IMPLICATIONS OF THE GAUSSIAN INTENSITY DISTRIBUTION OF LASER-BEAMS ONTHE PERFORMANCE OF THE PHASE DOPPLER TECHNIQUE, SIZING UNCERTAINTIES

The influence of the Gaussian intensity distribution of the incident l aser beams on sizing measurements by phase-Doppler velocimetry has bee n investigated using geometrical optics approximation, considering the interference between contributions from reflection at the external su rface of a droplet, refraction through the droplet and those refracted after one and two reflections at the inner surface of the droplet. Th e results have considered the use of forward- (scattering angles betwe en 30 and 75 degrees), back- (scattering angles between 140 and 180 de grees) and side- (scattering angles between 80 and 130 degrees) scatte red 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. Th e results have demonstrated the influence of phase and amplitude valid ations 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 r esulting sizing uncertainties after amplitude and phase validations we re between 5 and 10% for forward-scattered light collected at 30 degre es and +9%/-100% and +20%/-16% for back-scattered light collected at 1 50 degrees for droplet-to-probe diameter ratios of 1.67 and 0.24, resp ectively. 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 degrees. Although these si zing errors correspond to optical arrangements, which may not be avail able in commercially available phase Doppler systems, experimental res ults from Willman et al, (Proc. 7th Int. Symp. on Applications of Lase r Technologies to Fluid Mechanics, 1994) using commercial instruments indicate similar errors. Sizing with forward-scattered light is prefer able overall, but for flows with limited optical access, sizing with s ide-scattered light is preferable to back-scattered light due to lower sizing errors. Droplet refractive index influences the response curve s and for refractive indices of 1.33 and 1.4, back-scattered light sho uld be collected between scattering angles of 145 and 160 degrees and of 155 and 160 degrees, respectively, and that for side-scattered ligh t at around 120 and 104 degrees, respectively, and for both arrangemen ts the collection optics are required to be within a small range of an gles around the bisector plane of the beams. (C) 1997 Elsevier Science Ltd.