Stereoscopic PIV and Its Application on
Lobed Jet Mixing Flow Research
Hui HU, Toshio Kobayashi, Tetsuo Saga and Nobuyuki Taniguchi
Institute of Industrial Science, University of Tokyo
A “classical” PIV system
s
A typical PIV system always includes many sub-systems:
• flow field seeding
• flow field illumination
• particle image acquisition
• PIV image processing
Flow field with
tracer particles
Illumination system
(Laser and optics)
Synchronizer
display
camera
computer
The shortage of “classical” PIV technique
s
s
The "classical" PIV technique is just two dimensional method, which is only
capable of recording the projection of velocity into the plane of the laser sheet,
i.e the out-of-plane velocity component is lost while the in-plane components
are affected by an unrecoverable error due to the perspective transformation
(Nisino, 1999). For highly three-dimension flows, this can lead to substantial
measurement error of the local velocity vector.
In order to get the out-of plane velocity component, some three components
PIV (3C-PIV) and three-dimensional PIV (3-D PIV) techniques were also be
proposed. They include:
• stereoscopic PIV technique
• Dual-plane PIV technique
• 3-D PTV technique
• Holographic PIV (HPIV)
Velocity three-components reconstruction by stereoscopic PIV
dx11
Laser Sheet
dx1
dx12
x1
α1
x3
α2
V
dx3
x2
β1
x1
x3
β2
dx21
V
dx1
dx22
Camera 1
Camera 2
dx3
x2
x3
Camera arrangement for stereoscopic PIV
Laser Sheet
Laser Sheet
Camera 1
Camera 2
(a) Camera Offset
Camera 1
Laser Sheet
Camera 1
Camera 2
(c) Secheimpflug
Camera 2
(b)Lens Offset
Scheimpflug arrangement
Laser sheet (object plane)
Optical lens
Image planes
Perspective effect due to camera tilt
Left camera image of grids
Rectangular grid in fluid
Right camera image of grids
Velocity reconstruction
Between exposure t and t+∆t, a particle at x moves to x+∆x, the displacement of its image:
∆X
(c)
= F ( x + ∆x) − F ( x)
(c )
C= 1,2 for left and right camera
(c)
X: camera space
x: flow space
Performing a Taylor series expansion:
 ∆X 1(1)   F1,1(1)
 (1)


(1)
 ∆X 2   F2,1
=  (2)

( 2) 
 ∆X 1   F1,1
 ∆X ( 2 )   F ( 2 )
 2   2,1
∂F
= i
∂x j
(c)
Where:
Fi , j
(c)
F1, 2
(1)
(1)
F2, 2
(2)
F1, 2
(2)
F2, 2
(1)
F1, 3 

(1)  ∆ x1 

F2, 3 
( 2 )  ∆x2 
F1, 3 

∆
x
3
( 2 ) 
F2, 3 
c = 1,2 , i = 1,2 and
j = 1,2,3
Velocity reconstruction
Assume the relationship function (F(x) (c)) between the fluid flow space(x1, x 2, x 3,) and
camera space (X 1 (1), X 2 (1), X 1 (2) and X1 (2) ) can be expressed as an polynomial function:
F ( x) = a0 + a1 x1 + a2 x2 + a3 x3 + a4 x12
+ a5 x1 x2 + a6 x2 + a7 x1 x3 + a8 x2 x3 + a9 x3
2
2
+ a10 x1 + a11 x1 x2 + a12 x1 x2 + a13 x2 + a14 x1 x3
3
2
2
3
2
+ a15 x1 x2 x3 + a16 x2 2 x3 + a17 x1 x 2 3 + a18 x2 x32
+ a19 x1 + a20 x1 x2 + a21 x1 x3 + a x x
4
3
2
2
1 3
22 1 2
+ a23 x2 + a24 x1 x3 + a25 x1 x2 x3 + a26 x1 x2 x3
4
3
2
2
+ a27 x2 x3 + a28 x1 x3 + a29 x1 x2 x3 + a30 x2 x3
3
2
2
2
2
2
Calibration plate for stereoscopic PIV
The mapping function()
∂X
∂X
∂X
∂Y ∂Y
∂Y
|L ,
|L ,
|L ,
|L ,
|L,
|L
∂x
∂y
∂z
∂x
∂y
∂z
∂X
∂X
∂X
∂Y
∂Y
∂Y
|R ,
|R ,
|R ,
|R ,
|R ,
|R
∂x
∂y
∂z
∂x
∂y
∂z
30
30
20
0
-10
-20
20
L dX/d y
0.01 6
0.01 4
0.01 2
0.01 0
0.00 8
0.00 6
0.00 4
0.00 2
0.00 0
-0.00 1
-0.00 3
-0.00 5
-0.00 7
-0.00 9
-0.01 1
10
0
-10
-20
-30
-30
-20
- 10
0
10
20
30
40
- 40
-30
-20
- 10
0
10
20
30
40
- 40
20
0
-10
-20
-30
0
-10
-20
-30
0
X mm
10
20
30
40
0
10
20
30
40
20
Ld Y/dy
15.823
15.773
15.722
15.671
15.621
15.570
15.520
15.469
15.418
15.368
15.317
15.267
15.216
15.165
15.115
10
Y mm
10
- 10
- 10
30
20
L dY/d x
0.38 2
0.33 0
0.27 9
0.22 7
0.17 5
0.12 4
0.07 2
0.02 1
-0.03 1
-0.08 3
-0.13 4
-0.18 6
-0.23 7
-0.28 9
-0.34 1
-20
-20
X mm
30
-30
-30
X mm
30
Y mm
-20
-30
X mm
- 40
0
-10
-30
- 40
L dX/d z
-5.00 1
-5.09 8
-5.19 6
-5.29 3
-5.39 0
-5.48 8
-5.58 5
-5.68 2
-5.77 9
-5.87 7
-5.97 4
-6.07 1
-6.16 9
-6.26 6
-6.36 3
10
L dY/d z
0.67 1
0.56 2
0.45 3
0.34 5
0.23 6
0.12 8
0.01 9
-0.09 0
-0.19 8
-0.30 7
-0.41 5
-0.52 4
-0.63 3
-0.74 1
-0.85 0
10
Y mm
Y mm
10
Y mm
Ld X/dx
15.138
15.046
14.953
14.861
14.768
14.676
14.583
14.491
14.398
14.306
14.213
14.121
14.029
13.936
13.844
Y mm
20
30
0
-10
-20
-30
- 40
-30
-20
- 10
0
X mm
10
20
30
40
- 40
-30
-20
- 10
0
X mm
10
20
30
40
To calculate the displacement in flow space
(∆x1, ∆x2 and ∆x3 )
 ∆X

