Analysis of Hypersonic Boundary Layer Turbulence by Means of Focused Laser Differential Interferometry

Abstract

This thesis investigates a hypersonic turbulent boundary layer over a cone with cold walls and a sharp nose tip. The analyses include frequency spectra of density fluctuations up to a frequency of 10 MHz, as well as an analysis of their convection velocities, at multiple wall-normal locations inside the boundary layer and in the near field above it. Experimental measurements are obtained under Mach 7.4 and unit Reynolds number 4.2 · 10^6 m−1 in the free-piston driven High Enthalpy Shock Tunnel Göttingen (HEG), using the optical technique of Focused Laser Differential Interferometry (FLDI). A method is proposed to accurately measure the separation distance between the probes of multi-foci FLDI, to allow reliable measurements of convection velocities using cross-correlation between the signals. The method is based on the detection of a propagating weak blast wave generated by an electric spark, and is verified to have similar accuracy and precision than the method of directly imaging the beams, but exhibits increased flexibility. Convection velocities measured in the near field of the hypersonic boundary layer are in agreement with free stream data reported in the literature at similar Mach numbers. The measured frequency spectra of hypersonic turbulent boundary layer density fluctuations show regions with well-defined power laws typical for pressure fluctuations. These spectra are compared with Large-Eddy Simulation (LES) results for a conical turbulent boundary layer, calculated at the experimental test conditions. Direct comparisons are performed by simulating the FLDI response in the numeric flow field, by means of computational FLDI (cFLDI). The cFLDI algorithm is validated using the same blast wave measurements obtained when measuring the separation distance between FLDI probes. To that end, an analytic methodology is proposed to reconstruct the pressure waveform of the spherical blast wave, when detected with the straightline FLDI. Independence between the cFLDI algorithm and the reconstruction formulation allow the cFLDI code to be validated once the computational response of the reconstructed flow field and the experimental data that generated it are in agreement. The results of the direct comparison between the hypersonic turbulent conical boundary layer frequency spectra calculated with LES and experimentally probed in HEG are in reasonable agreement, once the bandwidth constraints of each are adequately considered. It is also verified that in the present case, in which the divergence of the FLDI beams in the probed region is small, the complex cFLDI algorithm may be substituted by a simple line integral of density variations in the numeric flow field, without significant losses. These observations offer a framework for practical numerical and experimental comparisons, which are necessary to validate simulations and turbulence models. The results of this thesis will help to overcome the current lack of experimental data concerning high-speed turbulent flows, especially at high frequencies.