An improved viscous/acoustic splitting method by analyzing source effects

The origin and effect of each term in the equations of the viscous/acoustic splitting (VAS) method are studied in this paper. With its rigorous mathematical derivation, the VAS method could be an improved version of Lighthill’s acoustic analogy method (referred to here as the ILAA method). The ILAA method contains a new monopole acoustic source due to the time derivative of the incompressible pressure and a modified quadrupole acoustic source due to the increment in momentum flux and viscous stress from the compressible/incompressible flow. Based on the incompressible Navier–Stokes equations, the VAS method is also considered as an ILAA method in which the quadrupole acoustic source is due to the compressible momentum flux, compressible viscous stress and the incompressible pressure. A source decomposition method is proposed by which the sound waves are sorted by the source terms. We analyze the effects of each source in the VAS method and propose an improved VAS (IVAS) method by distinguishing between an unstable source and acoustic radiation sources. Using the IVAS method suppresses the pseudo-sound waves that are excited by the additional unstable source that is generated by the waves spreading in a non-uniform velocity field, and the radiating quadrupole source in the ILAA method (VAS method) is retained to the utmost extent.