Sound generated by vortex ring impingement on a heated wall

An analysis is made of the sound generated when a vortex ring impinges normally on a heated section of a plane wall. The unsteady convective diffusion occurring when the vortex is close to the wall causes a rapid increase in heat transfer and the emission of sound of monopole type. The approximate dependence on vortex Reynolds number of the enhancement of heat transfer is deduced from recent experiments reported by Arévalo et al. [Vortex ring head-on collision with a heated vertical plate, Physics of Fluids   19 (2007) 083603-1–083603-9], and is used to derive a scaling law for the acoustic pressure. The sound pressure signature is dominated by a large amplitude pulse associated with an explosive, but brief increase in the rate of heat transfer at the start of the vortex–wall interaction. The quadrupole sound pressure also produced during impingement on the wall is found to be smaller than the thermally induced sound by a factor proportional to M2T0/(Tw-T0)M2T0/(Tw-T0) where M  , TwTw, T0T0 respectively denote the Mach number of the vortex motion, the mean wall temperature and the fluid temperature at large distances from the wall.