Thermal Modeling of a Cylindrical Lithium-Ion Battery in 2D

Thermal management is crucial for safety and for ensuring long lifetimes of batteries. High temperatures typically shorten the battery lifetime by increasing the rate of the degrading processes, and therefore active cooling may be needed for high power applications. Another aspect of thermal management is that large temperature gradients within a single battery, or battery pack, need to be avoided since they may lead to non-uniform current densities and non-uniform aging phenomena.

The varying length scales and complex geometries of a Li-ion battery requires some consideration. The individual layers forming the battery cells are typically of the scale of tens of micrometers in the normal direction to the layers, but up to tens of centimeters in the sheet direction, and are usually wound into multilayer geometries. When it comes to the actual battery or battery pack, the geometries may be in the scale of centimeters up to meters (for the case of an electric vehicle), and can consist of hundreds of individual cells. Resolving these geometries with a full three-dimensional model of the battery chemistry is computationally costly.

However, since the heat conductivity of the components of a lithium-ion battery is quite high in relation to the heat generated, one can in many cases assume the battery to have a fairly uniform temperature profile. Furthermore, if the battery chemistry is not heavily affected by small temperature changes, little detail is lost by describing the battery chemistry using a lumped model, based on the average temperature of the battery.

This example simulates an air-cooled cylindrical 18650 lithium-ion battery during a charge-discharge cycle, followed by a relaxing period. A lumped battery model is used to model the battery cell chemistry, and a two-dimensional axisymmetrical model is used to model the temperature in the battery. The two models are coupled by the generated heat source and the average temperature using the Electrochemical Heating multiphysics coupling node.

Model Definition

Cell model

The cell model is created using the Lumped Battery interface. The interface requires inputs such as the battery capacity and initial state-of-charge, and consists of lumped parameters that represent the ohmic, activation and concentration overpotential contributions. A detailed description on how to optimize the parameters of the lumped model against experimental data can be found in the Application Libraries example Parameter Estimation of a Time-Dependent Lumped Battery Model.

The lumped model can either solved in a global version, where the battery variables are defined globally, or in a local version where the variables are solved for locally in the same spatial dimension as the heat transfer physics interface. In this model, the Lumped Battery interface uses the global model of coupling to the Heat Transfer in Solids interface. The global model requires an average (global) value of temperature from the Heat Transfer interface and similarly provides an average value of the generated heat source in the active material domain to the Heat Transfer interface. On the other hand, the local model requires the local value of temperature in the active material domain from the Heat Transfer interface and provides the local value of the generated heat source to the Heat Transfer interface. The local model can be used when there is a large variation in temperature across the active battery material, and it becomes essential to consider local values of the generated heat source in the thermal model.

The Electrochemical Heating multiphysics coupling node is used to couple the temperature and the generated heat source between the Lumped Battery and Heat Transfer in Solids interfaces.

A square wave function is used to set an alternating charge/discharge current at a 7.5C rate with a cycle time of 600 s followed by a relaxing period after 1500 s; see Figure 2. (A 1C rate corresponds to the charge/discharge current required to fully charge or discharge in one hour; 7.5C corresponds to a 7.5 times higher current).

The cell is set to an initial state of charge of 20%.

Thermal model

The thermal model is in 2D with axial symmetry, using the Heat Transfer in Solids interface. The reason for using axial symmetry is that, for a spirally wound battery of this type, the heat conduction in the spiral direction can be neglected (Ref. 2). Furthermore, rather than modeling the heat conduction in each layer of the wound sheets in the radial direction (for example, in each positive electrode layer, each separator layer, and so on), the wound sheets are modeled as one active battery material domain. These approximations have been shown to be reasonable for spiral wound battery cells cooled by natural convection (Ref. 2).

The geometry (9 mm radius, 65 mm high, see Figure 1) consists of three domains:

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Battery canister (steel, 0.25 mm thick)

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Active battery material domain (wound sheets of cell material)

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Mandrel (isolator around which the battery cell sheets are wound, 2 mm radius)

Figure 1: Geometry of the thermal model

The active battery material is assumed to consist of one or several battery cells wound spirally into a cylinder. As an effect of this, the thermal conductivities are anisotropic in the thermal model, with a higher thermal conductivity along the battery sheets, the cylinder length direction, than in the normal direction to the sheets, the radial direction (see Ref. 1).

In the radial direction the thermal conductivity, kT,r, is calculated from the formula

where Li are the thicknesses of the different layers of the cell, and kT,i the thermal conductivities of the materials constituting these layers.

The thermal conductivity in the cylinder length direction, kT,ang, is calculated according to

The density, ρbatt, and heat capacity, Cp,batt, for the active battery material are calculated similarly according to

The heat source generated in the active battery material domain is specified using the Electrochemical Heating multiphysics coupling node.

On the battery canister surface, a heat flux boundary condition is specified using a heat transfer coefficient of h = 20 W/(m2·K) and an external temperature of 298.15 K. This would typically correspond to air cooling by low velocity forced convection.

The initial temperature of the battery is set to 298.15 K.

Results and Discussion

Figure 2 shows the cell potential and the load cycle current.

Figure 2: Cell potential and current load.

Figure 3 shows the maximum, minimum and average temperatures of the battery during the simulation. The temperature differences between the minimum and maximum never exceed 3 K. Also, the difference in heating rate between charge and discharge is due to the entropy effects (reversible heating).

Figure 3: Mean, maximum, and minimum temperature.

Returning to Figure 2 it is also seen that the cell potential of the different cycles is not largely affected by the small temperature changes in Figure 3. Note that the battery model currently includes temperature dependence of the open circuit voltage. Additionally, it could include temperature dependence of the lumped parameters.

Figure 4 shows the temperature in the battery cylinder at 1500 s. The temperature maximum is located in the active battery material in the center of the battery.