Abstract
The physical and mathematical formulation and results of the numerical solution of the problem for ignition of a coniferous tree (pine) by a cloud-to-ground lightning discharge are presented. The problem is considered in a flat formulation in a cylindrical coordinate system. The features of current flow and heat transfer are considered taking into account the localization of reactive wood and the presence of a surface layer of water. A parametric analysis was carried out, and the conditions for the ignition of a tree trunk were determined in a typical range of the exposure to negative and positive discharges.
TopMathematical Statement
The flow of electric current has its own characteristics in the event of a lightning strike into the trunk of a coniferous tree, since the resistance of the wood of the resinous tree itself is much greater than the bark and subcrustal layer. Therefore, the electric current of a lightning discharge in the trunk of a coniferous tree passes mainly through the outer layers, without penetrating inside. Of particular interest is the study of heat transfer taking into account the localization of the so-called reactive wood. Such wood is formed in the lower part of the branches of coniferous trees and is also called compression wood. Reactive wood differs from ordinary wood by its physicochemical properties (Esau, 1980).
To describe the modeled process, the following physical model is adopted. 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. The heating of the trunk wood occurs due to the Joule heat generated in the subcrustal zone of the tree trunk and in the surface layer of water. As a result of the electric current, the wood heats up and when critical heat fluxes from the subcrustal zone of the trunk to the ignition surface and its temperature are reached, the wood is ignited. The influence of wood moisture on the ignition process is neglected.
The solution area is shown in Fig. 1.a, 1.c, where the numbers indicate the areas: 1 - the core of the tree trunk; 2 - subcortical zone; 3 - tree bark; 4 - wood from the upper part of the branches; 5 - reactive wood of the lower part of the branches; 6 - part of the subcortical zone, which has the same properties as area 4; 7 - part of the subcortical zone, which has the same properties as area 5; 8 - part of the core, which has the same properties as area 4; 9 - part of the core, which has the same properties as area 5; 10, 11 - air; 12.13 - surface layer of water. The boundaries of the regions are indicated in Fig. 1.b, 1.d.
Key Terms in this Chapter
Ignition: Inflammation of forest fuel caused by definite source of high temperature or energy.
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.
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.
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.
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.
Lightning Activity: An atmospheric phenomenon characterized by discharges of the cloud-to-cloud and cloud-to-ground class.
Mathematical Simulation: The production of a computer model of forest fire conditions and prerequisites, especially for the purpose of study.
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: ground forest fuel (needles, leaves and dry grass, small branches) and crown forest fuel (needles, small branches).
Monitoring: Monitoring refers to the periodic calculation of the parameters of forest fire danger with a portion of information available in real time.