Transcript PPT - Lcgui.net

Imaging Techniques for Flow and Motion Measurement
Lecture 21
Shadowgraph, Schielieren and
Speckle Photography
Lichuan Gui
University of Mississippi
2011
1
Refractive Index in Gas
The Gladstone-Dale Formula:
n 1  K
1 e2 L
fi
K

2 me m  i2   2
n – refractive index
K – Gladstone-Dale constant
 – density
e – charge of an electron
me – mass of an electron
L – Loschmidt’s number
m – molecular weight
 – frequency of visualizing light
i – resonant frequency of distorted electron
fi – oscillator strength of distorted electron
In gas mixture of N components:
N
K   Kn
n 1
n

2
Deflection of Light Ray in Gas
Refractive index in compressible flow at certain time:
n  n  x, y , z 
Light ray in an inhomogeneous refractive field:
- Undisturbed light ray would arrive at Q
- Deflected light ray arrives at point Q*
- Optical length covered by deflected ray
different from that of undisturbed
i.e. t*t
Quantities can be measured in photographic film:
- The displacement QQ *
Shadowgraph
- The angular deflection      *
Schlieren method
- The phase shift between both rays    *
Mach-Zehnder interferometer
3
Deflection of Light Ray in Gas
Relations between refractive index and measured quantities:
 x l 
2
1
 y l
2

1
1 n
dz
n x
1 n
dz
n y
tan  x  
2
tan  y  
2
1
1
1 n
dz
n x
1 n
dz
n y
1 2
t  t  t   nx, y, z   n  dz
c 1
*
4
Shadowgraph
Schematic arrangement of two typical shadowgraph systems
Photo film or screen
Light source
Spherical mirrors or lenses
Camera lens
Optical disturbance (test object)
Focus plane
5
Shadowgraph
Working principle: detecting second derivatives  2n x 2 ,  2n y 2
Object
Ph
n y  0 &  2n y 2  0
Uniform illumination
n y  0 &  2n y 2  0
Uniform illumination
n y  0 &  2n y 2  0
Non-uniform illumination
y
z
6
Shadowgraph
APLLICATION: DETACHED SHOCK WAVE
The shadowgraph of a supersonic flow
around a finned hemisphere
The bow shock is detached Because of
the blunt body.
The flow behind the nearly normal portion
of the shock is subsonic. Thus, no Mach
waves are seen near the line of symmetry.
As the subsonic flow sweeps over the
body, it accelerates, ultimately becomes
sonic and then supersonic.
The position of the transition to supersonic
flow can be estimated by noting the
position of the first appearance of Mach
lines on the body.
Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/
7
Shadowgraph
APPLICATION: A .308 CALIBER BULLET
Shadowgraph of Winchester .308 caliber
bullet traveling at about 2800 ft/sec,
M=2.5.
Curvature of the Mach lines generated at
the nose
Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/
8
Shadowgraph
APPLICATION: SHOCK WAVES AROUND THE X-15
Classical shock wave pattern
around a free-flight model of the
X-15 at M=3.5.
In the lower half of the image,
the convergence of the
downstream shocks with the
main bow shock is clearly seen.
Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/
9
Schlieren Method
Schematic arrangement of a Toeplor Schlieren system
Spherical mirrors or lenses
Photo film or screen
Light source
Optical disturbance (test object)
Detecting 1st derivatives
n x , n y
Imaging techniques for fluid flow measurements
10
Schlieren Method
Different configurations of Schlieren system
Double-path systems
Z-shaped system
11
Schlieren Method
APPLICATION: PENETRATION OF ALUMINUM FOIL BY A BULLET
Pattern of waves generated as a .222
caliber bullet passes through a hanging
sheet of aluminum foil.
The reflected shock is clearly seen at the
left of the foil.
A second spherical shock surface can be
seen on the right side of the foil.
The small disturbances just behind the
shock are bits of the foil ejected at
impact.
Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/
12
Schlieren Method
APPLICATION: REFRACTION OF SHOCK WAVES
The schlieren photo at the right reveals
the pattern of waves generated by a .222
caliber bullet traveling at about Mach 3.
The bullet has just passed through the
plume of a candle and the different
densities in the heated plume have
refracted the lower set of shock waves.
Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/
13
Schlieren Method
Full-Scale Schlieren Images
Heat Released from Gas Grill
Heat from space heater, lamp& person
Cold Air Dragged From A Freezer
From http://www.mne.psu.edu/psgdl/FSSPhotoalbum/index1.htm
14
Speckle Photography
Two schemes of Speckle pattern formation
Example of digital speckle image
15
Speckle Photography
Two possible configuration of the system:
1. Object between light source and speckle generator


0
  M  0  M    d
16
Speckle Photography
Two possible configuration of the system:
2. Speckle generator between light source and object
0


  M  0  M    l
17
Speckle Photography
Example of speckle photography system:
(U Köpf 1972)
18
Speckle Photography
Example of speckle photography system:
(Wernekinck and Merzkirch 1986)
19
Speckle Photography
Evaluation of speckle photograph
- Young’s fringes method
- Correlation-based digital interrogation
20
Background Oriented Schlieren (BOS)
A simplified speckle photography technique:
Speckle generator
Background
image between
between light
light source
source and
and object
object
White light
0


Background
image
  M  0  M    l
21
Background Oriented Schlieren (BOS)
Ring method for axis symmetric density field reconstruction
y
- Density field includes k=1,2,3, , M rings
- Known environment density n0
- Constant density nk in rings
- Compute nk from outside to inside
n1 n2 n3   
nk

nM n0
22
x
Background Oriented Schlieren (BOS)
Ring method for axis symmetric density field reconstruction
Known variables at yk :
nk+1, *k , ’k
k+1
*k
k
Variable to be determined: nk
 yk
 rk
 k 1  sin 1 
 *
 k


k
yk
’k+1
’k
k
rk
nk 1  sin  k 1  nk  sin  k
nk 1  sin  k 1  nk  sin  k
nk+1
nk
 k 1   k 1
 k 1   k*   k   k
 k   k   k 1   k
1 
k 
y k   k*   k

 k  sin   
2
 rk 
 k*   k
2
nk 
nk 1  sin  k 1
sin  k
 rk  
nk  1
K
23
Background Oriented Schlieren (BOS)
Application in jet flow test:
24
Homework
– References
• F. Klinge, T. Kirmse, J. Kompenhans (2003) Application of Quantitative
Background Oriented Schlieren (BOS): Investigation of a Wing Tip
Vortex in a Transonic Wind Tunnel. Proceedings of PSFVIP-4, June 35, Chamonix, France
– Final report
• Taking part in a BOS test
• Processing a pair of BOS recording
• Completing a report including
1. brief description of the BOS technique
2. brief description of the experimental setup
3. vector plot of background image displacement
4. contour plot of density distribution