Instantaneous PIV/PTV-based pressure gradient estimation: a framework for error analysis and correction

Abstract

A framework for the exact determination of the pressure gradient estimation error in incompressible flows given erroneous velocimetry data is derived which relies on the calculation of the curl and divergence of the pressure gradient error over the domain and then the solution of a div–curl system to reconstruct the pressure gradient error field. In practice, boundary conditions for the div–curl system are unknown, and the divergence of the pressure gradient error requires approximation. The effect of zero pressure gradient error boundary conditions and approximating the divergence are evaluated using three flow cases: (1) a stationary Taylor vortex; (2) an advecting Lamb–Oseen vortex near a boundary; and (3) direct numerical simulation of the turbulent wake of a circular cylinder. The results show that the exact form of the pressure gradient error field reconstruction converges onto the exact values, within truncation and round-off errors, except for a small flow field region near the domain boundaries. It is also shown that the approximation for the divergence of the pressure gradient error field retains the fidelity of the reconstruction, even when velocity field errors are generated with substantial spatial variation. In addition to the utility of the proposed technique to improve the accuracy of pressure estimates, the reconstructed error fields provide spatially resolved estimates for instantaneous PIV/PTV-based pressure error.