Abstract
The results of the numerical implementation of the spatial formulation for the problem of coniferous tree ignition by an electric current of a cloud-to-ground lightning discharge are presented. The problem is solved in a three-dimensional formulation in a cylindrical coordinate system. The axisymmetric formulation of the problem is considered. Localization of reactive wood, structural inhomogeneity of the bark, current-voltage characteristics of a cloud-to-ground lightning discharge, and chemical reaction in the gas phase are taken into account. The conditions for the ignition of a coniferous tree in the typical range of the discharge effect are revealed.
TopMathematical Statement
According to (Esau, 1980; Yavorskiy and Seleznev, 1984), the electric current of a cloud-to-ground lightning discharge passes in the subcortical zone of the coniferous tree trunk without penetrating inside. The main assumptions and suggestions: 1) reactive wood is formed in the lower part of the branches (Esau, 1980); 2) the approximation of an “ideal” crack in the bark is used (Baranovskiy and Kuznetsov, 2017); 3) in the calculations only the part of the branch growing from the trunk is considered. The rest of the continuation is not considered, since it was previously established that during the exposure to electric current the outer part of the branch does not have time to warm up; 4) the main product of pyrolysis is carbon monoxide (Grishin, 1997); 5) the leading chemical reaction is the oxidation of carbon monoxide to carbon dioxide (Grishin and Shipulina, 2002); 6) the tree is considered as a conductor of the resistor type, for which Ohm's and Joule-Lenz's laws are valid (Yavorskiy and Seleznev, 1984).
The following physical model is adopted to describe the simulated process. A freestanding coniferous tree is considered. At a fixed moment in time, a lightning discharge of a certain polarity and duration strikes the tree trunk. It is believed that the current-voltage characteristics of the discharge are the same for different sections of the tree trunk. As a result of the flow of electric current in the subcortical zone, the wood is heated by the release of Joule heat. In the process of further heating, thermal decomposition of wood occurs with the formation of gaseous pyrolysis products. The pyrolysis products instantly enter the gas phase and mix with the oxidizing agent. At certain temperatures and concentrations of reagents, a chemical oxidation reaction of carbon monoxide occurs. It is considered that ignition occurs if the critical values of the following parameters are reached: 1) the heat flux from the chemical reaction zone exceeds the heat flux from the subcrustal zone of the tree; 2) the temperature of the gas mixture. The influence of wood moisture on the ignition process is neglected. The solution domain is shown in Fig. 1a, and the boundaries of the regions are indicated in Fig. 1.b.
Figure 1. Solution domain (a) and subdomain boundaries (b)
Key Terms in this Chapter
Lightning Activity: An atmospheric phenomenon characterized by discharges of the cloud-to-cloud and cloud-to-cloud-to-ground class.
Meteorological Parameters: Physical characteristics of local weather conditions in the forested area under consideration. Key parameters include ambient temperature, soil temperature, precipitation, wind speed, solar radiation, cloud cover, dew point temperature. These parameters are used for mathematical modeling of the drying of a layer of forest fuel.
Mathematical Simulation: The production of a computer model of forest fire conditions and prerequisites, especially for the purpose of study.
Ignition: Inflammation of forest fuel caused by definite source of high temperature or energy.
Monitoring: Monitoring refers to the periodic calculation of the parameters of forest fire danger with a portion of information available in real time.
Forest Fuel: It can be considered like dead and live forest fuel. Main types of forest fuel which can be involved in combustion during forest fire: cloud-to-ground forest fuel (needles, leaves and dry grass, small branches) and crown forest fuel (needles, small branches).
Cloud-to-Ground Lightning Discharge: An electrical discharge during a thunderstorm that occurs between a cloud and the earth’s surface. It is a natural source of forest fires.
Forest Fire: Uncontrolled aerothermochemical phenomenon characterized by step-by-step mechanism which includes following stages: inert heating, moisture evaporation, high temperature terpens evaporation, dry organic matter pyrolysis, flammable combustion and smoldering.
Ignition Delay: Time before flame flash after forest fuel heating.
Prediction: Under the prediction of forest fires is the calculation of the parameters of forest fire danger with a certain projection in advance in order to have enough time to anticipate an emergency. The calculation in this case is carried out in a mode ahead of the real time of the development of the catastrophe - the occurrence of a forest fire.