Mode-switching and nonlinear effects in compressible flow over a cavity

Abstract

Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible flow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (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 article 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 is verified by instantaneous schlieren images acquired simultaneously with the unsteady pressures. 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. Higher-order spectral methods were employed to investigate potential quadratic nonlinear interactions between the Rossiter modes and to determine if they are responsible for the low-frequency mode present in the autospectrum. In turn, this low-frequency mode could interact with the Rossiter modes to modulate their amplitude. Significant nonlinearities, in the form of sum and difference frequencies of the Rossiter modes, are present in the l/d=2 cavity at M∞=0.4, while nonlinear effects are much smaller in the l/d=4 at M∞=0.6. The bispectral analysis indicates that quadratic interactions between Rossiter modes in the near-field pressure are not responsible for the observed low-frequency peak in the pressure autospectrum. Furthermore, the low-frequency mode does not exhibit a strong nonlinear coupling with the Rossiter modes.

Numerical Simulation of Flow over an Airfoil with a Cavity

“…12) shear-layer modes at different instants in time. A similar mode switching has been observed for cavities on planar walls [17]. Estimates of the hydrodynamic wavelength of the structures downstream of the cavity reveal that =W 1 and =W 0:5 for the first and second modes, consistent with Rossiter's [18] observations.…”

Processing and analysis methods for transonic cavity flow

“…For example, the second CFD mode (Figure 9d) shows three maxima at travel times of 19, 27, and 35. Those amplitude oscillations, denoted as mode amplitude modulation, were also described in experimental works [5]. The SAS model shows good 6 Results and Discussion…”

“…Time averaged quantities as SPL, OASPL or the mean flow are well known in cavity flow. However, the unsteady cavity flow physics including standing waves, mode switching, and modulation of the tonal amplitude are not captured by time averaging, and retained attention only recently [5]. Joint time-frequency methods like the wavelet transform [6] are able to dissect the temporal behaviour of the tones, and have proved that there is no strong non-linear coupling between modes [5].…”

“…However, the unsteady cavity flow physics including standing waves, mode switching, and modulation of the tonal amplitude are not captured by time averaging, and retained attention only recently [5]. Joint time-frequency methods like the wavelet transform [6] are able to dissect the temporal behaviour of the tones, and have proved that there is no strong non-linear coupling between modes [5]. In this work, joint time-frequency methods are extended to perform a joint space-time-frequency analysis of the pressure field, to validate the flow dynamics of the obtained CFD solutions.…”

Modeling and Feedback Control for Subsonic Cavity Flows: A Collaborative Approach

“…In different flow conditions, either a strong single-mode or multiple-mode resonance occurs [28,45]. In the latter case, rapid switching between modes has also been observed [8,37,22].…”