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A Study on Road Tunnel Fires Using Hazmat, with Emphasis on Critical Ventilation Velocity
0957–5820/05/$30.00+0.00 # 2005 Institution of Chemical Engineers Trans IChemE, Part B, September 2005 Process Safety and Environmental Protection, 83(B5): 443–451
www.icheme.org/journals doi: 10.1205/psep.04214
A STUDY ON ROAD TUNNEL FIRES USING HAZMAT, WITH EMPHASIS ON CRITICAL VENTILATION VELOCITY ` and B. FABIANO E. PALAZZI, F. CURRO DICheP Chemical & Process Engineering Department ‘G.B. Bonino’, University of Genoa, Italy
O
ne of the main protective measures to be adopted in case of fires in road/rail tunnels is represented by suitable longitudinal ventilation systems being able to avoid fire and smoke exposure of humans, and to create a safe route upstream for evacuation. The key design parameter is the so-called critical ventilation velocity, i.e. the minimum speed of the longitudinal ventilation avoiding the spread of the smoke produced by fire in the upstream direction, known as ‘backlayering’. In several studies, the critical velocity was correlated to the fire heat release rate on the basis of semi-empirical models, already adopted in describing nonconfined fires. However, experimental runs both on a laboratory scale and on a real scale, evidenced that such correlations are valid only in connection with fires of limited extent, while at high rates of heat release and when the flame height reaches the tunnel ceiling, the critical velocity can tend asymptotically to a maximum value vca. In this study, reference was made to the worst scenario of hydrocarbon pool fire extended to the whole tunnel section. The main hypotheses the model is based upon are uniform distribution of chemico-physical properties of fire and smoke along the considered transverse section of the tunnel. The evaluation of the critical velocity is performed by solving mass, momentum and energy balances obtained considering possible dynamic interactions among the different fluxes (backlayering, air, flame/smoke column). In particular, the inertial action exerted by fresh air on backlayering was determined on the basis of the experimental results. The asymptotic value of the critical velocity resulting by mathematical modelling is in good agreement with those proposed by other authors, for example by means of complex CFD (computational fluid dynamics) studies. Moreover, the developed model is easily adaptable to the evaluation of vca, when dealing with geometrical conditions different from the ones studied here e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels. Keywords: fire; hazardous materials; transportation; tunnel; ventilation.
INTRODUCTION
many countries. High profile accidents were recorded in railway tunnels too, e.g., the Channel tunnel fire, the Kaprun fire and raised a large amount of public debate about rail safety (Beale, 2002). Due to the sharp reduction of vehicle pollutant emissions, the ventilation of road tunnels is more and more determined by the need of controlling smoke in case of fire. In fact, recent severe accidents, such as the one in Mont Blanc (Italy/France), have evidenced the need of extending the conventional concept of ‘hazardous materials’ to a broader range of transported goods and the relevance of prevention and limitation of consequences measures in case of fire in road- and railtunnels. One of the main protective measures to be adopted in case of fire in tunnels is represented by suitable longitudinal ventilation systems being able to avoid fire and smoke exposure of humans, and create a safe route upstream for evacuation. The presence of adequate ventilation was considered by Fuller (1985) to provide a significant tactical advantage when tackling fires, by increasing the visibility and diluting toxic and flammable fumes. The key
Despite the relative recent move towards ‘inherently safe’ materials, the relentless drive of consumerism has required increased quantities of dangerous goods to be manufactured, transported, stored and used year on year (Thomson, 1998). Incidents related to transportation of hazardous materials are comparable in number and severity to those occurring in process plant: a survey from MHIDAS database revealed that of all fire accidents, 28% occurred in process plants while 27% took place during transport (Planas-Cuchi et al., 1997). Heavy goods traffic by road has continually increased over many years and, in order to reduce the traffic impact over environment and population, the actual number of road tunnels has grown in Correspondence to: Professor B. Fabiano, Department of Chemical and Process Engineering, ‘GB Bonino’, University of Genoa, via Opera Pia 15, 16145 Genova, Italy. E-mail: [email protected]
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design parameter is the so-called critical ventilation velocity, i.e., the minimum speed of the longitudinal ventilation avoiding the spread of smoke and combustion products in the upstream direction, phenomenon known as ‘backlayering’. In several studies, the critical velocity vc was correlated to the fire heat release rate Q on the basis of semi-empirical models already adopted in describing nonconfined fires. For example (Oka and Akinson, 1995; Wu and Bakar, 2000), by adopting the Froude’s number conservation, a relationship was found in the form vc ¼ f (Q 1/3). However, experimental runs performed both on a laboratory scale (Oka and Akinson, 1995; Kunsch, 2002) and on a real scale (Bendelius, 1996; French, 1994; Fabiano et al., 2002) evidenced that such correlations are valid only in connection with fires of limited extension, while at high rates of heat release and when the flame height reaches the tunnel ceiling, the critical velocity tends asymptotically for a maximum value vca (Oka and Akinson, 1995; Wu and Bakar, 2000). For practical purpose and with a conservative approach, it is therefore essential to determine the critical velocity connected to the worst conditions i.e., its maximum value vca. The experimental phase of this paper was performed in a laboratory scale-tunnel under natural ventilation, forced ventilation, presence/absence of obstacles and different tunnel slopes. In the modelling study, reference was made to the worst scenario of hydrocarbon pool fire extended to the whole tunnel section. The main hypotheses the model is based upon are uniform distribution of chemicophysical properties of fire and smoke along the considered transversal section of the tunnel. The evaluation of the critical velocity is performed by solving mass, momentum and energy balances obtained considering possible dynamic interactions among the different fluxes (backlayering, air, flame/smoke column). In particular, the inertial action exerted by fresh air on backlayer was determined on the basis of the experimental results. The asymptotic value of the critical velocity resulting by mathematical modelling is in good agreement with those proposed by other authors, for example by means of complex CFD (computational fluid dynamics) studies. Moreover, the presented model is easily adaptable to the evaluation of vca, when dealing with geometrical conditions different from the here studied ones e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels. EXPERIMENTAL Materials and Methods The laboratory phase consisted in the simulation of a fire inside a laboratory tunnel scaled down 30 : 1 relative to the tunnel ‘Brasile’ of the two-lane highway A7 from Genoa to Milan (Italy). Real-scale experiments have been carried out in the tunnel ‘Brasile’ to simulate the evolving scenarios following an accident with fire development and to verify the effectiveness of smoke and fire management strategies and protective technologies (Fabiano et al., 2002). The total length of the laboratory tunnel is 6.0 m, the internal radius is 0.15 m, the height from the floor is 0.2 m and the width at the floor level is 0.28 m. The model, reproduced in Figure 1, is made of fire-proof concrete, with a Pyrex-glass made testing chamber (Fabiano et al., 2003).
