Investigation of instability growth in a hypersonic boundary layer using schlieren visualization

Abstract

Hypersonic boundary layer transition plays a significant role in the design of hypersonic vehicles as a turbulent boundary layer has higher heat transfer compared to a laminar boundary layer. Transition is a complex phenomenon and various parameters decide how a boundary layer undergoes transition to turbulence. For a hypersonic cone boundary layer, the linear stability theory predicts the second mode waves to be the most unstable instability wave. Hence studying the second mode wave development is crucial from the point of view of hypersonic boundary layer transition control. The second mode waves cause density fluctuations which enables these structures to be visualized in a schlieren image. This thesis applies the wavelet analysis to schlieren images to study the growth of the second mode waves in a hypersonic boundary layer. The wavelet analysis is a signal processing technique which allows to studywaves in frequency/wavelength spectrumwithout loss in temporal/spatial information unlike conventional techniques like the Fourier analysis. High speed schlieren visualization experiments were performed on a 7± half angle cone in the high enthalpy shock tunnel in Goettingen (HEG), and the images which successfully captured the instability waves were used for the present study. By applying the wavelet analysis to schlieren images the following is concluded 1) the second mode waves amplifies structures towards the boundary layer edge, 2) A linear wave packet has higher amplitudes concentrated at the leading edge, which gets redistributed towards the center first and then later to a uniformdistribution over the whole length of the wave packet, 3) the first harmonic of the second mode wave develops in regions of strong second mode growth, 4) analysis on the growth rates of the second mode fundamental and its first harmonic showed that in regions of harmonic growth there was fundamental wave decay and vice versa, implying a possible energy exchange between the two waves and 5) strong low frequency waves were also detected in the schlieren images, these waves were more dominant during transition while the second mode waves and its harmonics die. The results from the study sheds more light into the instability development in a hypersonic boundary layer in the following ways: 1) the property of the second mode waves to amplify structures near the boundary layer edge explains why early researchers observed these waves close to the boundary layer edge, 2) linear wave packets with higher amplitudes concentrated at the leading edge of the wave packet, which was predicted from DNS simulations has been experimentally verified, 3) interaction between the fundamental wave and its first harmonic is shown by analysis on the spatial growth rates and 4) the strong presence of low frequency structures during boundary layer transition shows the second mode instability is not the only dominant instability for the hypersonic cone boundary layer under adiabatic wall conditions, as predicted by the linear stability theory.