Direct measurement of the vorticity field in digital particle images

Abstract

A new method called direct measurement of vorticity (DMV) for digital particle images is described in this paper. Unlike previous methods for calculating the vorticity in particle image velocimetry (PIV), the vorticity is determined directly from the average angular displacement of rotation between two matched patterns. In order to improve the stability and precision of the angular displacement, polar coordinates are used instead of Cartesian coordinates to depict gray level patterns. The results of a Monte Carlo simulation of an Oseen-vortex flow indicate that the accuracy of the DMV method is independent of the spatial resolution of the velocity sampling, and the errors in the velocity field will not be propagated into the vorticity field as occurs with some finite difference methods. Therefore, the DMV method is a good method to be used to extract the vorticity field from velocity data that has higher levels of uncertainty.