Figure 1. Laboratory wind tunnel (1 ¼ longitudinal ventilation fan; 2 ¼ fire-proof floor; 3 ¼ fire-proof concrete tunnel; 4 ¼ data acquisition module; 5 ¼ stainless steel thermocouples; 6 ¼ Pyrex glass testing chamber; 7 ¼ fire source).
The upstream backlayering flow of hot gases and temperature profile inside the tunnel were detected by using K-type stainless steel thermocouples (Hanna Instruments) of diameter 0.25 mm. Air speed was measured by an anemometer with a 16 mm helical probe (Testo S.p.A., Milan, Italy). Noise connected to ventilation in the different operative conditions was measured by a class 1 sound level meter (Delta Ohm, Padova, Italy). An experimental procedure similar to the one presented by Wu and Bakar (2000) was adopted to measure critical velocity accurately. Firstly, the ventilation velocity required to control the length of backlayering flow to 10, five and one times of the tunnel height were measured systematically. Then the critical velocity extrapolated to zero backlayering length was applied to verify that no backlayer exists in the upstream of the fire. In order to evaluate the effectiveness of possible evasive actions including evacuation, escape and sheltering, under different ventilation conditions, we considered a survival temperature of 708C, which corresponds to a survival time of 60 minutes (Bengston, 1996). Results Figures 2– 4 show the isotherm curves and the iso-time lines representing the time taken for the temperature to reach the survival temperature previously defined. The study of the temperatures in the fire plume showed that the critical ventilation velocity is determined by the interaction of the fire with the fresh air flow and the tunnel walls. In absence of forced velocity (Figure 2), we have observed a slight tilt of the flame towards the upstream direction: the tilt effect implies worsening conditions for tunnel users, making possible a domino effect. The maximum temperature display has not a symmetrical profile (contrary to the case of natural ventilation and absence of obstacles inside the tunnel) and the area where the temperature does not exceed 308C is more limited, in the absence of obstacles; therefore less extended is also the portion of the tunnel where the temperature is always less than 708C. In the central portion, there is an area where the temperature exceeds 4008C; this area is larger upstream (more than 30 cm). In presence of fresh air supplied by longitudinal ventilation system, a rapid air entrainment into the fire plume
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Figure 2. Highest temperature and time to reach 708C without forced ventilation (v ¼ 0 m s21). This figure is available in colour online via www.icheme. org/journals
upstream causes a local acceleration in the air velocity inside the tunnel that forces the fire to tilt at a certain angle from the vertical. In the case of critical-velocity forced ventilation, which value measured 0.65 m s21 at the given heat release rate, the flame is inclined in the air flow direction, with a flame tilt angle of about 458 (Figure 3). The pattern of maximum temperatures is not symmetrical relative to the fire location, as the ones downstream are appreciably higher than in the analogous case under natural ventilation. By comparing the analogous case under natural ventilation, it may be observed how, downstream, at 120 cm, the area where the temperature never reaches the threshold value is considerably narrower (below 13 cm), whereas the intervals at which the temperatures are reached in increasingly shorter times are much narrower.
In the case of forced ventilation at velocity of 0.47 m s21, i.e., lower than critical velocity (Figure 4), the flame, after switching on the fan, is inclined about 308 with respect to the road surface. As regards the pattern of maximum temperatures upstream, the areas where maximum temperatures between 2008C and 4008C are recorded may be observed to widen, because the smoke tends to stagnate in the upstream portion of the tunnel. In the portion around the flames, there is an area where the temperature exceeds 4008C. Upstream, the temperature exceeds 708C in a wider area than in the cases of natural and critical ventilation, because of the smoke stagnation. Downstream temperature never exceeds 708C and the times taken, in the various sections, to reach such temperatures are lower than under the condition of natural ventilation, but higher than in case of critical ventilation.
