Lecture # 14: Advanced Particle Image Velocimetry TechniqueLecture # 14: Advanced Particle Image Velocimetry Technique ... by solving Equation (4-20) with least square method Calibration

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 # 14: Advanced Lecture # 14: Advanced Particle Image Particle Image VelocimetryVelocimetry TechniqueTechnique

AerEAerE 311L & AerE343L Lecture Notes311L & AerE343L Lecture Notes


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


Effect of the outEffect of the out--ofof--plane velocity for 2plane velocity for 2--D PIV measurementsD PIV measurements

CameraCamera

Laser SheetLaser Sheet

ZZ

XX

Laser sheet

In-plane velocity

Out-of-plane velocity

y x

z

Real velocity

132.1%132.1%--0.050.05--0.060.065.05.04,0004,0001.701.7015.015.07.57.5HH

41.30%41.30%0.3940.3940.3630.3635.05.04,0004,0000.340.3415.015.07.57.5GG

13.75%13.75%0.7480.7480.6980.6985.05.04,0004,0000.170.1715.015.07.57.5FF

7.12%7.12%0.9800.9800.9910.9915.05.04,0004,0000.0170.01715.015.07.57.5AA

AVEAVE--ERRERRCRCR--VVCRCR--UUDDMMNNWWMMVVXXVVMMcasecase VVM M : average velocity (pixel/interval): average velocity (pixel/interval)VVXX : maximum Velocity (pixel/interval): maximum Velocity (pixel/interval)WWM M : out of plane velocity (laser width/interval): out of plane velocity (laser width/interval)N: tracer numberN: tracer numberDD M M : tracer average diameter (pixel): tracer average diameter (pixel)AverAver--Err: average error of PIV results without Err: average error of PIV results without

subsub--pixel interpolation.pixel interpolation.


Stereoscopic PIV techniqueStereoscopic PIV technique

Camera 1Camera 1 Camera 2Camera 2


αα11

αα22

ZZ

XX

X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

Displacement vectors in left camera Displacement vectors in left camera Displacement vectors in right camera Displacement vectors in right camera

-40-30

-20-10

010

2030X m

-40

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z

W m /s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.00



Lens 1Lens 1

Image recording plane 1Image recording plane 1


Lens 2Lens 2

Image recording plane 2Image recording plane 2


lenslens

Image recording planeImage recording plane


C. Angle displacement C. Angle displacement arrangement with arrangement with sheimpflugsheimpflug condition condition

b. angle b. angle displacement displacement arrangement arrangement

a. lens a. lens translation translation arrangement arrangement

lenslens

Image recording planeImage recording plane





a. image of left cameraa. image of left camera b. rectangular grid in the object plane c. image ofb. rectangular grid in the object plane c. image of left cameraleft cameraThe perspective effect of the angle displacement arrangementThe perspective effect of the angle displacement arrangement



αα11

αα22

ZZ

XX


Mapping Function for Stereo PIVMapping Function for Stereo PIV

)()()(i

cc xFX =

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

ΔΔΔ

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

Δ

Δ

Δ

Δ

3

2

1

)2(3,2

)2(3,1

)1(3,2

)1(3,1

)2(2,2

)2(2,1

)1(2,2

)1(2,1

)2(1,2

)2(1,1

)1(1,2

)1(1,1

)2(2

)2(1

)1(2

)1(1

xxx

FFFF

FFFF

FFFF

XXXX

3,2,12,1,2,1)(

)(, ===

∂∂

= jicx

FFj

cic

ji



αα11

αα22

ZZ

XX

xFX ci Δ∇≅Δ )()(

Laser sheet

In-plane velocityOut-of-plane velocity

y x

z

Real velocity


Mapping Function for Stereo PIVMapping Function for Stereo PIV)()()(

icc xFX =



αα11

αα22

ZZ

XX

2230

229

2228

327

226

225

324

423

3122

2221

320

419

218

217

21615

214

313

212

211

310

2987

265

243210),,(

zyaxyzazxazyazxyayzxazxayayxazxayxaxayzaxzazyaxyzazxayaxyayxaxazayzaxzayaxyaxazayaxaazyxF

++++++++++++++++++++++++++++++=

ZZ

XXLocation Z=0Location Z=0Location Z=Location Z=--0.5mm0.5mm

Location Z=0.5mmLocation Z=0.5mm

Laser light sheetLaser light sheet

a. image from the left camera b. image from the right camera a. image from the left camera b. image from the right camera


