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A numerical study of the interaction of water spray with a fire plume
Fire Safety Journal 37 (2002) 631–657
A numerical study of the interaction of water spray with a fire plume Jinsong Huaa,*, Kurichi Kumara, Boo Cheong Khoob, Hong Xuec a
Computational Fluid Dynamics Division, Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, 117528, Singapore b Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore c Mechanical Engineering Department, California State Polytechnic University, Pomona, CA 91768, USA Received 4 October 2001; received in revised form 13 February 2002; accepted 15 May 2002
Abstract Water spray-based fire extinguishing equipment such as sprinklers has been widely used in fire suppression and control. However, the fire extinguishing mechanism in such devices is not well understood due to the complexity of the physical and chemical interactions between water spray and fire plume. Currently, quantitative approaches (e.g. numerical modeling) to estimate the performance and effectiveness of water spray systems have not been developed to a stage where they can be used to optimize the design for different operating environments and types of fire. In the present work, a numerical simulation approach is introduced to provide a quantitative analysis of the complex interactions occurring between water spray and fire plume. The effects of several important factors (namely water spray pattern, water droplet size and water spray flow rate) on the fire suppression mechanism are investigated. The simulations show that the water spray with solid cone pattern and finer water droplet size is more effective in extinguishing fires than the one with hollow cone pattern and coarse water droplet size. To suppress a fire, the water spray flow rate has to be more than a certain critical value. However, using too high water spray flow rate does not increase fire suppression efficiency but only leads to increased operational cost because of the excess water flow rate. In the current paper, the principles of fire suppression with water spray are also discussed, which are useful in designing more effective water spray fire suppression systems. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fire plume; Water spray; Simulation; Two-phase flow
*Corresponding author. Tel.: +65-6419-1111; fax: +65-6778-0522. 0379-7112/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 2 ) 0 0 0 2 6 - 7
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Nomenclature A Ad CD cd Cvapor Dd Dvapor g E hm ht hfg k md m ’ mfu mox Mp Psat Pr Qp R Re Rfu Sf Sc Sh T Tdew Tbp t u ui Vg ; Vd xi
Model constant for Arrhenius finite reaction rate (4.2 1015/[kg/m3]3/s) or droplet surface area (m2) Cross section area of water droplet (m2) Drag coefficient between a droplet and the gas phase. Specific heat of water droplet (J/kg/K) Water vapor mole fraction Diameter of water droplet (m) Mass diffusion coefficient of water vapor (m2/s) Gravitational acceleration (m/s2) Activation energy for the chemical reaction (J/mol) Mass transfer coefficient (m/s) Heat transfer coefficient (J/k/m2/s) Latent heat of water vaporization (J/kg) Turbulence kinetic energy (m2/s2) or thermal conductivity (J/m/k) Mass of droplet (kg) Water evaporation rate (kg/s) Mass fraction of fuel Mass fraction of oxygen Mass exchange between the gas and water droplet phases (kg/m3/s) Saturated vapor pressure (N/m2) Prandtl number The heat exchange between the gas and water droplet phases (J/m3/s) Universal gas constant (8.314 J/mol/K) Reynolds number Fuel consumption rate (kg/m3/s) Source/sink term for variable f Schmidt number Sherwood number Temperature (K) Water vapor dew point (K) Water boiling point (K) Time (s) Velocity vector Velocity component in direction i (m/s) Velocity of gas phase and water droplet Coordinate in direction i
Greek letters a; b Model constant for the Arrhenius finite reaction rate (a ¼ 2:8; b ¼ 1:2) Gi The diffusion coefficient for variable f r Fluid density e Turbulence dissipation rate (m2/s3)
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f mg
633
Variable in the governing equation Viscosity of gas phase (kg/m/s)
Subscripts g Gas phase d Droplet phase vapor Water vapor
1. Introduction Water spray system like the standard sprinkler is still considered to be one of the most effective and reliable fire fighting tools. Recently, the development of fine water spray systems offers a new dimension to the current fire extinguishing capability and has many potential applications in the future. For example, the fine water spray system could be used to replace Halon fire extinguishing system. It is also well suited for suppressing fires involving electrical appliances where the influence of water wetting could be dangerous, and for fighting fire in aircraft and ship machine rooms where water supply is limited [1]. Since the concept and mechanism behind the fine water spray system is quite different from that of standard sprinklers [2], considerable attention has been paid to investigate the mechanism behind fine water spray (or water mist) employed to extinguish and control fires. Experimental results have proven that water mist fire suppression system could extinguish fire more efficiently with a relatively small quantity of water compared to the coarse water spray produced by conventional sprinkler systems. The performance of fine water spray systems may be affected by many factors such as water flow rate, spray nozzle type, droplet size, location of sprinkler head, ventilation condition, combustion reaction characteristics and properties of the burning material. Currently, there is insufficient knowledge for a quantitative assessment of which combination of these factors will lead to an optimal design of water spray system. For example, the fire suppression mechanism may be dominated by the evaporative cooling of water droplets within the fire plume, or by the droplets that penetrate the fire plume and cool the burning surface of the fire, or by the droplets that cool the environment around the flame. Factors like these pose a challenge for the fundamental understanding of water spray and fire plume interaction. The engineering design of water spray systems also imposes stringent requirements to develop a quantitative approach to estimate and predict the effectiveness/performance of the water spray system for various fire scenarios. Computational fluid dynamics (CFD) has already been proven to be a useful and powerful tool in fire safety science to model fire phenomena. A number of CFD studies on fire growth, spread and smoke movement have been reported in the literature. Some of the computational models [3–6] have been validated against experimental data and have been proven to be successful in predicting smoke flow patterns and smoke temperature distributions in rooms, tunnels and warehouses. On
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the contrary, the fire extinction process has not been subject to such a thorough investigation using CFD modeling. Recently, many research groups have started efforts to develop a computational approach to model the complete fire extinction process with water spray. The notable early work on modeling fire suppression with sprinklers was carried out by Alpert [7]. The study modeled the gas/water droplet flows in two dimensions and took into account three modes of interactions between fire plume and water droplet (namely mass, momentum, and energy transfer). Three-dimensional numerical studies were conducted by Chow and Fong [8] to examine sprinkler spray interaction with fire-induced hot smoke layer. They considered only the coupling of momentum and energy between the gas and water droplet phases. To simplify the problem, the sprinkler discharge pattern was treated as a constant hollow cone, and was assumed to be unaffected by the airflow. Hence, no droplet trajectories were calculated. The effect of water spray on the airflow was accounted for by the additional source terms in the momentum and energy equations. Nam [2,9] investigated the penetration capability of commercial sprinkler sprays by numerical simulation. In his work, steady-state simulations were conducted to study the interaction of fire plume and water spray. In order to avoid modeling the complex chemical reaction in the fire combustion, the fire was treated simply as a prescribed heat source. Hassan [10] also conducted steady-state simulations on the use of fine water sprays to extinguish fires in computer cabinets. In his study, the fire extinction model took into account some aspects of chemical reaction in fires. However, from a realistic point of view, since any fire extinction process is time dependent, the assumption of steady state may not be able to capture all the relevant aspects. Hoffmann and Galea [11–13] performed, by extending the field-fire modeling technique, transient simulations of the interaction between water spray and fire plume. Unfortunately, they considered only the momentum and thermal interactions between the water spray and fire and disregarded the effect of chemical reaction in fire combustion. Novozhilov et al. [14–16] simulated the extinguishment of wood fire with the water spray. They developed a relatively comprehensive model, combining the water spray model with the fire extinction model. The model included not only the momentum and thermal interactions but also the chemical reactions in fires. In addition, they conducted transient simulations to treat the fire plume/water spray interaction. However, their interests were mainly on investigating the wood fire extinguishment by water sprinkler. Besides cooling the burning surface after the water droplets penetrate through the fire plume, the water spray can also significantly cool the fire plume and affect the chemical reaction rate inside the plume. The penetration process of water spray droplets determines how fast and how many water droplets would be able to pass through the fire plume and finally reach the burning surface. Hence, the dynamic interaction between the water droplets and fire plume plays an important role in fire extinguishment using water sprays. In the present work, a CFD approach is adopted to model the comprehensive interactions between water spray and fire plume. The focus is on studying the effect of water spray characteristics on fire suppression mechanism and efficiency. Hence, the suppression processes of a fire (produced by a
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burner in an open quiescent environment) using the water sprays of different spray characteristics are examined by numerical simulation. The important water spray characteristics taken into account in this study are the water spray pattern (hollow or solid spray cones), water droplet size and the spray flow rate. The numerical model accounts for the following aspects of the water spray/fire plume interactions: (1) the coupling of mass, momentum and energy transfer between the fire plume and water spray; (2) the effects of chemical reaction dynamics on the fire combustion due to the cooling and dilution resulting from water evaporation; (3) the transient nature of fire extinction. This paper is organized as follows. The mathematical approach to model the fire plume/water spray interactions is described in Section 2. Section 3 illustrates the physical problem and some of simplifying assumptions made in this study. This is followed by the simulation results and discussion in Section 4. The effects of water spray pattern, water droplet size and spray flow rate are analyzed in detail. Finally, Section 5 provides the conclusions obtained from the current study.
2. Mathematical modeling To study the interaction between water spray and fire plume, the numerical model should include the flow of two main fluid phases (gas phase and water droplet spray) and account for the interactions between them. The gas phase involves the general airflow and the fire combustion, while the liquid phase includes the movement of (evaporative) water droplets injected from a spray nozzle. At present, there are two widely used numerical modeling approaches to model such two-phase flow problem. They differ in the way the water droplets in the spray are tracked, i.e. Eulerian– Eulerian or Eulerian–Lagrangian methods. In the Eulerian–Eulerian approach, both the gas and water droplet phases are treated as interspersed continua occupying the same space, and their share of space is measured by their volume fraction. The two phases interact with each other via friction, heat and mass transfer, and the calculation depends on the quantity or volume fraction of each phase in the grid cell. This approach was applied in the works of Hoffmann and Galea [11–13], Parasad [17,18] and Hassan [10]. For the Eulerian–Lagrangian method [8,9,19], the gas phase is regarded as a continuum while the water droplet phase is treated as individual particles and are traced using a Lagrangian approach. The momentum, heat and mass transport of these discrete particles are calculated by taking into account the various interacting forces with the gas phase. The effect of the particles on the gas phase is taken into account by introducing appropriate source terms in the conservation equations for the gas phase. A comparison of these two methods reveals that the Eulerian–Eulerian method is more suitable for the dense phase modeling, while the Eulerian–Lagrangian is more suitable for the dilute phase modeling [20]. Because the volume fraction of water droplet phase is quite small [9] in the current study, the Eulerian–Lagrangian method is used to simulate the interaction between fire plume and water spray.
