1. © 2009, TSI Incorporated Stereoscopic Particle Image Velocimetry

2. © 2009, TSI Incorporated Stereoscopic PIV Need for Stereoscopic Measurements Most flows are three-dimensional in nature Need simultaneous measurement of the three orthogonal components 2D flow measurements using a Single camera –Edges of the images are viewed obliquely –Out-of-plane motion “appears” to be in-plane motion –Errors due to these need to be corrected Stereoscopic measurement eliminates these errors

3. © 2009, TSI Incorporated Stereoscopic Technique View the light sheet from two perspectives –Two cameras set up at different angles to illuminated plane Each camera captures a pair of images 2D image displacements for each camera image field –3D displacement obtained from the two 2D displacements Calibration or Mapping function generation –imaging point markers in the flow using both cameras calibration grid with equally spaced markers used –Effect of window refraction and distortion accounted for –Mapping function generates a one-to-one correspondence between marker positions and their image locations in the camera

4. © 2009, TSI Incorporated Particle Image Velocimetry 3 Component measurements Three Component PIV Measurements –Measurement of 3 components of velocity simultaneously –Illumination : using a light sheet –3 components of measurements in a plane

5. © 2009, TSI Incorporated System Components PIV laser and light sheet optics Two P OWER V IEW ( or PIVCAM ) cameras, lenses Mounting fixture for the Scheimpflüg configuration Two high speed camera interfaces Stereoscopic camera alignment mount Dual-plane Dual-sided (DPDS) target plate LaserPulse Synchronizer Stereoscopic I NSIGHT software package Tecplot –includes Tecplot package

6. © 2009, TSI Incorporated Scheimpflüg Stereoscopic Arrangements back-scatter forward-scatter side-scatter Measurement plane parallel to the bisector of the camera axes

7. © 2009, TSI Incorporated Plane of Focus Out of Focus: behind plane of focus Out of Focus: in front of plane of focus Point of Focus CCD Array Camera Lens Only Particles in the light sheet can be captured by the camera The plane of focus is parallel to the sensing array Portions of light sheet in front of and behind the plane of focus are out of focus Scheimpflüg Stereoscopic Arrangement

8. © 2009, TSI Incorporated Scheimpflüg Stereoscopic Arrangement Object plane (Light sheet) Lens principal plane Scheimpflüg Condition Plane of Focus Axis of Sensing Array Axis of Lens By rotating the sensing array with respect to the lens plane most of the objective plane can be focused

9. © 2009, TSI Incorporated Scheimpflüg Stereoscopic Arrangement Object plane (Light sheet) Combine for a 3D Vector Left Camera ViewRight Camera View

10. © 2009, TSI Incorporated Velocity vector in the light sheet Z x f = (x +  x, y +  y, z +  z ) Image plane XiXi XfXf d1d1 d0d0 XX Y - axis normal to the plane of the paper B x i = (x, y, z) A xx Laser light sheet

11. © 2009, TSI Incorporated 3-D Displacements in the flow  X left =  x fluid (dX left /dx fluid )+  y fluid (dX left /dy fluid )+  z fluid (dX left /dz fluid )  Y left =  x fluid (dY left /dx fluid )+  y fluid (dY left /dy fluid )+  z fluid (dY left /dz fluid )  X right =  x fluid (dX right /dx fluid ) +  y fluid (dX right /dy fluid )+  z fluid (dX right /dz fluid )  Y right =  x fluid (dY right /dx fluid ) +  y fluid (dY right /dy fluid )+  z fluid (dY right /dz fluid )  X,  Y are the measured image displacements -  x left corresponds to the image displacement in the left camera  x,  y and  z are the particle displacements in the flow

12. © 2009, TSI Incorporated Perspective effect due to camera tilt A A B B B B A A A A B B Regular grid in fluid Left camera image of grid Right camera image of grid

13. © 2009, TSI Incorporated Stereoscopic technique - Calibration Image recording plane Camera 1 Image recording plane Camera 2 Calibration target Refracting wall Registration of the two cameras - align to view the same region Distortion correction due to different media Generates mapping function to map the vectors in the camera plane back to the object plane

14. © 2009, TSI Incorporated Mapping function generation Calibration Use rectangular grid of dots as calibration plate –Plate with grid markings Dual-Plane Dual-Sided (DPDS)Target –Introduced by TSI –No need to traverse –Plate with grid markings in multiple planes on both sides of the plate Calibration grid defines the coordinate system Align the calibration plate with the light sheet DPDS Target

15. © 2009, TSI Incorporated Calibration Target Dual-plane target Image of the target from the left camera Image of the target from the right camera

16. © 2009, TSI Incorporated Display and Post Processing INSIGHT Stereo & TecPlot

17. © 2009, TSI Incorporated Remote control for PIV systems Remote Scheimpflug control Remote focusing Remote aperture control –Used for Underwater applications, Large tunnels Facilities where remote access is needed

18. © 2009, TSI Incorporated Guidelines for good Results Interrogation spot size small enough so that one vector correctly describes the flow within that region –velocity gradient within the region is negligible Three or more particle pairs per interrogation spot –improvement in accuracy is small for cases for more than 5 pairs of images Max. in-plane displacement –< 1/4 of interrogation spot size Min. in-plane displacement –could be zero Maximum out of plane displacement –Less than ¼ of light sheet thickness