Flow Chart for Stereo PIV measurementsFlow Chart for Stereo PIV measurements

CrossCross--CorrelationCorrelationoperation by usingoperation by usingHRHR--PIV method toPIV method tocalculate calculate DDXX LL, , DDYY LL

CrossCross--CorrelationCorrelationoperation by usingoperation by usingHRHR-- PIVmethodPIVmethod totocalculate calculate DDXX RR, , DDYY RR

InIn--situ calibration forsitu calibration forggeneraleneral mapping functionmapping function

XXLL((x,y,zx,y,z), Y), Y LL((x,y,zx,y,z))InIn--situ calibration forsitu calibration for

General mapping functionGeneral mapping functionXXRR((x,y,zx,y,z), Y), Y RR((x,y,zx,y,z))

Grid for Right imageGrid for Right imagerecording camerarecording camera

Grid for left imageGrid for left imagerecording camerarecording camera

Derivatives of the mapping functionDerivatives of the mapping functiondXdX LL((x,y,zx,y,z)/)/ dxdx, , dXdX LL((x,y,zx,y,z)/)/ dydy, , dXdX LL((x,y,zx,y,z)/)/ dzdz,,dYdY LL((x,y,zx,y,z)/)/ dxdx, , dYdY LL((x,y,zx,y,z)/)/ dydy, , dYdY LL((x,y,zx,y,z)/)/ dzdz,,

Derivatives of the mapping functionDerivatives of the mapping functiondXdX RR((x,y,zx,y,z)/)/ dxdx, , dXdX RR((x,y,zx,y,z)/)/ dydy, , dXdX RR((x,y,zx,y,z)/)/ dzdz,,dYdY RR((x,y,zx,y,z)/)/ dxdx, , dYdY RR((x,y,zx,y,z)/)/ dydy, , dYdY RR((x,y,zx,y,z)/)/ dzdz,,

ThreeThree--dimensionaldimensionaldisplacement vectordisplacement vector

((DDx, x, DDy, y, DDz) reconstructionz) reconstructionby solving Equation (4by solving Equation (4--2200))with least square methodwith least square method

Calibration imagesCalibration imagesfrom the left imagefrom the left imagerecording camerarecording camera

Calibration imagesCalibration imagesfrom the rightfrom the rightimageimagerecording camerarecording camera

XX LL, Y, Y LL XX RR, Y, Y RR

xx,,y,zy,z xx,,y,zy,z

Coordinate values of the point (Coordinate values of the point ( xx,y,y ))in the objective planein the objective plane

ThreeThree--dimensional displacementdimensional displacementvector (vector ( DDx, x, DDy, y, DDz) at the z) at the the point (the point ( x,yx,y))

PIV images of left cameraPIV images of left camera PIV images of right cameraPIV images of right camera

Differential Differential operationoperation Differential Differential operationoperation

InIn--situ calibration to situ calibration to determine the determine the mapping functionmapping function

To reconstruct the 3To reconstruct the 3--component of the component of the velocity vector using velocity vector using the mapping functionthe mapping function


Stereoscopic PIV systemStereoscopic PIV system

Measurement region80mm by 80mm

Laser sheet

Lobed nozzle

650mm

650mm

250

250

Synchronizer

Double-pulsed Nd:YAG Laser

optics

Host computer

high-resolution CCD cameras



X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000


a. PIV image from the left cameraa. PIV image from the left camera b. PIV image from the right camerab. PIV image from the right camera



X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

X P IX E L

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000


-30-20

-100

1020

30X mm

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.00

20 m/s


Measurements ResultsMeasurements Results

-30-20

-100

-40

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z

W m/s18.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00

X mm

Ym

m

-20 0 20 40-40

-30

-20

-10

0

10

20

30

40

W m/s18.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00

10 m/s

-30-20

-100

1020X m

-40

-30

-20

-10

0

10

20

30

40

Ym

m

X

Y

Z

W m/s18.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00 X mm

Ym

m

-40 -20 0 20 40-40

-30

-20

-10

0

10

20

30

18.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00

10 m/s

a. instantaneous velocitya. instantaneous velocity b. instantaneous velocity (Xb. instantaneous velocity (X--Y plane view)Y plane view)

c. ensemblec. ensemble--averaged velocityaveraged velocity d. ensembled. ensemble--averegedavereged velocity(Xvelocity(X--Y plane view)Y plane view)


