Mathematical modeling of wildland fire initiation and spread

Highlights

• A multiphase wildfire model has been developed and incorporated into the PHOENICS CFD software.

• The model accounts for drying, pyrolysis, char combustion, turbulent gaseous combustion and convective, conductive and radiative heat transfer.

• The mathematical model was validated using the experimental data.

Abstract

The aim of this paper is to create a user-friendly computational tool for analysis of wildland fire behavior and its effect on urban and other structures. A physics-based multiphase Computational Fluid Dynamics (CFD) model of wildfire initiation and spread has been developed and incorporated into the multi-purpose CFD software, PHOENICS. It accounts for all the important physicochemical processes: drying, pyrolysis, char combustion, turbulent combustion of gaseous products of pyrolysis, exchange of mass, momentum and energy between gas and solid phase, turbulent flow and convective, conductive and radiative heat transfer. Turbulence is modeled by using a RNG k-ε model and the radiative heat transfer is represented by the IMMERSOL model. The Arrhenius-type kinetics are used for heterogeneous reactions and the eddy-breakup approach is applied for gaseous combustion. The model has been validated using the experimental data.

Introduction

Wildland fires are extremely complex and destructive phenomena and their behavior depends on the state of vegetation, meteorological conditions and ground terrain. Experimental studies of wildfire behavior are expensive and challenging tasks. This makes the development of robust and accurate models of wildfire behavior an extremely important activity. There are various types of wildland fire models: statistical, empirical, semi-empirical and physics-based. This paper is devoted to the development and validation of a physics-based multiphase Computational Fluid Dynamics (CFD) model of wildland fire initiation and spread and smoke dispersion.

Over the past 30 years, significant progress in the development of physics-based wildfire models has been achieved. In particular, fully physical multiphase wildfire models have been developed by Grishin et al., 1986, Grishin, 1997, Porterie et al., 1998, Porterie et al., 2000, Porterie et al., 2005, Morvan and Dupuy, 2001, and Mell et al. (2007).

According to a review by Morvan (2011), one of the most advanced fully physical multiphase wildfire models is the three-dimensional (3D) model, WFDS (Wildland urban interface Fire Dynamics Simulator), developed at the Building and Fire Research Laboratory (BFRL) of NIST. The validation of WFDS is ongoing: its recent validation was conducted by Menage et al. (2012) by using the experimental data of Mendes-Lopes et al. (2003) on surface fire propagation in a bed of Pinus pinaster needles. The same set of data was also used by Porterie et al. (2000) in validating their multiphase model.

In recent years, a number of experimental and theoretical works have been performed by El Houssami et al., 2016, El Houssami et al., 2018, Padhi et al., 2016, and Frangieha et al. (2018)) to study the combustion of different porous wildland fuels. Numerical simulations were compared to laboratory experiments carried out with porous pine needles beds (El Houssami et al., 2016, El Houssami et al., 2018), shrub fuels (Padhi et al. (2016)) and grass (Frangieha et al. (2018)). The relevance of various sub-models used to close the multiphase CFD models was assessed.

The process of forest fire propagation was analyzed by Grishin (1997) and Perminov (2013) with use of simplified two-dimensional (2D) multiphase formulation. The equations of three-dimensional (3D) model were integrated by these researchers over the height of the forest canopy and the resulting 2D system of equations was solved to study the dynamics of wildfire spread and the preventive measures such as fire breaks and barriers. The dynamic turbulent viscosity was determined using simplified local equilibrium model of turbulence (Grishin, 1997) and the Arrhenius-type kinetics were applied for both heterogeneous reactions and gaseous combustion.

In the present study, a fully physical multiphase 3D model of wildland fire behavior was developed and incorporated into the commercial general-purpose CFD software, PHOENICS, employed as a framework and a solver (http://www.cham.co.uk/phoenics.php). The model contains the main features proposed by previous researchers, i.e. Grishin (1997) and Porterie et al., 1998, Porterie et al., 2000, and it accounts for all the important physical and physicochemical processes: drying, pyrolysis, char combustion, turbulent combustion of gaseous products of pyrolysis, exchange of mass, momentum and energy between gas and solid phase, turbulent gas flow and convective, conductive and radiative heat transfer. The use of PHOENICS software as a framework for modeling allows model applications by potential users (students, researchers, fire management teams, etc.) without any special CFD background due to availability of user-friendly software interface, documentation and technical support. Moreover, an open and general structure of software enables users to modify the model, test various built-in models of turbulence and radiation, try various numerical schemes and import geometries from CAD packages in order to model complex shapes of objects in wildland-urban interface (WUI).

The novelty of the current paper relative to the previous studies is that a physics-based multiphase 3D wildfire model, which is based on available data on chemical kinetics of heterogeneous reactions, eddy-break-up approach for gaseous combustion, RNG k-ε turbulence model and IMMERSOL radiation model, has been incorporated for the first time into the general-purpose CFD software and validated using the experimental data of Mendes-Lopes et al. (2003) on surface fire propagation in a bed of pine needles. In the following sections, the physical and mathematical formulation is presented (section 2), the numerical method is described (section 3) and the simulation results are discussed and compared with experimental data (section 4).