Robust low noise sensitivity of PIV-based pressure measurement by omnidirectional integration

We derived an analytical expression for the error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method. The pressure calculation for the boundary points is an iterative process and the error decreases for each iteration. The inner domain pressure is a one-step calculation which uses the boundary point solution. For the inner domain, the error is an average of the boundary error and the integration truncation error. The analysis shows that the omnidirectional integration provides an effective mechanism to reduce the sensitivity to random noise. We verified those results using a direct numerical simulation (DNS) database of isotropic turbulence flow, with a homogeneously distributed random noise added to the entire field of DNS pressure gradient. The random noise has a magnitude varying randomly within the range of ±40% of the maximum DNS pressure gradient. A total of 1000 statistically independent noise distributions achieved by using different random number seeds. Three different methods are compared. The average error is 0.15±0.07 for the Poisson approach, 0.028±0.003 for the Circular Virtual Boundary method and 0.027±0.003 for the Rotating Parallel Ray method, indicating the validity of the expressions derived.