Reconstructing Pressure from PIV Velocity Measurements: a Novel Approach

The purpose of this work is to develop an innovative procedure for reconstructing the pressure field from PIV velocity measurements of unsteady, incompressible flows. The proposed technique is based on a generalization of the Glowinski-Pironneau method for the uncoupled solution of the incompressible Navier-Stokes equations written with primitive variables. The underlying mathematical formulation allows indeed to overcome some of the drawbacks affecting the techniques proposed so far in the literature, such as the use of ad hoc boundary conditions for the pressure and insufficient robustness with respect to measurement errors. The problem is discretized by Taylor-Hood finite elements and a Fortran90 solver is developed. The method is first applied on an exact solution of the Navier-Stokes equations, showing a second order convergence of the error for the pressure variable, measured in infinity norm. The robustness of the method with respect to the error in the velocity measurements is tested for both stochastic and deterministic perturbations. Then the proposed technique is applied to the PIV database of the flow around a pitching airfoil employed to investigate the dynamic stall. The computed pressure is compared with direct pressure measurements, showing very encouraging results.