1. Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
Phone: (Lab), (Cell)

2. Lecture 20. Particle image displacement methods and others

3. Particle image displacement methods
- Optical, non- or minimally-intrusive, fluid flow measurement technique;
- Instantaneous flow measurements in two-dimensional (2D) area or three-dimensional (3D) volume field of views;
- Basic procedure of particle image displacement methods
1. Flow visualization
- Flow field seeded with small tracer particles
- Particles usually illuminated by a laser light sheet
2. Image recording
- Particle images captured by an imaging system
- Saved in photographic film or digital image file
3. Image evaluation
- Young’s fringes method
- Particle image identification
- Correlation-based algorithm

4. Particle image displacement methods
Example:

5. Particle image displacement methods
Three groups of methods
Particle tracking velocimetry (PTV)
- flow seeded with tracer particles of very low concentration
- very low image number density in photo or video recordings
- single particle can be identified in image recording
- particle image tracking possible from frame to frame
- low information density in measurement plane
Laser speckle velocimetry (LSV)
- flow seeded with tracer particles of very high concentration
- very high image number density in photo or video recordings
- single particle can not be identified in image recording
- particle image tracking impossible from frame to frame
- high information density in measurement plane
Particle image velocimetry (PIV)
- flow seeded with tracer particles of high concentration
- high image number density in photo or video recordings
- single particle can be identified in image recording
- particle image tracking impossible from frame to frame
- high information density in measurement plane

6. Particle image displacement methods
Single frame image recordings
Single exposure - Long exposure time - Velocity determined by trajectory - Direction ambiguity - Low particle number density required
Double exposure - Short exposure time - Velocity determined by displacement - Direction ambiguity - Methods to avoid direction ambiguity: a. color/intensity tagging b. Image shifting techniques
Multi-exposure - Short exposure time - Velocity determined by displacement - Direction ambiguity - Used to increase particle image number - Limited in steady flow

7. Particle image displacement methods
Multi frame image recordings
- velocity determined with particle image displacement between frames
- double/Multi exposure used to increase image number in steady flow

8. Particle image displacement methods
Frequently used evaluation methods
LID – low image density (PTV)
HID – high image density (PIV)
LS – laser speckle mode (LSV)

9. Particle image displacement methods
Data reduction
Image plane
Objective Lens
Laser light sheet
Scale factor:  = L/L’
Time interval: t
Velocity: V=S/t=·S’/ t
Laser light sheet
Image plane
Objective Lens S S’ L L’

10. Particle image displacement methods
Evaluation methods
Particle trajectory identification
Image recording
- single frame
- single long time exposure
- low image density
- film or digital recording
Evaluation
- read film recordings with
a microscope system
- identify particle trajectories
in digital recording y x

11. Particle image displacement methods
Evaluation methods
Young’s fringes method
Image recording
- positive film
- single frame
- double/multiple exposed
- HID & LS mode
laser PC
2D traverse system
CCD camera
frosted glass
Young’s fringes system
- SM inversely proportional to SA
- fringes perpendicular to particle image displacement

12. Particle image displacement methods
Evaluation methods
Particle image tracking
PIV recording - Minimum 2 frames - Single exposure - LID mode - Film or digital recording
Evaluation - Identify particle images & determine position of each particle image center - Pairing particles in two frames (many algorithms) - Velocity determined by position difference of paired particles & t t1 t2 o x y
(x2, y2)
(x1, y1)

13. Particle image displacement methods
Evaluation methods
Correlation-based interrogation m n
(m, n) -S S o
Auto-
correlation
(m’,n’)
Cross-correlation

14. Particle image displacement methods
Standard 2D PIV
Light
sheet
t=t0
Lens
Measurement
volume
Laser
t=t0
Image #1
Single exposed recording
Fluid flow seeded with
small tracer particles
Double exposed recording
Exposure #1
Lens system & Camera

