Experimental Investigation of Boundary-Layer Transition in High-Speed Two-Dimensional Boundary Layers

Abstract

This dissertation focuses on Mack’s first- and second-mode instabilities in planarboundary layers. Experiments were first conducted on a flat plate in the Quiet Mach 4 Ludwieg Tube at the University of Arizona. Data showed presence of first-mode waves, but the amplitudes were too low to cause the boundary layer to transition. The frequency and wave angle of these first-mode waves agreed well with theory. No second-mode waves were detected in these experiments. The Reynolds number in this facility was too low to perform meaningful boundary-layer transition experiments. As such, experiments were then conducted on a hollow cylinder in the Mach 5 Ludwieg Tube at the University of Arizona, which has a larger maximum Reynolds number. In this conventional wind tunnel, the transition from a laminar boundary layer to a turbulent boundary layer was observed. The unit Reynolds numbers for these experiments ranged from Re′ = 6.5 × 106m−1 to 18.5 × 106m−1. The experimental data show evidence of the first and second modes in this boundary layer, as predicted by linear stability theory. The main instrumentation used in the experiments were surface pressure transducers and Z-type schlieren imaging. The pressure data showed spectral content in frequency bands where linear stability theory (LST) predicts the second mode to exist. The second mode becomes unstable at the locations predicted by LST and the experimentally measured second-mode growth rates agree well with second-mode growth rates from LST. The first-mode waves did not produce a significant signal in the pressure data, which is expected since these waves are often difficult to detect with surface pressure sensors. However, wave angle calculations performed on the pressure data in the predicted first-mode frequency range showed an oblique wave angle that was consistent with the first-mode wave angles of LST. First-mode structures were pronounced in the schlieren data and their shape and wavelength agree with LST amplitude reconstruction. The second-mode waves show some resemblance to the structures predicted by LST, but there are subtle differences as well. Nonlinear analysis of the pressure data was conducted to understand the ultimate breakdown mechanism. It appears that an interaction between low-frequency first-mode waves that starts around Rex = 2×106 is causing boundary-layer transition. The Reynolds transition number measured was approximately Rex = 3.5 × 106.