High precision imagebased tracking of a rigid body

High precision image-based tracking of a rigid body moving within a fluid Stuart Laurence, Jan Martinez Schramm German Aerospace Center (DLR), Göttingen, Germany APS/DFD, 23 November 2010 Folie 1

Motivation Visualization-based techniques an attractive option for measuring displacements (and derived quantities) of rigid bodies in fluids, as they are completely non-intrusive Particularly attractive force-measurement in short-duration hypersonic facilities, as few other options available However, measurement precision critical – in past (film-based analog techniques) displacement measurements limited to ~50 μm Focus here on edge-detection-based techniques combined with leastsquares fitting (suitable for silhouette images from schlieren, etc. ) Assumptions: no changes to body profile; motion two dimensional + one axis of rotation Folie 2

Analytic-fitting technique Edge detection Model edge tracing and subpixel detection Least-squares fitting Folie 3

Free-flight measurements with analytic-fitting technique Image-based measurements show reasonable agreement with accelerometer measurements Response time for 14 kfps estimated to be ~0. 5 ms Folie 4

Problems with analytic-fitting technique Model cross-sectional profile must be expressible analytically (can be avoided by using, e. g. , splines) For all but simplest geometries, fitting procedure is iterative (slow!) Reasonably complete profile required for convergence Folie 5

Edge-tracking technique Based on matching closest edge-points in reference and displaced images Edge angle assumed to be the same for each edgepoint pair Folie 6

Edge-tracking technique Based on matching closest edge-points in reference and displaced images Edge angle assumed to be the same for each edgepoint pair linear least-squares problem for Δx and Δy a) no errors b) with errors Folie 7

Application of edge-tracking technique Folie 8

Error estimation through artificial image analysis Errors introduced by pixellation/edgedetection (can be reduced through more precise algorithms) and CCD noise (unavoidable at given light conditions) Such errors can be estimated through analysis of artificially constructed images Folie 9

Error determination from calibrated sphere measurements Precision-machined 40 -mm diameter sphere controlled by linear displacement stepper Magnification ~300 μm/pixel Position determination from tracking techniques compared with inputted displacements Standard error ~1. 3 μm (A) Shimadzu HPV-1; (B) Telephoto lens; (C) Precision-machined sphere; (D) Linear displacement stage; (E) Light source; (F) Light-diffusing material Folie 10

Errors in constant acceleration measurements Error in measured constant acceleration, a, can be determined from assumed displacement error (δ): (n = number of measurement points) For micron-level precision in displacement, accurate (~1%) acceleration measurements possible even for millisecond test times Folie 11

Errors in constant acceleration measurements Error in measured constant acceleration, a, can be determined from assumed displacement error (δ): (n = number of measurement points) For micron-level precision in displacement, accurate (~1%) acceleration measurements possible even for millisecond test times Folie 12

Conclusions Technique originally developed for bodies with analytically expressible cross-sections Generalized to arbitrary body geometries Displacement measurements to micron level for wind-tunnel scale models – allows acceleration measurements to <1% under typical conditions Generalization to three-dimensional motions? Folie 13

Application of edge-tracking technique Folie 14

Shock-wave surfing Error in edge-point locations Optical distortions can become problematic for large fields-of-view Can be corrected for using reference images Folie 15

Shock-wave surfing Displacements Optical distortions can become problematic for large fields-of-view Can be corrected for using reference images Folie 16

Shock-wave surfing Force coefficients Optical distortions can become problematic for large fields-of-view Can be corrected for using reference images Folie 17