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1
Imaging Techniques for Flow and Motion Measurement
Lecture 21
Lichuan Gui
University of Mississippi
2011
Shadowgraph, Schielieren andShadowgraph, Schielieren and
Speckle PhotographySpeckle Photography
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Refractive Index in Gas Refractive Index in Gas
22
2
2
1
i
i
e
f
m
L
m
eK
e – charge of an electronme – mass of an electronL – Loschmidt’s numberm – molecular weight – frequency of visualizing lighti – resonant frequency of distorted electron fi – oscillator strength of distorted electron
The Gladstone-Dale Formula:
Kn 1n – refractive indexK – Gladstone-Dale constant – density
In gas mixture of N components:
N
n
nnKK
1
3
Deflection of Light Ray in GasDeflection of Light Ray in Gas
Refractive index in compressible flow at certain time: zyxnn ,,
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
- The angular deflection *
- The phase shift between both rays *
Shadowgraph
Schlieren method
Mach-Zehnder interferometer
4
dzx
n
nlx
2
1
1
dzy
n
nly
2
1
1
dzx
n
nx
2
1
1tan
dzy
n
ny
2
1
1tan
dznzyxnc
ttt 2
1,,
1*
Deflection of Light Ray in GasDeflection of Light Ray in Gas
Relations between refractive index and measured quantities:
5
ShadowgraphShadowgraph
Schematic arrangement of two typical shadowgraph systems
Light source Spherical mirrors or lenses
Optical disturbance (test object)
Photo film or screen
Camera lens
Focus plane
6
ShadowgraphShadowgraph
Working principle: detecting second derivatives 2222 , ynxn
0&0 22 ynyn
0&0 22 ynyn
0&0 22 ynyn
z
y
PhObject
Uniform illumination
Uniform illumination
Non-uniform illumination
7
ShadowgraphShadowgraphAPLLICATION: 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/
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ShadowgraphShadowgraphAPPLICATION: 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/
9
ShadowgraphShadowgraphAPPLICATION: 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/
Imaging techniques for fluid flow measurements 10
Schlieren MethodSchlieren Method
Schematic arrangement of a Toeplor Schlieren system
Optical disturbance (test object)
Photo film or screen
Light source
Spherical mirrors or lenses
Detecting 1st derivatives
ynxn ,
11
Schlieren MethodSchlieren Method
Different configurations of Schlieren system
Z-shaped systemDouble-path systems
12
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/
Schlieren MethodSchlieren Method
13
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/
Schlieren MethodSchlieren Method
14
Full-Scale Schlieren Images
Schlieren MethodSchlieren Method
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
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Speckle PhotographySpeckle Photography
Two schemes of Speckle pattern formation
Example of digital speckle image
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Speckle PhotographySpeckle Photography
Two possible configuration of the system:
1. Object between light source and speckle generator
dMM 0
0
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Speckle PhotographySpeckle Photography
Two possible configuration of the system:
2. Speckle generator between light source and object
0
lMM 0
18
Speckle PhotographySpeckle Photography
Example of speckle photography system:
(U Köpf 1972)
19
Speckle PhotographySpeckle Photography
(Wernekinck and Merzkirch 1986)
Example of speckle photography system:
20
Speckle PhotographySpeckle Photography
Evaluation of speckle photograph
- Young’s fringes method
- Correlation-based digital interrogation
Background Oriented Schlieren (BOS)Background Oriented Schlieren (BOS)
21
A simplified speckle photography technique:
0
lMM 0
White light
Speckle generator between light source and object
Backgroundimage
Background image between light source and object
22
Background Oriented Schlieren (BOS)Background Oriented Schlieren (BOS)
Ring method for axis symmetric density field reconstruction
n 2n 1 n 3 n k n M n 0
y
x
- Density field includes k=1,2,3, , M rings
- Known environment density n0
- Constant density nk in rings
- Compute nk from outside to inside
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Background Oriented Schlieren (BOS)Background Oriented Schlieren (BOS)
Ring method for axis symmetric density field reconstruction
Known variables at yk :
nk+1, *k , ’k
Variable to be determined: nk
*11 sin k
k
kk r
y
kkkk nn sinsin 11
kkkk nn sinsin 11
11 kk
k
n kn k+ 1
k+ 1
k
’ k+ 1
r ky k
* k ’ k
k
kkkk *
1
kkkk 12
*kk
k
2sin
*1 kk
k
kk r
y
k
kkk
nn
sin
sin 11
K
nr kk
1
24
Background Oriented Schlieren (BOS)Background Oriented Schlieren (BOS)
Application in jet flow test:
– 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 3-5, 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 technique2. brief description of the experimental setup3. vector plot of background image displacement4. contour plot of density distribution
HomeworkHomework