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+4ms+4ms

Classic 2Classic 2--D PIV measurementD PIV measurement

-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

Camera 1 Camera 2

Laser Sheet

α1

α2

Z

X

X PIXEL

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

X PIXEL

YP

IXE

L

0 500 10000

100

200

300

400

500

600

700

800

900

1000

Displacement vectors in left camera Displacement vectors in right camera

-40-30

-20-10

010

2030X m

-40

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z

W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.009.008.007.006.005.004.00

C. Derived Velocity fieldC. Derived Velocity field

Stereoscopic PIV measurementStereoscopic PIV measurement


DualDual--plane Stereoscopic PIV System!? plane Stereoscopic PIV System!? Why???Why???

•• Vorticity vector is defined as the curl of the velocity Vorticity vector is defined as the curl of the velocity vector vector ::

•• Simultaneous measurementsSimultaneous measurements of velocity vectors of velocity vectors (three(three--components) at least components) at least at two at two spatially separated spatially separated planesplanes are need in order to get all threeare need in order to get all three--components components of vorticity vectors. of vorticity vectors.

•• Development of a Development of a DualDual--plane Stereoscopic PIV plane Stereoscopic PIV systemsystem to achieve the stereoscopic PIV to achieve the stereoscopic PIV measurements at two parallel planes measurements at two parallel planes simultaneously.simultaneously.

;yu

xv

z ∂∂

−∂∂

=ϖ

Measurement plane

““ClassicalClassical”” PIV or SPIV systems can only PIV or SPIV systems can only provide measurement results in one single provide measurement results in one single

plane instantaneouslyplane instantaneously

z

xy

Measurement plane 1

DualDual--plane Stereoscopic PIV system can plane Stereoscopic PIV system can achieve stereoscopic PIV measurements at achieve stereoscopic PIV measurements at

two parallel planes simultaneouslytwo parallel planes simultaneously

Measurement plane2

z

xy

xw

zu

zv

yw

yx ∂∂

−∂∂

=∂∂

−∂∂

= ϖϖ ;


DualDual--plane Stereoscopic PIV System!? plane Stereoscopic PIV System!? How???How???

•• Key point for the simultaneous Key point for the simultaneous stereoscopic PIV measurements at two stereoscopic PIV measurements at two parallel planes is to achieve parallel planes is to achieve scattering scattering light separation.light separation.

Measurement plane 1Measurement plane 1

The scattering light signals from two The scattering light signals from two measurement planes will be mixed measurement planes will be mixed

without special considerationwithout special consideration

Measurement plane2Measurement plane2

zz

xxyy

polarization separation methodpolarization separation method

PP-- polarization(horizontal)polarization(horizontal)

SS-- polarization(vertical)polarization(vertical)

zz

xxyy

•• polarization separation method.polarization separation method.

•• The polarization of Mie scattering light The polarization of Mie scattering light is conservative in air.is conservative in air.

Color 1Color 1

Color 2Color 2Color (wavelength) separation methodColor (wavelength) separation method

zz

xxyy•• color (wavelength) separation methodcolor (wavelength) separation method..


Optical SetOptical Set--up for Dualup for Dual--plane SPIV Illumination plane SPIV Illumination

Double-pulsed Nd:YAG laser set A

Double-pulsed Nd:YAG laser set B

8a7b 8b

6aV

5a

7a

Half wave plate 11

10a

Laser tube 1

Laser tube 2

Laser tube 3

Laser tube 4

9a

Mirror 12

9b

6b

10b SHGSHG

Polarizer 13

Mirror 15

Cylindrical lens 14

Laser sheets

V

VV

V(s)

V(s)V

H(p)

H(p)

VV V

V (s)

1 to 4 : laser tube 5,8,11: half wave plate6,9, 10,15: mirror 7,13: polarizer 14: cylinder lens


SetSet--up for Dualup for Dual--plane SPIV Image Recordingplane SPIV Image Recording

Vertically polarized laser sheet(S-polarized lights)

Schiemflug condition

Horizontally polarized laser sheet (P-polarized lights)