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2.1. Gas phase modeling (fire modeling) The fire plume is created by the combustion of the gas fuel, methane, injected through a nozzle located on the floor in an open quiescent environment. Single-step irreversible chemical reaction is assumed: CH4 þ 2O2 -CO2 þ 2H2 O:
ð1Þ
The airflow and combustion reaction can be described by the conservation equations of mass, momentum, energy and species along with the sub-models for turbulence and combustion. The governing equations for the gas phase can be expressed in the following general form: q ðrfÞ þ rðrufÞ ¼ rðGf rfÞ þ Sf ; qt
ð2Þ
where r stands for the mixture (fuel, air and hot combustion products) density; u for the velocity vector, and t for the time. The symbol f stands for any of the following variables: (1) three velocity components ui in the ith direction; (2) mass fractions of chemical species mi ; (3) enthalpy h; (4) turbulence kinetic energy k; and (5) turbulent dissipation rate e: The definitions of the diffusion coefficient Gf and the source terms Sf for the various variables represented by f are provided in Table 1. The terms Sp ; Mp and Qp in the source term Sf (see Table 1) represent the inter-phase momentum, mass and heat exchanges between the gas and water spray phases, respectively. 2.1.1. Turbulence model Standard two-equation k2e model [21], modified to incorporate the buoyancy effect, has been widely used to estimate the turbulence characteristics of the gas phase flow in fire modeling, and the present study adopts the same approach. By solving these two equations, the turbulence kinetic energy and its dissipation rate are Table 1 Definition of some of the variables in the governing equations Dependent variable f
Diffusion coefficient Geff;f
Source term Sf
Continuity 1 Momentum ui
0 m þ mt
0
Kinetics energy k Dissipation rate e
m þ mt =sk m þ mt =sk
qp q quj þ m þ ðr rref Þgi Sp qxi qxj qxi Pk þ GB re e ðC1 Pk C2 reÞ k Rfu rox Rfu rH2 O Rfu Mp rCO2 Rfu Rfu HC Qp
Species mfu m=Sc þ mt =sf Species mox m=Sc þ mt =sf Species mH2 O m=Sc þ mt =sf Species mCO2 m=Sc þ mt =sf Enthalpy h m=Sc þ mt =sf quj qui quj m qr Pk ¼ mt þ ; Gb ¼ gi t ; Rfu ¼ Araþb mafu mbox eE=RT qui quj qui rsh qxi Sp ; Mp ; Qp represent the inter phase momentum, mass and heat exchange, respectively.
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obtained which are then used to calculate the turbulent effective diffusion coefficient. The effect of water droplet phase on the turbulence of gas phase is ignored in the present work to simplify the problem. 2.1.2. Combustion model A fire sub-model is required to close the above set of governing equations. One of the common methods used by the fire science community is to replace the complicated combustion process [1,9] by a simple prescribed heat source (either volume or surface) model to represent the fire. However, to accordingly describe the fire, a combustion model that accounts for the chemical reactions between fuel and oxygen must be included. The popular combustion models such as Eddy-break-up (EBU) model [16] and Arrhenius finite reaction rate model are typically used to estimate the chemical reaction rate in the fire combustion [17]. EBU model is more suitable for the combustion process in which the turbulent diffusion and mixing of reactants dominate the chemical reaction rate, while the Arrhenius reaction rate model is more suitable where the chemical reaction kinetics is the dominant factor in the chemical reaction [1]. In the current problem of water spray/fire plume interaction, the chemical reaction kinetics in the fire plume is significantly affected by the reaction temperature and reactant concentrations, and may be the dominating factor in the fire extinction mechanism. Therefore, the Arrhenius finite reaction rate model is used in the present study to estimate the combustion rate in fire extinction [22]. It is represented as follows: Rfu ¼ Araþb mafu mbox eE=RT ;
ð3Þ
where A; a and b are the model constants. mfu and mox are the mass fractions of fuel and oxygen, respectively. E stands for the activation energy of the chemical reaction. r; T; R are the gas density, temperature and universal gas constant, respectively. 2.2. Water spray modeling (water droplet phase modeling) In order to reduce the complexity of the interaction between the hot fire plume and the cold water spray, some assumptions on water sprays have been made to simplify the problem in the present study: (1) Water droplets are considered to be spherical in shape. The collision, deformation, break-up and coalescence of droplets are ignored. This is a reasonable simplification when the volume fraction of water spray is usually small as is the case in this study. (2) The water droplets interact only with the mean gas flow so that the effects of turbulence on droplet dispersion are not considered. (3) Water evaporation on the droplet surface has little influence on the drag coefficient. The motion of a water droplet can be described with the following expression, taking into account the drag force from the surrounding airflow and the gravity
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force [19]: md
dV d 1 ¼ CD Ad rg ðV d V g Þ jV d V g j þ md g; 2 dt
ð4Þ
where 24 ð1 þ 0:15Re0:687 Þ; Re rg V d V g Dd Re ¼ ; mg
CD ¼
ð5Þ
ð6Þ
where, V d ; md ; Ad and Dd are the water droplet velocity, mass, cross section area and diameter, respectively. V g ; rg and mg represent the gas phase velocity, density and viscosity, respectively. Here, g is the acceleration due to gravity. The drag coefficient may be reduced due to high water evaporation rate through the droplet surface. However, the water-evaporation rate is relatively small on the droplet surface [12,13] in the current study. Therefore, Eq. (5) can still be used to estimate the effect of drag, as was done in the previous works [8,14–16,19]. The heat transfer between the water droplet phase and the main gas phase plume is calculated by the following equations, taking into consideration the heat absorption due to water evaporation and convective heat transfer around the water droplet: m d cd
dTd ¼ ht AðTg Td Þ þ m ’ d hfg ; dt
ð7Þ
where md ; cd ; A and Td are the mass, specific heat, surface area, and temperature of the water droplet, respectively. Here, hfg is the latent heat of water vaporization, and ht is the convective heat transfer coefficient, which can be evaluated using the following relationship [23,24]: Nu ¼
ht D d ¼ 2:0 þ 0:6Re1=2 Pr1=3 ; kg
ð8Þ
where kg is the thermal conductivity of gas phase. The evaporation rate (m ’ d ) of a water droplet in a hot gaseous environment is due to the rates of vaporization (m ’ vapor ) and boiling (m ’ b) m ’d ¼ m ’ vapor þ m ’ b:
ð9Þ
The vaporization rate of a water droplet in a warm environment is calculated using the following expression [23,24]: Pg Psat ðTd Þ m Cvapor ð10Þ ðTdew oTd oTbp Þ; ’ vapor ¼ hm A RTd RTg Sh ¼
hm D d ¼ 2:0 þ 0:6Re1=2 Sc1=3 ; Dvapor
ð11Þ
where hm is the mass transfer coefficient. Psat and Pg are the saturated vapor pressure and static pressure in the gas phase. Cvapor is the vapor mole fraction, and Dvapor the
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mass diffusion coefficient of water vapor in the gas phase. Tvapor and Tbp are the vapor dew point and boiling point, respectively, of water at atmospheric pressure. Finally, the boiling rate of a water droplet in a warm environment can be estimated by the following equation [25]: pffiffiffiffiffiffi 4kg cg ðTg Td Þ dDd ¼ ð1 þ 0:23 ReÞ ln 1 þ ðTd XTbp ; Dd > 0Þ; ð12Þ hfg dt rd cg Dd 1 dDd ; m ’ b ¼ rd pD2d 2 dt
ð13Þ
where cg is the specific heat of gas phase and rd the density of water. 2.3. Numerical solution procedure The unsteady governing equations described above for the gas phase are solved by an iterative method utilizing a finite volume method. The equations for the gas phase are discretized on an unstructured mesh, and solved numerically using SIMPLE scheme. For the droplet phase of water spray, a Lagrangian method is used to track the movement of water droplets. The droplets are introduced into the computational domain at each time step. The coupling between the gas phase and water spray phase is taken into account by assigning appropriately the source terms in the momentum, heat and species conservation equations.
3. Physical problem A three-dimensional CFD model is developed to investigate the interaction between fire plume and water spray. The schematic diagram of the central section of the computational domain is shown in Fig. 1. In this study, the fire plume is produced by burning the gas fuel methane. The gas fuel is injected into the open quiescent environment from a square burner nozzle (0.25 m 0.25 m). The water spray nozzle is located 1.8 m directly above the center of the burner surface. 3.1. Fire model A relatively stable fire plume is produced when the gas fuel burns in an open quiescent environment. The methane is supplied from a nozzle on the floor at a constant rate resulting in a heat generation rate of around 53 kW. The burning rate of methane is estimated using the Arrhenius finite reaction rate model. The steadystate calculation of the methane gas combustion is first performed to obtain a fully developed fire plume. Then, this fully developed fire plume is used as the initial condition (base state) for subsequent transient simulations to investigate the dynamic interaction between the fire plume and the water spray.
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Fig. 1. Schematic model of the water spray/fire plume interaction.
3.2. Water spray model The formation of water droplets from a sprinkler spray involves many complex processes and presents difficulties for modeling it numerically. Since the primary aim of this work is not on the droplet formation, we adopt Nam’s [9] approach to represent the water spray. He characterized the water spray by measuring the water droplet size, spray velocity, flow rate and discharge angle of the water droplets. A Lagrangian approach can be used to track the water droplet trajectories from the spray nozzle. However, it is impossible to track the trajectory of every water droplet due to the tremendous number of droplets in the water spray. Therefore, the concept of droplet group [19] is used to group water droplets with similar characteristics, and trace the movement of this finite water droplet groups. In the current work, to understand the effect of water spray on fire suppression, the interactions between fire plume and water sprays of different spray patterns (i.e. hollow and solid spray cone patterns), water drop sizes as well as various spray flow rates are investigated. Some other factors, such as water spray mass flow rate, spray angle and speed, have been studied previously in the experimental work of Kim et al. [26] and Yao et al. [27]. The water spray parameters used in our simulations are listed in Table 2. These parameters, associated with each study case, reflect the typical
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Table 2 The water spray parameters used in the simulations Case no.
