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”