Effect of Variable Parameters

*Fire Safety and Management Awareness*

64 (2016).

academy of sciences. Technical sciences,

[26] T. Ma, L. Li, Q. Wang, C. Guo, Construction of intumescent flame retardant and hydrophobic coating on wood substrates based on thiol-ene click chemistry without photoinitiators, Composites Part B: Engineering, 177

[27] D. Lin, X. Zeng, H. Li, X. Lai, T. Wu, One-pot fabrication of

science, 533 (2019) 198-206.

superhydrophobic and flame-retardant coatings on cotton fabrics via sol-gel reaction, Journal of colloid and interface

[28] S. Wi, S. Yang, U. Berardi, S. Kim, Assessment of recycled ceramicbased inorganic insulation for

improving energy efficiency and flame retardancy of buildings, Environment international, 130 (2019) 104900.

[29] F. Zafar, E. Sharmin, Flame Retardants. London: IntechOpen; (2019). DOI: 10.5772/intechopen.82783

[30] S.S. Priyanka, R. Sangeetha, S. Suvedha, M.G. Vijayalakshmi, Android

Controlled Fire Fighting Robot, Ineternational journal of innovative science Engg. and Technology, Volumn,

3 (2017).

(2019) 107357.

[18] E.K. Zavadskas, J. Antucheviciene, T. Vilutiene, H. Adeli, Sustainable decision-making in civil engineering, construction and building technology,

[19] D. Sahu, S. Kumar, S. Jain, A. Gupta, Experimental and numerical simulation studies on diesel pool fire, Fire and Materials, 40 (2016) 1016-1035.

[20] B. Lattimer, J. Hodges, A. Lattimer, Using machine learning in physicsbased simulation of fire, Fire Safety

[21] P. Ghasemi, A. Babaeinesami, Simulation of fire stations resources considering the downtime of machines: A case study, Journal of Industrial Engineering and Management Studies, 7

[22] E.J. Sugeng, M. de Cock, P.E. Leonards, M. van de Bor, Electronics, interior decoration and cleaning patterns affect flame retardant levels in the dust from Dutch residences, Science of The Total Environment, 645 (2018)

[23] K. Shikinaka, M. Nakamura, R.R. Navarro, Y. Otsuka, Non-flammable and moisture-permeable UV protection films only from plant polymers and clay minerals, Green Chemistry, 21 (2019)

[24] W. Guo, X. Wang, J. Huang, Y. Zhou, W. Cai, J. Wang, L. Song, Y. Hu, Construction of durable flameretardant and robust superhydrophobic coatings on cotton fabrics for water-oil separation application, Chemical Engineering Journal, (2020) 125661.

[25] R. Olawoyin, Nanotechnology: The future of fire safety, Safety science, 110

Sustainability, 10 (2018) 14.

Journal, (2020) 102991.

(2020) 161-176.

1144-1152.

498-502.

**8**

(2018) 214-221.

**Chapter 2**

**Abstract**

energy.

**11**

**1. Introduction**

Numerical Study on the Outdoor

Wind Effects on Movement

*Brady Manescau, Khaled Chetehouna, Quentin Serra,*

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

**Keywords:** outdoor wind, CFD, FDS, sensitivity analysis, corridor, smoke spread

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 along a Corridor

*Aijuan Wang and Eric Florentin*

#### **Chapter 2**

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

*Brady Manescau, Khaled Chetehouna, Quentin Serra, Aijuan Wang and Eric Florentin*

#### **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.

**Keywords:** outdoor wind, CFD, FDS, sensitivity analysis, corridor, smoke spread

#### **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.

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].

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

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

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 xi for i ¼ 1 … r, where r is the number of parameters, and the dependence in time is omitted to simplify the notations as:

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 [17–19]. 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

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

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

> Xr 1≤i<j≤r

Mij xi, xj

� � þ … þ M1, … ,rð Þ x1, … , xr

(2)

into account the entire domain of variation of each parameter.

i¼1

Mið Þþ xi

with a �10% variation around its nominal value.

interactions [21]:

**13**

T ¼ Mð Þ¼ x1, … , xr M0 þXr

T ¼ Mð Þ x1, … , xr (1)

conclusion is presented in Section 5.

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

**2.1 Global sensitivity analysis**

**2. Sensitivity analysis methodology**

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.

*Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

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**

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

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

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

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

modified according to the intensity of the external wind.

bands as the quantitative feature of the model output.

smoke spread in a compartment.

*Fire Safety and Management Awareness*

investigations.

**12**

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 xi for i ¼ 1 … r, where r is the number of parameters, and the dependence in time is omitted to simplify the notations as:

$$\mathbf{T} = \mathcal{M}(\mathbf{x\_1}, \dots, \mathbf{x\_r}) \tag{1}$$

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 [17–19]. 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 �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]:

$$\mathbf{T} = \mathcal{M}(\mathbf{x\_1}, \dots, \mathbf{x\_r}) = \mathbf{M}\_0 + \sum\_{i=1}^r \mathbf{M}\_i(\mathbf{x\_i}) + \sum\_{1 \le i < j \le r}^r \mathbf{M}\_{\overline{\mathbf{z}}}(\mathbf{x\_i}, \mathbf{x\_j}) + \dots + \mathbf{M}\_{1, \dots, r}(\mathbf{x\_1}, \dots, \mathbf{x\_r}) \tag{2}$$

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

$$\mathbf{M}\_0 = \int \mathcal{M}(\mathbf{x}\_1, \dots, \mathbf{x}\_r) d\mathbf{x}\_1 \dots d\mathbf{x}\_r \tag{3}$$

indices ~

~ Si ¼ P α∈ Af gi α Y2 α D~ with Af gi

~ Sti ¼

Si, and the total sensitivity indices ~

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

M~ 0 ¼ ð

D~ ¼ ð

P α ∈ Atf gi α Y2 α D~ with Atf gi

projection or by regression [23].

f g Yα ¼ argmin 1

70 samples.

**15**

**3. Numerical modelling**

**3.1 Governing equations**

the metamodel. This regression approach leads to:

Q X Q

@

q¼1

analytical functions of the chaos coefficients Yα [20]:

M~ ð Þ� x1, … , xr M~ 0 � �2

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

α ¼ αð Þ1 , … , αð Þr

α ¼ αð Þ1 , … , αð Þr

To compute the chaos coefficients Yα, 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

Here, we apply the second technique: it consists in searching the set of coefficients minimizing in the least-squares sense, the L2 distance between the model and

α∈ Aα

YαΦα x1,q, … , xr,q � � !2 0

The system is solved in a mean least-squares sense with a number Q of sampling points x1,q, … , xr,q � � 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 secondorder Legendre polynomials. This leads to Np ¼ 36 stochastic modes, so that the number of sampling points is Q ¼ 72. Roots of the third-order Legendre polynomial, Ψ3 xi,q � � ¼ 0, are chosen as sampling points. The results presented here were validated using the jackknife technique with 100 replications of a random subset of

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 messagepassing interface (MPI) [25]. Reactive flows are modelled using a turbulence model based on a LES approach, a combustion model based on the eddy dissipation

M x1,q, … , xr,q � � � X

Sti of the metamodel can be computed as

α∈ Aαnf g 0, … , 0

� � such as : αð Þi 6¼ 0 � � (12)

Y2

α (10)

1

A (13)

(11)

M x ~ ð Þ 1, … , xr dx1 … dxr ¼ Yf g 0, … ,0 (9)