Figure 3. Highest temperature and time to reach 708C with forced longitudinal ventilation at a critical velocity of 0.65 m s21. This figure is available in colour online via www.icheme.org/journals
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Figure 4. Highest temperature and time to reach 708C with forced longitudinal ventilation at velocity 0.47 m s21. This figure is available in colour online via www.icheme.org/journals
Overall, the results confirmed that the critical ventilation velocity becomes independent of the heat release rate when the heat release rate is sufficiently high, as reported by Oka and Atkinson (1995). MODELLING As already noted, experimental and theoretical studies from several researchers pointed out that the critical velocity increases as the fire heat release rate Q increases, up to an asymptotic value vca. As an example, according to Oka and Atkinson (1995) one can write (1)
where:
v ¼ Q ¼
8 < :
vmax
Q 0:12
1=3
vmax
(1 þ 3:57Q#2=3 )1=2 #1=3 Q 1 þ 6:13Q#2=3 Q pg1=2 H 5=2 Q# ¼ g=g 1
v ¼ 1:44
Critical Ventilation Limitations
vc ¼ v (gH)1=2
with vmax ranging from 0.22 to 0.38, depending on the tunnel type and on the flame location during the different experimental runs. According to Bendelius (1996), equation (1) is still valid, but in this case:
g ¼ cpf/cvf p ¼ ambient pressure, Pa From equations (4) and (5), vca can be obtained under the condition Q # ! 1, as follows
Q ra ta cpf g1=2 H 5=2
(2)
Q ¼ heat release rate, kJ s21 ta ¼ ambient temperature, K r ¼ ambient air density, kg m23 cpf ¼ specific heat of the hot gases, kJ kg21 K21 g ¼ acceleration of gravity, m s22 H ¼ tunnel height, m
(7)
where:
v ¼
8 < :
vmax vmax
Q 0:20
1=3
for Q 0:20 for Q . 0:20
where vmax ¼ 0.40, while H is a characteristic tunnel dimension, defined as 4A H ¼ (8) 2p
Then vca ¼ vmax (gH)1=2
(6)
At last, according to Wu and Bakar (2000) 1=2 vc ¼ v (gH)
for Q 0:12
(5)
where
vca ffi 0:44(gH)1=2 for Q 0:12
(4)
(3)
A ¼ area of the tunnel section, m2 p ¼ perimeter of the tunnel section, m
Trans IChemE, Part B, Process Safety and Environmental Protection, 2005, 83(B5): 443–451
ROAD TUNNEL FIRES USING HAZMAT In this last case, one obtains 1=2 vca ¼ 0:40(gH)
(9)
It can be noticed that, in the different models, the heat release of the fire is considered as a free variable, without any specific limitation. In this work, the calculation of the asymptotic value vca will be faced following a different approach, taking into account that: . a stoichiometric relationship between the fire heat release rate Q and the air flow rate can be established, in that the fire is generally fed by fresh air supplied by ventilation systems; . as demonstrated in the following paragraph of this paper, the smoke flow rate has been upper limited, due to the finite dimensions of the tunnel. The definition of a limiting value of Q will allow in the following paragraphs, to calculate an analytical expression of vca, relying only on the dynamic interactions among the different flows. The obtained relation for vca can directly be correlated to the geometric characteristics of the tunnel.
Limiting Smoke Flow Rate As tunnel dimensions are finite, the smoke flow rate in _ f can not exceed a particular characteristic case of fire, m _ fl . In order to value, here defined as ‘limiting flow’, m
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evaluate this flow, reference is made to Figure 5, where is depicted a plane tunnel, characterized by a rectangular section A ¼ DH, with a central fire at steady-state conditions. The following regions can be identified in Figure 5: . an acceleration region where, due to density difference with respect to external air, smoke accelerates until it attains the velocity vz; . a compression – expansion region, located near the tunnel ceiling, where the smoke firstly slows down while at the same time it is compressed, secondly it is subjected to expansion, with subsequent acceleration and at last move towards the tunnel ends, under a velocity vb. A cautious estimate of the limiting flow of the smoke can be obtained under the following hypotheses: (1) mechanical energy conservation during the transformations to which the smoke is subjected as time goes on (compression, expansion, kinetic energy variation, speed direction variation); (2) smoke particles during the acceleration phase cover the maximum distance. The former hypothesis is in connection with the kinetic energy maximum of the smoke out of the tunnel and correspondingly with the maximum smoke flow, at the given exit section: 2Ab ¼ 2DHb, the latter implies that smoke velocity is maximum, once the buoyancy force gets fixed, i.e., the smoke density rf and, therefore, the smoke temperature Tf are constant.
Figure 5. Fire and smoke schematization in a plane tunnel, at steady-state conditions, without longitudinal ventilation.
