3D Baffled Piston
This example is of a piston in a rigid baffle modeled using the 3D capabilities of FEWaves. The results of this analysis can be compared directly to the 2D Axi-symmetric testcase presented earlier. The 2D model had the piston as a velocity source on a g_edge surrounded by fluid, the 3D model has the piston of radius a = 0.23873 as a g_face facing into a volume of water. The mechanical impedance will be compared with the 2D results and plotted.
The 3D model is extruded from the geometry file (2dpiston.geo) and the 2D mesh (2dpiston.fem) provided with your installation files. The 2D mesh is further refined using the refinement file 2dpiston.ref. The 3D geometry created follows this sketch:
Absorbing boundary conditions are applied on the three non-symmetric geometric faces of the fluid volume as shown. The fluid volume has dimensions WxWxL as shown. Following the criteria of at least one wavelength at the highest frequency with 16 elements/wavelength, the dimensions of the water volume are W = 0.75+a and L = 0.75 meters. Symmetry planes exist at the XZ and YZ planes because only 1/4 of the piston face is modeled. The XY face has no absorbing boundary condition since to represent the rigid baffle, in which the normal velocity is zero, which relates to a natural boundary condition in finite elements. A velocity of 10-6 m/s applied on the piston surface completes the required boundary conditions. The resultant 3D geometry (3dpiston.geo and 3dpiston.fem) is shown below:
There are some points worth mentioning here. 3D finite element mesh sizes can quickly become too large for your computer resources, so it is imperative that you keep the mesh size consistent with the accuracy you require. This means pulling the outer boundaries towards the source as much as possible and keeping the mesh density to a minimum. Also, you may notice that as you extrude this geometry, all the geometric face outlines continue to be seen independent of what regions you associate them with. This is an artifact of our extrusion process so you want to take special caution when choosing surfaces when applying the boundary conditions.
As in the 2D case, the analysis is run from 50 to 4000 Hz and the mechanical impedance is calculated. The following plot shows the result compared to the 2D model results.
The variation with frequency shows excellent agreement with the 2D and theoretical results. Slight differences are due to the fact that the 3D mesh is only a first order approximation to the velocity source: the finite element mesh would need to be increased to second order to better track the 2D solution.