**1. Introduction**

Fire is an irreversible process that involves the production of flame, heat, smoke and toxic gases, which can cause material losses, physical trauma, severe burns, respiratory and cardiovascular diseases, and death [1,2]. The main causes of fire are electrical failures, activities related to cooking, friction that occurs in machines and equipment, cutting and welding processes, improper handling of materials and equipment, leakage or release of flammable liquids and/or gases, human errors or unsafe human behavior, such as smoking in inappropriate places, and arson [1,3–9].

Researchers are unanimous in asserting that the main threat of death from fires is smoke [2,10–17]. According to Anseeuw et al. [14], 60% to 80% of deaths at the fire scene are attributed to smoke inhalation. This is because, during a fire, the burning of solid fuels causes a reduction in the oxygen concentration in the environment and an incomplete combustion of gases, generating highly toxic products such as CO and HCN, contributing to the occurrence of death by asphyxiation at the fire scene [10]. In addition to the problem of inhalation, smoke can cause fear, panic, tearing and irritation of the eyes, and reduced visibility, factors in turn make it difficult to safely exit the building.

Stefanidou et al. [2] presented the main toxic and irritating chemicals generated by the combustion of common building materials, as well as the main factors that contribute to the development of smoke inhalation injuries. In general, the smoke initially affects the upper airways (upper respiratory tract) of the fire victim and may, in a short time, becoming a complex life-threatening systemic disease, affecting all organs in the body [18].

In a fire, as the materials undergo combustion, they release hot smoke that, being lighter than ambient air, moves vertically upwards faster than horizontally, developing an inverted cone shape, well known as a plume. When the plume reaches the top of the building, with a certain speed, the smoke spreads radially across the ceiling, forming a layer of smoke (or hot gases). After the smoke covers the entire ceiling, it tends to move vertically downwards until the entire environment is filled with smoke or until mass flow rate entering the hot gas layer is balanced by the mass flow rate of exhaustion [12].

The smoke layer interface height, an extremely important parameter in the design of smoke exhaust systems, is defined as the distance, vertically, between the building floor and the smoke layer interface. Thus, it is of great importance, for people's survival, that the smoke layer interface height is above the height of their heads, for a sufficient time, so that an efficient evacuation from the fire scene is possible, that is, that this procedure occurs with minimal toxic gases inhalation.

In Brazil, the subject of fire safety started to be widely discussed after the tragedy that occurred at a nightclub located in the city of Santa Maria-RS, in January 2013. At that time, where 242 people died and almost 700 were injured. Even so, until the present moment, there is no national standard in the country that defines the parameters to be adopted in smoke control design. In the absence of these standards, the Technical Instructions established by the Fire Department of the Military Police of the State of São Paulo, 2019, which have as reference several specifications contained in international regulations, such as the NFPA and DIN standards, provide minimum fire safety requirements and, in some cases, specifying design parameters and fire protection systems installation.

Given the above, scientific studies related to fires in closed compartments are crucial for the design of smoke control systems, allowing the development and improvement of engineering strategies and techniques aimed at protecting the lives of its occupants, the facilities and equipment.

The use of computational fluid dynamics (CFD) to solve problems related to confined fires has become quite popular due to advances in computational power and numerical methods [19]. This technique has provided a better understanding of the behavior of this phenomenon and has made it possible to reduce costs, time and risks, when compared to experimental analyzes, especially in hypothetical scenarios of fires that are difficult to be implemented through experiments [17]. However, it is important to emphasize that experimental tests play important role in the development and validation of mathematical models to be used as the CFD tools.

One of the main CFD software packages used to study the behavior of fires in buildings is the Fire Dynamics Simulator (FDS), developed and available at no cost from the National Institute for Standards and Technology (NIST, Gaithersburg, MD, USA). In order to reduce or even eliminate the uncertainties of the numerical results, several studies proposed to verify [20,21] and validate [12,16,17,22–26] the models used by the FDS software.

In addition to the FDS software, other CFD tools have already been used in the literature to study the behavior of fires in closed environments, such as CFX [27–29], FLUENT [30,31] and ISIS CODE [32–34].