15. Particle image displacement methods
Standard 2D PIV
Light
sheet
t=t0+t
Lens
Measurement
volume
Laser
Image #1
t=t0
Fluid flow seeded with
small tracer particles
t=t0+t
Image #2
Exposure #2
Exposure #1
Lens system & Camera
Single exposed recording
Double exposed recording

16. Particle image displacement methods
Micro-scale PIV (MPIV)
Nd:YAG Laser
Micro Device
Flow in
Flow out
Glass
cover
CCD Camera
(1280x1024 pixels)
Beam
Expander
Epi-fluorescent
Prism / Filter Cube
Microscope
Nd:YAG LASER
MICROSCOPE
BEAM EXPANDER
CCD CAMERA
MCROFLUIDIC DEVICE
Flood Illumination
l=532 nm
Focal Plane
l = 610 nm
Micro-Fluidics Lab Purdue University
Micro-PIV image pair

17. Particle image displacement methods
Stereo PIV (SPIV)
- 3 velocity components in a plane
- Two cameras
- Translation systems (lateral displacement)
- Rotational systems (angular displacement) Scheimpflug condition

18. Particle image displacement methods
Holographic PIV (HPIV)
- 3 velocity components in a 3 dimensional volume
- Complex and precise illumination
a. Hologram recording
b. Hologram reconstruction

19. Particle image displacement methods
Other image-based methods
Defocusing PIV (Pereira et al. 2000)
Allow images to become defocused
Single camera/ color CCD, particle image tracking
Multiple-sheet PIV (Raffel et al.,1995 )
Multiple laser light sheet, single camera
3D scanning PIV (Brücker, 1997)
Scanning a 3D volume with a laser beam
Single high speed camera
X-ray & Echo PIV
Molecular Tagging Velocimetry
Temperature measurement with particle Brownian motion
More

20. Measurement of wind velocity
Cup anemometers
Propeller anemometers
Vane anemometers
Sonic anemometers

21. Homework
- Read textbook on page
Questions and Problems: 9 on page 287
- Due on 10/12

22. Try to write a Matlab program
function [Cm Sx Sy]=peaksearch(C,sr)
% INPUT PARAMETERS
% C - correlation function
% sr - search radius
% OUTPUT PARAMETERS
% Cm - high correlation peak value
% (Sx,Sn) - displacement
[M N]=size(C);
i0=int16(M/2); % high peak search - begin
j0=int16(N/2);
ix=0;
jy=0;
Cm=0;
for i=i0+1-sr:i0+1+sr
for j=j0+1-sr:j0+1+sr
max=0;
for i1=i-1:i+1
for j1=j-1:j+1
if max<C(i1,j1)
max=C(i1,j1);
end
if C(i,j)>=max & C(i,j)>Cm
ix=i;
jy=j;
Cm=C(i,j);
end % high peak search -end
% SUB-PIXEL FIT
dx=(C(ix+1,jy)-C(ix-1,jy))/(4*C(ix,jy)-2*C(ix+1,jy)-2*C(ix-1,jy));
dy=(C(ix,jy+1)-C(ix,jy-1))/(4*C(ix,jy)-2*C(ix,jy+1)-2*C(ix,jy-1));
%Displacement
Sx=dx+double(ix-i0);
Sy=dy+double(jy-j0);
Main program:
clear;
A1=imread('A001_1.bmp');
G1=img2xy(A1);
M=64;
N=64;
x=400;
y=200;
g1=sample01(G1,M,N,x,y);
Sx=10.6;
Sy=12.3;
g2=sample01(G1,M,N,x+Sx,y+Sy);
g1=g1-mean(mean(g1));
g2=g2-mean(mean(g2));
c=xcorr2(g1,g2);
[cm Sx Sy]=peaksearch(c,20)
% C=xy2img(c);
% imwrite(C,'C.bmp','bmp');
Results:
cm = e+06
Sx =
Sy = 22