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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 28. Direct Correlation & MQD Method

  3. Direct Correlation & MQD Method g2(i+m,j+n) m n Direct Correlation (w/o FFT) Method 1: g2(i,j) limited in the window frame j N A g1(i,j) i o M

  4. Direct Correlation & MQD Method g2(i+m,j+n) m n Direct Correlation (w/o FFT) Method 2: g2(i,j) not limited in the window frame j A N g1(i,j) i o M

  5. Direct Correlation & MQD Method Particle Image Pattern Tracking Tracking ensemble of particle images 2nd recording Image pattern at (m,n) 1st recording tracked image pattern

  6. Direct Correlation & MQD Method MN dimensional vectors Quadratic difference of the vectors Minimum-quadratic-difference (MQD) method Double exposure Single exposures Particle Image Pattern Tracking Minimum-quadratic-difference (MQD) method

  7. Direct Correlation & MQD Method Normalized MQD tracking functions Particle Image Pattern Tracking Modified MQD tracking function - D*(m,n) and D(m,n) identical for determining particle image displacement - 3-point Gaussian fit directly applied to D*(m,n)

  8. Direct Correlation & MQD Method Particle Image Pattern Tracking Correlation-based tracking method Correlation-based tracking function

  9. Direct Correlation & MQD Method Particle Image Pattern Tracking Modified correlation-based tracking function zero

  10. Direct Correlation & MQD Method tr(m,n)/D*(m,n) j  A m N   g2(i+m,j+n) g1(i,j) n 2 i o M  2 Particle Image Pattern Tracking Tracking area & tracking radius   Tracking radius

  11. Direct Correlation & MQD Method Zero padding: Periodical, with FFT: Particle Image Pattern Tracking Acceleration with FFT No periodical, no FFT: g1(i,j) g2(i,j)

  12. Direct Correlation & MQD Method 0 Particle Image Pattern Tracking Acceleration with FFT for [‑ m < , ‑ n < ]

  13. Direct Correlation & MQD Method Test computer: IBM 6×86 P166+ Correlation tracking with FFT [pixel] Particle Image Pattern Tracking Computation time

  14. Direct Correlation & MQD Method Particle Image Pattern Tracking Evaluation error Image pattern tracking methods - periodical error distribution on particle image displacement (1 pixel period) - MQD has higher accuracy for ideal PIV images, but more sensitive to noises Correlation algorithm - error dependent on particle image displacement, high accuracy at very small displacement Evaluation error for ideal PIV recordings by using different algorithmswith a 64x64-pixel interrogation window Imaging techniques for fluid flow and insect motion experiments

  15. Matlab function for reconstruction of evaluation sample File name: sample2.m function[g]=sample2(G,M,N,x,y,sr,mode) %INPUT PARAMETERS % G - gray value distribution of the PIV recording % M - interrogation window width % N - interrogation window height % x - horizontal position of interrogation window % y - vertical position of the interrogation window % sr - search radius % mode - (1) for first evaluation sample % OUTPUT PARAMETERS % g - gray value distribution of the evaluation sample for i=1:M+2*sr for j=1:N+2*sr g(i,j)=double(G(i+x-int16(M/2)-sr,j+y-int16(N/2)-sr)); end end g=g-mean(mean(g)); % subtracted by mean gray value if mode==1 for i=1:M+2*sr for j=1:N+2*sr if i>sr & i<=M+sr & j>sr & j<= N+sr continue; end g(i,j)=0; % zero padding end end end

  16. Class project: practice with option #2 Main program: A1=imread('A001_1.bmp'); % input image file A2=imread('A001_2.bmp'); % input image file G1=img2xy(A1); % convert image to gray value distribution G2=img2xy(A2); % convert image to gray value distribution Mg=32; % interrogation grid width Ng=32; % interrogation grid height M=32; % interrogation window width N=32; % interrogation window height [nxny]=size(G1); row=ny/Mg-1; % grid row number col=nx/Ng-1; % grid column number sr=12; % search radius for i=1:col for j=1:row x=i*Mg; y=j*Ng; g1=sample2(G1,M,N,x,y,sr,1); % evaluation samples for correlation tacking g2=sample2(G2,M,N,x,y,sr,2); [C m n]=correlation(g1,g2); [cm vxvy]=peaksearch(C,m,n,sr,0,0); % particle image displacement U(i,j)=vx; V(i,j)=vy; X(i,j)=x; Y(i,j)=y; end end quiver(X,Y,U,V); % plot vector map

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