1 2 3 4 5 6 7 8 9
Parameters for water sprays Spray pattern
Drop diameter (mm)
Hollow cone Hollow cone Solid cone Solid cone Solid cone Solid cone Solid cone Solid cone Solid cone
270 135 270 200 135 100 270 270 270
Mass flow rate (kg/s)
Outlet speed (m/s)
Discharge angle
15
801
0.5
0.1 1.0 3.0
scenarios that would be expected from a sprinkler/water mist system [9,26,28]. The distribution of water flow rate for the solid water spray nozzle is assumed to be uniform across the outlet cross section of the nozzle. The droplet sizes in the various water sprays are allowed to vary from 100 to 270 mm in diameter. However, for each water spray, we assume that the water droplets have a uniform size at the discharge point. Since the primary interest of the current work is to study the interaction between fire plume and water spray, the interaction between the wall/burning surface and water spray droplet is not considered, as it would add further complications to the problem. This will be investigated in a future study.
4. Results and discussion The interaction between the water spray and the fire plume includes primarily the following three aspects: (a) momentum interaction: the injection of a water spray can significantly change the gas flow pattern in the fire plume, which in turn affects the flame structure and its heat and mass transfer characteristic; (b) thermal interaction: the evaporation of water droplet will cool the fire plume; (c) chemical reaction interaction: the chemical reaction rate in the fire plume is reduced due to lowered reaction temperature caused by the heat absorption of the evaporating water droplets. It is also due to the dilution of the reactant (fuel and air) resulting from the vapor generated by vaporizing water droplets. Obviously, the performance of a water spray to suppress fire may be affected by any combination of the above interactions. In order to better understand the role of each of the above interactions, numerical simulations have been carried out to investigate the effect of water spray pattern, water droplet size, and spray flow rate.
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4.1. Effect of water spray pattern The simulation results of steady-state combustion of gas fuel in an open quiescent environment are shown in Figs. 2(A)–7(A), where the velocity, temperature and water vapor concentration distributions within the fire plume are illustrated. This is taken to be the base case or the initial state from which the transient events develop. Fig. 2(A) shows the gas velocity vectors in the base-state fire plume. The fuel gasmethane is injected from the fuel nozzle located on the floor and burns in the open environment. The combustion heat raises the gas temperature as shown in Fig. 3(A), and builds up a hot fire plume. The simulation results from the use of a hollow water spray in the fire extinguishing process are shown in Figs. 2–4. Fig. 2 shows the temporal velocity vectors of the gas phase when the water spray is activated from a hollow cone type nozzle. After the water spray is activated at time t ¼ 0; the water droplets shoot out at a high velocity of 15 m/s. Because of their high speed, the water droplets entrain the surrounding cool air moving at a speed of about 5–6 m/s as shown in Fig. 2(B). As time progresses, more cool air is entrained into the droplet airflow stream as shown in Fig. 2(C). The entrainment initially enhances the downdraft of cool air, and then it impinges on the burner surface and spreads outward along the floor as shown in Figs. 2(D) and (E). This results in cooling the surrounding space of fire plume and eventually leading to the total suppression of the fire. Fig. 3 shows the temporal distributions of the gas phase temperature when the hollow water spray is used to suppress the fire (Case 1). The first point to note, from Fig. 3(B), is the water spray cutting off the fire plume. Then, the downward draft of cool air pushes the fire plume outward and cools it as well, as shown in Figs. 3(C) and (D). Finally, the fire gets suppressed. The effect of water evaporation on fire suppression is illustrated in Fig. 4 by means of temporal water vapor concentrations. Evaporation of water takes place when the droplets make contact with the fire plume. A high water vapor concentration is observed during the initial period of activation of the water spray, as shown in Fig. 4(B). This is attributed to the existence of high-temperature fire plume close to the water spray discharge point. As time progresses, the water droplets spread downward to the outer edge of the fire plume as shown in Figs. 2(C)–(E). Because the ambient temperature in the outer region of the fire plume is lower, the water evaporation rate is also lower, and hence the lower water vapor concentration as well. It can also be seen from Fig. 4 that the water vapor concentration in the core of the fire plume does not change significantly during the entire fire suppression process. This implies that the chemical reaction in the fire plume is not influenced significantly by the water vapor dilution. The results from the use of a solid water spray on fire suppression (Case 3) are now discussed. The solid water spray has exactly the same parametric configurations as the hollow water spray except for the spray pattern. The temporal variations of gas phase velocity, temperature and water vapor concentration for the solid water spray case are presented in Figs. 5–7, respectively. In the case of solid water spray, the water droplets are sprayed out through the entire surface of the nozzle outlet as shown in Fig. 5(B). Consequently, the central part of the water spray is delivered
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Fig. 2. The temporal vector plots of the gas phase velocity during the interaction of the hollow-cone water spray with the fire plume (case 1).
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Fig. 3. The temporal contour plots of the gas phase temperature (K) during the interaction of the hollowcone water spray with the fire plume [Case 1]. (H represents the vertical distance from the burning surface and R the horizontal distance from the center of burning surface.)
directly to the core part of the fire plume, resulting in higher water evaporation rate because of the elevated temperature. This helps the central part of the fire plume to be cooled down as the evaporating water droplets absorbs the heat, as shown in
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Fig. 4. The temporal contour plots of the water vapor concentration during the interaction of the hollowcone-type water spray with the fire plume (case 10).
Figs. 6(C) and (D). The water vapor concentration distributions shown in Figs. 7(C) and (D) also support the fact that the evaporating water droplets create much higher water vapor concentration in the core part of fire plume where the chemical reaction for combustion occurs. This result can be contrasted to the water concentration in
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Fig. 5. The temporal vector plots of the gas phase velocity during the interaction of the solid-cone water spray with the fire plume (case 3).
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Fig. 6. The temporal contour plots of the gas phase temperature (K) during the interaction of the solidcone water spray with the fire plume (case 3).
the base combustion case as depicted in Fig. 7(A). As a result of the high water vapor concentration in the fire plume core, the fire combustion rate is significantly lowered. This is because of the lower reaction temperature due to high heat absorption by the water droplets, and because of the dilution of reactant concentration by water vapor.
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Fig. 7. The temporal contour plots of the water vapor concentration (mass fraction) during the interaction of the solid-cone-type water spray with the fire plume (case 3).
As time progresses, the heat generation from the fire is reduced due to lower reaction rate, and eventually the fire is extinguished. Comparing the fire plume and water spray interaction behavior for these two types of nozzles (i.e. hollow spray cone and solid spray cone) based on the results
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2500
Gas phase temperature (K)
Case 1 Case 3
Case 2 Case 5
2000
1500
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
Time (s) Fig. 8. The variation gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water spray pattern.
presented above, it can be concluded that the fire suppression mechanism for the two nozzle types is different. In general, the solid cone-type spray nozzle is more effective because it delivers some of the water droplets directly to the region where chemical reaction occurs in the fire plume. As discussed above, this leads to a reduction in the chemical reaction rate by lowering the reaction temperature and diluting the reactant concentration, and hence a faster suppression of the fire. On the other hand, water droplets from the hollow spray cone nozzle only entrain the air from the surrounding regions to form a cool airflow stream that impinges and cools the hot fire plume. The chemical reaction rate is not affected by the vapor dilution in this case. Therefore, it takes the hollow cone water spray longer time period to suppress the same size fire compared to the solid cone water spray. This conclusion can also be obtained from Fig. 8, which show temperature histories for the two types of water spray at a point located on the centerline and 0.03 m above the burner surface for the same fire. 4.2. Effect of water droplet size The effect of water droplet size on fire suppression is examined by simulation cases 4 and 6, and the results are shown in Figs. 9–12. Here, the droplet size considered for the water sprays in the two simulation cases are 100 and 200 mm in diameter, respectively. The temporal distribution of water evaporation rate for the two droplet sizes, along the vertical centerline through the burning surface, is shown in Figs. 9(A) and (B), respectively. It can be clearly seen from Fig. 9 that there are always two peaks in the water evaporation rate curve at a given time instance. Peak 1 is due to the water evaporation in the cool entrained airflow, and peak 2 is due to the strong
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Water evaporation rate ( kg/m 3s)
1.4E-04
Peak 2 1.2E-04
t=0.05s t=0.15s t=0.25s t=0.35s t=0.45s
1.0E-04 8.0E-05 6.0E-05
Peak 1
4.0E-05 2.0E-05 0.0E+00 0.0
0.5
1.0
(A)
1.5
2.0
2.5
H (m)
Water evaporation rate (kg/m3s)
1.4E-04 1.2E-04
Peak 2
1.0E-04 8.0E-05
t=0.10s t=0.20s t=0.30s t=0.40s t=0.50s
6.0E-05
Peak 1 4.0E-05 2.0E-05 0.0E+00 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 9. The temporal distributions of water droplet evaporation rate along the vertical central line of the burning surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 4).
heating effect from the fire plume. After the water droplets are injected from the nozzle, they start to evaporate immediately (refer to peak 1) since the water vapor concentration in the entrained airflow region is lower than the vapor saturation concentration. As the water droplets penetrate deeper into the fire plume, they are heated up. As a result, the saturation vapor concentration around the water droplets becomes higher as well. This leads to higher evaporation rate of the water droplet (refer to peak 2) in the fire plume. As the interaction between the fire plume and the water spray continues, the fire plume is cooled and its physical size is reduced subsequently. At the same time, the water evaporation rate peak 2 moves downward along the vertical direction. Comparing the evaporation rate magnitudes for different drop sizes shown in Figs. 9(A) and (B), it can been see that the smaller droplets produce higher water evaporation rate.
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Gas phase temperature (K)
2500
2000
t=0.05s t=0.15s t=0.25s
1500
t=0.35s t=0.45s
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
H (m)
(A)
Gas phase temperature (K)
2500
2000
1500
t=0.10s
t=0.20s
t=0.30s
t=0.40s
t=0.50s
t=0.60s
1000
500
0 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 10. The temporal distribution of gas phase temperature along the vertical central line of the burning surface for different water drop size: (A) 100 mm (case 6) and (B) 200 mm (case 4).
