CFD Modeling of Battery with Transport Equations

How to simulate a CFD model of Battery using ANSYS FLUENT?


Introduction to Scope of  Battery Modeling

Energy storage classification

  • From the Ragone plot, it is observed that lithium-ion batteries are better to other electrochemical cells for Electrical vehicle (EV), plug-in 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
  • Lithium-ion batteries are more suitable for vehicle applications because they have nearly twice the amount of specific energy and energy density in comparison to the nickel-metal hydride (NiMH) batteries which are used in the HEV
Energy storage classification for EV and IC Engines
Energy storage classification for EV and IC Engines
  • The Ragone diagram shows electrochemical energy storage devices and internal-combustion (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
Range plot for electrochemicals energy storage devices and traditional internal-combustion engine for power density.
Energy storage devices and traditional IC engine for power density


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 single-speed 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
    • electro-chemistry 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
    • Multi-scale Multi-Domain 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 Lithium-Ion battery

  • The mechanism of a lithium-ion battery is shown below
  • Lithium-ion (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 lithium-containing 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 non-aqueous 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
Mechanism and Configuration of Lithium-Ion battery
Mechanism and Configuration of Lithium-Ion battery
  • 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 Lithium-Ion 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 Cp are the fluid density and the specific heat, respectively
    • Kx, Ky and Kz 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 lithium-ion 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
The equation for Phase transition & Ion transport

 The equation for Phase transition & Ion transport

Equations for Energy Dissipation

Equations of Electrical model for Lithium-ion batteries

Where, SOC = state-of-charge (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
Heat Transfer Modelings of Battery
Heat Transfer Modelings of Battery
  •  A basic energy equation can be applied to the battery to find the temperature distribution
Heat Transfer Modelings of Battery
Heat Transfer Modelings of Battery

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,

Sh = 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 𝐸𝑠𝑡 presents stored combined thermal and mechanical energy, Eg is the heat (thermal energy) generation rate
  • Ein and Eout are inlet and outlet thermal and mechanical energy transport rate across the control surfaces
Heat Exchanger of Battery
Heat Exchanger of Battery
  • The steady-flow energy equation


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 Cp is heat capacity, Qgen is the heat generation (source term), and the heat exchange rate is transferred by convection Qconv and radiation Qrad.

  • 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
  • Qgen is represented as a source of current, and Cp allows to store energy as a capacitor. Internal cell temperature Tin 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 state-of-charge (SOC) and temperature of the cell
  • The term I (VOC − 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 state-of-charge (SOC): It is estimated by ampere-hour integration or Coulomb counting method

where SOCt=0 = 1 (when the battery is 100% charged)

CN = the nominal capacity of the cell



NTGK Model

  • The NTGK model is developed  on a dual potential multi-scale multi-domain (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 σneg refer to the positive and negative electrode, respective
  • The heat due to electrochemical reactions qech is written as

  • The volumetric current transfer rate j is formulated

  • Vol = the volume of the active zone,
  • Cref = 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 deep-of-discharge (DoD), these functions are computed as following equations

where C1 and C2 are constants for a specific battery, and Tref is the reference temperature


Multi-scale Multi-Domain Model

Multi-scale Multi-Domain Model of Battery
Multi-scale Multi-Domain Model of Battery
  • The following diagram shows the multiple scales in the battery system


Thermal and electrochemical coupled Modeling approach

Thermal and electrochemicals coupled Modeling approach
Thermal and electrochemicals coupled Modeling 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 (one-dimensional 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 thermal-electrochemical models used in literature is provided in Table.


MSMD Model

  • Multi-scale Physics and Micro-macroscopic Modelings approach applied into a Lithium-ion battery


Battery Model in ANSYS FLUENT

Selection of MSMD Model 

  • FLUENT solves the following governing equation to model battery
  • Mass conservation

  • Energy equation coupled with electro-chemistry, short circuit


  • FLUENT window for Battery model

Selection of Battery Model in ANSYS FLUENT

  • Models constant in battery models for  Electric circuit  models
Battery parameters ANSYS FLUENT CFD modeling of battery
Battery parameters ANSYS FLUENT CFD modeling of battery


User-Defined Functions for PCM Properties

  • User-defined functions (UDFs) are used to define the temperature-dependent properties of phase change material
  • ANSYS FLUENT user interface can be used to define thermal properties of phase change material and battery cell
User defined Functions for CFD Modelings of Battery
User-defined Functions for CFD Modelings of Battery

Case study

CFD Model of Battery with Equivalent Circuit Model

  • CFD model is developed using ANSYS space claim and workbench
  • It is simulated using ANSYS fluent

CFD model of battery using ANYSS FLUENT

  • The Mesh model is created in ANSYS Meshing platform with hexahedral elements


Meshing of battery model

  • CFD results can be presented for temperature variation over battery cells

 Case study of NTGK Model in FLUENT

  • The details of cells
    • Dimensions: Diameter: 25 mm, Height: 80 mm
    • Battery model: 26650 lithium-ion cylindrical cell
    • Nominal voltage: 3.70V
    • Charge voltage limit: 4.20V
    • Cut-off voltage: 2.8
    • Nominal capacity : 4.5 Ah
  • Details of CFD Model :
    • CFD results of cylindrical cells are presented below using NTGK models in ANSYS FLUENT for 0.5 C
    •  Multi Scale-Multi Domain (MSMD) model  with the NTGK electro-chemical approach  is used  for CFD analysis of  the  Li-ion battery cell
    • Electrical and thermal field coupling of the battery is computed at the battery’s cell scale.
    • Convective heat transfer is considered from the outer surface of cell

Temperature _Contours_battery_during_Discharge_CFD_Results

  • During discharge, as voltage decreases and the temperature of cells increases

 Temperature _rise_battery_during_DIscharge_CFD_Results             


  • 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



  1. National Renewable Energy, Transportation and Mobility research, Multi-domain Multiscale 

Leave a Comment