Introduction to Laser Doppler Velocimetry

8/14/2019 Introduction to Laser Doppler Velocimetry

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Introduction to Laser Doppler Velocimetry

Ken Kiger

Burgers Program For Fluid Dynamics

Turbulence School

College Park, Maryland, May 24-27


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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 Mercedes-Benz

E-class model car in wind tunnel


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Phase Doppler Anemometry (PDA)

Single point particle sizing/velocimetry method

Drop Size and Velocity

measurements in an atomizedStream of Moleten Metal

Droplet Size Distributions

Measured in a KeroseneSpray Produced by a Fuel Injector


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Laser Doppler Anemometry

LDA

A high resolution - single point technique for velocity measurements in turbulent flows

Basics 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 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)


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LDA in a nutshell

Benefits Essentially non-intrusive Hostile environments Very accurate No calibration High data rates

Good spatial & temporal resolution

Limitations 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


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General wave propagation

Review of Wave Characteristics

txAtx 2cos,

x

A

x,t

Re Aei kx t

A = Amplitude

k = wavenumber

x = spatial coordinate

t = time

= angular frequency

= phase

2k

c

c

22


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Electromagnetic waves: coherence

Light is emitted in wavetrains

Short duration, t Corresponding phase shift, (t); where may vary on scale t> t

Light is coherentwhen the phase remains constant for

a sufficiently long time Typical duration ( tc) and equivalent propagation length ( lc) over

which some sources remain coherent are:

Interferometry is only practical with coherent light sources

E Eo exp i kx t t

Source nom (nm) lc

White light 550 8 mMercury Arc 546 0.3 mm

Kr86 discharge lamp 606 0.3 m

Stabilized He-Ne laser 633 400 m


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Electromagnetic waves: irradiance

Instantaneous power density given by Poynting vector

Units of Energy/(Area-Time)

More useful: average over times longer than light freq.

S c 2 oE B S c oE2

I ST

c o E2

T

c o2

E E c o

2E0

2

tdtfT

f

T

T

t

t

T

2

2

1Frequency Range

6.10 x 1014

5.20 x 1014

3.80 x 1014


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LDA: Doppler effect frequency shift

Overall Doppler shift due two separate changes

The 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

b

ke

k

u

se


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LDA: Doppler shift, effect I

Frequency Observed by Particle

The first shift can itself be split into two effects (a) the number of wavefronts the particle passes in a time t, as though the

waves were stationary

b

ke

k

Number of wavefronts particle passes

during tdue to particle velocity:


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Frequency Observed by Particle

The first shift can itself be split into two effects (b) the number of wavefronts passing a stationary particle position over the

same duration, t

k

keb

tc

tcNumber of wavefronts that pass a

stationary particle during tdue to the

wavefront velocity:


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The net effect due to a moving observer w/ a

stationary source is then the difference:

ttc beu Number of wavefronts that pass a

moving particle during tdue to

combined velocity (same as usingrelative velocity in particle frame):

Net frequency observed by

moving particle

cf

cc

tf

b

b

p

eu

eu

1

1

swavefrontof#

0


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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 moving source and stationary detector (classic train whistleproblem)

u

tseu

se

tc

receiver

lens

u

Distance a scattered wave front would travel

during t in the direction of detector, if u

were 0:

tc

p

s

p

ss

f

c

tf

ttc eueu

emittedwavesofnumber

by wavetraveleddistancenet

Due to source motion, the distance ischanged by an amount:

Therefore, the effective scattered

wavelength is:

tseu


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LDA: Doppler shift, I & II combined

Combining the two effects gives:

For u


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LDA: problem with single source/detector

Single beam frequency shift depends on:

velocity magnitude

Velocity direction

observation angle

Additionally, base frequency is quite high

O[1014] Hz, making direct detection quite difficult

Solution?

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

bsobsc

fff eeu 00

to 1111 cos rkEE

to 2222 cos rkEE

P

cos 1t cos 2t

1

2 cos 1 2 t cos 1 2 t


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Repeat, but allow for different frequencies

Optical Heterodyne

I c o

2E1 E2 E1 E2

I

c o

2 Eo1

2

Eo22

2Eo1Eo2 cos k1 k2 r 1 2 t 1 2

1

2Io1 Io2 2 Io1Io2cos k1 k2 r 1 2 t 1 2

ACIPEDI

E1

E01

expi k1x

1t

1 E

01expi

1

E2 E02 expi k2x 2t 2 E02 expi 2

I c o2

Eo12 Eo2

2 2E01E02 expi1 2 exp i 1 2

2

I c o

2Eo1

2 Eo22 E01 expi 1 E02 exp i 2 E01 exp i 1 E02 expi 2

I c o

2Eo1

2 Eo22 2E01E02 cos 1 2


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How do you get different scatterfrequencies?