The thermal interaction between fire plume and water spray for different water droplet sizes is illustrated in Figs. 10(A) and (B) in terms of the temporal temperature profile along the vertical centerline through the burning surface. The variation of interaction zones between fire plume and water spray with time is indicated with the arrows shown in Fig. 10. After the water spray is activated, it first cools the top part of the fire plume to the level of local environment temperature. With further amount of water spray, the extent of the fire plume becomes smaller and smaller until it is finally extinguished. Fig. 10 also illustrates that the spatial distances between the thermal interaction zones for two adjacent time steps are always larger for the water spray with smaller droplet size. This indicates that the finer water spray can penetrate the fire plume faster than the coarser one. In addition, the temperature gradients in the thermal interaction zones are higher for the smaller droplet size than that of the coarser one. In fact, for the finer water spray,
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Gas phase velocity magnitude (m/s)
7 6
t=0.05s t=0.15s
5
t=0.25s t=0.35s
4
t=0.45s 3 2 1 0 0.0
0.5
1.0
1.5
2.0
2.5
H (m)
(A)
Gas phase velocity magnitude (m/s)
7 6
t=0.10s t=0.20s
5
t=0.30s 4
t=0.40s t=0.50s
3
t=0.60s
2 1 0 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 11. The temporal distributions of gas phase velocity magnitude along the central line of burner surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 4).
the penetration capability of every water droplet is lower due to the higher drag effect from the surrounding air. Hence, the size of the interaction zone between the fine water spray and the fire plume is smaller, which leads to a higher temperature gradient. Since the water evaporation rate is higher for the finer water spray, as shown in Fig. 9, it leads to higher heat absorption rate which then helps to cool the fire plume quickly. This in turn reduces the buoyancy force on the water droplet cloud, and help the finer droplet cloud to penetrate the fire plume more easily and quickly. Therefore, the finer water droplet cloud can suppress the fire plume more effectively. Fig. 11 shows the momentum interaction between water spray and fire plume in terms of the distribution of airflow speed along the vertical centerline though the burning surface. The downward airflow speed initially increases rapidly because of
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Water vapor mass fraction
0.25
t=0.05s
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t=0.15s t=0.25s
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t=0.35s t=0.45s
0.10
0.05
0.00 0.0
0.5
1.0
(A)
1.5
2.0
2.5
H (m) 0.25
Water vapo rmass fraction
0.20
0.15
t=0.20s
t=0.30s
t=0.40s
t=0.50s
t=0.60s
0.10
0.05
0.00 0.0
(B)
t=0.10s
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 12. The temporal distributions of water vapour mass fraction along the vertical central line of burner surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 6).
the strong drag effect from the water spray. As the water droplets move further downward, their drag effects on the surrounding air will reduce locally due to the ‘‘opening up’’ of the spray cone. This results in a reduction of the airflow speed. However, as the water spray spreads downward, more and more surrounding air is entrained into the airflow such that the air velocity increases again and maintains that velocity till its interaction with the fire plume. As shown in Fig. 11 the finer water spray will induce higher entrained air velocity, which in turn will deliver more cool air to the fire plume and hence provide more effective fire suppression. Obviously, the evaporation of the water droplet would not only cool the fire plume, but also increase the water vapor concentration there leading to the formation of a water vapor cloud indicated by the peak in the water vapor concentration curve, as shown in Fig. 12. As the water droplets move downward, the
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2500
Gas phase temperature (K)
Case 3 Case 4
2000
Case 5 Case 6
1500
1000
500
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (s)
Fig. 13. The variation of gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water droplet size.
water vapor cloud also moves downward. The vapor concentration in the fire plume becomes higher and higher, since the high plume temperature would lead to high water evaporation rate around the droplets. However, comparing the effect of water droplet size on the water vapor concentration, as shown in Figs. 12(A) and (B), the fine water spray is seen to produce a lower water vapor concentration even though it has higher water evaporation rate. Actually, the vapor concentration in the interaction zone depends on the balance between the evaporation rate and the convection transfer rate. For the fine water spray, the evaporation rate is high, and the air velocity is also high, which implies a higher convection transfer rate. Hence, the chemical reaction for fire combustion is not significantly affected by the dilution effects of the fine water spray compared to that of the coarse water spray. The fire suppression mechanism of the fine water spray still depends mainly on its cooling effect. The effect of using water sprays with different water droplet sizes (case 3–6) on suppressing the same fire is illustrated in Fig. 13 by means of the temporal gas temperature history at a point located on the centerline and 0.03 m above the burner surface. In the case of the finer water spray, the higher water evaporation rate cools the hot fire plume effectively and reduces the general buoyancy effect on the downward moving droplet cloud. As a result, the finer water spray takes less time than the coarser one to suppress the same size fire. 4.3. Effect of water spray flow rate Fig. 14 shows the temporal gas temperature history at the point located on the centerline and 0.03 m above the burner surface for the water sprays with different flow rates. It is obvious that the water spray with the higher flow rate would take less time to extinguish a fire. If the water flow rate is not high enough, the fire may not be
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Gas phase temperature (K)
2500
2000
Case 3
Case 7
Case 8
Case 9
1500
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (s) Fig. 14. The variation of gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water spray flow rate.
Time taken for fire suppression (s)
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Water spray flow rate (kg/s) Fig. 15. The variation of time taken for fire suppression against water spray flow rate.
suppressed (case 7) regardless of the time period the water spray is applied. This means that the flow rate of water spray should be higher than a critical value in order to suppress a certain size fire. Also, if the flow rate of the water spray increases, the time taken to suppress the same size fire does not decrease linearly. Fig. 15 shows the variation of the time taken to suppress the same fire as a function of the water spray flow rate. It is obvious from Fig. 15 that the fire suppression efficiency of a water spray system cannot be improved significantly by increasing the water spray flow rate beyond a certain threshold value. Moreover, if higher flow rates are used, more
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than the optimum value, the operational cost of the water spray system will become higher. Hence, an effective water spray system should be able to suppress fires in a relatively short-time period using a minimum amount of water.
5. Conclusions A numerical simulation approach has been developed to investigate the interaction between the fire plume and the water spray. The simulation results prove that the current approach has the capability to reasonably capture the interactions between the water spray and the fire plume taking in account the effects of momentum exchange, heat and mass transfer as well as chemical reaction. The effect of important water spray parameters such as spray patterns (solid and hollow cone sprays), water droplet size and water flow rate on fire suppression mechanism and effectiveness have also been analyzed. The solid water spray cone can extinguish fires more effectively than the hollow spray cone. The solid water spray delivers more water droplets to the core part of fire plume leading to a higher water evaporation rate. This not only helps to absorb more heat but also generates large quantity of water vapor. Both of these factors help to reduce the chemical reaction rate in the fire plume and leads to the extinction of fire. On the other hand, the water spray with hollow spray cone relies primarily on the entrained cool airflow to cool and extinguish the fire plume. As to the effect of water droplet size, the fine water spray works more effectively on fire extinction than the coarse water spray. This is due to the fact that the fine water spray leads to a higher water evaporation rate, which effectively cools the fire plume and reduces the buoyancy effect of the fire plume. The fine water spray is then able to penetrate and suppress the fire plume more effectively. The results on the effect of water supply flow rate show that the flow rate should be higher than a critical value to be able to suppress the fire. It is also important to note that, from an efficiency point of view, there is no need to use more than a certain quantity of water flow rate as it does not increase the efficiency of fire suppression system. The present study also provides some basic guidelines on designing more effective water spray systems for fire suppression.
Acknowledgements The authors would like to acknowledge the technical contributions from Ms Sophia Chan Hui Ling from the Department of Mechanical Production Engineering, National University of Singapore.
References [1] Mawhinney JR, Hadjisophocleous GV. The role of fire dynamics in design of water mist fire suppression system. Proceedings of INTERFLAM’96, 1996. p. 415–24.
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[2] Nam S. Numerical simulation of the penetration capability of sprinkler sprays. Fire Saf J 1999;32:307–29. [3] Cox G, Kumar S, Markatos NC. Some field model validation studies. Fire Safety Science. Proceedings of the First International Symposium, 1985. p. 159–71. [4] Cox G, Kumar S. Field modelling of fire in force ventilated enclosures. Combust Sci Technol 1987;52:7–23. [5] Sinai YL, Owens MP. Validation of CFD modelling of unconfined pool fire with cross-wind: flame geometry. Fire Saf J 1995;24:1–34. [6] Fletcher DF, Kent JH, Apte VB, Green AR. Numerical simulation of smoke movement from a pool fire in a ventilated tunnel. Fire Saf J 1994;23:305–25. [7] Alpert RL. Numerical modelling of the interaction between automatic sprinkler sprays and fire plumes. Fire Saf J 1985;9:157–63. [8] Chow WK, Fong NK. Numerical simulation on cooling of fire-induced air flow by sprinkler water sprays. Fire Saf J 1991;17:263–90. [9] Nam S. Development of a computational model simulating the interaction between a fire plume and a sprinkler spray. Fire Saf J 1996;26:1–33. [10] Hassan MA. A theoretical simulation of fire extinction by water spray in a computer cabinet. Appl Math Modelling 1996;20:804–13. [11] Hoffmann NA, Galea ER. Mathematical modeling of fire sprinkler systems. Appl Math Modelling 1989;13:298–306. [12] Hoffmann NA, Galea ER. An extension of the fire-field modelling technique to include fire-sprinkler interaction—I. The mathematical basis. Int J Heat Mass Transfer 1993;36:1435–44. [13] Hoffmann NA, Galea ER. An extension of the fire-field modelling technique to include fire-sprinkler interaction—II. The simulation. Int J Heat Mass Transfer 1993;36:1445–57. [14] Novozhilov V, Harvie DJE, Kent JH. A computational fluid dynamics study of wood fire extinguishment by water spray. Fire Saf J 1997;29:259–82. [15] Novozhilov V, Moghtaderi B, Fletcher DF, Kent JH. Numerical simulation of enclosed gas fire extinguishment by a water spray. J Appl Fire Sci 1995;5:135–46. [16] Novozhilov V, Moghtaderi B, Kent JH, Fletcher DF. Solid fire extinguishment by a water spray. Fire Saf J 1999;32:119–35. [17] Prasad K, Li C, Kailasanath K. Simulation of water mist suppression of small scale methanol liquid pool fires. Fire Saf J 1999;33:185–212. [18] Prasad K, Li C, Kailasanath K, Ndubizu C, Gopal R, Tatem PA. Numerical modelling of water mist suppression of methane–air diffusion flame. Combust Sci Technol 1998;132:132–325. [19] Kumar S, Heywood GM, Liew SK. Superdrop modelling of a sprinkler spray in a two-phase CFDparticle tracking model. Fire Safety Science. Proceedings of the Fifth International Symposium, 1997. p. 889–900. [20] Mostafa AA, Mongia HC. On the modeling of turbulent evaporating sprays: Eulerian versus Lagrangian approach. Int J Heat Mass Transfer 1987;30:2583–93. [21] Launder BE, Spalding DB. Lectures in mathematical modeling of turbulence. London: Academic Press, 1972. [22] Lange HC, Goey LPH. Two-dimensional methane/air flame. Combust Sci Technol 1993;92:423–7. [23] Ranz WE, Marshell Jr. WR. Evaporating from drops, Part I. Chem Eng Prog 1952;48:141–6. [24] Ranz WE, Marshell Jr. WR. Evaporating from drops, Part II. Chem Eng Prog 1952;48:173–80. [25] Kuo KKY. Principles of combustion. New York: Wiley, 1986. [26] Kim MB, Jang YJ, Kim JK. Burning rate of pool fire with downward-directed sprays. Fire Saf J 1996;27:37–48. [27] Yao B, Fan W, Liao G. Interaction of water mists with a diffusion flame in a confined space. Fire Saf J 1999;33:129–39. [28] Downie B, Polymeropoulos C, Gogos G. Interaction of a water mist with a buoyant methane diffusion flame. Fire Saf J 1995;24:359–81.
