Dependence of radiated sound frequency on vortex core dynamics in multiple vortex interactions

Abstract

Abstract With both theoretical analysis and measurement data, it has been identified previously that there exists a robust sound emission from a pair of counter-rotating aircraft wake vortices at the frequency of unsteady vortex core rotation. In a vortex system with multiple vortices, the sound emission frequency can be subjected to change because of interactions among the vortices. The behaviour of the influence, indicated by the ratio between the core size and the distance of the vortices and the underlining vortex core dynamic mechanisms, is investigated in this study. A vortex particle method is used to simulate the vortex core dynamics in two-dimensional, inviscid and incompressible flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. The study shows, without vortex merging, individual frequencies can be clearly identified that are due each to core rotation (self induction) and co-rotating motion of a vortex centre around the other (mutual induction). The ratio of the core size and the distance between vortices does not seem to significantly influence the frequency of vortex core rotation. With vortex merging, a single frequency due to the merged vortex core is generated.