Monopropellant droplet decomposition for large activation energies

The quasi-steady decomposition of a monopropellant droplet in a quiescent atmosphere is analyzed, in the limit of large activation energy, for a gas phase decomposition reaction of the Arrhenius type.An analytical relation is obtained for the pre-exponential rate constant, or the Damköhler number, as a function of the droplet vaporization rate. The curve giving the vaporization rate in terms of the Damköhler number has, for low values of the temperature at infinity, an S shaped form which exhibits ignition-extinction characteristics.With increasing values of the droplet vaporization rate above the pure vaporization value we pass from a nearly frozen regime, under which ignition conditions occur due to the large temperature sensitivity of the reaction rate, to a complete decomposition regime, in which practically all the fuel is decomposed in a thin reactive-diffusion zone, separated from the droplet surface by a transport region of lower temperature. For sufficiently large Damköhler numbers, the thin reaction zone is located close to the droplet surface, so that the flame structure becomes planar: a linear relation between the droplet radius and time is obtained in this case. The non planar effects are responsible for the extinction of the flame at low Damköhler numbers and ambient temperatures below the adiabatic flame temperature. For sufficiently low values of the ambient temperature, an intermediate regime exists in which the enhancement of the vaporization rate is due only to the fraction of the vaporized fuel decomposed at a thin reaction zone, not far from the droplet, where the temperature reaches its maximum value; the remaining fuel is decomposed very far from the droplet.