Journal of Combustion

Volume 2015, Article ID 513576, 17 pages

http://dx.doi.org/10.1155/2015/513576

## Calculation of Spotting Particles Maximum Distance in Idealised Forest Fire Scenarios

IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisbon, Portugal

Received 19 January 2015; Revised 13 May 2015; Accepted 24 May 2015

Academic Editor: Michael A. Delichatsios

Copyright © 2015 José C. F. Pereira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Large eddy simulation of the wind surface layer above and within vegetation was conducted in the presence of an idealised forest fire by using an equivalent volumetric heat source. Firebrand’s particles are represented as spherical particles with a wide range of sizes, which were located into the combustion volume in a random fashion and are convected in the ascending plume as Lagrangian points. The thermally thin particles undergo drag relative to the flow and moisture loss as they are dried and pyrolysis, char-combustion, and mass loss as they burn. The particle momentum, heat and mass transfer, and combustion governing equations were computed along particle trajectories in the unsteady 3D wind field until their deposition on the ground. The spotting distances are compared with the maximum spotting distance obtained with Albini model for several idealised line grass or torching trees fires scenarios. The prediction of the particle maximum spotting distance for a 2000 kW/m short grass fire compared satisfactorily with results from Albini model and underpredicted by 40% the results for a high intensity 50000 kW/m fire. For the cases of single and four torching trees the model predicts the maximum distances consistently but for slightly different particle diameter.

#### 1. Introduction

Spot fires occur during wild forest fires when burning debris transported by the wind and convection column land far from the active fire source. Under such occurrence there is a probability to ignite another fire with dangerous consequences for fire brigades and firefighting which should be considered by the decision support systems for wildfire management and planning [1–3]. Many firebrand transport models have been developed; see the pioneers’ works of Tarifa et al. [4], Lee and Hellman [5], and Albini [6]. Albini model predicts the maximum spotting distance [6–10] and has been included in several forest fire propagation models [11–17]. The computing time required to obtain predictions with the Albini model is much faster than real time, due to the inherent model based correlations. This is a great advantage over multidimensional Computational Fluid Dynamics (CFD) predictions; however it is believed that forest fire phenomena will benefit from CFD like for enclosure fire predictions; see, for example, [18–20].

The problem is of great complexity because a large number of random parameters are presented. The transport of firebrands involves several modelling difficulties: firstly the knowledge of the particle shape and size that lift off in the flame region; secondly the particle transport by unsteady wind and convection column fields; and last but not the least the probability to ignite a fire after particle landing. This work is only related to the transport of firebrand aiming to predict the particle maximum spotting distance. However it involves the coupled prediction of (i) the wind flow through and above vegetation; (ii) the fire source near region and convection column; and (iii) the particle heat and mass transfer and combustion along its trajectory.

The wind flow interaction with canopy trees has been extensively studied [21–25]. The vertical mean wind velocity displays an exponential profile type inside the forest and the turbulence levels are mainly due to turbulent kinetic energy production by shear at the canopy top, rather than by wake production by the individual elements. The flow within and above a forest is linked by turbulent motions, at larger scales relative to the forest depth, that are strongly intermittent in character [22, 26, 27]. Several attempts have been proposed to simulate the exchanges between a forest and the lower atmosphere by assembling averaged statistical turbulent models such as ; see [28–31]. These models are inadequate in representing the intermittent character of the flow. Large eddy simulation (LES) explicitly simulates the dominant energetic turbulent scales resolved by the three-dimensional mesh [32–34] and consequently it was used in this work.

Due to the disparity of scales in the fire heat release region from those of the remaining computational domain, it is almost impossible to resolve and to predict the heat release rate, but it is to be given as an input parameter. The so-called Lagrangian thermal elements [35, 36] are used to model the fire release heat as they are convected about by the thermal induced motion. Under this assumption, the fire is a large collection of blobs carried along by the large-scale motion and the heat release rate associated with each element is represented by a simple function with a time scale determined from the plume correlations summarised by [37]. A far more simplified model is to prescribe a heat source either on the surface or in volume, usually approximated by Gaussian profiles [38] and by correlations of the flame height as a function of the firepower intensity. This was the procedure adopted to model the fire itself and the source was assumed stationary since the propagation fire velocity is small compared with the wind velocity.

The pioneers’ works have employed the classical plume model approach of integral models to predict buoyant plumes in a cross flow responsible for firebrand lofting. Examples of developed simplified models are for initially axisymmetric jets [39, 40] and for buoyant plumes from fires [5, 7, 9] or integral plume models for line fires in a cross flow [41]. These models reduce the problem to a set of ordinary differential equations to be solved with an approximate expression or with an empirical fit to calculate the plume trajectory, width, velocity, and temperature. Three-dimensional field calculations of fire plumes have been extensively investigated; see, for example, [36, 38, 42]. In this work the latter approach is followed and a LES model was selected that takes into account explicitly the subgrid stresses and turbulent heat fluxes [43].

In the framework of time averaged turbulent flow modelling, the problem of the instantaneous velocity acting on the particle is usually treated under Lagrangian stochastic models; see [44] for a review. For the present purpose of the LES calculations during the firebrand trajectory it was assumed that the calculated instantaneous velocity field acts in the particle during the considered time step. There are three main ways on how to account with the with the wind interaction in the firebrands particles. The first way is to consider spherical particles with a wide range of sizes undergoing drag relative to the flow and moisture loss as they are dried and pyrolysis, char-combustion, and mass loss as they burn. Models to calculate flight paths of dispersed particles in a turbulent flow are well established and a spherical particle shape is assumed due to inherent difficulties to know the drag and momentum coefficients from other shapes; see, for example, [45]. The second way is to consider nonspherical particles shapes, cylinders or discs, under one-way coupling, meaning that the wind influences the nonspherical particle orientation relative to the local wind obtained by momentum balances, but with prescribed drag and momentum coefficients as a function of relative particle orientation. The third one would correspond to the intrusive real body geometry of the nonspherical particle and the calculation (with Chimera or moving meshes) of their wake that may interfere with the particle itself during tumbling, fluttering, or chaotic free fall motion.

