Calculation of the Material Interface in a Pressure-Wave Supercharger

Abstract

The material interface inside a pressure-wave supercharger is determined by solving both the Euler and the Navier-Stokes governing equations, so that the effect of viscosity on the smearing of the interface can be evaluated. Two different numerical techniques are used to resolve the interface. One technique is a straightforward application of finite difference methods to solve the governing equations. Another is a combination of finite difference and coordinate splitting methods. The first technique leads to a material interface that is smeared over many grid celts. This is essentially a consequence of numerical diffusion and/or dispersion that results from truncation error. On the other hand, the combined finite difference and coordinate splitting technique uses a finite difference scheme to solve the governing equations everywhere, except in small regions surrounding the interfaces. In these regions, the governing equations are first transformed into two sets of one-dimensional Lagrangian equations where density does not appear explicitly in the spatial derivatives. As a result, the boundary conditions of the interface are automatically connected. Then the transformed equations are solved using conventional finite difference schemes. This technique gives a very accurate determination of the material interface. The results also show that viscosity does not contribute to the smearing of the interface.