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Measurement Techniques
Digital Particle Image Velocimetry
Heat and Mass Transfer Laboratory (LTCM)
Sepideh Khodaparast
Marco Milan
Navid Borhani
Spring semester 2011
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! Introduction
! Particle Image Velocimetry features
!
System components for Particle Image Velocimetry
!
Principles of Particle Image Velocimetry
!
Practical test (TPA) description
Content
Spring semester 2011
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Origins of Particle Image Velocimetry
Ludwig Prandtl water tunnel (1904) Poohsticks (1928)
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Particle Image Velocimetry applications
Spring semester 2011
Fluid velocity measurement for fluid dynamic
characterization: Air flowing around a car or anaircraft, water running through hydroelectric turbine,
blood flow, etc.
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Particle Image Velocimetry features
Spring semester 2011
Advantages:
"
Non-intrusive technique: no modification of the flowproperty at the scale of interest
" Good resolution and accuracy: instantaneous velocityvector maps in a cross-section of the flow
"
2D-3D Velocity field reconstruction: 3D componentsmay be obtained with the use of a stereoscopicarrangement
Drawbacks:
"
Setup Time: need to optimize a number of parameters" Cost
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System components for Particle Image Velocimetry
Spring semester 2011
"
Test section, seeding particles
" Laser sheet
" Camera
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Principles of Particle Image Velocimetry
Spring semester 2011
FlowDirection
SeedingparticlesTube Wall
Time: tPosition: (x1, y1)
Time: t + !tPosition: (x2, y2)
Velocity vector at:
!"#$
%&
'(
'(=!
"#$
%& ++
'+
t
y y
t
x x y y x x
t t
1212
2
2121 ,2
,2
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Cross-correlation function
Spring semester 2011
! += dx s x I x I s R )()()( 21
" I1 and I2 are sub-area (interrogation windows) of the total frame
" x is the interrogation location
"
s is the shift between the images
( ) ( ) ( ) y y x x I y x I y x R x y
!+!+=!! "" ,,, 21
Two-dimensional discrete correlation function:
R(!"# !"%& '())*+,-(. /,0
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Particle Image Velocimetry protocol
Spring semester 2011
1 - Divide the images into a regular grid of
smaller regions: interrogation windows (IW)
2 - Each IW of the first image is correlated with
the corresponding IW of the second image
3 - Find the location of the displacement peak
and compute the velocity vector
4 - Reconstruct the flow velocity field
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Particle selection
Spring semester 2011
Capturing fluid motion
" Small enough to follow fluid motion
" Large enough to be visible
" Homogeneously distributed
" Tracer should not alter fluid / flow properties
Stokes number: F
V
v
flowof sticcharacteritime
timeresponse particleSt
!
!
==
_ _ _
_ _
Stv1: The particles will be unaffected by the fluid
Optimal particle image diameter: DI =2.5 pixels
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Seeding particle density(number of particle per interrogation window)
2
2
0
0
I I D M
z C N
!=
C Particle concentration!12 Light sheet ticknessDI Interrogation window sizeM0 Magnification
More particles: better signal to noise ratioUnambiguous detection of peak from noise
NI = 10
(10 particles per IW are sufficient to perform PIV)
NI = 5 NI = 10 NI = 15
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Maximum in-plane particle displacement
!345I = 0.00FI=1.00
0.28 0.56 0.850.64 0.36 0.16
!3 Particle displacement
DI Interrogation window sizeFI In plane loss-of-correlation
X,Y Displacements < quarter of the interrogation window size
Choose the sampling interval and the optical magnification factor so thatthe maximum image displacement is less than a quarter of the
interrogation window size
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Maximum out-of-plane particle displacement
!64 !10 = 0.00Fo=1.00
0.25 0.50 0.750.75 0.50 0.25
!6 Particle displacement normal to the observed plane
!12 Light sheet thicknessFo Out-of-plane loss-of-correlation
Z Displacement < quarter of the light sheet thickness
Define a suitable observation plane and choose a sampling interval sothat the particle shift normal to the observed plane is less than a
quarter of the light sheet thickness
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Spatial gradient - Interrogation window size
The PIV resolution is proportional to
the IW size. It has to be defined to
resolve local flow gradients
Keeping constant the particle size and density, altering the IW size will
change the number of particles used to calculate the local velocity in an
interrogation window. The total number of vector for a given image pair
depends directly on the IW size
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Interrogation window overlap
Overlap of the interrogation windows increase the number of particle
that are used in calculating the flow field
" Better spatial resolution
- Longer computational time
IW 1 IW 2
50% IW Overlap
Interrogation window offset
Offset increase the PIV accuracy for flow with a dominant direction. The
IW is shifted between the first and the second image
"
Better accuracy
- Longer computational timeIW Offset
Image 1 Image 2
IW 1 IW 1
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PIV Design rules
Spring semester 2011
Optimal particle image diameter
Image density
In-plane motion
Out-of-plane motion
DI =2.5 pixels
NI = 10
!!X ! < 0.25 IW Size
!!z ! < 0.25 light sheet thickness
The IW size and the sampling interval define the spatial and thetemporal resolution
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Practical test (TPA) description
1: Laminar flow
2: guidingvanes
3: elbow
PIV system components:
" Test section
"
Laser sheet" Camera
TP procedure:
1. Tune and calibrate the PIV system
2.
Record images at 3 differentlocations
3. Process the images on the PC
4.
Save and export the results
TP objectives:
"
PIV system tuning (Record nice images)
" Understand the principles of the PIV technique (ex: correlation function)
and the influence of the measurement parameters (n° of particles, size of
the IW, overlap, etc.)
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Enjoy the TPA !!!
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