Recently, experimental apparatus has been constructed in order to generate a controlled size and mass distribution of glowing firebrands; see, for example, [46, 47], allowing studying the combustibility of firebrand material such as pine cones and scales and pieces of bark eucalypt; see [48]. Theoretical models for the drag coefficient of nonspherical particles are being established (see [49–51]) but the wide range of random shapes, sizes, and terminal velocities requires validation tests before practical use in reactive multidimensional calculations.

The combustion model of the woody, cellulose, or coal fuel particles commonly includes drying, pyrolysis, and char-oxidation processes. Their burning characteristics and diameter at landing are related to the potential for the firebrand to ignite the adjacent vegetation [52–55] and reviews of the modelling chemical and physical processes of wood and biomass pyrolysis have been presented; see, for example, [56–58]. Firebrand propagation prediction is based on either plume model, coupled fire-atmosphere, or semiempirical models to predict the fire spread; see, for example, [59–61]. Particles trajectories and spotting distances have been obtained for a wide range of idealised cases using these main assumptions about the fire source responsible for the convection column; see, for example, [55, 61–63].

Physics based on coupled fire-atmosphere models consider approximations of the governing equations from the fluid dynamics, the combustion, and the thermal degradation of solid fuel (see, e.g., [64–66]) aiming to preclude the use of existing simplified empirical wildfire models because they do not predict general fire behaviour; however the high-resolution and the high-fidelity combustion are not currently appropriate because of their computational cost. Several physics based on coupled fire-atmosphere studies have been conducted (see [67–72]) and some of these studies have been applied to the fire spotting problem. Among them [71] has considered particle combustion of cylindrical and disk-shaped firebrands for several geometrical parameters. Discs travel further than cylinders; also firebrands from canopy fires travel further than firebrands from surface fires. Depending on where the burning occurs, for example, the faces or around their circumference, this influences the firebrand lifetimes. In addition the simulations reveal that the coupled fire-atmosphere behaviour dominates the trajectories and landing patterns.

The main difficulty in the validation of the Albini model or of a CFD model, under real conditions, is that large field forest fires only show the spotting fires signature on the ground after the fire has been extinguished and it is unknown if they correspond to the particle maximum spotting distance. The particle responsible for the maximum spotting distance may not ignite a fire in opposition to the other particles that spot too much shorter distances. Consequently the intercomparison of different models may contribute to estimating the error bar of the spotting distances pattern.

The main objective of this work is to compare the maximum spotting distance obtained with the Albini model with the spotting particles maximum distance obtained with LES and firebrand combustion models. Therefore in this work a coupled solution of the three-dimensional velocity and temperature unsteady fields is obtained and for each time step the particles are allowed to burn during their convection. For each particle size the calculated spotting distances as well as their char, ash, and temperature allow one to obtain the maximum spotting distance for a prescribed fire. Two classes of fires are presented: grass fires and burning of trees. For both cases the predicted maximum spotting distances are compared with Albini model’s results.

In the next section the models are briefly presented. The section of Results follows this, but prior to the firebrand transport results a LES benchmark test case was performed. It corresponds to the LES simulation of lower atmosphere with a homogeneous forest [22] to investigate the LES solution dependence on coarse grid resolution. Next, firebrand spotting is examined using a coupled fire/atmosphere LES (large eddy simulation) in which the processes of firebrand lofting, propagation, and deposition are connected. The idealised scenarios correspond to the Albini “spotting distance examples” [6] for short grass 2000 kW/m fire and wind-driven fire in chaparral 50000 kW/m fire. In addition torching trees were considered, based on the scenario given by [73], the first corresponding to a single Grand Fir tree and the second corresponding to four trees burning together. The paper closes with summary conclusions about the comparison of the maximum spotting distances.

#### 2. Mathematical and Numerical Model

##### 2.1. Governing Equation

The governing equations are the continuity Navier-Stokes and energy equations. The Boussinesq approximation is used and the equations include additional terms to account for the drag from the canopy trees and for the heat received by the air in contact with the vegetation. The filtered Navier-Stokes model equations can be expressed byHere is the pressure, is the gravitational acceleration, is the volumetric expansion coefficient, and and are the constant molecular diffusivities of momentum and heat. The bar denotes the average over a computational grid cell and the double primes the deviations thereof. The Coriolis force has been excluded as it has little direct bearing on scales of motion for the domain considered of the order of 1 km.

##### 2.2. The Subgrid-Scale (SGS) Model

There is a wide range of subgrid-scale (SGS) models as well as great knowledge of the modelling issues like gradient-diffusion hypothesis used in some of the large eddy simulations; see, for example, [74, 75]. For atmospheric flows the pioneer classical models (see, e.g., [33, 34]) have been being improved with models based on transport equations for the SGS stresses and fluxes. The second-order closure subgrid-scale equations model reported by [43] was selected for the present purpose to predict a plume at cross flow in the atmospheric surface layer. The model uses a transport equation for the subgrid-scale kinetic energy The turbulent heat and momentum fluxes and their respective anisotropic components,are determined from the following set of algebraically approximated second-order closure equations:Equations (6a) to (6c) were solved explicitly as proposed by [43] yieldingThe coefficients of the SGS model are listed in Table 1 according to [43].