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. 2 Lecture 36. Micro-scale velocimetry

3. 3 Used to carry heat around a circuit - on-chip IC cooling, micro heat pipes Used to create forces - micro thrusters Used to transmit powers - micro pumps and turbines Used to transport materials - distribute cells, molecules to sensors Micro-scale Fluids

4. 4 Need for Microfluidic Diagnostics Even though Re«1, flows still complicated Large surface roughness Imprecise boundary conditions Two-phase, non-Newtonian fluids Coupled hydrodynamics and electrodynamics Non-continuum effects

5. 5 Full-field Microfluidic Velocimetry X-ray microimaging Lanzillotto, et al., Proc. ASME, 1996, AD52, 789-795. Molecular-Tagging Velocimetry (MTV) Paul, et al., Anal. Chem., 1998, 70, 2459-2467. Micro-Particle Image Velocimetry (  PIV) Santiago, et al., Exp. Fluids, 1998, 25(4), 316-319.

6. 6 X-ray Microimaging X-rays Positives Can image inside normally opaque devices Negatives low resolution ~20-40  m depth averaged (2-D) requires slurry to scatter x-rays Phosphor screen

7. 7 Molecular-Tagging Velocimetry Positives minimally intrusive better with electrically- driven flows Negatives low resolution ~20-40  m depth averaged (2-D) greatly affected by diffusion UV laser Blue laser - working fluid contains photochromic indicator- temporarily capable of absorbing photons in red-green range after illuminated by ultraviolet light

8. 8 Micro-Particle Image Velocimetry Positives high resolution ~1  m small depth average ~2-10  m minimally intrusive Negatives requires seeding flow particles can become charged Pulse laser CCD microscope

9. 9 Flood Illumination =532 nm = 610 nm Nd:YAG LASER MICROSCOPE BEAM EXPANDER CCD CAMERA MCROFLUIDIC DEVICE Nd:YAG Laser Micro Device Flow in Flow out Glass cover CCD Camera (1280x1024 pixels) Beam Expander Epi-fluorescent Prism / Filter Cube Microscope Focal Plane Micro-PIV image pair Micro-Fluidics Lab Purdue University Typical MPIV System

10. 10 –Micro-scale resolution Dimension of investigated flow structure in region of 1  m – 1 mm Nano-scale particles used –Volume (flood) illumination Micro-scale light sheet not available 2D measurement in focus plane of microscope objective –Fluorescent technique Fluorescent particles e.g. excited by =532nm and emitting =610nm Low-pass or band-pass optical filters used to reduce noises Typical MPIV System

11. 11 –Typical problems Low signal to noise ratio because of –Low light intensity of nano-scale particles –Low light intensity of back scattering imaging –Illuminated particles out of focus plane Low particle image concentration Brownian motion of nano-scale particles Diffraction of nano-scale particles Large particle image displacement because of high magnification and time interval limit etc Typical MPIV System

12. 12 2 mm longest vector~2.25 mm/s (Provided by Micro Fluidics Lab at Purdue University) Example: Microcantilever Driven Flow

13. 13 Typical MPIV Image Microthruster: Magnification 40X Particle size 700 nm 500  m - Background image filtered - Particle image size d p =5  8 pixels - Image displacements S= 15  40 pixels - Image number density 3 in 32x32-pixel window

14. 14 MPIV Image Filter Typical MPIV image features - High single-pixel random noise level because of low light intensity scattered/emitted by nano-scale particles - High low-frequency noise level because of particle images out of the focus plane - Big particle images (d p >4 pixels, d p <4 pixels for standard PIV) because of high imaging magnification MPIV filter: For SP noiseFor LF noise - Filter radius r big enough so that useful particle image information not be erased

15. 15 MPIV Image Filter - Reduce influence of LF noises on the evaluation function Evaluation samplesEvaluation functions - Overall effect of MPIV in a micro-channel flow measurement Mean velocity profileStandard deviation

16. 16 Correlation functions of replicated measurements at one point in the steady flow: - position of the main correlation peak not change - height and position of correlation peaks resulting from noises vary randomly Average evaluation function method (Meinhart, Wereley and Santiago, 2000) - average instantaneous evaluation functions to increase the signal-to-noise rato - only for steady laminar flows + ++ = Average Correlation Function

17. Long-distance Forward-Scattering MPIV Problem/solution for applying PIV in micro-scale air jet flow 1. Seeding - more difficult than in liquid flow 2. Working distance - long for micro-scale air jet flow 3. Illumination - insufficient for sub-micron particles 4. High velocity - limited by high imaging magnification 5. Low image number density & unsteady flow - average correlation impossible - smoke particles (Raffel et al.: d p <  m) - long-distance microscope (QUESTAR QM 100: WD>100 mm) - forward-scattering configuration (Raffel et al.:  10 3 ) - advanced imaging system (PCO200: ∆t=200 ns) - individual image pattern tracking 17

