1. Introduction

This tutorial is a modification of Tutorial 1. The differences are marked in bold
and italics.

This tutorial presents how to create and simulate the heating of a simple battery geometry,
consisting of one large cell, a cooling plate and surrounding air. The geometry is presented
in Figure 1.

Figure 1: Battery assembly

Excel spreadsheets and msh files used in this tutorial have been prepared beforehand and are
available as an attachment.

2. Preparing the model

Let’s start by enforcing a good habit – clear your workspace and command window in Matlab
and make sure all other windows are closed.

clc
clear
close all

The case described in this tutorial is not complicated and therefore does not require parallel
toolbox.

2.1 Cell

We can now begin creating components of our assembly. First we will create the cell, which
is represented by a simple prism, depicted on Figure 2.

We have to create the cell prototype, which will be a virtual cell (not included anywhere in
the model), with set properties and dimensions. We specify the type of our cell (prismatic
or cylindrical) and its dimensions – the first three indices are the coordinates of the lower
left corner of the prism and the other three – are its dimensions (x,y,z) in meters. It is also
required to specify the material and electric properties of the cell, by appointing an Excel
spreadsheet in which the data is collected.

cell_prototype = defineCellPrototype('type','prismatic','dimensions', ...
[0, 0, 0, 0.1155, 0.264, 0.1055], 'data', ...
'tutorials/tutorial1/data/cell_data.xlsx');

Reading mesh from Gmsh, version = 4.1
Reading section: Entites... Done!
Reading section: Nodes... Done!
Reading section: Elements... Done!
Mesh read succesfuly.
Material data rho depends on .
Material data lambda_x, lambda_y, lambda_z depends on .
Material data cp depends on .
Material data R_0 depends on T, SOC.
Material data R_1 depends on T, SOC.
Material data C depends on T, SOC.
Material data capacity depends on .

The data in the spreadsheet must be compliant with a certain model. Parameters are specified
by writing the parameter name in a cell and its value below. It is also possible to enter nonconstant parameters,
depending for example on temperature. This can be done by adding
a column with a T title next to the column containing the parameter values. For
the cell electric parameters can also depend on the State of Charge (SOC), as
shown in the table below.

Figure 3: Cell properties

Now we can display the created component and check the generated mesh.

cell_prototype.plot

Figure 4: Cell mesh

Remember to save the cell prototype, in case you would like to use it in different models.

cell_prototype.saveComponent('tutorials\tutorial1\cell_proto')

In the next step we will have to put the cell in our simulation domain. We use the instantiateInLocation
function and specify the location matrix of our cell. We must define the
prototype which we want to use (in this case – the cell prototype).

cells = instantiateInLocation('prototype', cell_prototype, ...
'location_matrix', [0.02, 0, 0]);

Now we want to add the electric current profile onto the cell. Using an Excel
spreadsheet we load the current profile (as shown below), and rename the variables.

current = readtable("tutorials/tutorial3/data/electric_current.xlsx");
current.Properties.VariableNames = {'t','current'};

Figure 5: Electric current profile data

Figure 6: Electric current profile plot

Don’t forget to assign the loaded profile to our cell.

cells.setCellCurrentProfile(current);

In order to be able to append the cells to our battery module we have to define them inside
a cell casket.

cell_casket = defineCellCasket('cells', cells);

2.2 Cooling Plate

,p>After finishing the cell, we can move on to other components of the assembly. Next we will
create the cooling plate, on which the cell stands (shown on Figure 7).

Figure 7: Cooling plate

In this tutorial the cooling plate geometry will be made by loading a previously
made msh file. While defining the prototype, we have to define the msh file path,
the pipe radius, mass flow rate, inlet temperature and material properties of the
cooling plate and cooling fluid.

