High-resolution velocimetry from tracer particle fields using a wavelet-based optical flow method

Abstract

A wavelet-based optical flow method for high-resolution velocimetry based on tracer particle images is presented. The current optical flow estimation method (WOF-X) is designed for improvements in processing experimental images by implementing wavelet transforms with the lifting method and symmetric boundary conditions. This approach leads to speed and accuracy improvements over the existing wavelet-based methods. The current method also exploits the properties of fluid flows and uses the known behavior of turbulent energy spectra to semi-automatically tune a regularization parameter that has been primarily determined empirically in the previous optical flow algorithms. As an initial step in evaluating the WOF-X method, synthetic particle images from a 2D DNS of isotropic turbulence are processed and the results are compared to a typical correlation-based PIV algorithm and previous optical flow methods. The WOF-X method produces a dense velocity estimation, resulting in an order-of-magnitude increase in velocity vector resolution compared to the traditional correlation-based PIV processing. Results also show an improvement in velocity estimation by more than a factor of two. The increases in resolution and accuracy of the velocity field lead to significant improvements in the calculation of velocity gradient-dependent properties such as vorticity. In addition to the DNS results, the WOF-X method is evaluated in a series of two-dimensional vortex flow simulations to determine optimal experimental design parameters. Recommendations for optimal conditions for tracer particle seed density and inter-frame particle displacement are presented. The WOF-X method produces minimal error at larger particle displacements and lower relative error over a larger velocity dynamic range as compared to correlation-based processing.