Abstract
Based on a one-dimensional two-layer physical and mathematical model of ignition of a deciduous tree (birch), the influence of the m-components of a cloud-to-ground lightning discharge is estimated. The problem is solved in a cylindrical coordinate system. Typical cloud-to-ground lightning discharges are considered. An assessment of the influence of m-components was carried out for a typical range of changes in their characteristics. Surface temperature of tree trunk and heat flux to this surface are obtained during simulation.
TopPhysical And Mathematical Statement
The core of the deciduous tree is more saturated with moisture and, as a result, the electric current of the discharge passes in this area (Esau, 1980). The following physical model is used. At a certain point in time, a lightning discharge of a given polarity and duration of action strikes the trunk of a deciduous tree. It is assumed that current–voltage characteristics of the discharge are the same for different sections of the tree trunk. The discharge current has M components. Fig. 1 shows a typical discharge with M-components. The time is plotted on the abscissa, and the channel brightness in arbitrary units on the ordinate.
Figure 1. Discharge with M-components (Campos et al., 2007)
The warming of the trunk wood occurs due to the Joule heat released in the core of the tree trunk. As a result of the flow of electric current, the wood heats up and when critical heat fluxes from the core of the trunk to the ignition surface and its temperature are reached, the wood ignites. The solution domain is shown in Fig. 2, where the numbers indicate the zones: 1 - the core of the tree trunk; 2 - tree bark.
Figure 2. Scheme of the solution area
Mathematically, the process of heating a tree trunk before ignition with a ground lightning discharge is described by a system of non-stationary differential equations (Kuznetsov and Baranovskiy, 2009):
,
(1),
(2) Key Terms in this Chapter
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.
Ignition Delay: Time before flame flash after forest fuel heating.
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.
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.
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: ground forest fuel (needles, leaves and dry grass, small branches) and crown forest fuel (needles, small branches).
Lightning Activity: An atmospheric phenomenon characterized by discharges of the cloud-to-cloud and cloud-to-ground class.
M-Components: Are observed as an increase in the brightness of the channel during continuing current. M-components may have a peak in the range of kiloamperes.