Table of Contents
How to simulate a CFD model of Battery using ANSYS FLUENT?
Introduction to Scope of Battery Modelling
Energy storage classification
 From the Ragone plot, it is observed that lithiumion batteries are better to other electrochemical cells for Electrical vehicle (EV), plugin hybrid electric vehicle (PHEV) and hybrid electrical vehicle (HEV). However, none of battery system can has high energy or power density with gasoline (IC) engine
 Lithiumion batteries are more suitable for vehicle applications because they have nearly twice the amount of specific energy and energy density in comparison to the nickelmetal hydride (NiMH) batteries which are used in the HEV
 The Ragone diagram shows electrochemical energy storage devices and internalcombustion (IC) engine
 Timelines shown are the time constants of the devices which are obtained by dividing the energy density by the power density
 Different time is given battery and engine
Major Parts of Electric Vehicle
 Electric Engine or Motor: It is a prime mover and provides power to rotate the wheels. The electric motor can be DC or AC type, however for electric vehicle AC motors are widely used
 Inverter: it converts the electric current from DC into AC
 Drivetrain: Eves use a singlespeed transmission which transfers electric power from the motor to the wheels of vehicles
 Batteries (Power Bank): Battery modules store electricity required to drive an electric vehicle. The power capacity of the battery is measured in kW.
 Charging Point: EV charging point in the form of the plug to charge the battery modules
Battery Thermal Management System
 The battery management system (BMS) to provides essential for
 Thermal Protection due to overheating
 Protection due to voltage or fluctuation
 Avoid short circuit
 Prolong battery life
 State of charging (SOC) and state of health (SOH) c
Essential Subjects for CFD Modeling of Battery
CFD Modeling of battery is complex and we need to understand the following subject for numerical modeling
 Fluid dynamics: Different cooling fluids like air and water are used for heat removal from the heated battery. Fluid mechanics plays role to understand the laminar or turbulent flow.
 Electrochemistry: Electrical part (voltage, current, resistance, and capacitance) is involved in the battery. Electrode (anode and cathod) with different chemicals are used in batteries for charging and discharging. Hence. chemical reactions take place continuously during this process.
 Heat and mass transfer: Heat energy is generated due to the following process in the battery
 irreversible entropy generation
 Ohmic heat
 electrochemistry heat
 Chemical reaction: reactions similar to combustion are considered like the Arrhenius equation to find temperature dependence of reaction rates
 Coupling between Electrochemistry and Thermal Energy
 CFD Models for Battery
 NTGK model
 Multiscale MultiDomain Model
 Lumped Capacitance model is used to find temperature distribution over battery cell
 Numerical procedures for battery models are similar to other CFD problems
Mechanism and Configuration of LithiumIon battery
 The mechanism of a lithiumion battery is shown below
 Lithiumion (Li+ ) move from the cathode (negative electrode) to the anode (positive electrode) via a separator diaphragm to form a discharge cycle, and vice versa when charging
 The cathode is generally a carbon rod. The commercial and popular material is graphite
 The anode is a lithiumcontaining compound and is generally one of three materials:
 a layered oxide e.g. lithium cobalt oxide – LiCoO2
 a polyanion e.g. lithium iron phosphate – LiFePO4
 spinel e.g. lithium manganese oxide – LiMn2O4
 The electrolyte refers to a solution of lithium salt in a nonaqueous solvent such as ethylene carbonate or diethyl carbonate. The current collector for negative and positive electrodes is made of copper (Cu) and aluminum (Al) respectively
 Taking LiMn2O4/graphite as an example, the electrochemical reactions occurring at the electrode/electrolyte interfaces are described below.
 Composite Positive Electrode:
 Composite Negative Electrode
Governing Equation for Modeling of Battery
Prismatic and Cylindrical LithiumIon Batteries
 A variety of batteries (prismatic, cylindrical, and pouch type) are used in an electric vehicle. Each battery is modeled differently because of changes in geometry, chemical composition, cooling medium, packing and computational level accuracy
 The basic governing equations of the fluid flow and heat transfer for prismatic and cylindrical battery cells are discussed below. To solve the 3D transient flow over battery cells, the continuity equation, momentum and energy equations, are written as follows
 Continuity equation
 Momentum equations in x, y and Z directions are given as below
 Energy conservation equation for 3D heat generation within prismatic battery cell

 where ρ and C_{p} are the fluid density and the specific heat, respectively
 K_{x}, K_{y} and K_{z} are thermal conductivities of a battery cell in the respective X, Y and Z direction
 q is the heat generation rate per unit volume. Its value is equal to the volumetric heat generation Q (Battery voltage * current) per unit battery volume (V), q = Q/V
 The lithiumion battery has three types of heat generation (irreversible, ohmic heat, and reversible heat). It is computed by the following equations
Governing Equations for Electrochemical kinetics
 The reaction rate is given by the Butler equation
The equation for Phase transition & Ion transport
The equation for Phase transition & Ion transport
Equations for Energy Dissipation
Equations of Electrical model for Lithiumion batteries
Where, SOC = stateofcharge (SOC) of battery
Governing Equations for Thermal Modelings of Battery
 Heat transfer takes place from battery to surrounding medium
 During charging and discharging, heat is generated within the battery cell
 Within the solid battery, heat transfers by conduction, and from the outer surface, heat is carried out by convection and radiation
 A basic energy equation can be applied to the battery to find the temperature distribution
Equations for Thermal Model
Equations for Thermal Model with Heat Generation
Energy Equation
 The energy equation used for numerical simulation to model the battery as a solid is governed by
where ρ is the density,
cp = the specific heat,
k = the thermal conductivity,
T = the temperature,
S_{h }= the volumetric source term,
V~ = the velocity is obtained from the motion of the fluid.
