Dynamics Evolution Investigation of Mack Mode Instability in a Hypersonic Boundary Layer by Bicoherence Spectrum Analysis

Abstract

The instability of a hypersonic boundary layer on a cone is investigated by bicoherence spectrum analysis. The experiment is conducted at Mach number 6 in a hypersonic wind tunnel. The 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 streamwise direction to investigate the development of the unstable disturbances. The bicoherence spectrum analysis based on wavelet transform is employed to investigate the nonlinear interactions of the instability of Mack modes in hypersonic laminar boundary layer transition. The results show that wavelet bicoherence is a powerful tool in studying the unstable mode nonlinear interaction of hypersonic laminar-turbulent transition. The first mode instability gives rise to frequency shifts to higher unstable modes at the early stage of hypersonic laminar-turbulent transition. The modulations subsequently lead to the second mode instability occurrence. The second mode instability governs the last stage of instability and final breakdown to turbulence with multi-scale disturbances growth.

Experimental study on spectrum and multi-scale nature of wall pressure and velocity in turbulent boundary layer

“…Near-wall quasi-stream-wise vortices play a key role in producing high friction in the wall-bounded turbulent flow. [1][2][3][4][5][6][7][8] Aiming at skin-friction reduction and turbulence suppression, the opposition control was proposed by Choi et al [9] in their direct numerical simulation (DNS) for the first time. [10][11][12][13][14][15] However, it is impractical since the required velocity information very near the wall is usually unavailable.…”