� � such as : αð Þi 6¼ 0 and αð Þj 6¼ 0 for j 6¼ i � �

dx1 … dxr ¼ X

$$\int \mathcal{M}(\mathbf{x}\_{\mathbf{i}\_1}, \dots, \mathbf{x}\_{\mathbf{i}\_s}) \, d\mathbf{x}\_{\mathbf{i}\_1} \dots d\mathbf{x}\_{\mathbf{i}\_s} = \mathbf{0} \text{ for } \mathbf{1} \le \mathbf{i}\_1 < \dots < \mathbf{i}\_s \le \mathbf{r} \tag{4}$$

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

$$\text{var}(\mathbf{T}) = \mathbf{D} = \sum\_{i=1}^{\mathbf{r}} \mathbf{D}\_{\mathbf{i}} + \sum\_{1 \le i < j \le r}^{\mathbf{r}} \mathbf{D}\_{\mathbf{i}\<\mathbf{j}} + \dots + \mathbf{D}\_{1,\dots,\mathbf{r}} \tag{5}$$

The partial variances Di1, … ,is are defined by:

$$\mathbf{D}\_{\mathbf{i}\_{1},\ldots,\mathbf{i}\_{\star}} = \int \mathbf{M}\_{\mathbf{i}\_{1},\ldots,\mathbf{i}\_{\star}}(\mathbf{x}\_{\mathbf{i}\_{1}},\ldots,\mathbf{x}\_{\mathbf{i}\_{\star}})^{2} \mathbf{dx}\_{\mathbf{i}\_{1}}\ldots\mathbf{dx}\_{\mathbf{i}\_{\star}} \tag{6}$$

Then, the Sobol indices can be derived according to:

$$\mathbf{S}\_{\mathbf{i}\_1,\dots,\mathbf{i}\_s} = \frac{\mathbf{D}\_{\mathbf{i}\_1,\dots,\mathbf{i}\_s}}{\mathbf{D}} \tag{7}$$

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 Np orthogonal polynomials:

$$\mathcal{M}(\mathbf{x}\_1, \dots, \mathbf{x}\_\mathbf{r}) \approx \tilde{\mathcal{M}}(\mathbf{x}\_1, \dots, \mathbf{x}\_\mathbf{r}) = \sum\_{a \in A\_a} \mathbf{Y}\_a \Phi\_a(\mathbf{x}\_1, \dots, \mathbf{x}\_\mathbf{r}) \tag{8}$$

where Aα is a finite set of vectors of positive integers α ¼ αð Þ1 , … , αð Þr � � such as *card*ð Þ¼ Aα Np. Each of the multivariate polynomials Φα can be expressed as a product of monovariate polynomials Ψαð Þi of order αð Þi :

$$\Phi\_a(\mathbf{x\_1}, \dots, \mathbf{x\_r}) = \Psi\_{a\_{(1)}}(\mathbf{x\_1}) \times \dots \times \Psi\_{a\_{(r)}}(\mathbf{x\_r})$$

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: Pr i¼1αð Þi ≤p, where 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 M~ 0, the variance D, the first-order Sobol ~

*Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

indices ~ Si, and the total sensitivity indices ~ Sti of the metamodel can be computed as analytical functions of the chaos coefficients Yα [20]:

$$
\tilde{\mathbf{M}}\_0 = \int \tilde{\mathbf{M}}(\mathbf{x}\_1, \dots, \mathbf{x}\_r) d\mathbf{x}\_1 \dots d\mathbf{x}\_r = \mathbf{Y}\_{\{0,\dots,0\}} \tag{9}
$$

$$\tilde{\mathbf{D}} = \int \left( \tilde{\mathcal{M}}(\mathbf{x}\_1, \dots, \mathbf{x}\_r) - \tilde{\mathbf{M}}\_0 \right)^2 d\mathbf{x}\_1 \dots d\mathbf{x}\_r = \sum\_{a \in \mathcal{A}\_\mathbf{r} \backslash \{0, \dots, 0\}} \mathbf{Y}\_a^2 \tag{10}$$

$$\tilde{\mathbf{S}}\_{\mathbf{i}} = \frac{\sum\_{a \in \mathcal{A}\_{\mathbf{i}}^{\{\bar{\mathbf{i}}\}}} \mathbf{Y}\_{\alpha}^{2}}{\tilde{\mathbf{D}}} \text{ with } \mathcal{A}\_{\mathbf{a}}^{\{\bar{\mathbf{i}}\}} = \left\{ (\mathfrak{a}\_{(1)}, \dots, \mathfrak{a}\_{(r)}) \text{ such as } : \mathfrak{a}\_{(\bar{\mathbf{i}})} \neq \mathbf{0} \text{ and } \mathfrak{a}\_{(\bar{\mathbf{j}})} \neq \mathbf{0} \text{ for } \mathbf{j} \neq \mathbf{i} \right\} \tag{11}$$

$$\tilde{\mathbf{St}}\_{\mathbf{i}} = \frac{\sum\_{a \in \mathcal{A}\_{\mathbf{u}}^{\{\bar{i}\}}} \mathbf{Y}\_{\mathbf{a}}^{2}}{\tilde{\mathbf{D}}} \text{ with } \mathbf{A}\_{\mathbf{u}}^{\{\bar{i}\}} = \left\{ \left( \mathfrak{a}\_{(1)}, \dots, \mathfrak{a}\_{(r)} \right) \text{ such as } : \mathfrak{a}\_{(\bar{i})} \neq \mathbf{0} \right\} \tag{12}$$

To compute the chaos coefficients Yα, 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 L2 distance between the model and the metamodel. This regression approach leads to:

$$\mathbb{V}\left\{\mathbf{Y}\_{a}\right\} = \operatorname\*{argmin}\left(\frac{1}{\mathbf{Q}}\sum\_{\mathbf{q}=1}^{\mathbf{Q}}\left(\mathcal{M}\left(\mathbf{x}\_{\text{1,q}},\dots,\mathbf{x}\_{\text{r,q}}\right) - \sum\_{a\in A\_{a}} \mathbf{Y}\_{a}\Phi\_{a}\left(\mathbf{x}\_{\text{1,q}},\dots,\mathbf{x}\_{\text{r,q}}\right)\right)^{2}\right) \tag{13}$$

The system is solved in a mean least-squares sense with a number Q of sampling points x1,q, … , xr,q � � 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 secondorder Legendre polynomials. This leads to Np ¼ 36 stochastic modes, so that the number of sampling points is Q ¼ 72. Roots of the third-order Legendre polynomial, Ψ3 xi,q � � ¼ 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 messagepassing interface (MPI) [25]. Reactive flows are modelled using a turbulence model based on a LES approach, a combustion model based on the eddy dissipation

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

The variance of the model response according to variation of inputs can be

Di þ Xr

Mi1, … is xi1 , … , xis ð Þ2

Si1, … ,is ¼ Di1, … ,is

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

The polynomial chaos (PC) expansion consists in the projection of the model M

where Aα is a finite set of vectors of positive integers α ¼ αð Þ1 , … , αð Þr

as *card*ð Þ¼ Aα Np. Each of the multivariate polynomials Φα can be expressed as a

Φαð Þ¼ x1, … , xr Ψαð Þ1 ð Þ� x1 … � Ψαð Þr ð Þ xr

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

The interest in such a decomposition is that, due to orthonormal properties of the family of polynomials, the mean M~ 0, the variance D, the first-order Sobol

X α∈ Aα

1≤i<j≤r

Mð Þ x1, … , xr dx1 … *:*dxr (3)

Dij þ … þ D1, … ,r (5)

dxi1 … *:*dxis (6)

YαΦαð Þ x1, … , xr (8)

i¼1αð Þi ≤p, where p is the

~

� � such

D (7)

M xi1 , … , xis ð Þ dxi1 … *:*dxis ¼ 0 for 1≤i1 < … <is ≤r (4)

M0 ¼ ð

derived as a sum of partial variances as follows:

var Tð Þ¼ D ¼ Xr

The partial variances Di1, … ,is are defined by:

Di1, … ,is ¼

i¼1

ð

on the space spanned by a family of Np orthogonal polynomials:

Mð Þ x1, … , xr ≈M~ ð Þ¼ x1, … , xr

product of monovariate polynomials Ψαð Þi of order αð Þi :

criterion consists in prescribing the constraint: Pr

**14**

maximum order allowed for each monovariate polynomial.

