Pope, D. and Gogos, G. "Numerical Simulation of Fuel Droplet Extinction Due to Forced Convection," Combustion and Flame, 142:89-106 (2005)

The extinction of an envelope flame at the forward stagnation point of a liquid fuel droplet due to forced convection is numerically investigated. The droplet is oxidizing within an air stream at atmospheric pressure. Combustion is modeled using finite-rate chemical kinetics and a one-step overall reaction. The gas-phase solution is obtained using the quasi-steady equations of mass, momentum, species, and energy conservation. A new multicomponent formulation, which is appropriate for use with the finite-volume method, was developed to accurately describe the mass diffusion. Droplet circulation is accounted for by solving the quasi-steady mass and momentum conservation equations, for the liquid phase. The gas phase and liquid phase are coupled via interfacial conservation equations, and the complete set of governing equations is solved iteratively. Results for extinction velocity as a function of droplet diameter and freestream temperature are presented for an n-heptane droplet. Numerical predictions for n-heptane are in quantitative agreement with the limited n-heptane experimental data available in the literature, and in qualitative agreement with experimental results for a variety of fuels and over a wide range of ambient temperatures and droplet diameters. A linear dependence of the extinction velocity as a function of droplet diameter constitutes the present state of knowledge. This study predicts a nonlinear dependence for small diameters (d < 1 mm) and a linear dependence only for large diameters (d > 2 mm). The predictions also show that a form of the Damköhler number at extinction can be correlated with the Reynolds number through the use of the transfer number and appropriate dimensionless activation and adiabatic flame temperatures. A correlation that accurately reproduces the numerical predictions for extinction velocity over a wide range of droplet diameters and ambient temperatures is presented.  2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.