Experimental comparison of PIV-based pressure measurements in supersonic flows with shock waves

This paper evaluates the performance of the novel MacCormack method for particle image velocimetry (PIV)-based pressure reconstruction in real supersonic PIV experiments that include oblique shock waves generated by three different wedges of 10 degrees, 15 degrees, and 20 degrees with a free stream Mach number of 2.91. Besides, the precision of the widely used spatial integration methods and Poisson method for compressible flows is compared with that of the MacCormack method in the supersonic flows. The results show the good performance of the MacCormack method and its significant advantage in complex shock flows. The results are also consistent with the conclusions based on the synthetic velocity fields by (Liu et al 2017 Exp. Fluids 6 1-22), and further confirm the reliability of this method. The non-conservative spatial integration method usually achieves larger pressure distributions behind shock waves than theoretical values while the conservative spatial integration method performs much better but still fails to obtain accurate results in the strong shock flow. The Poisson method does not have obvious optimization compared to the spatial integration method. However, the pressure field reconstructed by the time-marching MacCormack method is constantly in good agreement with theory, which demonstrates the feasibility and advantage of this method in complex supersonic flows with strong shock waves.