Lecture # 07: Flow Visualization techniques: Shadowgraph and Schlieren

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1 AerE 311L & AerE343L Lecture Notes Lecture # 07: Flow Visualizatio techiques: Shadowgraph ad Schliere Dr. Hui H Hu Departmet of Aerospace Egieerig owa State Uiversity Ames, owa 50011, U.S.A

2 AerE311L: Lab#01 Visualizatio of shockwaves i a supersoic jet flow usig Schielre techique. Demostratio experimet oly Sig-i i sheet sigature No lab report

directio of wave propagatio ad ormal to each other.

3 The ature of light Accordig to classical electromagetic theory, light is cosidered ed to be radiatio that propagates through vacuum i free spaced i the form f of electromagetic waves, both oscillatig trasversely to the directio of wave propagatio ad ormal to each other. E B y Z ( x, t) ( x, t) = = E B y0 z0 x si π ( λ x si π ( λ t T t T ) ) λ : T : is wavelegth is the period of the oscillatio ν: The reciprocal of the period, is called frequecy, ν =1/T

The ature of light - RADATON TYPE Cosmic rays Gamma rays X-rays

Radio ad Televisio Electrical power waves WAVELENGTH RANGE λ <

380 m < λ < 750 m 750 m < λ < 10 7 m 10 6 m < λ < 10 9 m 10 7 m

4 The ature of light - RADATON TYPE Cosmic rays Gamma rays X-rays Disifectig radiatio Visible light Space heatig Microwaves Radar Radio ad Televisio Electrical power waves WAVELENGTH RANGE λ < 10-4 m 10-4 m < λ < 10-1 m 10 - m < λ < 10 m 10 m < λ < 380 m 380 m < λ < 750 m 750 m < λ < 10 7 m 10 6 m < λ < 10 9 m 10 7 m < λ < 10 9 m 10 8 m < λ < m m < λ < m m 17 m

The ature of light - The colors: visible light cosists of radiatio with wavelegth i the rage of 380~750m (1m=10-9 m) which correspods to the frequecy rage betwee 4.0 10 15 to 7.9 10 15 Hz.

5 The ature of light - The colors: visible light cosists of radiatio with wavelegth i the rage of 380~750m (1m=10-9 m) which correspods to the frequecy rage betwee to Hz. COLOR Ultraviolet (UV) Violet Blue Gree Yellow Orage Red ifrared WAVELENGTH RANGE 0.85 m < λ < 380 m 380 m < λ < 44 m 44 m < λ < 491 m 491 m < λ < 575 m 575 m < λ < 585 m 585 m < λ < 647 m 647 m < λ < 750 m 750 m < λ < 1000 m

The ature of light as photos Photo scatterig. oe fids experimetally that the frequecy of the scattered wave e is chaged, which does ot come out of a wave picture of light.

The photoelectric effect: Whe light is shoe at a metal plate, it is foud that electros are ejected.

givig up its eergy, This is eough to free the electro from the attractive forces holdig g it i the metal, ad it is accelerated towards the other side, causig a flow of

This is a feature f of the eergy that the electros gai whe struck by the light, but i the wave picture the eergy of the light depeds o the amplitude, ad ot o the frequecy.

6 The ature of light as photos Photo scatterig. oe fids experimetally that the frequecy of the scattered wave e is chaged, which does ot come out of a wave picture of light. However, whe the light is viewed as a photo with eergy proportioal to the associated light wave, excellet agreemet with w experimet is foud. The photoelectric effect: Whe light is shoe at a metal plate, it is foud that electros are ejected. These electros the get accelerated to a earby plate by a exteral potetial differece, ad a photoelectric curret is established, as below The photos hit a electro i the metal, givig up its eergy, This is eough to free the electro from the attractive forces holdig g it i the metal, ad it is accelerated towards the other side, causig a flow of charges ad hece a curret. t is foud experimetally that the photoelectric curret depeds critically o the frequecy of the light beig used. This is a feature f of the eergy that the electros gai whe struck by the light, but i the wave picture the eergy of the light depeds o the amplitude, ad ot o the frequecy. However, i the photo picture of light the eergy of the photo is proportioal to the frequecy of the associated wave, which therefore provides a atural explaatio of the frequecy depedece of the photoelectric curret. The explaatio, which was first give by Eistei ad which wo him the Nobel Prize. ε = hν Plack cost = Js

7 Refractive idex: Light propagate through media λ = c / v = 0 > 1 λ dex of refractio of a material geerally icreasig slightly with decreasig wavelegth of the light. Such pheomea is called dispersio. 1+ K Lρ = 1 K ρ Gas Air He CO H m Liquid Water Ethyl alcohol Turpetie Bezee L c Solid 0 Fused quartz Pyrex glass Crow glass Flit glass Plexiglas Lexa Polystyree sapphire zirco Diamod 3x10 8 m / s ~

8 Light Refractio Sell s Law: θ 1 = 1si θ1 si θ 1 < Medium 1 Medium θ

9 Example, Refractio i Water Water Surface Pole

10 Leses Poit Source Covex les Cocave les

$dex of refractio: Shadowgraph ad Schliere techique λ = c / v = 0 > 1 λ Deped o variatio of idex of refractio i a trasparet medium ad the resultig effect o a light$ $refractio. shadowgraph depictig the flow geerated by a bullet at supersoic speeds.$

