aere 311l & aere343l lecture notes

Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

HHui Huui HuDepartment of Aerospace Engineering, Iowa State University Department of Aerospace Engineering, Iowa State University

Ames, Iowa 50011, U.S.AAmes, Iowa 50011, U.S.A

Lecture # 13: Lecture # 13: Particle Image Particle Image VelocimetryVelocimetry TechniqueTechnique

AerEAerE 311L & AerE343L Lecture Notes311L & AerE343L Lecture Notes


ParticleParticle--based Flow Diagnostic Techniquesbased Flow Diagnostic Techniques

• Seeded the flow with small particles (~ µm in size)

• Assumption: the particle tracers move with the same velocity as local flow velocity!

Flow velocityFlow velocityVVff

Particle velocityParticle velocityVVpp

=

Measurement of particle velocity


ParticleParticle--based techniques: Particle Image based techniques: Particle Image VelocimetryVelocimetry (PIV)(PIV)

• To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows.

• To measure the displacements (ΔL) of the tracer particles between known time interval (Δt). The local velocity of fluid flow is calculated by U= Δ L/Δt .

A. t=tA. t=t00 B. t=tB. t=t00+10 +10 μμss C. Derived Velocity fieldC. Derived Velocity fieldX (mm)

Y(m

m)

-50 0 50 100 150

-60

-40

-20

0

20

40

60

80

100

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.95.0 m/sspanwise

vorticity (1/s)

shadow region

GA(W)-1 airfoil

t=tt=t00 tLUΔΔ

=

t= tt= t00++ΔΔttΔΔLL


PIV System SetupPIV System Setup

Illumination system(Laser and optics)

cameraSynchronizer

seed flow withtracer particles

Host computer

Particle tracers: Particle tracers: to track the fluid movement. to track the fluid movement. Illumination system: Illumination system: to illuminate the flow field in the interest region.to illuminate the flow field in the interest region.Camera: Camera: to capture the images of the particle tracers.to capture the images of the particle tracers.Synchronizer: Synchronizer: the control the timing of the laser illumination and the control the timing of the laser illumination and

camera acquisition.camera acquisition.Host computer: Host computer: to store the particle images and conduct image processing. to store the particle images and conduct image processing.


Tracer Particles for PIV Tracer Particles for PIV

•• Tracer particles should be Tracer particles should be neutrally buoyant neutrally buoyant andand small enough small enough to follow the flow to follow the flow perfectlyperfectly..

•• Tracer particles should be Tracer particles should be big enoughbig enough to to scatterscatter the illumination lights the illumination lights efficientlyefficiently ..

•• The scattering efficiency of trace particles also strongly depeThe scattering efficiency of trace particles also strongly depends on the ratio of the nds on the ratio of the refractive refractive indexindex of the particles to that of the fluid. of the particles to that of the fluid.

For example: the refractive index of For example: the refractive index of waterwater is considerably larger than that of is considerably larger than that of airair. . The scattering of particles in air is at least one order The scattering of particles in air is at least one order of magnitude more of magnitude more efficient than particles of the same size in water.efficient than particles of the same size in water.

hν

Incident lightScattering light

. d=1μm b. d=10μm c. d=30μm


•• A primary source of measurement error is the influence of graviA primary source of measurement error is the influence of gravitational forces when the density tational forces when the density of the tracer particles is different to the density of work fluiof the tracer particles is different to the density of work fluid.d.

•• The velocity lag of a particle in a continuously acceleration flThe velocity lag of a particle in a continuously acceleration fluid will be:uid will be:

Tracer Particles for PIVTracer Particles for PIV

μρ

τ

τ

μρρ

18

);exp(1()(

18)(

2

2

pps

sp

ppPs

d

tUtU

gdUUU

=

−−=

−=−=

rr

rrrUr

gdU ppg μ

ρρ18

)(2 −=

PUr


• Tracers for PIV measurements in liquids (water):

• Polymer particles (d=10~100 μm, density = 1.03 ~ 1.05 kg/cm3)

• Silver-covered hollow glass beams (d =1 ~10 μm, density = 1.03 ~ 1.05 kg/cm3)

• Fluorescent particle for micro flow (d=200~1000 nm, density = 1.03 ~ 1.05 kg/cm3).

