Measurements in Fluid Mechanics058:180 (ME:5180)

Time & Location: 2:30P - 3:20P MWF 3315 SC

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Guilichuan-gui@uiowa.edu

Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

2

Lecture 37. Stereo Particle Image Velocimetry

3

Stereo PIV system– Two cameras– Translation and angular configurations– Distorted particle images (angular system)– 3-D displacement reduced from two 2-D displacements– 3 velocity components in a plane

Stereoscopic PIV

Example

G. Calcagno, F.D. Felice, M. Felli, and F. Pereira, 24th Sym. Naval Hydro. (2002)

Test region

Test result

4

Laser light sheet X

Z

Stereoscopic PIV SPIV data reduction

t=t0

t=t0+tS

Laser light sheet X

Z

S

XZ

Standard PIV view

X Z not sensible

5

Stereoscopic PIV SPIV data reduction

Laser light sheet X

Z

S

XZ

1

X1

camera #1

X2

2

camera #2

11 tanZXX

22 tanZXX Stereo view

6

Stereoscopic PIV SPIV data reduction

- Particle image displacements: (X’1, Y’1) and (X’2, Y’2)

- Imaging scale factor: M1 and M2

11 tanZXX

YYY 21

22 tanZXX

21

2211

tantan

XMXM

Z

21

221112

tantan

tantan

XMXM

X

22211 YMYM

Y

No stereo effect in yz-plane

7

Stereoscopic PIV Error propagation in SPIV

221 XX

X

221 YY

Y

22

2

22

2

11

2214

1XXXXX X

X

X

X

22

21

2

22

2

11

2

4

1YYYYY Y

Y

Y

Y

212

1

2

1XXX

212

1

2

1YYY

,2

1

1

X

X

2

1

2

X

X

,2

1

1

Y

Y

2

1

2

Y

Y

:,,For 212121 YYXX

8

Stereoscopic PIV Error propagation in SPIV

21

21

tantan

XX

Z

211 tantan

1

X

Z

212 tantan

1

X

Z

21

12

12

221

21

1 tantan

tan1tan1

tantan

ZXXZ

21

22

2 tantan

tan1

ZZ

2

22

2

11

2

22

2

11

2

ZZ

X

Z

X

ZXXZ

9

Stereoscopic PIV Error propagation in SPIV

,cot2

1

21

X

Z

X

Z

tancot

2tan2

tan1 2

21

ZZZZ

:and,,2For 212121 XXX

2

22

2

11

2

22

2

11

2

ZZ

X

Z

X

ZXXZ

222

22 tancot2

cot

Z

X

ZZ

2

tancotDefine: ,cot XZ

222ZZZ

10

Stereoscopic PIV Error propagation in SPIV

[ ]

Z

/X

0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

[ ]

[

]

10 20 30 40 50 60 70 800.0

1.0

2.0

3.0

4.0

5.0

6.0

0.5000.4750.4500.4250.4000.3750.3500.3250.3000.2750.2500.2250.2000.1750.1500.1250.1000.0750.0500.0250.000

Z/|Z|

- Optimal view angle 45

222ZZZ

,cot XZ

ZZ

2

tancot

11

Camera #1 Camera #2

Lens Plane

Stereoscopic PIV

- Object plane || Lens plane || Image plane- Uniform magnification (Mn=di/do)- Easy to focus- Off-axis angle restricted by the lens (application limited)

Translation (lateral displacement) system

12

Object plane Lens plane Image plane

Mirror pair 1

Mirror pair 1 Mirror pair 2

Mirror pair 2

Aperture stop

Stereoscopic PIV Translation (lateral displacement) system

- Single camera configuration

- View angle is limited

Test

reg

i on

Ima

ge #

1Im

age

#2

13

Stereoscopic PIV Rotational (angular displacement) system- Scheimpflug condition - Distorted image (Mnconstant)

14

Stereoscopic PIV SPIV recording evaluation

1. Evaluation with image calibration

Distorted Image Calibrated Image Velocity mapPositive: a. Uniform spatial resolution

b. Simple procedure

Negative: Image interpolation error

Image calibration methods

Polynomial mapping

Preservation of straightness of lines – for high quality camera lens

1,

1 54

876

54

321

ybxb

bybxbY

ybxb

bybxbX

65432

22

1

65432

22

1

bybxbxybybxbY

ayaxaxyayaxaX

15

Stereoscopic PIV SPIV recording evaluation

2.Evaluation with velocity calibration

Distorted Image Velocity map Velocity calibration

Positive: No image interpolation

Negative: a. Non-uniform spatial resolution

b. Evaluation grid transfer required

Basic evaluation steps:

1.Determine transformation function between physical and image plane

2.Transfer uniform evaluation grid in physical plane to image plane

3.Evaluate the distorted SPIV recordings with the transformed evaluation grid

4.Transfer the evaluated displacement components to the physical plane

16

– References • Prasad AK (2000) Stereoscopic particle image velocimetry. Exp. Fluids

29, pp. 103-116

• Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, pp. 1465-1479

– Practice with EDPIV

• Compare image calibration and vector calibration with application example #9

Stereoscopic PIV

17

Large-Scale PIVRiver surface flow measurement

City map

river

Tower

Video set at 40m height

Camera view

Floating tracer

18

Large-Scale PIVRiver surface flow measurement

Original image

Calibrated image

Physical & image coordinates

Flow filed

19

Large-Scale PIVDistorted image calibration

Physical & image coordinates- Physical coordinates (X,Y)

- Image coordinates (x,y)

- Calibration marking points (Xk,Yk) (xk,yk) for k=1,2,,N

- Image calibration function

1,

1 54

876

54

321

ybxb

bybxbY

ybxb

bybxbX

Minimal N=4 for determining constants bi (i=1,2,,8)

- inverse calibration function

716242516574

6381143846

716242516574

8275532785

bbbbYbbbbXbbbb

bbbbYbbbXbbby

bbbbYbbbbXbbbb

bbbbYbbbXbbbx

Straight-line-conservedtransformation

20

Large-Scale PIVDistorted image calibration

4

3

2

1

4

3

2

1

8

7

6

5

4

3

2

1

444444

333333

222222

111111

444444

333333

222222

111111

1000

1000

1000

1000

0001

0001

0001

0001

Y

Y

Y

Y

X

X

X

X

b

b

b

b

b

b

b

b

yxYyYx

yxYyYx

yxYyYx

yxYyYx

XyXxyx

XyXxyx

XyXxyx

XyXxyx4 marking points

>4 marking points – least square approach

N

kkkkkkkkkkkkk YXbbybxbYXybYXxbbybx

1

287654321

8,,2,10

iforbi

21

Large-Scale PIVEvaluation of LSPIV recordings- Low-Image-Density PIV mode Particle image tracking or individual particle image pattern tracking

- Low Re-number in many cases Average correlation method for steady flows

Consecutive LSPIV recordings Evaluation results

Example of LSPIV tests for steady water surface flow

22

Large-Scale PIV

– References• Muto Y, Baba Y, Aya S (2002) Velocity measurements in open channel

flow with rectangular embayments formed by spur dykes. Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No.45B-2

• Fujita I, Aya S, Deguchi T (1997) Surface velocity measurement of river flow using video images of an oblique angle. Proc. 27th IAHR Cong., San Francisco, Vol.B, No.1, pp.227-232

– Practice with EDPIV

• Work with sample: IMAGE GROUP: DISTORTED PIV IMAGES