New formulation of Hardin-Pope equations for aeroacoustics

Predictions of aeroacoustic disturbances generated by low-speed unsteady fl ows can be obtained with the two-step method proposed by Hardin and Pope (H ardin, J. C., and Pope, S. D., "An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics," Theoretical and Computational Fluid Dynamics , Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed inform ation about the unsteady aerodynamic flowfield, which usually is obtained f rom a computational fluid dynamics solution. A new, conservative formulatio n of the equations governing acoustic disturbances is presented. The conser vative form of the governing equations is obtained after application of a t ransformation of variables that produces a set of inhomogeneous equations s imilar to the conservation-law form of the compressible Euler equations. Th e source term of these equations depends only on the derivatives of the hyd rodynamic variables. Explicit time marching is performed. A high-order accu rate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-bi ased formulas and flux-vector splitting. Solutions are obtained for the aco ustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.