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.
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 can create supported meshes for Composites on Clouds in SALOME, an open-source pre-processing finite element tool. A routine for creating mesh in SALOME is posted 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:
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Analysis output
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fillingmedium.xdmfcontains pressure distribution, velocity profile, and saturation over the entire domain during the analysis. The time-steps are based on the output time-step in theStepsection. -
flowfrontvstime.pvdshows 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.
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Debugging output
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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.
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domains.pvd shows the available cells in each time-step. The pressure equation in FEniCS is solved in the red cells.
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materials.pvd shows markers assigned to different sections of the medium. You can check here if the sections are well-implemented in your mesh.
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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 (8.78 seconds). The filling pattern and flow-front vs time are shown below.
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 with 100000 Pascals pressure 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.
Change the End time of the Step to 20000 seconds and Output time step to one second and create a Step. Then, submit the job in the next webpage. 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.
To use this mesh in an analysis, first create one and in the Mesh section, upload 2D_quarterDisk_10-9.unv from here. We have created two other files with different meshing for you to compare the effects of mesh-size on the runtime and the final results.
After uploading the mesh, set the viscosity to 0.01 Pa.s and create a 2D preform with 0.01 m thickness and 0.2 fibre volume fraction. K11 and K22 are 1e-8 and K12 is zero. Assign the preform to the AllDomain section with zero rotation.
For boundary condition, set Wall condition for OX and OY, zero Pressure for Outlet, and 100000 Pascal for Inlet. Without changing the default Step parameters, go to the next webpage and submit the job. The solver creates a message file during the analysis. This file contains an initialization report, a success message for each iteration, and a termination message. You can use this file for debugging purposes.
Moreover, the Flow-Front file is a zip file that contains a .pvd and another .vtu files, which can be processed via Paraview. P-S-V file is a .xdmf file that contains pressure distribution, saturation, and velocity profile.
The analytical fill time for a radial divergent flow with a constant pressure boundary condition is shown in the figure below:
For the current analysis, the filling time is 39.95 seconds, which is similar to the computational results.
If we change the Inlet boundary condition to velocity, for example, a flow rate of 0.01 m^3/s, then the analytical filling time is 2.50 seconds for a quarter disk based on the following equations:
Which is similar to the computational results:
The semicircular part is a test case in chapter 8 of Process modeling in composite manufacturing. The region B is an isotropic fabric preform with a low permeability and region A is the same preform with a distribution medium so that the effective in-plane permeability of region A is higher than region B. There are two point-gates to inject the resin and the pressure differential between the inlet and exit is 100000 Pascals. The resin viscosity is constant and equal to 0.1 Pa.s. Part thickness is 0.005 m and fibre volume fraction is 0.4.
More information about the meshing and location of gates and the vent is shown in the following figure, which is depicted from Process modeling in composite manufacturing
As is shown in the following figure, resin fills the outer region very fast (less than 200 seconds) and arrives at the ventilation point in 693 seconds, which is fairly similar to the results of LIMS software 671 seconds(reported in Process modeling in composite manufacturing)
The final 3D demonstration shows the filling of a B-pillar of a car for the prediction of the fill time. Upload 3D_B_Pillar.unv mesh available here.
The mesh looks like below:
We are going to use different tools in Composites on Clouds in this example. First, create a resin with 0.01 Pa.s viscosity.
Create Preform_1 with 0.02 m (the actual b-pillars are usually between 8 mm to 1.5 mm thick) thickness, 0.4 volume fraction, and 1e-10 for K11 and K22. For Preform_2 set 0.01 m thickness and the same volume fraction and 1e-11 for K11 and K22. Assign Preform_1 to the Face section and Preform_2 to the right_side and Left_side.
right, top, and left edges are Wall. bot edge is an Inlet with 100000 Pascals for pressure. Keep the Step properties to default values and Submit the job. You should see 978 cells which will be filled in 250 seconds. The filling pattern and flow-front at different time-steps are shown in the following figure:
Observing the resin injection process in a b-pillar section shows quite similar flow pattern, which is shown below:
The figure is depicted from here. Our next step is to find the material configuration and geometrical design from an experimental test and compare the flow-front pattern as well as pressure distribution and filling time to verify the model for an actual b-pillar test.