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The validity of previous hypotheses is strictly verified under the following conditions: . a very short tunnel, so that energetic dissipations (fluid– fluid and fluid –wall frictions) are really negligible; . combustion starting at ground level, for example due to an hydrocarbon pool fire occurring immediately. Under these conditions, with the hypothesis of uniform smoke temperature, the smokes gains kinetic energy, connected with its buoyancy thrust. This can be expressed as 1 2 H Hb rf vz ¼ (ra rf )g 2 2
Then, from equation (16), one can obtain a 0.94. More f ¼ 28:5 kg kmol1 , thus confirming the over, it results M f ffi Ma . It must be remarked that in previous hypothesis M case of combustion with excess of air, a is more proximate f is nearly equal to Ma . to 1 and M The velocity of air entrained from outside, in connection with the limit smoke flow rate, can be calculated by means of the expression
val ¼ (10)
_ al ð1=2Þm ð1=2Þa0:77ra A(gH)1=2 ¼ ra ð1=3ÞHD ra ð1=3ÞA
ffi 1:16a(gH)1=2
(17)
23
In equation (10), ra ffi 1.2 kg m is the air density at standard ambient conditions, while (H 2 Hb)/2 represents the average length of distance available for the acceleration of the ascending smoke. For equation (10) one can write vz ¼ ½(r 1)g(H Hb )1=2
(11)
where r¼
ra Tf ffi rf Ta
(12)
f ffi Ma ffi Equation (12) results under the assumption M f and Ma represent the mean 29 kg kmol21, where M molar mass of the smoke and of the air, respectively. On the basis of mechanical energy conservation, can be derived that vb ¼ vz and, subsequently, the mass flow rate of the smoke can be calculated as _ f ¼ 2Ab rf vb ¼ 2 m
ra DHb ½(r 1)g(H Hb )1=2 r
(13)
Equation (13) shows that the maximum value of the smoke flow rate is attained in connection with the conditions Hb ¼ (2/3) H and r ¼ 2 (Tf 596 K), as follows pffiffiffi 4 3 _ fl ¼ m r A(gH)1=2 ffi 0:77ra A(gH)1=2 9 a
(14)
An analogous limit fresh air flow rate corresponds to the limit smoke flow rate, as follows _ al ¼ am _ fl m
(15)
We can write
a¼
_a _a 1 m m ¼ ¼ _ c 1 þ ½ðMc =Ma Þ ð_nc =_na Þ _f m _a þm m
(16)
_ c is the fuel mass burning per time unit. where m From a practical viewpoint, a is a coefficient slightly lower than 1. In fact, for example, in case of stoichiometric combustion of hexane, the overall equation is 2 C6 H14 þ 19 O2 ! 12 CO2 þ 14 H2 O
comparable with the ones of the critical velocity presented in the previous paragraph. However, in order to provide positive smoke control, avoiding the smoke to exit at one end of the tunnel and providing clean air upstream of the fire, it is necessary to adopt a forced ventilation system. Given this argument, the model has to be modified, considering the main effects of the activation of the ventilation system on the smoke flow, which, as depicted in Figure 6, are: . the momentum of the advecting smoke column involving a longitudinal component; . drag effect between the air conveyed by the ventilation system and the backlayering. The development of the predictive model is presented in the next section. The main hypothesis the model is built upon is the uniformity of smoke temperature and, consequently, of its density (obviously smoke density is equal to backlayering density rb ¼ rf). An indication of the mean value and distribution of the smoke temperature in case of fire can be established making reference to Table 1, in which are presented the results from this study and from different researchers on fires in tunnels at a variety of scales, from small laboratory rigs, to full size tunnels. In the former case, the maximum temperatures of the ascending smoke are not particularly severe, in connection with values of the fire heat release rate by far lower than the ones allowed in the given tunnel. In any case, experimental results obtained from Wu and Bakar (2000) by means of accurate temperature measures in the acceleration region, are of particular interest to the purpose of the present study. Empirical evidence showed that as Q increases, the flame tends to extend to the full tunnel height, so that smoke temperature and density become more and more uniform, thus validating the hypothesis previously assumed in this study. A quantitative indication of the uniformity of the acceleration smoke region can be obtained from Table 2, in which are reported: . smoke temperature at the fuel pool level and at the tunnel ceiling; . values of the parameter (r 2 1)1/2, directly correlated to vz, according to equation (11); . the ratio rpv, which drops as Q increases, thus indicating a condition of uniformity of the chemico-physical properties, in the considered region.
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Figure 6. Model representation of the smoke flow, under forced longitudinal ventilation conditions.
Critical Velocity In order to obtain an analytical expression of the critical velocity, reference is made to the already-mentioned Figure 6, displaying . fuel pool extending to an area equal to DLp; . section 0 corresponding to the entrance of fresh air, forced by the ventilation system; . section 1 where fire starts: according to Wu and Bakar (2000) we assume that backlayering can not extend upstream of this section; . section 2, that is crossed by the ascending smoke column towards one side and by the backlayering towards the opposite side (in Figure 6, it is reproduced only the horizontal component of the smoke velocity, v2); . section 3, partially occupied by the smokes spreading towards the tunnel end downwards of the fire; . the most significant variables of the different flows.