Then, the Sobol indices can be derived according to:

ð

*Fire Safety and Management Awareness*

derive the sensitivity indices.

**2.2 Polynomial chaos expansion**

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]:

$$\frac{\partial \rho}{\partial \mathbf{t}} + \frac{\partial}{\partial \mathbf{x}\_{\circ}} \left(\rho \mathbf{u}\_{\circ}\right) = \mathbf{0} \tag{14}$$

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

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

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

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

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

nominal mesh size and D\* is the characteristic fire diameter [24]. The characteristic

ρ∞cpT∞

!2

ffiffi g p *=*5

D∗ ¼ Q\_

size of the domain is given by the nondimensional expression D∗

fire diameter D\* is determined using Eq. (18):

, a thermal conductivity of 46 W/(m�K)�1

*=*

∂x, where ∂x is the

(18)

, a

applied to measure the velocity of smoke.

*Schematic view of the experimental corridor and fire room.*

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Figure 1.**

of steel having a density of 7850 kg/m3

slice fields in the plane Y = 0.5 m.

**3.4 Mesh size resolution**

**17**

specific heat of 0.5 kJ/(kg�K), and an emissivity of 0.9.

$$\frac{\partial}{\partial \mathbf{t}} \left( \rho \mathbf{u}\_{\mathbf{i}} \right) + \frac{\partial}{\partial \mathbf{x}\_{\mathbf{j}}} \left( \rho \mathbf{u}\_{\mathbf{i}} \mathbf{u}\_{\mathbf{j}} \right) = -\frac{\partial \mathbf{p}}{\partial \mathbf{x}\_{\mathbf{i}}} + \rho \mathbf{g}\_{\mathbf{i}} + \frac{\partial}{\partial \mathbf{x}\_{\mathbf{j}}} \left\{ \mu \left( \frac{\partial \mathbf{u}\_{\mathbf{i}}}{\partial \mathbf{x}\_{\mathbf{j}}} + \frac{\partial \mathbf{u}\_{\mathbf{j}}}{\partial \mathbf{x}\_{\mathbf{i}}} - \frac{2}{3} \delta\_{\mathbf{i}\mathbf{j}} \frac{\partial \mathbf{u}\_{\mathbf{i}}}{\partial \mathbf{x}\_{\mathbf{i}}} \right) \right\} \tag{15}$$

$$\frac{\partial \rho \mathbf{Y}\_{\mathbf{k} \ast}}{\partial \mathbf{t}} + \frac{\partial}{\partial \mathbf{x}\_{\mathbf{j}}} \rho \mathbf{u}\_{\mathbf{j}} \mathbf{Y}\_{\mathbf{k} \ast} = \frac{\partial}{\partial \mathbf{x}\_{\mathbf{j}}} \left\{ (\rho \mathbf{D})\_{\mathbf{k} \ast} \frac{\partial}{\partial \mathbf{x}\_{\mathbf{j}}} \mathbf{Y}\_{\mathbf{k} \ast} \right\} + \dot{\mathbf{o}}\_{\mathbf{k} \ast}^{\prime\prime} \tag{16}$$

$$\frac{\partial}{\partial \mathbf{t}}(\rho \mathbf{h}) + \frac{\partial}{\partial \mathbf{x}\_{\circ}}(\rho \mathbf{u}\_{\circ} \mathbf{h}) = \frac{d\mathbf{p}}{d\mathbf{t}} + \dot{\mathbf{q}}''' + \lambda \frac{\partial^2}{\partial \mathbf{x}\_{\circ}^2} \mathbf{T} + \sum \frac{\partial}{\partial \mathbf{x}\_{\circ}} \left\{ \mathbf{h}\_{\mathbf{k}\*} (\rho \mathbf{D})\_{\mathbf{k}\*} \frac{\partial}{\partial \mathbf{x}\_{\circ}} \mathbf{Y}\_{\mathbf{k}\*} \right\} - \frac{\partial}{\partial \mathbf{x}\_{\circ}} \dot{\mathbf{q}}''\_{\mathbf{r}, \circ} \tag{17}$$

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].  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.

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

*Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Figure 1.** *Schematic view of the experimental corridor and fire room.*

concept (EDC), and a thermal radiation model based on a gray gas model for the

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

> ∂ ∂xj μ ∂ui ∂xj þ ∂uj ∂xi � 2 3 δij ∂ui ∂xi

ð Þ ρD k ∗

∂xj

T þX ∂

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

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 com-

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].  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

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

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

∂ ∂xj Yk ∗

� �

� � ¼ 0 (14)

þ ω\_ 000

� �

∂ ∂xj Yk ∗ (15)

(17)

k ∗ (16)

� ∂ ∂xj q\_ 00 r,j

� � � �

hk ∗ ð Þ ρD k ∗

∂ρ ∂t þ ∂ ∂xj ρuj

þ ρgi þ

∂x**2** j

∂xj

∂xi

dt þ q\_000 þ λ ∂**2**

ρujYk ∗ ¼ ∂

equation, and Eq. (17) represents the energy conservation equation.

radiation absorption coefficient [15, 16].

*Fire Safety and Management Awareness*

∂ ∂xj

ρuiuj � � ¼ � ∂p

∂ρYk ∗ ∂t þ ∂ ∂xj

ð Þ¼ ρuih dp

bustion heat of butane is 45182.83 kJ/kg.

plate with a thickness of 2.5 mm.

**16**

HRR, which corresponds to 1.5 MW full-scale.

**3.3 Computational domain and boundary conditions**

∂ ∂t ρuj � � þ

ð Þþ ρh ∂ ∂xj

**3.2 Fire modelling**

∂ ∂t 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 D∗ *=*∂x, where ∂x is the nominal mesh size and D\* is the characteristic fire diameter [24]. The characteristic fire diameter D\* is determined using Eq. (18):

$$\mathbf{D}^\* = \left(\frac{\dot{\mathbf{Q}}}{\rho\_{\text{osc}\_{\text{P}}\text{T}\_{\text{ov}}\sqrt{\mathbf{g}}}}\right)^{\sharp \boldsymbol{\xi}} \tag{18}$$

where D\* denotes the characteristic fire diameter, Q the Heat Release Rate, and \_ cp the specific heat.

Based on several experiments, the U.S. Nuclear Regulatory Commission recommends that the numerical range of D∗ *=*∂x be between 4 and 16 for simulations to produce favorable results at a moderate computational cost, since the larger the value of D∗ *=*∂x 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]:

$$\frac{\mathbf{D}^\*}{16} \le \delta\_\mathbf{x} \le \frac{\mathbf{D}^\*}{4} \tag{19}$$

reinforced by the suggestions of the various cases of validation of the FDS code

**Numerical grid Number of cells Relative gap (%) CPU time (h)**

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

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

**Temperature (°C) Smoke velocity (m/s)**

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"

**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

*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*

proposed in the user guide [24].

*Results of different numerical grid mesh sizes.*

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Table 1.**

**Figure 3.**

**19**

*height of 70 cm of FDS and experimental results [8].*

and each computation took about 9.6 h.

between wind and smoke flow can be reproduced.

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.