For a single beam

Frequency depends on directions of es and eb

Three 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)

bssc

fff eeu 00


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Dual beam method

Real MV formed by two beams

Beam crossing angle

Scattering angle

Forward Scatter

Configuration


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Dual beam method (cont)

Note that ,1 ,2 ( ) 2sin( / 2)b b ge e x

so:

gMeasure the component of in the directionu x1,2,0

2,2,0

02,

1,1,0

01,

bb

bss

bss

cff

c

fff

c

fff

eeu

eeu

eeu

Dg f2sin2

xu

21212121

2sin4cos2

2

1tIIIItI oooo gxurkk


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Fringe Interference description

Interference fringes seen as standing waves Particles passing through fringes scatter light in regions of

constructive interference

Adequate explanation for particles smaller than individual fringes

f

sxu

2sin2


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Gaussian beam effects

-Power distr ibution in MV wi l l be Gaussian shaped

-I n the MV, true plane waves occur only at the focal point

-Even for a perfect particle trajectory the strength of the

Doppler burst will vary with position

A single laser beam profile

F igures fr om Albrecht et. al., 2003


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Non-uniform beam effects

Centered Off Center

Particle Trajectory

DC

AC

DC+AC

- Off -center tr ajectory resul ts in weakened signal visibil i ty

-Pedestal (DC part of signal) is removed by a high pass f i l ter after

photomultiplierF igures fr om Albrecht et. al., 2003


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Multi-component dual beam

Three independent directions

xg^

xb^

TwoComponent Probe Looking

Toward the Transmitter


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Sign ambiguity

Change in sign of velocity has no effect on frequency

Ds f2sin2

xu

uxg> 0

uxg< 0

beam 2

beam 1

Xg

2121 2cos22 tfIII Doo rkk


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Velocity Ambiguity

Equal frequency beams

No difference with velocity direction cannot detect reversed flow Solution: Introduce a frequency shift into 1 of the two

beamsXgBragg Cell

fb = 5.8 e14

fb2 = fbragg + fb

fb1 = fb

,1 ,1 ,1

,2 ,2 ,2

,1 ,2 0

( )

( ) ( )

( )

bs b s b

bs b bragg s b

bD bragg b b bragg D

ff f

c

ff f fc

ff f f f

c

u e e

u e e

u e e

Hypothetical shift

Without Bragg Cell

2

01 02 cos( 2 { } )D braggI E f f t

I f fD< fbragg then u < 0

New Signal


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Frequency shift: Fringe description

Different frequency causes an apparent velocity infringes

Effect result of interference of two traveling waves as slightlydifferent frequency


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Directional ambiguity (cont)

nm, fbragg= 40 MHz and = 20

Upper limit on positive velocity limited onl y by

time response of detector

0( )2 sin( / 2)

D braggxg f fu

fbragg

uxg (m/s)

fD

s-1


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Velocity bias sampling effects

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 needto be corrected

Consider:

Uniform seeding density (# particles/volume)

Flow moves at steady speed of 5 units/sec for 4 seconds (giving 20samples) 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

8.620

2*48*16

520

20*5


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Laser Doppler AnemometryVelocity Measurement Bias

, ,n1 1x

1 1

U

N N n

xx i i x i i

i ix N N

i ii i

U U U

U

Mean Velocity nth moment

- The sampling rate of a volume of f lu id contain ing particles increases

with the velocity of that volume

- I ntroduces a bias towards sampli ng higher velocity particles

Bias Compensation Formulas


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Phase Doppler Anemometry

The overall phase difference

is proportional to particle diameter

The geometric factor,- Has closed form solution for p = 0 and 1 only

- Absolute value increases with elevation angle

relative to 0)

- Is independent of np for reflection

Multiple Detector

Implementation

Figures from Dantec

2 niD

, , ,np,ni

Introduction to Laser Doppler Velocimetry

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