Particle Image Velocimetry via Wavelet Analysis

Abstract

Novel analytical and image processing methods derived as part of the development of a digital particle image velocimetry system, based on multiresolution analysis, are presented. The derivation of wavelet-based multiresolution methods for velocity e eld reconstruction is addressed, and the experimental setup used for validation of results is described. New techniques are proposed with improved spatial resolution and reliability over some existing methods. The techniques are based on wavelet-based representations of digital particle image data that are used to calculate spatially localized and frequency localized e ltered correlations of successive images. An essential feature of the method is the development of windowed cross-correlation expressions for wavelet-based expansions that are not orthogonal (or biorthogonal) over the cross-correlation window. The methodology makes use of recently introduced ree nable functions and generalized connection coefe cients derived in wavelet-based e nite element methods. A conventional charge-coupled device camera is used with a frame rate of 30 frames/s and pixel resolution of 512 £ 480 per frame. The images are acquired in pairs at 30 frames/s, with a user-dee ned time delay between image pairs, to capture the e owe eld structure evolution. The e ow illumination was achieved using a 5-W, argon-ion laser. Finally, hardware and algorithm performance is demonstrated via sample water-tunnel experiments.