Lecture # 07: Flow Visualization techniques: Shadowgraph ...huhui/teaching/2010Sx/AerE343L-AerE311L/Lecture... · shadowgraph depicting the flow generated by a bullet at supersonic

Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Dr. HDr. Hui Huui Hu

Department of Aerospace EngineeringDepartment of Aerospace EngineeringIowa State University Iowa State University

Ames, Iowa 50011, U.S.AAmes, Iowa 50011, U.S.A

Lecture # 07: Flow Visualization techniques: Lecture # 07: Flow Visualization techniques: Shadowgraph and Shadowgraph and SchlierenSchlieren

AerEAerE 311L & AerE343L Lecture Notes311L & AerE343L Lecture Notes


AerE311L: Lab#01

•• Visualization of shockwaves in an supersonic jet Visualization of shockwaves in an supersonic jet flow using flow using SchielrenSchielren technique.technique.

•• Demonstration experiment onlyDemonstration experiment only

•• SignSign--in sheet signaturein sheet signature

•• No lab report No lab report


The nature of lightThe nature of light

•• According to classical electromagnetic theory, light is considerAccording to classical electromagnetic theory, light is considered to be ed to be radiation that propagates through vacuum in free spaced in the fradiation that propagates through vacuum in free spaced in the form of orm of electromagnetic waves, both oscillating transversely to the direelectromagnetic waves, both oscillating transversely to the direction of wave ction of wave propagation and normal to each other.propagation and normal to each other.

)(2sin),(

)(2sin),(

0

0

TtxBtxBTtxEtxE

zZ

yy

−=

−=

λπ

λπ

λλ : : is wavelengthis wavelengthT :T : is the period of the oscillationis the period of the oscillation

νν: : The reciprocal of the period, is called frequency, The reciprocal of the period, is called frequency, νν =1/T=1/T


The nature of light The nature of light --22

10101414 nm < nm < λλ < 10< 101717 nmnmElectrical power wavesElectrical power waves101088 nm < nm < λλ < 10< 101313 nmnmRadio and TelevisionRadio and Television101077 nm < nm < λλ < 10< 1099 nmnmRadarRadar101066 nm < nm < λλ < 10< 1099 nmnmMicrowavesMicrowaves750 nm < 750 nm < λλ < 10< 1077 nmnmSpace heatingSpace heating380 nm < 380 nm < λλ < 750 nm< 750 nmVisible lightVisible light10 nm < 10 nm < λλ < 380 nm< 380 nmDisinfecting radiationDisinfecting radiation1010--22 nm < nm < λλ < 10< 1022 nmnmXX--raysrays1010--44 nm < nm < λλ < 10< 10--11 nmnmGamma raysGamma raysλλ < 10< 10--44 nmnmCosmic raysCosmic rays

WAVELENGTH WAVELENGTH RANGERANGE

RADIATION TYPERADIATION TYPE


The nature of light The nature of light --22

•• The colors: visible light consists of radiation with wavelength The colors: visible light consists of radiation with wavelength in the range of in the range of 380~750nm (1nm=10380~750nm (1nm=10--99m) which corresponds to the frequency range between 4.0 m) which corresponds to the frequency range between 4.0 ××10 10 15 15 to 7.9 to 7.9 ××10 10 1515 Hz.Hz.

750 nm < 750 nm < λλ < 1000 nm< 1000 nminfraredinfrared647 nm < 647 nm < λλ < 750 nm< 750 nmRed Red 585 nm < 585 nm < λλ < 647 nm< 647 nmOrangeOrange575 nm < 575 nm < λλ < 585 nm< 585 nmYellow Yellow 491 nm < 491 nm < λλ < 575 nm< 575 nmGreenGreen424 nm < 424 nm < λλ < 491 nm< 491 nmBlueBlue380 nm < 380 nm < λλ < 424 nm< 424 nmViolet Violet 0.85 nm < 0.85 nm < λλ < 380 nm< 380 nmUltraviolet (UV)Ultraviolet (UV)

WAVELENGTH WAVELENGTH RANGERANGE

COLORCOLOR


The nature of light The nature of light –– as photonsas photons

–– Photon scattering.Photon scattering.•• one finds experimentally that the frequency of the scattered wavone finds experimentally that the frequency of the scattered wave is e is

changed, which does not come out of a wave picture of light. changed, which does not come out of a wave picture of light. However, when the light is viewed as a photon with energy However, when the light is viewed as a photon with energy proportional to the associated light wave, excellent agreement wproportional to the associated light wave, excellent agreement with ith experiment is found. experiment is found.

