The Critical Velocity and the Fire Development

The Critical Velocity and the Fire Development Wu, Y Department of Chemical & Process Engineering, Sheffield University, Mappin Street, Sheffield S1 3JD, UK ABSTRACT The critical velocity is strongly influenced by the heat release rate and the tunnel geometry. The critical velocity generally increases with increasing fire heat output for small to medium sized fires, however there is a ceiling for the critical velocity called super critical velocity when the critical velocity becomes insensitive to the fire power and remains constant once the fire reaches certain level. The current techniques for prediction of the values of the critical velocity for various tunnels were predominately based on semi-empirical equations obtained from the Froude Number preservation combining with some experimental data. Although the methods provided simple and effective semi-empirical solution to determine the value of the critical velocity, the Froude Number modeling failed to explain the existence of the super critical velocity. The fire plume theory explains that the super critical velocity is caused by the intermittent flame occupying the ceiling region when the heat release rate reaching the critical level and fire zone dominates the full height of the tunnel. The plume theory has observed the changes in fire and plume sizes and linked the fire development with the critical velocity. However it still couldn t describe the physical conditions which could be used to predict the super critical velocity. This paper examines the combustion characteristics of the fire zone under different ventilation conditions and establishes some fundamental changes in fire burning status when heat release rate reaches the critical level for the super critical velocity. The fire development under the ventilation is analyzed using combustion theory. Both CFD simulations and experimental measurements are used to identify the flame status under ventilation. KEYWORDS: critical ventilation velocity, fire development and combustion mode INTRODUCTION The critical velocity is normally referred to the minimum air velocity required to suppress the smoke backlayering spreading against the longitudinal ventilation flow during tunnel fire situations. The critical velocity has been the topic for various researches. The traditional theories are mainly based on applying the Froude Number preservation to the backlayering. Recent studies have made significant progress on identifying the influence of the fire power and the effect of the tunnel geometry on the critical velocity. It has been demonstrated that the critical velocity generally increases with increasing fire heat output for small to medium sized fires, however there is a ceiling for the critical velocity called super critical velocity when the critical velocity becomes insensitive to the fire power and remains constant once the fire reaches certain level. The reasons to cause the two distinct regimes in the relationship of critical velocity and the fire heat release rate are not very well understood. In the meanwhile, studies focusing on the relationship between ventilation and fire spread rate inside the tunnels showed that there are strong links between the fire development and the ventilation rate. Some evidence indicated that the critical ventilation conditions might promote fast fire spread rate inside the tunnels. This paper carries out an investigation of relationship of the critical velocity and the fire development by examining the fire burning status under different ventilation conditions. The combustion and aerodynamic theory developed for the compartment fire is applied to the tunnel fire situation to analyze the fire development stages. The objective is to reveal the fundamental changes in the physical conditions resulting the two distinct regimes in the correlations between the critical ventilation velocity and the fire heat release rate. 407

CRITICAL VENTILATION VELOCITY A previous study by the author [1] has established the relationship between the fire heat release rate and the critical velocity for the ventilation to eliminate the backlayering smoke flow by carrying out experimental tests in a group of tunnels. The tunnels used in the study have the same height but different geometries and the tunnel dimensions are shown in Figure 1. The experimentally measured critical velocity under different fire heat release rate as shown in Figure 2 demonstrated that the critical velocity depended on the fire power size and by the tunnel geometry. Figure 2 also demonstrated the existence of the super critical velocity for the tunnels. The super critical velocity is also depended on the tunnel geometry. The current techniques for prediction and correlation of the values of the critical velocity for various tunnels were predominately based on semi-empirical equations obtained from the Froude Number preservation combining with some experimental data. Froude Number modelling is often used as the scaling technique in fire situations where the Reynolds number is sufficiently large, turbulent conditions prevail and buoyancy forces are dominant. The Froude number is defined as: V 2 inertia forces Fr = gd = (1) gravity forces Where g is the force due to gravity, and V and D are characteristic values of velocity and length, respectively. Thomas [2] was one of the earliest who applied this technique in the study of the effect of ventilation velocity on fire plumes in ducts. He suggested that the flow character depended on the ratio of buoyancy to inertial force over a cross-section of the tunnel. Thomas suggested that when Froude number is equal to 1, the magnitude of buoyancy force and inertial force are similar, thus the backlayering does not occur. Based on this concept, he derived the relationship between the ventilation velocity and the heat release rate from the fire as: gq Uc = k 1 ' 3 ρocpt (2) where Uc is the critical ventilation velocity, Q is convective heat release rate per unit width of the tunnel, ρ o is the ambient air density, C p is the specific heat capacity of air, k is a constant and T is the smoke temperature. The value of k was determined experimentally. The later deployment [3-6] of Froude Number modelling for tunnel fires are all based on the foundation set by Thomas. Although the methods provided simple and effective semi-empirical solution to determine the value of the critical velocity, however the Froude Number modeling failed to explain the existence of the super critical velocity. Based on the Froude Number modeling, non-dimensional analysis methods [1, 7] was developed to correlate the experimental data on the critical velocity at different heat release rate and tunnel geometry, Wu and Bakar [1] proposed the non-dimensional group for the velocity and heat release rate as: V V = (3) g H and Q = Q ρ o C p T o g H 5. (4) where the characteristic length H is the hydraulic tunnel height, T o is ambient temperature. The nondimensional analysis has successfully correlated the critical velocity data obtained from different tunnels into a single formula as shown in Figure 3. The two distinct regimes of the critical velocity are clearly shown in Figure 3. 408

