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Schlieren & Shadowgraph Methods
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Models of Light
8o 3x10cV m/s
Physical (wave) model Wave Peaks
Geometric model
Light Rays
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Light From a Point Source
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Speed of Light in a MediumIndex of Refraction:
c
cn o c = speed of light in the medium
Typical values:
Medium n = co/c
Air 1.0003
Water 1.33
Crown glass 1.52
Plexiglas 1.51
Diamond 2.42
For gases:
kρ1n
= gas densityρk = 0.23 cm3/g for air
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Light Refraction
Medium 2
Medium 1
1θ
2θ
21 nn
Snell’s Law:
2211 θsin nθsin n
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Example, Refraction in Water
Water Surface
Pole
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Lenses
Focus
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Lenses
Point Source
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Direct Shadowgraphy
Point Source
Bubble of high density gas
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Shadowgraph Image
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Some Math
x
y
z
yεyn
nL
yε
or
yρ
nkL
yε
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The Basic Schlieren System
Point Source
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The Real Schlieren System
Extended Source
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Schlieren Image
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Schlieren vs. Shadowgraph
• Displays a mere shadow
• Shows light ray displacement
• Illuminance level responds to
• No knife edge used
• Displays a focused image
• Shows ray refraction angle, • Illuminance level responds to
• Knife edge used for cutoff
Shadowgraph Schlieren
xn
2
2
xn
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Mirrors
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ISU’s Z-type Schlieren System
1st Field Mirror 2nd Field Mirror
Screen/Instrument Panel
Light Source
Test SectionKnife Edge
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Light SourceLamp
Condenser Lens
Section A-A
A-A
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Setting Up The Schlieren System
Step 1: Find the focal length of the field mirrors
Focal Length
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Setting Up The Schlieren System
Step 2: Set up the first field mirror
1st Field Mirror
Light Source
Test Section
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Setting Up The Schlieren System
Step 3: Set up the second field mirror
1st Field Mirror
Light Source
Test Section
2nd Field Mirror
Screen/Instrument Panel
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Setting Up The Schlieren System
Step 4: Set up the knife edge
Focus the source image on the knife
Adjust the cutoff Obtain a uniform darkening of the image
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Uniform Darkening
Knife edge too close to second field mirror
Knife edge too far from second field mirror
Uniform darkening
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Some Notes
• The angle between the illuminator axis and the collimated beam should be kept to a minimum– Coma: Smearing of the mirror focus into a comet shape (cancelled out by
tilting the mirrors in opposite directions, i.e. z-type system)
– Astigmatism: Changes the focus into two short lines perpendicular to each other (limited by orienting the knife edge the same as the light source)
• A sheet of white paper is a good alignment tool
• A threaded bolt works well as a focusing tool
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References
• G.S. Settles, Schlieren & Shadowgraph Techniques, Springer-Verlag, 2001.
• D.C. Giancoli, Physics for Scientists & Engineers, Prentice Hall, 1988.
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