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What Is PIV ?J. Westerweel
Delft University of TechnologyThe Netherlands
Why use imaging?
Conventional methods(HWA, LDV)
• Single-point measurement
• Traversing of flow domain
• Time consuming
• Only turbulence statistics
Particle image velocimetry
• Whole-field method
• Non-intrusive (seeding)
• Instantaneous flow field
z
After: A.K. Prasad, Lect. Notes short-course on PIV, JMBC 1997
Coherent structures in a TBLKim, H.T., Kline, S.J. & Reynolds, W.C. J. Fluid Mech. 50 (1971) 133-160.
Smith, C.R. (1984) “A synthesized model of the near-wall behaviour in turbulent boundary layers.” In: Proc. 8th Symp. on Turbulence (eds. G.K. Patterson & J.L. Zakin) University of Missouri (Rolla).
PIV optical configuration
Multiple-exposure PIV image
PIV Interrogation analysis
Double-exposureimage
Interrogationregion
Spatialcorrelation
RP
RD+RD-
RC+RF
PIV result
“Hairpin” vortex
Turbulent pipe flowRe = 5300100×85 vectors
Instantaneous vorticity fields
Historical development
• Quantitative velocity data from particle streak photographs (1930)
• Laser speckle velocimetry; Young’s fringes analysis (Dudderar & Simpkins 1977)
• Particle image velocimetry
• Interrogation by means of spatial correlation
• ‘Digital’ PIV
• Stereoscopic PIV; holographic PIV
Definitions for PIV
• Source density: NC z
MdS
0
02
2
4
NC z
MDI I
0
02
2• Image density:
C tracer concentration [m-3]
z0 light-sheet thickness [m]
M0 image magnification [-]
d particle-image diameter [m]
DI interrogation-spot diameter [m]
D X t t u X t t dt
t
t
( ; , ) ( ),
X ti ( )2
X ti ( )1
D
Particletrajectory
Fluidpathline
u X t( , )
v ti ( )
After: Adrian, Adv. Turb. Res. (1995) 1-19
The displacement field
• The fluid motion is represented as a displacement field
NI << 1
NI >> 1
Particle tracking velocimetry
Particle image velocimetry
Prob(detect) ~ image density (NI)
Low image density
High image density
Velocity from tracer motion
xdsxIsxWxIxWsR
)()()()()( 2211Spatial correlation:
Evaluation at high image density
X t( ) Y t( )
Input Output
• Deterministic
Test signals:
Y t H s t X s ds( ) ( , ) ( )
• Stochastic
X t t t Y t H t t( ) ( ) ( ) ( , ) 0 0
H t t( , )
E X t
E X t X t t tE X t Y t H t t
( )
( ) ( ) ( )( ) ( ) ( , )
0
Impulse response
Linear system theory
G X t X X tii
N
( , ) ( )
1
H X X( , ) G X t( , )
G X t( , )
Input Output
H X X X X D X t t( , ) ( ; , )
Impulse response:
The tracer pattern
• G(X,t) represents the random ‘pattern’ of tracer particles that moves with the flow
Physical space Phase space
G X t
u X t
( , )
( , )
( )
( )
t
U t
t = PDF of t
0
0U
t
0
t
U U
0
Liouville’s theorem (continuity):
Homogeneous seeding:
Incompressible flow:
The tracer ensemble
• Consider the ensemble of all realizations of G(X,t) for given u(X,t)
Visualization vs. Measurement
Inherent assumptions
• Tracer particles follow the fluid motion
• Tracer particles are distributed homogeneously
• Uniform displacement within interrogation region
FLOW
RESULT
seeding
illumination
imaging
registration
sampling
quantization
enhancement
selection
correlation
estimation
validationanalysis
Interrogation
Acquisition
Pixelization
“Ingredients”