Instructor: Lichuan Gui lichuan-gui@uiowa lcgui

1. Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes. Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)Time & Location: 2:30P - 3:20P MWF 218 MLHOffice Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

2. Lecture 34. Multi-phase flow PIV techniques

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

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

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 recording Image for big particles Image for small particles

6. Digital Mask Technique • Phase separation according to particle image size 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 separation Results of small particle image

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

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

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

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

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

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

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

14. Define: MQD-based evaluation function: C1, C2, C3 and C4 are correlation travcking functions Correlation-based evaluation function: For both correlation interrogation and tracking Digital Mask Technique • Phase mask applied to continuous phase Masked evaluation function

15. 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. Digital Mask Technique • Test of the phase mask for continuous phase

16. Digital Mask Technique • Phase-separated evaluation with digital mask 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. Results w/o phase separation Results of masked correlation

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

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 mm2) Phase averaged velocity Flow around a vibrating cantilever

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

20. References • 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

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

22. Fast computation of unsharp mask - Compute Gsm(x,y) close to the edges of the image forx  r+1 or x> nx-r or y< r+1 or y>ny-r A

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

24. 4-P CDIC 24 Central difference window shift & image corection f1(i,j) f2(i,j) Correlation function improved with window shift (red) & image correction (blue) Clear correlation function high peak at the particle image displacement

25. 4-P CDIC Pixel displacement functions

26. 4-P CDIC 7 8 9 4 5 6 1 2 3 4-point image corection method Interrogation window - Particle image sisplacements at center and 4 corners (i.e. S1,S3,S5,S7,S9) determined according to a previus evaluation - Window shift determined with displacement in the window center, i.e. Sws=S5 - Image distortion at the 4 points determined as - Sdis(i,j) determined with bilinear interpolation according to Sdis(k) - f(i,j) determined with bilinear interpolation according to Sws and Sdis(i,j) - Mutipass interrogation with iterated number aropund 6.

27. 4-P CDIC 7 8 9 4 5 6 1 2 3 - 50% interrogation overlapp to determine particle image displacements at 5 points. Sx(4)=U(i-1,j) Sx(1)=U(i-1,j-1) Sx(7)=U(i-1,j+1) Interrogation window Sx(5)=U(i, j) Sx(2)=U(i , j-1) Sx(8)=U(i, j+1) Sx(6)=U(i+1,j) Sx(3)=U(i+1,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; - Bilinear interpolation to determine distortion function at each pixel in the interrogation window. 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; X=xm±swx/2 ±s_dis_x(i,j)/2 - Bilinear interpolation to determine gray value of ech pixel. 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