Advanced Protection Mechanism: Simulations

**Chapter 4**

**Abstract**

TUS were presented.

**1. Introduction**

products.

**47**

physical picture of the processes.

*and Kamen Grozdanov*

Mathematical Modeling and

*Ivan Antonov, Rositsa Velichkova, Svetlin Antonov*

The mathematical models of fire distribution in a confined space–in

**Keywords:** fire simulation, FDS, garages, buildings, numerical simulation

enough and difficult for mathematical interpretation. This is due to its

through Fluent and FDS using the PyroSim GUI are presented [1, 2].

Mathematical modeling and numerical simulations of fires are an essential decisive part of the solution of important problems related to fire safety, analysis of the development of fires in the investigation of their consequences. The methods that are used must have the necessary accuracy and reliability, as close as possible to the

The actual fire, as it is known, is an uncontrollable combustion process, complex

This chapter gives two different approaches in dealing with their complexity and implementation of solving the problem. On the other hand, an integrated, relatively simplified technical solution of a new system for preventing the spread of fires in underground garages is given, which is described in details in the chapter. The second part deals with the basic mathematical apparatus used in CFD-Fluent and FDS software. The results of two fire simulations made by the authors

nonstationarity and three-dimensionality, which complicate the modeling of the heat and mass transfer processes observed in them. In the case of fires indoors of underground garages, buildings, and rooms, the development of the fire is accompanied by a change in the chronicle composition and parameters of the combustion

underground garages and in buildings—are described. Integral and computational fluid mechanics methods are used. The chapter presents the results of a fire simulation using the software Fluent. It uses Reynolds-type turbulence models of the Fire Dynamic Simulation or PyroSim graphical interface with a solution model describing a turbulence. For both cases, the pictures of the spread of fire and smoke over time in an atrium of an administrative building and a five-story building of the

Fires in Confined Spaces

Simulation of Development of the

#### **Chapter 4**

## Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces

*Ivan Antonov, Rositsa Velichkova, Svetlin Antonov and Kamen Grozdanov*

#### **Abstract**

The mathematical models of fire distribution in a confined space–in underground garages and in buildings—are described. Integral and computational fluid mechanics methods are used. The chapter presents the results of a fire simulation using the software Fluent. It uses Reynolds-type turbulence models of the Fire Dynamic Simulation or PyroSim graphical interface with a solution model describing a turbulence. For both cases, the pictures of the spread of fire and smoke over time in an atrium of an administrative building and a five-story building of the TUS were presented.

**Keywords:** fire simulation, FDS, garages, buildings, numerical simulation

#### **1. Introduction**

Mathematical modeling and numerical simulations of fires are an essential decisive part of the solution of important problems related to fire safety, analysis of the development of fires in the investigation of their consequences. The methods that are used must have the necessary accuracy and reliability, as close as possible to the physical picture of the processes.

The actual fire, as it is known, is an uncontrollable combustion process, complex enough and difficult for mathematical interpretation. This is due to its nonstationarity and three-dimensionality, which complicate the modeling of the heat and mass transfer processes observed in them. In the case of fires indoors of underground garages, buildings, and rooms, the development of the fire is accompanied by a change in the chronicle composition and parameters of the combustion products.

This chapter gives two different approaches in dealing with their complexity and implementation of solving the problem. On the other hand, an integrated, relatively simplified technical solution of a new system for preventing the spread of fires in underground garages is given, which is described in details in the chapter.

The second part deals with the basic mathematical apparatus used in CFD-Fluent and FDS software. The results of two fire simulations made by the authors through Fluent and FDS using the PyroSim GUI are presented [1, 2].

#### **2. Fire extinguishing system in large underground garages: integral methods for investigation**

In the present part, a simple method (from a technological point of view) is offered for solution of the complex problem. It is suggested to isolate the parked in the garage cars in pairs by which will be operating a thick curtain of water at arisen burning. The necessary insulation for solid noncombustible barriers are replaced at this way [3–6].

#### **2.1 Operating principal**

Referring to **Figure 1**, cars are placed to ensure the possibility between the pairs to have enough distance for the implementation of water curtains. In case of burning over the car is formed upward convective flow, because of differences of the density of the products of combustion and the environment. This stream is proportional to the lift force:

$$dF\_A = -\left[\int\_f (\rho - \rho\_{ob})gdf\right]d\mathfrak{x},\tag{1}$$

where *f* is the area of fire ignition and *dx* is elementary stretch in the vertical direction.

The power of convective updraft is determined by the number of Archimedes:

$$Ar = \left(\frac{\rho\_{ok}}{\rho} - 1\right) \frac{gd\_h}{u\_0^2},\tag{2}$$

where *dh* is the hydraulic diameter of the outbreak of fire and *u*<sup>0</sup> is the initial value of the velocity of the upward flow. The velocity is determined according to [6]:

$$
u\_0^2 = \mathbf{1}, \Re Q^{\dagger \ddagger},\tag{3}$$

The convective flow that is formed is shown in **Figure 2**. The conditional flow

(**Figure 3**). The ambient air enters the fire zone from all directions, which heats and reverses the direction vertically. The second zone is a free convective flow that continues until it reaches the ceiling of the room where the flow changes character (zone III). In this zone, the jet is transformed into a radially semi-enclosed stream

The system includes fire sprinklers—quick response and standard sprinklers. Convective flow is reaching the garage ceiling under the influence of its temperature and a quick response sprinkler is switched on and the burning car is flushed with a water spray. Thus begins the process of extinguishing a fire in the initial stages. Further, propagating as a radial semi-closed jet, it reaches the "standard"

This stage is defined as the isolation of burning cars from the surrounding area

For the purpose of solving the task is used an integral method according to

can be divided into the following areas: Convective flow is formed in zone I

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

reaction sprinklers that are included on the water curtain [7, 8].

**2.2 Mathematical model of convective non-isothermal jet**

[9, 10]. The used equations are as follows [11–13]:

and spreads over the garage ceiling (zone IV).

and no other pairs are affected.

**Figure 2.**

**Figure 3.**

**49**

*Sketch of the convective flow.*

*Distribution of the fire.*

where *Q*, kW is the power of the fire.

**Figure 1.** *Distribution of cars in the garages.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Figure 3.** *Sketch of the convective flow.*

**Figure 2.**

**2. Fire extinguishing system in large underground garages: integral**

In the present part, a simple method (from a technological point of view) is offered for solution of the complex problem. It is suggested to isolate the parked in the garage cars in pairs by which will be operating a thick curtain of water at arisen burning. The necessary insulation for solid noncombustible barriers are replaced at

Referring to **Figure 1**, cars are placed to ensure the possibility between the pairs to have enough distance for the implementation of water curtains. In case of burning over the car is formed upward convective flow, because of differences of the density of the products of combustion and the environment. This stream is

ð

2 6 4

*ρ* � *ρok* ð Þ*gdf*

3 7 5

*dx*, (1)

, (2)

5, (3)

*f*

*Ar* <sup>¼</sup> *<sup>ρ</sup>ok*

*u*2

where *Q*, kW is the power of the fire.

of the velocity of the upward flow. The velocity is determined according to [6]:

<sup>0</sup> <sup>¼</sup> 1, 9*Q*<sup>1</sup>

where *f* is the area of fire ignition and *dx* is elementary stretch in the vertical

The power of convective updraft is determined by the number of Archimedes:

*<sup>ρ</sup>* � <sup>1</sup> � � *gdh*

where *dh* is the hydraulic diameter of the outbreak of fire and *u*<sup>0</sup> is the initial value

*=*

*u*2 0

*dFA* ¼ �

**methods for investigation**

*Fire Safety and Management Awareness*

this way [3–6].

direction.

**Figure 1.**

**48**

*Distribution of cars in the garages.*

**2.1 Operating principal**

proportional to the lift force:

The convective flow that is formed is shown in **Figure 2**. The conditional flow can be divided into the following areas: Convective flow is formed in zone I (**Figure 3**). The ambient air enters the fire zone from all directions, which heats and reverses the direction vertically. The second zone is a free convective flow that continues until it reaches the ceiling of the room where the flow changes character (zone III). In this zone, the jet is transformed into a radially semi-enclosed stream and spreads over the garage ceiling (zone IV).

The system includes fire sprinklers—quick response and standard sprinklers. Convective flow is reaching the garage ceiling under the influence of its temperature and a quick response sprinkler is switched on and the burning car is flushed with a water spray. Thus begins the process of extinguishing a fire in the initial stages. Further, propagating as a radial semi-closed jet, it reaches the "standard" reaction sprinklers that are included on the water curtain [7, 8].

This stage is defined as the isolation of burning cars from the surrounding area and no other pairs are affected.

#### **2.2 Mathematical model of convective non-isothermal jet**

For the purpose of solving the task is used an integral method according to [9, 10]. The used equations are as follows [11–13]:

• for amount of movement

$$\frac{d}{d\mathfrak{x}}\int\_{0}^{b} \rho u^{2}(\mathfrak{x}\mathfrak{y}^{j})d\mathfrak{y} = -\mathfrak{g}\int\_{0}^{b} (\rho - \rho\_{\text{ox}})(\mathfrak{x}\mathfrak{y})^{j}d\mathfrak{y} \tag{4}$$

• to preserve enthalpy flow

$$\frac{d}{dx}\int\_{0}^{b} \rho \Delta h u y^{j} dy = 0\tag{5}$$

These values correspond to the case at *<sup>x</sup>* <sup>¼</sup> *<sup>x</sup>*

extinguishing stream will flow over the burning car.

be always greater than the above values.

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Table 1**.

by the expression:

where,

case is

isothermal.

(**Figure 4**).

**Table 1.**

**Table 2.**

**51**

287 J*=*kgK, *<sup>T</sup>*<sup>0</sup> <sup>¼</sup> 600 K, *<sup>p</sup>* <sup>¼</sup> <sup>10</sup><sup>5</sup>

created from a burning car *D*<sup>0</sup> ¼ 0*:*5 m and height *H* ¼ 3÷4*:*5*m*, *x* of the garage will

The initial velocity calculated by Eq. (3) is *u*<sup>0</sup> ¼ 8*:*2 m*=*s and the time when the convective stream will reach the ceiling at different heights of the garage is given in

This means that less than 1 s sprinklers over the burning car will be activated and

The expansion (increasing of thickness) of the jet in height can be determined

*dx* <sup>¼</sup> <sup>0</sup>*:*<sup>22</sup> *<sup>ρ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>ρ</sup>ок*

*<sup>b</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>22</sup> *<sup>ρ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>ρ</sup>ок*

The density of the jet in the opening section is defined by Eq. (8): at *R* ¼

The density of the environment is *<sup>ρ</sup>env* <sup>¼</sup> <sup>11</sup>*:*2 kg*=*m<sup>3</sup> at the same pressure and temperature *Tenv* ¼ 293 K. At this density, the widening of the jet in the present

For a different height in the garage, the parameter *b* is given in **Table 2**. The last row in **Table 2** is given the extension of the isothermal jetð Þ *T*<sup>0</sup> ≈*Tenv* . Obviously a slight extension of non-isothermal convective flow comparing with the

h, m 3 3.5 4 4.5 Δ*t* 0.36 0.43 0.49 0.55

h (m) 3 3.5 4 4.5 b1 (m) 0.501 0.507 0.652 0.73 bsou (m) 0.651 0.77 7.74 1.98

*h—height of the garage, m; b0—initial width of the radial jet, m; b1—width of the radial jet, m.*

*h—height of the garage, m; Δ*t*—time of the fire to reach the ceiling, m.*

Reaching the ceiling vertical, the convective stream is transformed into radial jet

2*ρок*

At the relatively short distance to the ceiling, the high power of fire (the accepted conditions are *Q* ¼ 1500W and *T* ¼ 600K), the velocity and the temper-

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

ature of the rising convective stream do not change significantly.

*db*

*<sup>D</sup>*<sup>0</sup> ≥ 3÷3*:*5. When adopted fire size

, (11)

<sup>2</sup>*ρок* (12)

Pa in which for *<sup>ρ</sup>*<sup>0</sup> is received *<sup>ρ</sup>* <sup>¼</sup> <sup>0</sup>*:*58 kg*=*m3.

*b* ¼ 0*:*163*x* (13)

• for export of vertical upward mass flow

$$\frac{d}{d\mathfrak{x}}\limits\_{\mathfrak{l}}^{b}u(\rho-\rho\_{\alpha\mathbf{x}})(\pi\mathfrak{y})^{j}d\mathfrak{y}=\mathbf{0}\tag{6}$$

A simple solution can be made as (5) of enthalpy is replaced by a linear dependence on the widening of the jet

$$b = c\mathfrak{x} \tag{7}$$

On the right-hand side of Eq. (4) is written the Archimedes buoyancy. The significance of included symbols is as follows: *u* is the jet velocity; *y* is the transverse coordinate; *ρ* is the current density; *ρок* is the density of the environment; and Δ*h* is the enthalpy of the stream. The exponent j signifies: at j = 0 a flat stream and j = 1 an axis jet. The coordinate x is directed vertically upward.

There is a correlation between density and temperature:

$$
\rho = \frac{p}{RT},
\tag{8}
$$

where *p* is the pressure of the environment, *R* is the gas constant, and *T* is the absolute temperature. Similarity to transverse distribution of the velocity and the density (temperature) are initiated [1, 2], where solving Eqs. (4) and (6) leads to the parameters of the upward convective stream:

• the velocity of the upward stream

$$
\mu\_m = B\_u^{\prime \prime} D\_0^{1\_\circ} \Delta T\_{ni}^{4\_\circ} \overline{\mathfrak{X}}^{4\_\circ} \tag{9}
$$

• the temperature difference

$$
\Delta T\_m = T\_m - T\_{env} = B\_{\Delta T}^{\prime \prime} D\_0^{1\natural} \Delta T^{\prime \natural} \overline{\mathfrak{X}}^{\natural \natural},\tag{10}
$$

where *D*<sup>0</sup> is the initial diameter of the heat source of fire (the burning car); <sup>Δ</sup>*T*<sup>1</sup> <sup>¼</sup> *Tfl* � *<sup>Т</sup>env*; *<sup>x</sup>* <sup>¼</sup> *<sup>x</sup> D*<sup>0</sup> ; the constants *B*<sup>00</sup> *<sup>u</sup>* and *B*<sup>00</sup> <sup>Δ</sup>*<sup>T</sup>* have values *B*<sup>00</sup> *<sup>u</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>222</sup> *<sup>m</sup>*<sup>3</sup>*K*<sup>9</sup>*=*4 � �, *B*00 <sup>Δ</sup>*<sup>T</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>71</sup> *<sup>m</sup>*<sup>1</sup>*=*<sup>3</sup>*K*<sup>9</sup>*=*<sup>8</sup> � �.

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

These values correspond to the case at *<sup>x</sup>* <sup>¼</sup> *<sup>x</sup> <sup>D</sup>*<sup>0</sup> ≥ 3÷3*:*5. When adopted fire size created from a burning car *D*<sup>0</sup> ¼ 0*:*5 m and height *H* ¼ 3÷4*:*5*m*, *x* of the garage will be always greater than the above values.

At the relatively short distance to the ceiling, the high power of fire (the accepted conditions are *Q* ¼ 1500W and *T* ¼ 600K), the velocity and the temperature of the rising convective stream do not change significantly.

The initial velocity calculated by Eq. (3) is *u*<sup>0</sup> ¼ 8*:*2 m*=*s and the time when the convective stream will reach the ceiling at different heights of the garage is given in **Table 1**.

This means that less than 1 s sprinklers over the burning car will be activated and extinguishing stream will flow over the burning car.

The expansion (increasing of thickness) of the jet in height can be determined by the expression:

$$\frac{db}{d\mathbf{x}} = \mathbf{0}.22 \frac{\rho\_0 + \rho\_{\rm oc}}{2\rho\_{\rm oc}},\tag{11}$$

where,

• for amount of movement

*Fire Safety and Management Awareness*

• to preserve enthalpy flow

dence on the widening of the jet

*d dx* ð *b*

• for export of vertical upward mass flow

0

*<sup>ρ</sup>u*<sup>2</sup> *<sup>π</sup>y<sup>j</sup>* � �*dy* ¼ �*<sup>g</sup>*

*d dx* ð *b*

*d dx* ð *b*

axis jet. The coordinate x is directed vertically upward.

the parameters of the upward convective stream:

• the velocity of the upward stream

*D*<sup>0</sup>

• the temperature difference

<sup>Δ</sup>*T*<sup>1</sup> <sup>¼</sup> *Tfl* � *<sup>Т</sup>env*; *<sup>x</sup>* <sup>¼</sup> *<sup>x</sup>*

<sup>Δ</sup>*<sup>T</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>71</sup> *<sup>m</sup>*<sup>1</sup>*=*<sup>3</sup>*K*<sup>9</sup>*=*<sup>8</sup> � �.

*B*00

**50**

There is a correlation between density and temperature:

0

0

*ρ*Δ*huy <sup>j</sup>*

*<sup>u</sup> <sup>ρ</sup>* � *<sup>ρ</sup>ок* ð Þð Þ *<sup>π</sup><sup>y</sup> <sup>j</sup>*

A simple solution can be made as (5) of enthalpy is replaced by a linear depen-

On the right-hand side of Eq. (4) is written the Archimedes buoyancy. The significance of included symbols is as follows: *u* is the jet velocity; *y* is the transverse coordinate; *ρ* is the current density; *ρок* is the density of the environment; and Δ*h* is the enthalpy of the stream. The exponent j signifies: at j = 0 a flat stream and j = 1 an

*<sup>ρ</sup>* <sup>¼</sup> *<sup>p</sup>*

*um* ¼ *B*<sup>00</sup> *uD* 1*=*3 <sup>0</sup> Δ*T* 4*=*9 *пл x*<sup>1</sup>*=*

Δ*Tm* ¼ *Tm* � *Tenv* ¼ *B*<sup>00</sup>

; the constants *B*<sup>00</sup>

where *D*<sup>0</sup> is the initial diameter of the heat source of fire (the burning car);

where *p* is the pressure of the environment, *R* is the gas constant, and *T* is the absolute temperature. Similarity to transverse distribution of the velocity and the density (temperature) are initiated [1, 2], where solving Eqs. (4) and (6) leads to

> <sup>Δ</sup>*TD* 1*=*3 <sup>0</sup> Δ*T*<sup>8</sup>*=*9*x*5*=*

> > <sup>Δ</sup>*<sup>T</sup>* have values *B*<sup>00</sup>

*<sup>u</sup>* and *B*<sup>00</sup>

ð *b*

*<sup>ρ</sup>* � *<sup>ρ</sup>ок* ð Þð Þ *<sup>π</sup><sup>y</sup> <sup>j</sup>*

*dy* (4)

*dy* ¼ 0 (5)

*dy* ¼ 0 (6)

*b* ¼ *cx* (7)

*RT* , (8)

<sup>3</sup> (9)

3, (10)

*<sup>u</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>222</sup> *<sup>m</sup>*<sup>3</sup>*K*<sup>9</sup>

*=*4 � �,

0

$$b = \left[0.22 \frac{\rho\_0 + \rho\_{\text{ox}}}{2\rho\_{\text{ox}}}\right] \tag{12}$$

The density of the jet in the opening section is defined by Eq. (8): at *R* ¼ 287 J*=*kgK, *<sup>T</sup>*<sup>0</sup> <sup>¼</sup> 600 K, *<sup>p</sup>* <sup>¼</sup> <sup>10</sup><sup>5</sup> Pa in which for *<sup>ρ</sup>*<sup>0</sup> is received *<sup>ρ</sup>* <sup>¼</sup> <sup>0</sup>*:*58 kg*=*m3. The density of the environment is *<sup>ρ</sup>env* <sup>¼</sup> <sup>11</sup>*:*2 kg*=*m<sup>3</sup> at the same pressure and temperature *Tenv* ¼ 293 K. At this density, the widening of the jet in the present case is

$$b = 0.163x \tag{13}$$

For a different height in the garage, the parameter *b* is given in **Table 2**.

The last row in **Table 2** is given the extension of the isothermal jetð Þ *T*<sup>0</sup> ≈*Tenv* . Obviously a slight extension of non-isothermal convective flow comparing with the isothermal.

Reaching the ceiling vertical, the convective stream is transformed into radial jet (**Figure 4**).


**Table 1.**

*h—height of the garage, m; Δ*t*—time of the fire to reach the ceiling, m.*


#### **Table 2.**

*h—height of the garage, m; b0—initial width of the radial jet, m; b1—width of the radial jet, m.*

Due to the weak widening of the jet and the short distance to the ceiling, the mass flow is not increased significantly because the temperature, density, and relatively low mileage ceiling have not changed. The jet has retained its temperature and density, and the velocity according to [14] may be determined:

$$
u\_{\text{max}} = \mathbf{0}.88u\_0,\tag{14}$$

According to **Figure 4**, it is assumed *D*<sup>0</sup> ¼ *b*<sup>1</sup> that is already known and for flow

*b*0 <sup>0</sup> <sup>¼</sup> *<sup>Q</sup> πD*<sup>0</sup>

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

The cross-section of the radial jet as a function of *r* is determined by the

*S* ¼ 2*πrb*<sup>0</sup>

where *r* is the current radius, *b*<sup>0</sup> is the width of the jet to the corresponding *r*. Since the resulting stream is parietal and has parietal boundary layer whose

The width *b*<sup>0</sup> is calculated by Eq. (12) and for the case in Eq. (13) by replacing *x*

0 *r*;*c*

> 0 *r*

*S* ¼ 2*:*2*πc*

, Eq. (19) can be recast in the form:

<sup>0</sup> is calculated:

*:* (18)

, (19)

*S* ¼ 2*:*2*rb*<sup>0</sup> (20)

2*ρok*

<sup>2</sup> (22)

, (21)

<sup>0</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>22</sup> *<sup>ρ</sup><sup>o</sup>* <sup>þ</sup> *<sup>ρ</sup>ok*

rate in Eq. (16), the original width of the radial jet *b*<sup>0</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

The relationship *b*0ð Þ¼ *x f x*ð Þ is given in **Figure 6**.

