Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor

Abstract

In this chapter, a numerical investigation is presented in order to highlight the effects of outdoor wind on smoke movements along a corridor in a compartment. For this, the Computational Fluid Dynamics (CFD) code, fire dynamics simulator (FDS), was used to model the reactive flows in interaction with outdoor wind. The wind velocity is taken between 0 and 12.12 m/s, based on the experimental result data come from the work of Li et al. was performed. From numerical data, it was found that smoke stratification state in the corridor depends on Froude number (Fr) and it can be divided into three cases: stable buoyant stratification (Fr < 0.38), unstable buoyant stratification (0.38 ≤ Fr < 0.76), and failed stratification (Fr ≥ 0.76). When Fr ≥ 0.76, smoke stratification is completely disturbed and smoke occupies the entire volume of the compartment, highlighting a risk of toxicity to people. Indeed, it was observed that the velocity of the outdoor wind influences strongly the concentration of O2, CO2, CO, and visibility in the corridor and smoke exhaust. Moreover, for the input data used in the numerical modelling, the global sensitivity analysis demonstrated that the main parameters affecting the smoke temperature near the ceiling are the mass flux of fuel and the activation energy.

1. Introduction

Since the end of the Second World War, the construction of buildings has experienced an increase in growth due to the increase in the world population and economic growth in recent decades. With many buildings, the problem of housing for people no longer arises. However, by making an inventory of the generally very high number of victims in building fires, these developments present numerous challenges for fire safety engineering. Indeed, for the past 75 years, there have been many fires in large buildings. There is for example, during April 15, 2019, the violent fire that started in the roof of the Notre-Dame de Paris cathedral, and it ravaged the roof and the frame by destroying the roof base and damaging the vault. In order to reduce the number of deaths and property damage, fire safety engineering has focused on understanding the different phenomena present in a building fire [1]. Among these phenomena, Paul et al. [2] and Hull et al. [3] showed that smoke is the main cause of death due to toxicity. Indeed, smoke plume can be hazardous for people in two different ways: the toxic gases in smoke, such as carbon dioxide, are a fatal hazard [2, 3], and the smoke can make it difficult to rescue and evacuate people as it reduces visibility. In a compartment fire, it is therefore very important to know the characteristics of the smoke spread. The parameters that influence the smoke spread are mechanical ventilation and external atmospheric conditions. Generally, mechanical ventilation ensures smoke exhaust; however, external atmospheric conditions can disturb smoke flow. Moreover, smoke flows depend essentially on physical properties such as expansion, thermal pressure, thermal buoyancy, and wind effect. Variation in one of these parameters, such as the wind speed, can affect strongly smoke behavior [4, 5]. Considering this possibility, it is important to highlight the effects of external atmospheric conditions on smoke spread in a compartment.

Indeed, during a fire in a room, the presence of external wind through an opening contributes to disturbance of the smoke flow, which can impair the extraction process, thereby increasing the risk of death. In this context, many studies have been carried out in recent years to provide knowledge for fire safety engineering, including many full-scale [6, 7] and reduced scale [8, 9] experimental investigations.

At full scale, Tian et al. [6] showed that the more the wind velocity increases, the more the smoke temperature near the floor increases, in order to converge to the smoke temperature near the ceiling. Considering this, they highlighted that above a certain critical value of outdoor wind velocity, smoke stratification was disturbed, and smoke occupied the entire volume of the compartment. From scaling laws [10], small-scale experimental tests have been developed. Indeed, Li et al. [8] studied the influence of external wind velocity on the smoke flow in a small-scale facility. They showed that the driving forces of smoke flow through a high-rise building were modified according to the intensity of the external wind.

In addition to the experimental studies cited above, numerical simulations on smoke propagation in a compartment have also been conducted. For example, Li et al. [11] simulated smoke flows in a reduced scale (1:12) corridor under natural ventilation conditions using the CFD code FDS. In their work, they compared numerical data with experimental data and highlighted that FDS was able to simulate the temperature field and the level of smoke stratification for different heat release rates (HRR). In another example, Weng et al. [12] performed numerical simulations on the smoke flow in a subway tunnel fire equipped with an extraction system. Their results revealed that the temperature and the level of smoke stratification under the tunnel ceiling in the longitudinal direction increased with the HRR.

Considering the numerical studies presented above, it is shown that, using nice initial and boundary conditions, it is possible to make accurate simulations. Thus, in order to obtain accurate output results, it is necessary to define the input data correctly by carrying out a sensitivity analysis in order to find out the input parameters having the most influence on the output data. Two kinds of approach are classically used to achieve this: local and global approaches. For example, Batiot et al. [13] applied local and global sensitivity analysis on Arrhenius parameters in order to describe the kinetics of solid thermal degradation during fire phenomena, by determining four parameters (A, E, n, and ν). They stressed the specific role of A and E on the equation and showed the role and the influence of these parameters in the differential equation used to model the mass loss rate of a solid fuel as a function of the temperature and time. In a second example, Xiao et al. [14] applied global sensitivity analysis to an environmental model named Level E. The sensitivity indices used the energy distribution of the model output over different frequency bands as the quantitative feature of the model output.

Most of the numerical simulations that focused on the propagation of smoke in a ventilated or unventilated enclosure studied the level of smoke stratification as a function of the temperature profile and velocity. However, these numerical studies do not consider the effect of the external wind on smoke stratification in a corridor adjacent to a burning room with an opening. Using the data obtained by Li et al. [8], the aim of the present study was to highlight the ability of the fire dynamics simulator (FDS) to study smoke behavior according to the variation in outdoor wind velocity. This work, through a mesh resolution [15, 16], consists in reproducing the experimental conditions obtained in the work of Li et al. [8].

