Measurement Techniques Digital Particle Image Velocimetry

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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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m  Introduction

m  Particle Image Velocimetry features

m  System components for Particle Image Velocimetry

m  Principles of Particle Image Velocimetry

m  Practical test (TPA) description

Content


3 Lausanne, 08/03/2010

Origins of Particle Image Velocimetry

Ludwig Prandtl water tunnel (1904) ‘Poohsticks’ (1928)

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Particle Image Velocimetry applications


Fluid velocity measurement for fluid dynamic characterization: Air flowing around a car or an aircraft, water running through hydroelectric turbine, blood flow, etc.

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Particle Image Velocimetry features


Advantages: ü  Non-intrusive technique: no modification of the flow property at the scale of interest ü  Good resolution and accuracy: instantaneous velocity vector maps in a cross-section of the flow ü  2D-3D Velocity field reconstruction: 3D components may be obtained with the use of a stereoscopic arrangement Drawbacks: ü  Setup Time: need to optimize a number of parameters

ü  Cost

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System components for Particle Image Velocimetry


ü  Test section, seeding particles

ü  Laser sheet

ü  Camera

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Principles of Particle Image Velocimetry


Flow Direction

Seeding particles Tube Wall

Time: t Position: (x1, y1)

Time: t + Δt Position: (x2, y2)

Velocity vector at: ⎟

⎠

⎞⎜⎝

⎛Δ

−

Δ

−=⎟

⎠

⎞⎜⎝

⎛ ++Δ

+ tyy

txxyyxx

tt

1212

2

2121 ,2

,2

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Cross-correlation function


∫ += dxsxIxIsR )()()( 21

ü  I1 and I2 are sub-area (interrogation windows) of the total frame ü  x is the interrogation location ü  s is the shift between the images

( ) ( ) ( )yyxxIyxIyxRx y

Δ+Δ+=ΔΔ ∑∑ ,,, 21

Two-dimensional discrete correlation function:

R(Δx, Δx)= Correla-on Map

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Particle Image Velocimetry protocol


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


Capturing fluid motion

ü  Small enough to follow fluid motion ü  Large enough to be visible ü  Homogeneously distributed ü  Tracer should not alter fluid / flow properties

Stokes number: F

Vv flowofsticcharacteritime

timeresponseparticleStττ

==___

__

Stv<<1: The particles and fluids will be in near equilibrium Stv>>1: The particles will be unaffected by the fluid

Optimal particle image diameter: DI =2.5 pixels

11 Spring semester 2011

Seeding particle density (number of particle per interrogation window)

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0II D

MzCN Δ

=

C Particle concentration Δz0 Light sheet tickness DI Interrogation window size M0 Magnification

More particles: better signal to noise ratio Unambiguous detection of peak from noise NI = 10 (10 particles per IW are sufficient to perform PIV)

NI = 5 NI = 10 NI = 15


Maximum in-plane particle displacement

ΔX/DI = 0.00 FI=1.00

0.28 0.56 0.85 0.64 0.36 0.16

ΔX Particle displacement DI Interrogation window size FI In plane loss-of-correlation

X,Y Displacements < quarter of the interrogation window size Choose the sampling interval and the optical magnification factor so that the maximum image displacement is less than a quarter of the interrogation window size


Maximum out-of-plane particle displacement

ΔZ/ Δz0 = 0.00 Fo=1.00

0.25 0.50 0.75 0.75 0.50 0.25

ΔZ Particle displacement normal to the observed plane Δz0 Light sheet thickness Fo Out-of-plane loss-of-correlation

Z Displacement < quarter of the light sheet thickness

Define a suitable observation plane and choose a sampling interval so that the particle shift normal to the observed plane is less than a quarter of the light sheet thickness


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


Interrogation window overlap Overlap of the interrogation windows increase the number of particle

that are used in calculating the flow field

ü  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

ü  Better accuracy

- Longer computational time IW Offset

Image 1 Image 2

IW 1 IW 1

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PIV “Design rules”


Optimal particle image diameter

Image density

In-plane motion

Out-of-plane motion

DI =2.5 pixels

NI = 10

|ΔX | < 0.25 IW Size

|Δz | < 0.25 light sheet thickness

The IW size and the sampling interval define the spatial and the temporal resolution


Practical test (TPA) description

1: Laminar flow

2: guiding vanes

3: elbow

PIV system components: ü  Test section ü  Laser sheet ü  Camera

TP procedure: 1.  Tune and calibrate the PIV system 2.  Record images at 3 different

locations 3.  Process the images on the PC 4.  Save and export the results

TP objectives:

ü  PIV system tuning (Record nice images)

ü  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.)

18 Lausanne, 08/03/2010

Enjoy the TPA !!!

Measurement Techniques Digital Particle Image Velocimetry

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