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]:

$$\text{RG} = \mathbf{100} \times \frac{\sqrt{\sum\_{i=1}^{n} \left(\mathbf{y}\_{\text{pre},i} - \mathbf{y}\_{\text{exp},i}\right)^2}}{\sqrt{\sum\_{i=1}^{n} \left(\mathbf{y}\_{\text{exp},i}\right)^2}} \tag{20}$$

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

**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.*

**Table 1.**

where D\* denotes the characteristic fire diameter, Q the Heat Release Rate, and \_

Based on several experiments, the U.S. Nuclear Regulatory Commission recom-

∂x 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]:

After calculation, the range of mesh sizes was found to be: (0.0625 and 0.25 m).

It can be seen that the numerical results obtained with mesh sizes of 5 and 2.5 cm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

i¼1 ypre,i � y*exp* ,i � �2 r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �2 r (20)

i¼1 y*exp* ,i

D∗

∂x be between 4 and 16 for simulations to

4 (19)

*=*

D∗ 16 ≤δx ≤

Therefore, four different mesh sizes were used: 20, 10, 5, and 2.5 cm.

cm above the ground and in the centerline of the corridor near the exit.

mesh (6.83%). The relative gap (RG) is obtained by [26]:

RG ¼ 100 �

number of experimental points.

**Figure 2.**

**18**

*height of 70 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

Pn

where ypre is a predicted value, yexp is an experimental value, and n is the

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

time, the 5-cm mesh was used for the following calculations, this choice is

Pn

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

**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

produce favorable results at a moderate computational cost, since the larger the

cp the specific heat.

*=*

value of D∗

mends that the numerical range of D∗

*Fire Safety and Management Awareness*

*Results of different numerical grid mesh sizes.*

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.**

*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].*

**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.

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.

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

*Simulation of the smoke velocity field with (a) Vw = 0 m/s; (b) Vw = 1.73 m/s; (c) Vw = 3.46 m/s;*

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

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

*and (d) Vw = 5.20 m/s in the cross-section y = 0.5 m at 300 s.*

**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

for fire safety.

**Figure 4.**

**21**

*Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Figure 4.**

**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

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

It can be concluded from these different comparisons that the choice of a 5-cm

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

**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

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

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

height of 70 cm in the experiments, these values are in fact averages.

and experiment is observed in the other pictures (**Figure 3(c)** and **(d)**).

acceptable.

ceiling.

the smoke flow.

**20**

**4. Results and discussions**

*Fire Safety and Management Awareness*

**4.1 Outdoor wind effect on the smoke exhaust**

*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.*

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

**Figure 5.** *Influence of wind velocity on: (a) O2 concentration; and (b) CO2 concentration at 85 cm height.*

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.

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

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

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

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

the corridor gradually becomes homogeneous as the outdoor wind velocity increases and becomes better when the wind velocity reaches 5.20 m/s, indicating

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 sys-

**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

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 [27–29], smoke stratification depends on the Froude number. Smoke stratification is very stable up to a critical Froude number

that the more smoke is exhausted, the more visibility is improved.

tem, representing an unacceptable situation for fire safety.

this observation.

**23**

**Figure 6.**

*corridor.*

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

rate in the building is larger, producing more CO.

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.

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 *Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Figure 6.** *Influence of wind velocity on: (a) CO concentration; and (b) visibility at 55 cm height at the exit of the corridor.*

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 [27–29], smoke stratification depends on the Froude number. Smoke stratification is very stable up to a critical Froude number

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

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

corridor also indicates that more smoke is extracted.

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

The more the wind velocity increases, the more the CO2 concentration decreases

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

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

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

The distribution of CO concentration in the corridor gradually becomes homogeneous as the wind velocity increases. Although in this study the CO concentration

(**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 concentra-

tion in the corridor also contributes to people escaping from fires.

wind velocity cases.

*Fire Safety and Management Awareness*

**Figure 5.**

wind velocity.

building.

no wind.

**22**

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

*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*

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

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

fields of smoke movement in an enclosure with outdoor wind.

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

**Figure 8.**

**25**

*the cross-section y = 0.5 m at 300 s.*

**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.*

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.

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 *Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

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.*

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

*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*

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

fire safety.

**24**

**Figure 7.**

*smoke temperature in different heights of the corridor.*

*Fire Safety and Management Awareness*

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

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

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

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

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,

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

In addition, considering the importance of the effects of outside wind on reac-

be classified on quantitative grounds with a limited computational cost.

tive 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

following:

completely disturbed.

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

under-ventilated fire.

**27**

smoke exhaust in a compartment fire.

even slight ones, in the input parameters.

#### **Figure 9.** *Local sensitivity indices.*

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 MF and Ea depend on their mean value MF and Ea, on the tolerance interval �10%, and on the random dimensionless parameter ξMF and ξEa (whose values depend on the observation θ). 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:

$$\mathbf{MF}(\boldsymbol{\theta}) = \overline{\mathbf{MF}}(\mathbf{1} + \mathbf{0}.\mathbf{1} \,\mathsf{\xi}\_{\mathrm{MF}}(\boldsymbol{\theta}))$$

$$\mathbf{E}\_{\mathfrak{a}}(\boldsymbol{\theta}) = \overline{\mathbf{E}\_{\mathfrak{a}}}(\mathbf{1} + \mathbf{0}.\mathbf{1} \,\mathsf{\xi}\_{\mathrm{E}\_{\mathfrak{a}}}(\boldsymbol{\theta})) \tag{21}$$

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.

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

#### *Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

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:

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.

In addition, from a global sensitivity analysis, an investigation was carried out in

In this context, the values of the random parameters MF and Ea depend on their mean value MF and Ea, on the tolerance interval �10%, and on the random dimensionless parameter ξMF and ξEa (whose values depend on the observation θ). 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:

MFð Þ¼ θ MF 1ð Þ þ 0*:*1 ξMFð Þθ

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

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

In this chapter, a CFD code, namely fire dynamics simulator (FDS), was

employed to model the smoke spreading along a corridor induced by a

ð Þθ (21)

Eað Þ¼ θ Ea 1 þ 0*:*1 ξEa

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].

influence on the smoke temperature.

amount of species.

**Figure 9.**

*Local sensitivity indices.*

*Fire Safety and Management Awareness*

**5. Conclusion**

**26**

#### **Author details**

Brady Manescau1 \*, Khaled Chetehouna1 , Quentin Serra2 , Aijuan Wang1 and Eric Florentin2

**References**

firesaf.2007.10.003

[3] Hull TR, Brein D, Stec AA.

in buildings. Journal of Building Engineering. 2016;**8**:313-318. DOI: 10.1016/j.jobe.2016.02.014

414-421. DOI: 10.1016/j. firesaf.2017.04.037

233-243. DOI: 10.1016/j. applthermaleng.2017.01.099

857-865. DOI: 10.1016/j. applthermaleng.2016.07.141

**29**

[1] Yu-Ting E, Zhou L. The Research on the current safety status of high-rise building at home and abroad. Procedia Engineering. 2016;**135**:574-577. DOI: 10.1016/j.proeng.2016.01.108

*DOI: http://dx.doi.org/10.5772/intechopen.92978*

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

corridor induced by an adjacent compartment fire with outdoor wind. Applied Thermal Engineering. 2017;**111**:

Lu K. Fire-induced temperature distribution beneath ceiling and air entrainment coefficient characteristics in a tunnel with point extraction system.

