FEM Example Capacitance Two Balls/ru

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Тема Руководство Анализ конечных элементов Начинающие Not provided Sudhanshu Dubey 0.19 или выше None

Введение

This example is meant to show how to simulate the 6th example of Elmer GUI Tutorials, Electrostatic equation – Capacitance of two balls, using the new FEM Examples. It illustrates how to setup the example, study it's various parts, solve it using the Elmer Solver and visualise the results using Clip Filter.

Requirements

• A compatible version of FreeCAD designated in the tutorial overview.
• No external software is needed for loading the example, viewing the mesh and geometry as well as for visualizing the results.
• For solving the FEA, the solver software Elmer must be installed on your computer. See Elmer Solver for how to install Elmer.

Understanding the Simulation Case

This case presents the solution of the capacitance of perfectly conducting balls in free space. A voltage difference between the balls results to electric charge being introduced to the system. The balls have also self-capacitance that comes from the voltage difference with the far field. Therefore a symmetric capacitance matrix with of size 2 × 2 needs to be solved. The capacitances may be computed from two different voltage configurations.

Understanding the Model

• The model contains three spheres.
1. The two smaller ones are the perfectly conducting balls.
2. The bigger one is to simulate the surrounding air.
• The two smaller spheres are fused together and then that fusion is is cut from the bigger sphere.

Analysis container and its objects

1. Elmer solver
2. Electrostatic equation
3. a fluid material (to represent the surrounding air)
4. electrostatic constraint (3 of them)
5. Constant Vaccum Permittivity
6. a Gmsh FEM mesh
7. Mesh region (for the smaller spheres)

Visualizing Results

• Be sure the analysis is activated.
• Be sure the analysis still contains the result object, if not just re-run the solver.
• Make sure the mesh is invisible. If not, select the mesh object press Space to toggle the visibility.
• Double click on the SolverElmerResult to load in the task panel.
• Change the "Mode" to "Surface" and the "Field" to "potential". Press Ok.
• You will notice that the colour of the sphere has changed to blue and that the gradient on the right is showing values from 0 to +1. It should look something like this:

Post Processing the Result

• Now we can clearly see that potential distribution in and around the balls.

Finding the Capacitance

StatElecSolve: Capacitance matrix computation performed (i,j,C_ij)
StatElecSolve:   1  1    5.08013E+00
StatElecSolve:   1  2    1.70071E+00
StatElecSolve:   2  2    5.07960E+00
• Here, our desired result is C12 = 1.70071. This value is close to the 1.691 given in the Elmer GUI Tutorials. We can get an even closer value by making a finer Mesh Region but this activity is left for the user. Also, the user is advised to play with the Clip Filter to get a visual result similar to the first picture of this tutorial.