A. M. Grishin

Mathematical Modeling of the Ignition of Tree Crowns

Numerical calculations of the transition of a downstream (surface) forest fire into an upstream (crown) forest fire based on a general mathematical model of forest fires are presented. It is found that the ignition of the forest canopy is a gas-phase phenomenon. Critical conditions for the transition of a downstream into an upstream forest fire are determined. The numerical calculations are compared with experimental data.

Ignition of Combustible Forest Materials by a Radiant Energy Flux

The paper reports results of experimental ignition of litter layers consisting of needles of cedar, pine, and fir-tree, birch leaves, lichen (Cladonia), and moss (Pleurozium shreberi). It is established that the moss is ignited faster than the other combustible forest materials. It is shown that with equal moisture contents, the ignition times of needle litter from different trees are identical within the experimental error, and for litter of birch leaves, the ignition time is shorter than that for litter of coniferous trees. This difference is found to be due to differences in the interaction of the radiant flux with litter layers of needles and leaves. Minimum values of the ignition heat pulses for needle and leaf litter layers are estimated for various heat-flux densities. These values tend to a minimum for a heat-flux density of 0.5–0.8 MW/m2.

Experimental study of thermal and fire tornados

In [1] various types of tornado-like flows arising above a heated rotating disk in the quiescent-air atmosphere were studied and an illustrating diagram was also presented. In what follows, we will refer to one of these types, namely a sole tornado-like vortex, as a thermal tornado. In [2], different methods for physically modeling fire tornados were proposed. It was shown that formation of fire tornados depends neither on the method of their production nor the nature of combustible material. This phenomenon is determined rather by both the density of heat flow arising as a result of combustion and the angular velocity (or frequency ω = 1.1‐1.3 Hz) of rotation of the cylinder into which the combustible substance is placed. The goals of the present paper are to present a comparative study of thermal and fire tornados, to understand conditions causing the appearance of fire tornados, to identify their types, and to analyze their stability as a function of both the level of combustible liquid in the cylinder and gas-flow properties. In this study, ethyl alcohol was used as a combustible liquid. Two methods were employed for swirling combustible liquid and combustion products. We implemented swirling from below by the rotation of a substrate (cylindrical vessel) and from above by means of a fan. Our setup consisted of an Mi-22 electric heater, a base, an electric-current voltage regulator, and a circular steel disk 0.4 m in diameter. The combustible liquid was placed on a cylindrical steel substrate fixed to the disk. In different experiments, the diameter and height of the cylinder were (6, 7, 10, 12, or 20) 〈 10 ‐2 m and (2, 6, or 12) 〈 10 ‐2 m, respectively. A thermocouple and a thermal-flux sensor, whose signals had been registered by a KSP-4 recorder, were used as measuring tools. The shaft rotation frequency of an electric motor with the disk was specified by the voltage regulator and varied within the limits of 0 - 20 Hz. In addition, as distinct from the experiment performed in [2], in a number of cases, an immobile steel circular plate 2 〈 10 ‐3 m thick and 0.5 m in diameter was placed at heights of 0.4, 0.45, and 0.5 m above the rotating substrate. In the experiments, the temperature of this plate remained almost invariable, which allowed us to model the action of the inversion layer of atmosphere temperature on a fire tornado.

Ignition of a layer of combustible forest materials

Theoretical and experimental studies of the ignition of forest combustible materials by real ignition sources, which are modeled by a reference source, are reported. The time of ignition by the reference source is determined. The critical ignition energy is estimated, and its variation under real conditions is analyzed.

General mathematical model for forest fires and its applications

A review is presented of the results of physical and mathematical modeling of forest fires performed at the Tomsk State University. A general physical model for forest fires is proposed, and the basic system of equations along with basic boundary and initial conditions is given. A structure of the fire front and limiting conditions of its propagation are discussed. A new concept of forest-fire fighting is formulated.

Mathematical Model for Spread of Crown Fires in Homogeneous Forests and along Openings

The problem of spread of upper crown fires in homogeneous forests and along various openings (roads, motorways, power lines, etc.), which are potential fire hazardous areas, was formulated mathematically and solved numerically. Key words: mathematical modeling, crown forest fire front, front precursors.

Ignition of forest tracts by a high-altitude source of radiant energy

The problem of initiation of large-scale forest fires induced by technogenic catastrophes is solved in an axisymmetric formulation. Results of numerical calculations are given which imply that the ignition mechanism in this case is the same as for collisional catastrophes. A comparison of the limiting dimensions of ignition zones for nuclear charges of different energy yields shows good agreement between two-dimensional and quasi-one-dimensional approximations.

Formulation and Solution of the Problem of Drying of a Layer of Combustible Forest Materials

The drying of combustible forest materials is the most important and least studied stage of the multiphase process of their burning under natural conditions. Physical and mathematical modeling of the drying of a layer of combustible forest materials is performed in a conjugate formulation by solving the equations of a binary boundary layer and the equations of heat and mass transfer in a layer of combustible forest materials with corresponding boundary and initial conditions. Solutions of this problem for diurnal and seasonal changes in environmental temperature are obtained for three scenarios of development of weather conditions. The data obtained are compared with experimental data on drying of needles of pine and some other coniferous trees. A rigorous physicomathematical basis for prediction of forest fires is given.

On the ignition of a layer of combustible forest materials by light radiation

The ignition of a layer of combustible forest materials by luminous radiation was studied experimentally. The minimum radiant heat flux densities required to ignite combustible forest materials are determined for a neodymium-doped glass laser and a tungsten lamp. It is established that the heat flux, density increases with increase in the moisture content and density of the layer of combustible forest materials and decreases with increase in the diameter of the light spot, and the critical flux density is higher for the laser radiation than for the incandescent lamp.

IGNITION OF FOREST TRACTS AS A RESULT OF COSMIC OR TECHNOGENIC CATASTROPHES

Using a quasi-one-dimensional approximation, the problem of extensive forest fires caused by collisional or technogenic catastrophes is formulated and solved. Calculations show that the mechanism of ignition in both cases is the same, but the quantitative parameters of the processes (ignition time and limiting conditions, shape of ignition zone) differ significantly from each other. The cause is the difference in the mechanisms of energy release in the near-ground atmospheric layer during technogenic or collisional catastrophes.