FINITE ELEMENT ANALYSIS OF 3D VISCID PERIODIC WAVE PROPAGATION IN HYDRAULIC SYSTEMS

Abstract

A very compact description of viscid wave propagation in straight transmission lines with a circular cross section in frequency domain by a transcendental transfer matrix is known since several decades. The corresponding research results show that fluid friction is limited to small dynamic boundary layers whereas the remaining fluid domain exhibits practically no friction effect and has bulk flow characteristics. An explanation how this boundary layer transfers its dissipative effect to the bulk flow has been given by Gittler et al. using asymptotic expansion techniques. They found that the effect of the boundary layer on the bulk flow in the centre is given by radial velocity components. The authors have shown that the findings of Gittler et al. are generally valid in the 3D case exploiting matched asymptotic expansions. In this paper these results are developed further to exploit this dynamical boundary layer theory for an efficient Finite Element (FE) computation of viscid waves. Standard acoustic elements without viscosity as available in many FE codes combined with frequency dependent acoustic boundary conditions can be used to simulate 3D viscid wave propagation in frequency domain. Comparison with the analytical transmission line theory shows the validity and wide applicability of this approach. It is much more efficient than a direct resolution of the viscid boundary layer by a fine FE grid.