18. 18 Long-distance Forward-Scattering MPIV Experimental setup

19. 19 Long-distance Forward-Scattering MPIV Test & data acquisition Reduced image size 1024  256 pix for 60 fps (30 image pairs per second) 3 partitions in 4-GB memory for 3 axial positions in each test case Working distance 120 mm for measurement area 960  240  m 2 (0.94  m/pixel ) 1676 recording pairs in each group Time interval 200 ns PCO2000 camera 14-bit dynamic range 4-GB image memory 14.7 fps @ 2048  2048 pix Questar QM 100 Working distance up to 350 mm New Wave Solo II-30 532 nm Beam diameter: 2.5 mm Repetition Rate: 30 Hz

20. Sample PIV recordings pairs (red: 1st image, green: 2nd image) Vector maps obtained by individual particle image pattern tracking 20 Long-distance Forward-Scattering MPIV

21. 21 Long-distance Forward-Scattering MPIV Overlapped sample PIV recordings pairs (50 pairs) Overlapped vector maps (50 vector maps)

22. 22 Long-distance Forward-Scattering MPIV Remove erroneous vectors by using a median filter Calculate local mean, fluctuation & correlation on a regular grid (Test at y/D = 1.5, Re  3200, 1676 vector maps, 802412 raw vectors, 559259 valid vectors)

23. 23 Long-distance Forward-Scattering MPIV Mean velocity and velocity fluctuation at 3 positions along the jet axis (D=500 μm, Re  3200) High-speed air jet test results

24. 24 Meinhart CD, Wereley ST, Gray MHB (2000) Volume illumination for two- dimensional particle image velocimetry. Meas. Sci. Technol. 11, pp. 809-814 Wereley ST, Gui L, Meinhart CD (2002) Advanced algorithms for microscale velocimetry, AIAA Journal, Vol. 40, #6 References

25. 25 Matlab function for 4-P CDIC function[g]=sample4P(G,M,N,Xm,Ym,Sx,Sy,C) %INPUT PARAMETERS % G - gray value distribution of the PIV recording % M - interrogation sample width % N - interrogation sample height % Xm,Ym - interrogation sample location % Sx,Sy - displacements at 9 points % C=-1 for f1(i,j), C=1 for f2(i,j) % OUTPUT PARAMETERS % g - gray value distribution of the evaluation sample [nx ny]=size(G); % image size Xws=Sx(5);% window shift Yws=Sy(5); Xdis=Sx-(Sx(1)+Sx(3)+Sx(7)+Sx(9))/4; % distortion function Ydis=Sy-(Sy(1)+Sy(3)+Sy(7)+Sy(9))/4; % at 9 points Xpix=C*(Xws+Xdis)/2; % pixel displacement Ypix=C*(Yws+Ydis)/2; % at 9 points - Window shift determined with displacement in the window center, i.e. S ws =S 5 - Image distortion at the 4 points determined as - 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 C=-1:C=+1:

26. 26 Matlab function for 4-P CDIC gm=0; % initial average gray value nr=0; % initial number of effective pixels for i=1:M% column loop start for j=1:N % row loop start A=(M-i)*(N-j)/double((M-1)*(N-1)); % weighting coefficient for point 1 B=(i-1)*(N-j)/double((M-1)*(N-1)); % weighting coefficient for point 3 C=(M-i)*(j-1)/double((M-1)*(N-1)); % weighting coefficient for point 7 D=(i-1)*(j-1)/double((M-1)*(N-1)); % weighting coefficient for point 9 x_pix=Xpix(1)*A+Xpix(3)*B+Xpix(7)*C+Xpix(9)*D; % pixel displacement at current pixel y_pix=Ypix(1)*A+Ypix(3)*B+Ypix(7)*C+Ypix(9)*D; % pixel displacement at current pixel X=Xm+x_pix-M/2+i; % corresponding x position of current pixel in the PIV recording Y=Ym+y_pix-N/2+j; % corresponding y position of current pixel in the PIV recording I=int16(X);% integer portion of x-position J=int16(Y); % integer portion of y-position x=double(X)-double(I); % decimal portion of x-position y=double(Y)-double(J); % decimal portion of y-position if x<0 % adjust values so that x≥0, y≥0 I=I-1; x=x+1; end if y<0 J=J-1; y=y+1; end A C B D i=1 j=1 j=N i=M 1 3 79

