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.

A polynomial model with line-of-sight constraints for Lagrangian particle tracking under interface refraction

“…The cut-off frequency for assessing the contribution of the increment in particle acceleration to the cost function of all tracks is determined following the work of Gesemann [41]. To account for the large reconstruction errors near the track edges [42], a few points on each side of the track are removed from the final results. In this study, four points are removed on each side of the tracks in this work.…”

Special issue on uncertainty quantification in particle image velocimetry and Lagrangian particle tracking

“…A grid-free least-square method for pressure evaluation from scattered LPT data is assessed by Brobov et al [10]. The least-squares method can be used for reconstruction on irregular or regular grids and aims to minimization of random noise.…”