Toensuregoodparticleimagevelocimetrycorrelations,itisnecessarytocharacterizetheimportantvariablesthat control image acquisition and image analysis. Among these, image spot size as it changes across the entire imaging surfacebearsinvestigation.Therefore, wedescribeanerroranalysisforsubpixel resolutionofcorrelation peaksus- ingWhittaker' smethod.Theseresultsseta toleranceonoptimumimagespotsizes.Typicallensesarethenanalyzed usingray-tracesoftware,toascertainwhatopticalparametersandcameramisalignmentsareallowablewithinthese optimum tolerances. We then describe an alignment procedure that allows us to set a camera to those tolerances. O acquire high-quality particle image velocimetry (PIV) data, it is necessary to use a cross-correlation technique, for exam- ple, two-color or image-shifted PIV, to align carefully the optical system and use an optimized data analysis package. In recent work performed at the Colorado School of Mines (CSM), two PIV inves- tigations resultedin1 )an assessmentofthe effects ofparticleimage spot size on correlation accuracy, 2 ) determination of the minimum spot size for least error, and 3 ) the development of an experimental system that can reliably generate this minimum spot size. One of these projects involved the development of PIV analy- sis software that generates vector data from PIV images (Ref. 1; T. Drouillard and M. Linne, Experiments in Fluids, manuscript in preparation ). In that work, several techniques for resolving cor- relation peaks were evaluated. These included the basic centroid method, Whittaker' s reconstruction, an analytical three-pointGaus- sian e t, and a numerical e ve-point Gaussian e t using the Marquardt method. An assessment of reconstruction errors was included. The least error was produced by the e ve-point Gaussian e t using Mar- quardt nonlinear e tting, whereas Whittaker' s reconstruction was a close second. Furthermore, it was found that the size of the cor- relation peak (directly related to particle image spot size ) has the greatest effect on the accuracy of the reconstruction algorithm. This sets a tolerance on the image spot size. That work is discussed in detail by Drouillard and Linne (manuscript in preparation ). Asecond projectinvolvedthe development of a method by which a PIV experimental apparatus may beconsistently and reproducibly aligned to meet this tolerance on spot size. 2 This topic is of primary importance to chemical e lm-based techniques, where turnaround time is very long. It also has implications for digital systems, espe- cially when it is necessary to align a camera across a large system, from within a wind tunnel, for example. A portion of this inves- tigation included modeling photographic lens performance under ideal and nonideal conditions using computer-based geometric ray tracing.These resultsprovide insightinto howvariousexperimental cone gurations can lead to spot size variation, which in turn affects the accuracy of PIV analysis. Based on such results, a system for alignment of the experiment was developed. That work is the pri- mary focus of this paper.
Read full abstract