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 flow of electric current in the trunk of deciduous and coniferous trees is different. This is due to the fact that in deciduous trees, moisture is transported through vessels in the massive central part (Esau, 1980). The wetter central part is in this case a conductor of electric current. The study of the tree ignition by a lightning discharge was carried out using the following physical model. A free-standing deciduous tree grows on the land surface. In order to concretize the parameters of the model, birch is considered as an object of research. A cloud-to-ground lightning discharge strikes the trunk of this tree. The discharge electric current flows along the inner part of the birch trunk and in the surface layer of water. It is assumed that the electric current has the same parameters in different sections of the trunk. The Joule heat causes the wood in the trunk to heat up. When critical values of heat fluxes to the ignition surface and its temperature are reached, the wood ignites. Moisture transfer processes are not taken into account in this model.
Geometry of the problem. A cylinder is considered that models a tree trunk. A certain section of the trunk is considered. The solution area diagram is shown in Fig. 1, where 1 is the core, 2 is the bark of the tree trunk, 3 is the surface layer of water; Rw is the boundary of the surface layer of water, Rs is the outer radius of the trunk, R1 is the boundary between the inner region and the bark of the tree trunk.
Mathematically, the heating of tree by a cloud-to-ground lightning discharge before ignition is described by a system of non-stationary differential equations of heat conduction:
,
(1),
(2),
(3)Boundary conditions for equations (1) - (3):
r=0,
,
(4)r=R1, 
,
T1=
T2(5)r=Rs,
,
T2=
T3(6) Key Terms in this Chapter
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).
Monitoring: Monitoring refers to the periodic calculation of the parameters of forest fire danger with a portion of information available in real time.
Lightning Activity: An atmospheric phenomenon characterized by discharges of the cloud-to-cloud and cloud-to-cloud-to-ground class.
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.
Ignition: Inflammation of forest fuel caused by definite source of high temperature or energy.
Mathematical Simulation: The production of a computer model of forest fire conditions and prerequisites, especially for the purpose of study.
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.