Inviscid interactions between an oblique shock wave and a concave cylinder

Three-dimensional shock interactions dominated by the shock wave impinging on concave walls are commonly encountered in the three-dimensional inward-turning inlet. To reveal the flow physics of these interactions，a simplified model that consists of an oblique shock wave impinging on a concave cylinder was proposed. Inviscid numerical simulations and theoretical analysis were conducted at a freestream Mach number of 6 with a series of shock angles βi ranging from 14° to 29° to investigate the three-dimensional flowfield generated by the oblique shock wave impinging on the concave cylinder. The results show that the adverse pressure gradient on the symmetry plane is significantly higher than that of the two-dimensional scenario. For βi ≤ 25°，the transitions from the Mach reflection（MR）to regular reflection（RR）occur when the oblique shock sweeps from the sidewall to the symmetry plane，which forms the type MR-RR flow field. A bridge shock wave generated at the MR-RR transition point extends to the symmetry plane and then reflects on the symmetry plane，which generates a peak wall pressure higher than that of the two-dimensional oblique shock reflection on a flat plate. For βi≥25°，the shock reflections on the sidewall and the symmetry plane are both MR，forming the type MR-MR flow field. The bridge shock wave generated at the dividing point of the two MRs develops towards the sidewall. The flow past the sidewall collides on the symmetry plane，resulting in a peak wall pressure higher than that of a normal shock wave. When βi=25°，dual solutions of MR-RR and MR-MR of the flow field exist depending on different initial conditions. The formation mechanisms of the transition points and the dividing points in the two types of flow fields are revealed using a theoretical method，in which the three-dimensional shock interactions are transformed into a series of two-dimensional problems. The generation mechanisms and initial evolution characteristics of the bridge shock wave are clarified using this theoretical method. When βi ≥ 18°，the convergence of flow past the sidewall dominated by inviscid shock interactions are intensified on the symmetry plane，forming a streamwise counter-rotating vortex pair near the symmetry plane. The knowledge gained from the inviscid analyses is helpful to address the mechanisms of flow convergence and counter-rotating vortex pair phenomena in the inward-turning inlet. © 2024 Journal of Propulsion Technology. All rights reserved.