Viscous boundary layer correction on a pressure-field acoustic model

Abstract

Fluid viscosity plays an important role in many acoustics and structural acoustics problems. For example, using an inviscid approximation to the flow of fluid-loaded micro-electro-mechanical systems and micro-scale biological structures results in large errors in the predicted response. Using a linearized Navier--Stokes solution, however, increases the number of unknowns by at least a factor of three compared to an inviscid approximation where pressure is the only degree of freedom. In this work, an approximate boundary condition is developed to include fluid viscosity for coupled fluid-structure systems. The viscous effect is included as a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. This is the key step enabling the development of a variational formulation that is directly amenable for approximation in a finite element method (FEM) code as only a minor modification to existing structural acoustic code. Hence, this approach retains the great computational advantage over the conventional viscous FEM formulation. We show results demonstrating the accuracy of the approximate boundary condition as compared to the full three dimensional Navier-Stokes solution.