The pipe wall, inlet and outlet ids are know, so they can be defined by the User (if they
are not known, the pipe walls and inlet/outlet can be chosen interactively, what is shown in
Tutorial 2).

cooling_plate_prototype = defineCoolingPlatePrototype('mesh_path', ...
'tutorials/tutorial3/msh/cp.msh', 'pipe_radius', 0.007172/2, ...
'pipe_mass_flow_rate', 0.02, 'pipe_inlet_temperature', 15, ...
'cooling_plate_data','tutorials/tutorial3/data/cp_data.xlsx', ...
'coolant_data', 'tutorials/tutorial3/data/coolant_data.xlsx', ...
'pipe_wall_ids', [7, 10, 9, 8], 'pipe_inlet_ids', [5, 6, 7, 8], ...
'pipe_outlet_ids', [15, 16, 17, 18]);
Reading mesh from Gmsh, version = 4.1
Reading section: Entites... Done!
Reading section: Nodes... Done!
Reading section: Elements... Done!
Mesh read succesfully.
Pipe wall selected
Pipe inlet and outlet selected
Material data lambda depends on .
Material data rho depends on .
Material data cp depends on .
Material data rho depends on T.
Material data cp depends on T.
Material data lambda depends on T.
Material data nu depends on T.
Material data mi depends on T.
Material data beta depends on .

The Excel spreadsheets used in this step are shown below. To simplify the model, the cooling
fluid’s properties are assumed as constant and independent of the temperature.

At this point it is very important to check if the pipe walls, inlet and outlet have been specified correctly.

cooling_plate_prototype.showPipeWall

Again, remember to save the cooling plate prototype:

cooling_plate_prototype.saveComponent('tutorials\tutorial1\cp_proto')

Once the prototype is created, we have to insert it into the simulation domain.

cooling_plate = instantiateInLocation('prototype', ...
cooling_plate_prototype, 'location_matrix', [0, -0.02, -0.02]);

The component can now be displayed to make sure it has been created and placed correctly.

ui.utils.ComponentDisplayer.displayComponent(cooling_plate)

2.3 Heat component

The last component we need to create is the air surrounding the cell, which will be modeled
as a passive heat component. A mesh has been created beforehand and its path will be given
directly to the software.

Create the component in the same manner as before. The properties of the air are defined in
an Excel spreadsheet (displayed on Figure 11).

air_prototype = defineHeatComponentPrototype('mesh_path', ...
'tutorials/tutorial3/msh/air.msh', 'heat_component_data', ...
'tutorials/tutorial3/data/air_data.xlsx');

Reading mesh from Gmsh, version = 4.1
Reading section: Entites... Done!
Reading section: Nodes... Done!
Reading section: Elements... Done!
Mesh read succesfully.
Material data rho depends on .
Material data cp depends on .
Material data lambda depends on .

Additionally in this tutorial, we will add a boundary condition on the outer walls
of the heat component to simulate a battery housing. For this purpose we use the
addRobinBCWithConductiveSheet function where we specify the wall ids, heat transfer
coefficient , surrounding temperature, and thermal conductivity and thickness
of the housing.

air_prototype.bcs.addRobinBCWithConductiveSheet('ids', [1, 2, 3, 4, 6], ...
'alpha', 30, 't_inf', 15, 'lambda', 870, 'thickness', 0.002);

Remember to save the created prototype

air_prototype.saveComponent('tutorials/tutorial3/air_proto');

The same way as before, we have to place the object into our simulation domain:

air = instantiateInLocation('prototype', air_prototype, ...
'location_matrix',[0, 0, 0]);

The component must be translated, so it will be located in a proper place in the assembly.

air.translate([0, -0.02, 0.1255]);

The element is now placed correctly and can be displayed.

ui.utils.ComponentDisplayer.displayComponent(air)

2.4 Battery module

All of the components have now been created. We can combine them, to obtain the full
battery module.

Specify the cell caskets, cooling plates and heat components we want to use. Contacts inside
the module will be added separately, as their values are not all equal.

battery_module = defineBatteryModule('cell_caskets', cell_casket, ...
'cooling_plates', cooling_plate, 'heat_components', air);

Contacts are specified by stating the bodies between which the contact occurs, and the thermal conductivity
and thickness. We want to simulate a thermal pad between the cells and
cooling plate, with conductivity equal to

Lastly, we set an initial temperature, that will be applied to the whole battery module.

battery_module.setInitialCondition(20);

Our battery module is done! We can now compile the model and run our simulation.

