Theoretical studies in heterogeneous combustion

Abstract

The theory of the steady-state burning of a single spherically-symmetric liquid monopropellant droplet in an infinite inert atmosphere is formulated. Numerical solutions for the temperature and composition profiles and burning rate are obtained in the case of a one-step chemical reaction of the second order. It is shown that the size and location of the reaction zone depend strongly upon the activation energy. Approximate analytical solutions for the burning rate which are valid for large activation energies are obtained for arbitrary chemical reactions. The results indicate that the mass burning rate is proportional to the droplet radius raised to a power which varies from two at small activation energies to unity at large activation energies. The Shvab-Zeldovich formulation of the problem of burning of initially unmixed systems is developed and applied to the case of a single fuel droplet burning in an infinite oxidizing atmosphere. Some simplification over other methods for treating this problem is obtained, and the burning rate is shown to be unaffected by a distributed reaction zone when the Lewis number is unity. A general statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions and aerodynamic forces. The method is applied to the problem of the determination of the size distribution of a spray formed by the impingement of two streams of droplets of known properties. It is shown that if the two incident jets have a size distribution of a generalized Rosin-Rammler type, then the resulting spray belongs to the same class of distributions. The size history of evaporating sprays is also obtained from the theory. A spray combustion analysis given by Probert is extended to include more general size distributions and the effects of droplet interactions and relative motion of the droplets and the fluid. It is shown that sprays of a uniform size yield the highest combustion efficiency.