Abstract
The results of numerical simulation of heating a coniferous tree (pine) by cloud-to-ground lightning discharge are presented. The problem is solved in a one-dimensional formulation in a cylindrical coordinate system. A four-layer structure of the coniferous trunk is considered taking into account the core, subcortical layer, bark, and surface water layer. A parametric study of the effect of current-voltage characteristics typical of negative and positive cloud-to-ground lightning discharges on the process of heating the trunk wood has been carried out. The conditions for the ignition of a tree trunk in a typical range of variation of the parameters of the impact of the discharge are established.
TopMathematical Statement
The processes of current flow have their own characteristics in the event of a lightning strike in the trunk of a coniferous tree (belong to gymnosperms), for example, pine. In the structure of angiosperms, a significant role is played by the vessels along which moisture moves (Esau, 1980). The inner part of the trunk, penetrated by such transport channels, is a good conductor of electric current. One of the differences in the structure of coniferous wood is the absence of vessels (Esau, 1980). Therefore, the central part of the trunk of resinous conifers has much greater resistance than the bark and subcortical layer (Fig. 1). As a result of this, in a pine, the electric lightning discharge current passes mainly through the outer layers saturated with moisture (Esau, 1980).
The following physical model is considered. A separate coniferous tree grows on the surface of the land. A terrestrial lightning discharge of a certain polarity hits a tree trunk. An electric current from a ground lightning discharge flows through the trunk. It is assumed that in different sections of the trunk the current parameters are the same and it flows in the subcortical zone of the coniferous tree. As a result, the wood is heated due to the Joule heat, and when certain heat fluxes from the subcortical zone of the trunk and the critical temperature are reached, the wood ignites. The effect of wood moisture on the ignition process is neglected. The last assumption is justified enough for short-term rains with thunderstorms, as well as for the initial period of rain, when thunderstorm activity is usually maximum. It should be noted that the scenario of current flow in the surface water layer is also considered. This is consistent with a thunderstorm scenario, accompanied by precipitation.
The problem is solved for a cylinder that simulates a tree trunk. A certain section of the trunk is considered. The scheme of the solution domain is presented in Fig. 1, where 1 is the core, 2 is the subcortical zone, 3 is the bark of the tree trunk, 4 is the surface layer of water; Rw is ste water layer, Rs is the outer radius of the trunk, R1 is the interface between the subcortical zone and the bark, R2 is the interface between the core and the subcortical zone.
Mathematically, the process of heating a tree with a cloud-to-ground lightning discharge before ignition is described by a system of non-stationary differential heat equations:
,
(1),
(2),
(3) Key Terms in this Chapter
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.
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.
Lightning Activity: An atmospheric phenomenon characterized by discharges of the cloud-to-cloud and cloud-to-ground class.
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.
Mathematical Simulation: The production of a computer model of forest fire conditions and prerequisites, especially for the purpose of study.
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.
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 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).