In this chapter, a CFD approach was proposed to evaluate the effects of outdoor wind on the smoke spread induced by an adjacent compartment fire. In order to highlight the influence of the input parameters used as initial conditions in the computational modelling, a global sensitivity analysis was performed. For this, Section 2 presents an overview of the global sensitivity analysis methodology with polynomial chaos expansion. Section 3 defines the physical and numerical modelling, Section 4 focuses on numerical results and global sensitivity analysis, and the conclusion is presented in Section 5.

2. Sensitivity analysis methodology

2.1 Global sensitivity analysis

The aim of sensitivity analysis is to quantify the influence of the variation of an input parameter on the variation of an output, also called quantity of interest. In the present study, the quantity of interest is the predicted smoke temperature near the ceiling (X = 5.4 m, Y = 0.5 m, Z = 85 cm), filtered by a Savitzky-Golay algorithm (third-order) to eliminate high-frequency variations of temperature. It is expressed as a mapping of the input parameters ${\mathrm{x}}_{\mathrm{i}}$ for $\mathrm{i}=1\dots \mathrm{r}$ , where r is the number of parameters, and the dependence in time is omitted to simplify the notations as:

$$\mathrm{T}=\mathcal{M}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)$$ E1

Generally, there are two kinds of sensitivity analysis: local sensitivity analysis and global sensitivity analysis. The local sensitivity analysis is a simple approach in which the sensitivity indices are directly related to the derivatives of the quantity of interest with respect to each parameter [17, 18, 19]. It is called local because the local indices are only valid in a neighborhood of the nominal value [20]. While local approaches are restricted to the vicinity of the prescribed deterministic values, global sensitivity takes into account the entire domain of variation of each parameter.

To extend the approach in the case of larger variations of parameters, a probabilistic framework is adopted. Lacking knowledge on the probability density functions of the inputs, we assume that each of the parameters follows a uniform law with a $\pm 10\%$ variation around its nominal value.

Of interest in this chapter are the Sobol sensitivity indices. These indices are often associated to an analysis of variance (ANOVA) decomposition, which consists in the decomposition of the model response into main effects and interactions [21]:

$$\mathrm{T}=\mathcal{M}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)={\mathrm{M}}_0+\sum _{\mathrm{i}=1}^{\mathrm{r}}{\mathrm{M}}_{\mathrm{i}}\left({\mathrm{x}}_{\mathrm{i}}\right)+\sum _{1\le \mathrm{i}<\mathrm{j}\le \mathrm{r}}^{\mathrm{r}}{\mathrm{M}}_{\mathrm{ij}}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)+\dots +{\mathrm{M}}_{1,\dots ,\mathrm{r}}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)$$ E2

The decomposition is unique if summands satisfy the properties [20]:

$${\mathrm{M}}_0=\int \mathcal{M}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)\mathrm{d}{\mathrm{x}}_1\dots .\mathrm{d}{\mathrm{x}}_{\mathrm{r}}$$ E3

$$\int \mathcal{M}\left({\mathrm{x}}_{{\mathrm{i}}_1},\dots ,{\mathrm{x}}_{{\mathrm{i}}_{\mathrm{s}}}\right)\mathrm{d}{\mathrm{x}}_{{\mathrm{i}}_1}\dots .\mathrm{d}{\mathrm{x}}_{{\mathrm{i}}_{\mathrm{s}}}=0\text{for}1\le {\mathrm{i}}_1<\dots <{\mathrm{i}}_{\mathrm{s}}\le \mathrm{r}$$ E4

The variance of the model response according to variation of inputs can be derived as a sum of partial variances as follows:

$$var\left(\mathrm{T}\right)=\mathrm{D}=\sum _{\mathrm{i}=1}^{\mathrm{r}}{\mathrm{D}}_{\mathrm{i}}+\sum _{1\le \mathrm{i}<\mathrm{j}\le \mathrm{r}}^{\mathrm{r}}{\mathrm{D}}_{\mathrm{ij}}+\dots +{\mathrm{D}}_{1,\dots ,\mathrm{r}}$$ E5

The partial variances ${\mathrm{D}}_{{\mathrm{i}}_1,\dots ,{\mathrm{i}}_{\mathrm{s}}}$ are defined by:

$${\mathrm{D}}_{{\mathrm{i}}_1,\dots ,{\mathrm{i}}_{\mathrm{s}}}=\int {\mathrm{M}}_{{\mathrm{i}}_1,\dots {\mathrm{i}}_{\mathrm{s}}}{\left({\mathrm{x}}_{{\mathrm{i}}_1},\dots ,{\mathrm{x}}_{{\mathrm{i}}_{\mathrm{s}}}\right)}^2\mathrm{d}{\mathrm{x}}_{{\mathrm{i}}_1}\dots .\mathrm{d}{\mathrm{x}}_{{\mathrm{i}}_{\mathrm{s}}}$$ E6

Then, the Sobol indices can be derived according to:

$${\mathrm{S}}_{{\mathrm{i}}_1,\dots ,{\mathrm{i}}_{\mathrm{s}}}=\frac{{\mathrm{D}}_{{\mathrm{i}}_1,\dots ,{\mathrm{i}}_{\mathrm{s}}}}{\mathrm{D}}$$ E7

Crude Monte Carlo simulations or sampling-based techniques can be applied to obtain these indices, but the associated numerical is prohibitive for computationally demanding models such as those used in this chapter. To overcome this difficulty, the exact model provided by simulations was substituted by an analytical approximation, called metamodel, for which the computation of Sobol indices is exact and analytical. In this chapter, a polynomial chaos expansion was used as metamodel to derive the sensitivity indices.

