Laser Doppler Velocimetry (LDV) Part - 01

Transcription

1 AerE 545 cla note #1 Laer Doppler elocimetry (LD) Part - 01 Hui Hu Department o Aeropace Engineering, Iowa State Univerity Ame, Iowa 50011, U.S.A

2 Technique or Flow elocity Meaurement Intruive technique Pitot-tatic probe hotwire, hot ilm etc... Flow velocity meaurement technique Non-intruive technique particle-baed technique molecule-baed technique Laer Doppler elocimetry (LD) Planar Doppler elocimetry (PD) Particle Image elocimetry (PI) etc Laer Induced Fluorecence (LIF) Molecular Tagging elocimetry (MT) etc

3 Particle-baed Flow Diagnotic Technique Seeded the low with mall particle (~ µm in ize) Aumption: the particle tracer move with the ame velocity a local low velocity! Flow velocity = Particle velocity p Meaurement o particle velocity

4 Laer Doppler elocimetry (LD) Laer Doppler velocimetry (LD, alo known a laer Doppler anemometry, or LDA) i a technique or meauring the direction and peed o luid like air and water. In it implet orm, LD croe two beam o collimated, monochromatic laer light in the low o the luid being meaured. A microcopic pattern o bright and dark tripe orm in the interection volume. Small particle in the low pa through thi pattern and relect light toward a detector, with a characteritic requency indicating, via the Doppler eect, the velocity o the particle paing through the probe volume. Intererence ringe

5 Doppler Shit The Doppler eect, named ater Chritian Doppler (an Autrian mathematician and phyicit ), i the change in requency and wavelength o a wave that i perceived by an oberver moving relative to the ource o the wave. Light rom moving object will appear to have dierent wavelength depending on the relative motion o the ource and the oberver. Oberver looking at an object that i moving away rom them ee light that ha a longer wavelength than it had when it wa emitted (a red hit), while oberver looking at an approaching ource ee light that i hited to horter wavelength (a blue hit).

6 Doppler Shit a. Stationary Sound Source b. Source moving with ource < ound c. Source moving with ource = ound ( Mach 1 - breaking the ound barrier ) d. Source moving with ource > ound (Mach uperonic)

7 Doppler Shit For wave that travel through a medium (ound, ultraound, etc...) the relationhip between oberved requency and emitted requency i given by: where v i the peed o wave in the medium v i the velocity o the ource For wave that travel at the peed o light, uch a laer light, the relationhip between oberved requency and emitted requency i given by: Becaue the detected requency increae or object moving toward the oberver, the object' velocity mut be ubtracted when motion i moving toward the oberver. (Thi i becaue the ource' velocity i in the denominator.) Converely, detected requency decreae when the object move away, and o the object' velocity i added when the motion i away.

8 Fundamental o LD Take the coordinate ytem to be at ret with repect to the medium, whoe peed o light wave i c. There i a ource moving with velocity and emitting light wave with a requency. There i a detector r moving with velocity r, and the unit vector rom to r i n i.e.. Then the requency r at the detector i ound rom I c>>, then the change in requency depend motly on the relative velocity o the ource and detector. ) in( ) in( ) in( ) ˆ ( ˆ 0 ˆ ˆ ˆ ˆ c c e e e e n c n i r r i r r r

9 Fundamental o LD By uing a laer bean o wavelength =488nm (Argon-Ion laer), the maximum Doppler hit rom a particle moving with a velocity o would be: =1.0m/ 4.1 MHz =10.0m/ 41 MHz =100.0m/ 410 MHz =1000m/ 4100 MHz However, ince C = m/, =488nm, then, =c/ = MHz. the Doppler hit in requency i very mall compared with the requency o the ource laer light. In practice, it i alway quit diicult to meaure the Doppler hit o requency accurately or lowpeed low by meauring the received total requency directly. in( ) in( ) Dual-beam LD technique wa developed to meaure the relative requency change due to the Doppler hit other than the total requency.

10 Fundamental o Dual-Beam LD I the intenity oeach cattered beam collected by thephotodetector varie inuoidal, A in ( i ) t, i i 1,. Then,the optical mixing othee beam on thephotoditector (heterodyn ing proce)produce an output vol tage E that i proportion al to the quireothe combinedlight intenity. E ~ { A1 in ( 1) t A in ( ) t} A1 in ( 1) t A in ( ) t A1 A[in ( 1) t][in ( 1) t] A1 in ( 1) t A in ( ) t A1 A[co ( 1 ) t] co ( 1 ) t] A1 in ( 1) t A in ( ) t co ( 1 ) t] A1 A[co ( 1 ) t] h ig h req u en cy lo w req u en cy I we deine, 1 ' then : E ~ a bin ' t ( e 1 ei 1) ( e ei ) ' 1 Since ei 1 ei, then in( ) ( ei ei 1) ' ' in( ) The above equation i independent o obervation angle!