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Title: Supersonic corner flows in rectangular channels
Author: Sabnis, Kshitij
ISNI:       0000 0004 9353 8845
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2020
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Rectangular channel geometries are widely encountered in supersonic flows, such as in wind tunnels and in aircraft inlets. Shock-boundary-layer interactions in these flows are known to exhibit significant three-dimensionality, due to the presence of sidewalls and associated corner boundary layers. The main effect is on the local separation of these corner regions, which then affects the wider flow field. Successful prediction of the overall flow therefore relies on the corner separation to be determined accurately. This, in turn, requires knowledge of the flow momentum distribution within the corner boundary layers. However, numerical methods struggle to reliably compute these flows and there is not much experimental data on supersonic corner boundary layers for comparison. This thesis addresses the outstanding gap in knowledge by performing validation-quality experiments on the corner regions of a Mach 2.5 channel flow, with a unit Reynolds number of approximately 40 million per metre. The experiments are conducted in the rectangular test section of a supersonic wind tunnel at the University of Cambridge. An analysis of the wind tunnel experiments, alongside computational data provided by the US Air Force Research Laboratory, reveals that the corner boundary layers are strongly influenced by the geometry of the two-dimensional nozzles used to produce the supersonic flow. The dominant effect is related to bulk vertical velocities within the sidewall boundary layers, induced by vertical pressure gradients in the nozzle. For some very particular geometries, a second influence may be associated with a region of separated flow immediately ahead of the nozzle, which generates vortices within the sidewall boundary layer. Through these mechanisms, the nozzle geometry is seen to strongly influence both the thickness and the structure of the corner boundary layers. High-quality experimental data in the corner regions are used to validate relevant numerical methods. Simple linear eddy-viscosity type turbulence models are found to compute these flows particularly poorly, with a 7% discrepancy in streamwise velocity. This is largely due to the fact that they do not capture known, stress-induced, corner vortices. However, the quadratic constitutive relation improves prediction of the corner boundary-layer structure, reducing experimental-computational differences by as much as half. This improvement is associated with vorticity generation in these corner regions, albeit with slightly different properties to the physical vortices. This production of vorticity depends only on the presence of a quadratic term in the eddy-viscosity model and not on which particular quadratic term is used. A more general form of the quadratic constitutive relation with one additional term is proposed, which appears to exhibit substantial improvements in the prediction of turbulent stress anisotropies. The nozzle geometry effects are exploited to produce two otherwise-identical experimental setups with distinctly different momentum distributions in the corner boundary layers. A full-span wedge introduces an oblique shock with flow deflection angle, 8 degrees, which impinges on the floor boundary layer. The two setups exhibit quite dissimilar separation behaviour, not only in the corner regions but also on the tunnel's centre span, with a difference in central separation length of as much as 35%. The observed behaviour is consistent with expectations based on local flow momentum affecting corner separation size, and on the displacement effect of this corner separation influencing the wider flow.
Supervisor: Babinsky, Holger Sponsor: US Air Force Office of Scientific Research
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Supersonic ; Compressible flow ; Supersonic wind tunnels ; Corner flows ; Rectangular channel flow