2.1.1. Methods and Models of FDS

FDS is a powerful fire simulator software developed by the National Institute of Standards and Technology of America. This software is very flexible and widely used in the field of fire, and it can predict a variety of substances such as smoke and carbon monoxide. The accuracy of FDS has been verified by a large number of experiments [8].

FDS is used for governing equations, which are solved via the numerical method [9,10]: Mass conservation equation:

$$\frac{\partial \rho}{\partial t} = \nabla \cdot (\rho u) \tag{1}$$

where *ρ* is the density, *t* is the time, *u* is the velocity vector, and ∇ is the Hamiltonian operator. Momentum conservation equation:

$$
\rho \left[ \frac{\partial u}{\partial t} + (u \cdot \nabla)u \right] + \nabla \cdot p = \rho g + f + \nabla \cdot \tau \tag{2}
$$

where *g* is the acceleration of gravity, *f* is the volume force vector, *τ* is the viscous tension per unit area, and *p* is the pressure.

Energy conservation equation:

$$\frac{\partial}{\partial t}(\rho h) + \nabla[\rho h u] = \frac{\partial p}{\partial t} + u \cdot \nabla p - \nabla \cdot q\_{\tau} + \nabla \cdot (k \nabla T) + \sum\_{i} \nabla \cdot (h\_{i} \rho D\_{i} \nabla Y\_{i}) \tag{3}$$

where *h* is the specific enthalpy, *q<sup>r</sup>* is the thermal radiation flux, *T* is the temperature, *k* is the heat conductivity coefficient, *D<sup>i</sup>* is the diffusion coefficient of the *i*th ingredient, and *Y<sup>i</sup>* is the mass fraction of the *i*th ingredient.

Ingredient conservation equation:

$$\frac{\partial}{\partial t}(\rho Y\_i) + \nabla \cdot (\rho Y\_i u) = \nabla \cdot (\rho D\_i \nabla Y\_i) + m\_i^m \tag{4}$$

where *m<sup>i</sup> <sup>m</sup>* is the mass production rate of the *i*th ingredient.

Ideal gas state equation:

$$p\_0 = \rho TR \sum\_{i} \left( Y\_i / M\_i \right) = \rho TR / M \tag{5}$$

where *p<sup>0</sup>* is the background pressure, *R* is the molar gas constant, *M* is the molecular weight of mixed gas, and *i* is the *i*th ingredient.