2.2 Polynomial chaos expansion

The polynomial chaos (PC) expansion consists in the projection of the model M on the space spanned by a family of ${\mathrm{N}}_{\mathrm{p}}$ orthogonal polynomials:

$$\mathcal{M}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)\approx \stackrel{\sim }{\mathcal{M}}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)=\sum _{\mathrm{\alpha }\in {\mathrm{A}}_{\mathrm{\alpha }}}{\mathrm{Y}}_{\mathrm{\alpha }}{\mathrm{\Phi }}_{\mathrm{\alpha }}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)$$ E8

where ${\mathrm{A}}_{\mathrm{\alpha }}$ is a finite set of vectors of positive integers $\mathrm{\alpha }=\left({\mathrm{\alpha }}_{\left(1\right)},\dots ,{\mathrm{\alpha }}_{\left(\mathrm{r}\right)}\right)$ such as $\mathit{card}\left({\mathrm{A}}_{\mathrm{\alpha }}\right)={\mathrm{N}}_{\mathrm{p}}$ . Each of the multivariate polynomials ${\mathrm{\Phi }}_{\mathrm{\alpha }}$ can be expressed as a product of monovariate polynomials ${\mathrm{\Psi }}_{{\mathrm{\alpha }}_{\left(\mathrm{i}\right)}}$ of order ${\mathrm{\alpha }}_{\left(\mathrm{i}\right)}$ :

$${\mathrm{\Phi }}_{\mathrm{\alpha }}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)={\mathrm{\Psi }}_{{\mathrm{\alpha }}_{\left(1\right)}}\left({\mathrm{x}}_1\right)\times \dots \times {\mathrm{\Psi }}_{{\mathrm{\alpha }}_{\left(\mathrm{r}\right)}}\left({\mathrm{x}}_{\mathrm{r}}\right)$$

Legendre polynomials were used here because of the assumption of a uniform probability density function for each input parameter. To reduce the number of stochastic coefficients and thus the computational burden, a classical truncation criterion consists in prescribing the constraint: ${\sum }_{\mathrm{i}=1}^{\mathrm{r}}{\mathrm{\alpha }}_{\left(\mathrm{i}\right)}\le \mathrm{p}$ , where $\mathrm{p}$ is the maximum order allowed for each monovariate polynomial.

The interest in such a decomposition is that, due to orthonormal properties of the family of polynomials, the mean ${\stackrel{\sim }{\mathrm{M}}}_0$ , the variance $\stackrel{\sim }{\mathrm{D}}$ , the first-order Sobol indices ${\stackrel{\sim }{\mathrm{S}}}_{\mathrm{i}}$ , and the total sensitivity indices ${\stackrel{\sim }{\mathrm{St}}}_{\mathrm{i}}$ of the metamodel can be computed as analytical functions of the chaos coefficients ${\mathrm{Y}}_{\mathrm{\alpha }}$ [20]:

$${\stackrel{\sim }{\mathrm{M}}}_0=\int \stackrel{\sim }{\mathrm{M}}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)\mathrm{d}{\mathrm{x}}_1\dots \mathrm{d}{\mathrm{x}}_{\mathrm{r}}={\mathrm{Y}}_{\left\{0,\dots ,0\right\}}$$ E9

$$\stackrel{\sim }{\mathrm{D}}=\int {\left(\stackrel{\sim }{\mathcal{M}}\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{r}}\right)-{\stackrel{\sim }{\mathrm{M}}}_0\right)}^2\mathrm{d}{\mathrm{x}}_1\dots \mathrm{d}{\mathrm{x}}_{\mathrm{r}}=\sum _{\mathrm{\alpha }\in {\mathrm{A}}_{\mathrm{\alpha }}\backslash \left\{0,\dots ,0\right\}}{\mathrm{Y}}_{\mathrm{\alpha }}^2$$ E10

$${\stackrel{\sim }{\mathrm{S}}}_{\mathrm{i}}=\frac{{\sum }_{\mathrm{\alpha }\in {\mathrm{A}}_{\mathrm{\alpha }}^{\left\{\mathrm{i}\right\}}}{\mathrm{Y}}_{\mathrm{\alpha }}^2}{\stackrel{\sim }{\mathrm{D}}}\text{with}{\mathrm{A}}_{\mathrm{\alpha }}^{\left\{\mathrm{i}\right\}}=\left\{\left({\mathrm{\alpha }}_{\left(1\right)},\dots ,{\mathrm{\alpha }}_{\left(\mathrm{r}\right)}\right)\text{such}\mathrm{as}:{\mathrm{\alpha }}_{\left(\mathrm{i}\right)}\ne 0\text{and}{\mathrm{\alpha }}_{\left(\mathrm{j}\right)}\ne 0\text{for}\mathrm{j}\ne \mathrm{i}\right\}$$ E11

$${\stackrel{\sim }{\mathrm{St}}}_{\mathrm{i}}=\frac{{\sum }_{\mathrm{\alpha }\in {\mathrm{At}}_{\mathrm{\alpha }}^{\left\{\mathrm{i}\right\}}}{\mathrm{Y}}_{\mathrm{\alpha }}^2}{\stackrel{\sim }{\mathrm{D}}}\text{with}{\mathrm{At}}_{\mathrm{\alpha }}^{\left\{\mathrm{i}\right\}}=\left\{\left({\mathrm{\alpha }}_{\left(1\right)},\dots ,{\mathrm{\alpha }}_{\left(\mathrm{r}\right)}\right)\text{such}\mathrm{as}:{\mathrm{\alpha }}_{\left(\mathrm{i}\right)}\ne 0\right\}$$ E12

To compute the chaos coefficients ${\mathrm{Y}}_{\mathrm{\alpha }}$ , intrusive and nonintrusive approaches can be used. The intrusive approach [22] consists in using PC expansion as an a priori function in the numerical solver. The development of a specific code is needed. It results in a single run of a very large problem. Here, we only consider nonintrusive techniques, in which the chaos coefficients are evaluated with repeated runs of a determinist program. Chaos coefficients can be evaluated by projection or by regression [23].