Qin et al. [20] investigated the influence of different exhaust systems for a fire in a gymnasium with a capacity for 18,000 people, using the FDS software. The authors observed that an increase in the speed of the mechanical exhaust fan positioned on the ceiling, in the range between 2.0 and 3.0 m/s, does not necessarily promote a more efficient smoke exhaustion, thus, there is a critical speed that depends on the heat release rate (HRR) from the fire. Further, the downward vertical displacement of smoke layer for the mechanical exhaust fan at a speed of 3.0 m/s occurred more quickly as compared to the natural exhaust system located in the same position. For the cases in which the mechanical exhaust fans were installed on the walls, the smoke exhaust occurred much more efficiently as compared to the use of natural exhaust fans in the same position, and a critical speed was not obtained, that is, the higher the fan speed, the lower the downward vertical displacement of the smoke. In this last analysis, an increase in speed from 1.5 to 3.0 m/s of the mechanical exhaust fan provided a more efficient smoke exhaust.

Qin et al. [12] validated the FDS software by comparing numerical results with experimental data for a fire in an atrium with internal dimensions of 22.40 m × 11.90 m and 27.00 m height, and cases with low (560 kW) and high (4 MW) HRR. For both cases, it was observed that the natural smoke exhaust vents are more efficient when located on the roof of the atrium. On the other hand, when the exhaust vents are located on the walls of the atrium, higher positions are preferred. Subsequently, the authors evaluated the influence of the positioning of the burners, noting that the smoke layer descends more rapidly when the burner is located in the center of the atrium.

Xiao [24] compared numerical results using FDS with experimental data of temperature and mass flow rate in the doorway of a room with dimensions of 9.75 m × 4.88 m × 2.44 m (length × width × height). This compartment has only one opening and a 0.46 m<sup>2</sup> propane burner with different heat release rates. From the obtained results, the author observed a reasonable agreement between the results of temperature and mass flow rate in the opening for the cases with and without sprinkler. A greater discrepancy was observed between the numerical and experimental results of temperature and mass flow rate in the opening, for the case with sprinkler, due to the stronger turbulence, uncertainties in the fire spread rate and in the water behavior (spray angles, number of drops per second, initial speed and average drop diameter).

Ayala et al. [26] showed good agreement between the numerical results obtained by the FDS software and the experimental data of 1.36 MW and 2.34 MW pool fires burning inside a 20 m cubic atrium with a natural ventilation system. In addition, the authors showed that the area-to-height-squared ratio of the atrium, in the range of 0.3 to 3.8, does not present significant effects on the temperature and smoke layer growth.

Abotaleb [16] performed a numerical analysis using the FDS software to evaluate the influence of smoke management techniques in a building with dimensions of 10.00 m × 10.00 m and 12.00 m in height. The author observed that using six mechanical make-up air on the walls and a mechanical exhaust fan on the roof with total volumetric flow rates equivalent to 36 and 40 air changes per hour (ACH), respectively, decreasing the downward vertical displacement of the smoke layer interface height and the average temperature by 71.18% and 31.6%, respectively.

Shih et al. [35] performed a numerical simulation using the FDS software, proving that make-up air has a significantly influences on the effectiveness of a natural smoke exhaust system in a tall space, with dimensions of 8.00 m × 1.00 m and 10.00 m height, under fire scenario. In the research, the authors used the Schlieren photography technique, that allows visualization of the post-combustion hot gas distribution in the model space, to validate the simulation results.

Yuen et al. [17] used the FDS software to numerically evaluate the efficiency of natural exhaust fans and a smoke curtain in an atrium. In this research, the values of temperature and smoke layer interface height were compared with experimental measures reported by Hägglund et al. [36], obtaining good agreement for both cases (with and without a smoke curtain). The authors observed that the smoke curtain is efficient to compartmentalize the smoke, as long as its height is sufficient to completely block the spread of smoke to the other side of the environment.

