Experiments on compressible flow-induced cavity oscillations

Abstract

Multiple peaks of comparable strength in unsteady pressure autospectra often characterize compressible flowinduced cavity oscillations. Yet it is unclear whether these peaks (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This paper describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the Short Time Fourier Transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This hypothesis is also verified by instantaneous schlieren images. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-frequency peak seen in the autospectrum. Polyspectra are used to investigate potential quadratic nonlinear interactions. Significant nonlinearities are present in a L/D 2 cavity at Mach 0.4, while nonlinear effects are much smaller in a L/D 4 cavity at Mach 0.6. These results lead to the hypothesis that when three Rossiter modes (fc>fb> fa) are present and satisfy the relation fc (fa +fh) = Af~ 0, significant nonlinear coupling can occur between the modes, leading to a low-frequency amplitude modulation of the primary modes at fm = Af and larger than normal SPL. Even when this condition is not satisfied, the difference interactions between the primary modes, namely (fa, -fa), (fb, -fb) and (£, -fc), create a low-frequency mode that appears in the power spectrum and amplitude modulates the Rossiter modes.