A Consideration of Energy from the Viewpoint of Computational Aeroacoustics

Abstract

The propagation of acoustic energy from a sound source to the far field is a fundamental problem of acoustics. In this paper, a finite volume, multistage time stepping, Euler code is used to investigate the use of CFD algorithms for the direct calculation of the acoustic field. The two dimensional, compressible, inviscid flow about an accelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder surface to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is shown. Energy is the quantity of interest in the calculations since various components of energy have physical meaning. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy following the body. In the calculations, entropy generation is due to a combination of physical mechanisms and numerical error. In the case of propagating acoustic waves, entropy generation seems to be a measure of numerical damping associated with the discrete flow solver.