3. Calculations

3.1 Model assembly and reduction

The model is reduced and assembled using the assembleModel function. Adding tic and toc
will allow to measure the assembly time.

t1 = tic;
m = assembleModel(battery_module);
t2 = toc(t1);

During the process various messages will be displayed in the command window. It is advised
to read them, to assure the accuracy of the created model. It is specifically important to
check if the number of contacts found by the software corresponds to the actual number of
contacts in your model.

Found 1 thermal couples in BatteryModule: between CellCasket and
CoolingPlate.
Found 5 thermal couples in BatteryModule: between CellCasket and
HeatComponent.
Found 1 thermal couples in BatteryModule: between CoolingPlate and
HeatComponent.
Assembling domain 1. Number of nodes: 58744. Number of elements: 35221 ...
Elapsed time: 0.98319 s.
Assembling domain 2. Number of nodes: 53000. Number of elements: 30829 ...
Elapsed time: 0.85646 s.
Assembling domain 3. Number of nodes: 1807. Number of elements: 987 ...
Elapsed time: 0.042403 s.
Assembling couple 1
Elapsed time: 9.1382 s.
Assembling couple 2
Elapsed time: 3.5057 s.
Assembling couple 3
Elapsed time: 3.5539 s.
Assembling couple 4
Elapsed time: 1.6606 s.
Assembling couple 5
Elapsed time: 1.4923 s.
Assembling couple 6
Elapsed time: 4.0121 s.
Assembling couple 7
Elapsed time: 24.3793 s.
Assembling thpipe couple 1
Elapsed time: 0.21104 s.
Reducing domain 1. Number of nodes: 58744. Number of elements: 35221 ...
Elapsed time: 12.5668 s.
Reducing domain 2. Number of nodes: 53000. Number of elements: 30829 ...
Elapsed time: 21.4534 s.
Reducing domain 3. Number of nodes: 1807. Number of elements: 987 ...
Elapsed time: 0.20228 s.
Assembling and reducing nonlinear domain 1 out of 3
Elapsed time: 0.0004127 s.
Assembling and reducing nonlinear domain 2 out of 3
Elapsed time: 9.13e-05 s.
Assembling and reducing nonlinear domain 3 out of 3
Elapsed time: 8.83e-05 s.

3.2 Running the calculations

Once the model is compiled we can run the simulation. As the first parameter we specify
the time step in seconds, next the number of time steps we want to simulate, and
then the time step of the electrical calculation.

m.runReducedMerged(10,60,1);

Congratulations, your simulation is done!

3.3 Post-processing and export

To have a clear space for post-processing we can close all the figures and define our axes ratio.

close all
cla
ax = gca;

Now using different post processing functions, we can plot temperatures in chosen
bodies. Four parameters can be plotted:

• Minimum temperature over time

• Maximum temperature over time

• Mean temperature over time

• Current over time

Let’s plot out the minimum temperatures in the cells of our battery. The functions take in the name of the whole created model, it’s name after reduction and
the type of components from which we want to display the solution.

plotComponentsMinTempOverTime(battery_module, m, 'cell', ax)

The same can be done with the maximum and mean temperature.

cla
plotComponentsMaxTempOverTime(battery_module, m, 'cell', ax)

cla
plotComponentsMeanTempOverTime(battery_module, m, 'cell', ax)

Another interesting value can be the outlet temperature of the cooling fluid and
its temperature profile throughout the pipe at a given time step. The outlet temperature
can be plotted by specifying the cooling plate which is of interest and the
reduced model.

cla
plotCoolantOutletTempOverTime(cooling_plate, m, ax)

cla
plotCoolantTempProfile(cooling_plate, m, 60, ax)

We can also plot the solution for the whole battery for a selected time step:

plotSolution(battery_module, m, 60)

exportSolutionToVTK(battery_module, m, ...
'tutorials/tutorial3/tutorial3_vtk');
exportSolutionToCSV(battery_module, m, ...
'tutorials/tutorial3/tutorial3_solution.xls');,