A numerical study of the interaction of water spray with a fire plume Jinsong Huaa,*, Kurichi Kumara, Boo Cheong Khoob, Hong Xuec a
Computational Fluid Dynamics Division, Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, 117528, Singapore b Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore c Mechanical Engineering Department, California State Polytechnic University, Pomona, CA 91768, USA Received 4 October 2001; received in revised form 13 February 2002; accepted 15 May 2002
Abstract Water spray-based fire extinguishing equipment such as sprinklers has been widely used in fire suppression and control. However, the fire extinguishing mechanism in such devices is not well understood due to the complexity of the physical and chemical interactions between water spray and fire plume. Currently, quantitative approaches (e.g. numerical modeling) to estimate the performance and effectiveness of water spray systems have not been developed to a stage where they can be used to optimize the design for different operating environments and types of fire. In the present work, a numerical simulation approach is introduced to provide a quantitative analysis of the complex interactions occurring between water spray and fire plume. The effects of several important factors (namely water spray pattern, water droplet size and water spray flow rate) on the fire suppression mechanism are investigated. The simulations show that the water spray with solid cone pattern and finer water droplet size is more effective in extinguishing fires than the one with hollow cone pattern and coarse water droplet size. To suppress a fire, the water spray flow rate has to be more than a certain critical value. However, using too high water spray flow rate does not increase fire suppression efficiency but only leads to increased operational cost because of the excess water flow rate. In the current paper, the principles of fire suppression with water spray are also discussed, which are useful in designing more effective water spray fire suppression systems. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fire plume; Water spray; Simulation; Two-phase flow
*Corresponding author. Tel.: +65-6419-1111; fax: +65-6778-0522. 0379-7112/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 2 ) 0 0 0 2 6 - 7
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Nomenclature A Ad CD cd Cvapor Dd Dvapor g E hm ht hfg k md m ’ mfu mox Mp Psat Pr Qp R Re Rfu Sf Sc Sh T Tdew Tbp t u ui Vg ; Vd xi
Model constant for Arrhenius finite reaction rate (4.2 1015/[kg/m3]3/s) or droplet surface area (m2) Cross section area of water droplet (m2) Drag coefficient between a droplet and the gas phase. Specific heat of water droplet (J/kg/K) Water vapor mole fraction Diameter of water droplet (m) Mass diffusion coefficient of water vapor (m2/s) Gravitational acceleration (m/s2) Activation energy for the chemical reaction (J/mol) Mass transfer coefficient (m/s) Heat transfer coefficient (J/k/m2/s) Latent heat of water vaporization (J/kg) Turbulence kinetic energy (m2/s2) or thermal conductivity (J/m/k) Mass of droplet (kg) Water evaporation rate (kg/s) Mass fraction of fuel Mass fraction of oxygen Mass exchange between the gas and water droplet phases (kg/m3/s) Saturated vapor pressure (N/m2) Prandtl number The heat exchange between the gas and water droplet phases (J/m3/s) Universal gas constant (8.314 J/mol/K) Reynolds number Fuel consumption rate (kg/m3/s) Source/sink term for variable f Schmidt number Sherwood number Temperature (K) Water vapor dew point (K) Water boiling point (K) Time (s) Velocity vector Velocity component in direction i (m/s) Velocity of gas phase and water droplet Coordinate in direction i
Greek letters a; b Model constant for the Arrhenius finite reaction rate (a ¼ 2:8; b ¼ 1:2) Gi The diffusion coefficient for variable f r Fluid density e Turbulence dissipation rate (m2/s3)
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f mg
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Variable in the governing equation Viscosity of gas phase (kg/m/s)
Subscripts g Gas phase d Droplet phase vapor Water vapor
1. Introduction Water spray system like the standard sprinkler is still considered to be one of the most effective and reliable fire fighting tools. Recently, the development of fine water spray systems offers a new dimension to the current fire extinguishing capability and has many potential applications in the future. For example, the fine water spray system could be used to replace Halon fire extinguishing system. It is also well suited for suppressing fires involving electrical appliances where the influence of water wetting could be dangerous, and for fighting fire in aircraft and ship machine rooms where water supply is limited [1]. Since the concept and mechanism behind the fine water spray system is quite different from that of standard sprinklers [2], considerable attention has been paid to investigate the mechanism behind fine water spray (or water mist) employed to extinguish and control fires. Experimental results have proven that water mist fire suppression system could extinguish fire more efficiently with a relatively small quantity of water compared to the coarse water spray produced by conventional sprinkler systems. The performance of fine water spray systems may be affected by many factors such as water flow rate, spray nozzle type, droplet size, location of sprinkler head, ventilation condition, combustion reaction characteristics and properties of the burning material. Currently, there is insufficient knowledge for a quantitative assessment of which combination of these factors will lead to an optimal design of water spray system. For example, the fire suppression mechanism may be dominated by the evaporative cooling of water droplets within the fire plume, or by the droplets that penetrate the fire plume and cool the burning surface of the fire, or by the droplets that cool the environment around the flame. Factors like these pose a challenge for the fundamental understanding of water spray and fire plume interaction. The engineering design of water spray systems also imposes stringent requirements to develop a quantitative approach to estimate and predict the effectiveness/performance of the water spray system for various fire scenarios. Computational fluid dynamics (CFD) has already been proven to be a useful and powerful tool in fire safety science to model fire phenomena. A number of CFD studies on fire growth, spread and smoke movement have been reported in the literature. Some of the computational models [3–6] have been validated against experimental data and have been proven to be successful in predicting smoke flow patterns and smoke temperature distributions in rooms, tunnels and warehouses. On
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the contrary, the fire extinction process has not been subject to such a thorough investigation using CFD modeling. Recently, many research groups have started efforts to develop a computational approach to model the complete fire extinction process with water spray. The notable early work on modeling fire suppression with sprinklers was carried out by Alpert [7]. The study modeled the gas/water droplet flows in two dimensions and took into account three modes of interactions between fire plume and water droplet (namely mass, momentum, and energy transfer). Three-dimensional numerical studies were conducted by Chow and Fong [8] to examine sprinkler spray interaction with fire-induced hot smoke layer. They considered only the coupling of momentum and energy between the gas and water droplet phases. To simplify the problem, the sprinkler discharge pattern was treated as a constant hollow cone, and was assumed to be unaffected by the airflow. Hence, no droplet trajectories were calculated. The effect of water spray on the airflow was accounted for by the additional source terms in the momentum and energy equations. Nam [2,9] investigated the penetration capability of commercial sprinkler sprays by numerical simulation. In his work, steady-state simulations were conducted to study the interaction of fire plume and water spray. In order to avoid modeling the complex chemical reaction in the fire combustion, the fire was treated simply as a prescribed heat source. Hassan [10] also conducted steady-state simulations on the use of fine water sprays to extinguish fires in computer cabinets. In his study, the fire extinction model took into account some aspects of chemical reaction in fires. However, from a realistic point of view, since any fire extinction process is time dependent, the assumption of steady state may not be able to capture all the relevant aspects. Hoffmann and Galea [11–13] performed, by extending the field-fire modeling technique, transient simulations of the interaction between water spray and fire plume. Unfortunately, they considered only the momentum and thermal interactions between the water spray and fire and disregarded the effect of chemical reaction in fire combustion. Novozhilov et al. [14–16] simulated the extinguishment of wood fire with the water spray. They developed a relatively comprehensive model, combining the water spray model with the fire extinction model. The model included not only the momentum and thermal interactions but also the chemical reactions in fires. In addition, they conducted transient simulations to treat the fire plume/water spray interaction. However, their interests were mainly on investigating the wood fire extinguishment by water sprinkler. Besides cooling the burning surface after the water droplets penetrate through the fire plume, the water spray can also significantly cool the fire plume and affect the chemical reaction rate inside the plume. The penetration process of water spray droplets determines how fast and how many water droplets would be able to pass through the fire plume and finally reach the burning surface. Hence, the dynamic interaction between the water droplets and fire plume plays an important role in fire extinguishment using water sprays. In the present work, a CFD approach is adopted to model the comprehensive interactions between water spray and fire plume. The focus is on studying the effect of water spray characteristics on fire suppression mechanism and efficiency. Hence, the suppression processes of a fire (produced by a
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burner in an open quiescent environment) using the water sprays of different spray characteristics are examined by numerical simulation. The important water spray characteristics taken into account in this study are the water spray pattern (hollow or solid spray cones), water droplet size and the spray flow rate. The numerical model accounts for the following aspects of the water spray/fire plume interactions: (1) the coupling of mass, momentum and energy transfer between the fire plume and water spray; (2) the effects of chemical reaction dynamics on the fire combustion due to the cooling and dilution resulting from water evaporation; (3) the transient nature of fire extinction. This paper is organized as follows. The mathematical approach to model the fire plume/water spray interactions is described in Section 2. Section 3 illustrates the physical problem and some of simplifying assumptions made in this study. This is followed by the simulation results and discussion in Section 4. The effects of water spray pattern, water droplet size and spray flow rate are analyzed in detail. Finally, Section 5 provides the conclusions obtained from the current study.
