Cross-correlation analysis of particle image fields for velocity measurement

In order to improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double or multiple exposure recordings. Furthermore with improved technology in high speed photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability. An analytic model and a Monte Carlo simulation are generalized from previous work on the optimization of direct auto-correlation methods to determine an expanded set of non-dimensional parameters that are most significant in optimizing the algorithm in terms of the above criteria. These parameters are the data validation criterion, the particle image density, the relative in-plane image displacement, the relative out-of-plane particle displacement, the velocity gradient, the ratio of the interrogation spot sizes and the relative spot size separation. For the direct cross-correlation method of single exposure double-frame systems which model video array detector interrogation and of double exposure single-frame systems which generalize earlier direct auto-correlation methods of interrogation of photographic recordings, optimal system parameters are recommended for a range of velocity fields in order to eliminate signal bias and to minimize loss of signal strength. It has been shown that signal bias resulting from velocity gradients in the flow field which exists in auto-correlation analysis can be eliminated in cross-correlation interrogation by appropriate choice of the optimal parameters. Comparisons of resolution, detection rate, accuracy and reliability are made with earlier direct auto-correlation methods for double and multiple-pulsed systems.