Equilibrium Wall Model for Surface Pressure from PIV with Curvature and Reynolds Stress Correction

Extraction of pressure from PIV is a key challenge in experimental fluid dynamics. To date, surface pressure from PIV has been elusive due to the inherent difficulties in obtaining reliable velocity data close to the wall. Attempts to circumvent the problem, which rely on naïve linear or parabolic extrapolation techniques, have had mixed success. Large pressure gradients near the wall exacerbate the problem and 10% relative deviation from reference tap data is typical. This work examines an equilibrium wall model derived from the thin shear layer equations, which incorporates wall curvature and Reynolds stress. We applied the model to direct numerical simulation, large eddy simulation, and experimental data. We found modest improvements in high-pressure-gradient regions, such as the suction peak of an airfoil and the turbulent wake of a Gaussian bump. Unlike the naïve extrapolation methods, the model remains reliable even when large sections of near-wall data are corrupt. In the wake of a stalled airfoil, there was a consistent negative bias of about 0.15 delta Cp across all extrapolation techniques. This wake recovery bias is also reported in the literature, suggesting an area for further research.