International Journal of Thermal Sciences. 2018;**134**:363-369. DOI: 10.1016/j.ijthermalsci.2018.08.023

[10] Quintiere JG. Scaling and Dimensionless Groups. 2006. DOI:

[11] Li A, Zhang Y, Hu J, Gao R. Reduced-scale experimental study of the temperature field and smoke

in the underground hydraulic machinery plant. Tunnelling and Underground Space Technology. 2014;

**41**:95-103. DOI: 10.1016/j.tust.

[12] Weng MC, Yu LX, Liu F,

**42**:96-104. DOI: 10.1016/j.

[13] Batiot B, Rogaume T, Collin A, Richard F, Luche J. Sensitivity and uncertainty analysis of Arrhenius parameters in order to describe the kinetic of solid thermal degradation during fire phenomena. Fire Safety Journal. 2016;**82**:76-90. DOI: 10.1016/j.

[14] Xiao S, Lu Z, Wang P. Multivariate global sensitivity analysis for dynamic models based on wavelet analysis. Reliability Engineering and System

tust.2014.02.007

firesaf.2016.03.007

Nielsen PV. Full-scale experiment and CFD simulation on smoke movement and smoke control in a metro tunnel with one opening portal. Tunnelling and Underground Space Technology. 2014;

2013.11.009

development of the bus bar corridor fire

10.1002/0470091150.ch12

[9] Tang F, He Q, Mei F, Shi Q, Chen L,

420-430. DOI: 10.1016/j. applthermaleng.2016.09.086

[2] Paul KT, Hull TR, Lebek K, Stec AA. Fire smoke toxicity: The effect of nitrogen oxides. Fire Safety Journal. 2008;**43**:243-251. DOI: 10.1016/j.

Quantification of toxic hazard from fires

[4] Li M, Gao Z, Ji J, Li K, Sun J. Wind effects on flame projection probability from a compartment with opposing openings. Fire Safety Journal. 2017;**91**:

[5] Fan C, Zhang L, Jiao S, Yang Z, Li M, Liu X. Smoke spread characteristics inside a tunnel with natural ventilation under a strong environmental wind. Tunnelling and Underground Space Technology. 2018;**82**:99-110. DOI: 10.1016/j.tust.2018.08.004

[6] Tian X, Zhong M, Shi C, Zhang P, Liu C. Full-scale tunnel fire experimental study of fire-induced smoke temperature profiles with methanol-gasoline blends. Applied Thermal Engineering. 2017;**116**:

[7] Zhong MH, Shi CL, He L, Shi JH, Liu C, Tian XL. Smoke development in full-scale sloped long and large curved tunnel fires under natural ventilation. Applied Thermal Engineering. 2016;**108**:

[8] Li SC, Huang DF, Meng N, Chen LF, Hu LH. Smoke spread velocity along a

1 INSA Centre Val de Loire, University of Orléans, PRISME, Bourges, France

2 INSA Centre Val de Loire, University of Orléans, University of Tours, LaMé, Bourges, France

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Numerical Study on the Outdoor Wind Effects on Movement Smoke along a Corridor DOI: http://dx.doi.org/10.5772/intechopen.92978*

#### **References**

[1] Yu-Ting E, Zhou L. The Research on the current safety status of high-rise building at home and abroad. Procedia Engineering. 2016;**135**:574-577. DOI: 10.1016/j.proeng.2016.01.108

[2] Paul KT, Hull TR, Lebek K, Stec AA. Fire smoke toxicity: The effect of nitrogen oxides. Fire Safety Journal. 2008;**43**:243-251. DOI: 10.1016/j. firesaf.2007.10.003

[3] Hull TR, Brein D, Stec AA. Quantification of toxic hazard from fires in buildings. Journal of Building Engineering. 2016;**8**:313-318. DOI: 10.1016/j.jobe.2016.02.014

[4] Li M, Gao Z, Ji J, Li K, Sun J. Wind effects on flame projection probability from a compartment with opposing openings. Fire Safety Journal. 2017;**91**: 414-421. DOI: 10.1016/j. firesaf.2017.04.037

[5] Fan C, Zhang L, Jiao S, Yang Z, Li M, Liu X. Smoke spread characteristics inside a tunnel with natural ventilation under a strong environmental wind. Tunnelling and Underground Space Technology. 2018;**82**:99-110. DOI: 10.1016/j.tust.2018.08.004

[6] Tian X, Zhong M, Shi C, Zhang P, Liu C. Full-scale tunnel fire experimental study of fire-induced smoke temperature profiles with methanol-gasoline blends. Applied Thermal Engineering. 2017;**116**: 233-243. DOI: 10.1016/j. applthermaleng.2017.01.099

[7] Zhong MH, Shi CL, He L, Shi JH, Liu C, Tian XL. Smoke development in full-scale sloped long and large curved tunnel fires under natural ventilation. Applied Thermal Engineering. 2016;**108**: 857-865. DOI: 10.1016/j. applthermaleng.2016.07.141

[8] Li SC, Huang DF, Meng N, Chen LF, Hu LH. Smoke spread velocity along a

corridor induced by an adjacent compartment fire with outdoor wind. Applied Thermal Engineering. 2017;**111**: 420-430. DOI: 10.1016/j. applthermaleng.2016.09.086

[9] Tang F, He Q, Mei F, Shi Q, Chen L, Lu K. Fire-induced temperature distribution beneath ceiling and air entrainment coefficient characteristics in a tunnel with point extraction system. International Journal of Thermal Sciences. 2018;**134**:363-369. DOI: 10.1016/j.ijthermalsci.2018.08.023

[10] Quintiere JG. Scaling and Dimensionless Groups. 2006. DOI: 10.1002/0470091150.ch12

[11] Li A, Zhang Y, Hu J, Gao R. Reduced-scale experimental study of the temperature field and smoke development of the bus bar corridor fire in the underground hydraulic machinery plant. Tunnelling and Underground Space Technology. 2014; **41**:95-103. DOI: 10.1016/j.tust. 2013.11.009

[12] Weng MC, Yu LX, Liu F, Nielsen PV. Full-scale experiment and CFD simulation on smoke movement and smoke control in a metro tunnel with one opening portal. Tunnelling and Underground Space Technology. 2014; **42**:96-104. DOI: 10.1016/j. tust.2014.02.007

[13] Batiot B, Rogaume T, Collin A, Richard F, Luche J. Sensitivity and uncertainty analysis of Arrhenius parameters in order to describe the kinetic of solid thermal degradation during fire phenomena. Fire Safety Journal. 2016;**82**:76-90. DOI: 10.1016/j. firesaf.2016.03.007

[14] Xiao S, Lu Z, Wang P. Multivariate global sensitivity analysis for dynamic models based on wavelet analysis. Reliability Engineering and System

**Author details**

*Fire Safety and Management Awareness*

Brady Manescau1

Eric Florentin2

Bourges, France

**28**

\*, Khaled Chetehouna1

\*Address all correspondence to<EMAIL_ADDRESS>
provided the original work is properly cited.

