Three-dimensional shock wave reflection transition in steady flow

Surujhlal, Divek
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This work details findings of an analytical, numerical and experimental investigation into the physical nature of three-dimensional shock reflection transition. Steady flow shock reflections comprise two types: regular reflection and Mach reflection. Reflection studies have previously been conducted using double-wedge symmetrical test piece configurations. It had been found by previous researchers that the expansion waves resulting from the side edges of the wedges would influence the reflection plane. The three-dimensional nature of real experimental flows gives rise to there generally being a coexistence of regular reflection (at the central portions) and Mach reflection (towards the outer peripheral portions) in between which transition occurs. It is the object of this work to understand three-dimensional transition for flow fields in which edge effects do not influence the reflection plane. Specially modified test piece geometry was developed for this purpose. Experimental tests were required for validation of the numerical models of the flow field. This was achieved by obtaining oblique shadowgraphs with optical orientation in both yaw and roll to assist in visualising the three-dimensional features of the flow field. These were compared with numerically reconstructed images at the same oblique orientations using a novel reconstruction technique. The main objective of this work was to identify the degree of correspondence of the threedimensional transition conditions to those of two-dimensional flows. This was facilitated by means of reducing the three-dimensional analysis to an effective two-dimensional one. It was found that the three-dimensional transition points occur at a higher effective angle than predicted by twodimensional criteria, and tend towards two-dimensional criteria at reduced free-stream Mach numbers and increased model geometrical spreads. Another important aspect of this work was the nature of the intersection line in the vicinity of the transition point, i.e., the point of impingement of the incident wave and its Mach surface on the horizontal symmetry plane in between the test pieces. Here it was found that a cusp exists in the sweep profile of the intersection line at the transition point. This was proved from a theoretical standpoint based on a model developed for the analysis of the flow in the vicinity of transition. Evidence of this from the numerical and experimental results is given as well. Higher geometrical spreads and lower free-stream Mach numbers were found to create flatter intersection line profiles at the horizontal symmetry plane on which the transition points were located further forward towards the apex of this line and which gave rise to greater transverse deflections for the streamlines passing through the regular reflection portions. Further discussion revolves around the nature of the shear and Mach surfaces. The Mach surface heights (representative of the triple line trajectories) are shown to increase monotonically. The shear layer edge trajectory, which originates at the sweep cusp, was found to show considerable transverse divergence but in keeping with the nature and extent of the transition cusp sweep differential, which in some cases was found to be large enough to cause a strong shock solution for the Mach reflection portion. In this case the shear surface edge trajectory diverted from trends seen for other models. The nature of the shear surface as a whole revealed interesting insights into the negative triple configuration of the Mach reflection portions which comprised of convex Mach surfaces. This is in contrast to the geometry obtained for the Mach surface for full Mach reflection numerically studied with a highly-spread geometry. Here, the flat Mach surface was found to increase monotonically towards the periphery in contrast to what was found for flows with edge influences on the Mach surface. It is suggested that this is what precludes complex reflection (central Mach reflection, transitioning to regular reflection further out, with a further transition to Mach reflection at the periphery) from being obtained in such flow fields.
A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy,2018