Figure 1. The dimensions of the cross-section of the experimental tunnels. Figure 2: The measured critical velocity against the fire heat release rate in the tunnels. Figure 3: The non-dimensional analysis of the critical velocity against the heat release rate. 409

THE PLUME THEORY Based on the temperature measurements inside the tunnels, a fire plume theory is developed and used to explain the super critical velocity. McCaffrey s [8] fire plume theory has been extended to describe the fire plume in tunnels. The fire plume in tunnel is considered to have the same three regimes. The gross feature of each regime is the same as described by McCaffrey for free plumes. However the fire plume shapes are completely different from a free fire plume. The fire plume consists of persistent flame zone, the intermittent flame zone and the buoyant plume zone under the ceiling and downstream. Two fire plume distribution regimes are identified as shown in Figure 4 for low heat release rate and in Figure 5 for high heat release rate. The plume distributions are proposed based on the temperature distributions measured inside the tunnels at critical velocity conditions and at low, medium and high heat release rates. Figure 6 shows the temperature distribution in the fire zone measured in the narrow tunnel A at three HRRs and Figure 7 shows the temperature distribution in the square tunnel B. The measured temperature contours were used to analyse the fire plume regimes in tunnels. These two plume distributions were directly linked with the two regimes in the variation of critical velocity with fire heat release rate. At low HRR, the persistent and intermittent flames lay low inside the tunnel, with only the buoyant smoke flow reaching the ceiling. The critical velocity varies as the one-third power of the heat release rate in this situation. At high HRR, the intermittent flame reaches and dominates areas under the ceiling. In this situation, the critical velocity became nearly or completely independent of heat output. According to McCaffrey s fire plume theory, the plume exhibits the feature of constant flow velocity in the intermittent flame. Therefore the dominance of the intermittent flame under the ceiling could offer an explanation to the insensitivity of critical velocity to the HRR once the fire grows to a critical level. The plume theory has observed the changes in fire and plume sizes and linked the fire development with the critical velocity. However it still couldn t describe the physical conditions which could be used to predict the super critical velocity. Ventilation Flow Buoyant Plume: Backlayering Intermittent Flame Buoyant Plume Fuel bed Persistent Flame Figure 4 : Illustration of the fire plume distribution in the fire zone at low heat release rate. Ventilation Flow Buoyant Plume: Backlayering Persistent Flame Intermittent Flame Buoyant Plume Fuel bed Figure 5: Illustration of the fire plume distribution in the fire zone at high heat release rate. 410

(a) 3.0 kw, Uc = 0.43 m/s 4 0 0 (b) 7. kw, Uc = 0.46 m/s 4 5 600 6 0 0 (c) 15.0 kw, Uc = 0.48 m/s 0 600 7 800 5 5 8 700 0 4 6 900 4 0 Figure 6: Measured Figure temperature 6.14 : Measured contours temperature in tunnel contours A in for tunnel 3.0 A for kw, 3.0 7.5kW kw, and 15 kw fire at critical conditions. 7. kwand 15.0 kwat critical conditions 411

(a) Q = 3.0 kw, Uc = 0.48 m/s 4 0 0 Distance downstream from fire source(mm) (b) Q = 7. kw, Uc = 0.56 m/s 4 5 600 0 0 (c) Q = 15.0 kw, Uc = 0.60 m/s 5 0 5 600 6 0 4 700 4 0 Figure 6.5 : Measured temperature contours in tunnel B for 3.0 kw, Figure 7: Measured temperature 7. kwand contours 15.0 kwat in critical tunnel conditions B for 3.0 kw, 7.5kW and 15 kw fire at critical conditions. 412

