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Elastic light scattering measurements on non-uniform particle flow fields: theoretical considerations

Flow field non-uniformity effects on the sizing results from inversion of multi-angle elastic light scattering signals were investigated and found to be significant for measurement systems where the scale of the flow field variation and the scattering probe volume were similar. Particulate flow fields, such as those produced by multi-element diffusion burners used in flame synthesis processes, generally form two-dimensional patterns perpendicular to the axis of the carrier flow. Expansion of the spatial particle number density field in terms of the double Fourier series is used to derive relationships that quantitatively estimate the accuracy of measurement results. In this paper, we present the Fourier analysis used to quantify effects of probe volume size and alignment. Special attention is given to measurements of low spatial resolution, i.e. measurements that provide information on the global (cross-sectional) average particle size distribution. After brief discussions on the general requirements for the diagnostics layout (probe volume size) and incorporation of the systematic errors in signal inversion for global average measurements, the analysis for a typical flow field produced by a Hencken burner is presented. The results of this analysis indicate that the dimensions of the probe volume have to be about three times larger than the characteristic length of the particle field in order to avoid excessively large uncertainties in measurement results.