Analytical parametrizations of droplet collision efficiency on cylinders - A review study

Within the scope of this work several major ice accretion parameterizations have been investigated, staring from the original Langmuir and Blodgett work 1946) on the water droplet trajectories, up to and including the Finstad et al. model (1988a) of overall collision efficiency, which is part of the current governing ISO 12494 standard (2001), thus covering a timeframe of several decades of investigations in icing modeling. This paper provides a general and mathematical review of those parameterizations, includes necessary formulae for calculations of the droplet overall collision efficiency, starting with the trajectory evaluation, and discuses underlying assumptions and approximations made by respective authors. This discussion might be of interest to icing modelers who wish to obtain more general understanding of icing modeling. As an application example, two experimental datasets have also been used for the droplet overall collision efficiency calculations and comparison. These experiments span large amount of operating conditions, thus covering significant range of the droplet inertia parameter range, K, and the overall collision efficiency, E, values which should cover majority of possible icing conditions. The results show that for higher values of the droplet inertia parameter (K), the monodisperse distribution yields good agreement with the experimental values, however, with gradual decrease in values of droplet's inertia parameter, the MVD approximation tends to underestimate the overall collision efficiency when compared with the experimental and spectrum-averaged values. Moreover, for very low values of K and E, roughly corresponding to the limits provided in ISO 12494, the MVD approximation tends to underestimate the overall collision efficiency significantly. For those cases the recalculation of droplet trajectories using full spectrum is recommended. If actual droplet distribution spectrum is not available, it is recommended to carry out the analysis using the Langmuir distributions, such as widely used 'Langmuir D' distribution (Wright, 2008), (Bidwell, 2012), (Papadakis et al., 2007).