Characterisation of the Chaotic Dynamics in the Spontaneous Combustion of Coal Stockpiles

This paper describes studies of some fundamental aspects of the spontaneous combustion of coal stock-piles by means of a transient, two-dimensional model in the presence of weak natural convection. The model includes mass, energy, and momentum balance equations. the main assumptions made in the model are: planar, two-dimensional symmetry. Boussinesq approximation for density changes in the gas-phase, quasi-steady conditions for momentum balance, and negligible consumption of the solid reactant. Results of numerical simulations are presented and discussed, illustrating the ignition process when achieving stationary combustion, as well as oscillating combustion conditions. The Rayleigh number is changed to study its influence on the dynamic behavior of the system. The use of nonlinear analysis tools allows the characterization of the oscillating behavior found. Such tools are: the calculation of the power spectra density of a sampled time series, and the estimation of the attractor dimension through the Grassberger-Procaccia algorithm. The dynamics of the system become chaotic for a range of values of the Rayleigh number. Further increase of the natural convection parameter leads to more stable periodic, and eventually stationary, long-term behavior.