An experimental and theoretical investigation of instabilities in hypersonic flat plate boundary layer flow

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Abstract
As part of an investigation on hypersonic boundary layer transition, the first successful instantaneous hot-wire and fluctuating pressure measurements have been conducted in the Ludwieg-tube facility of DLR at a free-stream Mach number of M∞=5. The disturbance amplitudes [root-mean-square (RMS) values] of the fluctuations of Pitot pressure and mass flow are smaller than the values measured in conventional, i.e., continuously driven or blowdown, hypersonic wind tunnels. Hot-wire measurements in the laminar boundary layer on a flat plate in the same wind tunnel at Mach 5 did not show the expected dominance of high-frequency second mode instabilities, predicted by linear stability theory and found in other experiments. On the other hand, the growth of natural disturbances within a broad frequency band up to 50 kHz could be observed on the flat plate. The measured amplification rates are in good agreement with theoretical results for three-dimensional first mode disturbances. The theoretical investigations were based on a local and nonlocal instability analyses of similarity profiles for flat plate boundary layer flow at M∞=5. Whereas the local analysis is limited to parallel model flows, nonlocal analysis additionally takes into account the nonparallel basic flow and the nonuniform disturbance flow evolution. Surprisingly, the first rather than second mode instability wave growth is found to be dominant in the Ludwieg-tube experiment. This result deviates from measurements obtained in other wind tunnels. It indicates that not only transition locations but also instability wave growth for hypersonic boundary layer flows are strongly dependent on the disturbance environment of the individual wind tunnel. Due to the very low initial, high-frequency disturbance amplitude level in the free stream of the Ludwieg-tube, second mode instabilities may not grow to significant values or not be present at all. As such a free-stream disturbance spectrum can also be expected under free-flight conditions, the Ludwieg tube may be a suitable wind tunnel to adequately simulate boundary layer flow transition along smooth surface, hypersonic flight vehicles.

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