Pressure reconstruction from Lagrangian particle tracking with FFT integration

Abstract

Volumetric time-resolved pressure gradient fields in unsteady flows can be estimated through flow measurements of the material acceleration in the fluid and the assumption of the governing momentum equation. In order to derive pressure, almost exclusively two numerical methods have been used to spatially integrate the pressure gradient until now: first, direct path integration in the spatial domain, and second, the solution of the Poisson equation with numerical methods. We propose an alternative method by integrating the pressure gradient field directly in Fourier space with a standard FFT function. The method is fast and easy to implement. We demonstrate the accuracy of the integration scheme on a synthetic pressure field and apply it to an experimental example based on acceleration data from Lagrangian particle tracking with high seeding density (Shake-The-Box method).