A quadrupole correction model to suppress spurious sound with moving permeable integral surfaces

Ffowcs Williams–Hawkings (FW–H) equation is the extension of the Lighthill’s acoustic analogy equation for sound prediction with moving boundaries. However, the spurious sound often arises from vortex structures crossing through permeable FW–H surfaces. This work aims to approximate the contribution of the vortex structures to far-field sound using the Lighthill stress tensor flux and subtract the resulting spurious sound. Based on the frequency-domain Lighthill stress tensor quadrupole correction model, a quadrupole correction model is proposed to account for the effect of a moving integral surface on the spurious sound. Based on the frozen flow assumption and far-field approximation of the FW–H equation’s Green’s function, the proposed model incorporates the FW–H surface’s velocity into the integrand of the quadru-pole correction model by solving an algebraic equation of the quadrupole volume integral term. The proposed model is validated by the far-field sound prediction of flows over a circular cylinder and a convecting vortex.