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.

本文的目的是修正亚音速和超音速流动条件下矩形腔的腔共振频率的 Rossiter-Heller 公式。提出了两项​​修改；第一个是使用文献实验数据的二阶多项式拟合作为空腔纵横比函数的无量纲时间滞后系数。第二个修改包括在计算反向声传播时间时考虑反向流动对流效应，通过在公式中包括反向流动马赫数，表示为自由流马赫数和腔纵横比的函数。对逆流马赫数的标度分辨流动模拟结果进行二阶多项式拟合，推导出最终的共振频率公式。针对 5 到 10 范围内的纵横比的三个值，以及 0.6 到 1.35 范围内的自由流马赫数的四个值，研究了这两种修改的影响。得出的结论是，考虑到这两种修改会产生全局更准确的共振频率预测。最后，尝试确定在第四和第五罗斯特-赫勒共振模式周围的深超音速情况下观察到的附加音调的性质。