This work enhances the state-of-the-art in modeling spray combustion in turbulent flows. The current de facto standard models spray droplets as Lagrangian points [Abramzon and Sirignano, Int. J. Heat and Mass Trans., 1989]. The model computes the combustion rate of droplets through the solution of a system of ordinary differential equations governed by the evolution of relevant non-dimensional variables. The primary non-dimensional variables are the Reynolds number which reflects boundary layer growth and the Spalding heat and mass numbers which characterize the potential for heat and mass transfer, respectively. This model neglects any information about the dynamics of the droplets themselves including the deformation of the droplets due to aerodynamic forces and the internal flow that is generated inside of droplets due to viscous shear from the gas convection. Thus the approach effectively treats droplet vaporization and combustion as a gas phase heat and mass transfer process. The classical explanation given for the neglect of these phenomena is that the droplet is so small, that the influence of these phenomena become negligible. However, our recent work challenges this idea [ASME IMECE 2019; Eastern States Sec- tion of the Combustion Institute 2020; APS Division of Fluid Dynamics 2020]. We have demonstrated that these phenomena have measurable impact on the vaporization rate of droplets, and accordingly affect the nature of their combustion as well. Therefore new modeling approaches are warranted.&nbsp; 
This work uses perturbation theory to derive a novel model for the vaporization of non-spherical droplets. Compared to previous efforts in this area, the work uses a physics-based approach by incorporating ideas from the theory of Taylor and Acrivos [J. Fluid Mech. 1964]. The perturbation strategy expands the droplet shape using spherical harmonics, and the theory charac- terizes the shape of the droplet via the Weber number. The Weber number describes the ratio between surface tension and aerodynamic stresses, and therefore is the appropriate non-dimensional group to describe aerodynamically induced droplet deformation. The introduction of this parameter is key as it is a parameter that can be easily measured in experiments, and thus connects theory with application. An initial perturbation analysis is performed based upon the classical droplet combustion solution in the limit of both zero Reynolds number and zero Weber number. The theory indicates that the effect of droplet deformation can be accounted for by a correction to the droplet combustion rate that is quadratic in the droplet Weber number. The extension of the theory to conditions relevant for aviation gas turbine-engines is discussed.

On the Vaporization Rate and Flame Shape of Non-Spherical Droplets

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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