*<sup>b</sup>*<sup>0</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>22</sup> *<sup>ρ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>ρ</sup>ok*

When substituted in Eq. (19) we get the following:

<sup>2</sup>*ρok <sup>r</sup>* <sup>¼</sup> *<sup>c</sup>*

expression:

thickness is approximately 0.1*b*<sup>0</sup>

respectively, *b*<sup>0</sup> ¼ 0*:*163*r*.

*Change of the flow rate at different heights of the garage.*

*Change of the initial weight at different heights of the garage.*

with *r*, then we have:

**Figure 5.**

**Figure 6.**

**53**

where for *u*<sup>0</sup> ¼ 8*:*2 m*=*s it is *u*max ¼ 7*:*2 m*=*s.

It is assumed that the starting size of the radial jet is equal to that obtained in **Table 2**, *b*1, that is *D*<sup>0</sup> ¼ *b*1.

Width of the radial jet *b*<sup>0</sup> is determined by the flow rate *Q* at the intersection of the reverse flow. The flow rate is amount of initial flow rates *Q*<sup>0</sup> and increase its height due to suction of air from the environment. The flow rate of ejecting fluid is considered proportional to the square of the relative increase in the width of the jet *b*1�*b*<sup>0</sup> *b*0 <sup>2</sup> and the distance *x* divided by the duration of the process Δ*t*.

$$Q\_{cj} \approx \left(\frac{b\_1 - b\_0}{b\_0}\right)^2 \frac{\varkappa}{\Delta t}, \text{m}^3/\text{s} \tag{15}$$

In this, total flow rate is obtained as the sum of normal and ejecting flow rate:

$$Q = Q\_0 + Q\_{\neq}, \mathbf{m}^3/\mathbf{s},\tag{16}$$

where *Q*<sup>0</sup> ¼ *u*<sup>0</sup> *πd*<sup>2</sup> *n* <sup>4</sup> , when *dn* ¼ 0*:*5 m and *u*<sup>0</sup> ¼ 8 m*=*s we have:

$$Q = Q\_0 + Q\_{\varepsilon j} = u\_0 \frac{\pi d\_n^2}{4} + \left(\frac{b\_1 - b\_0}{b\_0}\right)^2 \frac{\varkappa}{\Delta t} \tag{17}$$

The flow rate of the respective heights *x* ¼ 3; 3*:*5; 4; 4*:*5 m of the garage is shown in **Figure 5** where it is defined by the relationship given in Eq. (12), respectively and in case of a leak by Eq. (13).

**Figure 4.** *Sketch of radial jet.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

According to **Figure 4**, it is assumed *D*<sup>0</sup> ¼ *b*<sup>1</sup> that is already known and for flow rate in Eq. (16), the original width of the radial jet *b*<sup>0</sup> <sup>0</sup> is calculated:

$$b\_0' = \frac{Q}{\pi D\_0}.\tag{18}$$

The relationship *b*0ð Þ¼ *x f x*ð Þ is given in **Figure 6**.

The cross-section of the radial jet as a function of *r* is determined by the expression:

$$S = 2\pi r b',\tag{19}$$

where *r* is the current radius, *b*<sup>0</sup> is the width of the jet to the corresponding *r*. Since the resulting stream is parietal and has parietal boundary layer whose thickness is approximately 0.1*b*<sup>0</sup> , Eq. (19) can be recast in the form:

$$S = 2.2rb'\tag{20}$$

The width *b*<sup>0</sup> is calculated by Eq. (12) and for the case in Eq. (13) by replacing *x* with *r*, then we have:

$$b' = \left[ 0.22 \frac{\rho\_0 + \rho\_{ok}}{2\rho\_{ok}} \right] r = c' r; c' = 0.22 \frac{\rho\_o + \rho\_{ok}}{2\rho\_{ok}},\tag{21}$$

respectively, *b*<sup>0</sup> ¼ 0*:*163*r*.

Due to the weak widening of the jet and the short distance to the ceiling, the mass flow is not increased significantly because the temperature, density, and relatively low mileage ceiling have not changed. The jet has retained its temperature

It is assumed that the starting size of the radial jet is equal to that obtained in

and the distance *x* divided by the duration of the process Δ*t*.

In this, total flow rate is obtained as the sum of normal and ejecting flow rate:

<sup>4</sup> , when *dn* ¼ 0*:*5 m and *u*<sup>0</sup> ¼ 8 m*=*s we have:

*πd*<sup>2</sup> *n* 4 þ

The flow rate of the respective heights *x* ¼ 3; 3*:*5; 4; 4*:*5 m of the garage is shown in **Figure 5** where it is defined by the relationship given in Eq. (12), respectively and

*b*<sup>1</sup> � *b*<sup>0</sup> *b*0 <sup>2</sup>

*<sup>Q</sup>* <sup>¼</sup> *<sup>Q</sup>*<sup>0</sup> <sup>þ</sup> *<sup>Q</sup><sup>е</sup>j*, m<sup>3</sup>

*Qej* <sup>≈</sup> *<sup>b</sup>*<sup>1</sup> � *<sup>b</sup>*<sup>0</sup> *b*0 <sup>2</sup>

*Q* ¼ *Q*<sup>0</sup> þ *Q<sup>е</sup><sup>j</sup>* ¼ *u*<sup>0</sup>

Width of the radial jet *b*<sup>0</sup> is determined by the flow rate *Q* at the intersection of the reverse flow. The flow rate is amount of initial flow rates *Q*<sup>0</sup> and increase its height due to suction of air from the environment. The flow rate of ejecting fluid is considered proportional to the square of the relative increase in the width of the jet

> *x* Δ*t* , m<sup>3</sup>

*u*max ¼ 0*:*88*u*0, (14)

*=*s (15)

*=*s, (16)

<sup>Δ</sup>*<sup>t</sup>* (17)

*x*

and density, and the velocity according to [14] may be determined:

where for *u*<sup>0</sup> ¼ 8*:*2 m*=*s it is *u*max ¼ 7*:*2 m*=*s.

**Table 2**, *b*1, that is *D*<sup>0</sup> ¼ *b*1.

*Fire Safety and Management Awareness*

where *Q*<sup>0</sup> ¼ *u*<sup>0</sup>

in case of a leak by Eq. (13).

*πd*<sup>2</sup> *n*

*b*1�*b*<sup>0</sup> *b*0 <sup>2</sup>

**Figure 4.** *Sketch of radial jet.*

**52**

When substituted in Eq. (19) we get the following:

$$S = 2.2\pi c'r^2\tag{22}$$

**Figure 5.** *Change of the flow rate at different heights of the garage.*

**Figure 6.** *Change of the initial weight at different heights of the garage.*

The average velocity of the ceiling of the room depending on *r* is obtained by:

$$
u\_m = \frac{\mathcal{Q}}{\mathcal{S}}\,,\tag{23}$$

In the vicinity of the burning car to sprinkler curtain, a distance of *l*≤2 m will trigger three (to five) fast sprinklers. At a longer distance, it will trigger maximum of three quick sprinklers of water curtain plus the main ones over the burning car and eventually those are lying in the range of *l* ¼ 4 m ceiling sprinklers so that the

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

To create a smokeless zone under a layer of smoke floating [14], air exhaust systems are designed and installed for smoke and hot gases. An exhaust ventilation system for smoke and hot gases is a scheme of safety equipment designed to perform a positive role in spin fire. The smoke is drawn in the direction of the noncarrier partition EI from a velocity of 2 m/s to 5 m/s. Standard allowed velocity of 5 m/s, but it should be taken into consideration that this velocity would affect

From Abramovich [14], the density of the thermal load in the premises for the storage of combustible materials according to their purpose, is determined the heat capacity of the prevailing materials. The ventilation system to remove smoke and heat (VSRSH) has to reach its designed performance level within 60 s of receiving the command signal. Each VSRSH has to ensure receipt of sufficient fresh air that

Heat transfer by convection and radiation is defined according to [3, 10]. Thermal effects are expressed by the intensity of the heat flow *hnbt*,W*=*m<sup>2</sup> to the surface of the element is determined taking into account the heat transfer by convection

*hnbt* <sup>¼</sup> *hnbt*,*<sup>c</sup>* <sup>þ</sup> *hnbt*,*<sup>r</sup>*,W*=*m<sup>2</sup>

*hnbt*,*<sup>r</sup>* <sup>¼</sup> <sup>Φ</sup>*εmε<sup>f</sup> σ θ*ð Þ <sup>1</sup>*<sup>r</sup>* <sup>þ</sup> <sup>273</sup> <sup>2</sup> � ð Þ *<sup>θ</sup><sup>m</sup>* <sup>þ</sup> <sup>273</sup> <sup>4</sup> h i,W*=*m<sup>2</sup> (28)

where heat transfer by convection *hnbt*,*<sup>c</sup>* is given by the relationship

*hnbt*,*<sup>c</sup>* ¼ *α<sup>c</sup> θ<sup>g</sup>* � *θ<sup>m</sup>*

Convection component of the intensity of the heat flow is determined by:

temperature near the exposed fire element [°C]; and *θ<sup>m</sup>* is the surface temperature

Radiating components of net heat flux per unit surface area are defined as *hnbt*,*<sup>r</sup>* ¼

The coefficient of heat transfer by convection *α<sup>c</sup>* is determined by the nominal curves corresponding to "temperature–time." On indirectly heated surface elements, the intensity of heat flow *hnbt* is determined by Eq. (16) where *<sup>α</sup><sup>c</sup>* <sup>¼</sup> <sup>4</sup> <sup>W</sup>

*hnbt*,*<sup>t</sup>* ¼ *α<sup>c</sup> θ<sup>g</sup>* � *θ<sup>m</sup>*

radiation heat transfer *hnbt*,*<sup>r</sup>* is given by the dependence:

where *α<sup>c</sup>* is the heat transfer coefficient by convection <sup>W</sup>

The coefficient of heat transfer by convection has value *<sup>α</sup><sup>c</sup>* <sup>¼</sup> <sup>9</sup> <sup>W</sup>

<sup>Φ</sup>*εm<sup>ε</sup> <sup>f</sup> σ θ*ð Þ <sup>1</sup>*<sup>r</sup>* <sup>þ</sup> <sup>273</sup> <sup>2</sup> � ð Þ *<sup>θ</sup><sup>m</sup>* <sup>þ</sup> <sup>273</sup> <sup>4</sup> h i,W*=*m<sup>2</sup>

considering that the effects of heat transfer by radiation are included.

, (26)

m2 <sup>K</sup> � �; *<sup>θ</sup><sup>g</sup>* is the gas

m2 <sup>K</sup> � �,

, where: Ф is the factor of configuration,

m2 <sup>K</sup> � �.

� �,W*=*m<sup>2</sup> (27)

� �,W*=*m<sup>2</sup> (29)

number of activated sprinklers will increase [10].

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

negatively and lead to the merging of streams of pure air.

enters the room for the expense of the flue products.

**2.3 Thermal impact**

and radiation, such as:

of the element [°C].

**55**

respectively:

$$
\mu\_m = \frac{Q}{2.2\pi c'r^2}, \text{m/s} \tag{24}
$$

Parking average velocity depending on *r* at the four heights is shown in **Figure 7**. **Figure 8** shows the time to reach the appropriate distance:

$$
\Delta t = \frac{r}{u\_m},
\text{s}
\tag{25}
$$

This means that in the first 2 s, all sprinklers at distance of 2 m away from the burning car will be triggered. For longer distances, the remote sprinklers will act at a condition if the temperature of the burning car does not decrease too quickly. For maximum calculated time of 7.7 s could not be expected too much decrease of the temperature, which leads to the conclusion that the ceiling temperature will be much greater than the starting temperature of "fast" sprinklers so that at *tp* ¼ 57°C or T = 330°K will always remain less than the temperature of the wall jet which initial temperature is 600°K.

With the removal from the water curtain, it is possible to turn on the other ceiling sprinklers that are in the range.

**Figure 7.** *Average velocity at different heights of garage.*

**Figure 8.** *Time to reach the sprinklers at different heights of garage.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

In the vicinity of the burning car to sprinkler curtain, a distance of *l*≤2 m will trigger three (to five) fast sprinklers. At a longer distance, it will trigger maximum of three quick sprinklers of water curtain plus the main ones over the burning car and eventually those are lying in the range of *l* ¼ 4 m ceiling sprinklers so that the number of activated sprinklers will increase [10].

To create a smokeless zone under a layer of smoke floating [14], air exhaust systems are designed and installed for smoke and hot gases. An exhaust ventilation system for smoke and hot gases is a scheme of safety equipment designed to perform a positive role in spin fire. The smoke is drawn in the direction of the noncarrier partition EI from a velocity of 2 m/s to 5 m/s. Standard allowed velocity of 5 m/s, but it should be taken into consideration that this velocity would affect negatively and lead to the merging of streams of pure air.

From Abramovich [14], the density of the thermal load in the premises for the storage of combustible materials according to their purpose, is determined the heat capacity of the prevailing materials. The ventilation system to remove smoke and heat (VSRSH) has to reach its designed performance level within 60 s of receiving the command signal. Each VSRSH has to ensure receipt of sufficient fresh air that enters the room for the expense of the flue products.

#### **2.3 Thermal impact**

The average velocity of the ceiling of the room depending on *r* is obtained by:

*um* <sup>¼</sup> *<sup>Q</sup>*

Parking average velocity depending on *r* at the four heights is shown in **Figure 7**.

<sup>Δ</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>r</sup> um*

This means that in the first 2 s, all sprinklers at distance of 2 m away from the burning car will be triggered. For longer distances, the remote sprinklers will act at a condition if the temperature of the burning car does not decrease too quickly. For maximum calculated time of 7.7 s could not be expected too much decrease of the temperature, which leads to the conclusion that the ceiling temperature will be much greater than the starting temperature of "fast" sprinklers so that at *tp* ¼ 57°C or T = 330°K will always remain less than the temperature of the wall jet which

With the removal from the water curtain, it is possible to turn on the other

*um* <sup>¼</sup> *<sup>Q</sup>* 2*:*2*πc*<sup>0</sup>

**Figure 8** shows the time to reach the appropriate distance:

respectively:

*Fire Safety and Management Awareness*

initial temperature is 600°K.

**Figure 7.**

**Figure 8.**

**54**

ceiling sprinklers that are in the range.

*Average velocity at different heights of garage.*

*Time to reach the sprinklers at different heights of garage.*

*<sup>S</sup>* , (23)

*<sup>r</sup>*<sup>2</sup> , m*=*<sup>s</sup> (24)

, s (25)

Heat transfer by convection and radiation is defined according to [3, 10]. Thermal effects are expressed by the intensity of the heat flow *hnbt*,W*=*m<sup>2</sup> to the surface of the element is determined taking into account the heat transfer by convection and radiation, such as:

$$h\_{nbt} = h\_{nbt, \varepsilon} + h\_{nbt, r} \text{ W/m}^2,\tag{26}$$

where heat transfer by convection *hnbt*,*<sup>c</sup>* is given by the relationship

$$h\_{\rm nbt,c} = a\_c (\theta\_\text{g} - \theta\_\text{m}) \text{, W/m}^2 \tag{27}$$

radiation heat transfer *hnbt*,*<sup>r</sup>* is given by the dependence:

$$h\_{nbt,r} = \Phi \varepsilon\_m \varepsilon\_f \sigma \left[ \left( \theta\_1 r + 273 \right)^2 - \left( \theta\_m + 273 \right)^4 \right], \text{W/m}^2 \tag{28}$$

Convection component of the intensity of the heat flow is determined by:

$$h\_{nbt,t} = a\_c (\theta\_\text{g} - \theta\_m), \text{W/m}^2 \tag{29}$$

where *α<sup>c</sup>* is the heat transfer coefficient by convection <sup>W</sup> m2 <sup>K</sup> � �; *<sup>θ</sup><sup>g</sup>* is the gas temperature near the exposed fire element [°C]; and *θ<sup>m</sup>* is the surface temperature of the element [°C].

The coefficient of heat transfer by convection *α<sup>c</sup>* is determined by the nominal curves corresponding to "temperature–time." On indirectly heated surface elements, the intensity of heat flow *hnbt* is determined by Eq. (16) where *<sup>α</sup><sup>c</sup>* <sup>¼</sup> <sup>4</sup> <sup>W</sup> m2 <sup>K</sup> � �. The coefficient of heat transfer by convection has value *<sup>α</sup><sup>c</sup>* <sup>¼</sup> <sup>9</sup> <sup>W</sup> m2 <sup>K</sup> � �, considering that the effects of heat transfer by radiation are included.

Radiating components of net heat flux per unit surface area are defined as *hnbt*,*<sup>r</sup>* ¼ <sup>Φ</sup>*εm<sup>ε</sup> <sup>f</sup> σ θ*ð Þ <sup>1</sup>*<sup>r</sup>* <sup>þ</sup> <sup>273</sup> <sup>2</sup> � ð Þ *<sup>θ</sup><sup>m</sup>* <sup>þ</sup> <sup>273</sup> <sup>4</sup> h i,W*=*m<sup>2</sup> , where: Ф is the factor of configuration, *<sup>ε</sup><sup>m</sup>* is the emitting surface element, *<sup>ε</sup> <sup>f</sup>* the transmission of fire, *<sup>σ</sup>* <sup>¼</sup> <sup>5</sup>*:*<sup>67</sup> � <sup>10</sup><sup>8</sup> WK4 m2 h i is the constant of Stefan-Boltzmann, *θ<sup>r</sup>* is the effective temperature of the radiation environment [**°**C], and *θ<sup>m</sup>* is the surface temperature of the element [**°**C]. Transmission of fire is equal to *ε <sup>f</sup>* ¼ 1.

*<sup>R</sup>* <sup>¼</sup> *<sup>δ</sup>*

*Q* ¼ 0*:*666*μρ*

For the whole surface of the water curtain:

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

4–6 mH2O.

**space**

explosions.

*ρ ∂u ∂t* þ *ρu ∂u ∂x* þ *ρv ∂u ∂y* þ *ρw*

*ρ ∂v ∂t* þ *ρu ∂v ∂x* þ *ρv ∂v ∂y* þ *ρw ∂v <sup>∂</sup><sup>z</sup>* ¼ � *<sup>∂</sup><sup>p</sup> ∂y* þ *μ*

**57**

assumed: *divV*!

<sup>¼</sup> 0, *<sup>∂</sup><sup>u</sup>*

Equations for movements [9].

Continuity equation:

for the optical density of the gas mixture.

*<sup>∂</sup><sup>x</sup>* <sup>þ</sup> *<sup>∂</sup><sup>v</sup> <sup>∂</sup><sup>y</sup>* <sup>þ</sup> *<sup>∂</sup><sup>w</sup>*

> *∂ρ ∂t* þ *<sup>∂</sup>*ð Þ *<sup>ρ</sup><sup>u</sup> ∂x* þ *<sup>∂</sup>*ð Þ *<sup>ρ</sup><sup>v</sup> ∂y* þ

*∂u <sup>∂</sup><sup>z</sup>* ¼ � *<sup>∂</sup><sup>p</sup> ∂x* þ *μ*

þ *∂ ∂y μT ∂u ∂y* þ *∂v ∂x*

þ *∂ ∂x μT ∂u ∂y* þ *∂v ∂x*

*<sup>c</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>51</sup>

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

Flow rate of the water curtain for 1 m<sup>2</sup> of lateral surface is defined by:

*rR H*

ffiffiffiffiffiffiffi <sup>2</sup>*gh* <sup>p</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>467</sup> *<sup>l</sup>*

Water curtains are constructed so that the entire hole is irrigated with finely dispersed water. For this purpose, sprinklers are placed over the hole and next to it. When they are placed at the top of the hole, it is possible for unprotected areas to remain through which it is possible for a penetration of hot gases to occur.

Sprinkler heads that are used to spray jets are spaced 0.5 m in protecting small

holes and 1.25–1.5 m in protecting large holes. For sprinkler heads which are situated at a distance greater than 3 m, it is required head pressure of the water

**3. Numerical simulations: mathematical model of flow in a confined**

mechanics of fluids. These are the continuity equations, the Navier-Stokes equations in modification according to the Businex hypothesis (μeff = μ + μt), the energy equation (1st law of Thermodynamics), the Clapeyron equation for the gas

mixture. Fire currents run at low speeds in the absence of detonation and

*<sup>∂</sup><sup>z</sup>* � 0.

