Correcting for sub-grid filtering effects in particle image velocimetry data

Abstract

Particle image velocimetry methodology results in a spatial averaging of the real velocity field into a set of discrete measured velocities: one for each interrogation cell. In the absence of measurement noise, this filtering process results in a reduction of the measured turbulent kinetic energy and other second-order statistics of the velocity field. The reduction in this energy will naturally be dependent upon the amount of turbulent energy at lengthscales smaller than can be resolved by the interrogation cells that make up the measurement grid. This paper investigates the effects of sub-grid scale filtering on the second-order statistics of velocity. Several experiments are reported for which interrogation cell size to turbulent integral lengthscale ratios were varied. In addition, synthetic turbulent velocity fields with known spatial correlation functions are used to support experimental results and provide calibration for the estimation of the level of sub-grid filtering. It is suggested that to accurately capture most turbulent kinetic energy using PIV the interrogation cell should be at least of order ten times smaller than the integral lengthscale of the flow. A method is then provided to estimate the level of sub-grid filtering should the interrogation cell be larger than this limit up to around the size of the integral lengthscale. With interrogation cells larger than this lengthscale then sub-grid filtering is such that second-order statistics are reduced by over 50% and it should be considered unwise to rely on any second-order statistics from such a scenario, corrected or otherwise.