Abstract
The model of the ignition and extinction of liquid fuel droplets presented in this paper is an application of stability theory, and specifically of Liapunov's first (indirect) method, which is well developed for lumped parameter autonomous systems. Since the behavior of liquid droplets is usually represented by a distributed nonautonomous system, an important part of the paper deals with the method by which the equations governing droplet combustion are reduced to the form appropriate to this analysis. The model consists of two unsteady autonomous coupled ordinary differential equations in temperature and oxygen mass fraction. Far field assumptions have made it necessary to treat the fuel mass fraction as a parameter. The results include the familiar S curves of temperature versus Damköhler number, as well as a great deal of detailed information about the static and the dynamic stability of the transitions between steady state evaporation and steady state combustion.
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