Here, we apply the second technique: it consists in searching the set of coefficients minimizing in the least-squares sense, the ${\mathrm{L}}_2$ distance between the model and the metamodel. This regression approach leads to:

$$\left\{{\mathrm{Y}}_{\mathrm{\alpha }}\right\}=\text{argmin}\left(\frac{1}{\mathrm{Q}}\sum _{\mathrm{q}=1}^{\mathrm{Q}}{\left(\mathcal{M}\left({\mathrm{x}}_{1,\mathrm{q}},\dots ,{\mathrm{x}}_{\mathrm{r},\mathrm{q}}\right)-\sum _{\mathrm{\alpha }\in {\mathrm{A}}_{\mathrm{\alpha }}}{\mathrm{Y}}_{\mathrm{\alpha }}{\mathrm{\Phi }}_{\mathrm{\alpha }}\left({\mathrm{x}}_{1,\mathrm{q}},\dots ,{\mathrm{x}}_{\mathrm{r},\mathrm{q}}\right)\right)}^2\right)$$ E13

The system is solved in a mean least-squares sense with a number $\mathrm{Q}$ of sampling points $\left({\mathrm{x}}_{1,\mathrm{q}},\dots ,{\mathrm{x}}_{\mathrm{r},\mathrm{q}}\right)$ larger than the number of coefficients to be identified. Typically, in the literature, the number of sampling points is equal to twice the number of polynomial coefficients. In this study, the metamodel is computed using second-order Legendre polynomials. This leads to ${\mathrm{N}}_{\mathrm{p}}=36$ stochastic modes, so that the number of sampling points is $\mathrm{Q}=72$ . Roots of the third-order Legendre polynomial, ${\mathrm{\Psi }}_3\left({\mathrm{x}}_{\mathrm{i},\mathrm{q}}\right)=0$ , are chosen as sampling points. The results presented here were validated using the jackknife technique with 100 replications of a random subset of 70 samples.

3. Numerical modelling

3.1 Governing equations

The simulations were carried out using the CFD code fire dynamics simulator (FDS) version 6.5.3 [24]. It solves the Navier-Stokes equations using an explicit finite difference scheme. As a CFD code, FDS models the thermally driven flow with an emphasis on smoke and heat transport. It is a large eddy simulation (LES) model using a uniform mesh and has parallel computing capability using message-passing interface (MPI) [25]. Reactive flows are modelled using a turbulence model based on a LES approach, a combustion model based on the eddy dissipation concept (EDC), and a thermal radiation model based on a gray gas model for the radiation absorption coefficient [15, 16].

The models are based on the numerical solving of Navier-Stokes equations. These equations calculate mass, momentum, species, and energy conservation [25]:

$$\frac{\mathrm{\partial \rho }}{\mathrm{\partial t}}+\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left(\mathrm{\rho }{\mathrm{u}}_{\mathrm{j}}\right)=0$$ E14

$$\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left(\mathrm{\rho }{\mathrm{u}}_{\mathrm{j}}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left(\mathrm{\rho }{\mathrm{u}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{j}}\right)=-\frac{\mathrm{\partial p}}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{i}}}+\mathrm{\rho }{\mathrm{g}}_{\mathrm{i}}+\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left\{\mathrm{\mu }\left(\frac{\mathrm{\partial }{\mathrm{u}}_{\mathrm{i}}}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}+\frac{\mathrm{\partial }{\mathrm{u}}_{\mathrm{j}}}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{i}}}-\frac{2}{3}{\mathrm{\delta }}_{\mathrm{ij}}\frac{\mathrm{\partial }{\mathrm{u}}_{\mathrm{i}}}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{i}}}\right)\right\}$$ E15

$$\frac{\mathrm{\partial \rho }{\mathrm{Y}}_{\mathrm{k}\ast }}{\mathrm{\partial t}}+\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\mathrm{\rho }{\mathrm{u}}_{\mathrm{j}}{\mathrm{Y}}_{\mathrm{k}\ast }=\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left\{{\left(\mathrm{\rho D}\right)}_{\mathrm{k}\ast }\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}{\mathrm{Y}}_{\mathrm{k}\ast }\right\}+{\dot{\mathrm{\omega }}}_{\mathrm{k}\ast }^{\prime \prime \prime }$$ E16

$$\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left(\mathrm{\rho h}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left(\mathrm{\rho }{\mathrm{u}}_{\mathrm{i}}\mathrm{h}\right)=\frac{\mathrm{dp}}{\mathrm{dt}}+{\dot{\mathrm{q}}}^{\prime \prime \prime }+\mathrm{\lambda }\frac{{\mathrm{\partial }}^{\mathbf{2}}}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}^{\mathbf{2}}}\mathrm{T}+\sum \frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}\left\{{\mathrm{h}}_{\mathrm{k}\ast }{\left(\mathrm{\rho D}\right)}_{\mathrm{k}\ast }\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}{\mathrm{Y}}_{\mathrm{k}\ast }\right\}-\frac{\mathrm{\partial }}{\mathrm{\partial }{\mathrm{x}}_{\mathrm{j}}}{\dot{\mathrm{q}}}_{\mathrm{r},\mathrm{j}}^{\prime \prime }$$ E17

where Eq. (14) represents the mass conservation equation, Eq. (15) represents the momentum conservation equation, Eq. (16) represents the species conservation equation, and Eq. (17) represents the energy conservation equation.

3.2 Fire modelling

The modelling was carried out using the Deardorff turbulence model and extinction model based on a critical flame temperature. The combustion model is based on the finite rate combustion using Arrhenius parameters (A: pre-exponential factor and Ea: activation energy). The fire source was modelled as a gas burner using butane as fuel with mass flux given by the experimental data [8]. The combustion heat of butane is 45182.83 kJ/kg.