Table 1. Main parameter and experimental results obtained in this study and by other researchers and calculated value of maximum critical velocity (vca,max). Q H D (kW) (m) (m)
Tunnel Wu (2) This study Memorial (4) Eureka (5)
1 2 3
3 7.5 15 1.5 104 105 105
0.25 0.25 0.25 0.20 6.5 6.5 5.5
A (m2)
T (K)
0.25 500 0.0625 0.25 700 0.0625 0.25 800 0.0625 0.30 0.05 600 7.0 46 600 7.0 46 900 6.2 34 1100
As already remarked, the main hypothesis the model is built upon is the uniformity of the chemico-physical smoke properties (in particular, temperature and density). We assume, as well, that the progressive reduction of the backlayering height is connected to the smoke entrainment by the fresh air. Making reference to the volume control between sections 2 and 3, the momentum balance can be written as follows _ m2 )v2 ¼ m _ f vb m _ b2 vb _f þm (m
(18)
assuming that drag effect at the tunnel ceiling is negligible and that vb ¼ vz, with vz resulting from equation (11). Defining as A2 and Ab2 the subsections of section 2 where the opposite flows extend, by definition it must arise A2 þ Ab2 ¼ A
(19)
_ b2 m _f þm _ b2 _a m m þ ¼ rb v 2 rb v b ra v a
(20)
vc vca,max (m s21) (m s21) 0.48 0.56 0.60 0.65 2.5 3.0 2.8
0.78 0.78 0.78 0.70 4.0 4.0 3.7
Table 2. Elaboration of experimental results from Wu and Bakar (2000). Tunnel
_ g TFv Q (kW) (K)
Wu (2) 1 2 3
3 7.5 15
TFp (K)
400 800 600 900 700 1000
(rv 1)1=2 (rp 1)1=2 0.59 1.01 1.16
Trans IChemE, Part B, Process Safety and Environmental Protection, 2005, 83(B5): 443–451
1.30 1.42 1.53
rpv ¼ ½(rp 1)= (rv 1)1=2 2.2 1.4 1.3
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By combining equations (18) and (20), also taking into account equations (12) and (16), one obtains (remembering that rb ¼ rf) va ¼ vb
_ b2 _f m a m a 1b ¼ vb _ b2 _ f þ 3m rm r 1 þ 3b
(21)
where b is the smoke fraction bringing about backlayering: b¼
_ b2 m _f m
(22)
As it results Ab2 ¼ A ¼A
_ b2 ra va _ b2 a 1 b m m ¼A r _ a rb v b _ f r 1 þ 3b am m b(1 b) 1 þ 3b
(23)
one can write Hb2 ¼ H
Ab2 b(1 b) ¼H 1 þ 3b A
(24)
Assuming that Hb Hb2, equation (11) yields a conservative estimate of vb
(1 b)2 vb ¼ ðr 1ÞgH 1 þ 3b
maximum values of the critical velocity (vca, max), calculated by means of the model here presented, under the condition a ¼ 1. It must be noticed that a fairly good agreement is always verified between the calculated values (vca, max) and the experimental values (vc) of the critical velocity obtained in each experiment in connection with the most severe tested fires, in terms of thermal power. As already reported, the minimum constraint for a safe intervention or evasive actions does not inevitably correspond to vanishing of backlayering. The safety constraint can be expressed as follows: the back flow must not extend upstream of the fire, i.e., making reference to Figure 6, the backlayering must stop at section 1. Assuming a linear decrease with x of the smoke mass flow rate in the backlayering, x being the upstream distance from the origin fixed at section 2, yields _ b2 f rb vb Dx _b ¼ m m
where f is the entrainment constant of smoke into the fresh air flow. The distance at which backlayering is zero can be calcu_ b ¼ 0, in the form lated from equation (29), imposing m xe ¼
_ b2 Ab2 H b(1 b) m ¼ ¼ f 1 þ 3b f rb vb D fD
(30)
One can also write (see Figure 6)
1=2 (25)
xe ¼ (H Hb )
Combining equations (25) and (21) results in (r 1)1=2 1 b2 va ¼ a (gH)1=2 r (1 þ 3b)3=2
(29)
¼H (26)
_ b2 _f m v2 (1 þ b)2 m ¼H _ b2 _b þm vz 1 þ 3b m
1 b2 1 þ 3b
(31)
By comparing equations (30) and (31), one obtains Hence, the fresh air velocity depends on the parameters a, r and b, respectively, linked to the stoichiometric, thermal and fluid-dynamic characteristics of the combustion process. In particular, in backlayering absence (b ¼ 0) and under the condition r ¼ 2, equation (26) yields the maximum value of the critical velocity va ¼ vca, max ¼
a (gH)1=2 2
(27)
Considering, as an example, the already studied hexane (a ¼ 0.94), results in vca, max ffi 0:47(gH)1=2
(28)
i.e., a value that is comparable with the ones available in literature and presented in paragraph ‘Critical ventilation limitations’ of this paper. RESULTS AND DISCUSSION Table 1 summarizes the experimental results obtained in this study and by other researchers, together with main experimental parameters adopted in full-scale and laboratory tests. The last column of the same table reports the
b¼
f 1f
(32)
Equation (32) allows obtaining, as a function of the entrainment constant f, the value of b in connection of which backlayering becomes zero, just in the tunnel section where the fire starts. Generally speaking, the value of f is to be obtained on experimental basis. However, under the hypothesis that backlayering is comparable to a plane jet (Kunsch, 2002). According to Rulkens et al. (1983), we can assume that f ¼
AR ffi 0:01–0:04 4
(33)
Complete stoichiometric combustion of hexane yields 2C6 H14 þ 19 O2 ! 12 CO2 þ 14 H2 O then, from equation (16), we obtain a 0.94. Table 3 shows, as a function of different values of the entrainment constant f : . the corresponding values of b, according to equation (32);
Trans IChemE, Part B, Process Safety and Environmental Protection, 2005, 83(B5): 443–451
ROAD TUNNEL FIRES USING HAZMAT Table 3. Calculation of model parameters f 0 0.01 0.04 0.1
b
vca (gH)1=2
0 0.01 0.04 0.11
0.47 0.45 0.40 0.30
. the values of the reduced critical velocity vca (gH)1=2 , obtained by means of equation (26), in connection with a ¼ 0.94 (hexane), r ¼ 2 and the previously obtained values of b. It can be observed that the calculated values of vca (gH)1=2 are in good agreement with the ones presented in paragraph ‘Critical ventilation limitations’, from different researchers, when f is in the range 0– 0.1. The presence of adequate and well-designed ventilation provides a decisive tactical advantage when tackling fires from hazardous materials in road- and rail-tunnels. In fact, the possibility of fighting a tunnel fire, at relatively close range, is strictly connected to the provision of forced ventilation system enabling free access from the upstream side, also allowing a safe exit way for persons involved. The approach proposed in this study allows obtaining the values of the critical velocity vca by means of equation (26), once given realistic values of the parameter f (and therefore of b). The model was validated, over a large range of fire sizes, by experimental runs carried out on a laboratory scale and by large-scale data obtained by different researchers. A fairly good agreement was verified with both laboratory-scale measurements and large-scale fire trials, so the model can be used with a good degree of confidence for the prediction of the critical ventilation velocity for a tunnel. Overall, the general model outlined here, if compared with the existing ones in literature, appears of easier application in designing a forced ventilation system to control the movement of smoke from fires. Moreover, its application can be easily extended, by proper arrangements, to geometrical conditions different from the ones studied here e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels.