•Quantum dots (d= 2 ~ 10 nm)

• Tracers for PIV measurements in gaseous flows:

• Smoke …

• Droplets, mist, vapor…

• Condensations ….

• Hollow silica particles (0.5 ~ 2 μm in diameter and 0.2 g/cm3 in density for PIV measurements in combustion applications.

•Nanoparticles of combustion products

Tracer Particles for PIVTracer Particles for PIV


illumination systemillumination system

•• The illumination system of PIV is always composed of light sourcThe illumination system of PIV is always composed of light source and optics. e and optics.

•• LasersLasers: such as Argon: such as Argon--ion laser and ion laser and Nd:YAGNd:YAG Laser, are widely used as light Laser, are widely used as light source in PIV systems due to their ability to source in PIV systems due to their ability to emit monochromatic lightemit monochromatic light with with high high energy densityenergy density which can easily be bundled into thin light sheet for illuminatwhich can easily be bundled into thin light sheet for illuminating ing and recording the tracer particles without chromatic aberrationsand recording the tracer particles without chromatic aberrations..

•• OpticsOptics: always consisted by a set of cylindrical lenses and mirrors t: always consisted by a set of cylindrical lenses and mirrors to shape the o shape the light source beam into a planar sheet to illuminate the flow fielight source beam into a planar sheet to illuminate the flow field.ld.

laser optics

Laser beamLaser sheet


DoubleDouble--pulsed pulsed Nd:YagNd:Yag Laser for PIVLaser for PIV


Optics for PIVOptics for PIV


CamerasCameras

•• The widely used cameras for PIV: The widely used cameras for PIV:

•• Photographic filmPhotographic film--based cameras based cameras or or ChargedCharged--Coupled Device (CCD) camerasCoupled Device (CCD) cameras..

••Advantages of CCD cameras: Advantages of CCD cameras:

•• It is fully digitizedIt is fully digitized

•• Various digital techniques can be implemented for PIV image proVarious digital techniques can be implemented for PIV image processing.cessing.

•• Conventional autoConventional auto-- or crossor cross-- correlation techniques combined with special correlation techniques combined with special framing techniques can be used to measure higher velocities.framing techniques can be used to measure higher velocities.

•• Disadvantages of CCD cameras:Disadvantages of CCD cameras:

•• Low temporal resolution (defined by the video framing rate): Low temporal resolution (defined by the video framing rate):

•• Low spatial resolution:Low spatial resolution:


Interlaced CamerasInterlaced Cameras

• The fastest response time of human being for images is about ~ 15Hz• Video format:

– PAL (Phase Alternating Line ) format with frame rate of f=25Hz (sometimes in 50Hz). Used by U.K., Germany, Spain, Portugal, Italy, China, India, most of Africa, and the Middle East

– NTSC format: established by National Television Standards Committee (NTSC) with frame rate of f=30Hz. Used by U.S., Canada, Mexico, some parts of Central and South America, Japan, Taiwan, and Korea.

Even fieldEven field(2,4,6(2,4,6……640)640)

Old fieldOld field(1,3,5(1,3,5……639)639)

Even field

Odd field

16.6ms16.6ms

1 frameF=30Hz

480 pixels by 640 pixels480 pixels by 640 pixels

Interlaced cameraInterlaced camera

timetime


Progressive scan cameraProgressive scan camera

•• All image systems produce a clear image of the background All image systems produce a clear image of the background •• Jagged edges from motion with interlaced scan Jagged edges from motion with interlaced scan •• Motion blur caused by the lack of resolution in the 2CIF sample Motion blur caused by the lack of resolution in the 2CIF sample •• Only progressive scan makes it possible to identify the driverOnly progressive scan makes it possible to identify the driver

1st frameExp=33.33ms

2nd frameexp=33.33ms


Synchronizer Synchronizer •• Function of Synchronizer: Function of Synchronizer:

•• To control the timing of the laser illumination and camera acquTo control the timing of the laser illumination and camera acquisitionisition

1stpulsed

2ndpulsed

Timing of pulsed laser

Timing of CCD camera

time

1st frame exposure

2nd frame exposure

Δt33.33ms(30Hz)

To laser To camera

From computer

Synchronizer


Host computerHost computer

•• To send timing control parameter to synchronizer. To send timing control parameter to synchronizer.

