ABSTRACT
Wildland fire spread is one of the most challenging problems faced by reserved or unreserved vegetation in many developed and developing nations, because it can lead to serious environmental hazards in claiming lives, properties, animals and some other valuable treasures. This thesis establishes an approximate analytical solution that is capable of analysing fire spread in a real-time coupled atmospheric wildland fire, in determining the effect of temperature, oxygen concentration, volume fraction of dry organic substance, volume fraction of moisture and volume fraction of coke. The analytical solution is obtained via direct integration and eigenfunction expansion technique, which depicts the influence of the parameters involved in the system. The effect of change in parameters values such as Frank-Kamenetskii number, Radiation number, Peclet energy number, Peclet mass number, Activation energy number and Equilibrium wind velocity are presented graphically and discussed. The results obtained show that Frank-Kamenetskii number reduces the temperature. Radiation number and Peclet energy number reduces the temperature, oxygen concentration and volume fraction of coke while they enhances volume fractions of dry organic substance and moisture. Activation energy number reduces the temperature and volume fraction of coke while it enhances volume fractions of dry organic substance and moisture. Also, Peclet mass number and Equilibrium wind velocity both enhance oxygen concentration. The inference drawn from this is that an increase in Radiation number will remove heat from the burning scene. Similarly, reducing wind velocity will limit the oxygen contact with fuel. With continuous supply of heat, the ignition of additional fuel will continue as long as there is enough oxygen present. Thus, it is obvious that these three elements (heat, fuel and oxygen) must be present before combustion can occur. Varying anyone of the elements will vary the intensity or otherwise of the fire. Armed with this knowledge, the fire fighters are better equipped to manage fire.
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background to the Study
The term ‗wildfire‘ which also means wildland fire, rural fire or forest fire refers to an unplanned, unwanted or uncontrolled fire in an area of combustible vegetation occurring most likely in rural areas (Scott and Glasspool, 2006).
Forest fire ignition could be as a result of; human action (intentional) in clearing of land, extreme/intensive drought, in rare cases thunderstorm (lightning) and hunter‘s burning bush in search of wild animals. For both human, extreme/intensive drought and lightning-caused fires, there is a geographical gradient of fire ignition, mainly due to variations in climate and fuel composition but also to population density for instance. The timing of fires depends on their causes. In populated areas, the timing of human-caused fires is closely linked to human activities and peaks in the afternoon whereas, in remote areas, the timing of lightning-caused fires is more linked to weather conditions and the season, with most such fires occurring in summer. Better tools for modelling forest fire behaviour are important for managing fire suppression, planning controlled burns to reduce the fuels, as well as to help assess fire danger (Anne et al., 2012).
Basically, there four types of fire models which are; surface fire, crown fire, spotting fire and ground fire. Surface fire models deals with the fire that burns the vegetation closed to the surface, such as brush, small trees, or herbaceous plants. Crown fire models are somewhat complementary to surface fire models and studied how the fire spreads over the canopy of trees in a given forest. Spotting fire models provides the equations to analyse those new fire caused by incandescent pieces of the main fire transported out of the main fire perimeter. Finally, ground fire models focused their attention on those physical processes that occur in the substrate of the soil when a fire takes place (Carlos, 2014)
The greatest aim of any analysing system is to enable an end user to carry out useful and meaningful analysis. A useful analysis is one that helps the user achieve a particular aim. The field of wildland fire behaviour, aims primarily to stop the spread of the fire or to at least reduce its impact on life and property. The earliest efforts at wildland fire behaviour analysis concentrated on analysing the likely danger posed by a particular fire or set of conditions prior to the outbreak of a fire. These fire danger systems were used to assess the level of preparedness of suppression resources or to aid in the identification of the onset of bad fire weather for the purpose of calling total bans on intentionally lit fire (Perminov, 2018).
The forest fire are very complicated phenomena. At present, fire services can forecast the danger rating of or the specific weather elements relating to forest fire. There is need to understand and analyse forest fire initiation, behaviour and spread (Perminov, 2018).
It seems more promising to use methods of mathematical modeling that will allow taking into account the dynamics of this process in space and time.
