Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method

Abstract

This paper reports a theoretical analysis and the corresponding numerical and experimental validation results of the error propagation characteristics of the omnidirectional integration method used for pressure reconstruction from the PIV measured pressure gradient. The analysis shows that the omnidirectional integration provides an effective mechanism in reducing the sensitivity of the reconstructed pressure to the random noise embedded in the measured pressure gradient. Accurate determination of the boundary pressure values is the first step in ensuring the accuracy of the reconstructed pressure. The boundary pressure error consists of two parts, with one part decreasing exponentially in magnitude and eventually vanishing, and the other remaining as a constant with small magnitude through iteration. These results are verified by using a direct numerical simulation database of isotropic turbulence flow superimposed with noise at various noise levels and spatial distribution schemes to simulate noise embedded data. The nondimensionalized average error of the reconstructed pressure based on 1000 statistically independent pressure gradient field realizations with a 40% added noise level is 0.854 ± 0.406 for the pressure Poisson equation with Neumann boundary condition, 0.154 ± 0.015 for the circular virtual boundary omnidirectional integration and 0.149 ± 0.015 for the rotating parallel ray omnidirectional integration. If the converged boundary pressure values obtained by the rotating parallel ray are used as Dirichlet boundary conditions, the average pressure error by Poisson is reduced to 0.151 ± 0.015. Of the different variations of the omnidirectional methods, the parallel ray method shows the best performance and therefore is the method of choice. Comparisons of the performance of these pressure reconstruction methods using an experimentally obtained turbulent shear layer flow over an open cavity are in agreement with the conclusions obtained with the DNS simulation data. With the noise added DNS data, limitations regarding the pressure reconstruction methods in determining pressure fluctuation statistics are also identified and quantified.