2. Mathematical modeling To study the interaction between water spray and fire plume, the numerical model should include the flow of two main fluid phases (gas phase and water droplet spray) and account for the interactions between them. The gas phase involves the general airflow and the fire combustion, while the liquid phase includes the movement of (evaporative) water droplets injected from a spray nozzle. At present, there are two widely used numerical modeling approaches to model such two-phase flow problem. They differ in the way the water droplets in the spray are tracked, i.e. Eulerian– Eulerian or Eulerian–Lagrangian methods. In the Eulerian–Eulerian approach, both the gas and water droplet phases are treated as interspersed continua occupying the same space, and their share of space is measured by their volume fraction. The two phases interact with each other via friction, heat and mass transfer, and the calculation depends on the quantity or volume fraction of each phase in the grid cell. This approach was applied in the works of Hoffmann and Galea [11–13], Parasad [17,18] and Hassan [10]. For the Eulerian–Lagrangian method [8,9,19], the gas phase is regarded as a continuum while the water droplet phase is treated as individual particles and are traced using a Lagrangian approach. The momentum, heat and mass transport of these discrete particles are calculated by taking into account the various interacting forces with the gas phase. The effect of the particles on the gas phase is taken into account by introducing appropriate source terms in the conservation equations for the gas phase. A comparison of these two methods reveals that the Eulerian–Eulerian method is more suitable for the dense phase modeling, while the Eulerian–Lagrangian is more suitable for the dilute phase modeling [20]. Because the volume fraction of water droplet phase is quite small [9] in the current study, the Eulerian–Lagrangian method is used to simulate the interaction between fire plume and water spray.
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2.1. Gas phase modeling (fire modeling) The fire plume is created by the combustion of the gas fuel, methane, injected through a nozzle located on the floor in an open quiescent environment. Single-step irreversible chemical reaction is assumed: CH4 þ 2O2 -CO2 þ 2H2 O:
ð1Þ
The airflow and combustion reaction can be described by the conservation equations of mass, momentum, energy and species along with the sub-models for turbulence and combustion. The governing equations for the gas phase can be expressed in the following general form: q ðrfÞ þ rðrufÞ ¼ rðGf rfÞ þ Sf ; qt
ð2Þ
where r stands for the mixture (fuel, air and hot combustion products) density; u for the velocity vector, and t for the time. The symbol f stands for any of the following variables: (1) three velocity components ui in the ith direction; (2) mass fractions of chemical species mi ; (3) enthalpy h; (4) turbulence kinetic energy k; and (5) turbulent dissipation rate e: The definitions of the diffusion coefficient Gf and the source terms Sf for the various variables represented by f are provided in Table 1. The terms Sp ; Mp and Qp in the source term Sf (see Table 1) represent the inter-phase momentum, mass and heat exchanges between the gas and water spray phases, respectively. 2.1.1. Turbulence model Standard two-equation k2e model [21], modified to incorporate the buoyancy effect, has been widely used to estimate the turbulence characteristics of the gas phase flow in fire modeling, and the present study adopts the same approach. By solving these two equations, the turbulence kinetic energy and its dissipation rate are Table 1 Definition of some of the variables in the governing equations Dependent variable f
Diffusion coefficient Geff;f
Source term Sf
Continuity 1 Momentum ui
0 m þ mt
0
Kinetics energy k Dissipation rate e
m þ mt =sk m þ mt =sk
qp q quj þ m þ ðr rref Þgi Sp qxi qxj qxi Pk þ GB re e ðC1 Pk C2 reÞ k Rfu rox Rfu rH2 O Rfu Mp rCO2 Rfu Rfu HC Qp
Species mfu m=Sc þ mt =sf Species mox m=Sc þ mt =sf Species mH2 O m=Sc þ mt =sf Species mCO2 m=Sc þ mt =sf Enthalpy h m=Sc þ mt =sf quj qui quj m qr Pk ¼ mt þ ; Gb ¼ gi t ; Rfu ¼ Araþb mafu mbox eE=RT qui quj qui rsh qxi Sp ; Mp ; Qp represent the inter phase momentum, mass and heat exchange, respectively.
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obtained which are then used to calculate the turbulent effective diffusion coefficient. The effect of water droplet phase on the turbulence of gas phase is ignored in the present work to simplify the problem. 2.1.2. Combustion model A fire sub-model is required to close the above set of governing equations. One of the common methods used by the fire science community is to replace the complicated combustion process [1,9] by a simple prescribed heat source (either volume or surface) model to represent the fire. However, to accordingly describe the fire, a combustion model that accounts for the chemical reactions between fuel and oxygen must be included. The popular combustion models such as Eddy-break-up (EBU) model [16] and Arrhenius finite reaction rate model are typically used to estimate the chemical reaction rate in the fire combustion [17]. EBU model is more suitable for the combustion process in which the turbulent diffusion and mixing of reactants dominate the chemical reaction rate, while the Arrhenius reaction rate model is more suitable where the chemical reaction kinetics is the dominant factor in the chemical reaction [1]. In the current problem of water spray/fire plume interaction, the chemical reaction kinetics in the fire plume is significantly affected by the reaction temperature and reactant concentrations, and may be the dominating factor in the fire extinction mechanism. Therefore, the Arrhenius finite reaction rate model is used in the present study to estimate the combustion rate in fire extinction [22]. It is represented as follows: Rfu ¼ Araþb mafu mbox eE=RT ;
ð3Þ
where A; a and b are the model constants. mfu and mox are the mass fractions of fuel and oxygen, respectively. E stands for the activation energy of the chemical reaction. r; T; R are the gas density, temperature and universal gas constant, respectively. 2.2. Water spray modeling (water droplet phase modeling) In order to reduce the complexity of the interaction between the hot fire plume and the cold water spray, some assumptions on water sprays have been made to simplify the problem in the present study: (1) Water droplets are considered to be spherical in shape. The collision, deformation, break-up and coalescence of droplets are ignored. This is a reasonable simplification when the volume fraction of water spray is usually small as is the case in this study. (2) The water droplets interact only with the mean gas flow so that the effects of turbulence on droplet dispersion are not considered. (3) Water evaporation on the droplet surface has little influence on the drag coefficient. The motion of a water droplet can be described with the following expression, taking into account the drag force from the surrounding airflow and the gravity
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force [19]: md
dV d 1 ¼ CD Ad rg ðV d V g Þ jV d V g j þ md g; 2 dt
ð4Þ
where 24 ð1 þ 0:15Re0:687 Þ; Re rg V d V g Dd Re ¼ ; mg
CD ¼
ð5Þ
ð6Þ
where, V d ; md ; Ad and Dd are the water droplet velocity, mass, cross section area and diameter, respectively. V g ; rg and mg represent the gas phase velocity, density and viscosity, respectively. Here, g is the acceleration due to gravity. The drag coefficient may be reduced due to high water evaporation rate through the droplet surface. However, the water-evaporation rate is relatively small on the droplet surface [12,13] in the current study. Therefore, Eq. (5) can still be used to estimate the effect of drag, as was done in the previous works [8,14–16,19]. The heat transfer between the water droplet phase and the main gas phase plume is calculated by the following equations, taking into consideration the heat absorption due to water evaporation and convective heat transfer around the water droplet: m d cd
dTd ¼ ht AðTg Td Þ þ m ’ d hfg ; dt
ð7Þ
where md ; cd ; A and Td are the mass, specific heat, surface area, and temperature of the water droplet, respectively. Here, hfg is the latent heat of water vaporization, and ht is the convective heat transfer coefficient, which can be evaluated using the following relationship [23,24]: Nu ¼
ht D d ¼ 2:0 þ 0:6Re1=2 Pr1=3 ; kg
ð8Þ
where kg is the thermal conductivity of gas phase. The evaporation rate (m ’ d ) of a water droplet in a hot gaseous environment is due to the rates of vaporization (m ’ vapor ) and boiling (m ’ b) m ’d ¼ m ’ vapor þ m ’ b:
ð9Þ
The vaporization rate of a water droplet in a warm environment is calculated using the following expression [23,24]: Pg Psat ðTd Þ m Cvapor ð10Þ ðTdew oTd oTbp Þ; ’ vapor ¼ hm A RTd RTg Sh ¼
hm D d ¼ 2:0 þ 0:6Re1=2 Sc1=3 ; Dvapor
ð11Þ
where hm is the mass transfer coefficient. Psat and Pg are the saturated vapor pressure and static pressure in the gas phase. Cvapor is the vapor mole fraction, and Dvapor the
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mass diffusion coefficient of water vapor in the gas phase. Tvapor and Tbp are the vapor dew point and boiling point, respectively, of water at atmospheric pressure. Finally, the boiling rate of a water droplet in a warm environment can be estimated by the following equation [25]: pffiffiffiffiffiffi 4kg cg ðTg Td Þ dDd ¼ ð1 þ 0:23 ReÞ ln 1 þ ðTd XTbp ; Dd > 0Þ; ð12Þ hfg dt rd cg Dd 1 dDd ; m ’ b ¼ rd pD2d 2 dt
ð13Þ
where cg is the specific heat of gas phase and rd the density of water. 2.3. Numerical solution procedure The unsteady governing equations described above for the gas phase are solved by an iterative method utilizing a finite volume method. The equations for the gas phase are discretized on an unstructured mesh, and solved numerically using SIMPLE scheme. For the droplet phase of water spray, a Lagrangian method is used to track the movement of water droplets. The droplets are introduced into the computational domain at each time step. The coupling between the gas phase and water spray phase is taken into account by assigning appropriately the source terms in the momentum, heat and species conservation equations.
