Perturbed Compressible Equations for Aeroacoustic Noise Prediction at Low Mach Numbers

A revised formulation of a hydrodynamic/acoustic splitting method is proposed for aeroacoustic noise prediction of wall-bounded shear flows at low Mach numbers. Based on the analysis of perturbed vorticity transport equation, a set of perturbed compressible equations (PCE) is derived to handle properly the near-field compressibility effects. The accuracy of the formulation is verified for a dipole tone of laminar flow past a circular cylinder at freestream Mach number M(infinity) = 0.3 and Reynolds number based on the cylinder diameter, Re(D) = 200. It is shown that the computational results of PCE are in excellent agreement with those of direct acoustic numerical simulation (DNS) and Curie's acoustic analogy. Finally, the computational efficiency of the present PCE is demonstrated by employing an acoustic grid coarser than the hydrodynamic grid such that a time step can be shared for both. It is found that PCE is about three times faster than DNS for the present cylinder tone problem and this speed-up can be increased up to 5-7 for Mach numbers less than 0.2.