Wavelet Analysis And Cross Bispectrum Analysis Of Flow Instability For Hypersonic Sharp Cone Boundary Layer

Hypersonic boundary layer instability and transition is one of the key fundamental problems to aeronautic and astronautic engineering as it is characterized by attendant increases in wall heat transfer and skin friction drag of hypersonic vehicles. These increases have significant impacts on the performance control, fuel consumption, structural design and thermal protection system of hypersonic vehicles. Experimental investigation of hypersonic boundary layer instability on a 5°half-angle sharp cone is performed at Mach 6 in a hypersonic gun wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface along the streamwise direction to investigate the development of the unstable disturbance.In this paper a new analysis method based on wavelet transform is presented for investigating the evolution mechanism of the second mode unstable disturbance during the hypersonic boundary layer transition. The fluctuating surface-thermal-flux signals have been decomposed by multi-scale wavelet analysis. The power spectrum, bispectrum and cross-bispectrum have been investigated based on wavelet coefficients. The conditional phase-averaging waveforms were extracted to provide the developing and evolution details of the unstable disturbance.From the plane representation of the wavelet coefficients, it can be seen that some local high magnitudes of the wavelet coefficients exist at different time in the scale range of 200KHz to 300KHz corresponding to the second-mode disturbance. At the last station X=480mm, the disturbance is fully developed and the transition reaches its peak. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals. The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The magnitude reaches its peak at the station where X=240mm. From then on, the magnitude begins to decrease and its shape changes from anti-symmetric to more symmetric.From the bispectrum analysis, it can be seen that the second-mode disturbance affects the hypersonic flow with together the first-mode disturbance at early stage. With the development of the boundary layer, the effects of two modes both increase, but the effect of the second-mode is greater. At X=480mm the first mode and the second mode can be identified clearly. The cross-bispectrum analysis shows that phase-locked interactions between every frequency are apparent, and the effects of the second-mode disturbances are from slender to strong, which are consistent with the results of power spectrum and bispectrum.In this paper, the new technique based on wavelet transformation and wavelet cross-bispectrum analysis provides a significant method for investigating the evolution mechanism of the second mode unstable disturbance during the hypersonic boundary layer transition. At hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer. This second mode instability precedes the final breakdown of the hypersonic laminar boundary layer and transition to turbulence.