Huang et al. [37] performed a numerical analysis using the FDS to evaluate the relationship between the obscuration ratio, the main parameter of smoke detectors, and soot yield, which is defined as the mass of soot produced per mass of fuel reacted. The simulated compartment has dimensions 10.00 m × 7.00 m × 4.00 m (length × width × height) without openings to the outside and a with fire source in the center. After analyzing several fire scenarios, the authors observed that the smoke speed, in the vertical, was 0.54 m/s and, the higher the soot yield, the higher the obscuration rate. In addition, the results of the simulation indicate that, at a height of 3.00 m from the floor, the diameter of the smoke plume varied between 0.30 and 0.60 m during the first 300 s of firing.

Tan et al. [38] numerically investigated the influence of HRR and ambient pressure on the efficiency of the smoke extraction system in road tunnel fires using FDS software. In addition, the authors showed that there is a critical exhaust rate at which there is an excessive fresh air discharge from the exhaust vent, decreasing the efficiency of the system.

More recently, Wang et al. [39] performed several numerical simulations to investigate the influence of different smoke control systems on smoke flow, temperature and visibility in a subway station, assisting passenger evacuation and firefighting. As results, the authors presented the best scheme for air control and smoke exhaustion for different fire locations.

Despite the importance, no studies were found to evaluate, jointly, the influence of the type and dimensions of the exhaust system, HRR, natural ventilation (openings in the lower region of the compartment for air intake) and smoke curtain in the temperature distribution and smoke dispersion during a fire in an enclosed space.

Thus, complementing the cited works, the main purpose of this work is to evaluate the thermo-fluid dynamic behavior of smoke originated from a fire in an enclosed space using the FDS software. The studied cases were elaborated in order to verify the influence of the HRR, natural exhaust fans, mechanical exhaust fans, smoke curtain and ventilation (opening windows) in the lower compartment at the smoke layer interface height, in the temperature distribution in the simulated compartment and in the exhaust volumetric flow rate. In addition, the influence of the smoke curtain and opening windows on the pressure and smoke velocity vector fields inside the compartment under analysis are also evaluated.

#### **2. Methodology**

#### *2.1. The Physical Problem and the Computational Domain*

The physical problem under study consists in evaluating the fluid dynamic behavior, spread and exhaust of the smoke generated from a burner located in a closed compartment. The compartment has dimensions 30.00 m × 15.00 m × 6.00 m (length × width × height), containing a door and four windows (of the same dimension), four exhaust fans, a smoke curtain and a burner centered in the right quadrant of the compartment, as shown in Figure 1.

The FDS software developers recommend that the computational domain should be extended beyond the physical domain when there are openings (doors, windows and exhaust vents), in order to guarantee a pressure boundary condition in the openings that is closer to reality [40]. In view of this recommendation, Wang et al. [41] carried out a numerical study and proved that the values predicted by the FDS software for the mass flow through a door were closer to the experimental data for greater distances between the limit of the computational domain and the opening of the physical domain.

Thus, in this research, the computational domain was extended 2 m beyond the dimensions of the compartment on the three faces where there are openings to the external environment. After extension, the computational domain started to have the following dimensions: 32.00 m × 17.00 m × 8.00 m, as shown in Figure 1.

domain.

8.00 m, as shown in Figure 1.

**2. Methodology** 

during a fire in an enclosed space.

under analysis are also evaluated.

*2.1. The Physical Problem and the Computational Domain* 

rate. In addition, the results of the simulation indicate that, at a height of 3.00 m from the floor, the

Tan et al. [38] numerically investigated the influence of HRR and ambient pressure on the efficiency of the smoke extraction system in road tunnel fires using FDS software. In addition, the authors showed that there is a critical exhaust rate at which there is an excessive fresh air discharge

More recently, Wang et al. [39] performed several numerical simulations to investigate the influence of different smoke control systems on smoke flow, temperature and visibility in a subway station, assisting passenger evacuation and firefighting. As results, the authors presented the best

Despite the importance, no studies were found to evaluate, jointly, the influence of the type and dimensions of the exhaust system, HRR, natural ventilation (openings in the lower region of the compartment for air intake) and smoke curtain in the temperature distribution and smoke dispersion