451 REFERENCES
Beale, C.J., 2002, Recent railway industry accidents: learning points for the process industries, Trans IChemE, Part B, Proc Safe Env Prot, 80(1): 25–32. Bendelius, A.G., 1996, The Memorial Tunnel Fire Ventilation Test Program, Proc. 1st Conf. “Protezione contro il rischio di incendi nelle gallerie ferroviarie e stradali”, Rome, Italy, 65, 19–36. Bengston, S., 1996, Objectives of fire and smoke control, in Fire and Smoke Control in Road Tunnel, PIARC Committee on Road Tunnels, 2nd draft. Fabiano, B., Curro`, F., Palazzi, E. and Pastorino, R., 2002, Environmental and accident risk connected to road tunnel fires: experimental and theoretical investigation, Int. Conf. on Environmetrics TIES 2002. The International Environmetrics Society, Genova, Italy, 37. Fabiano, B., Curro`, F., Cazzola, D., Palazzi, E., Pastorino, R. and Del Borghi, M., 2003, A study on risk assessment of road tunnel fires by full-scale testing, Proc. 14th International Conference IUAPPA, Dubrovnik, Croatia, 6– 10 October 2003, Kresimir Sega (ed). CAPPA Publisher, 467–474. French, S.E., 1994, EUREKA 499-HGV fire test, Proc. Int. Conf. on Fires in Tunnels, Bords, Sweden, 63–85. SP Report 1994:54 (Swedish National Testing and Research Institute). Fuller, B., 1985, Problems of safety for firemen underground, Fire Int., Dec/Jan 1985/1986: 37– 39. Kunsch, J.P., 2002, Simple model for control of fire gases in a ventilated tunnel, Fire Safety Journal, 37 (1): 67–81. Oka, Y. and Atkinson, G.T., 1995, Control of smoke flow in tunnel fires, Fire Safety Journal, 25 (4): 305–322. Planas-Cuchi, E., Montiel, H. and Casal, J., 1997, A survey on the origin, type and consequences of fire accidents in process plants and in the transportation of hazardous materials, Trans IChemE, Part B, Proc Safe Env Prot, 75(1): 3–8. Rulkens, P.F.M., Bongers, A.J.P., Ten Brink, G.P. and Guldemond, C.P., 1983, The application of gas curtains for diluting flammable gas clouds to prevent their ignition, Loss Prevention and Safety Promotion in the Process Industries IV, EFCE Publication Series n. 33, vol. 1, Pergamon Press, UK, F15–F25. Thomson, B.J., 1998, International co-operation in hazardous materials accident prevention, Proc. of International Workshop on Safety in the Transport, Storage and Use of Hazardous Materials, NRIFD, Tokyo, Japan, 211–224. Wu, Y. and Bakar, M.Z.A., 2000, Control of smoke flow in tunnel fires using longitudinal ventilation systems—a study of the critical velocity, Fire Safety Journal, 35 (4): 363–390.
ACKNOWLEDGEMENTS This research was supported in part by the MIUR (Ministry of Instruction, University and Research, Rome)—D.M. n. 235 Uff. VIII/2001. The manuscript was received 13 August 2004 and accepted for publication after revision 28 January 2005.
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www.icheme.org/journals doi: 10.1205/psep.04214
A STUDY ON ROAD TUNNEL FIRES USING HAZMAT, WITH EMPHASIS ON CRITICAL VENTILATION VELOCITY ` and B. FABIANO E. PALAZZI, F. CURRO DICheP Chemical & Process Engineering Department ‘G.B. Bonino’, University of Genoa, Italy
O
ne of the main protective measures to be adopted in case of fires in road/rail tunnels is represented by suitable longitudinal ventilation systems being able to avoid fire and smoke exposure of humans, and to create a safe route upstream for evacuation. The key design parameter is the so-called critical ventilation velocity, i.e. the minimum speed of the longitudinal ventilation avoiding the spread of the smoke produced by fire in the upstream direction, known as ‘backlayering’. In several studies, the critical velocity was correlated to the fire heat release rate on the basis of semi-empirical models, already adopted in describing nonconfined fires. However, experimental runs both on a laboratory scale and on a real scale, evidenced that such correlations are valid only in connection with fires of limited extent, while at high rates of heat release and when the flame height reaches the tunnel ceiling, the critical velocity can tend asymptotically to a maximum value vca. In this study, reference was made to the worst scenario of hydrocarbon pool fire extended to the whole tunnel section. The main hypotheses the model is based upon are uniform distribution of chemico-physical properties of fire and smoke along the considered transverse section of the tunnel. The evaluation of the critical velocity is performed by solving mass, momentum and energy balances obtained considering possible dynamic interactions among the different fluxes (backlayering, air, flame/smoke column). In particular, the inertial action exerted by fresh air on backlayering was determined on the basis of the experimental results. The asymptotic value of the critical velocity resulting by mathematical modelling is in good agreement with those proposed by other authors, for example by means of complex CFD (computational fluid dynamics) studies. Moreover, the developed model is easily adaptable to the evaluation of vca, when dealing with geometrical conditions different from the ones studied here e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels. Keywords: fire; hazardous materials; transportation; tunnel; ventilation.