Camera 3

Mirror

Camera 2

250 250

Polarizing beamsplitter cubes

Camera 1

Lens plane Mirror

Image plane

Camera 4

To laser system

Synchronizer


AeroAero--engine:engine:enhance mixing between hot highenhance mixing between hot high--speed flow exhaust from speed flow exhaust from corecore--engineenginewith cold lowwith cold low--speed bypass flowspeed bypass flow•• civilian airplanes: civilian airplanes: reduce jet noise during takereduce jet noise during take--off and landingoff and landingthrust augmentationthrust augmentation

•• Military airplanes: Military airplanes: reduce the length of the hot plume, therefore, reduce the length of the hot plume, therefore, reduce the infrared emission signals to improve reduce the infrared emission signals to improve its survivability from the attack of infrared its survivability from the attack of infrared guided missiles. guided missiles.

Combustion: Combustion: enhance mixing between the fuel with enhance mixing between the fuel with air in the combustion chamberair in the combustion chamber•• improve combustion efficiencyimprove combustion efficiency•• suppression pollutant formationsuppression pollutant formation

Concept of Lobed Mixer/NozzleConcept of Lobed Mixer/Nozzle

Lobed mixer/nozzle Lobed mixer/nozzle

NASA modelNASA model

Turbo-fan aero-engine


Vortex Structures Downstream a Lobed Mixer/NozzleVortex Structures Downstream a Lobed Mixer/Nozzle

The lobed nozzle The lobed nozzle used in the present studyused in the present study

Two kinds of vortex structures are considered to play important Two kinds of vortex structures are considered to play important roles for the roles for the mixing enhancement in a lobed mixing flow:mixing enhancement in a lobed mixing flow:•• AzimuthalAzimuthal ((spanwisespanwise) vortex structures) vortex structures due to the Kelvindue to the Kelvin--Helmholtz Helmholtz

instability at the interface between two streams.instability at the interface between two streams.•• LargeLarge--scale scale streamwisestreamwise vorticesvortices generated by the special geometry of the generated by the special geometry of the

lobed trailing edgelobed trailing edge


Laser Induced Fluorescence (LIF) Flow Visualization Laser Induced Fluorescence (LIF) Flow Visualization (Axial Slices, Re=6,000)(Axial Slices, Re=6,000)

Lobe trough sliceLobe peak slice

Lobe trough sliceLobe peak slice

Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!X/D=1.0 X/D=1.5 X/D=2.0

X/D=0.25 X/D=0.5 X/D=0.75

Laser Induced Fluorescence (LIF) Flow Visualization (Cross Sections, Re=3,000)


Measurement region80mm by 80mm

Laser sheet with P-polarization direction

Lobed nozzle

650mm

650mm

25 0

25 0

Synchronizer

cylinder lens Host computer

high-resolution CCD camera 3

Double-pulsed

Nd:YAG Laser set A

Polarizer cube

Polarizing beam splitter cubes

Mirror #3

Mirror #4

Half wave (λ/2) plateMirror #1

Mirror #2


Laser sheet withS-polarization direction

S-polarized laser beamP-polarized laser beam



Double-pulsed

Nd:YAG Laser set B

Experimental SetExperimental Set--upup

Flow condition :Flow condition :UUjetjet = 20 m/s= 20 m/sD = 40 mmD = 40 mmRe= 60,000Re= 60,000

Centrifugal compressor

Cylindricalplenum chamber

Convergent connection

Test nozzle

Two-dimension translationmechanism

System setupSystem setup

Jet supply systemJet supply system

Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!-30

-20-10

010

2030

X mm

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.00

20 m/s

A. Instantaneous velocity field at Z=10mm plane

B. the simultaneous velocity field at Z=12mm plane

The Simultaneous Measurement Results of theThe Simultaneous Measurement Results of theDualDual--plane Stereoscopic PIV System at Two Parallel Planesplane Stereoscopic PIV System at Two Parallel Planes

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1020

30X mm

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.00

20 m/s


Distributions of Three Components of Vorticity VectorsDistributions of Three Components of Vorticity Vectors

-11.

0

-11.0

-11.0

-11.0

-9.0

-9.0-9.0

-9.0

-7.0

-7.0-7.0

-7.0

-7.0

-7.0

-5.0

-5.0

-5.0

-5.0

-5.0

-3.0

-3.0

-3.0 -3.0

-3.0

-3.0

-1.0

-1.0

-1.0

-1.0

-1.0

-1.0

-1.0

-1.0

1.0

1.0

1.01.

