Experiments in Fluids

, Volume 16, Issue 1, pp 61–69 | Cite as

The cross sectional area difference method — a new technique for determination of particle concentration by laser doppler anemometry

  • H. -E. Albrecht
  • M. Borys
  • W. Fuchs
Originals

Abstract

A new technique for the determination of particle concentration from the signals of a laser Doppler anemometer (LDA) is described. It is based on a statistical relation between the number of Doppler periods, or the amplitude of the Doppler signals, and the particle concentration. The technique allows the mass flux of the dispersed phase of a two-phase flow to be obtained from the data set of a conventional one-dimensional (ID) LDA. The technique has been called the “cross sectional area difference method”. Simulations and first experimental results are presented and discussed.

List of symbols

a, b, c

half-axes of measurement control volume (mcv)

a1, b1, c1

half-axes of detection volume

cL

velocity of light

dm

beam waist diameter

dp

particle diameter

dpc

diameter of the calibration particle

dpmin

minimum detectable particle diameter

e

elementary charge

h

Planck's constant

i

number of particle size classes

k

wavenumber

m

visibility

m′

refractive index

n(dp)

particle concentration

n(dpi)

concentration of ith particle class

n

vector of n(d pi )

q

exponent of size dependence of G(d p )

vx

x-velocity component

Δx

fringe spacing

y0, z0

coordinates of particle trajectory and cross sectional area

A

cross sectional area of mcv

A

matrix of ΔA1

a1

cross sectional area of detection volume

ΔA1

difference of neighbouring cross sectional areas

CA

normalisation constant for linear graduation of amplitude

CN

normalisation constant for Doppler periods

Cscat

non-size-dependent factor of G(d p )

Cx

normalisation constant for nonlinear graduation of amplitude

F(ω)

power spectral density

G(dp)

integral scattering function

H

number of accumulated counts

Hmax

maximum number of accumulated counts

I

amplitude of Doppler signal

Imax

I for a particle passing through the origin of the mcv

Is

trigger level

K

logarithmic amplitude ratio

Kmax

logarithmic amplitude ratio for I s

ΔKx

degree of linear class width of amplitude

ΔKA

degree of nonlinear class width of amplitude

N

number of Doppler periods

Nm

number of Doppler periods required by signal validation

Nmax

N for a particle passing through the origin of the mcv

N0

fringe number inside mcv along x-axis

PL

laser power

S0

particle arrival rate

S1

trigger rate

ΔS1

contribution to trigger rate coming from ΔA1

ΔS1

vector of ΔS1i

ΔS1i

contribution to trigger rate coming from ith class of distribution

ηQ

quantum efficiency

λ

wavelength of laser light

ϕ

off-axis angle

Ψ

elevation angle

ω

angular frequency

θ

beam intersection angle

φ

phase difference

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References

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • H. -E. Albrecht
    • 1
  • M. Borys
    • 1
  • W. Fuchs
    • 1
  1. 1.Department of Electrical EngineeringUniversity of RostockRostockGermany

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