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    Tutorial: Thermal Analysis of a Differential Casing

    This article provides a step-by-step tutorial for the thermal analysis of a front differential casing. The objective of this simulation is to analyze the temperature distribution across the casing in operation mode.

    temperature field differential casing thermal simulation
    Figure 1: The temperature field of the differential casing.

    This tutorial teaches how to:

    • Set up and run a thermal simulation.
    • Assign boundary conditions, material, and other models to the simulation.
    • Mesh the geometry with the SimScale standard meshing algorithm.
    • Explore the results using SimScale online post-processor.

    The typical SimScale workflow will be followed:

    1. Prepare the CAD model for the simulation.
    2. Set up the simulation.
    3. Set up the mesh.
    4. Run the simulation.
    5. Analyze the results.

    1. Prepare the CAD Model and Select Analysis Type

    To start, you can import a copy of the project into your workbench to follow along the steps by clicking the button below:

    The following picture shows what should be visible after importing the tutorial project. You can find the geometry ‘Differential_Casing’ and the 3D model displayed. You can interact with the model as with any CAD program.

    CAD model differential casing thermal simulation
    Figure 2: CAD model displayed in the viewer.

    1.1 Create the Topological Entity Set

    Especially interesting for our simulation is the creation of Topological Entity Sets, which basically means that we can group faces together for later boundary condition assignment. To start, select the geometry element in the tree at the left panel.

    The Topological Entity Sets can be found at the right panel:

    topological entity sets differential casing thermal simulation
    Figure 3: Topological Entity Sets.

    A number of entity sets are already provided in the initial project, but one set for the ‘Heated Region 2’ boundary condition is still missing. The picture below shows how to create it:

    creating topological entity set differential casing thermal simulation
    Figure 4: Select the faces for the topological entity set.
    1. Select the corresponding set of faces as shown.
    2. Click the ‘+’ icon at the right of Topological Entity Sets in the right panel.

    In the pop-up dialog that appears, name the set ‘Heated Region 2’ and click the blue ‘Create new set’ button.

    creating topological entity set differential casing thermal simulation
    Figure 5: Naming and creating the topological entity set.

    1.2 Create a Heat Transfer Simulation

    Now the simulation setup can be started. Follow these steps to create a new simulation:

    create simulation differential casing thermal simulation
    Figure 6: Create new simulation.
    1. Select the ‘Differential_Casing‘ geometry element at the left panel.
    2. Click the blue ‘Create Simulation’ button in the pop-up window.

    The simulation library window appears. Select the ‘Heat Transfer‘ analysis type and click the blue Create Simulation button as shown in the picture:

    simulation library differential casing thermal simulation
    Figure 7: SimScale simulation library.

    Now a new tree will be automatically generated in the left panel with all the parameters and settings that are necessary to define to perform such an analysis. All parts that are completed are highlighted with a green check. Parameters that need to be specified have a red circle, while the blue circle indicates an optional setting that does not need to be filled out. You should see the interface as shown in Figure 8 below:

    simulation tree differential casing thermal simulation simscale
    Figure 8: Simulation tree and simulation setup panel after creating the Heat Transfer simulation

    You can read more details about the heat transfer simulation type in our documentation page and the SimWiki page.

    2. Setup the Simulation

    2.1 Material Model

    Next, add the material model from the ‘Material Library’. First, we start with clicking the ‘+’ button next to the ‘Materials’ tree element at the left panel. This pops-up a ‘Material Library’ from which we select ‘Aluminium‘ and click on the blue Apply button. This will then load the standard properties for Aluminium.

    materials library differential casing thermal simulation
    Figure 9: SimScale materials library

    In the pop-up material properties window, our only body is automatically selected. Accept the selection with the blue check-mark button.

    assigning a material to the thermal casing domain
    Figure 10: Assigning a material to the domain

    2.2 Boundary Conditions

    Now, we come to define the boundary conditions. To create a boundary condition, click on the ‘+’ button option next to the ‘Boundary conditions‘ element at the left panel, and select the required boundary condition type from the drop-down menu, as shown in the figure.

    creating boundary condition differential casing thermal simulation
    Figure 11: Creating a boundary condition

    We can see that we can define either temperature or heat flux boundary conditions. For our simulation, we’ll only need heat flux boundary conditions, since we will assign a specific heat load inside the casing and a convection condition on the outside.

