No 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.

Experimental results are presented that show the existence of organized structures in a compressible, turbulent boundary layer. Results were obtained using arrays of hot wires and wall pressure transducers in a Mach-3 zero-pressure-gradient boundary layer. The VITA method of conditional sampling was used to deduce average pressure events at the wall and mass flux events throughout the boundary layer; these results show qualitative similarity to those found in incompressible flows. By conditioning upon the middle hot wire from a three-wire probe, evidence is found suggesting that structures exist of a height comparable with the boundary-layer thickness. Furthermore, two-point conditional sampling was used to show that an average pressure event could be extracted by conditioning upon mass-flux events. From this procedure we found that the structures maintain their shape as they travel downstream and also that their spanwise extent is very limited.The inferred angle from correlations between two hot wires, and between a hot wire and a wall-pressure transducer, indicate that the average structure is inclined at approximately 45° for a large part of the boundary layer. This result agrees well with structures observed in schlieren photographs of supersonic boundary layers. Measurements of the instantaneous angle show a wide distribution of structure angles, and the general behaviour of the large-scale structures is consistent with the hairpin loop model of wall turbulence.

This paper reports an experimental investigation of the instantaneous structure of a supersonic turbulent boundary layer (M= 2.86,Reθ= 82000) over a short region of longitudinal concave surface curvature. The radius of curvature was 12 initial boundary-layer thicknesses and the turning angle was 16°. Severe distortion of the boundary layer occurred, as evidenced by an alteration of the mean velocity profiles and an increase in wall shear stress of 125%. The large-scale organized motions in the boundary layer were significantly altered as illustrated by changes in the character of the mass flux ‘fronts’ (large gradients in the fluctuating streamwise mass flux).

A comparison of the turbulence structure of subsonic and supersonic boundary layers reveals that, despite broad similarities, significant differences exist. The length scales derived from space-time correlations indicate that the spanwise scales are almost identical but that the streamwise scales in the supersonic flow are about half the size of those in subsonic flow. The large-scale structures in the subsonic boundary layer appear to move slightly slower, and lean more toward the wall than those observed in supersonic flows, and their shear stress content is distributed differently among the four quadrants. These observations should have a strong impact on deriving turbulence models for high Reynolds number supersonic flows.