A set of perturbed compressible equations(PCE), based on a hydrodynamic/acoustic splitting method, is proposed for aeroacoustic noise prediction of low Mach number viscous flows. The present formulation corrects the deficiency of previous splitting methods that have no control over the coupling effects between the incompressible vorticity and the perturbed velocities. The validation test shows that the present PCE solution is in excellent agreement with those of direct acoustic numerical simulation(DaNS) and Curle's acoustic analogy for a laminar dipole tone from a 2D circular cylinder at Reynolds number based on the cylinder diameter, ReD=200 and free stream Mach number, M∞ = 0.3. Computational efficiency and accuracy requirements for PCE are also investigated for a vortex scattering noise from the trailing-edge of a thin plate at Reynolds number based on the plate thickness, Reh= 2000 and M∞ = 0.3. The test results indicate that the computational efficiency can be achieved with an acoustic grid at lower resolution, as long as the projection quality of the total derivative of the incompressible pressure, DP/Dt field is retained.
The least-squares finite element method for low-mach-number compressible viscous flows