1.2 Statement of the Research Problem
In global context, fire outbreak is becoming alarming due to intractable practice. Analysis of vegetation fire spread has been a challenge to researchers and managers for several decades, but in spite of the various models and fire behaviour forecasting systems that have been developed over the years as described by Sullivan (2009a, 2009b, 2009c), there is not yet a commonly accepted fire behaviour simulator that can be applied in operational conditions for large and complex fire. This is due to the complexity of the physical and chemical processes that are involved in large-scale fire requiring a large number of input parameters that are not easy to obtain and physical models that are not yet fully developed. Physical models have been formulated mathematically and implemented in numerical codes like Grishin (1994), Albini (1996), Linn et al. (2002), Se´ro-Guillaume and Margerit (2002) and Mell et al. (2007). Nevertheless, practical applications of these models are not yet possible owing to large computational requirements and uncertainty regarding the description of key physical processes. Based on these scenarios, there is need for this study to broaden and sharpen the scope of what is already known about fire spread analysis and coupled atmospheric-wildland fire.
1.3 Significance of the Study
Wildland fire is one of the most complicated problems discovered worldwide and they cause a lot of havoc to biodiversity as well as local ecology. Fire spread is difficult to fight/combat in nature, yet it cannot be done away with, but can only be controlled, suppressed or managed. However, in a recent time, fire spread model gained more attention in order to enhance suppression rate. It is therefore important for us to widen our knowledge on wildland fire spread. Based on this, we present a mathematical model to analyse fire spread process, thus making the research significant.
1.4 Scope and Limitation
The thesis focuses on the mathematical model for analysing fire spread in a real-time coupled atmospheric-wildland fire. It is limited to approximate analytical simulation of the governing model equations.
1.5 Aim and Objectives
The aim of this research work is to establish an analytical solution that is capable of analysing fire spread in real-time coupled atmospheric-wildland fire.
The objectives of this study are to:
i. Formulate mathematical equations governing forest fire propagation.
ii. Obtain the analytical solution of the model using direct integration and eigenfunction expansion technique
iii. Provide the graphical representation of the solutions obtained.
1.6 Definition of Terms
Active crown fire: This occurs when the surface fire and crown fire are linked. Surface intensity is sufficient to ignite tree crowns, and fire spread and intensity in the tree crowns encourages surface fire spread and intensity.
Combustion: Is a flame speed which is the measured rate of expansion of the flame front in a combustible reaction.
Crown fire: This is a forest fire that spreads from treetop to treetop at great speed ahead of the ground fire.
Emissions: Is the production and discharge of gaseous substance into the atmosphere.
Fire: Is a chemical reaction involving the bonding of oxygen with carbon or other fuel, with the production of heat and the presence of flame.
Firebrand: Is a piece of burning wood.
Fire prediction: Is a way of forecasting the outbreak of fire.
Fire spread: Is the rate at which fire is propagated through radiation, convection and conduction.
Flame: A stream of burning vapour or gas, emitting light and heat.
Mass fire: Is a fire resulting from many simultaneous ignitions that generates a high level of energy output.
Modeling: Is the generation of a physical, conceptual or mathematical representation of a real phenomenon that is difficult to observe directly.
Peatbog fire: This is also known as underground or root fire, and it is a wildland fire caused by the burning of tree roots. This type of fire can burn for a great length of time, until its fuel is totally consumed or exhausted.
Running crown fire: Is the crown fire that covers the entire forest from the soil surface to the top of the tree crowns or passes through the trees and the underbrush, herbage and moss layer.
Solid fuel: Refers to various forms of solid material that can be burnt to release energy, providing heat and light through the process of combustion.
Surface fire: Is a forest fire that burns only the surface litter and undergrowth.
Suppression: Is an act of stoppage or reduction of fire spread.
Wildland fire: Is an unwanted or unplanned fire in an area of combustible vegetation.
Wind: Is the movement of atmospheric air usually caused by convection or differences in air pressure.
This material content is developed to serve as a GUIDE for students to conduct academic research
MATHEMATICAL MODELLING FOR ANALYSING FIRE SPREAD IN A REAL-TIME COUPLED ATMOSPHERIC WILDLAND FIRE
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