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Measurements in Fluid Mechanics
058:180:001 (ME:5180:0001)
Time & Location: 2:30P - 3:20P MWF 218 MLH
Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
[email protected]
http://lcgui.net
Lecture 17. Flow visualization with optical techniques
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Flow visualization with optical techniques
Refractive index
𝑛=
𝑐
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
n – refractive index
K – Gladstone-Dale constant
 – density
(T=273K, =589nm)
1 e2 L
fi
K

2 me m  i2   2
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
N
In gas mixture of N components:
K   Kn
n 1
n

Kn – value of the n-th component
n – density of the n-th component
= 1+2+3++N
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Flow visualization with optical techniques
Light deflection in variable refractive-index media
Medium 1 & 3 with uniform refractive index n0
Medium 2 with variable refractive index n(x,y)
for very small :
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:
- The displacement
QQ *
Shadowgraph
- The angular deflection      *
- The phase shift between both rays
Schlieren method
  *
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
Camera lens
Optical disturbance (test section)
Focus plane
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Flow visualization with optical techniques
The shadowgraph method
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
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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
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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Flow visualization with optical techniques
Interferometry
𝑡
𝑚𝑖𝑟𝑟𝑜𝑟
𝑏𝑒𝑎𝑚 𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟
𝐼2
𝑛 𝑥, 𝑦
∆𝜃
𝑛0
𝑏𝑒𝑎𝑚 𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟
𝑥1
𝑡0
𝐼𝑡𝑜𝑡
𝐼1
𝑥2
𝑚𝑖𝑟𝑟𝑜𝑟
Phase difference:
Light intensity:
𝐼1 = 𝐴 ∙ sin 2𝜋𝑣𝑡
𝐼2 = 𝐴 ∙ sin 2𝜋𝑣𝑡 − ∆𝜃
𝐼𝑡𝑜𝑡 = 𝐼1 + 𝐼2 = 𝐴 sin 2𝜋𝑣𝑡 + sin 2𝜋𝑣𝑡 − ∆𝜃
= 2𝐴cos
∆𝜃
∆𝜃
sin 2𝜋𝑣𝑡 −
2
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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Homework
- 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
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