, Quentin Serra2

1 INSA Centre Val de Loire, University of Orléans, PRISME, Bourges, France

2 INSA Centre Val de Loire, University of Orléans, University of Tours, LaMé,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Aijuan Wang1 and

Safety. 2018;**170**:20-30. DOI: 10.1016/j. ress.2017.10.007

[15] Sellami I, Manescau B, Chetehouna K, de Izarra C, Nait-Said R, Zidani F. BLEVE fireball modeling using fire dynamics simulator (FDS) in an Algerian gas industry. Journal of Loss Prevention in the Process Industries. 2018;**54**. DOI: 10.1016/j.jlp.2018.02.010

[16] Magnognou B, Garo JP, Coudour B, Wang HY. Risk analysis of unburnt gas ignition in an exhaust system connected to a confined and mechanically ventilated enclosure fire. Fire Safety Journal. 2017;**91**:291-302. DOI: 10.1016/ j.firesaf.2017.03.036

[17] Saltelli A, Ratto M, Tarantola S, Campolongo F. Sensitivity Analysis Practice: A Guide to Scientific Models. 2006. DOI: 10.1016/j.ress.2005.11.014

[18] Sobol IM. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computation. 1993;**1**:407-414. DOI: 10.18287/0134-2452-2015-39-4-459-461

[19] Crestaux T, Le Maître O, Martinez JM. Polynomial chaos expansion for sensitivity analysis. Reliability Engineering and System Safety. 2009;**94**:1161-1172. DOI: 10.1016/j.ress.2008.10.008

[20] Chaos M. Application of sensitivity analyses to condensed-phase pyrolysis modeling. Fire Safety Journal. 2013;**61**: 254-264. DOI: 10.1016/j.firesaf.2013. 09.016

[21] Yi L, Gao Y, Niu JL, Yang SJ. Study on effect of wind on natural smoke exhaust of enclosure fire with a twolayer zone model. Journal of Wind Engineering and Industrial Aerodynamics. 2013;**119**:28-38. DOI: 10.1016/j.jweia.2013.05.005

[22] Xiu D, Lucor D, Su C-H, Karniadakis GE. Stochastic modeling of flow-structure interactions using

generalized polynomial chaos. Journal of Fluids Engineering. 2002;**124**:51. DOI: 10.1115/1.1436089

[23] Eldred M, Burkardt J. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In: 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics; 2009. DOI: 10.2514/ 6.2009-976

[24] Mcgrattan K, Mcdermott R. Fire Dynamics Simulator User's Guide. 6th ed. 2016. DOI: 10.6028/NIST.SP.1019

[25] McGrattan K, Hostikka S, McDermott R, Floyd J, Weinschenk C, Overholt K. Fire Dynamics Simulator Technical Reference Guide Volume 1: Mathematical Model. NIST Special Publications. 1018-1. 1; 2017. DOI: 10.6028/NIST.SP.1018

[26] Menage D, Chetehouna K, Mell W. Numerical simulations of fire spread in a *Pinus pinaster* needles fuel bed. Journal of Physics Conference Series. 2012;**395**. DOI: 10.1088/1742-6596/395/1/012011

[27] Newman JS. Experimental evaluation of fire-induced stratification. Combustion and Flame. 1984;**39**:33-39

[28] Tang F, Li LJ, Dong MS, Wang Q, Mei FZ, Hu LH. Characterization of buoyant flow stratification behaviors by Richardson (Froude) number in a tunnel fire with complex combination of longitudinal ventilation and ceiling extraction. Applied Thermal Engineering. 2017;**110**:1021-1028. DOI: 10.1016/j.applthermaleng.2016.08.224

[29] Huang DF, Li SC. An experimental investigation of stratification characteristic of fire smoke in the corridor under the effect of outdoor wind. Journal of Wind Engineering and Industrial Aerodynamics. 2018;**179**:173-183. DOI: 10.1016/j.jweia.2018.05.021

**31**

**Chapter 3**

**Abstract**

interface.

**1. Introduction**

Shifting Wildfire Trends and

Twenty-first Century

*Rebecca Abney and Qin Ma*

Management Implications for the

Anthropogenic climate change is projected to impact a significant proportion of ecosystems throughout the world. These shifts in climate are already impacting a diversity of wildland and urban ecosystems, and they are projected to increase wildfire frequency and severity in many regions. This projected increase is the result of the interaction of altered drought, precipitation, and temperature regimes. Understanding shifts in wildfire regimes is critical for managers at the wildlandurban interface that work to protect structures and human life. This chapter will explore how ongoing and future shifts in climate will drive alterations to natural fire regimes in the United States, with focus on implications for the wildland-urban

**Keywords:** climate change, fire regime, urban-natural interface, wildfire

infrastructure has become more damaging and costly.

Fire is a global phenomenon that has historically maintained the structure and function of a range of ecosystems. Many ecosystems are adapted to periodic fire events, known as fire regimes, that describe the interval and severity of fire in a particular system. However, human influences in the twentieth century have changed the frequency and severity of wildfire in many forested ecosystems and understanding these shifts of fire regimes has been a major topic of investigation for the past several decades. This research has elucidated the numerous, complex, and interactive environmental factors driving shifts in wildfire regimes. Annually, 450 mHa of the Earth surface is burned due to wildfire [1], and the severity of wildland fires across the US has increased since the 1980s [2]. This is important because as the size, severity, and frequency of fires have changed, their influence on human

The wildland-urban interface (WUI) is the boundary where human civilization and unmanaged lands meet. Currently, this interface occupies over 770,000 km2 in the US, and increases in area classified as WUI are driven by ongoing development that pushes urban environments further into wildland areas [3]. Increasing development into the WUI puts increasing numbers of structures, mainly residential homes, and human lives at risk to damage or loss via wildfire. Further, the

Wildland Urban Interface in the

#### **Chapter 3**

Safety. 2018;**170**:20-30. DOI: 10.1016/j.

*Fire Safety and Management Awareness*

generalized polynomial chaos. Journal of Fluids Engineering. 2002;**124**:51. DOI:

[23] Eldred M, Burkardt J. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In: 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics; 2009. DOI: 10.2514/

[24] Mcgrattan K, Mcdermott R. Fire Dynamics Simulator User's Guide. 6th ed. 2016. DOI: 10.6028/NIST.SP.1019

McDermott R, Floyd J, Weinschenk C, Overholt K. Fire Dynamics Simulator Technical Reference Guide Volume 1: Mathematical Model. NIST Special Publications. 1018-1. 1; 2017. DOI:

[26] Menage D, Chetehouna K, Mell W. Numerical simulations of fire spread in a *Pinus pinaster* needles fuel bed. Journal of Physics Conference Series. 2012;**395**. DOI: 10.1088/1742-6596/395/1/012011

evaluation of fire-induced stratification. Combustion and Flame. 1984;**39**:33-39

[28] Tang F, Li LJ, Dong MS, Wang Q, Mei FZ, Hu LH. Characterization of buoyant flow stratification behaviors by Richardson (Froude) number in a tunnel fire with complex combination of longitudinal ventilation and ceiling extraction. Applied Thermal

Engineering. 2017;**110**:1021-1028. DOI: 10.1016/j.applthermaleng.2016.08.224

[29] Huang DF, Li SC. An experimental

characteristic of fire smoke in the corridor under the effect of outdoor wind. Journal of Wind Engineering and Industrial Aerodynamics. 2018;**179**:173-183. DOI:

investigation of stratification

10.1016/j.jweia.2018.05.021

[27] Newman JS. Experimental

[25] McGrattan K, Hostikka S,

10.6028/NIST.SP.1018

10.1115/1.1436089

6.2009-976

Chetehouna K, de Izarra C, Nait-Said R, Zidani F. BLEVE fireball modeling using fire dynamics simulator (FDS) in an Algerian gas industry. Journal of Loss Prevention in the Process Industries. 2018;**54**. DOI: 10.1016/j.jlp.2018.02.010

[16] Magnognou B, Garo JP, Coudour B, Wang HY. Risk analysis of unburnt gas ignition in an exhaust system connected

to a confined and mechanically ventilated enclosure fire. Fire Safety Journal. 2017;**91**:291-302. DOI: 10.1016/

[17] Saltelli A, Ratto M, Tarantola S, Campolongo F. Sensitivity Analysis Practice: A Guide to Scientific Models. 2006. DOI: 10.1016/j.ress.2005.11.014

[18] Sobol IM. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and

Computation. 1993;**1**:407-414. DOI: 10.18287/0134-2452-2015-39-4-459-461

[20] Chaos M. Application of sensitivity analyses to condensed-phase pyrolysis modeling. Fire Safety Journal. 2013;**61**: 254-264. DOI: 10.1016/j.firesaf.2013.