•• To store the particle images and conduct image processing.To store the particle images and conduct image processing.

Host computerTo synchronizer

Image data from camera


SingleSingle--frame techniqueframe technique

particleparticleStreak lineStreak line

VVL=V*L=V*ΔΔtt

singlesingle--pulsepulse MultipleMultiple--pulsepulse

Particle streak Particle streak velocimetryvelocimetry


MultiMulti--frame techniqueframe techniquea. T=ta. T=t00

b. T=tb. T=t11

c. T=tc. T=t22

a. T=ta. T=t33

t=tt=t00

tLUΔΔ

=

t= tt= t00++ΔΔttΔΔLL


Image Processing for PIVImage Processing for PIV

•• To extract velocity information from particle images.To extract velocity information from particle images.

t=t0 t=t0+4ms

A typical PIV raw image pair

Y/D

X/D

-2 -1 0 1 2 31

1.5

2

2.5

3

3.5

4

4.5

5

1.1001.0501.0000.9500.9000.8500.8000.7500.7000.6500.6000.5500.5000.4500.4000.3500.3000.2500.2000.1500.100

Velocity U/Uin

Image processing


Particle Tracking Particle Tracking VelocimetryVelocimetry (PTV)(PTV)

t=t0 t=t0+Δt

Low particle-imagedensity case

1.1. Find position of the particles at each Find position of the particles at each imagesimages

2.2. Find corresponding particle image pair Find corresponding particle image pair in the different image frame in the different image frame

3.3. Find the displacements between the Find the displacements between the particle pairs.particle pairs.

4.4. Velocity of particle equates the Velocity of particle equates the displacement divided by the time interval displacement divided by the time interval between the frames.between the frames.


Particle Tracking Particle Tracking VelocimetryVelocimetry (PTV)(PTV)--22

Particle position of time step t=t1

Search region for time step t=t4



FourFour--frameframe--particleparticletracking algorithm tracking algorithm

1.1. Find position of the particles at each Find position of the particles at each imagesimages

2.2. Find corresponding particle image pair Find corresponding particle image pair in the different image frame in the different image frame

3.3. Find the displacements between the Find the displacements between the particle pairs.particle pairs.

4.4. Velocity of particle equates the Velocity of particle equates the displacement divided by the time interval displacement divided by the time interval between the frames.between the frames.

PTV results


CorrelationCorrelation--based PIV methodsbased PIV methods

high particle-image density

t=t0 t=t0+Δt Corresponding flow velocity field


CorrelationCorrelation--based PIV methodsbased PIV methods

t=t0 t=t0+Δt

　　　　 Searching window size (SB)

SB

SA

SA Interrogation window

　　　　

SB

q(x,y) P(x,y) SB

( )dvgyxgdvfyxf

dvgyxgfyxfqpR

22)),(()),((

)),(()),((,

∫∫∫

−−

−−=Correlation coefficient

function


Cross Correlation OperationCross Correlation Operation

Signal A: Signal A:

Signal B: Signal B:

( )dxuxgdxxf

dxuxgxfuR

])([*])([

)](*)([22

∫∫∫

+

+=


1 4 7 10 13 16 19 22 25 28 31S1

S10

S19

S280.7

0.75

0.8

0.85

0.9

0.95

1

Correlation coefficient distributionCorrelation coefficient distribution

( )dvgyxgdvfyxf

dvgyxgfyxfqpR22

)),(()),(()),(()),((,

∫∫

∫

−−

−−=

R(p,q)Peak location


Comparison between PIV and PTVComparison between PIV and PTV•• Particle Tracking Particle Tracking VelocimetryVelocimetry::

