COMSOL 6.4 - Jelly Roll Using a Flattened Geometry

This example replicates the results of the Jelly Roll tutorial model using a flattened representation of the wound spiral-based geometry. See that model entry for details on the background, original geometry, materials, and the general physics setup.

The spiraling aspects of the true jelly roll geometry are a bit cumbersome to work with, in regards to, for instance, visualizing simulation results in the layers, or introducing additional geometry objects like multiple tabs in the interior of the jelly roll.

In this tutorial we perform the model calculations on a flattened (not rolled) version of the jelly roll. In the flattened geometry representation, special boundary conditions are needed in order to couple geometrically detached boundaries together mathematically.

The flattened geometry has the advantage of requiring less mesh elements since the local curvature of the roll does not need to be resolved but with the disadvantage that the transport equations on the flattened geometry neglect the effect of the local curvature of the layers. However, as seen when comparing the temperature and potential profiles, the flattened geometry accurately reproduces the original jelly roll tutorial, indicating that we can perform this flattening transformation with only a limited effect on the results.

Model Definition

Like the original jelly roll model, this tutorial uses a pseudostationary approach, only accounting for the ohmic voltage losses in the electronic conductors and the electrolyte and the activation overpotentials due to the charge transfer reactions in the electrodes. The current distribution is modeled using a interface.

In the current distribution model, a ground condition is used at the negative terminal, where as a 1C total current condition is applied at the positive terminal.

The temperature distribution in the jelly roll is modeled using a interface, applying the resulting heat sources from the current distribution model using an multiphysics node. A convective cooling boundary condition on the outer area of the jelly roll is used, prescribing a cooling heat flux proportional to the surface temperature and the exterior temperature (25°C).

Figure 1 shows the model geometry. Each layer in the roll, as well as the tabs, are drawn as rectangular blocks. The layers are 60 mm high.

Figure 1: Model geometry.

In the original spiral geometry all layers in the roll differ in length. This is due to the winding of the spiral in combination with a different starting radius at the center of the spiral for each layer. In the flattened geometry representation we will approximate this effect by grouping the layers into two parts, centered around the positive and negative current collectors, with the length of the layers in each part being based on the corresponding current collector (approximately 22.8 and 20.6 cm, respectively). Each separator is split into two domains at mid thickness, with one domain placed in the negative part, and one domain placed in the positive part. In order to be able to use mapped meshes with the same amount of elements at the mid-separator boundaries (see below about linear extrusion operators), the geometry is finalized as an assembly, with assembly pair boundaries located between the separators and the electrodes.

Figure 2 shows the meshed model geometry as seen from above, scaled 100 times in the through-plane direction. An offset distance has been added between the negative and positive parts for easier visualization and selection handling in the user interface. The mesh is swept in the through-plane direction.

Figure 2: Model geometry, seen from above, scaled 100 times in the through-plane direction. The location of the mid-separator source and destination boundaries, used for coupling the negative and positive parts together, are indicated in the figure.

In order to couple the temperature and electrolyte potentials, and the corresponding local fluxes of heat and current, along the mid-separator boundaries between the two parts, linear extrusion operators are added. The linear extrusion operators maps each point on a source boundary to its corresponding location at a destination boundary.

The linear extrusion operators are then used to define pointwise constraints on the destination boundaries, prescribing continuity in temperature and potential according to T = linext(T) and ϕl = linext(ϕl). This condition is accomplished internally by balancing the local fluxes of heat and current, scaled by the relative differences in area of the source and destination boundaries. Mapped meshes are used on the source and destination boundaries, ensuring the same amount of mesh elements, with a one-to-one mapping of the mesh node points. This avoids spurious oscillations in the solution.

Results and Discussion

Figure 3 and Figure 4 show the simulated potential distribution in the negative and positive current collectors, respectively, for the jelly roll when subjected to a 1C discharge.

Figure 3: Potential in the negative current collector and tab.

Figure 4: Potential in the positive current collector and tab.

Figure 5 shows the corresponding temperature distribution. In all, Figure 3 to Figure 5 reproduce the results of the original Jelly Roll tutorial very closely.

Figure 5: Temperature distribution.

The flattened geometry now allows for easy visualization of the cross-separator current densities as shown in Figure 6 and Figure 7.

Figure 6: Current distribution in the through-plane direction of one of the separators.

Figure 7: Current distribution in the through-plane direction of the other separator.