–– The photoelectric effect: The photoelectric effect: •• When light is shone at a metal plate, it is found that electronsWhen light is shone at a metal plate, it is found that electrons are are

ejected. These electrons then get accelerated to a nearby plate ejected. These electrons then get accelerated to a nearby plate by an by an external potential difference, and a photoelectric current is external potential difference, and a photoelectric current is established, as belowestablished, as below

•• The photons hit an electron in the metal, giving up its energy, The photons hit an electron in the metal, giving up its energy, This This is enough to free the electron from the attractive forces holdinis enough to free the electron from the attractive forces holding it in g it in the metal, and it is accelerated towards the other side, causingthe metal, and it is accelerated towards the other side, causing a a flow of charges and hence a current.flow of charges and hence a current.

•• It is found experimentally that the photoelectric current dependIt is found experimentally that the photoelectric current depends s critically on the frequency of the light being used. This is a fcritically on the frequency of the light being used. This is a feature eature of the energy that the electrons gain when struck by the light, of the energy that the electrons gain when struck by the light, but in but in the wave picture the energy of the light depends on the amplitudthe wave picture the energy of the light depends on the amplitude, e, and not on the frequency. and not on the frequency.

•• However, in the photon picture of light the energy of the photonHowever, in the photon picture of light the energy of the photon is is proportional to the frequency of the associated wave, which proportional to the frequency of the associated wave, which therefore provides a natural explanation of the frequency therefore provides a natural explanation of the frequency dependence of the photoelectric current.dependence of the photoelectric current.

•• The explanation, which was first given by Einstein and which wonThe explanation, which was first given by Einstein and which wonhim the Nobel Prize.him the Nobel Prize.

JsconstPlanckh

3410624.6 −×== νε


Light propagate through mediaLight propagate through media

•• Refractive index:Refractive index:

•• Index of refraction of a material generally increasing slightly Index of refraction of a material generally increasing slightly with decreasing with decreasing wavelength of the light. Such phenomena is called wavelength of the light. Such phenomena is called dispersion.dispersion.

1/ 0 >==λλvcn

ρρ

L

L

KKn

−+

=1

21

2.422.42DiamondDiamond

1.921.92zirconzircon

1.771.77sapphiresapphire589nm589nm

1.591.59PolystyrenePolystyrene

1.581.58LexanLexan

1.511.51PlexiglasPlexiglas

1.57~1.891.57~1.89Flint glassFlint glass1.5011.501BenzeneBenzene1.000131.00013HH22

1.521.52Crown glassCrown glass1.4721.472TurpentineTurpentine1.000451.00045COCO22

1.471.47Pyrex glassPyrex glass1.3611.361Ethyl alcoholEthyl alcohol1.000361.00036HeHe

1.461.46Fused quartzFused quartz1.3331.333WaterWater1.000291.00029AirAir

nnSolidSolidnnLiquidLiquidnnGasGas

sm /3x10c 80 ≈


Light RefractionLight Refraction

Medium 2Medium 1

1θ

2θ

21 nn <

Snell’s Law:

2211 θsin nθsin n =


Example, Refraction in WaterExample, Refraction in Water

Water Surface

Pole


LensesLenses

Point Source

Convex lensConvex lens

Concave lensConcave lens


Shadowgraph and Shadowgraph and SchlierenSchlieren techniquetechnique

•• Index of refraction:Index of refraction:

•• Depend on variation of index of refraction Depend on variation of index of refraction in a transparent medium and the resulting in a transparent medium and the resulting effect on a light beam passing through the effect on a light beam passing through the test sectiontest section

•• Shadowgraph systems: are used to indicate Shadowgraph systems: are used to indicate the variation of the second derivatives the variation of the second derivatives (normal to the light beam) of the index of (normal to the light beam) of the index of refraction.refraction.

•• SchlierenSchlieren Systems: are used to indicate Systems: are used to indicate the variation of the first derivative of the the variation of the first derivative of the index of refraction index of refraction

1/ 0 >==λλvcn

shadowgraph depicting the flow generated by a bullet shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew at supersonic speeds. (by Andrew DavidhazyDavidhazy ))

SchlierenSchlieren images of the muzzle blast and images of the muzzle blast and supersonic bullet from firing a .30supersonic bullet from firing a .30--06 caliber 06 caliber highhigh--powered rifle (by Gary S. Settlespowered rifle (by Gary S. Settles ))


•• Shadowgraph and Shadowgraph and SchlierenSchlieren Systems are Systems are often used in shock waves and flame often used in shock waves and flame phenomena, in which density gradient is phenomena, in which density gradient is quite big.quite big.

•• While these techniques are mostly used for While these techniques are mostly used for qualitative flow visualization, they can be qualitative flow visualization, they can be used to determine pressure, density or used to determine pressure, density or temperature measurements theoretically. temperature measurements theoretically.

