1、Introduction to Laser Doppler Velocimetry,Ken KigerBurgers Program For Fluid Dynamics Turbulence School College Park, Maryland, May 24-27,Laser Doppler Anemometry (LDA),Single-point optical velocimetry method,Study of the flow between rotating impeller blades of a pump,3-D LDA Measurements on a 1:5
2、Mercedes-Benz E-class model car in wind tunnel,Phase Doppler Anemometry (PDA),Single point particle sizing/velocimetry method,Drop Size and Velocity measurements in an atomized Stream of Moleten Metal,Droplet Size Distributions Measured in a Kerosene Spray Produced by a Fuel Injector,Laser Doppler A
3、nemometry,LDA A high resolution - single point technique for velocity measurements in turbulent flowsBasics Seed flow with small tracer particles Illuminate flow with one or more coherent, polarized laser beams to form a MV Receive scattered light from particles passing through MV and interfere with
4、 additional light sources Measurement of the resultant light intensity frequency is related to particle velocity,A Back Scatter LDA System for One Velocity Component Measurement (Dantec Dynamics),LDA in a nutshell,Benefits Essentially non-intrusive Hostile environments Very accurate No calibration H
5、igh data rates Good spatial & temporal resolutionLimitations Expensive equipment Flow must be seeded with particles if none naturally exist Single point measurement technique Can be difficult to collect data very near walls,General wave propagation,Review of Wave Characteristics,A = Amplitude k = wa
6、venumber x = spatial coordinate t = time= angular frequency e = phase,Electromagnetic waves: coherence,Light is emitted in “wavetrains” Short duration, Dt Corresponding phase shift, e(t); where e may vary on scale tDtLight is coherent when the phase remains constant for a sufficiently long time Typi
7、cal duration (Dtc) and equivalent propagation length (Dlc) over which some sources remain coherent are:Interferometry is only practical with coherent light sources,Source lnom (nm) Dlc White light 550 8 mm Mercury Arc 546 0.3 mm Kr86 discharge lamp 606 0.3 m Stabilized He-Ne laser 633 400 m,Electrom
8、agnetic waves: irradiance,Instantaneous power density given by Poynting vector Units of Energy/(Area-Time)More useful: average over times longer than light freq.,Frequency Range,6.10 x 1014,5.20 x 1014,3.80 x 1014,LDA: Doppler effect frequency shift,Overall Doppler shift due two separate changes The
9、 particle sees a shift in incident light frequency due to particle motion Scattered light from particle to stationary detector is shifted due to particle motion,LDA: Doppler shift, effect I,Frequency Observed by Particle The first shift can itself be split into two effects (a) the number of wavefron
10、ts the particle passes in a time Dt, as though the waves were stationary,Number of wavefronts particle passes during Dt due to particle velocity:,LDA: Doppler shift, effect I,Frequency Observed by Particle The first shift can itself be split into two effects (b) the number of wavefronts passing a st
11、ationary particle position over the same duration, Dt,Number of wavefronts that pass a stationary particle during Dt due to the wavefront velocity:,LDA: Doppler shift, effect I,The net effect due to a moving observer w/ a stationary source is then the difference:,Number of wavefronts that pass a mov
12、ing particle during Dt due to combined velocity (same as using relative velocity in particle frame):,Net frequency observed by moving particle,LDA: Doppler shift, effect II,An additional shift happens when the light gets scattered by the particle and is observed by the detector This is the case of a
13、 moving source and stationary detector (classic train whistle problem),receiver lens,Distance a scattered wave front would travel during Dt in the direction of detector, if u were 0:,Due to source motion, the distance is changed by an amount:,Therefore, the effective scattered wavelength is:,LDA: Do
14、ppler shift, I & II combined,Combining the two effects gives:For u c, we can approximate,LDA: problem with single source/detector,Single beam frequency shift depends on: velocity magnitude Velocity direction observation angleAdditionally, base frequency is quite high O1014 Hz, making direct detectio
15、n quite difficultSolution? Optical heterodyne Use interference of two beams or two detectors to create a “beating” effect, like two slightly out of tune guitar strings, e.g.Need to repeat for optical waves,Repeat, but allow for different frequencies,Optical Heterodyne,How do you get different scatte
16、r frequencies?,For a single beamFrequency depends on directions of es and ebThree common methods have been used Reference beam mode (single scatter and single beam) Single-beam, dual scatter (two observation angles) Dual beam (two incident beams, single observation location),Dual beam method,Real MV
17、 formed by two beams Beam crossing angle g Scattering angle q,Forward Scatter Configuration,Dual beam method (cont),Note that,so:,Fringe Interference description,Interference “fringes” seen as standing waves Particles passing through fringes scatter light in regions of constructive interferenceAdequ
18、ate explanation for particles smaller than individual fringes,L,Gaussian beam effects,Power distribution in MV will be Gaussian shaped In the MV, true plane waves occur only at the focal point Even for a perfect particle trajectory the strength of theDoppler burst will vary with position,A single la
19、ser beam profile,Figures from Albrecht et. al., 2003,Non-uniform beam effects,Centered,Off Center,Particle Trajectory,DC,AC,DC+AC,Off-center trajectory results in weakened signal visibility Pedestal (DC part of signal) is removed by a high pass filter afterphotomultiplier,Figures from Albrecht et. a
20、l., 2003,Multi-component dual beam,Three independent directions,xg,xb,Two Component Probe Looking Toward the Transmitter,Sign ambiguity,Change in sign of velocity has no effect on frequency,uxg 0,uxg 0,beam 2,beam 1,Xg,Velocity Ambiguity,Equal frequency beams No difference with velocity direction ca
21、nnot detect reversed flow Solution: Introduce a frequency shift into 1 of the two beams,beam 2,beam 1,Xg,Bragg Cell,fb = 5.8 e14,fb2 = fbragg + fb,fb1 = fb,Hypothetical shift Without Bragg Cell,If DfD fbragg then u 0,New Signal,Frequency shift: Fringe description,Different frequency causes an appare
22、nt velocity in fringes Effect result of interference of two traveling waves as slightly different frequency,Directional ambiguity (cont),l = 514 nm, fbragg = 40 MHz and g = 20Upper limit on positive velocity limited only by time response of detector,fbragg,uxg (m/s),DfD s-1,Velocity bias sampling ef
23、fects,LDA samples the flow based on Rate at which particles pass through the detection volume Inherently a flux-weighted measurement Simple number weighted means are biased for unsteady flows and need to be corrected Consider: Uniform seeding density (# particles/volume) Flow moves at steady speed o
24、f 5 units/sec for 4 seconds (giving 20 samples) would measure:Flow that moves at 8 units/sec for 2 sec (giving 16 samples), then 2 units/sec for 2 second (giving 4 samples) would give,Laser Doppler Anemometry,Velocity Measurement Bias,Mean Velocity,nth moment,- The sampling rate of a volume of fluid
25、 containing particles increaseswith the velocity of that volume - Introduces a bias towards sampling higher velocity particles,Bias Compensation Formulas,Phase Doppler Anemometry,The overall phase difference is proportional to particle diameter,The geometric factor, b - Has closed form solution for p = 0 and 1 only- Absolute value increases with y (elevation anglerelative to 0) - Is independent of np for reflection,Multiple Detector Implementation,Figures from Dantec,