The mathematical model is based on the equations used in the computational

In the case of a fire without detonation, combustion, and explosions, it can be

To these are added the equations for smoke propagation (smoke content) and

*∂*2 *u ∂x*<sup>2</sup> þ

*∂*2 *v ∂x*<sup>2</sup> þ

� � � �

� � � �

*<sup>∂</sup>*ð Þ *<sup>ρ</sup><sup>w</sup>*

*∂*2 *u ∂y*<sup>2</sup> þ

*∂*2 *v ∂y*<sup>2</sup> þ

� �

� �

*∂*2 *u ∂z*<sup>2</sup>

þ *∂ ∂z μT ∂u ∂z* þ *∂w ∂x* � � � � (36)

*∂*2 *v ∂z*<sup>2</sup>

þ *∂ ∂z μT ∂v ∂z* þ *∂w ∂x* � � � � (37)

*<sup>∂</sup><sup>z</sup>* <sup>¼</sup> *<sup>J</sup>* (35)

<sup>þ</sup> <sup>2</sup> *<sup>∂</sup> ∂x μT ∂u ∂x* � �

<sup>þ</sup> <sup>2</sup> *<sup>∂</sup> ∂y μT ∂v ∂y* � �

<sup>2</sup>*:*<sup>8</sup> <sup>¼</sup> <sup>0</sup>*:*182 m (32)

m2 (33)

*s*

*<sup>Q</sup><sup>H</sup>* <sup>¼</sup> <sup>11</sup>*:*2*l=<sup>s</sup>* (34)

#### **2.4 Determination of the intensity of water curtain**

Because of the difficulties associated with the construction of fire walls, experiments are conducted so that these areas to be reduced to such proportions that the primarily split up do not disturb of the process. In many cases, such as in buildings of first degree of fire resistance, as already noted, firewalls did not provide the detriment of fire safety. In connection with this arises a need of using such fire barriers that could effectively limit the spread of fire and at the same time would give some freedom for internal layout of buildings with different functions, which is the case of the water curtain [15].

When calculating water curtains, the assumption must simultaneously satisfy the following conditions:

Structural parts of the building to withstand the effects of fire on one side and the passage of flames or hot gases to be prevented by the transfer of heat to the unexposed side. The ability of the structural parts of the building to withstand the effects of fire on one side and prevent the transfer of heat from the exposed to the unexposed side. The transfer is limited so that it does not ignite either the unexposed surface, or any other material in the immediate vicinity. The structural element is designed to serve as a barrier against the heat and to ensure the protection of people who are close to it.

The effectiveness of water curtains is assessed according to the amount of absorbed heat.

It is known that the dependence of the growth temperature of the source of radiation of maximum energy moves to the side of the shorter waves. This follows from the law of Vin:

$$
\lambda\_{\text{max},T}T = 0.29 = \text{const} \tag{30}
$$

where *λ* is the wavelength in m,*T* is the temperature at the surface of water curtain, °K.

Good enough inter-phase and heat-absorbing surfaces have water drops of size <sup>200</sup> � <sup>10</sup>�<sup>6</sup> . It is considered that in the best case, sprinklers spray water of size less then 1000 μm.

#### **2.5 Required flow rate for air curtain**

The current has the following characteristics: density of the radiation heat flux is 1500 W/m2 ; density of the irradiation protected material is 900 W/m<sup>2</sup> ; height of the hole–4 m; length of the hole–6 m; pressure of water in sprinkler–0.6 MPa (6 atm) and the radius of the water drops–0.0006 m (600 μm).

Opacity density of the curtain:

$$\delta = \frac{2.303 \log q\_{\text{max}}}{q\_{\text{wp}}} = 0.51 \tag{31}$$

Thickness of the curtain:

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

$$R = \frac{\delta}{c} = \frac{0.51}{2.8} = 0.182 \text{ m} \tag{32}$$

Flow rate of the water curtain for 1 m<sup>2</sup> of lateral surface is defined by:

$$Q = 0.666 \mu \rho \frac{rR}{H} \sqrt{2gh} = 0.467 \frac{l}{s} \text{ m}^2 \tag{33}$$

For the whole surface of the water curtain:

*<sup>ε</sup><sup>m</sup>* is the emitting surface element, *<sup>ε</sup> <sup>f</sup>* the transmission of fire, *<sup>σ</sup>* <sup>¼</sup> <sup>5</sup>*:*<sup>67</sup> � <sup>10</sup><sup>8</sup> WK4

environment [**°**C], and *θ<sup>m</sup>* is the surface temperature of the element [**°**C].

Transmission of fire is equal to *ε <sup>f</sup>* ¼ 1.

*Fire Safety and Management Awareness*

is the case of the water curtain [15].

tion of people who are close to it.

**2.5 Required flow rate for air curtain**

Opacity density of the curtain:

Thickness of the curtain:

and the radius of the water drops–0.0006 m (600 μm).

absorbed heat.

curtain, °K.

<sup>200</sup> � <sup>10</sup>�<sup>6</sup>

1500 W/m2

**56**

then 1000 μm.

from the law of Vin:

the following conditions:

**2.4 Determination of the intensity of water curtain**

is the constant of Stefan-Boltzmann, *θ<sup>r</sup>* is the effective temperature of the radiation

Because of the difficulties associated with the construction of fire walls, experiments are conducted so that these areas to be reduced to such proportions that the primarily split up do not disturb of the process. In many cases, such as in buildings of first degree of fire resistance, as already noted, firewalls did not provide the detriment of fire safety. In connection with this arises a need of using such fire barriers that could effectively limit the spread of fire and at the same time would give some freedom for internal layout of buildings with different functions, which

When calculating water curtains, the assumption must simultaneously satisfy

Structural parts of the building to withstand the effects of fire on one side and the passage of flames or hot gases to be prevented by the transfer of heat to the unexposed side. The ability of the structural parts of the building to withstand the effects of fire on one side and prevent the transfer of heat from the exposed to the

unexposed surface, or any other material in the immediate vicinity. The structural element is designed to serve as a barrier against the heat and to ensure the protec-

The effectiveness of water curtains is assessed according to the amount of

It is known that the dependence of the growth temperature of the source of radiation of maximum energy moves to the side of the shorter waves. This follows

where *λ* is the wavelength in m,*T* is the temperature at the surface of water

Good enough inter-phase and heat-absorbing surfaces have water drops of size

The current has the following characteristics: density of the radiation heat flux is

; density of the irradiation protected material is 900 W/m<sup>2</sup>

hole–4 m; length of the hole–6 m; pressure of water in sprinkler–0.6 MPa (6 atm)

*<sup>δ</sup>* <sup>¼</sup> <sup>2</sup>*:*303 log *<sup>q</sup>изл qкр*

. It is considered that in the best case, sprinklers spray water of size less

*λ* max ,*TT* ¼ 0*:*29 ¼ *const* (30)

; height of the

¼ 0*:*51 (31)

unexposed side. The transfer is limited so that it does not ignite either the

m2 h i

$$\mathbf{Q}^{H} = \mathbf{11.2l/s} \tag{34}$$

Water curtains are constructed so that the entire hole is irrigated with finely dispersed water. For this purpose, sprinklers are placed over the hole and next to it. When they are placed at the top of the hole, it is possible for unprotected areas to remain through which it is possible for a penetration of hot gases to occur.

Sprinkler heads that are used to spray jets are spaced 0.5 m in protecting small holes and 1.25–1.5 m in protecting large holes. For sprinkler heads which are situated at a distance greater than 3 m, it is required head pressure of the water 4–6 mH2O.

#### **3. Numerical simulations: mathematical model of flow in a confined space**

The mathematical model is based on the equations used in the computational mechanics of fluids. These are the continuity equations, the Navier-Stokes equations in modification according to the Businex hypothesis (μeff = μ + μt), the energy equation (1st law of Thermodynamics), the Clapeyron equation for the gas mixture. Fire currents run at low speeds in the absence of detonation and explosions.

In the case of a fire without detonation, combustion, and explosions, it can be assumed: *divV*! <sup>¼</sup> 0, *<sup>∂</sup><sup>u</sup> <sup>∂</sup><sup>x</sup>* <sup>þ</sup> *<sup>∂</sup><sup>v</sup> <sup>∂</sup><sup>y</sup>* <sup>þ</sup> *<sup>∂</sup><sup>w</sup> <sup>∂</sup><sup>z</sup>* � 0.

To these are added the equations for smoke propagation (smoke content) and for the optical density of the gas mixture.

Continuity equation:

$$\frac{\partial \rho}{\partial t} + \frac{\partial(\rho u)}{\partial \mathbf{x}} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial \mathbf{z}} = f \tag{35}$$

Equations for movements [9].

$$\begin{split} \rho \frac{\partial u}{\partial t} + \rho u \frac{\partial u}{\partial x} + \rho v \frac{\partial u}{\partial y} + \rho w \frac{\partial u}{\partial z} &= -\frac{\partial p}{\partial x} + \mu \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} \right) + 2 \frac{\partial}{\partial x} \left[ \mu\_T \frac{\partial u}{\partial x} \right] \\ &+ \frac{\partial}{\partial y} \left[ \mu\_T \left( \frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} \right) \right] + \frac{\partial}{\partial x} \left[ \mu\_T \left( \frac{\partial u}{\partial z} + \frac{\partial w}{\partial x} \right) \right] \end{split} \tag{36}$$

$$\begin{split} \rho \frac{\partial v}{\partial t} + \rho u \frac{\partial v}{\partial x} + \rho v \frac{\partial v}{\partial y} + \rho w \frac{\partial v}{\partial z} &= -\frac{\partial p}{\partial y} + \mu \left( \frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} + \frac{\partial^2 v}{\partial z^2} \right) + 2 \frac{\partial}{\partial y} \left[ \mu\_T \frac{\partial v}{\partial y} \right] \\ &+ \frac{\partial}{\partial x} \left[ \mu\_T \left( \frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} \right) \right] + \frac{\partial}{\partial x} \left[ \mu\_T \left( \frac{\partial v}{\partial x} + \frac{\partial w}{\partial x} \right) \right] \end{split} \tag{37}$$

$$\begin{aligned} \rho \frac{\partial w}{\partial t} + \rho u \frac{\partial w}{\partial x} + \rho v \frac{\partial w}{\partial y} + \rho w \frac{\partial w}{\partial z} &= -\frac{\partial p}{\partial z} + \mu \left( \frac{\partial^2 w}{\partial x^2} + \frac{\partial^2 w}{\partial y^2} + \frac{\partial^2 w}{\partial z^2} \right) + 2 \frac{\partial}{\partial x} \left[ \mu\_T \frac{\partial w}{\partial x} \right] \\ &+ \frac{\partial}{\partial x} \left[ \mu\_T \left( \frac{\partial u}{\partial x} + \frac{\partial w}{\partial x} \right) \right] + \frac{\partial}{\partial y} \left[ \mu\_T \left( \frac{\partial v}{\partial x} + \frac{\partial w}{\partial y} \right) \right] \end{aligned} \tag{38}$$

Equations for heat exchange (1st law of Thermodynamics)

$$\begin{aligned} \rho C\_p \left( \frac{\partial T}{\partial t} + u \frac{\partial T}{\partial \mathbf{x}} + v \frac{\partial T}{\partial \mathbf{y}} + w \frac{\partial T}{\partial \mathbf{z}} \right) &= \frac{\partial}{\partial \mathbf{x}} \left[ \left( \lambda + \lambda\_t + \lambda\_f \right) + \frac{\partial T}{\partial \mathbf{x}} \right] + \frac{\partial}{\partial \mathbf{y}} \left[ \left( \lambda + \lambda\_t + \lambda\_f \right) + \frac{\partial T}{\partial \mathbf{y}} \right] \\ &+ \frac{\partial}{\partial \mathbf{z}} \left[ \left( \lambda + \lambda\_t + \lambda\_f \right) + \frac{\partial T}{\partial \mathbf{z}} \right] + q + \varepsilon \end{aligned} \tag{39}$$

where *cp* is the specific heat content at constant pressure; *λ* is the coefficient of thermal conductivity; *λ<sup>i</sup>* is the coefficient of turbulent thermal conductivity; *λ<sup>p</sup>* is the coefficient of radiation thermal conductivity; and *qv* is the intensity of internal heat sources.

Here, *qv*, can be represented by *qv* ¼ *qvc* þ *qvr* þ *qvb*, where *qvk* is the intensity of internal convective heat sources; *qvb* is the intensity of internal combustion sources; and *qvr* is the intensity of internal sources due to radiation heat transfer.

Gas condition equation is given by:

$$p = \rho TR,\tag{40}$$

*<sup>ρ</sup>* <sup>¼</sup> <sup>X</sup>*<sup>n</sup> i*�1

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

*<sup>R</sup>* <sup>¼</sup> <sup>X</sup>*<sup>n</sup> i*�1

*cp* <sup>¼</sup> <sup>X</sup>*<sup>n</sup> i*�1 *χcpi*

where *α<sup>i</sup>* is the bulk concentration of the *i*th component and H*<sup>i</sup>* is its mass

They can be considered as temperature dependent or considered permanent.

The values of these parameters are determined at constant pressure (*p* ¼ *const*).

The characteristic equation summarizes the main partial differential equations, which are solved sequentially in software for each of the flow parameters. The type

where Φ is the dependent variable—velocity components, enthalpy, concentration of the components of the gas medium, optical density of the smoke, respectively; *Г* is the diffusion coefficient for the corresponding Φ; and *S* is the source

Most often, a CFD-Fluent turbulence *k* � *ε* model is applied. In this model, the coefficient of turbulent viscosity *υ<sup>t</sup>* is represented by the Kolmogorov-Prandtl dependence, as the ratio of kinematic turbulent energy *k* and the rate of

*k*2

*∂x* � �<sup>2</sup>

To close the system of equations at FDS, as in all other cases in turbulent flows, it is necessary to use appropriate models of turbulence. In this case, the large eddy

þ

*∂v ∂y* � �<sup>2</sup>

þ

*υ<sup>t</sup>* ¼ *C<sup>μ</sup>*

*<sup>∂</sup><sup>x</sup>* ð Þþ *<sup>ρ</sup>*<sup>Φ</sup> *div*ð Þ¼ *<sup>ρ</sup>w*<sup>Φ</sup> *div*ð Þþ *<sup>Г</sup>grad* <sup>Φ</sup> *<sup>S</sup>*, (46)

• gas constant

concentration.

dissipation *ε*:

where

**59**

*<sup>k</sup>* <sup>¼</sup> <sup>1</sup> 2

**3.3 FDS turbulence modeling**

• specific heat capacity

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

**3.1 A characteristic equation**

*∂*

member. The values for Eq. (46) are given in [9].

**3.2 Modeling the turbulence using CFD**

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>u</sup>*0<sup>2</sup> <sup>þ</sup> *<sup>v</sup>*0<sup>2</sup> <sup>þ</sup> *<sup>w</sup>*0<sup>2</sup> <sup>p</sup> ; *<sup>ε</sup>* <sup>¼</sup> *<sup>υ</sup> <sup>∂</sup><sup>u</sup>*

of equation is as follows:

*αiρ<sup>i</sup>* (43)

*χiRi* (44)

, (45)

*<sup>ε</sup>* , (47)

*∂w ∂z* � �<sup>2</sup> " # (48)

where *R* is the universal gas constant.

Law for the conservation of the mass of the *i*th gas that is a part of the mixture is

$$
\rho \frac{\partial \chi\_i}{\partial t} + \rho u \frac{\partial \chi\_i}{\partial x} + \rho v \frac{\partial \chi\_i}{\partial y} + \rho w \frac{\partial \chi\_i}{\partial z} = \frac{\partial}{\partial x} \left( \rho D \frac{\partial \chi\_i}{\partial x} \right) + \frac{\partial}{\partial y} \left( \rho D \frac{\partial \chi\_i}{\partial y} \right) + \frac{\partial}{\partial z} \left( \rho D \frac{\partial \chi\_i}{\partial x} \right) + m\_i,\tag{41}
$$

where *D* is the diffusion coefficient, representing the sum of the coefficient of gas diffusion *Di* and the coefficient of turbulent diffusion *Dt*ð Þ *D* ¼ *Di* þ *Dt* ; *χ* is the mass concentration of the *i*th gas; *mi* is the intensity of internal mass sources arising from the formation (disappearance) of molecules of a gas, a consequence of the ongoing chemical reactions of combustion in fires.

The law (equation) for preserving the optical density of smoke is of the form:

$$\frac{\partial D\_{on}}{\partial t} + u \frac{\partial D\_{on}}{\partial \mathbf{x}} + v \frac{\partial D\_{on}}{\partial \mathbf{y}} + w \frac{\partial D\_{on}}{\partial \mathbf{z}} = q\_D,\tag{42}$$

where *Don* is the smoke-generating capacity of the combustible material and *qD* is the intensity of the internal sources of optical density of the smoke formed by the ongoing reaction of combustion in a fire [3].

The thermophysical parameters of the mixture of gases involved and the result of combustion in a fire take into account the chemical composition of this mixture. It consists of oxygen, nitrogen, and combustion products - carbon monoxide, nitrogen, sulfur, etc., involved in the process combustible ingredients. They are defined as follows:

• density of the mixture

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

$$
\rho = \sum\_{i=1}^{n} a\_i \rho\_i \tag{43}
$$

• gas constant

*ρ ∂w ∂t* þ *ρu*

*ρCp*

*∂T ∂t* þ *u ∂T ∂x* þ *v ∂T ∂y* þ *w ∂T ∂z*

heat sources.

*ρ ∂χi ∂t* þ *ρu ∂χi ∂x* þ *ρv ∂χi ∂y* þ *ρw*

*∂w ∂x* þ *ρv ∂w ∂y* þ *ρw*

*Fire Safety and Management Awareness*

Gas condition equation is given by:

where *R* is the universal gas constant.

*∂χi <sup>∂</sup><sup>z</sup>* <sup>¼</sup> *<sup>∂</sup> ∂x*

ongoing chemical reactions of combustion in fires.

*∂Don ∂t*

ongoing reaction of combustion in a fire [3].

defined as follows:

**58**

• density of the mixture

þ *u*

*∂Don ∂x* þ *v*

*∂w <sup>∂</sup><sup>z</sup>* ¼ � *<sup>∂</sup><sup>p</sup> ∂z* þ *μ*

Equations for heat exchange (1st law of Thermodynamics)

¼ *∂ ∂x*

þ *∂ ∂z*

and *qvr* is the intensity of internal sources due to radiation heat transfer.

þ *∂ ∂x μT ∂u ∂z* þ *∂w ∂x*

*∂*2 *w ∂x*<sup>2</sup> þ

*λ* þ *λ<sup>t</sup>* þ *λ<sup>f</sup>* <sup>þ</sup>

where *cp* is the specific heat content at constant pressure; *λ* is the coefficient of thermal conductivity; *λ<sup>i</sup>* is the coefficient of turbulent thermal conductivity; *λ<sup>p</sup>* is the coefficient of radiation thermal conductivity; and *qv* is the intensity of internal

Here, *qv*, can be represented by *qv* ¼ *qvc* þ *qvr* þ *qvb*, where *qvk* is the intensity of internal convective heat sources; *qvb* is the intensity of internal combustion sources;

Law for the conservation of the mass of the *i*th gas that is a part of the mixture is

þ *∂ ∂y*

*<sup>ρ</sup><sup>D</sup> <sup>∂</sup>χ<sup>i</sup> ∂x* 

where *D* is the diffusion coefficient, representing the sum of the coefficient of gas diffusion *Di* and the coefficient of turbulent diffusion *Dt*ð Þ *D* ¼ *Di* þ *Dt* ; *χ* is the mass concentration of the *i*th gas; *mi* is the intensity of internal mass sources arising from the formation (disappearance) of molecules of a gas, a consequence of the

The law (equation) for preserving the optical density of smoke is of the form:

*∂Don ∂y*

where *Don* is the smoke-generating capacity of the combustible material and *qD* is the intensity of the internal sources of optical density of the smoke formed by the

The thermophysical parameters of the mixture of gases involved and the result of combustion in a fire take into account the chemical composition of this mixture. It consists of oxygen, nitrogen, and combustion products - carbon monoxide, nitrogen, sulfur, etc., involved in the process combustible ingredients. They are

þ *w*

*∂Don*

*λ* þ *λ<sup>t</sup>* þ *λ<sup>f</sup>* <sup>þ</sup>

*∂*2 *w ∂y*<sup>2</sup> þ

*∂T ∂x*

*∂*2 *w ∂z*<sup>2</sup>

þ *∂ ∂y μT ∂v ∂z* þ *∂w ∂y*

þ *∂ ∂y*

*p* ¼ *ρTR*, (40)

*<sup>ρ</sup><sup>D</sup> <sup>∂</sup>χ<sup>i</sup> ∂y*  þ *∂ ∂z*

*<sup>∂</sup><sup>z</sup>* <sup>¼</sup> *qD*, (42)

*<sup>ρ</sup><sup>D</sup> <sup>∂</sup>χ<sup>i</sup> ∂z* 

þ *mi*,

(41)

þ *q* þ *ε*

*∂T ∂z*

<sup>þ</sup> <sup>2</sup> *<sup>∂</sup> ∂z μT ∂w ∂z* 

*λ* þ *λ<sup>t</sup>* þ *λ<sup>f</sup>* <sup>þ</sup>

(38)

*∂T ∂y*

(39)

$$R = \sum\_{i=1}^{n} \chi\_i R\_i \tag{44}$$

• specific heat capacity

$$\mathcal{L}\_p = \sum\_{i=1}^n \chi c\_{p\_i},\tag{45}$$

where *α<sup>i</sup>* is the bulk concentration of the *i*th component and H*<sup>i</sup>* is its mass concentration.

The values of these parameters are determined at constant pressure (*p* ¼ *const*). They can be considered as temperature dependent or considered permanent.

#### **3.1 A characteristic equation**

The characteristic equation summarizes the main partial differential equations, which are solved sequentially in software for each of the flow parameters. The type of equation is as follows:

$$\frac{\partial}{\partial \mathbf{x}}(\rho \Phi) + \operatorname{div}(\rho w \Phi) = \operatorname{div}(\Gamma \text{grad } \Phi) + \mathbb{S},\tag{46}$$

where Φ is the dependent variable—velocity components, enthalpy, concentration of the components of the gas medium, optical density of the smoke, respectively; *Г* is the diffusion coefficient for the corresponding Φ; and *S* is the source member. The values for Eq. (46) are given in [9].