•• These techniques are often used to These techniques are often used to determine the integrated quantity over the determine the integrated quantity over the length of light beam.length of light beam.

shadowgraph image of plumes during solidification shadowgraph image of plumes during solidification process (by process (by LumLum CheeChee))

SchlierenSchlieren imageimage

Shadowgraph and Shadowgraph and SchlierenSchlieren techniquetechnique


Fundamentals of Fundamentals of SchlierenSchlieren SystemSystem

•• According to definition of index of refraction, According to definition of index of refraction, the light velocity will be V=Cthe light velocity will be V=Coo/n./n.

•• The slope of the wave front of the light:The slope of the wave front of the light:

•• If the angle is quite small.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

=

===−==

ΔΔΔ−=ΔΔ

=Δ

ΔΔΔΔ−=Δ−Δ=Δ

Δ=Δ

Δ+

α

α

τ

τ

ΔΔyy

ΔΔZZ

yy

ZZ

Parallel lightsParallel lights

dzdy

ΔΔ22ZZ

'αΔ

'αΔ

'αΔ

∫∫ =⇒≈

=⇒

===−=

dzdydnn

dzdydn

n

dzdy

nddzdydn

ndz

dydn

nndz

dyn

dnd

'1

)(1'

)(ln)(1][1])1(

[' 2

αα

α

1/ 0 >==λλvcn


Fundamentals of Fundamentals of SchlierenSchlieren SystemSystem

•• For a gas flow with density For a gas flow with density change:change:

Ldydn

af

II

Ldydn

af

IIn

dzdydn

af

II

yn

ny

dzdydn

af

IIdz

dydna

fII

Kk

Kk

Kk

Kk

Kk

ρρ

ρρ

ρρ

ρρ

α

α

0

02

0

02

0

02

0

0

2

2

1

11

11

'

−±=

Δ⇒

−±=

Δ⇒≈

−±=

Δ⇒

∂∂

−=

∂∂

±=Δ

⇒=

±=Δ

∫

∫∫

LyT

Tn

af

II

constyT

Tnnif

dzyT

Tn

afdz

dydn

af

II

yT

Tn

dydn

Kk

KKk

∂∂

∂∂

±=Δ

⇒

≅∂∂

∂∂

⇒→

∂∂

∂∂

=±=Δ

∂∂

∂∂

=

∫∫

2

22

1


Visualization of shock wave in a transonic/supersonic nozzle Visualization of shock wave in a transonic/supersonic nozzle using using SchlierenSchlieren techniquetechnique

Before turning on the Supersonic jetBefore turning on the Supersonic jet

AftyerAftyer turning on the Supersonic jetturning on the Supersonic jet


Shadowgraph techniqueShadowgraph technique

∫

∫

⋅−

=Δ

⇒

=

⋅−=≈Δ

⇒

⋅−≈Δ⋅−=

−ΔΔ

=−

=Δ

⋅+Δ=ΔΔΔ

=

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

α

α

αα

α

•• Sensitive is proposal to Sensitive is proposal to ZZscsc


Shadowgraph techniqueShadowgraph technique

Experimental setup with one converging mirrorExperimental setup with one converging mirror

Experimental setup without lens or mirrorExperimental setup without lens or mirror


Direct Shadowgraph

Point SourcePoint Source

Bubble of high Bubble of high density gasdensity gas


Schlieren vs. ShadowgraphSchlieren vs. Shadowgraph

ShadowgraphShadowgraph

•• Displays a mere shadowDisplays a mere shadow•• Shows light ray displacementShows light ray displacement•• Contrast level responds toContrast level responds to

•• No knife edge usedNo knife edge used

SchlierenSchlieren

•• Displays a focused imageDisplays a focused image•• Shows ray refraction angle, Shows ray refraction angle, εε•• Contrast level responds toContrast level responds to

•• Knife edge used for cutoffKnife edge used for cutoffyn∂∂

2

2

yn

∂∂


ExamplesExamples


ISU’s Z-type Schlieren System

1st Field Mirror 2nd Field Mirror

Screen/Instrument Panel

Light Source

Test SectionKnife Edge


Light SourceLight Source

LampCondenser Lens

Section A-A

A-A


Setting Up The Schlieren SystemSetting Up The Schlieren System

Step 1: Find the focal length of the field mirrors

Focal Length



Step 2: Set up the first field mirror

1st Field Mirror

Light Source

Test Section



Step 3: Set up the second field mirror

1st Field Mirror

Light Source

Test Section

2nd Field Mirror

Screen/Instrument Panel



Step 4: Set up the knife edge

Focus the source image on the knife

Adjust the cutoff Obtain a uniform darkening of the image


Uniform DarkeningUniform Darkening

Knife edge too close to second field mirror

Knife edge too far from second field mirror

Uniform darkening

Lecture # 07: Flow Visualization techniques: Shadowgraph ...huhui/teaching/2010Sx/AerE343L-AerE311L/Lecture... · shadowgraph depicting the flow generated by a bullet at supersonic

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