3. Physical problem A three-dimensional CFD model is developed to investigate the interaction between fire plume and water spray. The schematic diagram of the central section of the computational domain is shown in Fig. 1. In this study, the fire plume is produced by burning the gas fuel methane. The gas fuel is injected into the open quiescent environment from a square burner nozzle (0.25 m 0.25 m). The water spray nozzle is located 1.8 m directly above the center of the burner surface. 3.1. Fire model A relatively stable fire plume is produced when the gas fuel burns in an open quiescent environment. The methane is supplied from a nozzle on the floor at a constant rate resulting in a heat generation rate of around 53 kW. The burning rate of methane is estimated using the Arrhenius finite reaction rate model. The steadystate calculation of the methane gas combustion is first performed to obtain a fully developed fire plume. Then, this fully developed fire plume is used as the initial condition (base state) for subsequent transient simulations to investigate the dynamic interaction between the fire plume and the water spray.
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Fig. 1. Schematic model of the water spray/fire plume interaction.
3.2. Water spray model The formation of water droplets from a sprinkler spray involves many complex processes and presents difficulties for modeling it numerically. Since the primary aim of this work is not on the droplet formation, we adopt Nam’s [9] approach to represent the water spray. He characterized the water spray by measuring the water droplet size, spray velocity, flow rate and discharge angle of the water droplets. A Lagrangian approach can be used to track the water droplet trajectories from the spray nozzle. However, it is impossible to track the trajectory of every water droplet due to the tremendous number of droplets in the water spray. Therefore, the concept of droplet group [19] is used to group water droplets with similar characteristics, and trace the movement of this finite water droplet groups. In the current work, to understand the effect of water spray on fire suppression, the interactions between fire plume and water sprays of different spray patterns (i.e. hollow and solid spray cone patterns), water drop sizes as well as various spray flow rates are investigated. Some other factors, such as water spray mass flow rate, spray angle and speed, have been studied previously in the experimental work of Kim et al. [26] and Yao et al. [27]. The water spray parameters used in our simulations are listed in Table 2. These parameters, associated with each study case, reflect the typical
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Table 2 The water spray parameters used in the simulations Case no.
1 2 3 4 5 6 7 8 9
Parameters for water sprays Spray pattern
Drop diameter (mm)
Hollow cone Hollow cone Solid cone Solid cone Solid cone Solid cone Solid cone Solid cone Solid cone
270 135 270 200 135 100 270 270 270
Mass flow rate (kg/s)
Outlet speed (m/s)
Discharge angle
15
801
0.5
0.1 1.0 3.0
scenarios that would be expected from a sprinkler/water mist system [9,26,28]. The distribution of water flow rate for the solid water spray nozzle is assumed to be uniform across the outlet cross section of the nozzle. The droplet sizes in the various water sprays are allowed to vary from 100 to 270 mm in diameter. However, for each water spray, we assume that the water droplets have a uniform size at the discharge point. Since the primary interest of the current work is to study the interaction between fire plume and water spray, the interaction between the wall/burning surface and water spray droplet is not considered, as it would add further complications to the problem. This will be investigated in a future study.
4. Results and discussion The interaction between the water spray and the fire plume includes primarily the following three aspects: (a) momentum interaction: the injection of a water spray can significantly change the gas flow pattern in the fire plume, which in turn affects the flame structure and its heat and mass transfer characteristic; (b) thermal interaction: the evaporation of water droplet will cool the fire plume; (c) chemical reaction interaction: the chemical reaction rate in the fire plume is reduced due to lowered reaction temperature caused by the heat absorption of the evaporating water droplets. It is also due to the dilution of the reactant (fuel and air) resulting from the vapor generated by vaporizing water droplets. Obviously, the performance of a water spray to suppress fire may be affected by any combination of the above interactions. In order to better understand the role of each of the above interactions, numerical simulations have been carried out to investigate the effect of water spray pattern, water droplet size, and spray flow rate.
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4.1. Effect of water spray pattern The simulation results of steady-state combustion of gas fuel in an open quiescent environment are shown in Figs. 2(A)–7(A), where the velocity, temperature and water vapor concentration distributions within the fire plume are illustrated. This is taken to be the base case or the initial state from which the transient events develop. Fig. 2(A) shows the gas velocity vectors in the base-state fire plume. The fuel gasmethane is injected from the fuel nozzle located on the floor and burns in the open environment. The combustion heat raises the gas temperature as shown in Fig. 3(A), and builds up a hot fire plume. The simulation results from the use of a hollow water spray in the fire extinguishing process are shown in Figs. 2–4. Fig. 2 shows the temporal velocity vectors of the gas phase when the water spray is activated from a hollow cone type nozzle. After the water spray is activated at time t ¼ 0; the water droplets shoot out at a high velocity of 15 m/s. Because of their high speed, the water droplets entrain the surrounding cool air moving at a speed of about 5–6 m/s as shown in Fig. 2(B). As time progresses, more cool air is entrained into the droplet airflow stream as shown in Fig. 2(C). The entrainment initially enhances the downdraft of cool air, and then it impinges on the burner surface and spreads outward along the floor as shown in Figs. 2(D) and (E). This results in cooling the surrounding space of fire plume and eventually leading to the total suppression of the fire. Fig. 3 shows the temporal distributions of the gas phase temperature when the hollow water spray is used to suppress the fire (Case 1). The first point to note, from Fig. 3(B), is the water spray cutting off the fire plume. Then, the downward draft of cool air pushes the fire plume outward and cools it as well, as shown in Figs. 3(C) and (D). Finally, the fire gets suppressed. The effect of water evaporation on fire suppression is illustrated in Fig. 4 by means of temporal water vapor concentrations. Evaporation of water takes place when the droplets make contact with the fire plume. A high water vapor concentration is observed during the initial period of activation of the water spray, as shown in Fig. 4(B). This is attributed to the existence of high-temperature fire plume close to the water spray discharge point. As time progresses, the water droplets spread downward to the outer edge of the fire plume as shown in Figs. 2(C)–(E). Because the ambient temperature in the outer region of the fire plume is lower, the water evaporation rate is also lower, and hence the lower water vapor concentration as well. It can also be seen from Fig. 4 that the water vapor concentration in the core of the fire plume does not change significantly during the entire fire suppression process. This implies that the chemical reaction in the fire plume is not influenced significantly by the water vapor dilution. The results from the use of a solid water spray on fire suppression (Case 3) are now discussed. The solid water spray has exactly the same parametric configurations as the hollow water spray except for the spray pattern. The temporal variations of gas phase velocity, temperature and water vapor concentration for the solid water spray case are presented in Figs. 5–7, respectively. In the case of solid water spray, the water droplets are sprayed out through the entire surface of the nozzle outlet as shown in Fig. 5(B). Consequently, the central part of the water spray is delivered
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Fig. 2. The temporal vector plots of the gas phase velocity during the interaction of the hollow-cone water spray with the fire plume (case 1).
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Fig. 3. The temporal contour plots of the gas phase temperature (K) during the interaction of the hollowcone water spray with the fire plume [Case 1]. (H represents the vertical distance from the burning surface and R the horizontal distance from the center of burning surface.)
directly to the core part of the fire plume, resulting in higher water evaporation rate because of the elevated temperature. This helps the central part of the fire plume to be cooled down as the evaporating water droplets absorbs the heat, as shown in
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Fig. 4. The temporal contour plots of the water vapor concentration during the interaction of the hollowcone-type water spray with the fire plume (case 10).
Figs. 6(C) and (D). The water vapor concentration distributions shown in Figs. 7(C) and (D) also support the fact that the evaporating water droplets create much higher water vapor concentration in the core part of fire plume where the chemical reaction for combustion occurs. This result can be contrasted to the water concentration in
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Fig. 5. The temporal vector plots of the gas phase velocity during the interaction of the solid-cone water spray with the fire plume (case 3).
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Fig. 6. The temporal contour plots of the gas phase temperature (K) during the interaction of the solidcone water spray with the fire plume (case 3).
the base combustion case as depicted in Fig. 7(A). As a result of the high water vapor concentration in the fire plume core, the fire combustion rate is significantly lowered. This is because of the lower reaction temperature due to high heat absorption by the water droplets, and because of the dilution of reactant concentration by water vapor.
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Fig. 7. The temporal contour plots of the water vapor concentration (mass fraction) during the interaction of the solid-cone-type water spray with the fire plume (case 3).
As time progresses, the heat generation from the fire is reduced due to lower reaction rate, and eventually the fire is extinguished. Comparing the fire plume and water spray interaction behavior for these two types of nozzles (i.e. hollow spray cone and solid spray cone) based on the results
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2500
Gas phase temperature (K)
Case 1 Case 3
Case 2 Case 5
2000
1500
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
Time (s) Fig. 8. The variation gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water spray pattern.
presented above, it can be concluded that the fire suppression mechanism for the two nozzle types is different. In general, the solid cone-type spray nozzle is more effective because it delivers some of the water droplets directly to the region where chemical reaction occurs in the fire plume. As discussed above, this leads to a reduction in the chemical reaction rate by lowering the reaction temperature and diluting the reactant concentration, and hence a faster suppression of the fire. On the other hand, water droplets from the hollow spray cone nozzle only entrain the air from the surrounding regions to form a cool airflow stream that impinges and cools the hot fire plume. The chemical reaction rate is not affected by the vapor dilution in this case. Therefore, it takes the hollow cone water spray longer time period to suppress the same size fire compared to the solid cone water spray. This conclusion can also be obtained from Fig. 8, which show temperature histories for the two types of water spray at a point located on the centerline and 0.03 m above the burner surface for the same fire. 4.2. Effect of water droplet size The effect of water droplet size on fire suppression is examined by simulation cases 4 and 6, and the results are shown in Figs. 9–12. Here, the droplet size considered for the water sprays in the two simulation cases are 100 and 200 mm in diameter, respectively. The temporal distribution of water evaporation rate for the two droplet sizes, along the vertical centerline through the burning surface, is shown in Figs. 9(A) and (B), respectively. It can be clearly seen from Fig. 9 that there are always two peaks in the water evaporation rate curve at a given time instance. Peak 1 is due to the water evaporation in the cool entrained airflow, and peak 2 is due to the strong
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Water evaporation rate ( kg/m 3s)
1.4E-04
Peak 2 1.2E-04
t=0.05s t=0.15s t=0.25s t=0.35s t=0.45s
1.0E-04 8.0E-05 6.0E-05
Peak 1
4.0E-05 2.0E-05 0.0E+00 0.0
0.5
1.0
(A)
1.5
2.0
2.5
H (m)
Water evaporation rate (kg/m3s)
1.4E-04 1.2E-04
Peak 2
1.0E-04 8.0E-05
t=0.10s t=0.20s t=0.30s t=0.40s t=0.50s
6.0E-05
Peak 1 4.0E-05 2.0E-05 0.0E+00 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 9. The temporal distributions of water droplet evaporation rate along the vertical central line of the burning surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 4).
