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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 200

Numerical Methods for the Computation of Radiation and Moisture Effects in Fire Spread

L. Ferragut12, M.I. Asensio1 and S. Monedero1

1Department of Applied Mathematics,
2IUFFyM, University Institute of Fundamental Physics and Mathematics,
University of Salamanca, Spain

Full Bibliographic Reference for this paper
L. Ferragut, M.I. Asensio, S. Monedero, "Numerical Methods for the Computation of Radiation and Moisture Effects in Fire Spread", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 200, 2006. doi:10.4203/ccp.84.200

Summary
A numerical method is developed for fire spread simulation modelling. The model is a variant of the models in chapter one of reference [2], Model I in [1] or the model in [3] where we have introduced the influence of the moisture content and radiation. We consider the combustion of a porous solid, where a simplified energy conservation equation is applied.
 (105) (106) (107)

The rate of loss of fuel is given by
 (108) (109)

Which is coupled to the temperature by the arrhenius law through the term

 (110)

The effect of the vegetation moisture and endothermic pyrolysis is incorporated in the model by means of a multivalued function representing the enthalpy.

 (111)

Where the and are the non-dimensional evaporation heat and pyrolysis heat and , the temperatures of evaporation and pyrolysis.

The resolution of this multivalued operator is done using the Yosida approximation of a perturbed multivalued operator

 (112)

Which gives explicit values of and without the need of an iterative algorithm.

The nonlocal radiation term from the flames above the vegetable is based on a 3D transfer equation involving 2D calculations and taking into account the absortion by the gases.

 (113) (114)

We present two ways of computing the approximate solution of the radiative equation, by use of the characteristic method combined with a discrete ordinate method, and by the discontinuous Galerkin method together with a modified Runge-Kutta method [5].

Finally several representative examples are solved and compared with experimental data [4].

References
1
Margerit J, Séro Guillaume O. Modelling forest fires. Part II: reduction to two-dimensional models and simulation of propagation, Int. J. Heat and Mass Transfer 2002; 45:1723-1737. doi:10.1016/S0017-9310(01)00249-6
2
Cox G. Combustion Fundamentals of Fire. Academic Press, London, 1995.
3
Simeoni A, Larini M, Santoni PA, Balbi JH. Coupling of a simplified flow with a phenomenological fire spread model. C.R. Mecanique 2002; 330:783-790. doi:10.1016/S1631-0721(02)01532-2
4
J. Ventura, J.Mendes-Lopes, L. Ripado Temperature-Time curves in fire propagating in beds of pine needles. III International Confer. on Forest Fires Research.
5
B.Cockburn, G.E.Karniadakis, C.-W. Shu. Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering 11, Springer.

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