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**Easy & accurate procedure to perform Electrochemical-Thermal modelling of Lithium-ion cells/ Battery using Ansys Fluent**

April, 2021

Lithium-ion Cells are the most commonly used portable energy storage devices due to their high specific energy and energy density but have certain thermal issues that raise safety concerns. In this post, we are going to discuss accurate electrochemical-thermal models of Lithium cells of various chemistries and how to perform the modelling economically using step by step procedure. These developed models can be used for thermal analysis of different desired battery pack configurations and various battery cooling strategies.

In a Li-ion battery, the anode and cathode are made of active materials layered on the surface of metal foils. A polymer separator is placed between the foils of opposite polarity to avoid electrons from passing among them. The student version of Ansys Fluent is enough to perform this modelling, you don’t need the commercial version. To forecast the progress of the chemical, thermal, and electrical processes in a cell, ANSYS Fluent comprises the following models:

1. Using the Single-Potential Empirical Battery Model

2. Using the Dual-Potential MSMD and Cell Network Battery Models

The Single-Potential Empirical Battery Model is beneficial if the geometries of the current collector, electrodes, and separator can be fully determined. One potential equation is solved in the computational domain. This model is most suitable for electrode scale predictions in a single battery cell.

This model has limited ability in learning the full range of electrochemical phenomena in battery systems, especially systems having complex geometry. When constructing a battery cell, the anode-separator-cathode sandwich layer is typically wound or stacked up into a 'jelly roll' or a prismatic shape. It would be very costly to resolve all the layers explicitly, even for a single battery cell. Also, many industrial applications use a battery pack consisting of a large number of cells connected in series or parallel.

The ANSYS Fluent Dual Potential Multi-Scale Multi-Dimensional (MSMD) Battery model compensates these limitations by using a homogeneous model based on a multi-scale multi-dimensional approach. In this method, the whole battery is considered as an orthotropic continuum; thus, the mesh is no longer constrained by the microstructure of the cell. Two potential equations are solved in the battery domain. To fulfill different analysis needs, the model includes three electrochemical submodels, namely, the Newman, Tiedemann, Gu, and Kim (NTGK) empirical model, the Equivalent Circuit Model (ECM), and the Newman’s Pseudo-2D (P2D) model having a different level of complexity. The model offers the flexibility to study the physical and electrochemical phenomena that spread over various length scales in battery systems of different arrangements.

ANSYS Fluent has adopted a modeling technique using the 1D model originally proposed by Tiedemann and Newman [Ref 1] later used by Gu [Ref 2] and Kim et al [Ref 3] in their 2D study. Also, ANSYS has prolonged the model formulation for usage in 3D computations.

Thermal instability and non-uniform temperature distribution in the lithium-ion battery negatively affect its performance and lifespan [Ref 4],[Ref 5],[Ref 6] or may result in thermal runaway, which eventually appears as challenges to their calendar life, safety, and low-temperature operation. [Ref 7],[Ref 8] Various battery models have been proposed in the above aspects. For example, a mathematical model based on the equivalent circuits and electrochemical processes was given in detail by Seaman et al [Ref 9]. However, circuit-based battery models are considered less precise for electric mobility applications.

Figure 1 Newman p2d battery model

As shown in Figure 1 [Ref 10], a Newman pseudo-2-dimensional Li-ion cell model has a negative electrode, positive electrodes, separator, and 2-current collectors besides 2-electrodes. This Newman model is based on the theorems of porous electrodes and concentrated solutions. Thus this model can accurately capture electrochemical reactions and estimate the cell’s response under various operating conditions with better precision. The solid active material is modelled as a matrix of mono-sized spherical particles. The Li-ion migrates through active particles via solid-phase diffusion along the r-axis as shown.

This Li-ion transport phenomenon in the porous electrode and active particle can be described by the mass and charge conservation laws. Mass conservation governs the phase concentrations (Ce, Cs), while charge conservation governs phase potentials (φ+, φ-). Where the subscripts e and s are used to denote the electrolyte and electrode (solid) phases, respectively.

The Lithium conservation diffusion equation needs to be solved at every discretized spatial location in the electrode zone. The Li conservation equation is solved in the r-dimension of the spherical active material particles-the pseudo-second dimension. Hence the model is called Newman’s Pseudo 2-dimensional model.

Newman Pseudo Two-Dimensional (P2D) model is widely used as it can accurately capture Li-ion migration within the cell. One needs to generate the Nyquist plot for the selected cells and Warburg constants used in the determination of Li-ion diffusion coefficients from Electrochemical Impedance Spectroscopy (EIS). Electrochemical impedance is the response of an electrochemical system (cell) to an applied potential. The frequency dependence of this impedance can reveal underlying chemical processes. Electrochemical impedance is usually measured by applying an AC potential to an electrochemical cell and then measuring the current through the cell. Assuming that we are applying a sinusoidal potential excitation. The response to this potential is an AC signal. This current signal can be analyzed as a sum of sinusoidal functions. The recorded response is used to calculate the impedance using a mathematical technique. By repeating this at several frequencies, an electrochemical impedance spectrum is obtained. Electrochemical impedance is normally measured using a small excitation signal. This is done so that the cell's response is pseudo-linear.

The Nyquist Plot results from the simple equivalent circuit. Adding a double-layer capacitance and a charge transfer impedance, we get the equivalent circuit as shown in Figure 2. This equivalent circuit models a cell where polarization is due to a mixture of kinetic and diffusion processes. The Nyquist Plot for this circuit is illustrated in Figure 3.

