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Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL. Instructor: Lichuan Gui [email protected] Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net. - PowerPoint PPT Presentation
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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 [email protected]
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