A novel approach for reconstructing pressure from PIV velocity measurements

Abstract

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 in primitive variables and exploits a finite element discretization of the measurement grid. By virtue of the underlying mathematical formulation, 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 the insufficient robustness with respect to measurement errors, are overcome. The method is first applied to an exact solution of the Navier–Stokes equations, showing second order convergence of the L∞ error for the pressure variable. The robustness of the method with respect to stochastic perturbations in the velocity field is then tested and the results compared with other techniques proposed in the literature. Finally, the proposed technique is applied to both a phase-averaged and time-resolved PIV database of the flow around a pitching airfoil employed to investigate the dynamic stall. The reconstructed pressure is compared with direct pressure measurements, showing very encouraging results.