Thus, complementing the cited works, the main purpose of this work is to evaluate the thermofluid dynamic behavior of smoke originated from a fire in an enclosed space using the FDS software. The studied cases were elaborated in order to verify the influence of the HRR, natural exhaust fans, mechanical exhaust fans, smoke curtain and ventilation (opening windows) in the lower compartment at the smoke layer interface height, in the temperature distribution in the simulated compartment and in the exhaust volumetric flow rate. In addition, the influence of the smoke curtain and opening windows on the pressure and smoke velocity vector fields inside the compartment

The physical problem under study consists in evaluating the fluid dynamic behavior, spread and exhaust of the smoke generated from a burner located in a closed compartment. The compartment has dimensions 30.00 m × 15.00 m × 6.00 m (length × width × height), containing a door

diameter of the smoke plume varied between 0.30 and 0.60 m during the first 300 s of firing.

from the exhaust vent, decreasing the efficiency of the system.

scheme for air control and smoke exhaustion for different fire locations.

**Figure 1.** Physical domain under study (**a**) top view, (**b**) section A-A and (**c**) isometric view with transparent front wall. **Figure 1.** Physical domain under study (**a**) top view, (**b**) section A-A and (**c**) isometric view with transparent front wall.

The FDS software developers recommend that the computational domain should be extended beyond the physical domain when there are openings (doors, windows and exhaust vents), in order to guarantee a pressure boundary condition in the openings that is closer to reality [40]. In view of

(**c**)

for greater distances between the limit of the computational domain and the opening of the physical

Thus, in this research, the computational domain was extended 2 m beyond the dimensions of the compartment on the three faces where there are openings to the external environment. After extension, the computational domain started to have the following dimensions: 32.00 m × 17.00 m ×

The representative numerical mesh of the physical domain used in the simulations is composed entirely of structured, hexahedral, evenly spaced elements with aspect ratio equal to 1 (one), that is,

all sides of each element have the same dimension, as illustrated in Figure 2.

The representative numerical mesh of the physical domain used in the simulations is composed entirely of structured, hexahedral, evenly spaced elements with aspect ratio equal to 1 (one), that is, all sides of each element have the same dimension, as illustrated in Figure 2. *Energies* **2020**, *13*, x FOR PEER REVIEW 6 of 27

**Figure 2.** Details of the numerical mesh used in the simulations. **Figure 2.** Details of the numerical mesh used in the simulations.

#### *2.2. The Mathematical Model 2.2. The Mathematical Model*

For the numerical analysis, we used the FDS software, version 6.7.4, which solves the conservation equations of mass, species, linear momentum and energy, and of turbulence, with emphasis on the transport of smoke and heat. The FDS uses an approximation for low Mach numbers, developed by Rehm and Baum [42], large eddy simulation (LES) model to treat turbulence, and the Deardorff model [43] to calculate the turbulent viscosity. The FDS software also includes combustion, evaporation, pyrolysis and radiation heat transfer models. For the numerical analysis, we used the FDS software, version 6.7.4, which solves the conservation equations of mass, species, linear momentum and energy, and of turbulence, with emphasis on the transport of smoke and heat. The FDS uses an approximation for low Mach numbers, developed by Rehm and Baum [42], large eddy simulation (LES) model to treat turbulence, and the Deardorff model [43] to calculate the turbulent viscosity. The FDS software also includes combustion, evaporation, pyrolysis and radiation heat transfer models.

