An enthalpy-based pyrolysis model for charring and non-charring materials in case of fire
Introduction
In the development of a fire, flame spread always plays a very important role. In numerical simulations, this implies coupling of gas phase ‘Computational Fluid Dynamics’ (CFD) simulations, including turbulent combustion and radiation, to pyrolysis simulations in the solid material. In order to make such simulations possible, it is advantageous to keep the pyrolysis model simple.
During the past two decades, several researchers have developed numerical models for pyrolysis of charring materials, with different levels of complexity, such as: Arrhenius-type models [1]; ‘integral’ models [2], [3], [4], [5]; an ‘extended’ integral model [6]; a moving mesh model [7]; a dual mesh model [8]. A review on pyrolysis modelling has recently been provided in [9]. An interesting paper on pyrolysis modelling is reference [10]. For non-charring materials, it is common practice to work with a ‘heat of gasification’ at the pyrolysing surface and to consider a conduction problem in the solid materials (e.g. [2], [11], [12], [13], [14], [15]).
In the present paper, we describe in detail a simplified model, which is applicable to charring and non-charring materials, which can contain moisture. We also explain that the model is extendable for multi-dimensional solid-phase treatments, as required for general flame spread simulations. This is a difference to many existing simplified pyrolysis models, which might look very similar to the present model at first sight, but which are basically limited to one-dimensional configurations (or, at least, implementation for multi-dimensional solid-phase treatments becomes very cumbersome). Also, the present model can be combined with any model for the transport of gases or water vapour inside the solid material. In the same sense, e.g. a model for char oxidation can be added. We consider this beyond the scope of the present paper.
We deliberately avoid inclusion of pyrolysis kinetics. Whereas this limits the field of application to high-temperature pyrolysis and to situations where pyrolysis kinetics is not prevalent, it is relevant for flame spread situations as in a developing fire.
There are two major parts in the model description:
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the local relation between enthalpy and temperature;
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the energy equation to be solved in the solid material.
We first describe these parts in detail and define precisely what we mean by the ‘heat of pyrolysis’, in order to avoid any confusion on this term. Afterwards, we put our model and terminology in perspective with respect to existing models in the literature.
Next, numerical issues and implementation, including the solution procedure, are described in detail. An interesting feature of the model is the use of a fixed computational mesh.
Finally, we illustrate the accuracy of the results by means of a series of basic test cases. We discuss the following features:
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comparison to numerical reference results [5] and experimental data [16] for one-dimensional configurations in charring materials;
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the importance of the use of a piecewise linear approximation of the temperature field in the solid material for charring materials;
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sensitivity of the results with respect to the grid size and the time step;
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comparison to results [2] for PMMA;
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illustration that the model can deal with moisture in the solid;
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illustration that the model is applicable to multi-dimensional configurations, as required for general flame spread simulations.
The complete set of results aims at illustrating the robustness and accuracy of the simple model, with applicability to flame spread simulations in a developing fire.
Section snippets
Thermodynamics: introduction
In our model, we focus on the thermodynamic description of the phenomena. Our approach is largely based on [17], one of the first theoretical papers on this topic. Below, we elaborate this to obtain an easy-to-use enthalpy-based pyrolysis model for three-dimensional simulations on a fixed computational mesh. The approach is to consider five constituents: virgin solid material, char, volatiles, liquid water and water vapour. In [17], the endothermic pyrolysis process is assumed to take place at
Implementation and solution procedure
As described in the previous section, the model considers enthalpy as the basic variable, for which a transport equation is solved. We are, however, not interested in enthalpy itself, but rather in temperature distribution and volatile production. The latter is related to the motion of the pyrolysis front, which is assumed infinitely thin in the present model formulation. So, we require a procedure to reconstruct temperature and front position from the basic enthalpy variable. This is done,
Discussion of results
We restrict ourselves to configurations where the externally imposed heat flux is not computed from flame radiation, in order to avoid related uncertainty.
As initial condition, there is only virgin material at temperature T = Tamb = 300 K, which is well below the pyrolysis temperature. Unless stated otherwise, all results are obtained with the piecewise linear temperature field representation.
Summary and conclusions
Starting from a basic thermodynamic description of pyrolysis phenomena, a simplified pyrolysis model was described in detail. The basic model quantity is enthalpy, computed from the specific enthalpies of five constituents (dry virgin material, char, pyrolysis gases, liquid water and water vapour). The concept of heat of pyrolysis and its relation to formation enthalpies of individual constituents was revisited. It was explained how the developed model takes advantage of the use of pyrolysis
Acknowledgments
This research is funded by project G.0130.06 of the Fund of Scientific research – Flanders (Belgium) (FWO-Vlaanderen). The fourth author is Postdoctoral Fellow of the Fund of Scientific research – Flanders (Belgium) (FWO-Vlaanderen).
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