Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

Abstract: We present a straightforward method to solve gas damping problems for perfo-rated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver.The PPR equation is an extended Reynolds equation that includes additional terms modellingthe leakage flow through the perforations, and variable diffusivity and compressibility pro-files. The solution method consists of two phases: 1) determination of the specific admittanceprofile and relative diffusivity (and relative compressibility) profiles due to the perforation,and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections inthe slip-flow region are also included. Analytic profiles for circular and square holes withslip conditions are presented in the paper. To verify the method, square perforated damperswith 16 – 64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a ho-mogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (innormal to the surfaces) and torsional motion were simulated. The presented method extendsthe region of accurate simulation of perforated structures to cases where the homogenisationmethod is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.