3.3 Computational domain and boundary conditions

The experimental setup used as reference in the current numerical study represents a reduced scale (1:3) of a facility which contains a corridor and a fire room [8]. As shown in Figure 1, the dimensions of the corridor were 5.5 m (length) × 0.7 m (width) × 0.9 m (height) and the dimensions of the fire room were 2.0 m (length) × 1.7 m (width) × 1.0 m (height). The corridor and fire room were connected by a door whose dimensions were 0.7 m long by 0.3 m wide. The window in the fire room was opposite to the door and its dimensions were 0.5 m (width) × 0.5 m (height). The ceilings and floors of the corridor and fire room were made of steel plate with a thickness of 2.5 mm.

Figure 1.

Schematic view of the experimental corridor and fire room.

As shown in Figure 1, the fire source was in the middle of the fire room, and it was defined as a gas burner using liquefied petroleum gas as fuel. The fuel supply rates of the gas burner were controlled and monitored by a flow meter. The HRR in the experiments was determined by multiplying the mass flow rate and the combustion heat of liquefied petroleum gas. The fire size can be scaled up to 96.2 kW of HRR, which corresponds to 1.5 MW full-scale.

The wind can blow into the fire room through the window and the outdoor wind was generated by the fan and a static pressure box (cf. Figure 1). The velocity of the outdoor wind was adjusted by changing the AC frequency of the frequency converter. The velocity of the outdoor wind varied from 0 to 7.0 m/s and the corresponding full-scale outdoor wind velocity range was 0–12.12 m/s according to the scaling law of Froude modelling [12, 13]. Varying the wind velocity, eight experiments were conducted at an HRR of 96.2 kW, equaling 1.5 MW at full-scale.

The experiments were carried out with ambient temperature ranging from 6 to 16°C. K-type thermocouples with an accuracy of ±1°C were used for the temperature measurements in the corridor and fire room. Hot wire wind speed meters were applied to measure the velocity of smoke.

In order to model the geometry and the boundary conditions of the setup used during the experimental tests [8], the walls of the corridor and fireroom were made of steel having a density of 7850 kg/m³, a thermal conductivity of 46 W/(m·K)⁻¹, a specific heat of 0.5 kJ/(kg·K), and an emissivity of 0.9.

In simulations, the boundary condition at the window was modeled as an opening in the case without wind. With wind, a constant flow rate was set at the window using the velocity boundary used in the CFD code. In order to remain consistent with the experimental tests, a waiting time of 150 s was defined before activation of the outdoor wind velocity in the modelling. The simulations were performed in eight cases (Vw = 0, 1, 2, 3, 4, 5, 6, and 7 m/s, which correspond to Vw = 0, 1.73, 3.46, 5.20, 6.93, 8.66, 10.39, and 12.12 m/s full-scale). Similarly, the simulation results were converted into full-scale data according to the Froude number.

The smoke temperature, smoke velocity, concentration of O₂ and CO, and visibility in the corridor were analyzed by setting different devices in the plane (Y = 0.5 m), near the exit of the corridor (X = 5.4 m), at different heights (Z = 85, 70, 55, 40, and 25 cm). Moreover, other observations were carried out about the distribution of temperature, velocity, concentration of O₂ and CO₂, and visibility thanks to slice fields in the plane Y = 0.5 m.

3.4 Mesh size resolution

For numerical studies, it is important to choose the correct mesh size in order to obtain accurate simulation results. FDS provides a range of mesh sizes for mesh resolution. From a Poisson solver based on the fast Fourier transform (FFT), it is possible to obtain good numerical resolution by solving the governing equations. The mesh size was chosen in accordance with the recommendations made in the numerical studies [15, 16]. An optimal mesh size should meet two requirements: good results in terms of accuracy and a short calculation time. The optimal mesh size of the domain is given by the nondimensional expression $\raisebox{1ex}{${\mathrm{D}}^{\ast }$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\partial }\mathrm{x}$}\right.$ , where $\mathrm{\partial x}$ is the nominal mesh size and D* is the characteristic fire diameter [24]. The characteristic fire diameter D* is determined using Eq. (18):

$${\mathrm{D}}^{\ast }={\left(\frac{\dot{\mathrm{Q}}}{{\mathrm{\rho }}_{\infty {\mathrm{c}}_{\mathrm{p}}{\mathrm{T}}_{\infty }\sqrt{\mathrm{g}}}}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$$ E18

where D* denotes the characteristic fire diameter, $\dot{\mathrm{Q}}$ the Heat Release Rate, and ${\mathrm{c}}_{\mathrm{p}}$ the specific heat.

Based on several experiments, the U.S. Nuclear Regulatory Commission recommends that the numerical range of $\raisebox{1ex}{${\mathrm{D}}^{\ast }$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\partial }\mathrm{x}$}\right.$ be between 4 and 16 for simulations to produce favorable results at a moderate computational cost, since the larger the value of $\raisebox{1ex}{${\mathrm{D}}^{\ast }$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\partial }\mathrm{x}$}\right.$ used in the simulation, the more accurate the simulation result. Hence, the range of mesh sizes can be obtained by the following equation [15, 16]:

$$\frac{{\mathrm{D}}^{\ast }}{16}\le {\mathrm{\delta }}_{\mathrm{x}}\le \frac{{\mathrm{D}}^{\ast }}{4}$$ E19

After calculation, the range of mesh sizes was found to be: (0.0625 and 0.25 m). Therefore, four different mesh sizes were used: 20, 10, 5, and 2.5 cm. Figure 2(a) and (b) presents the comparisons between experiment and FDS predictions for these four different meshes. The comparisons were carried out on the evolution of the smoke temperature and smoke velocity, both measured 70 cm above the ground and in the centerline of the corridor near the exit.

