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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Long-distance Forward-Scattering MPIV
Experimental setup
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Long-distance Forward-Scattering MPIV
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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Long-distance Forward-Scattering MPIV
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Long-distance Forward-Scattering MPIV
• Overlapped sample PIV recordings pairs (50 pairs)
• Overlapped vector maps (50 vector maps)
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Long-distance Forward-Scattering MPIV
• 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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Long-distance Forward-Scattering MPIV
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
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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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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
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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
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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
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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