The master's thesis presents a mathematical model for analysis and simulation of wildfires. The computer program is intended to emulate the progression of ground fires. It is programmed in the Wolfram Mathematica software tool using the cellular automata (CA) method, which belongs among discrete techniques of modelling. The fundament of the CA algorithm is a semiempirical mathematical model. It is derived from the general energy balance, which is simplified based upon eight assumptions. The concept of heat transfer is empirical in nature. It uses a geometric model that is analogous to the point source one, but the magnitude of the flame heat flux (Q̇c) is contingent on the calibration factor (η), which is calibrated based on experimentally obtained data from the scientific literature. Moreover, to the primary CA algorithm an extension section is added, which is designed to simulate firebrand spreading. Unlike the elementary part of the program, it is founded on the stochastic principle and uses a larger CA neighbourhood.
The response of the calibrated mathematical model was tested by a parametric study and sensitivity analysis. The results of the parametric study, where we observed the dependence of rate of fire spread (ROS) on the value of individual model parameters, were compared with other published research data. The sensitivity analysis was performed on the principle of two level full factorial analysis in accordance with the DOE (Design Of Experiments) method. Based on the standard deviations (s), we determined which variables our mathematical model depended on the most. Data of the full factorial analysis was also evaluated in the Minitab program, where we used a t-test to assess whether influence of model parameters is statistically significant.
Considering the behaviour of simulations in different circumstances and results of the analysis of the mathematical model we have concluded, that the computer program is suitable to represent the development of ground fires. Furthermore, we have shown that a minimal ratio of combustible to non-combustible cells (p) is required for successful fire spread, which in the conditions of our numerical experiment was equal to 0,54. Moreover, the critical value of mass fraction of moisture in the fuel (Hu,k) is dependent upon the fuel load (W). All the tested variables in the mathematical model were statistically significant without any statistically significant difference between the influences of the initial fuel temperature (T0) and ignition temperature (Tvž). The predominant variables of the mathematical model are the reaction rate constant (kr) and the heat of combustion (Hcom), which primarily affect the heat release rate of the flame (Q̇c) and flame height (Hf). However, the specific heat of dry fuel matter (cs) had the smallest effect among all tested variables.
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