FFT integration of instantaneous 3D pressure gradient fields measured by Lagrangian particle tracking in turbulent flows

Abstract

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 from its gradient, 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 iterative solution of the Poisson equation. Instead, we propose an alternative third method that integrates the pressure gradient field in Fourier space. The method is fast (non-iterative) and does not need additional boundary conditions of the pressure field. We demonstrate the integration scheme on a synthetic pressure field and on an experimental example based on time-resolved acceleration data from high resolution Lagrangian particle tracking with the Shake-The-Box method.