Current distribution plots like this are valuable input to a battery designer, since they indicate significantly higher current densities in the area close to the tabs. We should remember that our model is pseudostationary, meaning that it is not accounting for redistribution of lithium in the cell. If the cell were to run for longer times, the current distribution plots shown above would eventually even out to a more homogeneous profile, as the distribution would accommodate for changes in local equilibrium potentials. However, a battery being cycled for short times around fixed state of charge would be exposed to more electrochemical wear in the areas close to the tabs, possibly resulting in accelerated aging.

Battery_Design_Module/Thermal_Management/jelly_roll_flattened

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

In the tree, select > .

Click .

In the tree, select .

Click

In the tree, select > .

Click

Geometry 1

Insert a geometry sequence from a file.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file jelly_roll_flattened_geom_sequence.mph.

In the toolbar, click

In the window, under click .

Disable the analysis of the geometry as the remaining small geometric details are needed.

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Definitions

Add a view with scaling in the y direction to facilitate selections in the window while setting up the physics and meshing.

In the window, under right-click and choose .

Camera

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the text field, type 100.

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

Geometry 1

In the window, collapse the > node.

Global Definitions

Geometry Parameters

In the window, under click .

In the window for , type Geometry Parameters in the text field.

Physics Parameters

In the toolbar, click

and choose > .

In the window for , type Physics Parameters in the text field.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file jelly_roll_flattened_parameters.txt.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Right-click and choose .

In the tree, select > .

Right-click and choose .

In the tree, select > > .

Right-click and choose .

In the tree, select > > .

Right-click and choose .

In the tree, select > > .

Right-click and choose .

In the toolbar, click

to close the window.

Materials

Aluminum (mat1)

In the window for , locate the section.

From the list, choose .

Copper (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Graphite, LixC6 MCMB (Negative, Li-ion Battery) (mat3)

In the window, click .

In the window for , locate the section.

From the list, choose .

NMC 111, LiNi0.33Mn0.33Co0.33O2 (Positive, Li-ion Battery) (mat4)

In the window, click .

In the window for , locate the section.

From the list, choose .

LiPF6 in 3:7 EC:EMC (Liquid, Li-ion Battery) (mat5)

In the window, click .

In the window for , locate the section.

From the list, choose .

Nickel

The negative tab consists of nickel metal, which is not available in the material library. Add a blank material node for nickel for now. We will add the required parameters later.

In the window, right-click and choose .

In the window for , type Nickel in the text field.

Locate the section. From the list, choose .

Secondary Current Distribution (cd)

Electrolyte 1

Now start defining the current distribution model.

In the window, under > click .

In the window for , locate the section.

From the σl list, choose . In the associated text field, type sigmal_eff.

Current Conductor 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

The electrode node defines electronic conduction in the metal phase domains. The conductivity is taken from the Material nodes by default, so no additional settings are needed here.

Porous Electrode 1

In the toolbar, click

and choose .

The porous electrode node defines the electronic and ionic conduction in the electrode and electrolyte phases, respectively. Since we use the same settings in the positive and negative electrode materials in this tutorial, it suffices to use one single node.

In the window for , locate the section.

From the list, choose .

Locate the section. From the σl list, choose . In the associated text field, type sigmal_eff.

From the list, choose .

Locate the section. From the σs list, choose . In the associated text field, type sigmas_eff.

From the list, choose .

Porous Electrode Reaction 1

In this tutorial we are only interested in the voltage losses, not the resulting cell voltage. Therefore we use the default value of 0 V for the equilibrium potential in both electrodes. The resulting potential at the positive current terminal will thereby equal the total polarization of the cell.

In the window, click .

In the window for , locate the section.

From the list, choose .

In the i0 text field, type i0.

Locate the section. In the av text field, type Av.

Electric Ground 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electrode Current 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Is,total text field, type I_1C.

Heat Transfer in Solids (ht)

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

Solid 1

In the window, under > click .

In the window for , locate the section.

From the ρ list, choose . From the Cp list, choose .

Initial Values 1

In the window, click .

In the window for , locate the section.

In the T text field, type T_ext.

Heat Flux 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the h text field, type hT.

In the Text text field, type T_ext.

Multiphysics

Electrochemical Heating 1 (ech1)

In the toolbar, click

and choose > .

Materials

LiPF6 in 3:7 EC:EMC (Liquid, Li-ion Battery) (mat5)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.35[W/(m*K)]	W/(m·K)	Basic

Nickel (mat6)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	1.4e7[S/m]	S/m	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	100[W/(m*K)]	W/(m·K)	Basic