0

1.0

1.0

3.0

3.0

3.0

3.0

3.0

5.0

5.0

5.0

5.0

7.0

7.0

7.0

7.0

7.0

9.0

9.0

9.0

9.0

9.0

11.0

11.0

11.0

11.0

11.0

X mmY

mm

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

11.009.007.005.003.001.00

-1.00-3.00-5.00-7.00-9.00

-11.00

Vorticity distribution(Y-component)

-11.0

-7.0

-7.0

-5.0

-5.0

-3.0

-3.0

-3.0

-3.0

-1.0

-1.0

-1.0

-1.0

-1.0

-1.0

-1.0

1.0

1.0

1.01.0

1.0

1.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

7.0

7.0 7.0

7.0

9.011.0

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

11.009.007.005.003.001.00

-1.00-3.00-5.00-7.00-9.00

-11.00

Vorticity distribution(X-component)

X mmY

mm

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

15.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.00

Vorticity distribution(in-plane)

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

4.503.502.501.500.50

-0.50-1.50-2.50-3.50-4.50

Vorticity distribution(Z-component)

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

15.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.00


d. instantaneous azimuthal vorticity22

yxplanein ϖϖϖ +=−

f. ensemble-averaged azimuthal

vorticity 22yxplanein ϖϖϖ +=−

e. ensemble-averaged streamwise

vorticity zϖ

-4.5

-4.5

-3.5

-2.5

-2.5

-2.5 -2.5

-1.5

-1.5

-1.5

-0.5-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

0.5

0.50.5

0.5

0.5

1.5

1.5

1.5

1.5

2.53.5

4.5

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

4.503.502.501.500.50

-0.50-1.50-2.50-3.50-4.50


c. instantaneous streamwise vorticity zϖb. instantaneous vorticity yϖa. instantaneous vorticity xϖ


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010

2030

X mm

-30

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-10

0

10

20

30

Ym

m

X

Y

Z

W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00

-40-30

-20-10

010

2030

X mm

-30

-20

-10

0

10

20

30

Ym

m

X

Y

Z

W m/s20.0019.0018.0017.0016.0015.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.003.002.00

Z=40mm plane

Measurement Results of the DualMeasurement Results of the Dual--plane Stereoscopic PIV Systemplane Stereoscopic PIV System

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

4.503.502.501.500.50

-0.50-1.50-2.50-3.50-4.50


10.0 m/s

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

12.0011.0010.00

9.008.007.006.005.004.003.00


10.0 m/s

Z=42mm plane


a. three-dimensional velocity vectors b.iso-surface of velocity field

Reconstructed ThreeReconstructed Three--dimensional Flow Fielddimensional Flow Field

Lobed mixerLobed mixer


a. Z=10mm cross planea. Z=10mm cross plane(Z/D=0.25)(Z/D=0.25)

b. b. Z=20mm cross planeZ=20mm cross plane(Z/D=0.50)(Z/D=0.50)

Evolution of Evolution of SpanwiseSpanwise KelvinKelvin--Helmholtz Vortex StructuresHelmholtz Vortex Structures

X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

15.0014.0013.0012.0011.0010.00

9.008.007.006.005.004.00


X mmY

mm

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

10.009.008.007.006.005.004.003.002.00


X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

6.005.605.204.804.404.003.603.202.802.402.00


X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

6.005.605.204.804.404.003.603.202.802.402.00


X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

6.005.605.204.804.404.003.603.202.802.402.00


X mm

Ym

m

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

40

6.005.605.204.804.404.003.603.202.802.402.00


c. Z=40mm cross planec. Z=40mm cross plane(Z/D=1.0)(Z/D=1.0)

d. Z=60mm cross planed. Z=60mm cross plane(Z/D=1.5)(Z/D=1.5)

e. Z=80mm cross planee. Z=80mm cross plane(Z/D=2.0)(Z/D=2.0)

f. Z=120mm cross planef. Z=120mm cross plane(Z/D=3.0)(Z/D=3.0)

pinch-off

broken down dissipated

grow up


a. Z=10mm cross planea. Z=10mm cross plane(Z/D=0.25)(Z/D=0.25)

b. b. Z=20mm cross planeZ=20mm cross plane(Z/D=0.50)(Z/D=0.50)