27. 27 Matlab function for 4-P CDIC if I>=1 & I =1 & J<ny % limited in the image frame Ga=double(G(I,J));% gray value at integer pixels Gb=double(G(I+1,J)); Gc=double(G(I,J+1)); Gd=double(G(I+1,J+1)); A=(1-x)*(1-y);% weighting coefficients for interpolation B=x*(1-y); C=(1-x)*y; D=x*y; g(i,j)=A*Ga+B*Gb+C*Gc+D*Gd; % bilinear interpolation gm=gm+g(i,j); % sum of gray values for averaging nr=nr+1; % count number of effective pixels else g(i,j)=-1; % temporary value for pixel out of image frame end end % row loop end end % column loop end gm=gm/double(nr); % average gray value of effective pixels for i=1:M for j=1:N if g(i,j)<0 g(i,j)=gm; % fill with average value for pixel out of image frame end A C B D I J J+1 I+1 Ga Gb GcGd

28. 28 Matlab program for 4-P CDIC clear; % clear variables A1=imread('A001_1.bmp'); % input 1st image in the recording pair A2=imread('A001_2.bmp'); % input 2nd image file G1=img2xy(A1); % convert image to gray value distribution G2=img2xy(A2); % convert image to gray value distribution Mg=16; % interrogation grid width Ng=16; % interrogation grid height M=2*Mg; % interrogation window width w. 50% overlap N=2*Ng; % interrogation window height w. 50% overlap sr1=12; % initial search radius sr2=6; % final search radius NN=6; % iteration number dU=[-12 12 3]; % parameters for error detection dV=[-12 12 3]; % parameters for error detection [nx ny]=size(G1); % determine size of the image col=400/Mg; % number of grid rows in limited area of 400-pixel in height fow=400/Ng; % number of grid columns in limited area of 400-pixel in width

29. 29 Matlab program for 4-P CDIC for i=1:col for j=1:row X(i,j)=double((i-1)*Mg+400); % x-position of interrogation point Y(i,j)=double((j-1)*Ng+300); % y-position of interrogation point U(i,j)=double(0); % initial particle image displacement in x-direction V(i,j)=double(0); % initial particle image displacement in y-direction end for nn=1:NN % iteration begin sr=int16((nn-1)*(sr2-sr1)/(NN-1)+sr1); % determine search radius if nn>1 [U V valid]=interpolation(U,V, valid); % interpolation for at wrong vectors [U V valid]=interpolation(U,V, valid); % second pass of interpolation end % iteration may be necessary in complicated case

30. 30 Matlab program for 4-P CDIC for i=1:col % column loop start for j=1:row % row loop start if nn==1 wsx=0; % set window shift to 0 in the first run wsy=0; else if valid(i,j)>0 wsx=U(i,j); % window shift determined with previous evaluation wsy=V(i,j); end nr=0; % determining particle image displacement at 9 points in the window begin for q=-1:1 for p=-1:1 nr=nr+1; % number of grid point in the window if i>1 & i 1 & j 1 % after the first run & when all the 9 pints have valid vectors sx(nr)=U(i+p,j+q); % determine displacements at 9 points in the window sy(nr)=V(i+p,j+q); % with results of previous evaluation else sx(nr)=wsx; % ignore image distortion sy(nr)=wsy; end end % determining particle image displacement at 9 points in the window end

31. 31 Matlab program for 4-P CDIC x=X(i,j); % determine horizontal coordinate of interrogation point y=Y(i,j); % determine vertical coordinate of interrogation point g1=sample4P(G1,M,N,x,y, sx, sy, -1); % evaluation sample with backward image correction g2=sample4P(G2,M,N,x,y, sx, sy, 1); % evaluation sample with forward image correction [C m n]=correlation(g1,g2); % calculating correlation function [cm vx vy]=peaksearch(C,m,n,sr,0,0); % determine particle image displacement U(i,j)=vx+wsx; % adjust particle image displacement with window shift V(i,j)=vy+wsy; % adjust particle image displacement with window shift end % row loop end end % column loop end valid=errordetection(U,V,dU,dV); % detect evaluation errors end % iteration end quiver(X,Y,U,V); % plot vector map

33. 33 Class project report content 1. Description of the problem 2. Description of methods used to solve the problem 3. Flow chart of computer program 4. Description of Matlab main program and functions - Matlab functions and main programs demonstrated in class can be used as reference - modification and improvement are encouraged 5. Presentation of results - 2D velocity vector plot with xy-coordinates in mm - reference vector or color map to show magnitude in m/s 6. Conclusion & discussions