The examples provided in the following sections are currently availabe as part of the VIBE package.
This example (located in the VIBE repository at examples/case3/) represents the geometry of a rolled cylindrical cell. The main model properties are given in the table below. [@Fig:cylinder-mesh] shows the geometry and the finite element mesh used to resolve the geometry of the cylindrical cell and the current collectors. The top hierarchy model has 168 (56 each for the cell-sandwich and positive and negative current collectors) zones in 4 quadrants. The zones describe different current collector and cell sandwich regions. The simulation uses 56 concurrent Dualfoil simulations for different cell-sandwich zones. Typical results are shown in [@Fig:cylinder-results]. The maximum temperature occurs at the cell core as expected.
* table here *
{#fig:cylinder-mesh width=4.0in}
{#fig:cylinder-results width=4.0in}
This example (located in the VIBE repository at examples/case6/) represents the geometry of a prismatic pouch cell. The electrochemistry is modeled using the NTG model instead of the DualFoil model. The cell under consideration is a 70mm x 110mm x 10mm 4.3 Ah pouch cell manufactured by Farasis Energy, Inc with the properties given in the table below. The pouch cell in the current study contained 17 cathode and 17 anode layers and the finite element mesh was divided into 71 corresponding zones for cell sandwich, current collectors, and pouch ([@Fig:pouch-mesh]).
* table here *
{#fig:pouch-mesh width=4.0in}
The example of the simulation results is shown in [@Fig:pouch-results] and represents a temperature distribution in a pouch cell following a discharge at 5C rate of applied current. At such high applied current significant increase in temperature can be observed in the cell core. The simulation results have been validated with the experiments involving IR temperature measurement on the surface of the pouch cell ([@Fig:pouch-results]b). Experiments agree well with the predicted temperature profiles for all C-rates.
{#fig:pouch-results width=4.0in}
In this example, the single pouch cell described in the previous section is used as a building block for a module, containing 4 cells in parallel or in series. The example is in the repository in examples/case7/. Meshes representing parallel (4P) and series (4S) module configurations are shown in [@Fig:cell-arrangement]. No cooling fins were placed between the cells in this model. The mesh consists of approximately 150,000 FE nodes and 308 zones in the whole module thus resolving each current collector. Concurrent electrochemical model runs (DualFoil was chosen in this case) were performed in 136 charge transfer zones within the module. The goal of this study was to estimate temperature variations across the cells connected in series and in parallel.
{#fig:cell-arrangement width=4.0in}
The results of the simulations when symmetric cooling to the module surfaces is applied with a convective heat transfer coefficient of 35 W m-2 K-1 are shown in [@Fig:cell-discharge]. As can be seen both parallel and series cases result in very similar distribution of temperature across the module. In both cases, a 5C discharge rate was applied.
{#fig:cell-discharge width=4.0in}
In this example, the mesh corresponding to the 4P module is used to simulate the dynamic discharge under the user supplied variable potentiostatic/galvanostatic conditions. The example can be found in examples/case10/. The model uses DualFoil and AMPERES Thermal components. An option of driving simulation under varying current (dynamic discharge) has been added in the current release. The key-value pair file (for detailed description of sections of the input and configuration files please see Appendix A) contains several lines dedicated specifically for this new option. The following keywords are used to describe the cycling profile:
NUMSEG - Number of segments in the cycling profile.
CURRDEN - List of current density values corresponding to each segment.
MODESEG - List of segment modes. Most commonly used are 0 for potentiostatic and 1 for galvanostatic.
CUTOFFL - Lower cut-off potential.
CUTOFFH - Upper cut-off potential.
NOTE: If the NUMSEG keyword is missing in the key-value pair input file, the simulation will assume a default constant current discharge.
To utilize the dynamic discharge capability, the time stepping must be specified using the EXPLICIT option in the simulation config file with explicitly specified values of time corresponding to the segments of the cycling profile. Please see Appendix A for detailed description of input and config files required to launch a simulation.
If zero current density is specified in CURRDEN, the simulation will be performed under potentiostatic condition using the OCP corresponding to the end of previous cycling segment.