INTRODUCTION
many countries. High profile accidents were recorded in railway tunnels too, e.g., the Channel tunnel fire, the Kaprun fire and raised a large amount of public debate about rail safety (Beale, 2002). Due to the sharp reduction of vehicle pollutant emissions, the ventilation of road tunnels is more and more determined by the need of controlling smoke in case of fire. In fact, recent severe accidents, such as the one in Mont Blanc (Italy/France), have evidenced the need of extending the conventional concept of ‘hazardous materials’ to a broader range of transported goods and the relevance of prevention and limitation of consequences measures in case of fire in road- and railtunnels. One of the main protective measures to be adopted in case of fire in tunnels is represented by suitable longitudinal ventilation systems being able to avoid fire and smoke exposure of humans, and create a safe route upstream for evacuation. The presence of adequate ventilation was considered by Fuller (1985) to provide a significant tactical advantage when tackling fires, by increasing the visibility and diluting toxic and flammable fumes. The key
Despite the relative recent move towards ‘inherently safe’ materials, the relentless drive of consumerism has required increased quantities of dangerous goods to be manufactured, transported, stored and used year on year (Thomson, 1998). Incidents related to transportation of hazardous materials are comparable in number and severity to those occurring in process plant: a survey from MHIDAS database revealed that of all fire accidents, 28% occurred in process plants while 27% took place during transport (Planas-Cuchi et al., 1997). Heavy goods traffic by road has continually increased over many years and, in order to reduce the traffic impact over environment and population, the actual number of road tunnels has grown in Correspondence to: Professor B. Fabiano, Department of Chemical and Process Engineering, ‘GB Bonino’, University of Genoa, via Opera Pia 15, 16145 Genova, Italy. E-mail: [email protected]
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design parameter is the so-called critical ventilation velocity, i.e., the minimum speed of the longitudinal ventilation avoiding the spread of smoke and combustion products in the upstream direction, phenomenon known as ‘backlayering’. In several studies, the critical velocity vc was correlated to the fire heat release rate Q on the basis of semi-empirical models already adopted in describing nonconfined fires. For example (Oka and Akinson, 1995; Wu and Bakar, 2000), by adopting the Froude’s number conservation, a relationship was found in the form vc ¼ f (Q 1/3). However, experimental runs performed both on a laboratory scale (Oka and Akinson, 1995; Kunsch, 2002) and on a real scale (Bendelius, 1996; French, 1994; Fabiano et al., 2002) evidenced that such correlations are valid only in connection with fires of limited extension, while at high rates of heat release and when the flame height reaches the tunnel ceiling, the critical velocity tends asymptotically for a maximum value vca (Oka and Akinson, 1995; Wu and Bakar, 2000). For practical purpose and with a conservative approach, it is therefore essential to determine the critical velocity connected to the worst conditions i.e., its maximum value vca. The experimental phase of this paper was performed in a laboratory scale-tunnel under natural ventilation, forced ventilation, presence/absence of obstacles and different tunnel slopes. In the modelling study, reference was made to the worst scenario of hydrocarbon pool fire extended to the whole tunnel section. The main hypotheses the model is based upon are uniform distribution of chemicophysical properties of fire and smoke along the considered transversal section of the tunnel. The evaluation of the critical velocity is performed by solving mass, momentum and energy balances obtained considering possible dynamic interactions among the different fluxes (backlayering, air, flame/smoke column). In particular, the inertial action exerted by fresh air on backlayer was determined on the basis of the experimental results. The asymptotic value of the critical velocity resulting by mathematical modelling is in good agreement with those proposed by other authors, for example by means of complex CFD (computational fluid dynamics) studies. Moreover, the presented model is easily adaptable to the evaluation of vca, when dealing with geometrical conditions different from the here studied ones e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels. EXPERIMENTAL Materials and Methods The laboratory phase consisted in the simulation of a fire inside a laboratory tunnel scaled down 30 : 1 relative to the tunnel ‘Brasile’ of the two-lane highway A7 from Genoa to Milan (Italy). Real-scale experiments have been carried out in the tunnel ‘Brasile’ to simulate the evolving scenarios following an accident with fire development and to verify the effectiveness of smoke and fire management strategies and protective technologies (Fabiano et al., 2002). The total length of the laboratory tunnel is 6.0 m, the internal radius is 0.15 m, the height from the floor is 0.2 m and the width at the floor level is 0.28 m. The model, reproduced in Figure 1, is made of fire-proof concrete, with a Pyrex-glass made testing chamber (Fabiano et al., 2003).
Figure 1. Laboratory wind tunnel (1 ¼ longitudinal ventilation fan; 2 ¼ fire-proof floor; 3 ¼ fire-proof concrete tunnel; 4 ¼ data acquisition module; 5 ¼ stainless steel thermocouples; 6 ¼ Pyrex glass testing chamber; 7 ¼ fire source).
