Optical determination of mean particle size in a tow-phase free-jet

Measurements of light scattering and extinction through ensembles of spherical particles can provide valuable particle size information. Most of the associated measurement techniques assume that the local particle size distribution function is independent of position within the ensemble. Physically realistic particle clouds, however, have spatial density variations caused by inertial effects and collision kinetics, which increase the complexity of the problem, and demand a more sophisticated analytical and experimental treatment. Using the results of Mie scattering theory, this work presents the development of analytical and experimental procedures for determining the average size and spatial distribution of particles in an axisymmetric ensemble. Cylindrically symmetric particulate-laden flow fields are a particularly useful class of spatially nonuniform particle ensembles that yield tractable solutions to the problem of particle size measurement. Basic definitions from the Mie theory that pertain to extinction and scattering from particle ensembles are reviewed, along with elements of fundamental statistics of size distributions. The standard approach for obtaining average particle size from extinction measurements through a uniform slab of particles is extended to the more general case of spatially nonuniform clouds that have radial symmetry. Multiple path extinction measurements are then combined with the analytical techniques of Abel inversions to ascertain the spatial dependence of the mean particle size. Methods for measuring the mean particle size of an ensemble based on diffraction and backscatter techniques are also developed, and the approach required to obtain information about the distribution of particle sizes using simultaneous extinction and backscatter measurements at several optical wavelengths is reviewed. The theoretical feasibility of using the proposed concepts for determining the mean particle size of an ensemble is demonstrated with a numerical simulation of scattering and extinction. Finally, the results of a simple multiple-path extinction experiment are described, in which the distributions of mass flux and mean particle size are deduced.