Evolution of LargeEvolution of Large--scale scale StreamwiseStreamwise Vortex StructuresVortex Structures

c. Z=40mm cross planec. Z=40mm cross plane(Z/D=1.0)(Z/D=1.0)

d. Z=60mm cross planed. Z=60mm cross plane(Z/D=1.5)(Z/D=1.5)

e. Z=80mm cross planee. Z=80mm cross plane(Z/D=2.0)(Z/D=2.0)

f. Z=120mm cross planef. Z=120mm cross plane(Z/D=3.0)(Z/D=3.0)

X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

4.503.502.501.500.50

-0.50-1.50-2.50-3.50-4.50

Streamwise Vortcitity

X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

4.503.502.501.500.50

-0.50-1.50-2.50-3.50-4.50


X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

2.501.791.070.36

-0.36-1.07-1.79-2.50


X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

2.501.791.070.36

-0.36-1.07-1.79-2.50


X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

2.501.791.070.36

-0.36-1.07-1.79-2.50


X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

2.501.791.070.36

-0.36-1.07-1.79-2.50


grow up

dissipated


Comparison of DualComparison of Dual--plane Stereoscopic PIV and LDV resultsplane Stereoscopic PIV and LDV results

Lobed nozzle

Laser sheet

LDV probe

CCD cameras

Measurement region650mm

650mm250

250

-5

0

5

10

15

20

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

time (s)

Vel

ocity (m

/s)

V-SPIV W-SPIV W-LDV V-LDV

Stereoscopic PIV measurement Results LDV measurement resultsEnsemble-averaged

out-of-planeVelocity W(m/s)

Deviation of the out-of-plane velocity

component STD(W)

Ensemble-averaged out-of-plane Velocity W

(m/s)

Deviation of theout-of-plane

velocity componentSTD(W)

WSPIV –WLDV

Point A(0,0,20)

17.271 0.600 16.973 0.640 0.298(1.7%)One laser sheet

on the other off Point B(0,0,40)

17.220 0.889 16.930 0.844 0.290(1.7%)

Point A(0,0,20)

17.126 0.581 16.904 0.509 0.222(1.3%)

Two lasersheets on

simultaneously Point B(0,0,40)

17.213 1.006 16.864 0.856 0.349(2.0%)


Mass Conservation EquationMass Conservation Equation

X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

1.200.930.670.400.13

-0.13-0.40-0.67-0.93-1.20

Error level in the massconservation equation

X mm

Ym

m

-40 -20 0 20 40 60-40

-30

-20

-10

0

10

20

30

40

0.450.350.250.150.05

-0.05-0.15-0.25-0.35-0.45

Error Level in the massconservation equation

Instantaneous distributionInstantaneous distribution(averaged value Q=0.35)(averaged value Q=0.35)

(equivalent error velocity (equivalent error velocity ΔΔw/Uw/U00=1.75%=1.75%))

ensembleensemble--averaged distributionaveraged distribution(averaged value Q=0.13)(averaged value Q=0.13)

(equivalent error velocity (equivalent error velocity ΔΔw/Uw/U00=0.65%=0.65%))

)(0 z

wyv

xu

UDQ

∂∂

+∂∂

+∂∂

= Z=40mm cross plane


3D3D--PTV TechniquesPTV Techniques

System setSystem set--upup measurement result of the flowmeasurement result of the flowover a over a ribletriblet surface surface

(Suzuki, (Suzuki, KasagiKasagi, 2000), 2000)


33--D PTVD PTV

((WillneffWillneff, ETH Zurich. 2003) , ETH Zurich. 2003)


Holographic PIV (HPIV) techniqueHolographic PIV (HPIV) technique

Recording systemRecording system

reconstruction systemreconstruction system

A typical instantaneous HPIV result by J. A typical instantaneous HPIV result by J. Katz group @ JHUKatz group @ JHU


Defocusing digital particle image Defocusing digital particle image velocimetryvelocimetry (DDPIV)(DDPIV)

Defocusing conceptDefocusing concept

M. M. GharibGharib group @ California group @ California Institute of TechnologyInstitute of Technology

Documents

Lecture # 14: Advanced Particle Image Velocimetry TechniqueLecture # 14: Advanced Particle Image Velocimetry Technique ... by solving Equation (4-20) with least square method Calibration