lecture # 11: flow visualization techniques: shadowgraph ...huhui/teaching/2014fx/class... ·...
TRANSCRIPT
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Dr. Hui Hu
Department of Aerospace EngineeringIowa State University
Ames, Iowa 50011, U.S.A
Lecture # 11: Flow Visualization techniques: Shadowgraph and Schlieren
AerE 344 Lecture Notes
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Shadowgraph and Schlieren technique
• Index of refraction:
• Depend on variation of index of refraction in a transparent medium and the resulting effect on a light beam passing through the test section
• Shadowgraph systems: are used to indicate the variation of the second derivatives (normal to the light beam) of the index of refraction.
• Schlieren Systems: are used to indicate the variation of the first derivative of the index of refraction
1/ 0 vcn
shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew Davidhazy )
Schlieren images of the muzzle blast and supersonic bullet from firing a .30-06 caliber high-powered rifle (by Gary S. Settles )
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• Shadowgraph and Schlieren Systems are often used in shock waves and flame phenomena, in which density gradient is quite big.
• While these techniques are mostly used for qualitative flow visualization, they can be used to determine pressure, density or temperature measurements theoretically.
• These techniques are often used to determine the integrated quantity over the length of light beam.
shadowgraph image of plumes during solidification process (by Lum Chee)
Schlieren image
Shadowgraph and Schlieren technique
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Introduction-3
• Index of refraction is a function of thermodynamic state (density) for homogeneous medium:
• Lorenz-Lorentz relationship:
• When n1, for gaseous flow:
• at standard condition, with no and o, :
• When first and second derivative is determined as in Schlieren and shadowgraph apparatus:
constnn
211
2
2
constnconstn 11
11
)1(11
00
000
0
nn
nnconstn
2
2
0
02
2
2
2
2
20
0
11
11
yn
nyyn
consty
yn
nyyn
consty
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Introduction-4
• Application of the Schlieren and shadowgraph techniques:
– Compressible flow with shock waves density changes– Natural convective flow density changes– Flame and combustion system: density changes
• Temperature changes inside flows:– For low speed flow with heat transfer:– P = constant
])(2[1
1
11
/
222
2
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2
yT
TyT
Tn
yn
yn
nT
yT
yT
Tn
yn
yn
yT
TyT
RTP
yRTP
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Fundamentals of Schlieren System
• According to definition of index of refraction, the light velocity will be V=Co/n.
• The slope of the wave front of the light:
• If the angle is quite small.
dynd
dzyd
dzdy
nddzdydn
ndz
dydn
nndz
dyn
dnd
dzdy
Zyn
nyZ
yyn
CZZZn
CZ
yy
)(ln
)(ln)(1][1])1(
['
)/)1(('
)/)1((
2
2
2
2
02
0
y
Z
y
Z
Parallel lights
dzdy
2Z
'
'
'
dzdydnn
dzdydn
n
dzdy
nddzdydn
ndz
dydn
nndz
dyn
dnd
'1
)(1'
)(ln)(1][1])1(
[' 2
1/ 0 vcn
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Fundamentals of Schlieren System
• For a gas flow with density change:
Ldydn
af
II
Ldydn
af
IIn
dzdydn
af
II
yn
ny
dzdydn
af
IIdz
dydna
fII
Kk
Kk
Kk
Kk
Kk
0
02
0
02
0
02
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2
2
1
11
11
'
LyT
Tn
af
II
constyT
Tnnif
dzyT
Tn
afdz
dydn
af
II
yT
Tn
dydn
Kk
KKk
2
22
1
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Visualization of shock wave in a transonic/supersonic nozzle using Schlieren technique
Before turning on the Supersonic jet
Aftyer turning on the Supersonic jet
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Alternative Schlieren system
A. Setup with one converging and one plane mirror
A. Setup with one converging mirror
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Shadowgraph technique
dzdy
ndnZ
II
dzdydn
n
dydZ
II
dydZ
ydZ
yy
III
II
dZyy
IyyI
a
sc
a
sc
scsc
sc
sc
sc
scsc
scsc
2
2
0
0
0
0
0
0
1 since
1
• Sensitive is proposal to Zsc
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Shadowgraph technique
Experimental setup with one converging mirror
Experimental setup without lens or mirror
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Direct Shadowgraph
Point Source
Bubble of high density gas
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Schlieren vs. Shadowgraph
Shadowgraph
• Displays a mere shadow• Shows light ray displacement• Contrast level responds to
• No knife edge used
Schlieren
• Displays a focused image• Shows ray refraction angle, • Contrast level responds to
• Knife edge used for cutoffyn
2
2
yn
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Examples
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Examples: Shlieren Photography
A cough
The firing of an AK-47. A simulated explosion in an airplane cabin.
An invisible gas leak
A hair dryer's effects
A glass of warm water
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Examples: Shadowgraph images
.
Shadowgraph Images of Re-entry Vehicles
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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 Source
LampCondenser 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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
AerE344 Lab#9: Visualization of shockwaves using Schielren technique
• Visualization of shockwaves in an supersonic jet flow using Schielren technique.
• Demonstration experiment only
• Sign-in sheet signature
• No lab report