Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties

Abstract

The influence of the Gaussian intensity distribution of the incident laser beams on sizing measurements by phase-Doppler velocimetry has been investigated using geometrical optics approximation, considering the interference between contributions from reflection at the external surface of a droplet, refraction through the droplet and those refracted after one and two reflections at the inner surface of the droplet. The results have considered the use of forward-(scattering angles between 30 and 75°), back-(scattering angles between 140 and 180°) and side-(scattering angles between 80 and 130°) scattered light to size transparent non-absorbing spherical droplets in the range of relative refractive indices between 1.33 and 1.4 and normal, or oblique trajectories relative to the fringes of the velocimeter. The results have demonstrated the influence of phase and amplitude validations and the logic of the signal processor on sizing uncertainties. The Gaussian intensity profile of the laser beams caused variations of phase difference and associated amplitude of the signal with droplet trajectory and, for the optical arrangement of the current work, the resulting sizing uncertainties after amplitude and phase validations were between 5 and 10% for forward-scattered light collected at 30° and +9%/−100% and +20%/−16% for back-scattered light collected at 150° for droplet-to-probe diameter ratios of 1.67 and 0.24, respectively. For side-scattered light, the phase validation logic is not valid and the sizing uncertainties after amplitude validation were +19%/−26% and ±5% for droplet-to-probe diameter ratios of 1.67 and 0.24, respectively, and scattering angle of 104°. Although these sizing errors correspond to optical arrangements, which may not be available in commercially available phase Doppler systems, experimental results from Willman et al. ( Proc. 7th Int. Symp. on Applications of Laser Technologies to Fluid Mechanics, 1994) using commercial instruments indicate similar errors. Sizing with forward-scattered light is preferable overall, but for flows with limited optical access, sizing with side-scattered light is preferable to back-scattered light due to lower sizing errors. Droplet refractive index influences the response curves and for refractive indices of 1.33 and 1.4, back-scattered light should be collected between scattering angles of 145 and 160° and of 155 and 160°, respectively, and that for side-scattered light at around 120 and 104°, respectively, and for both arrangements the collection optics are required to be within a small range of angles around the bisector plane of the beams.