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Instructor: Lichuan Gui lichuan-gui@uiowa lcgui

Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes. 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

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Instructor: Lichuan Gui lichuan-gui@uiowa lcgui

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  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 36. Micro-scale velocimetry

  3. Micro-scale Fluids • 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

  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. Full-field Microfluidic Velocimetry • X-ray microimagingLanzillotto, 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 (MPIV)Santiago, et al., Exp. Fluids, 1998, 25(4), 316-319.

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

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

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

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

  10. Typical MPIV System • 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 particlese.g. excited by =532nm and emitting =610nm • Low-pass or band-pass optical filters used to reduce noises

  11. Typical MPIV System • 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

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

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

  14. For SP noise For LF noise 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 (dp>4 pixels, dp <4 pixels for standard PIV) because of high imaging magnification MPIV filter: - Filter radius r big enough so that useful particle image information not be erased

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

  16. + = + ••••• + Average Correlation Function 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

  17. - more difficult than in liquid flow 1. Seeding - long for micro-scale air jet flow 2. Working distance - insufficient for sub-micron particles 3. Illumination - limited by high imaging magnification 4. High velocity - average correlation impossible 5. Low image number density & unsteady flow Long-distance Forward-Scattering MPIV Problem/solution for applying PIV in micro-scale air jet flow - smoke particles (Raffel et al.: dp<m) - long-distance microscope (QUESTAR QM 100: WD>100 mm) - forward-scattering configuration (Raffel et al.: 103) - advanced imaging system (PCO200: ∆t=200 ns) - individual image pattern tracking 17

  18. Long-distance Forward-Scattering MPIV Experimental setup

  19. New Wave Solo II-30 532 nm Beam diameter: 2.5 mm Repetition Rate: 30 Hz 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 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 m2 (0.94 m/pixel) 1676 recording pairs in each group Time interval 200 ns

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

  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 • High-speed air jet test results Mean velocity and velocity fluctuation at 3 positions along the jet axis (D=500 μm, Re  3200)

  24. References • MeinhartCD, 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 microscalevelocimetry, AIAA Journal, Vol. 40, #6

  25. Matlab function for 4-P CDIC 7 8 9 4 5 6 1 2 3 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 [nxny]=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 - 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 C=+1: C=-1:

  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 j=N B A D C j=1 i=1 i=M 1 3 7 9

  27. Matlab function for 4-P CDIC if I>=1 & I<nx & J>=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 end end J+1 B A D C J I I+1 Gd Gc Ga Gb

  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 [nxny]=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. 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 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. 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 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<col & j>1 & j<row & nn>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 end % determining particle image displacement at 9 points in the window end

  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 vxvy]=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

  32. 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

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