Figure 2 Equivalent circuit with Mixed Kinetic and Charge Transfer Control

Figure 3 Nyquist plot for mixed control circuit

In Figure 3 [Ref 11], L is the inductance given by the cables, and Rs shows a series of resistance corresponding to the battery terminals, cables, and mainly electrolyte resistance. RCT is the charge transfer resistance, between the electrode and electrolyte, CDL is the double layer capacitance, which corresponds to the SEI layer, and WDIFF is the diffusion impedance, modeled by a Warburg element (semi-infinite transmission line) at low frequencies.

Equivalent circuit models (ECM) use simple electronic circuits (resistors and capacitors) to imitate electrochemical processes occurring in the Li-ion cell. The model uses a simple circuit to represent a tortuous process to assist analysis and simplify calculations. These models are based on data collected from the battery cell under test. After the Nyquist plot of the battery is characterized, an ECM can be developed. Most commercial EIS software includes an option to create a specific and unique equivalent circuit model to more closely approximate the shape of the Nyquist plot produced by any particular battery cell.

There are four common parameters that represent battery chemistry when creating a model for a battery: Electrolytic (ohmic) resistance, Double-layer capacitance, Charge transfer resistance, and Warburg diffusion impedance. Electrolytic (ohmic) resistance increases as the battery ages and dominates when the frequency is greater than 1kHz. Double-layer capacitance consists of two parallel layers of opposite charges encompassing the electrode and dominates in the 1 Hz to 1kHz frequency range. Charge transfer resistance occurs from transferring electrons from one phase to another, that is, a solid (electrode) to a liquid (electrolyte).

Hardik et al. [Ref 11] published the work which is focussed on electrochemical-thermal modelling of commercially available cylindrical Li-ion cells of different chemistry for the tropical climate of India. In [Ref 11], the Warburg coefficient is extracted from the low-frequency domain of the Nyquist plot to determine the Li diffusion coefficient. The specifications given in datasheets by manufacturers are considered to calculate various parameters which are used directly or indirectly in the electrochemical-thermal model.

One can estimate the value of the convective heat transfer coefficient using the correlations given by Peter et al. [Ref 12] and subsequently can be used in the electrochemical thermal model. Material properties (thermal conductivity, density, heat capacity, electrical conductivity) that are used in the p2d model are estimated using co-relations given in Ansys Fluent Tutorial Guide. You can find the percentage of different materials using a material data sheet provided by the cell manufacturer which is useful in the determination of homogeneous cell properties. Figure 4 [Ref 11] represents the temperature distribution in XY-plane at 1C discharge rate for various chemistries, where heat accumulation is taken placed at the innermost part of the battery cell.

Figure 4 Temperature distribution in XY-plane at 1C discharge (e) ICR-2.6 (f) INR-2.6 (g) INR-3 (h) NCR-3.35

**References:**

Tiedemann and Newman. S.Gross Editor. “Battery Design and Optimization”. Proceedings, Electrochemical Soc. Princeton, NJ. 79-1. 39. 1979.

H. Gu. “Mathematical Analysis of a Zn/NiOOH Cell”. J. Electrochemical Soc.. Princeton, NJ. 1459-1. 464. July 1983.

U. S. Kim, C. B. Shin, and C.-S. Kim. “Effect of Electrode Configuration on the Thermal Behavior of a Lithium-Polymer Battery”. Journal of Power Sources. Princeton, NJ. 180. 909–916. 2008.

T. M. Bandhauer, S. Garimella, and T. F. Fuller, “A Critical Review of Thermal Issues in Lithium-Ion Batteries,” J. Electrochem. Soc., vol. 158, no. 3, pp. R1–R25, 2011, doi: 10.1149/1.3515880.

N. Omar et al., “Lithium iron phosphate based battery - Assessment of the aging parameters and development of cycle life model,” Appl. Energy, vol. 113, pp. 1575–1585, 2014, doi:10.1016/j.apenergy.2013.09.003.

A. Barré, B. Deguilhem, S. Grolleau, M. Gérard, F. Suard, and D. Riu, “A review on lithium-ion battery ageing mechanisms and estimations for automotive applications,” J. Power Sources, vol. 241, pp. 680–689, 2013, doi: 10.1016/j.jpowsour.2013.05.040.

Q. Wang, P. Ping, X. Zhao, G. Chu, J. Sun, and C. Chen, “Thermal runaway caused fire and explosion of lithium ion battery,” J. Power Sources, vol. 208, pp. 210–224, 2012, doi: 10.1016/j.jpowsour.2012.02.038.

C. Y. Jhu, Y. W. Wang, C. M. Shu, J. C. Chang, and H. C. Wu, “Thermal explosion hazards on 18650 lithium ion batteries with a VSP2 adiabatic calorimeter,” J. Hazard. Mater., vol. 192, no. 1, pp. 99–107, 2011, doi: 10.1016/j.jhazmat.2011.04.097.

A. Seaman, T. S. Dao, and J. McPhee, “A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation,” J. Power Sources, vol. 256, pp. 410–423, 2014, doi: 10.1016/j.jpowsour.2014.01.057.

R. Masoudi, T. Uchida, and J. McPhee, “Parameter estimation of an electrochemistry-based lithium-ion battery model,” J. Power Sources, vol. 291, pp. 215–224, 2015, doi: 10.1016/j.jpowsour.2015.04.154.

H. Shrimali, P. Patel, R. Patel, A. Ray, I. Mukhopadhyay, Electrochemical-thermal modelling of commercially available cylindrical lithium-ion cells for the tropical climate of India, Materials Today: Proceedings, 2021, ISSN 2214-7853, https://doi.org/10.1016/j.matpr.2020.11.871.

P. Van den Bossche, N. Omar, M. Al Sakka, A. Samba, H. Gualous, and J. Van Mierlo, Lithium-Ion Batteries Advances and Applications. Cherbourg-Octeville, France: Elsevier, 2014

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