058:180 (ME:5180)
Time & Location: 2:30P - 3:20P MWF 3315 SC
Office Hours: 4:00P – 5:00P MWF 223B-5 HL

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Flow visualization with optical techniques
Refractive index 𝑐 𝑛 = 𝑣 c – light speed in vacuum v – light speed in medium
Gladstone-Dale formula
- relation between refractive index and density of gases n

1

K

K

1
2
 e
2 m e
L m

 i
2 f
 i n – refractive index
K – Gladstone-Dale constant
 – density
 2
(T=273K,

=589nm) e – charge of an electron m e
– mass of an electron
L – Loschmidt’s number m – molecular weight f
 – frequency of visualizing light
 – resonant frequency of distorted electron i i
– oscillator strength of distorted electron
In gas mixture of N components: K
 n
N 

1
K n

 n
K n
 n
– value of the n-th component
– density of the n-th component

=

1
+

2
+

3
+

+

N
3

Flow visualization with optical techniques
Light deflection in variable refractive-index media
Medium 1 & 3 with uniform refractive index n
0
Medium 2 with variable refractive index n(x,y) for very small

: 𝑟𝛿𝜑
= 𝛿𝑡 𝑟𝛿𝑣 𝛿𝑟 𝑣 = 𝑟𝛿𝑣 𝛿𝑟 with geometrical simplification:
Differential equation for the ray path:
Light deflection angle:
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Flow visualization with optical techniques
Light deflection in variable refractive-index media
- 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:
Shadowgraph - The displacement QQ
*
- The angular deflection
     * Schlieren method
- The phase shift between both rays    * Interferometry
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Flow visualization with optical techniques
The shadowgraph method
Schematic arrangement of two typical shadowgraph systems
Photo film or screen
Light source Spherical mirrors or lenses
Optical disturbance (test section)
Camera lens
Focus plane
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Flow visualization with optical techniques
The shadowgraph method
Working principle: detecting second derivatives
 2 n
 x
2
,
 2 n
 y
2
Object Ph
 n
 y

0 &
 2 n
 y
2 
0 Uniform illumination
 n
 y

0 &
 2 n
 y
2 
0
 n
 y

0 &
 2 n
 y
2 
0 y
Uniform illumination
Non-uniform illumination z
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Flow visualization with optical techniques
The shadowgraph method
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/
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Flow visualization with optical techniques
The shadowgraph method
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 /
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Flow visualization with optical techniques
The shadowgraph method
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 /
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Flow visualization with optical techniques
The Schlieren method
Schematic arrangement of a Toeplor Schlieren system
Spherical mirrors or lenses Photo film or screen
Light source
Optical disturbance (test section)
Detecting 1st derivatives
 n
 x ,
 n
 y
Imaging techniques for fluid flow measurements
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Flow visualization with optical techniques
The Schlieren method
Different configurations of Schlieren system
Double-path systems
Z-shaped system
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Flow visualization with optical techniques
The 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/
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Flow visualization with optical techniques
The 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 /
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Flow visualization with optical techniques
The Schlieren method
Full-Scale Schlieren
Shock waves from a .44 Magnum
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Flow visualization with optical techniques
The Schlieren 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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Flow visualization with optical techniques
Interferometry 𝑚𝑖𝑟𝑟𝑜𝑟 𝑡 𝑏𝑒𝑎𝑚 𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟 𝑥
1 𝑛 𝑥, 𝑦 𝑛
0 𝑡
0 𝑏𝑒𝑎𝑚 𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟
𝐼
2
∆𝜃
𝐼
1 𝑥
2 𝑚𝑖𝑟𝑟𝑜𝑟
𝐼 𝑡𝑜𝑡
Phase difference:
Light intensity:
𝐼
1
= 𝐴 ∙ sin 2𝜋𝑣𝑡
𝐼
2
= 𝐴 ∙ sin 2𝜋𝑣𝑡 − ∆𝜃
𝐼 𝑡𝑜𝑡
= 𝐼
1
+ 𝐼
2
= 𝐴 sin 2𝜋𝑣𝑡 + sin 2𝜋𝑣𝑡 − ∆𝜃 = 2𝐴cos
∆𝜃
2 sin 2𝜋𝑣𝑡 −
∆𝜃
2
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Flow visualization with optical techniques
Mach-Zehnder interferometer
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Flow visualization with optical techniques
Mach-Zehnder interferometer
EXAMPLE the interference pattern of a horizontal annulus filled with air when the inner cylinder is heated isothermally. The outer tube is cooled by water at constant temperature. http://www.thermopedia.com/content/932/
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- Read textbook 10.3-10.5 on page 231 - 244
- Questions and Problems: 6 on page 246
(optional, but may add credit to midterm examination )
- Due on 10/05
20

Try to write a Matlab program
• to select an image sample in a 64×64-pixel window from an image at x=400, y=200 http://lcgui.net/ui-lecture2012/hw/00/A001_1.BMP
• to select another image sample with a window shift of S = ( 1.6, 2.3 )
S1.bmp
S2.bmp
Example of Matlab program: clear;
A1=imread('A001_1.bmp');
G1=img2xy(A1);
M=64;
N=64; x=400; y=200; g1=sample01(G1,M,N,x,y);
Sx=1.6;
Sy=2.3; g2=sample01(G1,M,N,x+Sx,y+Sy);
S1=xy2img(g1);
S2=xy2img(g2); imwrite(S1,'S1.bmp','bmp'); imwrite(S2,'S2.bmp','bmp');
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