A two-dimensional reaction-advection-diffusion model of the spread of fire in wildlands

Abstract

The aim of this research is to develop a model of the spread of wildfires that is computationally efficient and easy-to-use, yet comprehensive enough to capture the major phenomena that govern the behaviour of a real fire. Namely, the pyrolysation of wood; the combustion of a mono-phase medium composed of premixed gas of fuel and air; the heat transferred by diffusion, convection and radiation considering emission and absorption of hot semi-transparent gases; and the thermal energy transport due to atmospheric wind and spatial distribution of vegetation. The model consists of two coupled partial differential equations, one representing the mass formation of each chemical species involved in the combustion, and the other ensuring the balance of enthalpy. The dimensionality reduction sought by modelling these three-dimensional (3D) phenomena in two-dimensional (2D) space is an intricate problem that has been overcome by means of pseudo-3D terms in the energy balance equation. For instance, the convection in the direction perpendicular to the 2D domain of the model has been represented as heat loss whose magnitude is linearly dependent on the temperature difference between the ambient and the simulation domain. Thus, the pseudo-3D convection term acts as a sink of thermal energy. It is important to note, however, that some environment properties have necessarily been disregarded in the interest of efficiency. Thus, the effect of topography on the spread of fire has been ignored in this model. In addition, the balance of momentum in the simulation plane is not included in the formulation as air density is considered independent of temperature and the wind velocity field is steady-state and uniform. Furthermore, the diffusion coefficient is augmented to account for the energy transport due to convection inside the flattened vegetal substrate, which is abstractly represented as a pre-mixed gaseous layer. This augmentation has been calibrated for particular environment conditions such as the porosity of the fuel and its spatial distribution so that the model can be used as a tool for prediction of fire propagation. Making use of the 4th-Order Runge-Kutta method and running simulations for different constraints and boundary-initial conditions, results appear realistic. The presented fire-spread model is aimed at supporting the design of innovative fire management and suppression technologies and strategies, as well as to function as a decision-support tool to assist fire fighters in the use of current technology. Hence it must be both realistic and computationally efficient. Nonetheless, a more advanced 3D high-fidelity model is currently under development at the other end of the spectrum of the accuracy/efficiency trade-off with the aim to provide better insight into the fire dynamics.