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The Smouldering of Peat

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The Smouldering of Peat THE SMOULDERING OF PEAT A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2013 Kathleen Scott School of Mathematics Contents Abstract 5 Declaration 6 Copyright Statement 7 Acknowledgements 8 1 Introduction and Background 11 1.1 OverviewofWildfires .............................. 11 1.2 PeatCharacteristicsandPeatfires . .... 13 1.3 The Physics and Chemistry of Combustion . ... 17 1.4 Characteristics of Smouldering Combustion . ....... 19 1.5 CombustionInstabilities . ... 21 1.6 Other forms of Smouldering Combustion . .... 23 1.7 TheCurrentContributions . .. 25 2 Literature Review 27 2.1 Experimental Studies of Peat Combustion . ..... 27 2.2 KineticSchemes ................................. 34 2.3 ReactionRateLaws ............................... 37 2.4 Models of Smouldering Combustion . ... 39 2.5 Instabilities and Low Lewis Number Combustion . ...... 42 3 The Mathematical Model 45 3.1 TheProblem ................................... 45 3.2 TheModel..................................... 46 2 3.3 Non-dimensionalising the Model . .... 49 4 Spherically Symmetrical Combustion 55 4.1 Introduction.................................... 55 4.2 Solid Consumption Tending to 0 . 58 4.2.1 AnalyticalSolutions. 59 4.2.2 Superadiabatic Numerical Solution . ... 63 4.2.3 Adiabatic Numerical Solution . 67 4.3 Incomplete Solid Combustion . .. 71 4.3.1 AnalyticalSolutions. 72 4.3.2 Superadiabatic Numerical Solution . ... 74 4.3.3 Adiabatic Numerical Solution . 75 4.3.4 Cylindrically Symmetrical Numerical Solution . ...... 77 4.4 Conclusions .................................... 79 5 Combustion with an Imposed Gas Velocity 80 5.1 Introduction.................................... 80 5.2 The Travelling Wave Model . 81 5.2.1 Identifying a Travelling Wave Solution . ... 81 5.2.2 Profiles of the Travelling Wave Solution . ... 86 5.3 TheEffectsofHeatLoss ............................ 89 5.4 TheEffectsofGasVelocity.. .. ... .. .. ... .. .. .. ... .. 94 5.4.1 Self-travelling Combustion . .. 97 5.5 TheEffectoftheLewisNumber. 102 5.6 The Constant Density Assumption . 105 5.7 The Distance Between Neighbouring Fingers . ..... 109 5.8 Conclusions .................................... 113 6 Buoyancy-Driven Combustion 116 6.1 Introduction.................................... 116 6.2 ThePermeabilityofPeat ........................... 118 6.2.1 The Constant Molecular Weight Assumption . 128 6.3 TheEffectofPorosity.............................. 133 3 6.3.1 The Constant Porosity Assumption . 133 6.3.2 The Relationship Between Porosity and Permeability . ...... 135 6.3.3 Non-Constant Permeability Model . 139 6.4 Conclusions .................................... 146 7 Conclusions 148 A Constant Values 152 B Ember Storm Model 154 B.1 Introduction.................................... 155 B.2 EllipticalFireGrowth............................ 156 B.3 EmberStormModel............................... 157 B.4 SpreadofaSteady-StateEmberStorm. 161 B.5 Conclusions .................................... 163 Bibliography 164 Word count 47569 4 The University of Manchester Kathleen Scott Doctor of Philosophy The Smouldering of Peat February 6, 2013 A model examining underground smouldering peat combustion is presented. A one-step chemical reaction is considered where the gas and solid are assumed to be in thermal equilibrium. The full model allows porosity, permeability and gas density to vary and considers a buoyant velocity field determined by Darcy’s law. Due to the low bulk thermal conductivity of peat, the diffusion of oxygen through it is characterised by a Lewis number much less than one. This results in thermal-diffusive instabilities. These instabilities can cause flame balls to arise in gaseous combustion and a fingering regime to arise in solid combustion. Analytical solutions to simplified spherically symmetrical equations are derived. These equations assume diffusion to be the dominant transport mechanism as well as taking that the porosity, gas molecular weight and gas density all remain constant. The underlying structure of the combustion region is found to be analogous to that of a flame ball. When studied in cylindrical symmetry a single, stable finger can be modelled prop- agating against an imposed air flow. The effects of heat losses, velocity magnitude and the Lewis number can be studied and results are compared to existing experimental smouldering combustion data. Although no detailed experiments have studied this phenomenon in peat, predicted results capture key qualitative trends found in both filtration combustion of polyurethane foam and in the fingering combustion of pa- per. In addition to this, when the imposed air flow is reduced to zero a propagating combustion front is predicted, analogous to a self-travelling flame ball. When the velocity field is determined by Darcy’s law the dimensionless permeability of the peat plays a key role in determining the range of values over which fingering combustion can occur. Whilst there is little impact of taking the gas molecular weight to be constant, when porosity is allowed to vary and a relationship between porosity and permeability is included an over-blowing extinction limit is identified. This limit is not found in the constant-porosity model where a low-fuel extinction limit is predicted. Peats of differing ages and locations can possess significantly different characteristics. However, the fingering regime is predicted to occur within the range of parameters in which peat soils lie. Experiments suggest that fingering combustion can take the form of both sparse fingers and a complex fingering regime. The cylindrically symmetrical model can not capture tip-splitting. Hence the model does not explicitly account for the distance between two neighbouring fingers. However, an estimate for this value can be made if peat smouldering were to occur in a regime of multiple fingering. An averaged continuum model describing the spread of an ember storm is also presented. The dominant mechanism determining the spread-rate of the fire is the lofting and landing of embers and individual fires are taken to grow in an elliptical manner under the influence of the wind. When an ember storm is spreading at a steady speed, its spread rate is found to be described by a single similarity solution. 5 Declaration No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. 6 Copyright Statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intel- lectual property (the “Intellectual Property”) and any reproductions of copyright works in the thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and com- mercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any rele- vant Thesis restriction declarations deposited in the University Library, The Univer- sity Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regul- ations) and in The University’s Policy on Presentation of Theses. 7 Acknowledgements This research would not have been possible without the support of a number of people. Firstly I wish to thank my supervisor Prof. John Dold for suggesting the topic and providing his invaluable insight and guidance throughout my PhD. I am also grateful for the help, support and expertise of my supervisor Dr. Joel Daou. I would like to express my gratitude to the Manchester University School of Math- ematics and the Peak District National Park for their financial support, without which this work would not have been possible. Finally I would like to thank Adam, my family, friends and colleagues for their support. 8 Nomenclature A pre-exponential factor c specific heat d distance between neighbouring fingers D diffusivity g gravity F dimensionless heat loss constant K permeability of solid with respect to air K′ dimensionless permeability Le Lewis number m mass p variation from ambient pressure P pressure Q heat of reaction per mass of char R universal gas constant S propagation speed t time T temperature TA activation temperature u gas velocity V volume W molecular weight y mass fraction Y dimensionless mass fraction α heat release factor β Zeldovich number 9 10 δ ratio of characteristic gas density to characteristic
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