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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 edu http lcgui net

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

[email protected]

http://lcgui.net

slide3

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

slide4

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

slide5

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

slide6

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

slide7

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)

slide8

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Correlation-based tracking method

Correlation-based tracking function

slide9

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Modified correlation-based tracking function

zero

slide10

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

slide11

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)

slide12

Direct Correlation & MQD Method

0

Particle Image Pattern Tracking

Acceleration with FFT

for [‑ m < , ‑ n < ]

slide13

Direct Correlation & MQD Method

Test computer: IBM 6×86 P166+

Correlation tracking with FFT

[pixel]

Particle Image Pattern Tracking

Computation time

slide14

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

slide15

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

slide16

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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