•• Tracking individual particleTracking individual particle•• Limited to low particle image density caseLimited to low particle image density case•• Velocity vector at random points where tracer particles exist.Velocity vector at random points where tracer particles exist.•• Spatial resolution of PTV results is usually limited by the Spatial resolution of PTV results is usually limited by the

number of the tracer particlesnumber of the tracer particles

•• CorrelationCorrelation--based PIV:based PIV:•• Tracking a group of particlesTracking a group of particles•• Applicable to high particle image density caseApplicable to high particle image density case•• Spatial resolution of PIV results is usually limited by the sizeSpatial resolution of PIV results is usually limited by the size

of the interrogation window sizeof the interrogation window size•• Velocity vector can be at regular grid points.Velocity vector can be at regular grid points.

PTV

t=t0+Δt

PIV

Y/D

X/D

-2 -1 0 1 2 31

1.5

2

2.5

3

3.5

4

4.5

5

1.1001.0501.0000.9500.9000.8500.8000.7500.7000.6500.6000.5500.5000.4500.4000.3500.3000.2500.2000.1500.100

Velocity U/Uin


Estimation of differential quantitiesEstimation of differential quantities

X (mm)Y

(mm

)10 15 20 25 30 35

5

10

15

20


Estimation of differential quantitiesEstimation of differential quantities


Estimation of Estimation of VorticityVorticity distributiondistribution

yU

xV

z ∂∂

−∂∂

=ϖ


Estimation of Estimation of VorticityVorticity distributiondistribution

Stokes Theorem: Stokes Theorem:

dA

AdldV

yxz

C S

−Γ=⇒

•−=−=Γ ∫ ∫∫

ϖ

ϖrvrr


VorticityVorticity distribution Examplesdistribution Examples

-50 0 50 100 150 200 250 300-50

0

50

100

150

200-25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00

Spanwise Vorticity ( Z-direction )

Re =6,700

Uin = 0.33 m/s

X mm

Ym

m

Uou

t

water free surface

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 -3.2 -2.7 -2.2 -1.7 -1.2 -0.7 -0.2 0.3 0.8 1.3 1.810 m/sspanwise

vorticity (1/s)

shadow region

GA(W)-1 airfoil


EnsembleEnsemble--averaged quantitiesaveraged quantities

•• Mean velocity components in x, y directions: Mean velocity components in x, y directions:

••Turbulent velocity fluctuations:Turbulent velocity fluctuations:

•• Turbulent Kinetic energy distribution:Turbulent Kinetic energy distribution:

•• Reynolds stress distribution:Reynolds stress distribution:

NUuuN

ii /)('

1

2∑=

−= ∑=

−=N

ii Vvv

1

2)('

∑=

=N

ii NuU

1/ ∑

=

=N

ii NvV

1/

)''(21 22

vuTKE += ρ

∑=

−−−=−=

N

i

ii

NUvUuvu

1

))(('' ρρτ


EnsembleEnsemble--averaged quantitiesaveraged quantities

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0

10 m/s

shadow region

GA(W)-1 airfoil

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 vort: -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

10 m/s

shadow region

GA(W)-1 airfoil

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 -0.035 -0.025 -0.015 -0.005 0.005 0.015 0.025 0.035

shadow region

GA(W)-1 airfoil

NormalizedReynolds Stress

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100

shadow region

GA(W)-1 airfoil

T.K.E


Pressure field estimationPressure field estimation

)(1

)(1

2

2

2

2

2

2

2

2

yv

xv

yp

yvv

xvu

yu

xu

xp

yuv

xuu

∂∂

+∂∂

+∂∂

−=∂∂

+∂∂

∂∂

+∂∂

+∂∂

−=∂∂

+∂∂

ρμ

ρ

ρμ

ρ


Integral Force estimationIntegral Force estimation

FVdfAdPAdVVVdVt VCSCSCVC

rrrrrrr++•=•+

∂∂

∫∫∫∫........

~)( ρρρ

X (mm)

Y(m

m)

-20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0

10 m/s

shadow region

GA(W)-1 airfoil

aere 311l & aere343l lecture notes

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