Pressure evaluation from Lagrangian particle tracking data using a grid-free least-squares method

Abstract

The Lagrangian particle tracking shake-the-box (STB) method provides accurate evaluation of the velocity and acceleration of particles from time-resolved projection images for high seeding densities, giving an opportunity to recover the stress tensor. In particular, their gradients are required to estimate local pressure fluctuations from the Navier–Stokes equations. The present paper describes a grid-free least-squares method for gradient and pressure evaluation based on irregularly scattered Lagrangian particle tracking data with minimization of the random noise. The performance of the method is assessed on the basis of synthetic images of virtual particles in a wall-bound turbulent flow. The tracks are obtained from direct numerical simulation (DNS) of an initially laminar boundary layer flow around a hemisphere mounted on a flat wall. The Reynolds number based on the sphere diameter and free stream velocity is 7000, corresponding to a fully turbulent wake. The accuracy, based on the exact tracks and STB algorithm, is evaluated by a straightforward comparison with the DNS data for different values of particle concentration up to 0.2 particles per pixel. Whereas the fraction of particles resolved by the STB algorithm decreases with the seeding density, limiting its spatial resolution, the exact particle positions demonstrate the efficiency of the least-squares method. The method is also useful for extraction of large-scale vortex structures from the velocity data on non-regular girds.