A specially curved wedge for eliminating wedge angle effect in unsteady shock reflection

Abstract

A curved wedge with a specific shape is designed and manufactured to guarantee the wedge angle unvaried during the cylindrically converging shock moving along the wedge. Thus the variation of the wedge angle caused by the wedge will be eliminated in unsteady shock reflection. Different initial wedge angles are considered to observe regular reflection and Mach reflection. When Mach reflection occurs, it is found that direct Mach reflection is persisted over the wedge without wave pattern transitions, which differs from our previous work with varied wedge angles [Zhang et al. “Reflection of cylindrical converging shock wave over a plane wedge,” Phys. Fluids 28, 086101 (2016)]. Moreover, the Mach stem is nearly straight when the wedge angle is relatively large, and the trajectory of triple point can be well predicted by three-shock theory. It is believed that the straight Mach stem results from the coupling effect of the converging shock and the convexly curved wedge, which exert opposite effects on the Mach stem curvature. As the wedge angle reduces, the three-shock theory prediction deviates from the present results owing to the curved Mach stem. Stronger vortices are produced near the wall, which are caused by the interaction of two shear layers, and whether the stronger vortices will be generated near the wall depends on the reflection number of the shock wave over the tube wall and wedge. The length of disturbed shock front in the Mach reflection is found to increase nonlinearly due to the unsteady feature of the flow. The growth rate of length reduces as the shock converges because of the geometrical contraction effect. Further the lengths of the Mach stem and the disturbed shock front are compared, and the results show that although the difference exists between them, both of them show a similar variation tendency. Compared with our previous work with varied wedge angles, the variation of the wedge angle has great effects on the Mach stem length and wave pattern transitions. It is believed that the differences between the present study and the pseudo-steady shock reflection are mainly induced by the unsteady feature of the flow because the variation of the shock Mach number is limited and the wedge angle is constant.