#### 2.2.1. The Governing Equations 2.2.1. The Governing Equations

The governing equations (equation of state, conservation of mass, species, linear momentum and energy) that describe the physical problem under study are presented in Equations (1)–(5), as The governing equations (equation of state, conservation of mass, species, linear momentum and energy) that describe the physical problem under study are presented in Equations (1)–(5), as follows:

follows: (a) Mass conservation:

(a) Mass conservation:

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = \dot{m}\_{\text{b}}^{\text{""}} \, \text{ } \tag{1}$$

 ∇∙ ሺሻ = ሶ ᇱᇱᇱ, (1) where is the density, is the velocity vector and ሶ ᇱᇱᇱ is the source term associated with the addition of mass from evaporating droplets or other subgrid-scale particles that represent, for example, sprinkler and fuel sprays, vegetation, and any other type of small, unresolvable object. where <sup>ρ</sup> is the density, *<sup>u</sup>* is the velocity vector and . *m* 000 *b* is the source term associated with the addition of mass from evaporating droplets or other subgrid-scale particles that represent, for example, sprinkler and fuel sprays, vegetation, and any other type of small, unresolvable object.

(b) Species conservation: (b) Species conservation:

(c) Linear momentum conservation:

ሺሻ

$$\frac{\partial(\rho Y\_a)}{\partial t} + \nabla \cdot (\rho Y\_a \mathfrak{u}) = \nabla \cdot (\rho D\_a \nabla Y\_a) + \dot{m}\_a^{\prime\prime\prime} + \dot{m}\_{b,a^{\prime}}^{\prime\prime\prime} \tag{2}$$

where ఈ and ఈ are the mass fraction and diffusivity of species . ሶ <sup>ఈ</sup> ᇱᇱᇱ and ሶ ,ఈ ᇱᇱᇱ are the mass production rate per unit volume of species by chemical reactions and evaporating droplets/particles, respectively. where *Y*<sup>α</sup> and *D*<sup>α</sup> are the mass fraction and diffusivity of species α. . *m* 000 <sup>α</sup> and . *m* 000 *b*,α are the mass production rate per unit volume of species α by chemical reactions and evaporating droplets/particles, respectively.

(c) Linear momentum conservation:

$$\frac{\partial(\rho u)}{\partial t} + \nabla \cdot \rho uu = -\nabla p + \rho \mathbf{g} + f\_{\mathbf{b}} + \nabla \tau\_{ij\prime} \tag{3}$$

where *p* is the pressure, *g* is the gravitational acceleration vector, *f b* is the external force vector (excluding gravity) and τ*ij* is the viscous stress tensor. *Energies* **2020**, *13*, x FOR PEER REVIEW 7 of 27

(d) Energy conservation: where is the pressure, is the gravitational acceleration vector, is the external force vector

$$\frac{\partial(\rho h\_s)}{\partial t} + \nabla \cdot (\rho h\_s \mathbf{u}) = \frac{Dp}{Dt} + \dot{\boldsymbol{q}}''' - \dot{\boldsymbol{q}}\_b''' - \nabla \cdot \dot{\boldsymbol{q}}'',\tag{4}$$

where *h<sup>s</sup>* is the enthalpy, . *q* <sup>000</sup> is the heat release rate per unit volume from a chemical reaction and . *q* 000 *b* is the energy transferred to subgrid-scale droplets and particles (for example, sprinkler), and . *q* <sup>00</sup> represents the conductive, diffusive and radiative heat fluxes. ሺℎ௦ሻ ∇∙ ሺℎ௦ሻ <sup>=</sup> ሶ ᇱᇱᇱ െ ሶ ᇱᇱᇱ െ∇∙ሶ ᇱᇱ, (4) where ℎ௦ is the enthalpy, ሶ ᇱᇱᇱ is the heat release rate per unit volume from a chemical reaction and

(e) Equation of state (ideal gas law): ሶ ᇱᇱᇱ is the energy transferred to subgrid-scale droplets and particles (for example, sprinkler), and ሶ

(e) Equation of state (ideal gas law):

(d) Energy conservation:

$$p = \frac{\rho \overline{R}T}{M},\tag{5}$$

ᇱᇱ

where *R* is the universal constant, *T* is the absolute temperature and *M* is the molecular weight of the gas mixture. = ത , (5)

More information on the mathematical model and submodels used in this research can be found

More information on the mathematical model and submodels used in this research can be found in the FDS Technical Reference Guide [44]. where ത is the universal constant, is the absolute temperature and is the molecular weight of the gas mixture.

