What Is PIV ?

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What Is PIV ?

• J. Westerweel
• Delft University of Technology
• The Netherlands

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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

After A.K. Prasad, Lect. Notes short-course on
PIV, JMBC 1997
3
Coherent structures in a TBL
Kim, 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).
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PIV optical configuration
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Multiple-exposure PIV image
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PIV Interrogation analysis
RP
RD
RD-
RCRF
Double-exposure image
Spatial correlation
Interrogation region
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PIV result
Turbulent pipe flow Re 5300 10085 vectors
Hairpin vortex
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Instantaneous vorticity fields
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Historical development

• Quantitative velocity data from particle streak
  photographs (1930)
• Laser speckle velocimetry Youngs fringes
  analysis (Dudderar Simpkins 1977)
• Particle image velocimetry
• Interrogation by means of spatial correlation
• Digital PIV
• Stereoscopic PIV holographic PIV

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Definitions for PIV

• Source density

• Image density

C tracer concentration m-3 Dz0 light-sheet
thickness m M0 image magnification
- dt particle-image diameter m DI interrogatio
n-spot diameter m
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The displacement field

• The fluid motion is represented as a displacement
  field

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Velocity from tracer motion
Prob(detect) image density (NI)
Low image density
NI ltlt 1
Particle tracking velocimetry
High image density
NI gtgt 1
Particle image velocimetry
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Evaluation at high image density
Spatial correlation
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Linear system theory
Input
Output
Impulse response
Test signals

• Deterministic

• Stochastic

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The tracer pattern

• G(X,t) represents the random pattern of tracer
  particles that moves with the flow

Input
Output
Impulse response
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The tracer ensemble

• Consider the ensemble of all realizations of
  G(X,t) for given u(X,t)

Physical space
Phase space
Liouvilles theorem (continuity)
????t? PDF of ??t?
Homogeneous seeding
Incompressible flow
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Visualization vs. Measurement
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Inherent assumptions

• Tracer particles follow the fluid motion
• Tracer particles are distributed homogeneously
• Uniform displacement within interrogation region

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Ingredients
FLOW
sampling
seeding
quantization
Pixelization
illumination
enhancement
Acquisition
imaging
selection
registration
correlation
Interrogation
estimation
RESULT
validation
analysis