Shadowgraph, Schlieren and Interferometry Part - 01

Transcription

1 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

2 dex o reractio: λ c / v > λ Deped o variatio o idex o reractio i a trasparet medium ad the resultig eect o a light beam passig through the test sectio troductio- Shadowgraph systems: are used to idicate the variatio o the secod derivatives (ormal to the light beam) o the idex o reractio. Schliere Systems: are used to idicate the variatio o the irst directive o the idex o reractio shadowgraph depictig the low geerated by a bullet at supersoic speeds. (by Adrew Davidhazy ) tererometry systems: respose directly the dierece o optical path legth, especially givig the idex o relectio ield withi the low ield. Holographic itererometry image o shoc-vortex iteractio Schliere images o the muzzle blast ad supersoic bullet rom irig a caliber high-powered rile (by Gary S. Settles )

3 troductio- Shadowgraph ad Schliere Systems are ote used i shoc waves ad lame pheomea, i which desity gradiet is quite big. terereometry are ote used to study a low i which desity gradiet are small. While these techiques are mostly used or qualitative low visualizatio, they ca be used to determie pressure, desity or temperature measuremets theoretically. These techiques are ote used to determie the itegrated quatity over the legth o light beam. These techiques are usually used or -D D low without idex o reractio or desity variatios alog the beam. shadowgraph image o plumes durig solidiicatio process (by Lum Chee) temperature ields ad the heat traser aroud a heated cylider Schliere image

4 troductio-3 dex o reractio is a uctio o thermodyamic state (desity) or homogeeous medium: Lorez-Loretz Loretz relatioship: Whe, or gaseous low: at stadard coditio, with o ad ρ o, : ρ + cost Whe irst ad secod derivative is determied as i Schliere ad shadowgraph apparatus: cost ρ ρ cost cost ρ ρ ( ) ρ ρ ρ ρ ρ ρ cost ρ ρ ρ cost

5 troductio-4 Applicatio o the Schliere ad shadowgraph techiques: Compressible low with shoc waves Natural covective low desity chages desity chages Flame ad combustio system: desity chages Temperature chages iside lows: For low speed low with heat traser: P costat ρ P T ρ T ρ P / RT RT T ρ ρ T ρ T ρ T T ρ ρ ρ T [ ρ T ρ T + ( ) T ]

6 Copyright by Dr. Hui owa State Uiversity. All Rights Reserved! troductio-5 For reversible, adiabatic process: For reversible, adiabatic process: y P y y P y P y P P P cost P P cost P ) ( ) ( ) ( ) ( C C speciic heat; the ratio o is ) ( v p ρ ρ ρ ρ

7 Fudametals o Schliere System Accordig to deiitio o idex o reractio, the light velocity will be VC o /. The slope o the wave rot o the light: the agle Δα' is quite small. dy dz C ΔZ Δτ Δ Z ΔZ ΔZ y+δy C( Δ( ) / Δy) Δτ Δy Δ Z Δα' ( Δ( ) / Δy) ΔZ Δy d( ) dy d d d(l ) dα' [ ] dz [ ] dz ( ) dz dz dz dy dy dy dy d y d(l ) dz dy Parallel lights y λ c / v > λ Δy Δα' Δ ΔZ Z Z Δα' d( ) d d d(l ) dα' [ ] dz [ ] dz ( ) dz dz dy dy dy dy d d α' ( ) dz α' dz dy dy

8 Fudametals o Schliere System The itesity ater the shape razor blade (ie edge) beore the experimet a a The itesity ater the deormatio due to the variatio o the idex o reractio Δa Δa d + ( + ) a a Δ d Δa cotrast a d( cotrast) sesitivity : dα a Sesitivity is proportioal to ad iversely to a. α ± a

9 Fudametals o Schliere System The itesity ater the shape razor blade (ie edge) beore the experimet a a The itesity ater the deormatio due to the variatio o the idex o reractio Δa Δa d + ( + ) a a Δ d Δa cotrast a d( cotrast) sesitivity : dα a Sesitivity is proportioal to ad iversely to a. α ± a

10 Fudametals o Schliere System

11 Fudametals o Schliere System

12 Fudametals o Schliere System

13 Fudametals o Schliere System For a gas low with desity chage: Δ α ± a d Δ α' dz dy ρ ρ Δ ± a d ± dz a dy Δ ± a ρ dρ L ρ dy dρ dz dy

14 Fudametals o Schliere System For a gas low with costat pressure distributio: Δ d ± dz a dy T T ρ ρ Δ ρ dt ± dz a ρ T dy Δ P dt ± a ρ RT dy Δ P dt ± L a ρ RT dy dz

15 Fudametals o Schliere System For a liquid low: is a uctio o temperature T. d T dy T Δ d T ± dz a dy a T T i cost T Δ T ± L a T dz

16 Lab # 3-3 Visualizatio o shoc wave i a trasoic/supersoic ozzle usig Schliere techique

17 Alterative Schliere system A. Setup with oe covergig ad oe plae mirror A. Setup with oe covergig mirror

18 Holographic Schliere system