#### 2.2.2. Initial and Boundary Conditions in the FDS Technical Reference Guide [44].

2.2.3. Heat Release Rate

As an initial condition, atmospheric pressure P0, temperature T0, air relative humidity, RH0, velocity **u0**, and mass fractions for air Yair,0, and soot Ysoot,0 were considered. The values of these parameters are shown in Table 1. 2.2.2. Initial and Boundary Conditions As an initial condition, atmospheric pressure P0, temperature T0, air relative humidity, RH0, velocity **u0**, and mass fractions for air Yair,0, and soot Ysoot,0 were considered. The values of these

**Table 1.** Initial condition for the problem under study. parameters are shown in Table 1.


Open boundary conditions were used at the maximum and minimum extremes of the computational domain, as shown in Figure 3. This means that the fluid is allowed to flow into or out of the computational domain depending on the local pressure gradient (upwind boundary condition). Typically, in this kind of boundary condition, the gradients of the tangential velocity components are set to zero [44]. Open boundary conditions were used at the maximum and minimum extremes of the computational domain, as shown in Figure 3. This means that the fluid is allowed to flow into or out of the computational domain depending on the local pressure gradient (upwind boundary condition). Typically, in this kind of boundary condition, the gradients of the tangential velocity components are set to zero [44].

**Figure 3.** Boundary conditions used in the numerical simulation. **Figure 3.** Boundary conditions used in the numerical simulation.

#### 2.2.3. Heat Release Rate

The heat release rate (HRR) is the amount of energy per unit time that a material releases into the environment when it undergoes combustion. Once started, the fire goes through three stages: growth, fully developed (in which the HRR remains constant) and decay [45,46]. Normally the growth phase of the fire is modeled in such a way that the HRR is directly proportional to the time squared (*t*-squared fires) [47,48], that is:

*HRRgrowth* = α × *t* 2 , (6)

where α is the fire growth coefficient in kW/s <sup>2</sup> and *t* is the time in s.

#### *2.3. Numerical Solution Method*

The algorithm for solving the governing equations uses an explicit predictor-corrector finite difference scheme, with second-order precision in space and time. At each time step, between the predictor and corrector procedures, the algorithm checks whether the Courant-Friedrichs-Lewy (CFL) stability criterion is satisfied, that is:

$$\text{CFL} = \left. \delta \mathbf{t} \times \max \left( \frac{|\mathbf{u}|}{\delta \mathbf{x}}, \frac{|\mathbf{v}|}{\delta \mathbf{y}}, \frac{|\mathbf{w}|}{\delta \mathbf{z}} \right) < \text{CFL}\_{\text{max}} \tag{7}$$

where CFLmax varies between 0.8 and 1.0; δt is the time step, u, v and w are the components of the velocity vector in the x, y and z directions, respectively. If the criterion is not satisfied, the time step is adjusted (reduced), returning to the beginning of the predictor procedure. If the stability criterion is satisfied, the procedure continues to the corrective procedure. In this way, the time step in the numerical simulation is not constant.

In the FDS software, the spatial variables are discretized using a staggered grid [49], that is, scalar quantities (e.g., pressure, temperature, density), velocity components and vorticity components are assigned to the centers, faces and edges of each cell, respectively. The radiation heat transfer is quantified using the finite volume method and assuming gray gas radiation model [44].

#### *2.4. Thermo-Physical Properties of Materials*

The material used to model the floor, walls and ceiling of the compartment was concrete, 10 cm thick. The density ρ, specific heat cp, thermal conductivity k, and emissivity ε of the concrete are shown in Table 2.


**Table 2.** Thermo-physical properties of materials used in the simulations.

The source term of heat and smoke release was obtained considering the burning of wood, with chemical formulation CH1.7O0.74N0.002. The yields of soot (ysoot) and carbon monoxide (yCO), heat of combustion (∆h) and Heat Release Rate Per Unit Area (HRRPUA) are shown in Table 2.

The thermo-physical properties of the air are temperature-dependent (ideal gas law) and calculated by the software at each control volume and for each instant of time.
