1. 1 Imaging Techniques for Flow and Motion Measurement Lecture 21 Lichuan Gui University of Mississippi 2011 Shadowgraph, Schielieren and Speckle Photography

2. 2 Refractive Index in Gas e – charge of an electron m e – mass of an electron L – Loschmidt’s number m – molecular weight – frequency of visualizing light i – resonant frequency of distorted electron f i – oscillator strength of distorted electron The Gladstone-Dale Formula: n – refractive index K – Gladstone-Dale constant  – density In gas mixture of N components:

3. 3 Deflection of Light Ray in Gas Refractive index in compressible flow at certain time: Light ray in an inhomogeneous refractive field: - Undisturbed light ray would arrive at Q - Deflected light ray arrives at point Q* - Optical length covered by deflected ray different from that of undisturbed i.e. t*  t Quantities can be measured in photographic film: - The displacement - The angular deflection - The phase shift between both rays Shadowgraph Schlieren method Mach-Zehnder interferometer

4. 4 Deflection of Light Ray in Gas Relations between refractive index and measured quantities:

5. 5 Shadowgraph Schematic arrangement of two typical shadowgraph systems Light source Spherical mirrors or lenses Optical disturbance (test object) Photo film or screen Camera lens Focus plane

6. 6 Shadowgraph Working principle: detecting second derivatives z y PhObject Uniform illumination Non-uniform illumination

7. 7 Shadowgraph APLLICATION: DETACHED SHOCK WAVE The shadowgraph of a supersonic flow around a finned hemisphere The bow shock is detached Because of the blunt body. The flow behind the nearly normal portion of the shock is subsonic. Thus, no Mach waves are seen near the line of symmetry. As the subsonic flow sweeps over the body, it accelerates, ultimately becomes sonic and then supersonic. The position of the transition to supersonic flow can be estimated by noting the position of the first appearance of Mach lines on the body. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

8. 8 Shadowgraph APPLICATION: A.308 CALIBER BULLET Shadowgraph of Winchester.308 caliber bullet traveling at about 2800 ft/sec, M=2.5. Curvature of the Mach lines generated at the nose Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

9. 9 Shadowgraph APPLICATION: SHOCK WAVES AROUND THE X-15 Classical shock wave pattern around a free-flight model of the X-15 at M=3.5. In the lower half of the image, the convergence of the downstream shocks with the main bow shock is clearly seen. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

10. Imaging techniques for fluid flow measurements10 Schlieren Method Schematic arrangement of a Toeplor Schlieren system Optical disturbance (test object) Photo film or screen Light source Spherical mirrors or lenses Detecting 1st derivatives

11. 11 Schlieren Method Different configurations of Schlieren system Z-shaped system Double-path systems

12. 12 APPLICATION: PENETRATION OF ALUMINUM FOIL BY A BULLET Pattern of waves generated as a.222 caliber bullet passes through a hanging sheet of aluminum foil. The reflected shock is clearly seen at the left of the foil. A second spherical shock surface can be seen on the right side of the foil. The small disturbances just behind the shock are bits of the foil ejected at impact. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/ Schlieren Method

13. 13 APPLICATION: REFRACTION OF SHOCK WAVES The schlieren photo at the right reveals the pattern of waves generated by a.222 caliber bullet traveling at about Mach 3. The bullet has just passed through the plume of a candle and the different densities in the heated plume have refracted the lower set of shock waves. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/ Schlieren Method

14. 14 Full-Scale Schlieren Images Schlieren Method Heat Released from Gas Grill Heat from space heater, lamp& person Cold Air Dragged From A Freezer From http://www.mne.psu.edu/psgdl/FSSPhotoalbum/index1.htm

15. 15 Speckle Photography Two schemes of Speckle pattern formation Example of digital speckle image

16. 16 Speckle Photography Two possible configuration of the system: 1. Object between light source and speckle generator

17. 17 Speckle Photography Two possible configuration of the system: 2. Speckle generator between light source and object

18. 18 Speckle Photography Example of speckle photography system: (U Köpf 1972)

19. 19 Speckle Photography (Wernekinck and Merzkirch 1986) Example of speckle photography system:

20. 20 Speckle Photography Evaluation of speckle photograph - Young’s fringes method - Correlation-based digital interrogation

21. Background Oriented Schlieren (BOS) 21 A simplified speckle photography technique: White light Speckle generator between light source and object Background image Background image between light source and object

22. 22 Background Oriented Schlieren (BOS) Ring method for axis symmetric density field reconstruction - Density field includes k=1,2,3, , M rings - Known environment density n 0 - Constant density n k in rings - Compute n k from outside to inside

23. 23 Background Oriented Schlieren (BOS) Ring method for axis symmetric density field reconstruction Known variables at y k : n k+1,  * k,  ’ k Variable to be determined: n k

24. 24 Background Oriented Schlieren (BOS) Application in jet flow test:

25. –References F. Klinge, T. Kirmse, J. Kompenhans (2003) Application of Quantitative Background Oriented Schlieren (BOS): Investigation of a Wing Tip Vortex in a Transonic Wind Tunnel. Proceedings of PSFVIP-4, June 3- 5, Chamonix, France –Final report Taking part in a BOS test Processing a pair of BOS recording Completing a report including 1. brief description of the BOS technique 2. brief description of the experimental setup 3. vector plot of background image displacement 4. contour plot of density distribution Homework