A model for combustion of gaseous and liquid fuels in a refractory tube

Abstract

A model has been developed and solved for the combustion of liquid and gaseous fuels in a refractory tube. The model postulates plug flow, and therefore is restricted to the regime of turbulent flow. It also postulates that the liquid droplets vaporize prior to ignition and that the reaction rate can be represented by a global expression insofar as the energy balance is concerned. The solution of this model was greatly simplified by the approximate reduction of the integro-differential equation arising from radiative transfer to a differential equation. A convergent, exact solution for the resulting set of ordinary differential equations was obtained using finite-difference methods. The numerical solutions are in reasonable agreement with the experimental data of Chen and Churchill and Bernstein and Churchill for premixed propane and air and with those of Choi and Churchill for hexane droplets and air. The model provides a theoretical confirmation and explanation for the observed multiple, stationary states and the low (5–40 ppm) measured concentrations of NO x . However, the primary value of the model and method of solution is for the prediction of behavior for conditions not yet studied experimentally.