Tests and Examples

In this section, we present 4 test cases and 2 examples to verify our tool and show some of its capabilities. Moreover, you will learn how to submit different analyses in the following section.

Test case 1: 1D flow

The first analysis is an approximately 1D flow, which has the following

To use this mesh in an analysis, first create one and in the Mesh section, upload 1D_band.unv from here.

You should see the longside of the mesh in the X-direction. Confirm the mesh and set the viscosity to 0.01 Pa.s. Create a preform with 0.02 m thickness and 0.2 volume fraction of fibers (the volume fraction of resin is 1 - Phi, which will be later used to compute the analytical solution for this problem). Set K11 to 1e-8 m^2 and K12 and K22 equal to zero to have a 1D diffusion problem and assign the created preform to allDomain with no rotation. Now, for boundary conditions, choose the left edge and assign an Inlet with 100000 pascals Pressure. Then, choose the right edge and assign a Outlet condition with zero pressure. The other edge-group '2sides' would have a 'Wall' boundary condition. You can modify the boundary condition if you have not assign it properly or you want to compare different cases. Now, create a Step with default parameters and proceed to Submit webpage. Check the details in the Submit section and Submit job if everything looks ok. You can move to previous sections for modifications. You can also download the Configuration file or XML file of the analysis in the Submit page.

When the analysis is finished, you should see All CVs are filled!. We have different criteria for terminating the analysis. If you want all of the medium to be filled with resin, the termination criteria should be set to Fill everywhere, however, this might result in a stall analysis, if you end up with a dry region in the preform. To prevent this case, we use a threshold for the maximum number of stalled analysis, which is based on the change of saturation over consecutive iterations.

Click on Go to results. Composite on Clouds uses Paraview to visualize the results. The software will load in the results section and you can choose different outputs by clicking on the paper button on the upper left corner. Some of the results are described here:

• Analysis output

  • fillingmedium.xdmf contains pressure distribution, velocity profile, and saturation over the entire domain during the analysis. The time-steps are based on the output time-step in the Step section.
  • flowfrontvstime.pvd shows the flow front position at different times in a single graph. The graph is very useful when you want to see which part of the preform is going to be filled any time. Toggle on the legend of this graph and you will see that the maximum filling time is around 2.2 seconds. We will compare this to the analytical result of this problem to verify the code.

• Debugging output

  • boundaries.pvd shows markers assigned to different boundaries. The boundaries are marked with consecutive integers starting from one. Zero is assigned to internal boundaries and 99 is assigned to the flow-front.

  • domains.pvd shows the available cells in each time-step. The pressure equation in FEniCS is solved in the red cells.

  • materials.pvd shows markers assigned to different sections of the medium. You can check here if the sections are well-implemented in your mesh.

Verification

The 1D flow in a porous medium is governed by Darcy's equation. We can find the filling time by integrating the two sides of the equation.

Using the material properties mentioned above, the analytical filling time will be 9 seconds which is fairly similar (error: 3%) to the filling time found by the code (2.11 seconds). The filling pattern and flow-front vs time are shown below.

Test case 2: Anisotropic permeability

The second analysis is a 2D simulation on a rectangle with anisotropic permeability. The geometry is:

To use this mesh in an analysis, first create one and in the Mesh section, upload 2D_rectangle_CornerInlet.unv from here.

Now, assign 0.02 Pa.s for viscosity and create a preform with the following properties:

In the Section page, assign the preform to AllDomain and set the Rotate value to 45 degrees. This will turn the preform 45 degrees with respect to the X-axis.

Choose Inlet condition for the corner edge and Wall condition for the other four edges. The Wall condition prevents resin from going out of the domain, while the Outlet condition just reinforces pressure on the edge. Thus, you will have resin leakage on those boundaries. If you do not specify a value for the Outlet pressure, the solver assumes that the flow-front has zero gage pressure.

Create a Step with default values and Submit Job. You should see a maximum of 525 control volumes. Since we do not reinforce any Outlet with Wall boundary condition, the velocity at corners will be very small and the analysis will terminate with the Maximum Number of Idle iterations. When the analysis is terminated with termination criteria other than the Termination types specified by the user, we show a cautious message on the screen. When the analysis is finished, go to the Results section.

Looking at the results, the filling time is similar to the results of LIMS, which is a software for the simulation of liquid injection molding.

The filling pattern and flow-front are shown in the following figures:

For the anisotropic case, the flow front is an ellipse, extended along the rotated y-axis. Darcy's equation demonstrates that the ratio of 3 to 1 for permeability results in an aspect ratio of 1.7 to 1 between the semimajor and semiminor radii of ellipse.

If you use the 2D_rectangle_EdgeInlet.unv from here. instead of the previous mesh and try to create a 1D flow by setting left edge as Inlet and right edge as Outlet, you will see that, eventually, the flow-front is 2D due to the anisotropy of the preform.

Test case 3: Quarter of a disk

To use this mesh in an analysis, first create one and in the Mesh section, upload 2D_quarterDisk.unv from here.

3D Semicircle

3D B-Pillar

depicted from here