Pressure Field Reconstruction from Particle Image Velocimetry Data Using an Analytical Solution of the Pressure Poisson Equation with a Green’s Function Approach for an Axisymmetric Problem

Pressure field reconstruction from a Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) data is a well-studied topic with improvements to existing methods and new approaches continuously appearing in the literature. The reconstruction process is primarily achieved using two classical processes: direct integration of the Navier-Stokes equations and solution of the Pressure Poisson Equation (PPE) with the associated boundary conditions. More recently, a new method using integration in Fourier space technique has also emerged. Each approach has its set of benefits, which is debated in the literature. The focus of current work is a solution to a classical PPE, which is usually discretized and solved using standard numerical methods. In this work, we propose an analytical solution to the PPE problem using Green's function approach eliminating the need to address numerical aspects of the problem except to perform numerical integration. Two formulations of an axisymmetric problem are proposed: one with mixed and one with all Neumann boundary conditions. The ideal flow case is used to evaluate the difference in the results obtained from two formulations before applying both equations to the PIV data set of a self-propelled vortex.