#### **3.2 Modeling the turbulence using CFD**

Most often, a CFD-Fluent turbulence *k* � *ε* model is applied. In this model, the coefficient of turbulent viscosity *υ<sup>t</sup>* is represented by the Kolmogorov-Prandtl dependence, as the ratio of kinematic turbulent energy *k* and the rate of dissipation *ε*:

$$
\mu\_l = \mathcal{C}\_{\mu} \frac{k^2}{\varepsilon},
\tag{47}
$$

where

$$k = \frac{1}{2}\sqrt{u'^2 + v'^2 + w'^2}; \qquad \varepsilon = \overline{\nu \left[ \left(\frac{\partial u}{\partial \mathbf{x}}\right)^2 + \left(\frac{\partial v}{\partial \mathbf{y}}\right)^2 + \left(\frac{\partial w}{\partial \mathbf{z}}\right)^2 \right]} \tag{48}$$

#### **3.3 FDS turbulence modeling**

To close the system of equations at FDS, as in all other cases in turbulent flows, it is necessary to use appropriate models of turbulence. In this case, the large eddy

simulation model [9] known in this type of task as the LES model is recommended as the most appropriate. The model is described in detail in [9].

The model of large eddy simulation is based on the following: large-scale vortices differ markedly in the course of transition from one current to another, with the small-scale structure changing slightly. The field of large-scale structures needs to be defined. Continuity of flow parameters is assumed using Leonard's so-called filtering function. For each flow parameter, a = a + a0 . Dissipative combustion processes such as viscous thermal conductivity, diffusion, and impurity transfer are modeled. What is special about the model is that the scale of the vortex structures is smaller than the size of the data network. The parameters μ, λ, and D in the equations describing the process are replaced by expressions modeling their effect.

The strain rate tensor is used to determine μ. Thermal conductivity and impurity diffusion are determined by:

$$\begin{aligned} \lambda\_t &= \frac{\mu\_t \mathbf{c}\_p}{pr\_t} \\ (\rho D)\_t &= \frac{\mu\_t}{\mathbf{S}\_{0t}} \\ \mu\_t &= \rho v\_t \end{aligned} \tag{49}$$

In the case of laminar heat transfer and diffusion, respectively:

$$\begin{aligned} \lambda &= \frac{\mu c\_p}{pr} \\ (\rho D) &= \frac{\mu}{\mathbb{S}\_{\text{0t}}} \end{aligned} \tag{50}$$

The geometric model so drawn shows the location of the fire, that is, hazard

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

In real fires, there is a degree transition zone between lower cold smoke and

The first smoke curtain signal may be calculated from the beginning of the transition zone formation. Thus, it can be assumed that forecasts using equations of

After the 3D Atrium Model has been built (in the Gambit work environment), it is necessary to proceed with the "networking" procedure of the volume. Due to the large volume, it is not appropriate to use crosslinking of the elements in the same step. For this reason, a fine mesh is selected at the site of fire generation and its

In the present case, triangular elements were selected for the site of fire generation and the smoke hatches for the networking of persons with step 0.3 m. For the

**Figure 11** shows the velocity field in the atrium in vector form. It can be seen from the figure that high velocities are observed at the site of smoke generation,

this type depend on the exact application of the computer model.

departure from the room, while a larger one is used far from them.

both near the walls and the high part of the atrium.

other walls as well as the volume of the atrium, a step of 0.5 m is chosen.

generator and flue gas outlet (smoke hatches).

*Building with atrium subject to simulation study [20].*

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

higher hot smoke.

*Building fire development.*

**Figure 10.**

**61**

**Figure 9.**

The process of combustion in the fire is most often implemented using the "Part of the mixture" approach. It is a scalar quantity characterizing the mass concentration of one or more components of a gas mixture at a given point in the flow. To reduce the volume of calculations, the significant memorized are two components of the mixture: mass concentration of unburned fuel and burned, respectively. Combustion products. Radiant heat transfer is calculated by the equations for the emission of sulfur-containing gases, which, in fact, implies a constraint on the problem. Large-scale models may also be used in certain cases. FDS equations use the FVM finite volume method. In addition to using the LES turbulence model, successful attempts have been made to apply the direct numerical modeling method described in [9]. FDS has been tested in a number of laboratories and institutions in the United States. The validation done shows the possibility of its application in many cases [16].

#### **4. Computer modeling and numerical simulations**

A detailed description of the Fluent (CFD) program interface is given in [17–19]. Development of fire in atrium space: The development of fire occurred in a certain object—the building shown in **Figure 9** and **Figure 10**, located on Tsarigradsko shose Blvd., Sofia.

The arrangement of the air exchange in the atrium space in case of fire is shown in **Figure 10**. Atrium air exchange was implemented, showing zones with critical parameters of radiation, smoke, and fire. It is important to note that all of the above is possible only by knowing the respective velocity or temperature field of the air in the room [5].

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Figure 9.** *Building with atrium subject to simulation study [20].*

**Figure 10.** *Building fire development.*

simulation model [9] known in this type of task as the LES model is recommended

processes such as viscous thermal conductivity, diffusion, and impurity transfer are modeled. What is special about the model is that the scale of the vortex structures is

smaller than the size of the data network. The parameters μ, λ, and D in the equations describing the process are replaced by expressions modeling their effect. The strain rate tensor is used to determine μ. Thermal conductivity and impurity

> *<sup>λ</sup><sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>tcp prt* ð Þ *<sup>ρ</sup><sup>D</sup> <sup>t</sup>* <sup>¼</sup> *<sup>μ</sup><sup>t</sup>*

*μ<sup>t</sup>* ¼ *ρυ<sup>t</sup>*

*<sup>λ</sup>* <sup>¼</sup> *<sup>μ</sup>cp pr* ð Þ¼ *<sup>ρ</sup><sup>D</sup> <sup>μ</sup>*

In the case of laminar heat transfer and diffusion, respectively:

**4. Computer modeling and numerical simulations**

*S*0*<sup>t</sup>*

*S*0*<sup>t</sup>*

The process of combustion in the fire is most often implemented using the "Part of the mixture" approach. It is a scalar quantity characterizing the mass concentration of one or more components of a gas mixture at a given point in the flow. To reduce the volume of calculations, the significant memorized are two components of the mixture: mass concentration of unburned fuel and burned, respectively. Combustion products. Radiant heat transfer is calculated by the equations for the emission of sulfur-containing gases, which, in fact, implies a constraint on the problem. Large-scale models may also be used in certain cases. FDS equations use the FVM finite volume method. In addition to using the LES turbulence model, successful attempts have been made to apply the direct numerical modeling method described in [9]. FDS has been tested in a number of laboratories and institutions in the United States. The validation done shows the possibility of its application in

A detailed description of the Fluent (CFD) program interface is given in [17–19]. Development of fire in atrium space: The development of fire occurred in a

The arrangement of the air exchange in the atrium space in case of fire is shown in **Figure 10**. Atrium air exchange was implemented, showing zones with critical parameters of radiation, smoke, and fire. It is important to note that all of the above is possible only by knowing the respective velocity or temperature field of the air in

certain object—the building shown in **Figure 9** and **Figure 10**, located on

The model of large eddy simulation is based on the following: large-scale vortices differ markedly in the course of transition from one current to another, with the small-scale structure changing slightly. The field of large-scale structures needs to be defined. Continuity of flow parameters is assumed using Leonard's so-called

. Dissipative combustion

(49)

(50)

as the most appropriate. The model is described in detail in [9].

filtering function. For each flow parameter, a = a + a0

diffusion are determined by:

*Fire Safety and Management Awareness*

many cases [16].

the room [5].

**60**

Tsarigradsko shose Blvd., Sofia.

The geometric model so drawn shows the location of the fire, that is, hazard generator and flue gas outlet (smoke hatches).

In real fires, there is a degree transition zone between lower cold smoke and higher hot smoke.

The first smoke curtain signal may be calculated from the beginning of the transition zone formation. Thus, it can be assumed that forecasts using equations of this type depend on the exact application of the computer model.

After the 3D Atrium Model has been built (in the Gambit work environment), it is necessary to proceed with the "networking" procedure of the volume. Due to the large volume, it is not appropriate to use crosslinking of the elements in the same step.

For this reason, a fine mesh is selected at the site of fire generation and its departure from the room, while a larger one is used far from them.

In the present case, triangular elements were selected for the site of fire generation and the smoke hatches for the networking of persons with step 0.3 m. For the other walls as well as the volume of the atrium, a step of 0.5 m is chosen.

**Figure 11** shows the velocity field in the atrium in vector form. It can be seen from the figure that high velocities are observed at the site of smoke generation, both near the walls and the high part of the atrium.

The temperature distribution in the volume of the atrium is shown in **Figure 12**. Areas with higher temperatures are clearly visible—near the source of smoke and the surrounding wall above it, and near the dome of the atrium.

**Figure 13** shows the distribution of smoke in the atrium at various points in time for 120 s until equilibrium between the ascending and descending currents in the atrium is reached.

**Figure 14** shows the change in turbulent kinetic energy in the atrium. What is striking is the fact that there is an intense transfer of substances from the outbreak of the fire along the wall of the atrium to the dome, and then it slowly subsides. When smoke reaches the floor of the room, the turbulent kinetic energy is approximately zero.

Modern computer programs for numerical modeling of processes related to the simulation of air exchange in atriums can alleviate some regulatory requirements for protected premises (atriums), which can lead to significant savings for investors. If necessary, openings may be left open in the premises. With the use of fire ventilation, they will not have a negative effect on the parameters of the fire. In large areas, flue products may only be contained above the fire. The ability to make new, more practical, and economical architectural decisions is increasing.

Application of the FDS environment for predicting and restoring the spread of fires and damage in the building [21, 22].

An analysis is made in the FDS environment to look at the basic features on which it is based. In analyzing the program, it should be emphasized that it is related to the numerical mechanics of the fluids and software products built on this basis. The same system of private differential equations is used, with the difference between the CFD and the FDS medium in the equations used to describe the turbulence. Fluent programs utilize turbulence models, which narrows their applicability in the study of fires in unlimited space. Large Eddy Simulation (LES) is used for FDS. This expands the applicability in the study of currents and fires in open space, as well as the effect of wind, etc. Weather conditions when solving problems.

**Figure 12.**

**Figure 13.**

**63**

*The distribution of temperature in the volume of the atrium.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

*The distribution of smoke in the atrium at different times. (a) 1320 s, and (b) 1440 s.*

**Figure 11.** *The velocity field in atrium in vector form.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Figure 12.** *The distribution of temperature in the volume of the atrium.*

**Figure 13.** *The distribution of smoke in the atrium at different times. (a) 1320 s, and (b) 1440 s.*

The temperature distribution in the volume of the atrium is shown in **Figure 12**. Areas with higher temperatures are clearly visible—near the source of smoke and

**Figure 13** shows the distribution of smoke in the atrium at various points in time for 120 s until equilibrium between the ascending and descending currents in the

**Figure 14** shows the change in turbulent kinetic energy in the atrium. What is striking is the fact that there is an intense transfer of substances from the outbreak of the fire along the wall of the atrium to the dome, and then it slowly subsides. When smoke reaches the floor of the room, the turbulent kinetic energy is approximately zero. Modern computer programs for numerical modeling of processes related to the simulation of air exchange in atriums can alleviate some regulatory requirements for protected premises (atriums), which can lead to significant savings for investors. If necessary, openings may be left open in the premises. With the use of fire ventilation, they will not have a negative effect on the parameters of the fire. In large areas, flue products may only be contained above the fire. The ability to make

new, more practical, and economical architectural decisions is increasing.

fires and damage in the building [21, 22].

Application of the FDS environment for predicting and restoring the spread of

An analysis is made in the FDS environment to look at the basic features on which it is based. In analyzing the program, it should be emphasized that it is related to the numerical mechanics of the fluids and software products built on this basis. The same system of private differential equations is used, with the difference between the CFD and the FDS medium in the equations used to describe the turbulence. Fluent programs utilize turbulence models, which narrows their applicability in the study of fires in unlimited space. Large Eddy Simulation (LES) is used for FDS. This expands the applicability in the study of currents and fires in open space, as well as the effect of wind, etc. Weather conditions when solving problems.

the surrounding wall above it, and near the dome of the atrium.

atrium is reached.

*Fire Safety and Management Awareness*

**Figure 11.**

**62**

*The velocity field in atrium in vector form.*

**Figure 14.** *Change in turbulent kinetic energy in the atrium.*

The program is also used to analyze the spread of hazards in the work environment, both industrial and residential sites, as well as in the environment. This program allows to restore the development of fire in past events [5, 9, 16].

#### **4.1 Closed-loop fire development modeling using the PyroSim (FDS) program**

This simulation product is applicable to the modeling of fire development and the determination of the evacuation and extinguishing route indoors. The software environment offers intuitive function menus (graphical user interface) and provides results for the propagation of flue gases, hydrocarbons, and other substances during a fire, as well as the temperature distribution along the cross section of the model's geometry. The program serves not only the prediction of the situation, but also the investigation of fire in the setting of the initial ignition zone, as well as training. The simulations in the program are based on the computational dynamics of fluids, and in particular, low-velocity convective currents. The capabilities of the software make it possible to investigate fires from cooking stoves to oil derivative stores (oil bases). The program is also applicable to simulation of flame-free processes, including building ventilation testing.

A detailed description of how to work with the PyroSim interface is given in [17].

Development of fire in a training building: The development of a fire in study building 2 of TU-Sofia is investigated. The fire is assumed to start from the ground floor—one of the laboratories (**Figure 15**).

Specific examples of the application of the PyroSim software product are shown in **Figures 16–21** in a simulated fire in a training laboratory on the first floor of a technical building of the Technical University—Sofia. For the construction of the geometric model in **Figure 16**, the real barrier elements such as walls, doors, and windows, as well as the materials of which they are constructed with their respective melting/ignition temperatures, are taken into account.

as fast as possible on one of the stairs, which is a kind of chimney (chimney) for this part of the building. For the same period of time, smoke spreads down the corridor on the first floor. Since there are no smoke barriers (doors) installed between the same staircase and the corridors on the floors, it will spread to all floors and will make it difficult to evacuate people in the building. Partition doors are placed on the next staircase (to the right of the model shown in **Figures 18** and **19**), which are intended to prevent the smoke from burning the floors in the direction from the staircase to the corridors, but in this case the flue gases will meet on both sides. The same barriers and

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

**Figure 16.**

**Figure 15.**

*Building 2 of TU-Sofia.*

**Figure 17.**

**65**

*Working environment for drawing the geometric model.*

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

*Flue gas propagation in the building within 50 s of the simulation.*

Instantaneous flue gas images of the building are shown in **Figure 17** (for 50s), **Figure 18** (for 60s), and **Figure 19** (for 440 s). It is clear that the smoke is spreading *Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Figure 15.** *Building 2 of TU-Sofia.*

The program is also used to analyze the spread of hazards in the work environment, both industrial and residential sites, as well as in the environment. This program

**4.1 Closed-loop fire development modeling using the PyroSim (FDS) program**

This simulation product is applicable to the modeling of fire development and the determination of the evacuation and extinguishing route indoors. The software environment offers intuitive function menus (graphical user interface) and provides results for the propagation of flue gases, hydrocarbons, and other substances during a fire, as well as the temperature distribution along the cross section of the model's geometry. The program serves not only the prediction of the situation, but also the investigation of fire in the setting of the initial ignition zone, as well as training. The simulations in the program are based on the computational dynamics of fluids, and in particular, low-velocity convective currents. The capabilities of the software make it possible to investigate fires from cooking stoves to oil derivative stores (oil bases). The program is also applicable to simulation of flame-free

A detailed description of how to work with the PyroSim interface is given

Development of fire in a training building: The development of a fire in study building 2 of TU-Sofia is investigated. The fire is assumed to start from the ground

Specific examples of the application of the PyroSim software product are shown in **Figures 16–21** in a simulated fire in a training laboratory on the first floor of a technical building of the Technical University—Sofia. For the construction of the geometric model in **Figure 16**, the real barrier elements such as walls, doors, and windows, as well as the materials of which they are constructed with their respec-

Instantaneous flue gas images of the building are shown in **Figure 17** (for 50s), **Figure 18** (for 60s), and **Figure 19** (for 440 s). It is clear that the smoke is spreading

allows to restore the development of fire in past events [5, 9, 16].

processes, including building ventilation testing.

tive melting/ignition temperatures, are taken into account.

floor—one of the laboratories (**Figure 15**).

in [17].

**64**

**Figure 14.**

*Change in turbulent kinetic energy in the atrium.*

*Fire Safety and Management Awareness*

**Figure 16.** *Working environment for drawing the geometric model.*

*Flue gas propagation in the building within 50 s of the simulation.*

as fast as possible on one of the stairs, which is a kind of chimney (chimney) for this part of the building. For the same period of time, smoke spreads down the corridor on the first floor. Since there are no smoke barriers (doors) installed between the same staircase and the corridors on the floors, it will spread to all floors and will make it difficult to evacuate people in the building. Partition doors are placed on the next staircase (to the right of the model shown in **Figures 18** and **19**), which are intended to prevent the smoke from burning the floors in the direction from the staircase to the corridors, but in this case the flue gases will meet on both sides. The same barriers and

#### **Figure 18.**

*Flue gas propagation in the building within 60 s of the simulation.*

**Figure 20** shows the velocity distribution along the vertical section of a building for 3800 s of the simulation. It is clear that the first and last floors of the building and the staircase adjacent to the burning room are affected at the beginning of the

**Figure 21** shows the temperature distribution along the vertical section of a building for the 480th second of the simulation. From here, it is reported that in the fire zone in the laboratory the temperature is above 200°C, and at the site in the hallway in front of it, where the nearby staircase is, the temperature is above 120°C. As the building climbs, the temperature drops to about 60°C until the third floor, indicating that there should be no escape route in this area without protective clothing. By linking the data from the previous figures, the instructions for the mandatory availability of respiratory protection may also be added, as this is also

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

The results of the simulation of a fire occurring in a particular building give preliminary information about the flaws in its design with respect to fire safety. If taken into account, placing barriers in the right places, as well as revising the evacuation route from the building would lead to increased security in the event of a disaster or accident and to removal all people without damage to their health.

The results obtained in this chapter are first and foremost a practical application that allows solving problems related to fire prevention and analysis in a restricted area. The technical solution to limit the spread of fires is to use protective water curtains, as they isolate burning vehicles from the environment and thus prevent the transfer of fire to other vehicles in the underground garage. The solution can be

The results of the two simulations of fire in specific buildings indicate the possibility of Fluent and FDS-PyroSim software in analyzing fire spread, smoke, temperature, and harmfulness in confined spaces. As shown, these simulations can be used:

• in the case of designing buildings with fixed sprinklers and evacuation routes.

• in judicial analysis of the consequences of the fire by initiation of its

process, and then the other floors.

**Figure 21.**

**5. Conclusion**

**67**

the main route for the distribution of flue gases.

*Temperature distribution for the 480th second of the simulation.*

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

applied to any particular similar object.

development over time.

**Figure 19.** *Flue gas propagation in the building at 440 s of the simulation.*

reduced visibility in this enclosure will cause additional evacuation difficulties, because people will not easily notice where the barrier on the second staircase is and are likely to collide with it glass shutter door, which is closed by a mechanical machine (mechanism), which is a prerequisite for an accident during the evacuation and may lead to an increase in the number of casualties in the building.

**Figure 20.** *Speed distribution for 3800 s of simulation.*

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

**Figure 21.** *Temperature distribution for the 480th second of the simulation.*

**Figure 20** shows the velocity distribution along the vertical section of a building for 3800 s of the simulation. It is clear that the first and last floors of the building and the staircase adjacent to the burning room are affected at the beginning of the process, and then the other floors.

**Figure 21** shows the temperature distribution along the vertical section of a building for the 480th second of the simulation. From here, it is reported that in the fire zone in the laboratory the temperature is above 200°C, and at the site in the hallway in front of it, where the nearby staircase is, the temperature is above 120°C. As the building climbs, the temperature drops to about 60°C until the third floor, indicating that there should be no escape route in this area without protective clothing. By linking the data from the previous figures, the instructions for the mandatory availability of respiratory protection may also be added, as this is also the main route for the distribution of flue gases.

The results of the simulation of a fire occurring in a particular building give preliminary information about the flaws in its design with respect to fire safety. If taken into account, placing barriers in the right places, as well as revising the evacuation route from the building would lead to increased security in the event of a disaster or accident and to removal all people without damage to their health.

#### **5. Conclusion**

reduced visibility in this enclosure will cause additional evacuation difficulties, because people will not easily notice where the barrier on the second staircase is and are likely to collide with it glass shutter door, which is closed by a mechanical machine (mechanism), which is a prerequisite for an accident during the evacuation

and may lead to an increase in the number of casualties in the building.

*Flue gas propagation in the building within 60 s of the simulation.*

*Fire Safety and Management Awareness*

*Flue gas propagation in the building at 440 s of the simulation.*

**Figure 18.**

**Figure 19.**

**Figure 20.**

**66**

*Speed distribution for 3800 s of simulation.*

The results obtained in this chapter are first and foremost a practical application that allows solving problems related to fire prevention and analysis in a restricted area.

The technical solution to limit the spread of fires is to use protective water curtains, as they isolate burning vehicles from the environment and thus prevent the transfer of fire to other vehicles in the underground garage. The solution can be applied to any particular similar object.

