M-Components Mathematical Modeling for Coniferous Tree Ignition

Abstract

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Physical And Mathematical Statement

Due to the subcortical layer of coniferous tree is more saturated with moisture (Esau, 1980) than the resinous core, the electric current of lightning discharge in the trunk of such a tree passes mainly through the outer layers, without penetrating inside. The following physical model is used. At a certain point in time, a lightning discharge of a given polarity and duration strikes the coniferous tree trunk. It were 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. The trunk wood is heated due to the Joule heat generated in the subcortical zone of the tree trunk. As a result of the flow of electric current, the wood is heated and when critical heat fluxes from the subcortical zone of the trunk to the ignition surface and its temperature, 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 – the subcortical zone; 3 – the tree bark.

Figure 1.

Discharge with M-components (Campos et al., 2007)

Figure 2.

Scheme of the solution area

The mathematical model (Kuznetsov and Baranovskiy, 2008) describes heat transfer using non-stationary heat conduction equations:

,(1)

,(2)

.(3)

At the initial moment of time, the temperature field is determined by the following conditions:

Key Terms in this Chapter

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.

Monitoring: Monitoring refers to the periodic calculation of the parameters of forest fire danger with a portion of information available in real time.

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.

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).

Ignition Delay: Time before flame flash after forest fuel heating.

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.

Mathematical Simulation: The production of a computer model of forest fire conditions and prerequisites, especially for the purpose of study.

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.