Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui

2 Lecture 37. Stereo Particle Image Velocimetry

3 Stereo PIV system –Two cameras –Translation and angular configurations –Distorted particle images (angular system) –3-D displacement reduced from two 2-D displacements –3 velocity components in a plane Stereoscopic PIV Example G. Calcagno, F.D. Felice, M. Felli, and F. Pereira, 24 th Sym. Naval Hydro. (2002) Test region Test result

4 Laser light sheet X Z Stereoscopic PIV SPIV data reduction t=t 0 t=t 0 +  t S Laser light sheet X Z S XX ZZ Standard PIV view XX  Z not sensible

5 Stereoscopic PIV SPIV data reduction Laser light sheet X Z S XX ZZ 11 X1X1 camera #1 X2X2 22 camera #2 Stereo view

6 Stereoscopic PIV SPIV data reduction - Particle image displacements: (  X’ 1,  Y’ 1 ) and (  X’ 2,  Y’ 2 ) - Imaging scale factor: M 1 and M 2 No stereo effect in yz-plane

7 Stereoscopic PIV Error propagation in SPIV

8 Stereoscopic PIV Error propagation in SPIV

9 Stereoscopic PIV Error propagation in SPIV Define:

10 Stereoscopic PIV Error propagation in SPIV - Optimal view angle 45 

11 Camera #1Camera #2 Lens Plane  Stereoscopic PIV - Object plane || Lens plane || Image plane - Uniform magnification (M n =d i /d o ) - Easy to focus - Off-axis angle  restricted by the lens (application limited) Translation (lateral displacement) system

12 Object planeLens planeImage plane Mirror pair 1 Mirror pair 2 Aperture stop Stereoscopic PIV Translation (lateral displacement) system - Single camera configuration - View angle  is limited Test region Image #1 Image #2

13 Stereoscopic PIV Rotational (angular displacement) system - Scheimpflug condition - Distorted image (M n  constant)

14 Stereoscopic PIV SPIV recording evaluation 1. Evaluation with image calibration Distorted ImageCalibrated ImageVelocity map Positive: a. Uniform spatial resolution b. Simple procedure Negative: Image interpolation error Image calibration methods Polynomial mapping Preservation of straightness of lines – for high quality camera lens

15 Stereoscopic PIV SPIV recording evaluation 2.Evaluation with velocity calibration Distorted ImageVelocity mapVelocity calibration Positive: No image interpolation Negative: a. Non-uniform spatial resolution b. Evaluation grid transfer required Basic evaluation steps: 1.Determine transformation function between physical and image plane 2.Transfer uniform evaluation grid in physical plane to image plane 3.Evaluate the distorted SPIV recordings with the transformed evaluation grid 4.Transfer the evaluated displacement components to the physical plane

16 –References Prasad AK (2000) Stereoscopic particle image velocimetry. Exp. Fluids 29, pp Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, pp –Practice with EDPIV Compare image calibration and vector calibration with application example #9 Stereoscopic PIV

17 Large-Scale PIV River surface flow measurement City map river Tower Video set at 40m height Camera view Floating tracer

18 Large-Scale PIV River surface flow measurement Original image Calibrated image Physical & image coordinates Flow filed

19 Large-Scale PIV Distorted image calibration Physical & image coordinates - Physical coordinates (X,Y) - Image coordinates (x,y) - Calibration marking points (X k,Y k )  (x k,y k ) for k=1,2, ,N - Image calibration function Minimal N=4 for determining constants b i (i=1,2, ,8) - inverse calibration function Straight-line-conserved transformation

20 Large-Scale PIV Distorted image calibration 4 marking points >4 marking points – least square approach

21 Large-Scale PIV Evaluation of LSPIV recordings - Low-Image-Density PIV mode Particle image tracking or individual particle image pattern tracking - Low Re-number in many cases Average correlation method for steady flows Consecutive LSPIV recordingsEvaluation results Example of LSPIV tests for steady water surface flow

22 Large-Scale PIV –References Muto Y, Baba Y, Aya S (2002) Velocity measurements in open channel flow with rectangular embayments formed by spur dykes. Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No.45B-2 Fujita I, Aya S, Deguchi T (1997) Surface velocity measurement of river flow using video images of an oblique angle. Proc. 27 th IAHR Cong., San Francisco, Vol.B, No.1, pp –Practice with EDPIV Work with sample: IMAGE GROUP: DISTORTED PIV IMAGES