12 ea pda 0 dantecpda 2011

8/12/2019 12 Ea PDA 0 DantecPDA 2011

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Principles of Phase Doppler Anemometry

Dantec Measurement Technology

http://www.dantecmt.com

8/12/2019 12 Ea PDA 0 DantecPDA 2011


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Contents

• General Features

• Optical principles

• Light scattering considerations

• Phase-diameter relationship

• Sources of uncertainty

• DualPDA technique

• Application examples

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General features of PDA

• Extension of the LDA principle

• Simultaneous measurement of veloci ty (up to 3 components) and size of spherical particles as well as mass flux, concentration etc.

• First publication by Durst and Zaré in 1975

• First commercial instrument in 1984

• Non-intrusive measurement (opt ical technique), on-line and in-situ

• Absolute measurement technique (no calibration required)

• Very high accuracy

• Very high spatial resolution (small measurement volume)

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Preconditions for the application of PDA

• Optical access to the measurement area (usually from two directions)• Sphericity of particles (droplets, bubbles, solids)

• Homogeneity of particle medium(slight inhomogeneities may be tolerated if the concentration of theinhomogeneities is low and if the size of the inhomogeneities is much smaller than the wavelength used)

• Refractive indices of the particle and the continuous medium mustusually be known

• Particle size between ca. 0.5 µm and several mil limeters

• Max. particle number concentration is limited

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Principle setup of PDA

Optical parameters of a

PDA setup:

• Beam intersection angle θ

• Scattering angle ϕ

• Elevation angle ψ

• Polarization(parallel or perpendicular toscattering plane)

• Shape and size of detector aperture

X

Y

ϕ

Detector 1

Detector 2

Scattering plane

Flow

Zθ

ψ

ψ

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Optical principle of PDA

• A particle scatters light from twoincident laser beams

• Both scattered waves interfere inspace and create a beat signalwith a frequency which isproportional to the velocity of theparticle

• Two detectors receive this signalwith different phases

• The phase shift between thesetwo signals is proportional to thediameter of the particle

I n c

i d e n

t b e a m

s

D e t e c t o r 1D e t e c t o r 2

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Light scattering principles

A lightwave is fully described by:

• wavelength

• intensity

• polarization

• phase

The principle of the PDA technique is the scattering of plane lightwaves byspherical particles.

Scattering is composed of:

• diffraction

• reflection

• refraction

• absorption

An exact description of the scattering of light by a homogeneous sphere is

given by the full solution of Maxwell´s equations formulated by Mie in 1908.

Geometric optics (Snell´s law) is a simplified way to describe light scattering.

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Scattering modes

-2

1st order refraction

-1

1

2

-2 -1 1 2

Incident ray

Reflection

2nd order refraction

3rd order

4th order

5th order

6th order

7th order

8th order

n p

n m

n p > n mThe intensity of the incident ray ispartly reflected and refracted.

The intensity ratio is given by theFresnel coefficients and depends

on the incident angle, polarizationand relative refractive index.

The scattering angle is given bySnell´s law.

The phase is given by the opticalpath length of the ray.

Most of the intensity is containedin the first three scattering modes.

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Light scattering by droplets and bubbles

-2

-1

1

2

-2 -1 1 2

Water droplet in air Air bubble in water

I n c i d

e n

t

r a y s

I n c i d

e n

t

r a y s

-2

-1

1

2

-2 -1 1 2

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Phase relationships

Φ =−

2

2 1

π

λ

θ ψ

θ ψ φ

d p sin sin

( cos cos cos )

Φ =−

+ + − +

2

2 1 1 2 12

π

λ

θ ψ

θ ψ φ θ ψ φ

d n

n n

p rel

rel rel

sin sin

( cos cos cos ) ( ( cos cos cos

The phase shift between two detectors is:

For reflection:

For 1st order refraction:

No calibration constant is contained in these equations.

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Phase - diameter linearity

• A linear relationship between measured phase difference and particlediameter only exists, if the detector is positioned such that one lightscattering mode dominates.

5 10 15 20 25 30

-60

-40

-20

0

20

40

60

Diameter (micron)

P h a s e

( d e g

) Air bubble in water

Water droplet in air

Scattering angle: 50°

R e f r a c t i o n

R e

f l e c t

i o n

• Simultaneous detectionof different scattering

modes of comparableintensity leads to non-linearit ies in the phase-diameter relationship.

