Experimental and modelling investigation of the deformation, drag and break-up of drizzle droplets subjected to strong aerodynamics forces in relation to SLD aircraft icing

Abstract

The distortion, drag and break-up of drizzle droplets subjected to strong aerodynamic forces was investigated to understand the pre-impact behaviour of droplets in aircraft icing from supercooled freezing drizzle. The objective was to obtain a formulation and data for the drag properties of droplets distorted by the aerodynamic forces, which were beyond the scope of available experimental and modelling methods. A practical and efficient semi-empirical computer model was developed for small water droplets in air, 100µm < D < 500µm, at moderate Reynolds numbers, 350 < Re < 1500, and high Weber numbers 3 < We < 20. This used available experimental terminal velocity data for free-falling droplets, extrapolated to higher Weber numbers, and the numerical solution for sessile droplets on a horizontal unwettable surface, with corrections for the Reynolds number. A theory for bag break-up was developed based on the Rayleigh-Taylor instability of the windward droplet surface. The critical Bond number was 13.7, with a critical diameter of 10.1mm for free-falling water droplets, compared to the experimental value of 10mm diameter. The equivalent Weber number was 14.2 for free falling water droplets. Aerodynamic interaction between the closely-spaced droplets from a vibrating nozzle droplet generator resulted in irregular spacing and coalescence of droplets. In an alternative design a laminar jet impinged on a rotating slotted disk to achieve the necessary droplet spacing, but the significant size variability of the droplets degraded the experimental measurements. High-speed videos, to 50,000pps, and photographs were obtained of droplet distortion, break-up, coalescence and splashes using a high-intensity LED strobe flash. A specially-designed convergent wind tunnel was developed for experimental measurements, to validated the drag model and provide data for droplets distorted by aerodynamic forces. The convergent profile produced a rapidly-increasing Weber number at a sufficiently slow rate to avoid transients or droplet vibrations. A special instrument was developed, with three equispaced parallel laser beams and photo detectors, to determine the droplet velocity and acceleration. Droplet drag characteristics were measured up to Weber numbers of 16. Good agreement was obtained between droplet drag model and experimental results. The greatest discrepancy was about 20% at a Weber number of about 8.