Steady three-dimensional shock wave reflection transition phenomena.

Abstract

Abstract Shockwave reflection has in recent times been investigated as a threedimensional phenomenon where geometrical effects on the reflection patterns have been given more attention than previously. A typical example is that of a supersonic body flying over a ground plane, in which the bow wave reflects off the ground surface. Depending on the Mach number, the reflection can be regular below the body, but will then make a transition to the three-shock Mach reflection pattern at some lateral position. In this report symmetrically arranged wedges with a finite span (i.e. one above the other) were modeled and visualised in CFD in order to investigate the three-dimensional steady state transition from regular reflection to Mach reflection. This follows on the work done by Skews (2000) where it was observed from shadowgraph pictures that there seems to be a sudden jump at the transition point in the growth of the Mach stem. Contrary to what was observed by Skews (2000), the transition was found to be gradual and smooth in the current CFD simulations. High visual clarity from the CFD results could not be achieved, even after successive grid refinements were performed on and around the shockwaves, because of the averaging technique of fluid property values in cells performed by CFD codes. The flows in the vicinity of the transition are examined, with particular attention to the shear layers that are generated from the triple point lines. Because of the inclination of the Mach stem surface to the oncoming flow the Mach number behind this surface can be supersonic, in contrast to the two-dimensional case. The steady state reflection phenomenon where there is transition from Mach reflection to regular and then back to Mach reflection when moving laterally outward from the vertical symmetry plane was also investigated using the same CFD setup, but with a much wider wedge span. This particularly interesting situation suggests the existence of complex transition criteria. The aim was to reproduce numerically this phenomenon observed experimentally by Ivanov et al. (1999), and to see if these results can be replicated for a lower Mach number attainable using a local wind tunnel. Both aims were achieved, but with the same limitation mentioned above of the averaging technique of fluid property values by CFD codes. There are currently no analytical criteria for the prediction of shock wave reflection transition in the three-dimensional case, nor for the possible existence of a dual solution domain, as exist for two-dimensional flows. Parametric studies of the type discussed in this report should lead to a fuller understanding of the flow conditions of importance.