[21] Yi L, Gao Y, Niu JL, Yang SJ. Study on effect of wind on natural smoke exhaust of enclosure fire with a twolayer zone model. Journal of Wind

Aerodynamics. 2013;**119**:28-38. DOI:

Karniadakis GE. Stochastic modeling of flow-structure interactions using

Engineering and Industrial

10.1016/j.jweia.2013.05.005

[22] Xiu D, Lucor D, Su C-H,

[19] Crestaux T, Le Maître O, Martinez JM. Polynomial chaos expansion for sensitivity analysis. Reliability Engineering and System Safety. 2009;**94**:1161-1172. DOI: 10.1016/j.ress.2008.10.008

09.016

**30**

j.firesaf.2017.03.036

ress.2017.10.007

[15] Sellami I, Manescau B,

## Shifting Wildfire Trends and Management Implications for the Wildland Urban Interface in the Twenty-first Century

*Rebecca Abney and Qin Ma*

## **Abstract**

Anthropogenic climate change is projected to impact a significant proportion of ecosystems throughout the world. These shifts in climate are already impacting a diversity of wildland and urban ecosystems, and they are projected to increase wildfire frequency and severity in many regions. This projected increase is the result of the interaction of altered drought, precipitation, and temperature regimes. Understanding shifts in wildfire regimes is critical for managers at the wildlandurban interface that work to protect structures and human life. This chapter will explore how ongoing and future shifts in climate will drive alterations to natural fire regimes in the United States, with focus on implications for the wildland-urban interface.

 Introduction**

Fire is a global phenomenon that has historically maintained the structure and function of a range of ecosystems. Many ecosystems are adapted to periodic fire events, known as fire regimes, that describe the interval and severity of fire in a particular system. However, human influences in the twentieth century have changed the frequency and severity of wildfire in many forested ecosystems and understanding these shifts of fire regimes has been a major topic of investigation for the past several decades. This research has elucidated the numerous, complex, and interactive environmental factors driving shifts in wildfire regimes. Annually, 450 mHa of the Earth surface is burned due to wildfire [1], and the severity of wildland fires across the US has increased since the 1980s [2]. This is important because as the size, severity, and frequency of fires have changed, their influence on human infrastructure has become more damaging and costly.

The wildland-urban interface (WUI) is the boundary where human civilization and unmanaged lands meet. Currently, this interface occupies over 770,000 km2 in the US, and increases in area classified as WUI are driven by ongoing development that pushes urban environments further into wildland areas [3]. Increasing development into the WUI puts increasing numbers of structures, mainly residential homes, and human lives at risk to damage or loss via wildfire. Further, the

infrastructure required by the WUI presents an additional source of ignitions in areas that are primed to burn. While trees exhibit traits of fire resistance [4, 5], houses, in particular older structures, burn with greater intensity and speed. For example, the 2018 Camp Fire in the Sierra Nevada of California burned quickly through the town of Paradise while leaving many standing trees scorched but not completely burnt. While this fire had many complex causes [6], the quick spread of the fire through the town was a reason that escape was made difficult despite a populous aware and prepared for the danger.

While these changes in fire regimes have exacerbated the damage in WUI, anthropogenic climate change is expected to intensify the risk by fire to WUIs. Across the US, climate change in the next century is projected to drive increases in wildfire severity in some areas, and increased wildfire incidence in other areas [7]. Shifts in wildfire patterns will be driven by shifts in precipitation timing and amounts, vegetation, temperature regimes, and drought conditions [8–11]. While changing climate patterns have been reasonably well characterized, wildfire regimes are more complex to predict due to the interconnected nature of the drivers and heterogeneous nature of ignition sources. It is critical to understand and provide more accurate predictions for shifts in wildfire frequency and severity, due to the loss of life, economic damage, related catastrophic environmental events, such as flooding or water quality damage. This is particularly important as human development into the wildland areas, which are more prone to wildfires, has increased significantly over the past half century.

#### **2. Shifting wildfire regimes**

Fire regimes integrate the tendency of vegetation to burn and the climate conditions that promote fire in a metric that describes the spatial and temporal nature of fire in a particular region. While there are several ways to calculate these metrics [12] a general calculation includes a measure of how frequently a fire occurs at a location (i.e., the average fire return interval) and the effect that fire has on vegetation (i.e., the severity of the fire). Variability in fire regimes is driven by differences in elevation, vegetation life history, drought and precipitation patterns, land-use, among other ecosystem-specific parameters [13, 14]. Many animal and plant species have co-evolved with fire and are adapted to specific fire regimes [15]. Some densergrowing vegetation species are adapted to higher severity and stand-replacing burns, such as in the Northern Rockies, while other species are more adapted to lower and more moderate severity burns, such as in the southern Sierra Nevada.

The inherent complexity and spatial heterogeneity of fire regimes make it difficult to make general recommendations for fire management [15]. However, the implications of an expanding WUI and increasing trends of fire activity indicate a clear problem for fire management. This is compounded by the possibility that fire regimes may shift over time in response to anthropogenic driven changes in management, vegetation composition and density, and climate [16, 17].

#### **2.1 History of fire regimes in the US**

Historically, fire regimes were mostly driven by an ecosystem's vegetation, climate conditions, and human activities, which varied both spatially and temporally over the US. In the Northern Rocky Mountains, stand replacing fires are typical in pine forests of the region [18, 19]. Fires in this ecosystem occur at relatively low frequency (longer return intervals), but when they do occur, they can burn large areas of forest ecosystems at high severity, e.g., the Yellowstone fire in 1988 [20–22].

**33**

**Figure 1.**

*All photos are © R. Abney.*

*Shifting Wildfire Trends and Management Implications for the Wildland Urban Interface…*

In contrast, low-intensity fires occurred more frequently in the southwestern forests of New Mexico and Arizona, due to the dry and warm semi-arid climate and tree species that exhibited resistance to fires (e.g., *Pinus ponderosa*). Much of the southeast was historically occupied by longleaf pine (*Pinus palustris*, **Figure 1A**), which thrives in high frequency, low burn severity fire regimes [23]. Pre-European settlement, longleaf pine forests were managed by Native American populations, and post-settlement there was a significant decline in the land area of these forests [24]. Currently, they are managed via frequent prescribed fire and are often grown to produce pine straw [25]. While wildfires have been major drivers of the American landscape, natural ecosystems are continually adapting to fire regimes over time in response to shifts in vegetation, management, and climate. However, human activities, management, and climate change are also driving the interaction between fire

The shift in fire regimes in the Sierra Nevada is an example of the interactive effects of human management and climate change. Prior to Euro-American settlement, natural lighting strikes and fire activities by Native Americans were the main causes of fire ignitions in the Sierra Nevada [26]. Forests were burned with mixed-severity fires that included both light to moderate burning of understory and crown fires at the interval of a decade or two. The small trees and ground fuels were killed and cleaned in fires periodically, leaving patches of large, mature trees that are more resistant to wildfires due to thick bark that is hard to burn, preventing fire from spreading to the canopy [4, 5]. However, a combination of human influences changed the structure of these forests and made them more susceptible to frequent fires that spread through canopies. Early twentieth century logging practices preferentially selected for these larger trees, opening up space for denser thickets of small trees to colonize, leading to increases in forest density [27]. This change in structure was reinforced by widespread suppression of fires that historically cleared out undergrowth. Since the early twentieth century, fire suppression as a forest management technique was widely adopted after several large and severe wildfires

*Fire severity is in part controlled by the density of the fuels and fire return interval. In photo A, loblolly pine (*Pinus palustris*) plantation in Georgia is managed for pulpwood production with prescribed fire approximately every 3 years. This low severity, high frequency fire regime maintains an open canopy and lowdensity fuels. In photo B, a conifer forest in Yosemite National Park one-year post recovery after the Rim Fire.*

*DOI: http://dx.doi.org/10.5772/intechopen.93245*

and vegetation over the past several centuries.

