Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time

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Measurements in Fluid Mechanics058180001
(ME51800001)Time Location 230P - 320P MWF
218 MLHOffice Hours 400P 500P MWF 223B-5
HL
Instructor Lichuan Gui lichuan-gui_at_uiowa.edu http
//lcgui.net
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Lecture 36. Micro-scale velocimetry
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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

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Need for Microfluidic Diagnostics

• Even though Re1, 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

• Positives Can image inside normally opaque
  devices
• Negatives low resolution 20-40mm depth
  averaged (2-D) requires slurry to scatter x-rays

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Molecular-Tagging Velocimetry

• Positives minimally intrusive better with
  electrically- driven flows
• Negatives low resolution 20-40mm depth
  averaged (2-D) greatly affected by diffusion

- 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

• Positives high resolution 1 mm small depth
  average 2-10 mm minimally intrusive
• Negatives requires seeding flow particles can
  become charged

Pulse laser
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Typical MPIV System
Micro-Fluidics LabPurdue University
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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

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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

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Example Microcantilever Driven Flow
(Provided by Micro Fluidics Lab at Purdue
University)
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Typical MPIV Image
- Background image filtered
- Particle image size dp5 ? 8 pixels
- Image displacements S 15 ? 40 pixels
- 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 (dpgt4 pixels, dp lt4 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
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MPIV Image Filter
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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

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Long-distance Forward-Scattering MPIV
Problem/solution for applying PIV in micro-scale
air jet flow
- smoke particles (Raffel et al. dplt?m)
- long-distance microscope (QUESTAR QM 100
WDgt100 mm)
- forward-scattering configuration (Raffel et
al. ?103)
- advanced imaging system (PCO200 ?t200 ns)
- individual image pattern tracking
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Long-distance Forward-Scattering MPIV
Experimental setup
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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
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Long-distance Forward-Scattering MPIV

• 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

• 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

(Test at y/D 1.5, Re ? 3200, 1676 vector maps,
802412 raw vectors, 559259 valid vectors)
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Long-distance Forward-Scattering MPIV

• High-speed air jet test results

Mean velocity and velocity fluctuation at 3
positions along the jet axis (D500 µm, Re ? 3200)
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References

• 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

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Matlab function for 4-P CDIC
functiongsample4P(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),
C1 for f2(i,j) OUTPUT PARAMETERS g - gray
value distribution of the evaluation sample nx
nysize(G) image size XwsSx(5) window
shift YwsSy(5) XdisSx-(Sx(1)Sx(3)Sx(7)Sx(9
))/4 distortion function YdisSy-(Sy(1)Sy(3)
Sy(7)Sy(9))/4 at 9 points XpixC(XwsXdis)
/2 pixel displacement YpixC(YwsYdis)/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. SwsS5
- Image distortion at the 4 points determined as
C1
C-1
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Matlab function for 4-P CDIC
gm0 initial average gray value nr0
initial number of effective pixels for i1M
column loop start for j1N 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_pixXpix(1)AXpix(3)BXpix(7)CXpix(9)D
pixel displacement at current pixel
y_pixYpix(1)AYpix(3)BYpix(7)CYpix(9)D
pixel displacement at current pixel
XXmx_pix-M/2i corresponding x position of
current pixel in the PIV recording
YYmy_pix-N/2j corresponding y position of
current pixel in the PIV recording
Iint16(X) integer portion of x-position
Jint16(Y) integer portion of
y-position xdouble(X)-double(I)
decimal portion of x-position
ydouble(Y)-double(J) decimal portion of
y-position if xlt0 adjust values so
that x0, y0 II-1 xx1
end if ylt0 JJ-1 yy1
end
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Matlab function for 4-P CDIC
if Igt1 Iltnx Jgt1 Jltny limited in
the image frame Gadouble(G(I,J))
gray value at integer pixels
Gbdouble(G(I1,J))
Gcdouble(G(I,J1))
Gddouble(G(I1,J1))
A(1-x)(1-y) weighting coefficients for
interpolation Bx(1-y)
C(1-x)y Dxy
g(i,j)AGaBGbCGcDGd bilinear
interpolation gmgmg(i,j) sum of
gray values for averaging nrnr1
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 gmgm/double(nr)
average gray value of effective pixels for
i1M for j1N if g(i,j)lt0
g(i,j)gm fill with average value for pixel
out of image frame end end end
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Matlab program for 4-P CDIC
clear clear variables A1imread('A001_1.bmp')
input 1st image in the recording pair
A2imread('A001_2.bmp') input 2nd image file
G1img2xy(A1) convert image to gray value
distribution G2img2xy(A2) convert image to
gray value distribution Mg16 interrogation
grid width Ng16 interrogation grid height
M2Mg interrogation window width w. 50
overlap N2Ng interrogation window height w.
50 overlap sr112 initial search
radius sr26 final search radius NN6
iteration number dU-12 12 3 parameters for
error detection dV-12 12 3 parameters for
error detection nx nysize(G1) determine
size of the image col400/Mg number of grid
rows in limited area of 400-pixel in height
fow400/Ng number of grid columns in limited
area of 400-pixel in width
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Matlab program for 4-P CDIC
for i1col for j1row
X(i,j)double((i-1)Mg400) 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
nn1NN iteration begin srint16((nn-1)(sr
2-sr1)/(NN-1)sr1) determine search radius
if nngt1 U V validinterpolation(U,V,
valid) interpolation for at wrong vectors
U V validinterpolation(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 i1col column loop start for
j1row row loop start
if nn1 wsx0 set window
shift to 0 in the first run
wsy0 else if
valid(i,j)gt0 wsxU(i,j)
window shift determined with previous evaluation
wsyV(i,j)
end end nr0
determining particle image displacement at 9
points in the window begin for
q-11 for p-11
nrnr1 number of grid point in the
window if igt1 iltcol jgt1
jltrow nngt1 after the first run when all
the 9 pints have valid vectors
sx(nr)U(ip,jq) determine
displacements at 9 points in the window
sy(nr)V(ip,jq) 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
xX(i,j) determine horizontal
coordinate of interrogation point
yY(i,j) determine vertical coordinate of
interrogation point
g1sample4P(G1,M,N,x,y, sx, sy, -1) evaluation
sample with backward image correction
g2sample4P(G2,M,N,x,y, sx, sy, 1) evaluation
sample with forward image correction
C m ncorrelation(g1,g2)
calculating correlation function
cm vx vypeaksearch(C,m,n,sr,0,0) determine
particle image displacement
U(i,j)vxwsx adjust particle image
displacement with window shift
V(i,j)vywsy adjust particle image
displacement with window shift end row
loop end end column loop end
validerrordetection(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