 ∆X

 ∆X
 ∆X

(1)
1
(1)
2
( 2)
1
( 2)
2
(1)


F1,1
  (1)
  F2,1
 =  (2)
F
1,1


  F (2)
  2,1
F1, 2
(1)
(1)
F2, 2
(2)
F1, 2
(2)
F2, 2
F1, 3 

(1)  ∆ x1 

F2, 3 
( 2 )  ∆x2 
F1, 3 

∆
x
3
( 2 ) 
F2, 3 
(1)
A least squares method is used to determine the particle displacement
in flow space (∆x1, ∆x2 and ∆x3 )
Lobed mixer/nozzle concept
Application
Aviation : jet noise suppression,
improve propulsion efficiency,
reduce specific fuel consumption
Combustion:
improve combustion efficiency,
suppression pollutant formation,
device size reduction
The purpose of the present study
1. Research the vortical and turbulent structure changes in the jet flow
2. Analysis the mechanism of the mixing enhancement by lobed nozzles
Test nozzles
Circular nozzle
Lobed nozzle
The test lobed nozzle
Y
Lobe trough
Lobe peak
D=40mm
X
Z
Experiment set-up for stereoscopic PIV
LLS（Nd:YAG)
2D-LDV
Lobed Nozzle
φ 40
3D-PIV
23°
70×70
23°
544
Section 2
430
Flow Direction
Section 1
Measurement results
Y
Y
1 0 m/s
10 m/s
0
-20
-30
Y mm
20
Z
X
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
0
-20
-30
-20
-20
-10
-10
0
X mm
0
10
Xm
m
20
Instantaneous results
10
20
mean results
In the X/D=0.5 cross section of the lobed jet flow
Y mm
Z
X
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Measurement results
Y
Y
1 0 m/s
0
-20
-30
Y mm
20
1 0 m/s
X
Z
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
0
-20
-30
-20
-20
-10
-10
0
Xm
0
10
m
Xm
20
Instantaneous results
10
m
20
mean results
In the X/D=1.0 cross section of the lobed jet flow
Y mm
Z
X
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Measurement results
Y
Y
10 m/s
Z
X
1 0 m/s
-20
Z
20
0
-20
-30
-20
-10
0
Xm
-30
10
m
-20
20
-10
0
X mm
Instantaneous results
10
20
mean results
In the X/D=1.0 cross section of the circular jet flow
Y mm
0
Y mm
20
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
X
W m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Measurement results
Y
Y
Z
X
Y mm
1 0 m/s
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
0
-20
0
-20
-20
-10
-30
0
-20
10
m
-10
20
30
0
Xm
Instantaneous results
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
-30
Xm
X
Y mm
1 0 m/s
Z
10
m
20
30
mean results
In the lobe peak axial slice of the lobed jet flow
Measurement results
Y
Y
1 0 m/s
0
-20
Y mm
20
X
1 0 m/s
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
0
-20
-20
-30
0
Xm
-20
10
m
-10
20
0
30
Xm
Instantaneous results
X
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
-30
-10
Z
Y mm
Z
10
m
20
30
mean results
In the lobe trough axial slice of the lobed jet flow
Measurement results
Y
Y
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
0
-20
1 0 m/s
0
-20
-30
-20
-10
-10
0
Xm
0
10
m
20
Xm
30
X
U m/s
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
20
-30
-20
Z
Y mm
X
Y mm
1 0 m/s
Z
10
m
20
Instantaneous results
In the axial slice of the circular jet flow
30
mean results
The comparison of Stereoscopic PIV and LDV
measurement results
12
piv-v
piv-w
ldv-w
ldv-v
Velocity m/s
10
8
6
4
2
0
-2
0
10
20
30
40
50
60
70
80
90
100
time (*15) s
Stereoscopic PIV
X direction
Y direction
Z direction
In
plane
Out
plane
X direction
LDV
Y direction
u
Std(u)
v
Std(v)
w
Std(w)
u
Std(u)
v
Std(v)
22.75
1.12
0.79
0.94
-0.13
1.48
21.80
1.71
1.34
1.96
22.06
7.86
3.17
1.32
0.51
0.74
0.53
0.21
0.26
1.01
0.22
0.36
-0.33
-0.23
-0.42
0.73
0.24
0.45
21.85
7.42
3.37
2.92
0.70
0.77
1.49
0.41
0.58
2.82
0.37
0.86
Z direction
w
Std(w)