Figure 2.

The influence of grid cells on: (a) temperature at a height of 70 cm; and (b) smoke velocity without wind at a height of 70 cm.

It can be seen that the numerical results obtained with mesh sizes of 5 and 2.5 cm converge with the experimental results, while the results of the 20 and 10 cm meshes diverge. Moreover, the 2.5-cm mesh gives more accurate numerical results than the 5-cm mesh. As shown in Table 1, the relative gap (RG) of the calculation with the 2.5-cm mesh (3.85%) is slightly smaller than the calculation with a 5-cm mesh (6.83%). The relative gap (RG) is obtained by [26]:

Numerical grid	Number of cells	Relative gap (%)		CPU time (h)
		Temperature (°C)	Smoke velocity (m/s)
Mesh size 20 cm	1685	31.06	33.17	1.2
Mesh size 10 cm	11865	19.76	16.91	4.4
Mesh size 5 cm	94920	6.06	6.23	9.6
Mesh size 2.5 cm	759360	3.80	3.85	92.2

Table 1.

Results of different numerical grid mesh sizes.

$$\mathrm{RG}=100\times \frac{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{pre},\mathrm{i}}-{\mathrm{y}}_{\mathit{exp},\mathrm{i}}\right)}^2}}{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathit{exp},\mathrm{i}}\right)}^2}}$$ E20

where ypre is a predicted value, yexp is an experimental value, and n is the number of experimental points.

However, the calculation time with the 2.5-cm mesh is 10 times longer than with the 5-cm mesh. In addition, the relative gap of the 5-cm mesh is close to that of the 2.5-cm mesh. As it represents the best trade-off between precision and calculation time, the 5-cm mesh was used for the following calculations, this choice is reinforced by the suggestions of the various cases of validation of the FDS code proposed in the user guide [24].

With the 5-cm mesh, the total number of cells is 94920 and the simulation time is 1000 s with a time step of 0.010 s. The calculations were carried out using 20 processors in the ARTEMIS cluster of the “Région Centre Val de Loire—France” and each computation took about 9.6 h.

Figure 2(a) and (b) shows that the numerical results obtained with the 5-cm mesh are in agreement with experimental data as regards the evolution of smoke temperature and smoke velocity [8]. This indicates that with a 5-cm mesh, the boundary conditions can be satisfactorily modeled by FDS and that the interaction between wind and smoke flow can be reproduced.

Figure 3 plots the smoke velocity decays with different wind velocities: (a) Vw = 1.73 m/s; (b) Vw = 5.20 m/s; (c) Vw = 6.93 m/s; and (d) Vw = 10.93 m/s at 70 cm height. It can be seen that the predictions of the evolution of smoke velocities are similar to those of the experimental data [8]. Since the velocities were measured at a height of 70 cm in the experiments, these values are in fact averages.

Figure 3.

Smoke velocity with: (a) Vw = 1.73 m/s; (b) Vw = 3.46 m/s; (c) Vw = 6.93 m/s; and (d) Vw = 12.12 m/s at a height of 70 cm of FDS and experimental results [8].

Therefore, it is possible that for some values of the smoke velocity, the experimental data are underestimated or overestimated. In these conditions, predictions are overestimated at the start or at the end of the curves Figure 3(a) and (b). These small differences can be associated to the vortex waves that are not very well reproduced by the turbulence model. To try to improve it, a sensibility analysis can be performed on the different turbulence models [24]. However, good agreement between prediction and experiment is observed in the other pictures (Figure 3(c) and (d)).

It can be concluded from these different comparisons that the choice of a 5-cm mesh is suitable and that it can deal with reactive flows with a good accuracy. Leakage was neglected during the modelling, as the amount of leakage in the experiment is unknown. It is possible, therefore, that some simulation results may be under- or overestimated. Overall, however, the predictions of the simulations are acceptable.

4. Results and discussions

In this part of the chapter, the numerical results with different wind velocities (Vw = 1.73, 3.46, and 5.20 m/s) are discussed in terms of the effects of outdoor wind on smoke stratification and smoke extraction. A global sensitivity analysis was carried out in order to determine the effects of the input parameters on the output data. The target input parameters are mass flux (MF) of fuel, the material properties (conductivity λ, emissivity ε, density ρ, and specific heat cp), and the Arrhenius parameters (A, Ea). The target output data are the smoke temperature near the ceiling.

4.1 Outdoor wind effect on the smoke exhaust

Figure 4 presents the smoke velocity field with (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s; and (d) Vw = 5.20 m/s; in the cross-section y = 0.5 m at 300 s. The cross-section y = 0.5 m is the plane in the middle of the corridor. In Figure 4(a), taking this plane at the height of 70 cm, the maximum value of the smoke velocity is near the door and decreases with the distance from the door as shown in Figures 3 and 4. In addition, considering smoke stratification with a hot zone near the ceiling and a cold zone near the floor, it is observed that the buoyancy effects give the reverse observation. Near the floor, the smoke velocity increases with the distance, and using the vortex recirculation solved by the Deardorff turbulence model, the numerical solver can reproduce the vortex flow induced by the smoke flow.

Figure 4.

Simulation of the smoke velocity field with (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s; and (d) Vw = 5.20 m/s in the cross-section y = 0.5 m at 300 s.

From Figure 4, the maximum of smoke velocity in the corridor increases when the wind velocity increases. As mentioned previously, in these conditions, smoke exhaust can be disturbed. Outdoor wind can, however, contribute to the evacuation of smoke and fire extinction in that more smoke is extracted through the corridor when the wind velocity increases. It should nevertheless be mentioned that while ventilation and extraction systems play an important role in fire engineering [15], the efficiency of the smoke extraction system will be reduced and even be invalidated when the outdoor wind velocity is very high and the extraction system is installed in the windward surface of the compartment [21]. In this case, the extraction system cannot perform well, and smoke can spread along the entire compartment through the connected rooms. This situation is not acceptable for fire safety.

