Aeroacoustic computation of subsonic flows

The Expansion about Incompressible Flow (EIF) approach is a computational aeroacoustics (CAA) technique recently developed using ad hoc arguments. This approach splits the aeroacoustic problem into incompressible and perturbation parts, and in so doing offers significant computational advantages relative to direct simulation. The focus of this research is to derive the EIF equations using a rigorous analysis method, to characterize the physical meaning of the EIF variables, to provide a detailed understanding of the assumptions implicit in the governing equations, and to assess the performance of the EIF approach by computing the aeroacoustic fields for several flows. ^ The EIF equations are derived based on a Janzen-Rayleigh expansion of the compressible flow equations. Separate equation sets are developed in the near- and far-field regions by truncating the expanded equations using different orders in the Mach number squared. A series of composite equation sets, valid over the entire flow field, is constructed by matching the equations governing the near- and far-fields. The highest order composite equation set includes an infinite Mach number power series and is shown to be identical to the equation set used in the EIF approach. ^ A CAA solver is developed and integrated with two Navier Stokes solvers. The CAA solver includes a specially tailored non-reflecting boundary condition, optimized and conventional finite difference algorithms, and an efficient scheme for processing data from the incompressible flow solution. The solver is applied to several flows including a spinning vortex pair, a cylinder in cross flow, forced and unforced planar shear layers, and flow past rectangular cavities. These flows have distinctly different acoustic source types including compact and non-compact source regions, and dipole and quadrupole source distributions. In all cases, good results are obtained based on comparisons with analytical solutions, experimental measurements, and direct simulation predictions. The EIF approach is shown to require significantly reduced cpu-time relative to direct simulation. In addition, the lowest order perturbation equation set is shown to provide accurate aeroacoustic predictions as long as the Mach number is less than approximately 0.25. These equations are relatively simple to implement into a computer code and require 30% less cpu-time relative to the EIF equations.