1. Folie 1 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

2. Folie 2 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 for 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 least- squares fitting (suitable for silhouette images from schlieren, etc.) Assumptions: no changes to body profile; motion two dimensional + one axis of rotation

3. Folie 3 Analytic-fitting technique Edge detection Model edge tracing and sub- pixel detection Least-squares fitting

4. Folie 4 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

5. Folie 5 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

6. 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 edge- point pair

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

8. Folie 8 Application of edge-tracking technique

9. Folie 9 Error estimation through artificial image analysis Errors introduced by pixellation/edge- detection (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

10. Folie 10 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

11. 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

12. Folie 12 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

13. Folie 13 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?

14. Folie 14 Application of edge-tracking technique

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

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

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