    A. Heated Region 1

    We will start with the first inner heat loss boundary condition for the face set Heated Region 1. Select the Surface heat flux boundary condition from the boundary conditions drop-down menu. Give a heat flux value of 2900 \(W/m^2\), since this comes close to the thermal conditions we want to test in this simulation. Assign this to the Heated Region 1 entity set. Give an appropriate name to the boundary condition, such as ‘Heated region 1’.

    heat flux boundary condition differential casing thermal simulation
    Figure 12: Heated region 1 boundary condition.

    B. Heated Region 2

    The second boundary condition is also a heat flux boundary condition of type Surface heat flux with a value of 3600 W/m^2 assigned to face set Heated Region 2.

    heat flux boundary condition differential casing thermal simulation
    Figure 13: Heated region 2 boundary condition.

    C. Outside Faces

    The third boundary condition is a heat flux boundary condition of type Convective heat flux with a reference temperature of 19.85°C, and an h value of 24 W/m^2 K assigned to the face set Outside. The value for the outside heat transfer coefficient for the convection boundary condition is taken from literature and is rather a rough assumption since this coefficient won’t be constant over the whole surface in reality.

    convective boundary condition differential casing thermal simulation
    Figure 14: Outside boundary condition.

    These three boundary conditions are sufficient to simulate the thermal scenario we are interested in: Heat loss from the inside, and natural convection at the outside faces of the casing.

    3. Mesh Setup

    Select the mesh option and keep the default settings as shown in the figure below. You do not need to click the Generate button at this step, as the mesh will be computed as part of the simulation run.

    Figure 15: Mesh setup

    Note that the results generated with first order elements might not be as accurate as with second order elements, but choosing a second order mesh will lead to longer computing times, so it is avoided in this case.

    As for the fineness of the mesh, a Fineness level of 5 is enough. As a rule of thumb, one should make sure that the resulting mesh does have more than one volume layer across the cross-section of the model.

    Small feature suppresion value is also defined as 5e-4 in order to ignore features with sizes under the specified value. This will enhance better quality elements while reducing the unnecessary number of elements around small features which will have no effect on the solution.

    4. Start the Simulation

    The last thing to do for running this simulation is to create a run. The new run is created by clicking on the ‘+’ button next to ‘Simulation Runs’:

    In the pop-up window, you can give a meaningful name to the run, then click the blue ‘Start’ button to start the run.

    create new run differential casing thermal simulation
    Figure 16: New simulation run.

    The Job status box in the lower left again provides updates about the job status. Also, a Solver log is provided after a few seconds which shows the exact output of the actual computing algorithm. The simulation run should take a few minutes to be carried out. Once the simulation run is Finished we can Postprocess the results.

    5. Post-Processing

    Once the simulation run is finished, you can post-process the differential casing analysis results. To access the online post-processor on the platform you can use one of two methods:

    open online post-processor differential casing thermal simulation
    Figure 17: The two ways to access the online post-processor for a given simulation run.
    1. Select the ‘Solution Fields’ under the Run.
    2. Click the ‘Post-Process’ button in the Run dialog.

    The default view state for the thermal simulation is to display the temperature distribution profile:

    thermal analysis casing temperature
    Figure 18: Temperature profile on the differential casing

    In this plot image, the blue color corresponds to the colder regions, and red corresponds to the hotter. The minimum temperature is found to be 64.71\(°C\), while the maximum is 67.96 \(°C\).

    In case the temperature is displayed in Kelvins select the units drop-down menu to change to degree Celsius or other available temperature unit as desired.

    temperature settings kelvin to celsius
    Figure 19: Changing the temperature units

    We can visualize the temperature distribution inside the material by creating a Cutting Plane:

    cutting plane selection in  Simscale post-processor
    Figure 20: Steps to create a Cutting Plane visualization
    1. Select ‘Cutting Plane’ from the operations toolbar above.
    2. Use the Position slider to move and locate the cutting plane across the geometry
    3. Use the Orientation buttons to align the cutting plane normal to the global axes. In order to invert the portion of the geometry that is displayed, use the blue flip button.
    thermal casing temperature cutting plane
    Figure 21: Temperature profile within the casing on the cutting plane

    The temperature gradient across the material can be appreciated in this plot. The hot and cold regions are consistent with the applied boundary conditions. Notice how, due to the thin walls, the gradient across the thickness of the material is barely noticeable.

    Go ahead and try out for yourself what each one of the parameters does and what visualizations you can come up with. If you want to learn more about SimScale’s online post-processor, you can have a look at our post-processing guide.

    Congratulations, you finished the differential casing tutorial!


    If you have questions or suggestions, please reach out either via the forum or contact us directly.

    Last updated: October 5th, 2022