐27, 29, 31, 33, 35, 37. 9. Locate the Distribution section. In the Number of elements text field, type 6.



section. 3. From the Geometric entity level list, choose Boundary. 4. In the Selection field, click to paste 3, 8. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Triangular and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection field, click to paste 3, 8. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 1.5.

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choose Swept. 2. In the Settings window for Swept, locate the Geometric Entity Selection section. 3. From the Geometric entity level list, choose Domain. 4. In the Selection field, click to paste 1-‐2. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click


section. 7. From the Geometric entity level list, choose Domain. 8. In the Selection field, click to paste 1-‐2. 9. Locate the Distribution section. In the Number of elements text field, type 3.

Free Tetrahedral 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Free Tetrahedral. 2. In the Settings window for Free Tetrahedral, locate the Geometric Entity Selection

section. 3. From the Geometric entity level list, choose Boundary. 4. In the Selection field, click to paste 6, 8, 10, 12, 28, 30, 32, 34, 36, 38. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 right-‐click

Free Tetrahedral and choose Size. 6. In the Settings window for Size 1, locate the Geometric Entity Selection section. 7. From the Geometric entity level list, choose Boundary. 8. In the Selection field, click to paste 6, 8, 10, 12, 28, 30, 32, 34, 36, 38. 9. Locate the Element Size section. Select Custom. 10. Locate the Element Size Parameters section. For Maximum element size type 1.4.

Boundary Layers 1 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Boundary Layers. 2. In the Settings window for Boundary Layers, locate the Geometric Entity Selection

section. 3. From the Geometric entity level list, choose Domain. 4. From the Selection list, choose Flow Compartment. 5. In the Model Builder window, under Component 2 (comp2) > Mesh 2 > Boundary

Layers 1 click Boundary Layer Properties 1. 6. In the Settings window for Boundary Layer Properties 1, locate the Boundary Layer

Properties section. 7. In the Number of boundary layers text field, type 2. 8. In the Thickness adjustment factor text field, type 5.

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Free Tetrahedral 2 1. In the Model Builder window, under Component 2 (comp2) right-‐click Mesh 2 and

choose Free Tetrahedral. 2. In the Settings window for Free Tetrahedral, locate the Geometric Entity Selection

section and check that it is set to Remaining. ADD STUDY

1. On the Home toolbar, click Add Study to open the Add Study window. 2. Go to the Add Study window. 3. Find the Studies subsection. In the Select Study tree, select Preset

Studies>Stationary. 4. Click Add Study in the window toolbar. 5. On the Home toolbar, click Add Study to close the Add Study window.

STUDY 1 Step 1: Stationary

1. In the Model Builder window, under Study 1 click Step 1: Stationary. 2. In the Settings window for Stationary, locate the Physics and Variables Selection

section. 3. In the table, clear the Solve for check box for Lithium-‐Ion Battery.

Step 2: Current Distribution Initialization 1. On the Study toolbar, click Study Steps and choose Other> Current Distribution

Initialization. 2. In the Settings window for Current Distribution Initialization, locate the Physics

and Variables Selection section. 3. In the table, clear the Solve for check box for Heat Transfer and Laminar Flow.

Step 3: Time Dependent

1. On the Study toolbar, click Study Steps and choose Time Dependent>Time Dependent.

2. In the Settings window for Time Dependent, locate the Study Settings section. 3. In the Times text field, type 0 269.9 271.1 449.9 451.1 799.9 801.1 820. 4. From the Tolerance list, choose Physics controlled. 5. On the Study toolbar, click Study 1 > Solver Configurations > Solution 1 (sol1) >

Time Dependent Solver 1. 6. In the Settings window for Time Dependent Solver 1, locate the General section. 7. From the Defined by study step list, choose Step 3: Time Dependent. 8. In the Settings window for Time Dependent Solver 1, locate the Time Stepping

section.

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9. From the Steps taken by solver list, choose Strict. 10. On the Study toolbar, click Show Default Solver. 11. On the Study toolbar, click Compute.

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