A pressure field reconstruction scheme based on velocity data for strong shock-wave/boundary-layer interactions with regular and Mach reflections

In this paper, a non-intrusive pressure measurement scheme based on particle image velocimetry (PIV) is presented for the complex supersonic flows with intense shock systems, by elaborately combining the MacCormack method, the streamline-based method, and the spatial integration in conservative form. According to the detailed analyses of flow structures, the pressure fields are well reconstructed by the proposed scheme for the two typical shock-wave/boundary-layer interactions containing regular and Mach reflections, which are induced by the relatively strong oblique shock waves generated by the wedges of 21° and 17° in the freestreams of Mach 2.5 and 2.0, respectively. Based on the theoretical solutions by oblique shock relationship, free interaction theory, and shock polar analysis, this pressure reconstruction scheme is completely validated to effectively suppress the propagation of PIV velocity error to the pressure field and the accumulation of reconstructed pressure error behind the strong shock wave. Compared with the literature presently, this work would be the most challenging application of PIV-based pressure measurement to such complex supersonic flows with intense shock reflections, large oscillations, wide speed ranges, and various compressible flow structures. These good results could confirm the feasibility and high accuracy of the proposed reconstruction scheme and may greatly promote its applications in academic research and engineering test for supersonic flows in the future.