Numerical modeling of two-dimensional smoldering processes

A mathematical model along with a numerical solution procedure is presented for the simulation of flameless combustion (smoldering) of a solid in a stream of air. By assuming a global single-step combustion reaction, the problem is formulated via conservation equations of mass, species, linear momentum, and energy. Conservation equations are developed by volume averaging the microscopic conservation equations of the constituent phases (i.e., gaseous mixture, solid fuel, and ash). The model accounts for conduction in the solid, thermal radiation from the solid, and forced and natural convection flow and heat transfer in the gas stream. Also included in the problem formulation are the effects of transport processes such as the heatup and ignition of the solid sample, the smoldering of the solid, the motion of the burning front, and the formation of ash and transport of gas and heat in it. The transient two-dimensional governing equations of the problem, in terms of primitive variables, are discretized over nonuniform control-volumes and solved by an iterative numerical procedure. Different aspects of the model and solution procedure are also discussed. As a test problem, the smoldering of standard samples of charcoal (wood-coal) in a limiting oxygen index (LOI) flammability test apparatus is modeled. The results of the smoldering simulations are presented in terms of the field variations of velocity, composition, and temperature of the gas in the test chamber, the temperature distribution in the solid and ash, and the temporal position and velocity of the smoldering/burning front. The calculated transient burning rates are compared with the experimental data obtained in a LOI apparatus.