instructor: lichuan gui lichuan-gui@uiowa lcgui

Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)

Time & Location: 2:30P - 3:20P MWF 218 MLH

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan [email protected]

http://lcgui.net

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

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Lecture 36. Micro-scale velocimetry

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• 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

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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

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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.

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X-ray Microimaging

X-rays• Positives

Can image inside normally opaque devices

• Negativeslow resolution ~20-40mmdepth averaged (2-D)requires slurry to scatter x-

rays

Phosphor screen

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Molecular-Tagging Velocimetry

• Positivesminimally intrusivebetter with electrically-

driven flows• Negatives

low resolution ~20-40mm

depth averaged (2-D)greatly affected by

diffusion

UV laser

Blue laser

Blue laser

- working fluid contains photochromic indicator- temporarily capable of absorbing photons in red-green range after illuminated by ultraviolet light

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Micro-Particle Image Velocimetry

• Positiveshigh resolution ~1 mmsmall depth average ~2-10

mm minimally intrusive

• Negativesrequires seeding flowparticles can become

charged

Pulse laser

CCDmicroscope

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Flood Illumination

l=532 nm

l = 610 nm

Nd:YAG LASER

MICROSCOPE

BEAM EXPANDER

CCD CAMERA

MCROFLUIDIC DEVICE

Nd:YAG Laser

Micro Device

Flow in Flow out

Glasscover

CCD Camera(1280x1024 pixels)

BeamExpander

Epi-fluorescentPrism / Filter Cube

Microscope

Focal Plane

Micro-PIV image pair

Micro-Fluidics LabPurdue University

Typical MPIV System

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– 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

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– 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

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2 mm50 100 150 200 250 300

50

100

150

200

250

longest vector~2.25 mm/s

(Provided by Micro Fluidics Lab at Purdue University)

Example: Microcantilever Driven Flow

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Typical MPIV Image

Microthruster: Magnification 40X Particle size 700 nm

500 mm

- Background image filtered - Particle image size dp=5 8 pixels - Image displacements S= 15 40 pixels

Gray Value

Num

ber

ofpi

xels

0 50 100 150 200 250 300

- Image number density 3 in 32x32-pixel window

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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:

r

r

r

r

jyixGrr

jyixGyxG ,1212

1,

9

1,

1

1

1

1

For SP noise For LF noise

- Filter radius r big enough so that useful particle image information not be erased

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MPIV Image Filter

- Reduce influence of LF noises on the evaluation function

mn

(m,n)

( a )

No filter

mn

(m,n)

( b )

Micro-PIV image filter

Evaluation samples Evaluation functions

- Overall effect of MPIV in a micro-channel flow measurement

Mean velocity profile Standard deviation

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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

•••••

+

+ +

=N

1),(1 nm ),(2 nm

),( nmN

),( nmensemble

Average Correlation Function

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.: 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 tracking17

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Experimental setup

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Test & data acquisitionReduced image size 1024256 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 960240 m2 (0.94 m/pixel )

1676 recording pairs in each group

Time interval 200 ns

PCO2000 camera14-bit dynamic range4-GB image memory14.7 fps @ 20482048 pix

Questar QM 100Working distance up to 350 mm

New Wave Solo II-30532 nmBeam diameter: 2.5 mmRepetition Rate: 30 Hz

• Sample PIV recordings pairs (red: 1st image, green: 2nd image)

• Vector maps obtained by individual particle image pattern tracking

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• Overlapped sample PIV recordings pairs (50 pairs)

• Overlapped vector maps (50 vector maps)

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• Remove erroneous vectors by using a median filter

• Calculate local mean, fluctuation & correlation on a regular grid

x [m]

y[

m]

-400 -300 -200 -100 0 100 200 300 400

1400

1450

1500

1550

1600

0 1 2 3 4 5 6 7 8 9U-fluctuation [m/s]:

x [m]

y[

m]

-400 -300 -200 -100 0 100 200 300 400

1400

1450

1500

1550

1600

0 2 4 6 8 10 12 14 16 18V-fluctuation [m/s]:

x [m]

y[

m]

-400 -300 -200 -100 0 100 200 300 400

1400

1450

1500

1550

1600

-50 -40 -30 -20 -10 0 10 20 30 40 50uv [m2/s2]:__

(Test at y/D = 1.5, Re 3200, 1676 vector maps, 802412 raw vectors, 559259 valid vectors)

x [m]

y[

m]

-400 -300 -200 -100 0 100 200 300 400

1400

1450

1500

1550

1600

0 10 20 30 40 50 60 70 80 90 100Mean Velocity [m/s]:

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y [m]

x[

m]

250 500 750 1000 1250 1500 1750 2000 2250 2500 2750-500

-400

-300

-200

-100

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16 18

Velocity fluctuation [m/s]:

110 m/s

Mean velocity and velocity fluctuation at 3 positions along the jet axis(D=500 μm, Re 3200)

• High-speed air jet test results

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• 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

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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 shiftYws=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 displacementYpix=C*(Yws+Ydis)/2; % at 9 points

- Window shift determined with displacement

in the window center, i.e. Sws=S5

- Image distortion at the 4 points determined as

1,3,7,9kfor4

9731

SSSS

SkS kdis

- Particle image sisplacements at center and 4 corners (i.e. S1,

S3, S5, S7, S9) determined according to a previus evaluation

1 2 3

4 6

7 8 9

5

jixxjix diswspix ,2

1

2

1,1

jiyyjiy diswspix ,2

1

2

1,1

jixxjix diswspix ,2

1

2

1,2

jiyyjiy diswspix ,2

1

2

1,2

C=-1: C=+1:

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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

7 9

j

Njiyyi

MjixxGjif pixmpixm 2

,,2

,, 1111

j

Njiyyi

MjixxGjif pixmpixm 2

,,2

,, 2222

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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

A

C

B

D

I

J

J+1

I+1

Ga Gb

Gc Gd

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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

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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

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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

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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

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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

instructor: lichuan gui lichuan-gui@uiowa lcgui

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