#### *Shifting Wildfire Trends and Management Implications for the Wildland Urban Interface… DOI: http://dx.doi.org/10.5772/intechopen.93245*

In contrast, low-intensity fires occurred more frequently in the southwestern forests of New Mexico and Arizona, due to the dry and warm semi-arid climate and tree species that exhibited resistance to fires (e.g., *Pinus ponderosa*). Much of the southeast was historically occupied by longleaf pine (*Pinus palustris*, **Figure 1A**), which thrives in high frequency, low burn severity fire regimes [23]. Pre-European settlement, longleaf pine forests were managed by Native American populations, and post-settlement there was a significant decline in the land area of these forests [24]. Currently, they are managed via frequent prescribed fire and are often grown to produce pine straw [25]. While wildfires have been major drivers of the American landscape, natural ecosystems are continually adapting to fire regimes over time in response to shifts in vegetation, management, and climate. However, human activities, management, and climate change are also driving the interaction between fire and vegetation over the past several centuries.

The shift in fire regimes in the Sierra Nevada is an example of the interactive effects of human management and climate change. Prior to Euro-American settlement, natural lighting strikes and fire activities by Native Americans were the main causes of fire ignitions in the Sierra Nevada [26]. Forests were burned with mixed-severity fires that included both light to moderate burning of understory and crown fires at the interval of a decade or two. The small trees and ground fuels were killed and cleaned in fires periodically, leaving patches of large, mature trees that are more resistant to wildfires due to thick bark that is hard to burn, preventing fire from spreading to the canopy [4, 5]. However, a combination of human influences changed the structure of these forests and made them more susceptible to frequent fires that spread through canopies. Early twentieth century logging practices preferentially selected for these larger trees, opening up space for denser thickets of small trees to colonize, leading to increases in forest density [27]. This change in structure was reinforced by widespread suppression of fires that historically cleared out undergrowth. Since the early twentieth century, fire suppression as a forest management technique was widely adopted after several large and severe wildfires

#### **Figure 1.**

*Fire Safety and Management Awareness*

over the past half century.

**2. Shifting wildfire regimes**

**2.1 History of fire regimes in the US**

populous aware and prepared for the danger.

infrastructure required by the WUI presents an additional source of ignitions in areas that are primed to burn. While trees exhibit traits of fire resistance [4, 5], houses, in particular older structures, burn with greater intensity and speed. For example, the 2018 Camp Fire in the Sierra Nevada of California burned quickly through the town of Paradise while leaving many standing trees scorched but not completely burnt. While this fire had many complex causes [6], the quick spread of the fire through the town was a reason that escape was made difficult despite a

While these changes in fire regimes have exacerbated the damage in WUI, anthropogenic climate change is expected to intensify the risk by fire to WUIs. Across the US, climate change in the next century is projected to drive increases in wildfire severity in some areas, and increased wildfire incidence in other areas [7]. Shifts in wildfire patterns will be driven by shifts in precipitation timing and amounts, vegetation, temperature regimes, and drought conditions [8–11]. While changing climate patterns have been reasonably well characterized, wildfire regimes are more complex to predict due to the interconnected nature of the drivers and heterogeneous nature of ignition sources. It is critical to understand and provide more accurate predictions for shifts in wildfire frequency and severity, due to the loss of life, economic damage, related catastrophic environmental events, such as flooding or water quality damage. This is particularly important as human development into the wildland areas, which are more prone to wildfires, has increased significantly

Fire regimes integrate the tendency of vegetation to burn and the climate conditions that promote fire in a metric that describes the spatial and temporal nature of fire in a particular region. While there are several ways to calculate these metrics [12] a general calculation includes a measure of how frequently a fire occurs at a location (i.e., the average fire return interval) and the effect that fire has on vegetation (i.e., the severity of the fire). Variability in fire regimes is driven by differences in elevation, vegetation life history, drought and precipitation patterns, land-use, among other ecosystem-specific parameters [13, 14]. Many animal and plant species have co-evolved with fire and are adapted to specific fire regimes [15]. Some densergrowing vegetation species are adapted to higher severity and stand-replacing burns, such as in the Northern Rockies, while other species are more adapted to lower and

more moderate severity burns, such as in the southern Sierra Nevada.

agement, vegetation composition and density, and climate [16, 17].

The inherent complexity and spatial heterogeneity of fire regimes make it difficult to make general recommendations for fire management [15]. However, the implications of an expanding WUI and increasing trends of fire activity indicate a clear problem for fire management. This is compounded by the possibility that fire regimes may shift over time in response to anthropogenic driven changes in man-

Historically, fire regimes were mostly driven by an ecosystem's vegetation, climate conditions, and human activities, which varied both spatially and temporally over the US. In the Northern Rocky Mountains, stand replacing fires are typical in pine forests of the region [18, 19]. Fires in this ecosystem occur at relatively low frequency (longer return intervals), but when they do occur, they can burn large areas of forest ecosystems at high severity, e.g., the Yellowstone fire in 1988 [20–22].

**32**

*Fire severity is in part controlled by the density of the fuels and fire return interval. In photo A, loblolly pine (*Pinus palustris*) plantation in Georgia is managed for pulpwood production with prescribed fire approximately every 3 years. This low severity, high frequency fire regime maintains an open canopy and lowdensity fuels. In photo B, a conifer forest in Yosemite National Park one-year post recovery after the Rim Fire. All photos are © R. Abney.*

in the Northern Rockies that killed many and destroyed a number of settlements. The fire suppression efforts were successful in excluding low-severity fires, and this management strategy reduced the fire frequency to the lowest frequency measured in the past 3000 years [28]. Consequently, the accompanying densification of forests due to the fire deficit has contributed to increasing numbers of devastating fires in late twentieth and twenty-first centuries [29]. This shift in fire regimes is the result of combined factors including (1) the reduction of regular fire usage, which were regularly conducted by Native Americans to reduce fuel loads and to encourage culturally important vegetation [30]; (2) legacy of decades of fire-suppression that densified undergrowth which lead to increased spread of fire; (3) removal of large trees, which are resilient to low-to-medium fires, due to industrialized timber logging; (4) the disappearing of gaps among trees, which could have stopped fire from spreading, but were filled with smaller and denser trees that can easily act as continuous fuel sources and (5) species change from those with fire adverse traits, to shade-tolerant ones [31]. The current fire regime that includes more high-severity, large fire size, is a significant challenge to forest managers and is a critical risk to the safety of human life and development in the WUI.

#### **2.2 Drivers of wildfire change**

Drivers of wildfire include three main categories: regional climate, fuel availability and condition, and ignition sources. In areas of low fuel density, sources of ignition drive fire occurrence; however, in higher population density areas, such as the WUI, fuel availability drives fire occurrence [32]. Climate influences fire occurrence by the timing and amount of precipitation, temperature, and wind speed. Wildfire season starts when all these climate features reach their thresholds. The intensity of drought and strength of wind as well as the length of wildfire season is highly related to the severity and risk of wildfires. Westerling et al. [17] found that an extended fire season, resulting from earlier spring warming and extended drought in late fall, increased the fire frequency and severity in the Western US. This trend is predicted to continue as climate gets warmer and drier with ongoing climate change [7]. In the eastern US, precipitation and temperature patterns form a different climate, and thus different fire seasons than the western US. Southwestern forests are influenced by late-summer precipitation stemming from the North American monsoon that end fire-season earlier in the year. The pacific north-west and the Northern Rockies are routinely colder and wetter, thus interannual fire season lengths are short in general.