The results of the two simulations of fire in specific buildings indicate the possibility of Fluent and FDS-PyroSim software in analyzing fire spread, smoke, temperature, and harmfulness in confined spaces. As shown, these simulations can be used:


*Fire Safety and Management Awareness*

**References**

2004

[1] Puzach SV, Chumachenko AP, Kozlov YI, Bubnov VM, Rodin BC. Method of calculation with a computer program for determining the actual limits of fire resistance and modeling of actions of fire extinguishing systems. In: Mechanical Ventilation and Smoke Removal During Fires. Moscow: VDPO;

*DOI: http://dx.doi.org/10.5772/intechopen.91274*

Conference on Thermal Equipment, Renewable Energy and Rural

151155

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces*

2016

Development. E3S Web of Conferences TE-RE-RD 2019; Targoviste; Romania; 6 June 2019 through 8 June 2019; Vol. 112. 2019. Article number 01015; Code

[9] Antonov I. Applied Fluid Mechanics. Sofia: Technical University of Sofia;

[10] Marshall AM, di Marzo M. Modeling aspects of sprinkler spray dynamics in fires. Process Safety and Environmental

[11] Launder BE, Spalding DB. Lectures on Mathematical Models of Turbulence.

[12] Leonard A. Energy cascade in largeeddy simulation of turbulent fluid flows.

Protection. 2004;**82**(2):97-104

London: Academic Press; 1972

Advances in Geophysics. 1975;**18**

[13] Rodi W, Spalding DB. A twoparameter model of turbulence and its application to free jets. Warms and Stoffuberrtrag. 1970;**3**:585-595

[14] Abramovich GN. Theory of Turbulent Jets. Moscow; 2011. ISBN:

[15] Velichkova R, Antonov I, Nikolov K, Grozdanov K, Uzunova M. Modeling of the occurrence of fire in closed cars garages. In: EFEA' 2016. DOI: 10.1109/ EFEA.2016.7748807. Available from: http://ieeexplore.ieee.org/document/ 7748807/. Electronic ISBN: 978-1-

[16] Pichurov G, Stankov P, Ivanov M.

Radial jet predictions based on computational fluid dynamics. In: Healthy Buildings 2006: Creating a Healthy Indoor Environment for People, Proceedings, Vol. 5. 2006. pp. 125-128. ISBN: 978-1-62276-998-8

(Part A):237-248

978-5-4365-0031-

5090-0749-3

[2] PyroSim Example Guide. 2012. Available from: https://www.thunde rheadeng.com/pyrosim/tutorials/

Grozdanov K, Uzunova M. The possibility of replacing solid walls with water curtain applicable to a large underground garage. In: EFEA'2016, Belgrade, Serbia. 2016. DOI: 10.1109/EFEA.2016.7748805. Available from: http://ieeexplore.ieee.org/ document/774880/; electronic ISBN:

[4] Antonov IS. About a modification of k-ε model applicable to heat and mass transfer processes in two-phase turbulent flows. In: EMF'98 Science Conference Energy Efficiency and Environmental Protection. September 17–20, 1998, Sozopol, Proceedings. 1998. pp. 7-14

[5] CFD modeling of a large complex fire. Report 3120. Lund; 2000

[6] Drysdale D. An Introduction to Fire

[7] Stoyanov V, Terziev A, Uzunova M. Numerical study of distribution of smoke and hazards in underground parking areas considering the operation of ventilation. In: 2014 3rd International Symposium on Environmental Friendly Energies and Applications (EFEA);

[8] Terziev A. Study of the fire dynamics in a burning car and analysis of the possibilities for transfer of fire to a nearby vehicle. In: 8th International

Dynamics. UK: Wiley; 2011

St. Ouen. 2014. pp. 1-6

**69**

[3] Antonov I, Velichkova R,

978-1-5090-0749-3

#### **Author details**

Ivan Antonov, Rositsa Velichkova\*, Svetlin Antonov and Kamen Grozdanov Technical Univesity of Sofia, Sofia, Bulgaria

\*Address all correspondence to: rositsavelichkova@abv.bg

© 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.

*Mathematical Modeling and Simulation of Development of the Fires in Confined Spaces DOI: http://dx.doi.org/10.5772/intechopen.91274*

#### **References**

[1] Puzach SV, Chumachenko AP, Kozlov YI, Bubnov VM, Rodin BC. Method of calculation with a computer program for determining the actual limits of fire resistance and modeling of actions of fire extinguishing systems. In: Mechanical Ventilation and Smoke Removal During Fires. Moscow: VDPO; 2004

[2] PyroSim Example Guide. 2012. Available from: https://www.thunde rheadeng.com/pyrosim/tutorials/

[3] Antonov I, Velichkova R, Grozdanov K, Uzunova M. The possibility of replacing solid walls with water curtain applicable to a large underground garage. In: EFEA'2016, Belgrade, Serbia. 2016. DOI: 10.1109/EFEA.2016.7748805. Available from: http://ieeexplore.ieee.org/ document/774880/; electronic ISBN: 978-1-5090-0749-3

[4] Antonov IS. About a modification of k-ε model applicable to heat and mass transfer processes in two-phase turbulent flows. In: EMF'98 Science Conference Energy Efficiency and Environmental Protection. September 17–20, 1998, Sozopol, Proceedings. 1998. pp. 7-14

[5] CFD modeling of a large complex fire. Report 3120. Lund; 2000

[6] Drysdale D. An Introduction to Fire Dynamics. UK: Wiley; 2011

[7] Stoyanov V, Terziev A, Uzunova M. Numerical study of distribution of smoke and hazards in underground parking areas considering the operation of ventilation. In: 2014 3rd International Symposium on Environmental Friendly Energies and Applications (EFEA); St. Ouen. 2014. pp. 1-6

[8] Terziev A. Study of the fire dynamics in a burning car and analysis of the possibilities for transfer of fire to a nearby vehicle. In: 8th International

Conference on Thermal Equipment, Renewable Energy and Rural Development. E3S Web of Conferences TE-RE-RD 2019; Targoviste; Romania; 6 June 2019 through 8 June 2019; Vol. 112. 2019. Article number 01015; Code 151155

[9] Antonov I. Applied Fluid Mechanics. Sofia: Technical University of Sofia; 2016

[10] Marshall AM, di Marzo M. Modeling aspects of sprinkler spray dynamics in fires. Process Safety and Environmental Protection. 2004;**82**(2):97-104

[11] Launder BE, Spalding DB. Lectures on Mathematical Models of Turbulence. London: Academic Press; 1972

[12] Leonard A. Energy cascade in largeeddy simulation of turbulent fluid flows. Advances in Geophysics. 1975;**18** (Part A):237-248

[13] Rodi W, Spalding DB. A twoparameter model of turbulence and its application to free jets. Warms and Stoffuberrtrag. 1970;**3**:585-595

[14] Abramovich GN. Theory of Turbulent Jets. Moscow; 2011. ISBN: 978-5-4365-0031-

[15] Velichkova R, Antonov I, Nikolov K, Grozdanov K, Uzunova M. Modeling of the occurrence of fire in closed cars garages. In: EFEA' 2016. DOI: 10.1109/ EFEA.2016.7748807. Available from: http://ieeexplore.ieee.org/document/ 7748807/. Electronic ISBN: 978-1- 5090-0749-3

[16] Pichurov G, Stankov P, Ivanov M. Radial jet predictions based on computational fluid dynamics. In: Healthy Buildings 2006: Creating a Healthy Indoor Environment for People, Proceedings, Vol. 5. 2006. pp. 125-128. ISBN: 978-1-62276-998-8

**Author details**

**68**

Technical Univesity of Sofia, Sofia, Bulgaria

*Fire Safety and Management Awareness*

provided the original work is properly cited.

\*Address all correspondence to: rositsavelichkova@abv.bg

Ivan Antonov, Rositsa Velichkova\*, Svetlin Antonov and Kamen Grozdanov

© 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,

[17] Antonov SV, Antonov IV, Grozdanov K. Modelling and Simulation of Fire. Sofia: Technical University of Sofia; 2018

**Chapter 5**

**Abstract**

underground mines.

**1. Introduction**

modeling

**71**

Scenarios

Methodology for Optimal Fire

The purpose of this chapter is to develop a methodology that will contribute in locating optimal evacuation routes in case of fire that are based on minimal carbon monoxide (CO) exposure during the evacuation procedures. The proposed methodology is tested using simulated fire scenarios from which CO concentration over time curve is extracted from all available evacuation routes and presented in a weighted form based on the accumulating effect of CO inhalation in the form of fractional effective dose (FED). The safety limits of the FED model on which the optimization process is based are determined using a model for the prediction of carboxyhemoglobin (COHb) levels in human blood. The COHb model is associated with predicted clinical symptoms that are the basis for determining the level of incapacitation at which the mineworkers are incapable of completing their evacuation. Also in the process of improving the fire risk analysis, the proposed methodology enables the development of evacuation plans that are based on the results of modeled fire scenarios combined together with the results of the anticipated hazards generated by CO inhalation. The results presented in this chapter indicate a more precise approach in the process of planning the evacuation system inside the

**Keywords:** underground mines, fire, safety, evacuation, optimization, simulation,

Fires are one of the most serious accidents that can occur in underground mines due to the restricted ability to evacuate quickly from the confined excavations that can be filled quickly with smoke and noxious fumes [1]. The behavior of underground mine fires is difficult to predict due to their dependence on multiple factors that are closely related to the amount of flammable material, ignition location, ventilation system arrangement, time of occurrence, etc. [2]. These uncertainties associated with mine fire scenarios can have unexpected impacts on the evacuation process, firefighting, and rescue strategies and also further complicate the process

of design and implementation of fire protection systems.

Evacuations in Underground

Mines Based on Simulated

*Vancho Adjiski and Zoran Despodov*

[18] Antonov I, Terziev A. Tutorial on Applied Fluid Mechanics. Sofia: Technical University of Sofia; 2012

[19] Fluent Inc. Chapter 10. Modeling turbulence. UK: Fluent; 2001

[20] Grozdanov K. TS. Modeling of fire in auto accident with the purpose of event identification [PhD thesis]. Sofia; 2017

[21] FDS-SMV Official Website. Ford Dynamics Simulator and Smokeview. Available from: https://pages.nist.gov/ fds-smv/

[22] Puzach SV. Mathematical Modeling of Gas Dynamics and Heat and Mass Transfer in Solving Fire Safety Problems. Moscow: Russian Academy of Medical Science; 2003

#### **Chapter 5**

[17] Antonov SV, Antonov IV,

*Fire Safety and Management Awareness*

Sofia; 2018

fds-smv/

**70**

Grozdanov K. Modelling and Simulation of Fire. Sofia: Technical University of

[18] Antonov I, Terziev A. Tutorial on Applied Fluid Mechanics. Sofia: Technical University of Sofia; 2012

[19] Fluent Inc. Chapter 10. Modeling

[20] Grozdanov K. TS. Modeling of fire in auto accident with the purpose of event identification [PhD thesis]. Sofia; 2017

[21] FDS-SMV Official Website. Ford Dynamics Simulator and Smokeview. Available from: https://pages.nist.gov/

[22] Puzach SV. Mathematical Modeling of Gas Dynamics and Heat and Mass Transfer in Solving Fire Safety

Problems. Moscow: Russian Academy of

Medical Science; 2003

turbulence. UK: Fluent; 2001

## Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios

*Vancho Adjiski and Zoran Despodov*

## **Abstract**

The purpose of this chapter is to develop a methodology that will contribute in locating optimal evacuation routes in case of fire that are based on minimal carbon monoxide (CO) exposure during the evacuation procedures. The proposed methodology is tested using simulated fire scenarios from which CO concentration over time curve is extracted from all available evacuation routes and presented in a weighted form based on the accumulating effect of CO inhalation in the form of fractional effective dose (FED). The safety limits of the FED model on which the optimization process is based are determined using a model for the prediction of carboxyhemoglobin (COHb) levels in human blood. The COHb model is associated with predicted clinical symptoms that are the basis for determining the level of incapacitation at which the mineworkers are incapable of completing their evacuation. Also in the process of improving the fire risk analysis, the proposed methodology enables the development of evacuation plans that are based on the results of modeled fire scenarios combined together with the results of the anticipated hazards generated by CO inhalation. The results presented in this chapter indicate a more precise approach in the process of planning the evacuation system inside the underground mines.

**Keywords:** underground mines, fire, safety, evacuation, optimization, simulation, modeling

## **1. Introduction**

Fires are one of the most serious accidents that can occur in underground mines due to the restricted ability to evacuate quickly from the confined excavations that can be filled quickly with smoke and noxious fumes [1]. The behavior of underground mine fires is difficult to predict due to their dependence on multiple factors that are closely related to the amount of flammable material, ignition location, ventilation system arrangement, time of occurrence, etc. [2]. These uncertainties associated with mine fire scenarios can have unexpected impacts on the evacuation process, firefighting, and rescue strategies and also further complicate the process of design and implementation of fire protection systems.

Developing effective evacuation plans in case of fire in underground mine is the most important and sometimes the only option for safe evacuation of all involved in the fire scenario. The wide range of possibilities in the process of improving the evacuation plans in case of fire has motivated many researchers to make new or to modify the existing methodologies or procedures for developing effective and optimal evacuation plans.

• Analysis of production plans

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

the required production capacity.

the necessary steps presented on **Figure 1**.

the underground mine are also marked.

*Methodology for developing and locating fire scenarios in underground mines.*

**Figure 1.**

**73**

• Analysis of work processes and mechanization, etc.

The dynamics of mining activities to increase and fulfill production capacity generates a constant shift in production sites generally associated with mechanization that is likely to trigger a fire scenario. Due to this fact as a relevant indicator that realistically reflects and constantly updates, the list of possible fire locations would be a detailed analysis of daily or monthly production plans. This step involves a thorough analysis of the daily/monthly production plans that will detect any flammable materials mostly associated with the mechanization needed to achieve

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

A case study of the "SASA"-R.N. Macedonia mine was used in order to conduct

The steps shown in **Figure 1** are based on a simple analysis of the production plans that can detect all workplaces with the appropriate work cycle together with

To demonstrate the presented methodology, a 3D model of the underground ventilation network of the mine "SASA"-R.N. Macedonia is prepared on which all the necessary analysis and simulations will be performed (**Figure 2**). On the ventilation map, the possible fire locations along with the group of mineworkers identified using the proposed methodology on **Figure 1** and also the possible exits from

The process of modeling fire scenarios is closely related to the degree of uncertainty when it comes to the input data, which largely depends on the size of the fire itself [11, 12]. Examples of such input parameters that affect the fire models in underground mines are fire load, fire location, burn rate of materials, heat release rate, ventilation parameters, etc. Due to the stochastic nature of the input parameters related to the fire models, the appropriate results should be treated with caution. From the large list of stochastic input parameters, the authors decided to elaborate only on the process of obtaining fire load inputs, which largely depends on

the related mechanization which is often associated with fire scenarios.

Ji et al. [3] developed a visual model to simulate the evacuation process of miners to determine the evacuation time, exit flow rate, and evacuation path and show that simulation is effective technology to establish safe evacuation system. Chen et al. [4] developed 3D CFD model to reconstruct the laneway conveyor belt fire scenes under two ventilating conditions to investigate the influence of smoke movement on miner evacuation behaviors. Wang et al. [5] through example demonstrated the use of their proposed framework for human error risk analysis of coal mine emergency evacuation and also the method to evaluate the reliability of human safety barriers. Wu et al. [6] conducted emergency evacuation simulation and visualized analysis of underground mine water bursting disaster scene, to achieve the simulation of the dynamic process of individual or group behavior and to provide platform for rational evacuation under the situation of mine disaster. Adjiski et al. [7–9] completed many different manuscripts and projects in the field of simulation and modeling of fire scenarios and evacuation plans in underground mines.

To the authors' best knowledge and the extensive search of literature, a lack of methodologies and systems that focus on developing evacuation plans in case of fire in underground mines is shown. Due to the large number of factors from which the effective evacuation process depends, this field of research requires continuous upgrading to address all challenges and also to provide optimal evacuation routes that sometimes represent the only option for preventing loss of human lives.

This chapter is an extension and upgrade of the previously published works from the same author and hopefully will contribute to the process that will improve the methodologies and systems for optimal fire evacuations in underground mines.

#### **2. Methodology for developing underground mine fire scenarios**

In underground mines, a fire can occur wherever flammable material is found, but predicting it at all possible locations is practically impossible. So by analyzing this list of fire locations that have potential flammable materials, it is down to those places that have the highest risk of fire occurrence [10]. The process of conducting fire risk assessment is very straightforward and does not need to be considered in any further detail in this research.

What is new in this study is the proposal of methodology for quickly and efficiently locating and generating fire scenarios ready for simulation on the basis of which optimal evacuation plans will be developed.

To identify possible locations for fire scenarios in underground mines, different approaches can be used, such as [2, 9]:


*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

• Analysis of production plans

Developing effective evacuation plans in case of fire in underground mine is the most important and sometimes the only option for safe evacuation of all involved in the fire scenario. The wide range of possibilities in the process of improving the evacuation plans in case of fire has motivated many researchers to make new or to modify the existing methodologies or procedures for developing effective and

Ji et al. [3] developed a visual model to simulate the evacuation process of miners to determine the evacuation time, exit flow rate, and evacuation path and show that simulation is effective technology to establish safe evacuation system. Chen et al. [4] developed 3D CFD model to reconstruct the laneway conveyor belt fire scenes under two ventilating conditions to investigate the influence of smoke movement on miner evacuation behaviors. Wang et al. [5] through example demonstrated the use of their proposed framework for human error risk analysis of coal mine emergency evacuation and also the method to evaluate the reliability of human safety barriers. Wu et al. [6] conducted emergency evacuation simulation and visualized analysis of underground mine water bursting disaster scene, to achieve the simulation of the dynamic process of individual or group behavior and to provide platform for rational evacuation under the situation of mine disaster. Adjiski et al. [7–9] completed many different manuscripts and projects in the field of simulation and modeling of fire scenarios and evacuation plans in under-

To the authors' best knowledge and the extensive search of literature, a lack of methodologies and systems that focus on developing evacuation plans in case of fire in underground mines is shown. Due to the large number of factors from which the effective evacuation process depends, this field of research requires continuous upgrading to address all challenges and also to provide optimal evacuation routes that sometimes represent the only option for preventing loss

This chapter is an extension and upgrade of the previously published works

In underground mines, a fire can occur wherever flammable material is found, but predicting it at all possible locations is practically impossible. So by analyzing this list of fire locations that have potential flammable materials, it is down to those places that have the highest risk of fire occurrence [10]. The process of conducting fire risk assessment is very straightforward and does not need to be considered in

What is new in this study is the proposal of methodology for quickly and efficiently locating and generating fire scenarios ready for simulation on the basis of

To identify possible locations for fire scenarios in underground mines, different

from the same author and hopefully will contribute to the process that will improve the methodologies and systems for optimal fire evacuations in under-

**2. Methodology for developing underground mine fire scenarios**

optimal evacuation plans.

*Fire Safety and Management Awareness*

ground mines.

of human lives.

ground mines.

any further detail in this research.

approaches can be used, such as [2, 9]:

• Fire risk assessment

**72**

which optimal evacuation plans will be developed.

• Historical records of fire incidents in the mine

• Analysis of work processes and mechanization, etc.

The dynamics of mining activities to increase and fulfill production capacity generates a constant shift in production sites generally associated with mechanization that is likely to trigger a fire scenario. Due to this fact as a relevant indicator that realistically reflects and constantly updates, the list of possible fire locations would be a detailed analysis of daily or monthly production plans. This step involves a thorough analysis of the daily/monthly production plans that will detect any flammable materials mostly associated with the mechanization needed to achieve the required production capacity.

A case study of the "SASA"-R.N. Macedonia mine was used in order to conduct the necessary steps presented on **Figure 1**.

The steps shown in **Figure 1** are based on a simple analysis of the production plans that can detect all workplaces with the appropriate work cycle together with the related mechanization which is often associated with fire scenarios.

To demonstrate the presented methodology, a 3D model of the underground ventilation network of the mine "SASA"-R.N. Macedonia is prepared on which all the necessary analysis and simulations will be performed (**Figure 2**). On the ventilation map, the possible fire locations along with the group of mineworkers identified using the proposed methodology on **Figure 1** and also the possible exits from the underground mine are also marked.

The process of modeling fire scenarios is closely related to the degree of uncertainty when it comes to the input data, which largely depends on the size of the fire itself [11, 12]. Examples of such input parameters that affect the fire models in underground mines are fire load, fire location, burn rate of materials, heat release rate, ventilation parameters, etc. Due to the stochastic nature of the input parameters related to the fire models, the appropriate results should be treated with caution.

From the large list of stochastic input parameters, the authors decided to elaborate only on the process of obtaining fire load inputs, which largely depends on

**Figure 2.** *Ventilation map of the "SASA" mine with marked possible fire locations, group of mineworkers, and exits.*

the severity of the fire scenario itself. The process of modeling fire load inputs that are closely related to the inability to accurately determine the type and quantity of flammable material covered by a fire scenario is done using the Monte Carlo simulation technique. The reason for selecting and analyzing the fire load parameter is because of its immense contribution in generating the amount of toxic gases from which the complexity of the evacuation process depends. The reason for choosing the Monte Carlo simulation technique is because of its speed and simplicity of implementation and also the ability to generate a large amount of input data sampled randomly from their respective distributions [13–15].

The process of developing this model that incorporates the Monte Carlo simulation technique associated with the normal distribution defined by mean = 50, and standard deviation = 15, has been previously explained by the same author, and the entire methodology and reasons for selecting the highlighted parameters can be found here [16].

