Novel approach of FVS-based pressure reconstruction for PIV data in supersonic flows with shock waves

This paper proposes a high-accuracy approach to reconstructing pressure fields from planar velocimetry data, typically provided by Particle Image Velocimetry (PIV), with specific attention to its implementation for steady supersonic flows with strong shocks. Flux vector splitting (FVS) technique is utilized to discretize and approximate the conservative Navier-Stokes equations, with the assumption of adiabatic flow. The method is therefore named FVS method. The performance is systematically evaluated using numerically simulated velocity fields with an oblique shock wave. The new method possesses higher accuracy than conventional methods, the RMS error is less than 1 % in noise-free velocity data and 2.32 % in noisy condition with Gaussian noise of 3 sigma = 2 %. More important is the superior stability and convergence to the MacCormack method presented in the noisy condition, which ensure its engineering application value. Furthermore, the FVS method is applied in a PIV experiment with an oblique shock induced at Mach 2.91 and evaluated quantitatively. The advantageous results confirm its feasibility under experimental conditions. Thus, the new method indicates the potential to obtain pressure distributions of the entire supersonic flow field nonintrusively, which can further determine more aerodynamic parameters in aerospace engineering practice.