THE FIRE DEVELOPMENT The plume theory has pointed out that the critical velocity is very much interlinked with the fire development inside the tunnel. The development of the tunnel fire assembles the features of ventilated compartment fire. The fire development inside the compartment is controlled by a fuel-controlled combustion mode or a ventilation-controlled combustion mode. At the early stage, the fire is confined locally and the burning is depended on the release rate of combustible volatiles which is mainly produced by the radiation and convective heat transfer from the flame to fuel sources. At the flashover stage, the fuel supply becomes abundant and flame involves almost all combustible surfaces, the combustion mode switch from fuel-controlled to ventilation-controlled. For the analysis of the combustion modes inside the tunnel, the tunnel fire zone is further simplified in Figure 8 for low HRR and Figure 9 for high HRR. The characteristics of the combustion mode of a tunnel fires at the critical velocity conditions are examined in the present study based on the CFD simulations. The oxygen mole fraction contours and the temperature contours in the Tunnel A and B at critical ventilation conditions are shown in Figure 10. The average mole fractions at the exit of the tunnels are given in the Table 1. The results from the CFD simulations demonstrated that at low HRR of 3kW, there is high average oxygen level in the downstream exit of the tunnels and there is no obvious oxygen level drop in the combustion zone. The results indicate that the combustion has large excess air available, the combustion model inside the tunnel is fuel-controlled. At the high HRR, the average oxygen level in the exit dropped to 9%, there is a large area of zero oxygen level in the combustion zone and flame is elongated. The results could suggest that there is no excess air in the combustion zone. The present study considers the burning under the super critical velocity is at its stoichiometric conditions. The reason is that the stoichiometric burning produces the highest flame temperature according to the combustion theory for constant volume. Therefore super critical velocity should be derived under the conditions of the maximum the buoyancy force sustained by the highest flame temperature. Further experimental and CFD investigations are needed to verify this assumption. Buoyant Plume: Backlayering Ventilation Flow Combustion zone with excess air Fuel bed Downstream Smoke flow Figure 8: Simplified tunnel fire zone at low HRR under critical velocity conditions. Ventilation Flow Combustion zone without excess air Downstream Smoke flow Fuel bed Figure9: Simplified tunnel fire zone at high HRR under critical velocity conditions. 413

a) Oxygen contours in Tunnel A at 3 kw b) Temperature contours in Tunnel A at 3 kw c) Oxygen contours in Tunnel A at 15 kw d) Temperature contours in Tunnel A at 15 kw e) Oxygen contours in Tunnel B at 3 kw f) Temperature contours in Tunnel B at 3 kw g) Oxygen contours in Tunnel B at 15 kw h) Temperature contours in Tunnel B at 15 kw Figure 10: The oxygen mole fraction contours and temperature contours inside the Tunnel A and Tunnel B at critical velocity conditions. 414

Table 1: The average oxygen mole fraction at the tunnel exit calculated from the CFD simulations. Tunnel Heat Release Rate (kw) Average Oxygen Mole Fraction (%) A 3 13.5 A 15 9.2 B 3 16.1 B 15 14.2 VENTILATION AND THE FIRE SPREAD Proper use of ventilation to minimize fire development has always been a concerning issue. Since the fire critical velocity has two distinct regimes, the discussions of effect of ventilation on fire spread should consider for the circumstance of early stage of the fire development when the HRR is relatively small and fully developed fire where the fire grows to the critical level and super critical velocity can control the backlayering. The priorities could be very different in those two stages. As shown in Figure 11, the temperature contours in the Tunnel B demonstrates the influence of the ventilation on the fire plume by setting the ventilation in under-ventilated, critical ventilation velocity and over-ventilated conditions at the same small HRR. The results shows that the vertical high of the flame remained more or less the same, however the flame elongates in the horizontal direction. The elongated flame could enhance the fire spread to objects downstream of the fire. At this stage, priority could be people rescue and minimising the fire spread. Therefore over-ventilation of a small fire inside the tunnel has adverse effects on the fire spread. Once the fire is fully developed, the fire involves the entire vertical length of the tunnel, the burning is likely in the ventilation controlled mode and super critical velocity can be used to control the backlayering. Under this circumstance, it is likely that the fire has already spread in extensive length in the tunnel. The priority in this stage is likely to be access to the fire seat for fire fighting and therefore under-ventilation is not desirable. However if the ventilation is set at the super critical velocity, although the backlayering can be cleared for assessing the fires seat, but the combustion mode in the flame zone is likely at the stoichiometric conditions and the produce highest flame temperature. Under those conditions, overventilation would have the advantages of providing overall cooling effects in the fire zone and the downstream. CONCLUSIONS 1. The results of the experimental measurements and the CFD simulations have established two distinct regimes for the relationship of the critical velocity and the fire HRR. 2. A fire plume theory is proposed to describe the features of fire plume distributions under the two regimes. The plume theory offers simple explanations on the occurrence of the two regimes. 3. Based on the plume theory, the fire zone is further simplified to aid the discussions of the combustion characteristics of the plume. It is proposed that the underline physical condition for the super velocity could be due to the switch of the combustion mode from fuel controlled to ventilation controlled in the combustion zone. 4. Different strategy on the ventilation settings should be used to minimize the fire spread inside the tunnel. At the early stage of the fire, over-ventilation should be avoided to minimize the fire spread from the elongated plume. However at the late stage of fire development, over-ventilation provides overall cooling benefits for the tunnel. 415

(a) U = 0.25 m/s 0 (b) Uc = 0.48 m/s 0 (c) U = 0.96 m/s 0 Figure 11: The Figure temperature 6.4 : Measured contours temperature in the contours Tunnel in tunnel B in B under-ventilated, 3.0 kwfire critical ventilation velocity and over-ventilated conditions. 416

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