Critical conditions for carbon combustion

Abstract

The critical conditions for vigorous burning of spherical carbón partióles are derived using asymptotic techniques for large Zel'dovich numbers. The particle liíetime and the temperature history are obtained for both supercritical and subcritical regimes, when a carbón particle is suddenly exposed to a stagnant high temperature oxidizing atmosphere. For Damkóhler numbers below a critical number, that is, the subcritical regime, slow burning oceurs in the carbón particle. That means that throughout the life of the particle, the chemical reaction is controlled by kinetics. In this regime, the lifetime is extremely long. On the other hand, for Damkóhler numbers above the critical one, the process ends with a rapid increase of temperature finally reaching a reaction controlled by diffusion. In this supercritical regime, the life is relativelv short. For valúes of the reduced Damkóhler number very cióse to the critical one, a Ricatti equadon is derived for the non-dimensional temperature of the particle, the solution of which defines whether the particle undergoes subcritical or supercritical behavior.