The inputs in the next steps of the proposed methodology are the approximate values of the total fire load for the selected mechanization. To simplify the process of determining this data, we used the technical manual of the Scooptram ST7, from which we approximated the quantities for the tire, hydraulic fluid, and diesel fuel which will be threatened as total fire load (**Table 1**). Regardless of the fact that the amount of diesel fuel is stochastic in nature, and is dependent on a number of factors, to simplify the model, we will consider it a known value, and we will treat

*Generated scenarios along with the corresponding fire load distribution obtained from the Monte Carlo*

**Tire [kg] Diesel fuel [L] Hydraulic fluid [L]**

Scooptram ST7 238 \* 4 (tires) = 952 190 111

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

*Approximate fire load calculation for the fire scenario from Scooptram ST7.*

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

Following the analysis of the approximate amount of fire load, the next step is to model them using the previously mentioned Monte Carlo simulation technique, along with the necessary data for its normal distribution defined by mean and

For the purpose of this study using the Monte Carlo simulation model, we have generated 20 scenarios with different fire load distribution, which will give variations in the results from the fire scenarios, and we will analyze their impact on the

The purpose of fire models is to describe fire characteristics, such as heat release

Various case studies previously published from the same author are based on the modeling of fire scenarios in a number of different mine ventilation layouts [7–9].

**3. Modeling and simulation of fire scenarios in underground mines**

rate, the burning rate of material, smoke, generating toxic gases, etc., and the results of simulating these models will be as good as the inputs [9, 17]. In order to create a relevant fire model in underground mines, it must be based on an accurate ventilation model. This interconnection and accuracy of the fire and ventilation models will depend on the movement of smoke and toxic gases through the mine

facilities from which the evacuation process is based.

it in a further expansion of the research.

standard deviation [16].

**Table 1.**

**Figure 3.**

**75**

*simulation model.*

evacuation process (**Figure 3**).

What is new in this research is the development of a database that includes all fire scenarios in a predetermined location using the abovementioned methodology on **Figure 1**.

All fire scenarios are analyzed in terms of impact from the fire load input parameters on the evacuation process, that is, how different distribution of combustible materials from the same mechanization (or other composition of combustible materials) will impact the evacuation process.

The introduction of this database aims to select fire scenarios of the same type but with different fire load distribution, from which we can analyze the effects on the evacuation process. The results of this analysis can be used to improve the design of fire systems and evacuation plans and to test them for their effectiveness in different conditions.

From the simple analysis of the monthly production plan of "SASA" mine, we have extracted all work sites for ore exploitation and development of mining facilities with the appropriate work cycle together with the related mechanization. To present the methodology, we will only analyze fire scenarios generated by only one mechanization and present the optimal evacuation route for only one group of workers.

For the purposes of this analysis, we will present the results of the fire scenarios generated by the mechanization Scooptram ST7, located at the possible fire location 3, from where we will simulate the fire scenarios and calculate the optimal evacuation route for group 1 (**Figure 2**).

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*


**Table 1.**

*Approximate fire load calculation for the fire scenario from Scooptram ST7.*

#### **Figure 3.**

the severity of the fire scenario itself. The process of modeling fire load inputs that are closely related to the inability to accurately determine the type and quantity of flammable material covered by a fire scenario is done using the Monte Carlo simulation technique. The reason for selecting and analyzing the fire load parameter is because of its immense contribution in generating the amount of toxic gases from which the complexity of the evacuation process depends. The reason for choosing the Monte Carlo simulation technique is because of its speed and simplicity of implementation and also the ability to generate a large amount of input data sampled randomly from their respective

*Ventilation map of the "SASA" mine with marked possible fire locations, group of mineworkers, and exits.*

The process of developing this model that incorporates the Monte Carlo simulation technique associated with the normal distribution defined by mean = 50, and standard deviation = 15, has been previously explained by the same author, and the entire methodology and reasons for selecting the highlighted parameters can be

What is new in this research is the development of a database that includes all fire scenarios in a predetermined location using the abovementioned methodology

The introduction of this database aims to select fire scenarios of the same type but with different fire load distribution, from which we can analyze the effects on the evacuation process. The results of this analysis can be used to improve the design of fire systems and evacuation plans and to test them for their effectiveness

From the simple analysis of the monthly production plan of "SASA" mine, we have extracted all work sites for ore exploitation and development of mining facilities with the appropriate work cycle together with the related mechanization. To present the methodology, we will only analyze fire scenarios generated by only one mechanization and present the optimal evacuation route for only one group of

For the purposes of this analysis, we will present the results of the fire scenarios generated by the mechanization Scooptram ST7, located at the possible fire location

3, from where we will simulate the fire scenarios and calculate the optimal

All fire scenarios are analyzed in terms of impact from the fire load input parameters on the evacuation process, that is, how different distribution of com-

bustible materials from the same mechanization (or other composition of

combustible materials) will impact the evacuation process.

distributions [13–15].

*Fire Safety and Management Awareness*

found here [16].

in different conditions.

evacuation route for group 1 (**Figure 2**).

on **Figure 1**.

**Figure 2.**

workers.

**74**

*Generated scenarios along with the corresponding fire load distribution obtained from the Monte Carlo simulation model.*

The inputs in the next steps of the proposed methodology are the approximate values of the total fire load for the selected mechanization. To simplify the process of determining this data, we used the technical manual of the Scooptram ST7, from which we approximated the quantities for the tire, hydraulic fluid, and diesel fuel which will be threatened as total fire load (**Table 1**). Regardless of the fact that the amount of diesel fuel is stochastic in nature, and is dependent on a number of factors, to simplify the model, we will consider it a known value, and we will treat it in a further expansion of the research.

Following the analysis of the approximate amount of fire load, the next step is to model them using the previously mentioned Monte Carlo simulation technique, along with the necessary data for its normal distribution defined by mean and standard deviation [16].

For the purpose of this study using the Monte Carlo simulation model, we have generated 20 scenarios with different fire load distribution, which will give variations in the results from the fire scenarios, and we will analyze their impact on the evacuation process (**Figure 3**).

#### **3. Modeling and simulation of fire scenarios in underground mines**

The purpose of fire models is to describe fire characteristics, such as heat release rate, the burning rate of material, smoke, generating toxic gases, etc., and the results of simulating these models will be as good as the inputs [9, 17]. In order to create a relevant fire model in underground mines, it must be based on an accurate ventilation model. This interconnection and accuracy of the fire and ventilation models will depend on the movement of smoke and toxic gases through the mine facilities from which the evacuation process is based.

Various case studies previously published from the same author are based on the modeling of fire scenarios in a number of different mine ventilation layouts [7–9].

For this study, i.e., for simulating fire models across the 3D ventilation network, we used the VentSim software along with VentFIRE™ module that are interconnected because they belong to the same software package. With the help of VentSim software a 3D ventilation network with all working parameters is developed, while the VentFIRE™ module is used for simulation and calculation of the fire scenarios previously generated with the Monte Carlo simulation model.

The theoretical and the working principle of the VentSim software together with the VentFIRE™ module can be found here [18]. Fire models in some cases are analyzed by CFD software for the purpose of comparison between the results obtained from simpler computational methods. Due to the size and complexity of the underground mines, it should be emphasized that CFD analysis can only be used to represent a small section of the mine. The results of such CFD analyses that require a large number of computations which will generate only results related to the immediate proximity of the fire scenario cannot realistically represent the full image generated by the fire model [8, 19]. The functionality of the methodology presented in this chapter is based on the modeling and simulation of fire scenarios whose results can fully represent each time interval of the movement of smoke and fire gases through the whole ventilation network from which the evacuation process entirely depends.

In the process of modeling fire scenarios in VentFIRE™ module in addition to the fire load data presented in **Figure 3**, which was generated with the Monte Carlo simulation model, specific data are also required for each material which is presented in **Table 2**. For the purpose of providing this data, laboratory tests or fire databases containing such information may be used [20, 21].

The results of the fire models obtained by the VentFIRE™ module are in the form of a dynamic representation of the real-time fire progression and utilize a graphic visualization of the spread and concentration of combustion products and all the fire-related data throughout the ventilation system (**Figure 4**).

Monitoring points that are strategically placed throughout the ventilation network allow the extraction of data in the form of concentrations over time for all fire-related data. In this study, for the evaluation of the evacuation plans, only the CO concentration over time curve will be analyzed throughout the ventilation network. The results from the monitoring points will serve for realistic mapping of the CO inhalation throughout the evacuation route for anyone affected by the fire scenario. **Figure 5** shows the CO concentration measured from the monitoring point at the location for the fire scenario S-1.


**Figure 6** shows the average values of CO concentration vs. total duration time

*Average values of CO concentration at fire location and total time duration of the fire for all scenarios generated*

for all fire scenario variants generated by the Monte Carlo simulation model,

measured from the fire location.

*by the Monte Carlo simulation model.*

**Figure 4.**

**Figure 5.**

**Figure 6.**

**77**

*Screenshot from the fire scenario S-1 at 30 minutes from the fire ignition.*

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

*CO concentration over time curve at the fire scenario S-1 location.*

#### **Table 2.** *Input fire characteristics data for the fire load.*

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

**Figure 4.**

For this study, i.e., for simulating fire models across the 3D ventilation network,

The theoretical and the working principle of the VentSim software together with

In the process of modeling fire scenarios in VentFIRE™ module in addition to the fire load data presented in **Figure 3**, which was generated with the Monte Carlo

presented in **Table 2**. For the purpose of providing this data, laboratory tests or fire

The results of the fire models obtained by the VentFIRE™ module are in the form of a dynamic representation of the real-time fire progression and utilize a graphic visualization of the spread and concentration of combustion products and

Monitoring points that are strategically placed throughout the ventilation network allow the extraction of data in the form of concentrations over time for all fire-related data. In this study, for the evaluation of the evacuation plans, only the CO concentration over time curve will be analyzed throughout the ventilation network. The results from the monitoring points will serve for realistic mapping of the CO inhalation throughout the evacuation route for anyone affected by the fire scenario. **Figure 5** shows the CO concentration measured from the monitoring point

] 1150 832 760

Simplified chemical hydrocarbon formula C4H6 C12H23 C36H74 Heat of combustion [MJ/kg] 44 45 48 Burning rate of material [kg/m<sup>2</sup> ∗ s] 0.062 0.045 0.039 O2 consumed [kg/kg] 3.62 3.33 3.57 Yield CO2 [kg/kg] 0.9 3.2 3.3 Yield CO min [kg/kg] 0.13 0.019 0.1 Yield CO max [kg/kg] 0.23 0.21 0.24 Yield soot [kg/kg] 0.1 0.059 0.1

**Tire Diesel fuel Hydraulic fluid**

simulation model, specific data are also required for each material which is

all the fire-related data throughout the ventilation system (**Figure 4**).

databases containing such information may be used [20, 21].

at the location for the fire scenario S-1.

*Input fire characteristics data for the fire load.*

the VentFIRE™ module can be found here [18]. Fire models in some cases are analyzed by CFD software for the purpose of comparison between the results obtained from simpler computational methods. Due to the size and complexity of the underground mines, it should be emphasized that CFD analysis can only be used to represent a small section of the mine. The results of such CFD analyses that require a large number of computations which will generate only results related to the immediate proximity of the fire scenario cannot realistically represent the full image generated by the fire model [8, 19]. The functionality of the methodology presented in this chapter is based on the modeling and simulation of fire scenarios whose results can fully represent each time interval of the movement of smoke and fire gases through the whole ventilation network from which the evacuation process

interconnected because they belong to the same software package. With the help of VentSim software a 3D ventilation network with all working parameters is developed, while the VentFIRE™ module is used for simulation and calculation of the fire scenarios previously generated with the Monte Carlo simulation model.

we used the VentSim software along with VentFIRE™ module that are

entirely depends.

*Fire Safety and Management Awareness*

Density [kg/m<sup>3</sup>

**Table 2.**

**76**

**Figure 5.** *CO concentration over time curve at the fire scenario S-1 location.*

#### **Figure 6.**

*Average values of CO concentration at fire location and total time duration of the fire for all scenarios generated by the Monte Carlo simulation model.*

**Figure 6** shows the average values of CO concentration vs. total duration time for all fire scenario variants generated by the Monte Carlo simulation model, measured from the fire location.

These results highlight the impact of different fire load distribution, thus providing additional data for analysis during the process for determining the optimal evacuation routes.

#### **4. Methodology for determining the optimal evacuation routes based on simulated fire scenarios**

#### **4.1 Life safety assessment during evacuation based on fractional effective dose (FED) from CO inhalation**

Statistical underground mine fire evidence shows that most injuries and deaths are not caused by direct contact with the fire but by way of smoke and toxic gases inhalation [22].

While the fire scenario may be confined to a localized underground mine area, the smoke produced will rise and with the help of the ventilation system may spread rapidly through the mine.

The spread of smoke and toxic gases through the underground mine network will cause difficulties in the evacuation process, and therefore, there is a need for an effective methodology for planning and developing of optimal evacuation routes.

Purser [23] gives extensive review of smoke and toxic gases hazards, including exposure thresholds that can cause incapacitation and even death.

In underground mine fires, the most common asphyxiate is CO, and its effects of incapacitation depend from the gas concentrations and the durations of exposure.

The evacuation management system must be designed and evaluated against a set of criteria to ensure safe evacuation of the mineworkers, which can be achieved by analyzing the fire environments using modeling and simulation.

The proposed method in this book chapter involves the determination of accumulating exposure effect at regular discrete time increments to get the cumulative dosage in terms of FED for the total period of exposure. The exposure doses are calculated as a fraction of incapacitation at every time increment, and the value of FED = 1.0 represents the state of incapacitation in which mineworkers are incapable of completing their own evacuation.

Purser [24] suggests mathematical model for estimating toxic hazard from inhalation of CO from fire scenario in terms of time to incapacitation or death in form of FED and is given as follows:

$$\text{FED}\_{\text{Taxicity}} = \text{FED}\_{\text{CO}} \* \text{V}\_{\text{CO}\_2} + \text{FED}\_{\text{O}\_2} \tag{1}$$

$$\text{FED}\_{\text{CO}} = \sum\_{\text{t}\_1}^{\text{t}\_2} \frac{\text{K} \ast [\text{CO}]^{1,036}}{\text{D}} \Delta \text{t} \tag{2}$$

One of the limitations of this model is the lack of a clear safety margin between the values of the FED in which the transition in the evacuation process from safe to unsafe zone begins. As previously stated, for the evacuation to be considered safe,

**Activity K D** At rest 2,81945 ∗ 10<sup>4</sup> 40 Light work 8,2925 ∗ 10<sup>4</sup> 30 Heavy work 1,6585 ∗ 10<sup>4</sup> 20

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

5–10 Shortness of breath on vigorous exertion, possible tightness across forehead, statistically significant diminution of visual perception, manual dexterity, or ability to learn

21–30 Severe headache, pulsation in sides of head, impaired thinking, disturbed vision, fainting,

41–50 Brain damage, lethargy, seizures, syncope, death from severe cellular hypoxia if exposure

11–20 Atypical dyspnea, throbbing headache, dizziness, nausea, confusion and decreased

31–40 Severe headache, dizziness, respiratory failure, coma, intermittent convulsions

To improve the methodology in this regard, additional model is introduced that will allow to link the entire evacuation timeline with another parameter in the form of COHb prediction in the blood as a result of the CO inhalation generated by the

**4.2 Model for predicting carboxyhemoglobin (COHb) concentration as a result**

The overwhelming hazard in fires is the COHb buildup in the blood as a result of exposures to CO. Inhaled CO acts on the human body by competing with oxygen to combine with hemoglobin molecules in the blood, forming COHb rather than normal oxyhemoglobin (O2Hb) [25]. Exposure to a large concentration of CO is lethal, and the signs and symptoms produced are directly related to the percentage of

The most widely used mathematical model (Coburn-Forster-Kane (CFK)) was

implemented in order to predict COHb (%) blood level from CO exposure on

mineworkers during the underground mine fire scenario.

the FED value should be <1. The question here is how much less than 1?

fire scenario.

**79**

**Table 4.**

**Table 3.**

*Values for different activity levels for the constants K and D.*

2,5–4 Decreased exercise performance in patients with angina

exercise tolerance, dilatation of skin vessels

51–60 Same as above, coma, convulsions, Cheyne-Stokes respiration >70 Slowing and stopping of respiration and death within short period

*Approximate clinical symptoms associated with the blood COHb (%) level [26].*

easy fatigability, disturbed judgment

**COHb (%) Clinical symptoms**

0,4–1 Normal value for nonsmokers

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

is prolonged

**of CO inhalation**

COHb in the blood (**Table 4**).

$$V\_{\rm CO\_2} = \frac{\exp\left(0, 1903 \ast \text{\%CO2} + 2, 0004\right)}{7, 1} \tag{3}$$

$$\text{FED}\_{\text{O}\_2} = \sum\_{\text{t}\_1}^{\text{t}\_2} \frac{1}{\exp\left(8, 13 - 0, 54\left(20, 9\% - 9\% O\_2\right)\right)} \Delta \mathbf{t} \tag{4}$$

where CO (carbon monoxide) is the average concentration (ppm) over the time increment Δt in minutes, K and D are constants which depend on the activity of the person (**Table 3**), %CO2 is the carbon dioxide concentration, and (20,9-%O2) is the oxygen vitiation over the time increment Δt.

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*


**Table 3.**

These results highlight the impact of different fire load distribution, thus providing additional data for analysis during the process for determining the optimal

**4. Methodology for determining the optimal evacuation routes based**

**4.1 Life safety assessment during evacuation based on fractional effective dose**

Statistical underground mine fire evidence shows that most injuries and deaths are not caused by direct contact with the fire but by way of smoke and toxic gases

While the fire scenario may be confined to a localized underground mine area, the smoke produced will rise and with the help of the ventilation system may spread

The spread of smoke and toxic gases through the underground mine network will cause difficulties in the evacuation process, and therefore, there is a need for an effective methodology for planning and developing of optimal evacuation routes. Purser [23] gives extensive review of smoke and toxic gases hazards, including

In underground mine fires, the most common asphyxiate is CO, and its effects of incapacitation depend from the gas concentrations and the durations of exposure. The evacuation management system must be designed and evaluated against a set of criteria to ensure safe evacuation of the mineworkers, which can be achieved

The proposed method in this book chapter involves the determination of accumulating exposure effect at regular discrete time increments to get the cumulative dosage in terms of FED for the total period of exposure. The exposure doses are calculated as a fraction of incapacitation at every time increment, and the value of FED = 1.0 represents the state of incapacitation in which mineworkers are incapable

Purser [24] suggests mathematical model for estimating toxic hazard from inhalation of CO from fire scenario in terms of time to incapacitation or death in

t1

*<sup>V</sup>*CO2 <sup>¼</sup> exp 0, 1903 ð Þ <sup>∗</sup> %CO2 <sup>þ</sup> 2, 0004

where CO (carbon monoxide) is the average concentration (ppm) over the time increment Δt in minutes, K and D are constants which depend on the activity of the person (**Table 3**), %CO2 is the carbon dioxide concentration, and (20,9-%O2) is

FEDToxicity ¼ FEDCO ∗ VCO2 þ FEDO2 (1)

Δt (2)

Δt (4)

7, 1 (3)

<sup>K</sup><sup>∗</sup> ½ � CO 1,036 D

1 exp 8, 13 ð Þ � 0, 54 20, 9% ð Þ � %*O*<sup>2</sup>

exposure thresholds that can cause incapacitation and even death.

by analyzing the fire environments using modeling and simulation.

FEDCO <sup>¼</sup> <sup>X</sup>t2

evacuation routes.

inhalation [22].

rapidly through the mine.

**on simulated fire scenarios**

*Fire Safety and Management Awareness*

**(FED) from CO inhalation**

of completing their own evacuation.

form of FED and is given as follows:

FEDO2 <sup>¼</sup> <sup>X</sup>t2

the oxygen vitiation over the time increment Δt.

**78**

t1

*Values for different activity levels for the constants K and D.*


#### **Table 4.**

*Approximate clinical symptoms associated with the blood COHb (%) level [26].*

One of the limitations of this model is the lack of a clear safety margin between the values of the FED in which the transition in the evacuation process from safe to unsafe zone begins. As previously stated, for the evacuation to be considered safe, the FED value should be <1. The question here is how much less than 1?

To improve the methodology in this regard, additional model is introduced that will allow to link the entire evacuation timeline with another parameter in the form of COHb prediction in the blood as a result of the CO inhalation generated by the fire scenario.

#### **4.2 Model for predicting carboxyhemoglobin (COHb) concentration as a result of CO inhalation**

The overwhelming hazard in fires is the COHb buildup in the blood as a result of exposures to CO. Inhaled CO acts on the human body by competing with oxygen to combine with hemoglobin molecules in the blood, forming COHb rather than normal oxyhemoglobin (O2Hb) [25]. Exposure to a large concentration of CO is lethal, and the signs and symptoms produced are directly related to the percentage of COHb in the blood (**Table 4**).

The most widely used mathematical model (Coburn-Forster-Kane (CFK)) was implemented in order to predict COHb (%) blood level from CO exposure on mineworkers during the underground mine fire scenario.