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Intensity of scattered light

• The scattered lightintensity from thedifferent scatteringmodes varies atdifferent scattering

angles.• The scattering intensityalso depends on thepolarization orientationof the incident light.

-3 -2 -1 1 2 3 4 5

-3

-2

-1

1

23parallel

polarization

perpendicular polarization

1st order refraction

reflection

2nd order refraction

Lorenz-Mie

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2π ambiguity in a two-detector system

• The phase differenceincreases with increasingparticle size.

• Since phase is a modulo2π function, it cannotexceed 2 π , i.e. 360°.

• Therefore, if a particle hasa size that causes thephase to go beyond a 2 π

jump, a two-detector PDAcannot discriminate

between this size and amuch smaller particle.

Φ

Φ

Φ

Φ

Φ3

Φ3

′Φ 3

′Φ 3

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Dantec 57X40 FiberPDA

U 1

U 2 Front lens

Composite lens

Aperture plate

Measurementvolume

Multimodefibres Detector Unit

with PMTs.

U 3

• Easy setup and alignment

• Three receivers in one probe

• Exchangeable aperture masks

• Up to three velocity components

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Size range adaptation

• For a given optical configuration, the distance between the receivingapertures can be changed to adapt the size range.

• This can be achieved by exchanging the aperture mask in the receivingprobe.

• The Dantec FiberPDA has a set of three different masks:

A: small size range B: medium size range C: large size range

U1

U2

U3

A B C

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• the diameter of the intersection volumeof the transmitting beams

• the width of the projection of the slitshaped spatial fil ter which is mounted infront of the receiving fibers

The effective PDA measurement volume is muchsmaller than the intersection volume of thetransmitting laser beams.

The effective size of themeasurement volume isdetermined by:

Effective PDA measurement volume

U 1

U 2

U 3

Slit aperture

Projected slit

Intersectionvolume

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Sources for measurement uncertainties

• Oscillations in phase-diameter curve

• Low SNR due to low intensity or extinction

• Phase changes due to- surface distortions- inhomogeneous particles- mult iple scattering effects

• Gaussian intensity profile in the measurement volume

• Slit effect

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Slit effect

• Due to the projection of the receiving sli t aperture, the unwantedscattering mode becomes dominating for particle trajectories at oneedge of the slit projection.

Y

ZProjected sli t Intersection volume

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The DualPDA

• Measurement errors dueto trajectory and sliteffects are eliminated.

• Particularly optimized for applications to sprayswith transparent droplets.

• Enables improvedconcentration and massflux measurements.

• Provides the ability toreject non-sphericaldroplets.

X

Y

Z

ϕ

U1

U2

V1

V2

Scatteringplane

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Components of the DualPDA

Planar PDA

X

YZ

Main FlowDirection

Receiving Apertures

TransmittingOptics(Beams are inthe y-z plane) ϕ

TransmittingOptics(Beams are inthe x-z plane)

X

YZ

Main FlowDirection

Receiving Apertures

ϕ

Conventional PDA

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Configuration of the DualPDA

U1

U2V1 V2

A

B

C

Transmitting

Optics (2-D)

X

YZ

Main FlowDirection

Receiving

Apertures

ϕ

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Improved mass flux measurements

• The DualPDA canmeasure volume andmass flux with better accuracy.

This is confirmed bycomparing the

results from apatternator and theDualPDA.

0

0.05

0.1

0.15

0.2

0.25

0.3

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Position i n Spray Cone [mm]

n o r m a

l i z e d d r o p

l e t v o

l u m e

f l o w

[ - ]

DualPDAPatternator

pressure swirl atomizer

Traversingdirection

30°

Patternator tubes

D u a l P D A

FiberFlow85 mm

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Applications• Sprays and liquid atomization processes

- Water sprays- Fuel-, diesel injection- Paint coating- Agricultural sprays- Medical, pharmaceutical sprays- Cosmetic sprays

• Powder production- Spray drying- Liquid metal atomization

• Bubble dynamics- Cavitation- Aeration- Multiphase mass transfer

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Automotive Fuel Injection

Photo: AVL, Graz, Austria

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Nozzle Design

Photo: Gustav Schlick GmbH & Co., Untersiemau, Germany

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Aircraft Engine Fuel Injection

Photo: DLR, Institut für Antriebstechnik, Köln, Germany

12 ea pda 0 dantecpda 2011

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