A Numerical Solution of Reynolds System of Equations for Description of Forest Fire Initiation

A mathematical model for description of heat and mass transfer processes at crown forest fire initiation and spread has been designed. The forest canopy is considered as a homogeneous two temperatures, reacting and porous medium. Temperatures of condensed (solid) and gaseous phases are separated out. The first includes a dry organic substance, moisture (water in the liquid-drop state), condensed pyrolysis and combustion products (coke, ash), and mineral part of forest fuels. In the gaseous phase we separate out the components necessary to describe reactions of combustion (oxygen, combustible products of pyrolysis of forest fuels and the rest inert components). It is considered that 1) the flow has a developed turbulent nature, molecular transfer being neglected, 2) gaseous phase density doesn't depend on the pressure because of the low velocities of the flow in comparison with the velocity of the sound, 3) forest canopy is supposed to be non-deformed porous medium. To describe the transfer of energy by radiation diffusion approximation is used, while to describe convective transfer controlled by the wind and gravity, we use Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. A pressure correction procedure is used to establish the pressure and velocity fields. The algorithm is valid for small Mach number. To obtain discrete analogies a method of control volume is used. An iterative method for solving the nonlinearity algebraic equations is employed. The boundary-value problem is solved numerically using the method of splitting according to physical processes. In the first stage, the hydrodynamic pattern of flow and distribution of scalar functions are calculated. The system of ordinary differential equations of chemical kinetics obtained as a result of splitting is then integrated. A discrete analog for equations is obtained by means of the control volume method using the SIMPLE algorithm. The accuracy of the program is checked by the method of inserted analytical solutions. The chemical time step is selected automatically. As a result of mathematical modeling the fields of temperatures, mass concentrations of components of gaseous phase, volume fractions of components of solid phase, as well as vectorial fields of velocity at different instants of time with taking into account mutual influence of the overterrestrial layer of atmosphere and a crown fire on each other will be obtained. It allows investigating dynamics of forest fire initiation under influence of various external conditions: meteorology conditions and various kinds of forest combustible materials and their state (load, moisture etc.). A great deal of final and intermediate gaseous and dispersed combustion products of forest fuels is known to be exhausted into the atmosphere during forest fires: carbon monoxide, carbon dioxide, water, soot, smoke and etc. The results obtained agree with the laws of physics and experimental data. Since, owing to the requirements of ecological safety, large-scale experiments under field conditions are rarely permissible, mathematical modeling of forest fires using the model presented above is the very convenient method of studying the nature, limiting conditions of spread, structure and energetic of a forest fire.