Previous research by several authors validated both linear and nonlinear CFK model against observations made on subjects exposed to variable CO concentrations, and the consensus is that the model predictions works quite well. The CFK nonlinear model is given by the following Equation [27]:

$$\left[\text{COHb}\right]\_{\text{t}} = \frac{1}{\mathbf{A}\left(\frac{\text{AC}}{[\text{COHb}]\_{\text{0}}}\right)} + (\mathbf{1} - \mathbf{C})\mathbf{V}\_{\text{CO}}\mathbf{B} + (\mathbf{1} - \mathbf{C})\mathbf{P}\_{\text{1,CO}}\tag{5}$$

$$\mathbf{A} = \frac{\mathbf{PO}\_2}{\mathbf{M}[\mathbf{O}\_2 \mathbf{H} \mathbf{b}]} \tag{6}$$

$$\mathbf{B} = \frac{\mathbf{1}}{\mathbf{D}} + \frac{\mathbf{P}}{\mathbf{V\_a}} \tag{7}$$

$$\mathbf{C} = \mathbf{e}^{(-\frac{\mathbf{t} \cdot \mathbf{t}}{\nabla\_{\mathbf{b}} \mathbf{B}})} \tag{8}$$

These factors that influence mineworkers' escape speed can increase the exposure time from the fire scenario and thus present very important factors to be

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

We defined the mineworkers' normal evacuation speed by v0, and under the

The tunnel slope influences the mineworkers' evacuation (and also walking) speed, and the greater the slope the more influence it will have on the process. The tunnel slope influence under climbing situation is given by the following

where m is the standard human mass [kg], g is the gravity acceleration [m/s<sup>2</sup>

The smoke generated by the fire scenario is a major factor in determining tunnel visibility. This visibility factor has important effects on the evacuation speed of

Based on the reviewed literature, two threshold values hold a central function during an evacuation in a smoke-filled environment [30, 32]. The first threshold value is the visibility level at which evacuees in general can be expected to start reducing their evacuation speed. This value based on the reviewed experiments of the data presented from the literature was set to 3 meters as corresponding visibility

The second threshold value is the visibility level at which the mineworkers can

Practically, in the process of calculating the reduction of evacuation speed based

• All individuals in the group are assumed to be evacuating with the same speed.

• Visibility levels >3 m: mineworkers' evacuation speed is represented by

be assumed to be evacuating with their slowest speed. Based on the reviewed literature, the slowest speed during an evacuation in a smoke-filled environment is similar to movement in complete darkness which can be expected to be about 0,2 m/s [30]. In this analysis, the value for the slowest speed of evacuation will also be applied when the mineworkers will move through the evacuation stairs in the

on the smoke visibility level, the model is set in the following way:

When mineworkers pass down slope tunnels, we will assume no influence on their speed, and the model will treat this as normal evacuation speed v0

þ cos θ<sup>s</sup> (9)

],

kts <sup>¼</sup> mgv0 sin <sup>θ</sup><sup>s</sup> P0

considered in the process of determining optimal evacuation routes.

influence of the above factors, the evacuation speed will be vf.

*Methodology for implementation of the evacuation speed influence model.*

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

and θ<sup>s</sup> is the tunnel's angle of slope in degrees.

the mineworkers who are escaping.

threshold value [30, 33, 34].

ventilation raise.

1,2 m/s

**81**

Equation [31]:

**Figure 7.**

(i.e., kts ¼ 1Þ*:*

where:

M—Haldane constant, ratio of the affinity of Hb for CO to that of O2 = 240.

½ � O2Hb —oxyhemoglobin concentration = 0,2 ml ml�<sup>1</sup> blood.

½ � COHb <sup>t</sup>—carboxyhemoglobin concentration at time t in ml CO per ml blood.

½ � COHb <sup>0</sup>—initial concentration of carboxyhaemoglobin in blood

(%COHb = 0,5% for nonsmokers; %COHb >2% for 80% of smokers; %COHb = 10% for heavy smokers).

PO2—partial pressure of oxygen in lung capillaries = 13,3 kPa.

VCO—endogenous CO production rate = 0,007 ml min�<sup>1</sup> .

D—diffusion capacity of the lungs for CO = 225 ml min�<sup>1</sup> kPa (in reality this is not a constant but is altered by a number of factors including exercise).

P—Barometric pressure - saturated vapor pressure of water at 37°C = 95,1 kPa. Vb—blood volume 5500 ml.

P1,CO—partial pressure of CO in inspired air = 0,0101 kPa (adopted for the purposes of this model).

Va—alveolar ventilation rate = 6000 ml min�<sup>1</sup> .

t—duration of exposure [min].

The limitations in the CFK model are located with the physiological variables needed as input to the model which are difficult to measure, such as blood volume, endogenous production of CO, and the pulmonary diffusing capacity [28].

For the purpose of this study, an Excel model based on the CFK equation is built to predict the individual's COHb formation (%), as a result from CO inhalation. For simplification purposes the abovementioned physiological variables are set as default values (as defined in the equation).

The proposed model for predicting COHb (%) with appropriate clinical symptoms (**Table 4**) connected with the FED model can better determine the threshold in which the evacuation will be considered safe.

#### **4.3 Model for the conversion of the factors that influence the speed of evacuation**

To be able to calculate the optimal evacuation routes in underground mines, details about the tunnels' parameters should be provided. Each fire scenario generates factors that influence the complexity and the speed of the evacuation itself.

Based on extensive literature review, two factors are located that have most influence on the evacuation speed, and these factors are generalized in the form of tunnel slope and smoke visibility [7, 29–31]. The model framework is shown in **Figure 7**.

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

**Figure 7.**

Previous research by several authors validated both linear and nonlinear CFK model against observations made on subjects exposed to variable CO concentrations, and the consensus is that the model predictions works quite well. The CFK

<sup>A</sup> <sup>¼</sup> PO2

P Va

ð� tA

<sup>B</sup> <sup>¼</sup> <sup>1</sup> D þ

C ¼ e

½ � O2Hb —oxyhemoglobin concentration = 0,2 ml ml�<sup>1</sup> blood.

½ � COHb <sup>0</sup>—initial concentration of carboxyhaemoglobin in blood

PO2—partial pressure of oxygen in lung capillaries = 13,3 kPa. VCO—endogenous CO production rate = 0,007 ml min�<sup>1</sup>

not a constant but is altered by a number of factors including exercise).

M—Haldane constant, ratio of the affinity of Hb for CO to that of O2 = 240.

½ � COHb <sup>t</sup>—carboxyhemoglobin concentration at time t in ml CO per ml blood.

(%COHb = 0,5% for nonsmokers; %COHb >2% for 80% of smokers; %COHb = 10%

D—diffusion capacity of the lungs for CO = 225 ml min�<sup>1</sup> kPa (in reality this is

P—Barometric pressure - saturated vapor pressure of water at 37°C = 95,1 kPa.

.

P1,CO—partial pressure of CO in inspired air = 0,0101 kPa (adopted for the

The limitations in the CFK model are located with the physiological variables needed as input to the model which are difficult to measure, such as blood volume,

For the purpose of this study, an Excel model based on the CFK equation is built to predict the individual's COHb formation (%), as a result from CO inhalation. For simplification purposes the abovementioned physiological variables are set as

The proposed model for predicting COHb (%) with appropriate clinical symptoms (**Table 4**) connected with the FED model can better determine the threshold

To be able to calculate the optimal evacuation routes in underground mines, details about the tunnels' parameters should be provided. Each fire scenario generates factors that influence the complexity and the speed of the evacuation itself. Based on extensive literature review, two factors are located that have most influence on the evacuation speed, and these factors are generalized in the form of tunnel slope and smoke visibility [7, 29–31]. The model framework is shown in

endogenous production of CO, and the pulmonary diffusing capacity [28].

**4.3 Model for the conversion of the factors that influence the speed of**

<sup>þ</sup> ð Þ <sup>1</sup> � <sup>C</sup> VCOB <sup>þ</sup> ð Þ <sup>1</sup> � <sup>C</sup> P1,CO (5)

M O½ � 2Hb (6)

VbB<sup>Þ</sup> (8)

.

(7)

nonlinear model is given by the following Equation [27]:

A AC ½ � COHb <sup>0</sup>

½ � COHb <sup>t</sup> <sup>¼</sup> <sup>1</sup>

*Fire Safety and Management Awareness*

where:

for heavy smokers).

Vb—blood volume 5500 ml.

t—duration of exposure [min].

default values (as defined in the equation).

in which the evacuation will be considered safe.

Va—alveolar ventilation rate = 6000 ml min�<sup>1</sup>

purposes of this model).

**evacuation**

**Figure 7**.

**80**

*Methodology for implementation of the evacuation speed influence model.*

These factors that influence mineworkers' escape speed can increase the exposure time from the fire scenario and thus present very important factors to be considered in the process of determining optimal evacuation routes.

We defined the mineworkers' normal evacuation speed by v0, and under the influence of the above factors, the evacuation speed will be vf.

The tunnel slope influences the mineworkers' evacuation (and also walking) speed, and the greater the slope the more influence it will have on the process.

The tunnel slope influence under climbing situation is given by the following Equation [31]:

$$\mathbf{k}\_{\rm ts} = \frac{\text{mg} \mathbf{v}\_0 \sin \theta\_\mathbf{s}}{\mathbf{P}\_0} + \cos \theta\_\mathbf{s} \tag{9}$$

where m is the standard human mass [kg], g is the gravity acceleration [m/s<sup>2</sup> ], and θ<sup>s</sup> is the tunnel's angle of slope in degrees.

When mineworkers pass down slope tunnels, we will assume no influence on their speed, and the model will treat this as normal evacuation speed v0 (i.e., kts ¼ 1Þ*:*

The smoke generated by the fire scenario is a major factor in determining tunnel visibility. This visibility factor has important effects on the evacuation speed of the mineworkers who are escaping.

Based on the reviewed literature, two threshold values hold a central function during an evacuation in a smoke-filled environment [30, 32]. The first threshold value is the visibility level at which evacuees in general can be expected to start reducing their evacuation speed. This value based on the reviewed experiments of the data presented from the literature was set to 3 meters as corresponding visibility threshold value [30, 33, 34].

The second threshold value is the visibility level at which the mineworkers can be assumed to be evacuating with their slowest speed. Based on the reviewed literature, the slowest speed during an evacuation in a smoke-filled environment is similar to movement in complete darkness which can be expected to be about 0,2 m/s [30]. In this analysis, the value for the slowest speed of evacuation will also be applied when the mineworkers will move through the evacuation stairs in the ventilation raise.

Practically, in the process of calculating the reduction of evacuation speed based on the smoke visibility level, the model is set in the following way:


**Figure 8.** *Representation of relative reduction of speed in a smoke-filled environment according to the model.*

• Visibility levels ≤3 m: mineworkers' evacuation speed is represented by a relative reduction of 0,34 m/s per meter visibility in a smoke-filled environment down to the previously defined minimum speed of 0,2 m/s.

The correlation in this model is described by the following equation and by **Figure 8** [30]:

$$w = \min\left(1; \max\left(0, 2; 1, 2 - 0, 34 \* (3 - V)\right)\right) \tag{10}$$

where w is the evacuation speed [m/s] and V the visibility [m].

#### **5. Results and discussion**

Determining the optimal routes for evacuation in the case of underground mine fire makes the difference between life and death. In this book chapter, we established a methodology for calculating the optimal routes for evacuation in case of underground mine fire based on simulated scenarios. The methodology shown in **Figure 9** provides the necessary steps to assess the potential fire scenarios and to generate the necessary data on the basis of which all evacuation routes will be evaluated and the optimization process implemented.

The methodology consists of three parts, i.e., developing underground mine fire scenarios, modeling and simulation of fire scenarios, and determining the optimal evacuation routes based on the generated results. The parts of the presented methodology and the procedures for their implementation are presented in detail above.

For the purpose of this study, a case study of the "SASA"-R.N. Macedonia mine was used for determining the optimal routes for evacuations.

In the process of calculating all the parameters needed to determine the optimal evacuation routes, we will take into account the self-contained self-rescuer (SCSR). The use of SCSR in underground mining is a legal obligation in almost all countries around the world, so its introduction into the process of determining the optimal evacuation routes is a very important factor. The SCSR is a portable device that is used in underground mines to provide breathable air for the mineworkers when the surrounding atmosphere is filed with contaminants after emergency situation.

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

**Figure 9.**

**83**

*Proposed methodology implementation framework.*

Extensive research on fire reports provides the fact that sometimes this first line of defense from smoke inhalation in the form of SCSR fails to function properly due to technical problems or due to insufficient training of the mineworkers [35]. Because of this fact in this study, we will make two parallel analyses to calculate the

To present all the steps that the methodology is consists of, we will present the results obtained from only one fire location from which we will calculate the optimal evacuation routes for only one group of workers for all of the 20 fire scenarios generated by the Monte Carlo simulation model.

The results from the Monte Carlo simulation (**Figure 3**) are used as input fire load data for modeling and simulating fire scenarios in the VentFIRE™ module through the mine ventilation network (**Figure 2**). Following the simulation of all 20 fire scenarios from the same fire location, all possible evacuation routes for group 1 have been identified (**Figure 10**).

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

**Figure 9.** *Proposed methodology implementation framework.*

In the process of calculating all the parameters needed to determine the optimal evacuation routes, we will take into account the self-contained self-rescuer (SCSR). The use of SCSR in underground mining is a legal obligation in almost all countries around the world, so its introduction into the process of determining the optimal evacuation routes is a very important factor. The SCSR is a portable device that is used in underground mines to provide breathable air for the mineworkers when the surrounding atmosphere is filed with contaminants after emergency situation.

Extensive research on fire reports provides the fact that sometimes this first line of defense from smoke inhalation in the form of SCSR fails to function properly due to technical problems or due to insufficient training of the mineworkers [35]. Because of this fact in this study, we will make two parallel analyses to calculate the

• Visibility levels ≤3 m: mineworkers' evacuation speed is represented by a relative reduction of 0,34 m/s per meter visibility in a smoke-filled environment down to the previously defined minimum speed of 0,2 m/s.

*Representation of relative reduction of speed in a smoke-filled environment according to the model.*

The correlation in this model is described by the following equation and by

Determining the optimal routes for evacuation in the case of underground mine

The methodology consists of three parts, i.e., developing underground mine fire scenarios, modeling and simulation of fire scenarios, and determining the optimal evacuation routes based on the generated results. The parts of the presented methodology and the procedures for their implementation are presented in detail above. For the purpose of this study, a case study of the "SASA"-R.N. Macedonia mine

To present all the steps that the methodology is consists of, we will present the

The results from the Monte Carlo simulation (**Figure 3**) are used as input fire load data for modeling and simulating fire scenarios in the VentFIRE™ module through the mine ventilation network (**Figure 2**). Following the simulation of all 20 fire scenarios from the same fire location, all possible evacuation routes for group 1

results obtained from only one fire location from which we will calculate the optimal evacuation routes for only one group of workers for all of the 20 fire

established a methodology for calculating the optimal routes for evacuation in case of underground mine fire based on simulated scenarios. The methodology shown in **Figure 9** provides the necessary steps to assess the potential fire scenarios and to generate the necessary data on the basis of which all evacuation routes will be

where w is the evacuation speed [m/s] and V the visibility [m].

fire makes the difference between life and death. In this book chapter, we

evaluated and the optimization process implemented.

was used for determining the optimal routes for evacuations.

scenarios generated by the Monte Carlo simulation model.

have been identified (**Figure 10**).

**82**

*w* ¼ min 1; max 0, 2; 1, 2 ð Þ ð Þ � 0, 34 ∗ ð Þ 3 � *V* (10)

**Figure 8** [30]:

**Figure 8.**

**5. Results and discussion**

*Fire Safety and Management Awareness*

**Figure 10.** *Identification of possible evacuation routes for group 1 for all generated fire scenarios.*


#### **Table 5.**

*Results for group 1, evacuated along route 1 for scenario S-1.*

optimal evacuation routes in which we will introduce the use of a SCSR with a capacity of 30 minutes and the possibility of its non-functionality. By introducing this parameter in the form of functionality and non-functionality of SCSR, we can provide a detailed analysis that can predict the evacuation routes under different conditions.

To elaborate on the proposed methodology, we will present in details the results of scenario S-1.

After the development of the underground mine fire scenarios and their modeling and simulation inside the VentFIRE™ module, all the necessary data for the optimization process is gathered.

For the purpose of this analysis, an average evacuation speed of 1,2 m/s is assumed. The average evacuation speed will be affected by the tunnel slope and smoke visibility.

To calculate the impact on the average speed inside the evacuation process, An Excel model was built based on Eqs. 9 and 10. The results from the simulated fire scenario S-1, which are required as inputs for the FED, COHb, and route calculation models, are shown in **Tables 5**–**8**.

All of the gathered results from the models are stored and arranged in the database. The next step of the proposed methodology is to filter the results inside the database through a route calculation model that will sort out all the evacuation routes according to the level of CO exposure, i.e., the results obtained from the FED

The purpose of the route calculation model is to generate a list of all evacuation routes, which will include the data for route length and cumulative CO exposure in

and COHb model.

**Position Section**

**Position Section**

**Position Section**

**length [m]**

**length [m]**

**Table 6.**

**Table 7.**

**Table 8.**

**85**

**length [m]**

**Visibility [m]**

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

*Results for group 1, evacuated along route 2 for scenario S-1.*

**Visibility [m]**

*Results for group 1, evacuated along route 3 for scenario S-1.*

**Visibility [m]**

*Results for group 1, evacuated along route 4 for scenario S-1.*

**Slope [ o ]**

**Slope [ o ]**

**Slope [ o ]**

**Reduction of evacuation speed (from visibility and slope) [m/s]**

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

**Reduction of evacuation speed (from visibility and slope) [m/s]**

**Reduction of evacuation speed (from visibility and slope) [m/s]**

P1-P2 461 5,1 0 1,2 448 384 384 P2-P3 80 14 75 0,2 344 400 784 P3-P4 426 22 0 1,2 0 355 1139 P4-P5 671 25 0 1,2 0 559 1698 P5-P6 1689 25 0 1,2 0 1408 3106

P1-P2 667 5 0 1,2 448 556 556 P2-P3 340 2 6 0,34 881 1000 1556 P3-P4 80 25 75 0,2 0 400 1956 P4-P5 462 25 0 1,2 0 385 2341 P5-P6 1689 25 0 1,2 0 1408 3748

P1-P2 347 5,1 0 1,2 448 289 289 P2-P3 80 5,3 75 0,2 450 400 689 P3-P4 135 4,7 1,4 1 524 135 824 P4-P5 524 12 5,71 0,29 480 1807 2631 P5-P6 199 25 5,8 0,55 0 362 2993 P6-P7 797 25 1 0,65 0 1226 4219

**Average CO (ppm)**

**Average CO (ppm)**

**Average CO (ppm)**

**Evacuation time in section [s]**

**Evacuation time in section [s]**

**Evacuation time in section [s]**

**Cumulative time [s]**

**Cumulative time [s]**

**Cumulative time [s]**

the form of a FED through the evacuation process.

In the calculation process for the CO exposure over the entire evacuation route, we will include the SCSR in its two previously mentioned forms. To calculate the exposure from CO for each of the possible evacuation routes, the results shown in **Tables 5**–**8** are used as inputs to the FED and the COHb model. The results from the CO exposure based on FED and COHb models build inside Excel are shown in F**igures 11**–**14**.

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*


#### **Table 6.**

*Results for group 1, evacuated along route 2 for scenario S-1.*


**Table 7.**

optimal evacuation routes in which we will introduce the use of a SCSR with a capacity of 30 minutes and the possibility of its non-functionality. By introducing this parameter in the form of functionality and non-functionality of SCSR, we can provide a detailed analysis that can predict the evacuation routes under different

**Reduction of evacuation speed (from visibility and slope) [m/s]**

P1-P2 667 5 0 1,2 448 556 556 P2-P3 232 2 6 0,4 881 580 1136 P3-P4 495 4,6 6,1 0,3 514 1650 2786 P4-P5 524 12 5,71 0,29 480 1807 4593 P5-P6 199 25 5,8 0,55 0 362 4955 P6-P7 792 25 1 0,66 0 1200 6155

**Average CO (ppm)**

**Evacuation time in section [s]**

**Cumulative time [s]**

*Identification of possible evacuation routes for group 1 for all generated fire scenarios.*

**Slope [ o ]**

To elaborate on the proposed methodology, we will present in details the results

After the development of the underground mine fire scenarios and their modeling and simulation inside the VentFIRE™ module, all the necessary data for the

For the purpose of this analysis, an average evacuation speed of 1,2 m/s is assumed. The average evacuation speed will be affected by the tunnel slope and smoke visibility. To calculate the impact on the average speed inside the evacuation process, An Excel model was built based on Eqs. 9 and 10. The results from the simulated fire scenario S-1, which are required as inputs for the FED, COHb, and route calculation

In the calculation process for the CO exposure over the entire evacuation route, we will include the SCSR in its two previously mentioned forms. To calculate the exposure from CO for each of the possible evacuation routes, the results shown in **Tables 5**–**8** are used as inputs to the FED and the COHb model. The results from the CO exposure based on FED and COHb models build inside Excel are shown in

conditions.

**Table 5.**

**Figure 10.**

**Position Section**

**length [m]**

*Fire Safety and Management Awareness*

**Visibility [m]**

*Results for group 1, evacuated along route 1 for scenario S-1.*

of scenario S-1.

F**igures 11**–**14**.

**84**

optimization process is gathered.

models, are shown in **Tables 5**–**8**.

*Results for group 1, evacuated along route 3 for scenario S-1.*


**Table 8.**

*Results for group 1, evacuated along route 4 for scenario S-1.*

All of the gathered results from the models are stored and arranged in the database. The next step of the proposed methodology is to filter the results inside the database through a route calculation model that will sort out all the evacuation routes according to the level of CO exposure, i.e., the results obtained from the FED and COHb model.

The purpose of the route calculation model is to generate a list of all evacuation routes, which will include the data for route length and cumulative CO exposure in the form of a FED through the evacuation process.

