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

## Authors

- Received:
- Accepted:

DOI: 10.1007/BF00188508

- Cite this article as:
- Albrecht, H.-., Borys, M. & Fuchs, W. Experiments in Fluids (1993) 16: 61. doi:10.1007/BF00188508

- 4 Citations
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## 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)

*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