Heat Exchanger of Battery
 Heat balancing within heat exchanger for the controlled volume the conservation of energy is stated as
 Where 𝐸_{𝑠𝑡} presents stored combined thermal and mechanical energy, E_{g} is the heat (thermal energy) generation rate
 E_{in} and E_{out} are inlet and outlet thermal and mechanical energy transport rate across the control surfaces
 The steadyflow energy equation
where
𝑚 = Fluid mass within the tube = 𝜌𝑓𝑙𝑉𝑓𝑙) [kg]
𝑚̇ = Fluid mass flow rate through the heat exchanger [kg/s]
𝑇𝑖 , 𝑇𝑜 = Temperature of fluid entering and leaving tubes [°C]
𝐶𝑝 = Specific thermal capacity of fluid [J/ (kg·K)]
𝑞̇ = Heat transfer rate to the liquid in the tube [W]
Thermal Lumped Model
 The temperature distribution battery is determined by the lumped capacitance model of the battery cell. This is valid the Biot number is very small (Bi << 0.1)
where C_{p} is heat capacity, Q_{gen} is the heat generation (source term), and the heat exchange rate is transferred by convection Q_{conv} and radiation Q_{rad}.
 The thermal lumped model proposed by Forgez et. Al.
 where Ts , and Tamb = the surface temperature of the battery, and ambient temperature, respectively.
 The heat capacity, conduction resistance in the inner of the cell Rin, and external resistance Rout between the surface of the cell and surrounding fluid; can be determined via parameter identification
 Q_{gen} is represented as a source of current, and C_{p} allows to store energy as a capacitor. Internal cell temperature T_{in} could be computed as well
Heat Generation
 Bernardo et al. developed the following expression to compute the heat generation inside a battery
In above equation
 the current I is positive for discharging and negative for charging.
 Both open circuit potential (VOC) and the total internal resistance of the battery RT depend on the stateofcharge (SOC) and temperature of the cell
 The term I (V_{OC} − V) represents the heating due to the Joule effect (irreversible heat generation)
 The second term is the entropy change (reversible heat generation), attributed to electrochemical reactions
 Phase change effect, mixing effect, and simultaneous reactions are neglected in the Bernardi’s formulation
 Battery’s stateofcharge (SOC): It is estimated by amperehour integration or Coulomb counting method
where SOC_{t=0 }= 1 (when the battery is 100% charged)
C_{N} = the nominal capacity of the cell
CFD Model in ANSYS FLUENT
NTGK Model
 The NTGK model is developed on a dual potential multiscale multidomain (MSMD) framework and numerically find out the thermal and electric field of the battery as per the following equation
 where σ is the electric conductivity, φ is the electric potential, and subscripts pos and σ_{neg} refer to the positive and negative electrode, respective
 The heat due to electrochemical reactions q_{ech} is written as
 The volumetric current transfer rate j is formulated
 V_{ol }= the volume of the active zone,
 C_{ref} = the capacity of the battery used to obtain the parameters of the functions U and Y (from the Table),
 U and Yh are determined by the parameter estimation Tool in ANSYS Fluent by using discharging experiments. Based on the deepofdischarge (DoD), these functions are computed as following equations
where C_{1} and C_{2} are constants for a specific battery, and T_{ref} is the reference temperature
Multiscale MultiDomain Model
 The following diagram shows the multiple scales in the battery system
ThermalElectrochemical Coupled Modelings approach
Coupled and Decoupled Models
 The equation of Arrhenius law is applied for modeling of mass (species) transport and kinetic parameter ψ to couple electrochemical and thermal models
 lumped thermal model (onedimensional heat transfer) assumes uniform temperature variation over the battery cell. In this case the Biot number is very small (Bi< <1)
 2D thermal model can be used for a larger aspect ratio of the cell
 A summary of the coupled thermalelectrochemical models used in literature is provided in Table.
MSMD Model
 Multiscale Physics and Micromacroscopic Modelings approach applied into a Lithiumion battery
Battery Model in ANSYS FLUENT
Selection of Battery Model
 FLUENT solves the following governing equation to model battery
 Mass conservation
 Energy equation coupled with electrochemistry, short circuit
 FLUENT window for Battery model
 Models constant in battery models for Electric circuit models
UserDefined Functions for PCM Properties
 Userdefined functions (UDFs) are used to define the temperaturedependent properties of phase change material
 ANSYS FLUENT user interface can be used to define thermal properties of phase change material and battery cell
Case study
CFD Model of Battery
 CFD model is developed using ANSYS space claim and workbench
 It is simulated using ANSYS fluent
 Mesh model is created in ANSYS Meshing platform with hexahedral elements
 CFD results can be presented for temperature variation over battery cells
Conclusion
 Due to the demand for electric vehicles, battery design and optimization can be done using CFD analysis
 Battery modeling can be carried out using various CFD models. Battery modeling is complex due to coupled thermal and electrochemistry.
 ANSYS FLUENT is easy to use to find temperature distribution using battery model as per its chemistry and electrical connections
Reference
 National Renewable Energy, Transportation and Mobility research, Multidomain Multiscale