11 dex of refractio: Shadowgraph ad Schliere techique λ = c / v = 0 > 1 λ Deped o variatio of idex of refractio i a trasparet medium ad the resultig effect o a light beam passig through the test sectio Shadowgraph systems: are used to idicate the variatio of the secod derivatives (ormal to the light beam) of the idex of refractio. shadowgraph depictig the flow geerated by a bullet at supersoic speeds. (by Adrew Davidhazy ) Schliere Systems: are used to idicate the variatio of the first derivative of the idex of refractio Schliere images of the muzzle blast ad supersoic bullet from firig a caliber high-powered rifle (by Gary S. Settles )

While these techiques are mostly used for qualitative flow visualizatio, they ca be used to determie pressure, desity or

12 Shadowgraph ad Schliere techique Shadowgraph ad Schliere Systems are ofte used i shock waves ad flame pheomea, i which desity gradiet is quite big. While these techiques are mostly used for qualitative flow visualizatio, they ca be used to determie pressure, desity or temperature measuremets theoretically. These techiques are ofte used to determie the itegrated quatity over the legth of light beam. shadowgraph image of plumes durig solidificatio process (by Lum Chee) Schliere image

13 Fudametals of Schliere System Accordig to defiitio of idex of refractio, the light velocity will be V=C o /. The slope of the wave frot of the light: f the agle Δα' is quite small. dy dz C0 ΔZ = Δτ 1 Δ Z = ΔZ ΔZ y+δy = C0( Δ( ) / Δy) Δτ Δy Δ Z 1 Δα' = = ( Δ( ) / Δy) ΔZ Δy 1 d( ) dy 1 d 1 d d(l ) = dα' = [ ] dz = [ ] dz = ( ) dz = dz dz dy dy dy dy d y d(l ) = dz dy 1 d( ) = 1 d 1 d d(l ) dα' [ ] dz = [ ] dz = ( ) dz = dz dy dy dy dy 1 d 1 d α' = ( ) dz α' = dz dy dy Parallel lights y λ = c / v = 0 > 1 λ Δy Δα' Δ ΔZ Z Z Δα'

14 Copyright by Dr. Hui owa State Uiversity. All Rights Reserved! Fudametals of Fudametals of Schliere Schliere System System For a gas flow with desity For a gas flow with desity chage: chage: L dy d a f L dy d a f dz dy d a f y y dz dy d a f dz dy d a f K k K k K k K k K k ρ ρ ρ ρ ρ ρ ρ ρ α α ' = ± Δ = ± Δ = ± Δ = = ± Δ = = ± Δ L y T T a f cost y T T if dz y T T a f dz dy d a f y T T dy d K k K K k = ± Δ = = ± Δ = 1

15 Visualizatio of shock wave i a trasoic/supersoic ozzle usig Schliere techique Aftyer turig o the Supersoic jet Before turig o the Supersoic jet

16 Shadowgraph techique Δy sc = 0 Δysc Δysc = Δy + Z sc dα Δ sc 0 Δy = = Δysc dα dα = Z sc Z sc Δysc dy Δ dα = Z sc 0 dy 1 d sice α = dz a dy Δ Z sc d = dz dy 0 a Sesitive is proposal to Z sc

17 Shadowgraph techique Experimetal setup with oe covergig mirror Experimetal setup without les or mirror

18 Direct Shadowgraph Poit Source Bubble of high desity gas

19 Schliere vs. Shadowgraph Shadowgraph Displays a mere shadow Shows light ray displacemet Cotrast level respods to No kife edge used y Schliere Displays a focused image Shows ray refractio agle, ε Cotrast level respods to y Kife edge used for cutoff

20 Examples

21 SU s Z-type Schliere System Light Source 1 st Field Mirror d Field Mirror Test Sectio Scree/strumet Pael Kife Edge

22 Light Source Codeser Les Lamp A-A Sectio A-A

23 Settig Up The Schliere System Step 1: Fid the focal legth of the field mirrors Focal Legth

24 Settig Up The Schliere System Step : Set up the first field mirror Light Source 1 st Field Mirror Test Sectio

25 Settig Up The Schliere System Step 3: Set up the secod field mirror Light Source 1 st Field Mirror d Field Mirror Test Sectio Scree/strumet Pael

26 Settig Up The Schliere System Step 4: Set up the kife edge Focus the source image o the kife Adjust the cutoff Obtai a uiform darkeig of the image

27 Uiform Darkeig Kife edge too close to secod field mirror Kife edge too far from secod field mirror Uiform darkeig

Shadowgraph, Schlieren and Interferometry Part - 01

Shadowgraph, Schlieren and Interferometry Part - 01 AerE 545 class otes #8 Shadowgraph, Schliere ad tererometry Part - Hui Hu Departmet o Aerospace Egieerig, owa State Uiversity Ames, owa 5, U.S.A dex o reractio: λ c / v > λ Deped o variatio o idex o reractio