1. 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 lichuan-gui@uiowa.edu http://lcgui.net Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes.

2. Lecture 34. Multi-phase flow PIV techniques

3. 3 Fluorescent Technique Example: Orange solid particles in water and air flow using green laser Red channelGreen channelBlue channel True color recordings Phase separation

4. 4 Fluorescent Technique Background noise elimination Example: Fluorescent particles used in Micro PIV Micro channelMicro PIV recording

5. 5 Digital Mask Technique Phase separation according to particle image size Example: Solid particle in seeded water flow - Identify particle images in the recording and compute size of each particle image; - Extract image of the dispersed phase: Keep particle images bigger than a given threshold and fill the rest with zero - Extract image of the continuous phase: Set pixel values of the big particle images to zero or background intensity 2 phase recordingImage for big particlesImage for small particles

6. 6 Digital Mask Technique Evaluation results of the correlation-based interrogation - Without phase separation, uncertainty arises around interface of different phases; - Influence of dispersed phase (big particles) cannot be completely eliminated by just removing the big particle images Results w/o phase separationResults of small particle image Phase separation according to particle image size

7. 7 Digital Mask Technique Phase mask 2-Phase PIV recording G(x,y) Phase mask  (x,y) i o j g(i,j) xo y xo y i o j  (i,j) Define:

8. 8 Digital Mask Technique Phase mask applied to dispersed phase Schematic illumination of the masking procedure

9. 9 Digital Mask Technique Phase mask applied to dispersed phase Masked evaluation function - MQD function Define:

10. 10 Digital Mask Technique Phase mask applied to dispersed phase Masked evaluation function Define:and Define: correlation-based mask tech. MQD-based mask tech.

11. 11 Digital Mask Technique Phase mask applied to continuous phase Schematic illumination of the masking procedure

12. 12 Digital Mask Technique Phase mask applied to continuous phase Masked evaluation function - MQD function averaged with effective pixel numbers

13. 13 Digital Mask Technique Phase mask applied to continuous phase Masked evaluation function Define:

14. 14 Digital Mask Technique Phase mask applied to continuous phase Masked evaluation function Define: MQD-based evaluation function: Correlation-based evaluation function: For both correlation interrogation and tracking C 1, C 2, C 3 and C 4 are correlation travcking functions

15. 15 Digital Mask Technique Test of the phase mask for continuous phase Test samples: a – Original double exposed evaluation sample, b – Superimposed with a big particle image, c – Big particle image removed, d – Phase mask. Test results: a –  (m,n) for the original, b –  (m,n) for sample b, c –  (m,n) for sample c, d –  (m,n) phase masked.

16. 16 Results w/o phase separationResults of masked correlation Digital Mask Technique Evaluation results of the correlation-based interrogation - Without phase separation, uncertainty arises around interface of different phases; - With phase separation, velocity difference between 2 phases clarified. Phase-separated evaluation with digital mask

17. 17 Digital Mask Technique Application examples Two phase flows Bubbly water flowSolid/water flow

18. 18 Digital Mask Technique Application examples Elimination of visible background influence One of the PIV recording pairs at phase=0 (200  400 pixels / 13.3  26.7 mm 2 ) Phase averaged velocity Flow around a vibrating cantilever

19. 19 Digital Mask Technique Application examples Elimination of invisible background influence Flow around a blood cell

20. 20 Gui L, Merzkirch W (1996) Phase-separation of PIV measurements in two-phase flow by applying a digital mask technique. ERCOFTAC Bulletin 30: 45-48 Gui L, Wereley ST, Kim YH (2003) Advances and applications of the digital mask technique in Particle Image Velocimetry (PIV) experiments. Meas. Sci. Technol. 14, 1820-1828 References

21. 21 Definition - used to effectively remove low-frequency background noise in PIV recordings Fast computation of unsharp mask

22. A - Compute G sm (x,y) close to the edges of the image for x  r+1 or x> n x -r or y n y -r 22

23. Fast computation of unsharp mask 23 - Compute G sm (x,y) away from the edges of the image

24. Central difference window shift & image corection Clear correlation function high peak at the particle image displacement f 1 (i,j) f 2 (i,j) Correlation function improved with window shift (red) & image correction (blue) 24 4-P CDIC

25. Pixel displacement functions 25 4-P CDIC

26. 4-point image corection method - Window shift determined with displacement in the window center, i.e. S ws =S 5 - Image distortion at the 4 points determined as - S dis (i,j) determined with bilinear interpolation according to S dis (k) - f(i,j) determined with bilinear interpolation according to S ws and S dis (i,j) - Particle image sisplacements at center and 4 corners (i.e. S 1, S 3, S 5, S 7, S 9 ) determined according to a previus evaluation 123 46 789 5 Interrogation window - Mutipass interrogation with iterated number aropund 6. 26 4-P CDIC

27. 27 4-P CDIC - 50% interrogation overlapp to determine particle image displacements at 5 points. 123 46 789 5 Interrogation window - Bilinear interpolation to determine distortion function at each pixel in the interrogation window. - Bilinear interpolation to determine gray value of ech pixel. Sx(1)=U(i-1,j-1) Sx(2)=U(i, j-1) Sx(3)=U(i+1,j-1) Sx(4)=U(i-1,j) Sx(5)=U(i, j) Sx(6)=U(i+1,j) Sx(7)=U(i-1,j+1) Sx(8)=U(i, j+1) Sx(9)=U(i+1,j+1) wsx=Sx(5) S_dis_x(k)=Sx(k)-(Sx(1)+Sx(3)+Sx(7)+Sx(9))/4; A=(M-i)*(N-j)/double((M-1)*(N-1)); B=(i-1)*(N-j)/double((M-1)*(N-1)); C=(M-i)*(j-1)/double((M-1)*(N-1)); D=(i-1)*(j-1)/double((M-1)*(N-1)); s_dis_x(i,j)=S_dis_x (1)*A+S_dis_x (3)*B+S_dis_x (7)*C+S_dis_x (9)*D; A=(1-x)*(1-y); B=x*(1-y); C=(1-x)*y; D=x*y; g(i,j)=A*Ga+B*Gb+C*Gc+D*Gd;% bilinear interpolation X=xm ± swx/2 ± s_dis_x(i,j)/2