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.
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Abbreviations
- a, b, c :
-
half-axes of measurement control volume (mcv)
- a 1, b 1, c 1 :
-
half-axes of detection volume
- c L :
-
velocity of light
- d m :
-
beam waist diameter
- d p :
-
particle diameter
- d pc :
-
diameter of the calibration particle
- d pmin :
-
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(d p ):
-
particle concentration
- n(d pi ):
-
concentration of ith particle class
- n :
-
vector of n(d pi )
- q :
-
exponent of size dependence of G(d p )
- v x :
-
x-velocity component
- Δx :
-
fringe spacing
- y 0, z 0 :
-
coordinates of particle trajectory and cross sectional area
- A :
-
cross sectional area of mcv
- A :
-
matrix of ΔA 1
- a 1 :
-
cross sectional area of detection volume
- ΔA 1 :
-
difference of neighbouring cross sectional areas
- C A :
-
normalisation constant for linear graduation of amplitude
- C N :
-
normalisation constant for Doppler periods
- C scat :
-
non-size-dependent factor of G(d p )
- C x :
-
normalisation constant for nonlinear graduation of amplitude
- F(ω):
-
power spectral density
- G(d p ):
-
integral scattering function
- H :
-
number of accumulated counts
- H max :
-
maximum number of accumulated counts
- I ≈ :
-
amplitude of Doppler signal
- I max :
-
I ≈ for a particle passing through the origin of the mcv
- I s :
-
trigger level
- K :
-
logarithmic amplitude ratio
- K max :
-
logarithmic amplitude ratio for I s
- ΔK x :
-
degree of linear class width of amplitude
- ΔK A :
-
degree of nonlinear class width of amplitude
- N :
-
number of Doppler periods
- N m :
-
number of Doppler periods required by signal validation
- N max :
-
N for a particle passing through the origin of the mcv
- N 0 :
-
fringe number inside mcv along x-axis
- P L :
-
laser power
- S 0 :
-
particle arrival rate
- S 1 :
-
trigger rate
- ΔS 1 :
-
contribution to trigger rate coming from ΔA 1
- ΔS 1 :
-
vector of ΔS 1i
- ΔS 1i :
-
contribution to trigger rate coming from ith class of distribution
- η Q :
-
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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Albrecht, H.E., Borys, M. & Fuchs, W. The cross sectional area difference method — a new technique for determination of particle concentration by laser doppler anemometry. Experiments in Fluids 16, 61–69 (1993). https://doi.org/10.1007/BF00188508
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DOI: https://doi.org/10.1007/BF00188508