The first step in the optimization model is to group the evacuation routes into

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

The values of the FED parameter on which the grouping is based are determined

After grouping the routes into the abovementioned categories, they are filtered through a decision support process that applies the parameter optimization objectives. The optimization model is set so that there is no data in the first group to

For the routes in the first group in which the level is set to FED = 0, the model will select the shortest route in length which will represent the optimal evacuation

The same optimization process is also set for the second and the third group in which the level is set to FED>0 ≤ 0,5 and FED>0,5 ≤ 0,8 accordingly. The reason why this three groups are separated is to give an advantage in the optimization process to the routes with less CO exposure than on those with shorter lengths. For the routes in the fourth group in which the level is set to FED > 0,8 ≤ 1, the model will select the route with the minimum CO exposure presented in the form of FED. In this group, clinical symptoms of CO exposure predict conditions that can cause difficulties during the evacuation process, and because of this, the optimization is set based on the FED parameter with minimal value. The evacuation routes selected in this group should be treated with caution, and they should be thoroughly analyzed for opportunities to install additional evacuation support systems in cer-

For the routes in the fifth group in which the level is set to FED > 1, the model will treat all routes as unsafe for evacuation. If the proposed methodology in this study does not generate data which will fall into the first four groups, then an additional analysis should be performed using the developed ventilation model that shows the movement of smoke and toxic gases through the underground mining facilities. These results could serve to plan the action strategy for the rescue teams

Route 3 (rank 1) 0 3282 Route 4 (rank 2) 0 3327 Route 2 (rank 3) 0,24 2082 Route 1 (rank 4) 0,84 2912

*Ranked evacuation routes from the optimization process for scenario S-1 with the use of a SCSR.*

**FED Route length [m]**

using the COHb model from which COHb (%) concentrations in the blood are predicted for the same CO exposure which in turn are related to the clinical symp-

1.Group 1 of evacuation routes with a value of FED = 0

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

2.Group 2 of evacuation routes with a value of FED>0 ≤ 0,5

3.Group 3 of evacuation routes with a value of FED>0,5 ≤ 0,8

4.Group 4 of evacuation routes with a value of FED>0,8 ≤ 1

5.Group 5 of evacuation routes with a value of FED>1

continue to the next one until the last group is reached.

five categories:

toms presented in the **Table 4**.

route.

tain critical locations.

**Table 9.**

**87**

**Figure 11.**

*Results from the FED and COHb models, for inhalation of CO during evacuation along the route 1.*

**Figure 12.** *Results from the FED and COHb models, for inhalation of CO during evacuation along the route 2.*

**Figure 13.** *Results from the FED and COHb models, for inhalation of CO during evacuation along the route 3.*

**Figure 14.** *Results from the FED and COHb models, for inhalation of CO during evacuation along the route 4.*

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

The first step in the optimization model is to group the evacuation routes into five categories:

1.Group 1 of evacuation routes with a value of FED = 0

2.Group 2 of evacuation routes with a value of FED>0 ≤ 0,5

3.Group 3 of evacuation routes with a value of FED>0,5 ≤ 0,8

4.Group 4 of evacuation routes with a value of FED>0,8 ≤ 1

5.Group 5 of evacuation routes with a value of FED>1

The values of the FED parameter on which the grouping is based are determined using the COHb model from which COHb (%) concentrations in the blood are predicted for the same CO exposure which in turn are related to the clinical symptoms presented in the **Table 4**.

After grouping the routes into the abovementioned categories, they are filtered through a decision support process that applies the parameter optimization objectives. The optimization model is set so that there is no data in the first group to continue to the next one until the last group is reached.

For the routes in the first group in which the level is set to FED = 0, the model will select the shortest route in length which will represent the optimal evacuation route.

The same optimization process is also set for the second and the third group in which the level is set to FED>0 ≤ 0,5 and FED>0,5 ≤ 0,8 accordingly. The reason why this three groups are separated is to give an advantage in the optimization process to the routes with less CO exposure than on those with shorter lengths.

For the routes in the fourth group in which the level is set to FED > 0,8 ≤ 1, the model will select the route with the minimum CO exposure presented in the form of FED. In this group, clinical symptoms of CO exposure predict conditions that can cause difficulties during the evacuation process, and because of this, the optimization is set based on the FED parameter with minimal value. The evacuation routes selected in this group should be treated with caution, and they should be thoroughly analyzed for opportunities to install additional evacuation support systems in certain critical locations.

For the routes in the fifth group in which the level is set to FED > 1, the model will treat all routes as unsafe for evacuation. If the proposed methodology in this study does not generate data which will fall into the first four groups, then an additional analysis should be performed using the developed ventilation model that shows the movement of smoke and toxic gases through the underground mining facilities. These results could serve to plan the action strategy for the rescue teams


**Table 9.**

*Ranked evacuation routes from the optimization process for scenario S-1 with the use of a SCSR.*

**Figure 11.**

*Fire Safety and Management Awareness*

**Figure 12.**

**Figure 13.**

**Figure 14.**

**86**

*Results from the FED and COHb models, for inhalation of CO during evacuation along the route 1.*

*Results from the FED and COHb models, for inhalation of CO during evacuation along the route 2.*

*Results from the FED and COHb models, for inhalation of CO during evacuation along the route 3.*

*Results from the FED and COHb models, for inhalation of CO during evacuation along the route 4.*

or for a suggestion of additional systems that could help in the evacuation process for those affected by the fire scenario.

**Table 11** Shows every optimal evacuation route for group 1 based on the fire scenarios generated by the Monte Carlo simulation model. As previously mentioned the simulation process in the VentFIRE™ module is done from the same fire loca-

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios*

A methodology for determining optimal evacuation routes in case of underground mine fire has been developed based on the results from simulated fire scenarios. The presented methodology can be consistent with the actual situation of the mine because the development of the fire scenarios is based on the risk analysis generated from the current production plans, and the simulation of the developed

To address the stochastic nature of the fire scenarios, the methodology implements the Monte Carlo simulation technique to emphasize the fact related to the inability to accurately determine the input parameters for the fire modeling process. From the large list of stochastic input parameters that can have a noticeable effect on the fire scenarios itself, the authors decided to elaborate only on the process of obtaining fire load inputs, from which the size of the fire depends and thus the amount of generated toxic gases. The results of the proposed methodology point to the fact that by treating the stochastic input parameters presented in this chapter in the form of a fire load, the generated conditions influenced the process of deter-

The Monte Carlo simulation model with the above-defined parameters which follows the normal distribution is implemented on a case study from "SASA"-R.N. Macedonia mine. After the analysis with the proposed methodology, a fire scenario generated by the mechanization Scooptram ST7 is located which represents the total fire load. The stochastic model is set to generate 20 variations from the fire load that are treated as separate scenarios in the process of determining the optimal evacua-

The process of modeling and simulation of the generated fire scenarios is done with the VentFIRE™ module which uses the ventilation network to calculate the movement of the smoke and toxic gases from which the evacuation process

The fire parameters obtained from the simulated scenarios are used to calculate

The proposed methodology as the main factors influencing the evacuation process treats the inhalation of CO through the evacuation route presented in the form of FED and COHb, factors in the form of tunnel slope, and smoke visibility that

In the analysis presented in this chapter, differences in optimal routes for evac-

uation were located only in the conditions of SCSR malfunction. The results presented in **Table 11** highlight the importance of this additional analysis that is possible only by creating multiple variants of one fire scenario which is actually the underlying purpose of the proposed methodology. In the conditions of using the SCSR, the proposed methodology has determined and confirmed route 3 as optimal for evacuation in all variants of the generated fire scenarios. The results obtained from the conditions of SCSR malfunction located the changes in the optimal evacuation between routes 2 and 4 depending on the variable conditions that determined all the fire scenarios. This approach of analyzing fire scenarios offers certainty in the process of confirming the optimal route as well as locating possibilities for its

the optimal evacuation routes for each of the generated scenarios.

affect the speed of evacuation and also the SCSR.

change depending on the variable fire conditions.

scenarios are performed on the ventilation network from the mine.

tion for each of the generated scenarios.

*DOI: http://dx.doi.org/10.5772/intechopen.91213*

**6. Conclusion and future aspects**

mining the optimal evacuation routes.

tion routes.

depends.

**89**

**Table 9** shows the results from the optimization methodology for scenario S-1 in which the routes are sorted by their ranking, taking into account the use of a SCSR.

Considering the use of a SCSR, the optimal evacuation route for scenario S-1 is route 3 which has the best rating according to the present methodology.

**Table 10** shows the results from the optimization methodology taking into account the possibility of malfunction of the SCSR for scenario S-1.

The optimal evacuation route for scenario S-1 in which we assumed the malfunction of the SCSR is route 4 which according to the present methodology has the best rating.


#### **Table 10.**

*Ranked evacuation routes from the optimization process for scenario S-1 without the use of SCSR.*


#### **Table 11.**

*Optimal evacuation route for every fire scenario generated by the Monte Carlo simulation model.*

#### *Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

**Table 11** Shows every optimal evacuation route for group 1 based on the fire scenarios generated by the Monte Carlo simulation model. As previously mentioned the simulation process in the VentFIRE™ module is done from the same fire location for each of the generated scenarios.

#### **6. Conclusion and future aspects**

or for a suggestion of additional systems that could help in the evacuation process

**Table 10** shows the results from the optimization methodology taking into

The optimal evacuation route for scenario S-1 in which we assumed the malfunction of the SCSR is route 4 which according to the present methodology has the

**Optimal route with SCSR Optimal route without the use of SCSR**

**FED Route length [m]**

Scenario S-2 Route 3 FED = 0 Length = 3282 m Route 2 FED = 0,421 Length = 2082 m Scenario S-3 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,115 Length = 3327 m Scenario S-4 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,112 Length = 3327 m Scenario S-5 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,175 Length = 3327 m Scenario S-6 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,168 Length = 3327 m Scenario S-7 Route 3 FED = 0 Length = 3282 m Route 2 FED = 0,439 Length = 2082 m Scenario S-8 Route 3 FED = 0 Length = 3282 m Route 2 FED = 0,432 Length = 2082 m Scenario S-9 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,165 Length = 3327 m Scenario S-10 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,161 Length = 3327 m Scenario S-10 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,159 Length = 3327 m Scenario S-11 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,174 Length = 3327 m Scenario S-12 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,163 Length = 3327 m Scenario S-13 Route 3 FED = 0 Length = 3282 m Route 2 FED = 0,448 Length = 2082 m Scenario S-14 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,170 Length = 3327 m Scenario S-15 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,169 Length = 3327 m Scenario S-16 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,162 Length = 3327 m Scenario S-17 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,156 Length = 3327 m Scenario S-18 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,171 Length = 3327 m Scenario S-19 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,144 Length = 3327 m Scenario S-19 Route 3 FED = 0 Length = 3282 m Route 4 FED = 0,173 Length = 3327 m

*Optimal evacuation route for every fire scenario generated by the Monte Carlo simulation model.*

route 3 which has the best rating according to the present methodology.

Route 4 (rank 1) 0,18 3327 Route 2 (rank 2) 0,74 2082 Route 3 (rank 3) 0,69 3282 Route 1 (rank 4) 1,5 2912

*Ranked evacuation routes from the optimization process for scenario S-1 without the use of SCSR.*

account the possibility of malfunction of the SCSR for scenario S-1.

**Table 9** shows the results from the optimization methodology for scenario S-1 in which the routes are sorted by their ranking, taking into account the use of a SCSR. Considering the use of a SCSR, the optimal evacuation route for scenario S-1 is

for those affected by the fire scenario.

*Fire Safety and Management Awareness*

best rating.

**Table 10.**

**Table 11.**

**88**

A methodology for determining optimal evacuation routes in case of underground mine fire has been developed based on the results from simulated fire scenarios. The presented methodology can be consistent with the actual situation of the mine because the development of the fire scenarios is based on the risk analysis generated from the current production plans, and the simulation of the developed scenarios are performed on the ventilation network from the mine.

To address the stochastic nature of the fire scenarios, the methodology implements the Monte Carlo simulation technique to emphasize the fact related to the inability to accurately determine the input parameters for the fire modeling process. From the large list of stochastic input parameters that can have a noticeable effect on the fire scenarios itself, the authors decided to elaborate only on the process of obtaining fire load inputs, from which the size of the fire depends and thus the amount of generated toxic gases. The results of the proposed methodology point to the fact that by treating the stochastic input parameters presented in this chapter in the form of a fire load, the generated conditions influenced the process of determining the optimal evacuation routes.

The Monte Carlo simulation model with the above-defined parameters which follows the normal distribution is implemented on a case study from "SASA"-R.N. Macedonia mine. After the analysis with the proposed methodology, a fire scenario generated by the mechanization Scooptram ST7 is located which represents the total fire load. The stochastic model is set to generate 20 variations from the fire load that are treated as separate scenarios in the process of determining the optimal evacuation routes.

The process of modeling and simulation of the generated fire scenarios is done with the VentFIRE™ module which uses the ventilation network to calculate the movement of the smoke and toxic gases from which the evacuation process depends.

The fire parameters obtained from the simulated scenarios are used to calculate the optimal evacuation routes for each of the generated scenarios.

The proposed methodology as the main factors influencing the evacuation process treats the inhalation of CO through the evacuation route presented in the form of FED and COHb, factors in the form of tunnel slope, and smoke visibility that affect the speed of evacuation and also the SCSR.

In the analysis presented in this chapter, differences in optimal routes for evacuation were located only in the conditions of SCSR malfunction. The results presented in **Table 11** highlight the importance of this additional analysis that is possible only by creating multiple variants of one fire scenario which is actually the underlying purpose of the proposed methodology. In the conditions of using the SCSR, the proposed methodology has determined and confirmed route 3 as optimal for evacuation in all variants of the generated fire scenarios. The results obtained from the conditions of SCSR malfunction located the changes in the optimal evacuation between routes 2 and 4 depending on the variable conditions that determined all the fire scenarios. This approach of analyzing fire scenarios offers certainty in the process of confirming the optimal route as well as locating possibilities for its change depending on the variable fire conditions.

In order to further improve the methodology, we need to expand our research by introducing the other stochastic variables that may have impact on the evacuation process such as the physical status of mineworkers that is related to age, gender, exercise ability, and response ability.

**References**

pp. 1-19

pp. 7-54

(09)60261-1

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Serafimovski D. Prototype model for fire safety system in underground mining. American Journal of Mining and Metallurgy. 2017;**4**(1):62-67. DOI:

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Using Monte Carlo Analysis.

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Underground Mines. Pittsburgh, PA: National Institute for Occupational Safety and Health-NIOSH; 2005.

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This research provides a convenient methodology for improving the accuracy of determining the optimal evacuation routes which significantly can increase the safety in underground mines.

#### **Acknowledgements**

This work was financially supported by the Faculty of Natural and Technical Sciences—Mining Engineering, "Goce Delchev" University, Shtip, R.N. Macedonia.

#### **Author details**

Vancho Adjiski\* and Zoran Despodov Faculty of Natural and Technical Sciences, Mining Engineering, Goce Delchev University, Shtip, R.N. Macedonia

\*Address all correspondence to: vanco.adziski@ugd.edu.mk

© 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.

*Methodology for Optimal Fire Evacuations in Underground Mines Based on Simulated Scenarios DOI: http://dx.doi.org/10.5772/intechopen.91213*

#### **References**

In order to further improve the methodology, we need to expand our research by introducing the other stochastic variables that may have impact on the evacuation process such as the physical status of mineworkers that is related to age,

This research provides a convenient methodology for improving the accuracy of

determining the optimal evacuation routes which significantly can increase the

This work was financially supported by the Faculty of Natural and Technical Sciences—Mining Engineering, "Goce Delchev" University, Shtip, R.N. Macedonia.

Faculty of Natural and Technical Sciences, Mining Engineering, Goce Delchev

© 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,

\*Address all correspondence to: vanco.adziski@ugd.edu.mk

gender, exercise ability, and response ability.

safety in underground mines.

*Fire Safety and Management Awareness*

**Acknowledgements**

**Author details**

**90**

Vancho Adjiski\* and Zoran Despodov

provided the original work is properly cited.

University, Shtip, R.N. Macedonia

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[4] Chen P, Guo S, Wang Y. Human evacuation affected by smoke movement in mine fires. International Journal of Coal Science & Technology. 2016;**3**(1):28-34. DOI: 10.1007/ s40789-015-0100-3

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[8] Adjiski V. Possibilities for simulating the smoke rollback effect in underground mines using CFD software. GeoScience Engineering. 2014;**2014**(2):8-18. DOI: 10.2478/gse-2014-0008

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[11] Li X, Hadjisophocleous G, Sun X. Sensitivity and uncertainty analysis of a fire spread model with correlated inputs. Procedia Engineering. 2018; **211**(2018):403-414. DOI: 10.1016/j. proeng.2017.12.029

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[30] Fridolf K, Nilsson D, Frantzich H, Ronchi E, Arias S. Walking speed in smoke: Representation in life safety verifications. In: 12th International Performance-Based Codes and Fire Safety Design Methods Conference, Oahu, Hawaii. 2018. pp. 1-6

[15] Salem AM. Use of Monte Carlo simulation to assess uncertainties in fire

*Fire Safety and Management Awareness*

[23] Purser DA. Modelling toxic and physical hazard in fire. Fire Safety Science. 1989;**2**:391-400. DOI: 10.3801/

[24] Purser DA. Toxicity assessment of

[25] Dirks KN, Sturman A, Johns MD. Using health impacts to assess

atmospheric carbon monoxide models. Meteorological Applications. 2006;

[26] Chaloulakou A, Fili N, Spyrelis N.

[27] Coburn RF, Forster RE, Kane PB. Considerations of the physiological variables that determine the blood carboxyhæmoglobin concentrations in

Investigation. 1965;**44**:1899-1910. DOI:

Serafimovski D. System for prediction of carboxyhemoglobin levels as an indicator for on-time installation of selfcontained self-rescuers in case of fire in underground mines. GeoScience Engineering. 2019;**65**(4):23-37. ISSN: 1802-5420. DOI: 10.35180/gse-

[29] Ronchi E, Gwynne SMV, Purser DA. The impact of default settings on evacuation model results: A study of visibility conditions vs occupant walking speeds. In: Advanced Research Workshop - Evacuation and Human Behaviour in Emergency Situations-Santander, Spain. 2011. pp. 2-15

combustion products. In: SFPE Handbook of Fire Protection Engineering. 3rd ed. Quincy, MA: National Fire Protection Association

(NFPA); 2002. pp. 2-83

**13**(1):83-87. DOI: 10.1017/ S1350482705002057

Occupational exposure to CO concentrations in enclosed garages: Estimation of blood COHb levels. In: Environmental Pollution, Proceedings of the 5th International Conference, Thessaloniki, Greece. 2000. pp. 934-940

man. The Journal of Clinical

[28] Adjiski V, Despodov Z,

10.1172/JCI105296

2019-0021

IAFSS.FSS.2-391

[16] Adjiski V, Zubicek V, Despodov Z. Monte Carlo simulation of uncertain parameters to evaluate the evacuation process in an underground mine fire emergency. The Southern African Institute of Mining and Metallurgy. 2019;**119**(11):907-917. DOI: 10.17159/

[17] Gillies S, Wu HW. Case studies from simulating mine fires in coal mines and their effects on mine ventilation systems. In: Aziz N, editor. Coal 2004: Coal Operators' Conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy.

[18] Ventsim Visual™ User Guide. Ventsim Software by Chasm

[19] Adjiski V, Mirakovski D, Despodov Z, Mijalkovski S. CFD simulation of the brattice barrier method for approaching underground mine fires. Mining. Science. 2016;**23**: 161-172. DOI: 10.5277/ msc162313

Consulting. Capalaba, QLD, Australia;

[20] Hansen R, Ingason H. Heat release rate measurements of burning mining vehicles in an underground mine. Fire Safety Journal. 2013;**61**:12-25. DOI: 10.1016/j.firesaf.2013.08.009

[21] Roh JS, Ryou HS, Kim DH. Critical velocity and burning rate in pool fire during longitudinal ventilation. Tunneling Underground Space Technology. 2007;**22**(3):262-271

[22] Hansen R. Literature survey-fire and smoke spread in underground mines. In: MdH SiST 2009:2. Västerås: Mälardalens Högskola; 2009. pp. 7-67

consequence calculation. Ocean Engineering. 2016;**117**:411-430. DOI: 10.1016/j.oceaneng.2016.03.050

2411-9717/701/2019

2004. pp. 111-125

2014

**92**

[31] Guangwei Y, Dandan F. Escaperoute planning of underground coal mine based on improved ant algorithm. Mathematical Problems in Engineering. 2013;**2013**:32-46. DOI: 10.1155/2013/ 687969

[32] Ruixin Z, Rongshan N, Hongze Z, Yanqiang F. Experimental study on the escape velocity of miners during mine fire periods. Mathematical Problems in Engineering. 2018;**2018**:1-12. DOI: 10.1155/2018/9458785. Article ID: 9458785

[33] Fridolf K, Frantzich H, Ronchi E, Nilsson D. The relationship between obstructed and unobstructed walking speed: Results from an evacuation experiment in a smoke filled tunnel. In: 6th International Symposium on Human Behavior in Fire. Cambridge. 2015. pp. 537-548

[34] Fridolf K, Ronchi E, Nilsson D, Frantzich H. Movement speed and exit choice in smokefilled rail tunnels. Fire Safety Journal. 2013;**59**:8-21. DOI: 10.1016/j.firesaf.2013.03.007

[35] McAteer D. The Sago Mine Disaster. Buckhannon, West Virginia; 2016. p. 110. Available from: www.wvgov.org

**95**

Section 4

Safety Protocols with

Case Studies

Section 4
