1 Imaging Techniques for Flow and Motion Measurement Lecture 21 Lichuan Gui University of Mississippi 2011 Shadowgraph, Schielieren and Speckle Photography

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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

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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:

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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

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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

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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


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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.


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 ,

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Different configurations of Schlieren system

Z-shaped systemDouble-path systems

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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.



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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.



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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

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Two schemes of Speckle pattern formation

Example of digital speckle image

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Two possible configuration of the system:

1. Object between light source and speckle generator

dMM 0

0

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Two possible configuration of the system:

2. Speckle generator between light source and object

0

lMM 0

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Example of speckle photography system:

(U Köpf 1972)

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(Wernekinck and Merzkirch 1986)

Example of speckle photography system:

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Evaluation of speckle photograph

- Young’s fringes method

- Correlation-based digital interrogation

Background Oriented Schlieren (BOS)Background Oriented Schlieren (BOS)

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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

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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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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


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

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1 Imaging Techniques for Flow and Motion Measurement Lecture 21 Lichuan Gui University of Mississippi 2011 Shadowgraph, Schielieren and Speckle Photography