2D PIV Study of Grid Turbulence

Abstract

The aim of the current project was to analyse grid turbulence with a technique that allows for a direct measurement of velocity derivative statistics. Two-dimensional particle image velocimetry ($2D~PIV$) of highly resolved grid turbulence at $Re_{M}=U_{\infty}M/\nu = 16000$ where $M$ is the grid rod spacing was analysed. Data spanning the downstream range $65 < x/M < 145$ was captured separately on planes parallel to a water channel's floor and walls with a $PIV$ resolution within three times the Kolmogorov microscale $\eta_{{K}}$. Isotropic turbulence ($IT$), axisymmetric turbulence ($AT$), homogeneous turbulence ($HT$), all these theoretical frameworks have been checked against velocity derivative data. It was found that the data complies most satisfactorily with $HT$ only, and to a lesser extent with $IT$ and $AT$. The $2\times 2$ velocity-gradient tensor $VGT$ that can be formed from $2D~PIV$ data was used in a novel manner by plotting the joint probability density function ($PDF$) of its trace $p$ and determinant $q$. Under the assumptions of \textit{locally} isotropic turbulence, the observed asymmetry in this joint $PDF$ was explained as the result of the predominance of enstrophy amplification by vortex stretching. The observations were validated when compared with $2D$ slices of $3D$ data from a direct numerical simulation of isotropic flow. Finally, a study of homogenisation was carried out by mapping an area of $14M\times 4M$ in the down- and cross-stream directions respectively starting immediately at the grid. This unprecedented attempt was achieved by using $2D~PIV$ over the stitched fields of view of three cameras put side-by-side. The statistics - based on 10600 vector fields per case - in the wake of two carefully chosen grids were studied, showing that homogenisation is a rapid but gradual process. Collapse of statistics across the different grid geometries was achieved passed the region of initial flow transients by taking into account all relevant parameters: differences in grid geometry \textit{and} work done on the flow. This hints at a unique dependency of grid turbulence dynamics in the region of cross-stream homogenised flow. Two-point spatial correlation functions were used to study the footprint of the grid on the flow statistics, exhibiting complex $Re{M}-$dependent wake interactions between the grid rods. Their impact, however, is quickly washed away by the turbulence.