Figure 5 shows that when the outdoor wind velocity increases, the oxygen concentration increases and carbon dioxide concentration decreases. Figure 5 presents the influence of wind velocity on O₂ concentration and CO₂ concentration at a height of 85 cm (on the ceiling of the corridor), showing that the more wind velocity increases, the more oxygen concentration increases. After 300 s, the oxygen concentration remains stable when the wind velocity varies from 0 to 6.93 m/s. The oxygen concentration at 300 s was therefore used to compare the different wind velocity cases.

Figure 5.

Influence of wind velocity on: (a) O₂ concentration; and (b) CO₂ concentration at 85 cm height.

When the wind velocity is 1.73 m/s, the O₂ molar concentration increases only slightly compared to a situation without wind. When the wind velocity increases to 3.46 m/s, the O₂ molar concentration increases strongly compared to the case without wind. For a wind velocity of 6.93 m/s, the O₂ molar concentration increases to 20.2%, 1.8% higher than without wind. The rise in O₂ concentration in the corridor also indicates that more smoke is extracted.

The more the wind velocity increases, the more the CO₂ concentration decreases (Figure 5(b)). At a wind velocity of 6.93 m/s, the CO₂ molar concentration decreases to 0.3%, 1% lower than without wind. The decline of the CO₂ concentration in the corridor also contributes to people escaping from fires.

Using oxygen concentration field like the smoke velocity field in the Figure 4, the mean oxygen concentration in the corridor increases when the wind velocity increases, showing that a higher wind velocity can facilitate smoke exhaust.

It is also possible to highlight the influence of wind velocity on CO concentration and visibility. The evolutions of these latest are presented in Figure 6 at a height of 50 cm. The height of 50 cm represents the average height of a person measuring 165 cm in a full-scale building. From Figure 6(a), CO concentration decreases with wind velocity.

Figure 6.

Influence of wind velocity on: (a) CO concentration; and (b) visibility at 55 cm height at the exit of the corridor.

The outdoor wind can thus be an advantage for diluting the CO concentration. Figure 6(b) shows that the more the outdoor wind velocity increases, the more the visibility increases. Thus, the more wind blows in, the more smoke is diluted. However, the visibility becomes homogenous in the enclosure due to disturbance in the smoke stratification. In a fire with a heat release rate larger than the one used in this study, the poor visibility can be unfavorable for the evacuation of people in the building.

Using the CO concentration field similarly to the smoke filed, the average concentration of CO decreases with the increase in wind velocity. There are two zones: a thin zone near the floor and a thick zone near the ceiling in the case of no wind.

The distribution of CO concentration in the corridor gradually becomes homogeneous as the wind velocity increases. Although in this study the CO concentration is so small that it would have little effect on people’s health, the homogeneous distribution of CO concentration may cause serious problems when the heat release rate in the building is larger, producing more CO.

Moreover, concerning the visibility, it is shown that the visibility of the lower area in the corridor is very high and the visibility of the upper area in the corridor is very low due to smoke stratification when there is no wind. For this, the visibility in the corridor gradually becomes homogeneous as the outdoor wind velocity increases and becomes better when the wind velocity reaches 5.20 m/s, indicating that the more smoke is exhausted, the more visibility is improved.

In other words, smoke can exit the corridor faster when the wind velocity increases. It can be said that to some extent, the outdoor wind is helpful for smoke exhaust and an advantage for the evacuation of people in fires as it can decrease the concentration of toxic gas and improve visibility in the environment. However, in these conditions, the outdoor wind becomes a disturbance for the extraction system, representing an unacceptable situation for fire safety.

4.2 Outdoor wind effect on the smoke stratification and sensitivity analysis

In Li et al. [8], it was shown that the more wind velocity increased, the more severely the smoke stratification was disturbed. This observation was obtained by comparing the smoke temperature near the floor (height = 25 cm) and the smoke temperature near the ceiling (height = 85 cm). The tests were performed for three velocities. The results showed that above a wind velocity of 3.46 m/s, the smoke temperatures near the floor and the ceiling were similar. This similarity was taken to imply that the smoke occupied the entire corridor volume, due to the absence of smoke stratification, and the numerical data used in the current study confirmed this observation.

Thanks to Figure 7, it is possible to make a comparison between the smoke temperature near the ceiling and near the floor. It is constated that the more wind speed increases, the more the smoke stratification is disturbed. Smoke stratification is represented by the stability between the hot zone and the cold zone. The hot zone is formed by hot smoke and the cold zone is formed by cold air. Smoke stratification in an enclosure is due to the temperature difference between these two zones. In addition, as shown in the literature [27, 28, 29], smoke stratification depends on the Froude number. Smoke stratification is very stable up to a critical Froude number and becomes disturbed when the Froude number is larger than this critical value. It is known that the Froude number can be associated to velocity. So, smoke stratification is related to the smoke velocity in an enclosure. In Figure 7(a), when the wind velocity is 0 m/s, the smoke temperature near the ceiling and floor are about 5 and 60°C, indicating that smoke stratification is very stable. At a wind velocity of 1.73 m/s, the smoke temperature near the ceiling and floor are about 25 and 100°C, respectively. In this condition, there are still two zones. In Figure 7(b), there is a slight perturbation of the temperature near the ceiling, indicating a slight disturbance in the smoke stratification. However, from a wind velocity of 3.46 m/s, the smoke temperature near the ceiling and floor are similar with an average of 80°C. This means that above this velocity, there is no smoke stratification in the corridor and that smoke occupies the entire corridor. Under these conditions, there is a risk of toxicity for people. These observations confirm results reported in the literature [8] and highlight the ability of the CFD code to reproduce the effects of wind on the movement of smoke in an enclosure. Moreover, in these conditions, outdoor wind becomes a disturbance for smoke extraction, creating an unacceptable situation for fire safety.

