On the Rossiter-Heller frequency of resonant cavities

Abstract

The goal of this paper is to revise the Rossiter-Heller formula of cavity resonance frequencies for rectangular cavities in subsonic and supersonic flow conditions. Two modifications are proposed; the first one consists in using a second-order polynomial fit of literature experimental data for the non-dimensional time lag coefficient as a function of the cavity aspect ratio. The second modification consists in taking into account the reversed flow convective effects in the calculation of the backward acoustic propagation time, by including the reversed flow Mach number in the formula, expressed as a function of the free-stream Mach number and cavity aspect ratio. A second-order polynomial fit of scale-resolving flow simulation results of the reversed flow Mach number is used to derive the final resonance frequency formula. The effects of the two modifications are investigated for three values of the aspect ratio in the range 5 to 10, and four values of the free-stream Mach number in the range 0.6 to 1.35. It is concluded that taking into account both modifications yields globally more accurate predictions of the resonance frequencies. Finally, an attempt is made to identify the nature of additional tones observed for the deep supersonic case around the fourth and fifth Rossiter-Heller resonance modes.