Pope, D.N., Howard, D., Lu, K. and Gogos, G. â•œCombustion of Moving Droplets and Suspended Droplets: Transient Numerical Results,â•š AIAA Journal of Thermophysics and Heat Transfer, 19:273-281 (2005)

A numerical investigation of unsteady liquid fuel droplet combustion with droplet heating and internal circulation under forced convection is presented. The droplet is burning within an airstream at atmospheric pressure and under zero-gravity conditions. Combustion is modeled using finite rate kinetics and a one-step overall reaction. The numerical model includes a new multicomponent formulation, which is appropriate for use with the finite volume method, to describe mass diffusion in the gas phase accurately. Numerical results were obtained for both suspended droplets (constant relative velocity) and for moving droplets. It is shown that the flame configurations present in a burning droplet are a function of the time histories of both the Reynolds number and the Damköhler number. For a moving droplet, the Reynolds number decreases with time (due to both relative velocity and droplet size reduction), but the Damköhler number increases with time. For a suspended droplet, both the Reynolds number and the Damköhler number decrease with time due to the reduction in droplet size. As a result, for the same initial Reynolds number, suspended droplets may demonstrate different burning behavior than moving droplets. Within the range of initial Reynolds numbers considered (6, 8, and 50), a moving droplet tends to develop an envelope flame at some stage during its lifetime, whereas a suspended droplet develops an envelope flame only for low initial Reynolds numbers. The flame configurations present during droplet burning are of critical importance in determining the droplet lifetime. Nomenclature Q1 Q2 Q3 Q4 A = preexponential factor a = fuel concentration exponent in reaction rate equation b = oxygen concentration exponent in reaction rate equation C D = drag coefficient c p = specific heat capacity at constant pressure D a = Damköhler number, Eq. (12) D i j = binary diffusion coefficient for the i– j pair D im = effective diffusion coefficient for the ith species D T,i = thermal diffusion coefficient for the ith species d = droplet diameter E a = activation energy F F = friction drag force F P = pressure drag force F T = thrust drag force H 1 = downstream flame dimension H 2 = upstream flame dimension h = specific enthalpy K = evaporation constant k = thermal conductivity L = latent heat of vaporization ˙ m θ = local mass flux at droplet surface N = total number of chemical species n r = number of radial …