heating effect from the fire plume. After the water droplets are injected from the nozzle, they start to evaporate immediately (refer to peak 1) since the water vapor concentration in the entrained airflow region is lower than the vapor saturation concentration. As the water droplets penetrate deeper into the fire plume, they are heated up. As a result, the saturation vapor concentration around the water droplets becomes higher as well. This leads to higher evaporation rate of the water droplet (refer to peak 2) in the fire plume. As the interaction between the fire plume and the water spray continues, the fire plume is cooled and its physical size is reduced subsequently. At the same time, the water evaporation rate peak 2 moves downward along the vertical direction. Comparing the evaporation rate magnitudes for different drop sizes shown in Figs. 9(A) and (B), it can been see that the smaller droplets produce higher water evaporation rate.
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Gas phase temperature (K)
2500
2000
t=0.05s t=0.15s t=0.25s
1500
t=0.35s t=0.45s
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
H (m)
(A)
Gas phase temperature (K)
2500
2000
1500
t=0.10s
t=0.20s
t=0.30s
t=0.40s
t=0.50s
t=0.60s
1000
500
0 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 10. The temporal distribution of gas phase temperature along the vertical central line of the burning surface for different water drop size: (A) 100 mm (case 6) and (B) 200 mm (case 4).
The thermal interaction between fire plume and water spray for different water droplet sizes is illustrated in Figs. 10(A) and (B) in terms of the temporal temperature profile along the vertical centerline through the burning surface. The variation of interaction zones between fire plume and water spray with time is indicated with the arrows shown in Fig. 10. After the water spray is activated, it first cools the top part of the fire plume to the level of local environment temperature. With further amount of water spray, the extent of the fire plume becomes smaller and smaller until it is finally extinguished. Fig. 10 also illustrates that the spatial distances between the thermal interaction zones for two adjacent time steps are always larger for the water spray with smaller droplet size. This indicates that the finer water spray can penetrate the fire plume faster than the coarser one. In addition, the temperature gradients in the thermal interaction zones are higher for the smaller droplet size than that of the coarser one. In fact, for the finer water spray,
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Gas phase velocity magnitude (m/s)
7 6
t=0.05s t=0.15s
5
t=0.25s t=0.35s
4
t=0.45s 3 2 1 0 0.0
0.5
1.0
1.5
2.0
2.5
H (m)
(A)
Gas phase velocity magnitude (m/s)
7 6
t=0.10s t=0.20s
5
t=0.30s 4
t=0.40s t=0.50s
3
t=0.60s
2 1 0 0.0
(B)
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 11. The temporal distributions of gas phase velocity magnitude along the central line of burner surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 4).
the penetration capability of every water droplet is lower due to the higher drag effect from the surrounding air. Hence, the size of the interaction zone between the fine water spray and the fire plume is smaller, which leads to a higher temperature gradient. Since the water evaporation rate is higher for the finer water spray, as shown in Fig. 9, it leads to higher heat absorption rate which then helps to cool the fire plume quickly. This in turn reduces the buoyancy force on the water droplet cloud, and help the finer droplet cloud to penetrate the fire plume more easily and quickly. Therefore, the finer water droplet cloud can suppress the fire plume more effectively. Fig. 11 shows the momentum interaction between water spray and fire plume in terms of the distribution of airflow speed along the vertical centerline though the burning surface. The downward airflow speed initially increases rapidly because of
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Water vapor mass fraction
0.25
t=0.05s
0.20
t=0.15s t=0.25s
0.15
t=0.35s t=0.45s
0.10
0.05
0.00 0.0
0.5
1.0
(A)
1.5
2.0
2.5
H (m) 0.25
Water vapo rmass fraction
0.20
0.15
t=0.20s
t=0.30s
t=0.40s
t=0.50s
t=0.60s
0.10
0.05
0.00 0.0
(B)
t=0.10s
0.5
1.0
1.5
2.0
2.5
H (m)
Fig. 12. The temporal distributions of water vapour mass fraction along the vertical central line of burner surface for different water drop sizes: (A) 100 mm (case 6) and (B) 200 mm (case 6).
the strong drag effect from the water spray. As the water droplets move further downward, their drag effects on the surrounding air will reduce locally due to the ‘‘opening up’’ of the spray cone. This results in a reduction of the airflow speed. However, as the water spray spreads downward, more and more surrounding air is entrained into the airflow such that the air velocity increases again and maintains that velocity till its interaction with the fire plume. As shown in Fig. 11 the finer water spray will induce higher entrained air velocity, which in turn will deliver more cool air to the fire plume and hence provide more effective fire suppression. Obviously, the evaporation of the water droplet would not only cool the fire plume, but also increase the water vapor concentration there leading to the formation of a water vapor cloud indicated by the peak in the water vapor concentration curve, as shown in Fig. 12. As the water droplets move downward, the
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2500
Gas phase temperature (K)
Case 3 Case 4
2000
Case 5 Case 6
1500
1000
500
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (s)
Fig. 13. The variation of gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water droplet size.
water vapor cloud also moves downward. The vapor concentration in the fire plume becomes higher and higher, since the high plume temperature would lead to high water evaporation rate around the droplets. However, comparing the effect of water droplet size on the water vapor concentration, as shown in Figs. 12(A) and (B), the fine water spray is seen to produce a lower water vapor concentration even though it has higher water evaporation rate. Actually, the vapor concentration in the interaction zone depends on the balance between the evaporation rate and the convection transfer rate. For the fine water spray, the evaporation rate is high, and the air velocity is also high, which implies a higher convection transfer rate. Hence, the chemical reaction for fire combustion is not significantly affected by the dilution effects of the fine water spray compared to that of the coarse water spray. The fire suppression mechanism of the fine water spray still depends mainly on its cooling effect. The effect of using water sprays with different water droplet sizes (case 3–6) on suppressing the same fire is illustrated in Fig. 13 by means of the temporal gas temperature history at a point located on the centerline and 0.03 m above the burner surface. In the case of the finer water spray, the higher water evaporation rate cools the hot fire plume effectively and reduces the general buoyancy effect on the downward moving droplet cloud. As a result, the finer water spray takes less time than the coarser one to suppress the same size fire. 4.3. Effect of water spray flow rate Fig. 14 shows the temporal gas temperature history at the point located on the centerline and 0.03 m above the burner surface for the water sprays with different flow rates. It is obvious that the water spray with the higher flow rate would take less time to extinguish a fire. If the water flow rate is not high enough, the fire may not be
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Gas phase temperature (K)
2500
2000
Case 3
Case 7
Case 8
Case 9
1500
1000
500
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (s) Fig. 14. The variation of gas phase temperature with time at 0.03 m above the burner surface center considering the effect of water spray flow rate.
Time taken for fire suppression (s)
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Water spray flow rate (kg/s) Fig. 15. The variation of time taken for fire suppression against water spray flow rate.
suppressed (case 7) regardless of the time period the water spray is applied. This means that the flow rate of water spray should be higher than a critical value in order to suppress a certain size fire. Also, if the flow rate of the water spray increases, the time taken to suppress the same size fire does not decrease linearly. Fig. 15 shows the variation of the time taken to suppress the same fire as a function of the water spray flow rate. It is obvious from Fig. 15 that the fire suppression efficiency of a water spray system cannot be improved significantly by increasing the water spray flow rate beyond a certain threshold value. Moreover, if higher flow rates are used, more
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than the optimum value, the operational cost of the water spray system will become higher. Hence, an effective water spray system should be able to suppress fires in a relatively short-time period using a minimum amount of water.
5. Conclusions A numerical simulation approach has been developed to investigate the interaction between the fire plume and the water spray. The simulation results prove that the current approach has the capability to reasonably capture the interactions between the water spray and the fire plume taking in account the effects of momentum exchange, heat and mass transfer as well as chemical reaction. The effect of important water spray parameters such as spray patterns (solid and hollow cone sprays), water droplet size and water flow rate on fire suppression mechanism and effectiveness have also been analyzed. The solid water spray cone can extinguish fires more effectively than the hollow spray cone. The solid water spray delivers more water droplets to the core part of fire plume leading to a higher water evaporation rate. This not only helps to absorb more heat but also generates large quantity of water vapor. Both of these factors help to reduce the chemical reaction rate in the fire plume and leads to the extinction of fire. On the other hand, the water spray with hollow spray cone relies primarily on the entrained cool airflow to cool and extinguish the fire plume. As to the effect of water droplet size, the fine water spray works more effectively on fire extinction than the coarse water spray. This is due to the fact that the fine water spray leads to a higher water evaporation rate, which effectively cools the fire plume and reduces the buoyancy effect of the fire plume. The fine water spray is then able to penetrate and suppress the fire plume more effectively. The results on the effect of water supply flow rate show that the flow rate should be higher than a critical value to be able to suppress the fire. It is also important to note that, from an efficiency point of view, there is no need to use more than a certain quantity of water flow rate as it does not increase the efficiency of fire suppression system. The present study also provides some basic guidelines on designing more effective water spray systems for fire suppression.
Acknowledgements The authors would like to acknowledge the technical contributions from Ms Sophia Chan Hui Ling from the Department of Mechanical Production Engineering, National University of Singapore.
References [1] Mawhinney JR, Hadjisophocleous GV. The role of fire dynamics in design of water mist fire suppression system. Proceedings of INTERFLAM’96, 1996. p. 415–24.
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