Velocity, Velocity Gradient and Vorticity Statistics of Grid Turbulence Obtained Using Digital Cross-correlation PIV

TL;DR

This study uses digital PIV to analyze grid turbulence, revealing Gaussian velocity fluctuation PDFs and non-Gaussian velocity gradient and vorticity PDFs, with spatial correlations differing from previous single-point measurements.

Contribution

First detailed analysis of velocity, vorticity, and gradients in grid turbulence using digital PIV across a range of Reynolds numbers.

Findings

Velocity fluctuations follow Gaussian distribution.

Velocity gradients and vorticity have non-Gaussian PDFs.

Spatial autocorrelations differ from previous measurements.

Abstract

Grid turbulence is investigated using cross-correlation digital Particle Image Velocimetry (PIV) over a range of Taylor Reynolds Number (Re{\lambda}) from 5 to 44. Instantaneous velocity is measured directly and vorticity and velocity gradients are obtained indirectly. Measurements are taken at various downstream locations from the generating grid. Probability distribution functions (PDFs) are calculated for the fluctuating component of the velocity, the spatial velocity gradients and vorticity. The PDF of the velocity fluctuations has a Gaussian distribution while velocity gradients and vorticity are found to have non-Gaussian PDF distributions. The structure of the flow is investigated by calculating spatial autocorrelations for all measured and derived data. The spatial velocity autocorrelations differ from previous experimental measurements of grid turbulence, most of which have been determined from single-point measurements. This difference is believed to be due to differences in the way in which the measurements are made, and particularly to differences in the spatial size of the experimental domain.