Laser Doppler Velocimetry (LDV)

Transcription

1 AeE 545 cla note #1 Lae Dopple elocimety (LD) Pat - 01 Hui Hu Depatment o Aeopace Engineeing, Iowa State Univeity Ame, Iowa 50011, U.S.A

2 Technique o Flow elocity Meauement Intuive technique Pitot-tatic pobe hotwie, hot ilm etc... Flow velocity meauement technique Non-intuive technique paticle-baed technique molecule-baed technique Lae Dopple elocimety (LD) Plana Dopple elocimety (PD) Paticle Image elocimety (PI) etc Lae Induced Fluoecence (LIF) Molecula Tagging elocimety (MT) etc

3 Paticle-baed Flow Diagnotic Technique Seeded the low with mall paticle (~ µm in ize) Aumption: the paticle tace move with the ame velocity a local low velocity! Flow velocity Paticle velocity p Meauement o paticle velocity

4 Lae Dopple elocimety (LD) Lae Dopple velocimety (LD, alo known a lae Dopple anemomety, o LDA) i a technique o meauing the diection and peed o luid like ai and wate. In it implet om, LD coe two beam o collimated, monochomatic lae light in the low o the luid being meaued. A micocopic patten o bight and dak tipe om in the inteection volume. Small paticle in the low pa though thi patten and elect light towad a detecto, with a chaacteitic equency indicating, via the Dopple eect, the velocity o the paticle paing though the pobe volume. Inteeence inge

5 Dopple Shit The Dopple eect, named ate Chitian Dopple (an Autian mathematician and phyicit ), i the change in equency and wavelength o a wave that i peceived by an obeve moving elative to the ouce o the wave. Light om moving object will appea to have dieent wavelength depending on the elative motion o the ouce and the obeve. Obeve looking at an object that i moving away om them ee light that ha a longe wavelength than it had when it wa emitted (a ed hit), while obeve looking at an appoaching ouce ee light that i hited to hote wavelength (a blue hit).

6 Dopple Shit a. Stationay Sound Souce b. Souce moving with ouce < ound c. Souce moving with ouce ound ( Mach 1 - beaking the ound baie ) d. Souce moving with ouce > ound (Mach upeonic)

7 Dopple Shit Fo wave that tavel though a medium (ound, ultaound, etc...) the elationhip between obeved equency and emitted equency i given by: whee v i the peed o wave in the medium v i the velocity o the ouce Fo wave that tavel at the peed o light, uch a lae light, the elationhip between obeved equency and emitted equency i given by: Becaue the detected equency inceae o object moving towad the obeve, the object' velocity mut be ubtacted when motion i moving towad the obeve. (Thi i becaue the ouce' velocity i in the denominato.) Conveely, detected equency deceae when the object move away, and o the object' velocity i added when the motion i away.

8 Fundamental o LD Fundamental o LD Fundamental o LD Fundamental o LD Take the coodinate ytem to be at et with epect to the medium, whoe peed o light wave i c. Thee i a ouce moving with velocity and emitting light wave with a equency. Thee i a detecto moving with velocity, and the unit vecto om to i n i.e.. Then the equency at the detecto i ound om I c>>, then the change in equency depend motly on the elative velocity o the ouce and detecto. λ λ ) in( ) in( ) in( ) ˆ (ˆ 0 ˆ ˆ ˆ ˆ c c e e e e n c n i i

9 Fundamental o LD By uing a lae bean o wavelength λ488nm (Agon-Ion lae), the maximum Dopple hit om a paticle moving with a velocity o would be: 1.0m/ 4.1 MHz 10.0m/ 41 MHz 100.0m/ 410 MHz 1000m/ 4100 MHz Howeve, ince C m/, λ488nm, then, c/ λ MHz. the Dopple hit in equency i vey mall compaed with the equency o the ouce lae light. In pactice, it i alway quit diicult to meaue the Dopple hit o equency accuately o lowpeed low by meauing the eceived total equency diectly. in( ) in( λ λ ) Dual-beam LD technique wa developed to meaue the elative equency change due to the Dopple hit othe than the total equency.

10 Fundamental o Dual-Beam LD I the intenity o each catteed beam collected by the photo detecto vaie inuoidal, A ( i + ) t, i i 1,. Then, the optical mixing o thee beam on the photoditecto (heteodyning poce) poduce an output voltage E that i popotional to the quie o the combined light intenity. E ~ { A1 ( + 1) t + A ( + ) t} A1 ( + 1) t + A ( + ) t + A1 A[ ( + 1) t][ ( + 1) t] A1 ( + 1) t + A ( + ) t + A1 A[coπ ( 1 ) t] co π ( ) t] A1 ( + 1) t + A ( + ) t co π ( ) t] + A1 A[co π ( 1 ) t] high equency low equency I we deine, 1 ' then : E ~ a + b ' t ( e1 ei 1) ( e ei ) ' 1 λ λ Since ei 1 ei, then θ in( ) ( ei ei 1) ' θ λ λ λ θ ' θ in( ) The above equation i independent o obevation angle!