Figure 7.

Influence of wind velocity (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s; and (d) Vw = 5.20 m/s on smoke temperature in different heights of the corridor.

The smoke temperature field with (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s; and (d) Vw = 5.20 m/s in the cross-section y = 0.5 m at 300 s is shown in Figure 8. It can be clearly seen that when there is no outdoor wind, there is temperature stratification in the corridor. In addition, the temperature near the ceiling is much higher than the temperature near the floor. For a wind velocity of 1.73 m/s, smoke stratification is disturbed but still exists due to the presence of two zones, with a much smaller cold zone than hot zone. When the wind velocity is 3.46 m/s, smoke stratification almost disappears, as the smoke temperature is similar at the different heights and only the hot zone subsists. In this condition, smoke occupies the entire corridor. The phenomenon of temperature stratification in the corridor disappears completely when the wind velocity reaches 5.20 m/s (Figure 8(d)), as also shown with the curves in Figure 7(d). These results also show that thanks to simulations performed by FDS, it is possible to demonstrate the fields of smoke movement in an enclosure with outdoor wind.

Figure 8.

Smoke temperature field with (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s; (d) Vw = 5.20 m/s on the cross-section y = 0.5 m at 300 s.

In addition, from a global sensitivity analysis, an investigation was carried out in order to highlight the relative importance of seven parameters: mass flux MF, activation energy Ea, conductivity λ, emissivity ϵ, pre-exponential factor A, density ρ, and specific heat cp. The aim was to determine whether, among these seven parameters, even a slight modification of the input parameter may cause a large variation in the response. The quantity of interest is the temperature near the ceiling. A tolerance interval of ±10% was applied to each of the inputs so that for each of the inputs, a dimensionless random parameter is introduced. Its value depends on the realization θ and belongs to the interval [−1,1].

In this context, the values of the random parameters $\mathrm{MF}$ and ${\mathrm{E}}_{\mathrm{a}}$ depend on their mean value $\overline{\mathrm{MF}}$ and $\overline{{\mathrm{E}}_{\mathrm{a}}}$ , on the tolerance interval $\pm 10\%$ , and on the random dimensionless parameter ${\mathrm{\xi }}_{\mathrm{MF}}$ and ${\mathrm{\xi }}_{{\mathrm{E}}_{\mathrm{a}}}$ (whose values depend on the observation $\mathrm{\theta }$ ). For that, an analytical model is proposed to predict the time evolution of the quantity of interest for arbitrary values of mass flux (MF) and activation energy (Ea), such that:

$$\mathrm{MF}\left(\mathrm{\theta }\right)=\overline{\mathrm{MF}}\left(1+0.1{\mathrm{\xi }}_{\mathrm{MF}}\left(\mathrm{\theta }\right)\right)$$

$${\mathrm{E}}_{\mathrm{a}}\left(\mathrm{\theta }\right)=\overline{{\mathrm{E}}_{\mathrm{a}}}\left(1+0.1{\mathrm{\xi }}_{{\mathrm{E}}_{\mathrm{a}}}\left(\mathrm{\theta }\right)\right)$$ E21

Indeed, using the smoke temperature as out data based on the methodology of the sensitivity analysis proposed by Chaos [20], Figure 9 shows that the mass flux of the fuel and the activation energy are the two parameters which are an important influence on the smoke temperature.

Figure 9.

Local sensitivity indices.

Moreover, Figure 9 presents the first-order sensitivity and the total sensitivity indices. Considering this influence, it is very important to define the values of the mass flux of the fuel and the activation energy with a good accuracy in order to over or underestimate the out data such as the temperature, heat flux, pressure, and the amount of species.

5. Conclusion

In this chapter, a CFD code, namely fire dynamics simulator (FDS), was employed to model the smoke spreading along a corridor induced by a compartment fire. The focus was on the effects of outdoor wind on the dynamics of smoke spreading based on experimental data. Simulations were carried out by varying wind velocity from 0 to 12.12 m/s. Good agreement between experimental data and prediction was found, enabling investigation of smoke stratification, smoke exhaust, and a global sensitivity analysis. The major findings include the following:

1. By analyzing the temperature distribution in the corridor, it was found that smoke stratification can be strongly affected by the outdoor wind. For wind velocities higher than the critical value of 3.46 m/s, smoke stratification is completely disturbed.

2. When the wind velocity is higher than the critical value (here 3.46 m/s), O₂ concentration and visibility increase, while CO₂ and CO concentration tends to decrease. It is shown that the magnitude of the outdoor wind can facilitate smoke exhaust in a compartment fire.

3. The results of a global sensitivity analysis indicate that it is essential to define the most influential input parameters correctly, namely the mass flux of the fuel and the activation energy. If not, large deviations in the outputs of the numerical results such as smoke temperature may occur due to variations, even slight ones, in the input parameters.

4. Based on the amplitude of the metamodel coefficients, a reduced metamodel has been proposed. A prediction with a confidence interval can be easily implemented, leading to close agreement with the numerical results.

Through this work, it is demonstrated that CFD FDS can provide information about the movement of smoke in a corridor. Besides, it can be coupled with a polynomial chaos-based sensitivity analysis, which enables the input parameters to be classified on quantitative grounds with a limited computational cost.

In addition, considering the importance of the effects of outside wind on reactive flows induced by a fire in a building, it is important to study other study configurations. In this context, it would be important to also study the role of the outside wind on the ignition of smoke rich in unburnt gas in the case of an under-ventilated fire.