The upstream backlayering flow of hot gases and temperature profile inside the tunnel were detected by using K-type stainless steel thermocouples (Hanna Instruments) of diameter 0.25 mm. Air speed was measured by an anemometer with a 16 mm helical probe (Testo S.p.A., Milan, Italy). Noise connected to ventilation in the different operative conditions was measured by a class 1 sound level meter (Delta Ohm, Padova, Italy). An experimental procedure similar to the one presented by Wu and Bakar (2000) was adopted to measure critical velocity accurately. Firstly, the ventilation velocity required to control the length of backlayering flow to 10, five and one times of the tunnel height were measured systematically. Then the critical velocity extrapolated to zero backlayering length was applied to verify that no backlayer exists in the upstream of the fire. In order to evaluate the effectiveness of possible evasive actions including evacuation, escape and sheltering, under different ventilation conditions, we considered a survival temperature of 708C, which corresponds to a survival time of 60 minutes (Bengston, 1996). Results Figures 2– 4 show the isotherm curves and the iso-time lines representing the time taken for the temperature to reach the survival temperature previously defined. The study of the temperatures in the fire plume showed that the critical ventilation velocity is determined by the interaction of the fire with the fresh air flow and the tunnel walls. In absence of forced velocity (Figure 2), we have observed a slight tilt of the flame towards the upstream direction: the tilt effect implies worsening conditions for tunnel users, making possible a domino effect. The maximum temperature display has not a symmetrical profile (contrary to the case of natural ventilation and absence of obstacles inside the tunnel) and the area where the temperature does not exceed 308C is more limited, in the absence of obstacles; therefore less extended is also the portion of the tunnel where the temperature is always less than 708C. In the central portion, there is an area where the temperature exceeds 4008C; this area is larger upstream (more than 30 cm). In presence of fresh air supplied by longitudinal ventilation system, a rapid air entrainment into the fire plume
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Figure 2. Highest temperature and time to reach 708C without forced ventilation (v ¼ 0 m s21). This figure is available in colour online via www.icheme. org/journals
upstream causes a local acceleration in the air velocity inside the tunnel that forces the fire to tilt at a certain angle from the vertical. In the case of critical-velocity forced ventilation, which value measured 0.65 m s21 at the given heat release rate, the flame is inclined in the air flow direction, with a flame tilt angle of about 458 (Figure 3). The pattern of maximum temperatures is not symmetrical relative to the fire location, as the ones downstream are appreciably higher than in the analogous case under natural ventilation. By comparing the analogous case under natural ventilation, it may be observed how, downstream, at 120 cm, the area where the temperature never reaches the threshold value is considerably narrower (below 13 cm), whereas the intervals at which the temperatures are reached in increasingly shorter times are much narrower.
In the case of forced ventilation at velocity of 0.47 m s21, i.e., lower than critical velocity (Figure 4), the flame, after switching on the fan, is inclined about 308 with respect to the road surface. As regards the pattern of maximum temperatures upstream, the areas where maximum temperatures between 2008C and 4008C are recorded may be observed to widen, because the smoke tends to stagnate in the upstream portion of the tunnel. In the portion around the flames, there is an area where the temperature exceeds 4008C. Upstream, the temperature exceeds 708C in a wider area than in the cases of natural and critical ventilation, because of the smoke stagnation. Downstream temperature never exceeds 708C and the times taken, in the various sections, to reach such temperatures are lower than under the condition of natural ventilation, but higher than in case of critical ventilation.
Figure 3. Highest temperature and time to reach 708C with forced longitudinal ventilation at a critical velocity of 0.65 m s21. This figure is available in colour online via www.icheme.org/journals
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Figure 4. Highest temperature and time to reach 708C with forced longitudinal ventilation at velocity 0.47 m s21. This figure is available in colour online via www.icheme.org/journals
Overall, the results confirmed that the critical ventilation velocity becomes independent of the heat release rate when the heat release rate is sufficiently high, as reported by Oka and Atkinson (1995). MODELLING As already noted, experimental and theoretical studies from several researchers pointed out that the critical velocity increases as the fire heat release rate Q increases, up to an asymptotic value vca. As an example, according to Oka and Atkinson (1995) one can write (1)
where:
v ¼ Q ¼
8 < :
vmax
Q 0:12
1=3
vmax
(1 þ 3:57Q#2=3 )1=2 #1=3 Q 1 þ 6:13Q#2=3 Q pg1=2 H 5=2 Q# ¼ g=g 1
v ¼ 1:44
Critical Ventilation Limitations
vc ¼ v (gH)1=2
with vmax ranging from 0.22 to 0.38, depending on the tunnel type and on the flame location during the different experimental runs. According to Bendelius (1996), equation (1) is still valid, but in this case:
g ¼ cpf/cvf p ¼ ambient pressure, Pa From equations (4) and (5), vca can be obtained under the condition Q # ! 1, as follows
Q ra ta cpf g1=2 H 5=2
(2)
Q ¼ heat release rate, kJ s21 ta ¼ ambient temperature, K r ¼ ambient air density, kg m23 cpf ¼ specific heat of the hot gases, kJ kg21 K21 g ¼ acceleration of gravity, m s22 H ¼ tunnel height, m
(7)
where:
v ¼
8 < :
vmax vmax
Q 0:20
1=3
for Q 0:20 for Q . 0:20
where vmax ¼ 0.40, while H is a characteristic tunnel dimension, defined as 4A H ¼ (8) 2p
Then vca ¼ vmax (gH)1=2
(6)
At last, according to Wu and Bakar (2000) 1=2 vc ¼ v (gH)
for Q 0:12
(5)
where
vca ffi 0:44(gH)1=2 for Q 0:12
(4)
(3)
A ¼ area of the tunnel section, m2 p ¼ perimeter of the tunnel section, m
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ROAD TUNNEL FIRES USING HAZMAT In this last case, one obtains 1=2 vca ¼ 0:40(gH)
(9)
It can be noticed that, in the different models, the heat release of the fire is considered as a free variable, without any specific limitation. In this work, the calculation of the asymptotic value vca will be faced following a different approach, taking into account that: . a stoichiometric relationship between the fire heat release rate Q and the air flow rate can be established, in that the fire is generally fed by fresh air supplied by ventilation systems; . as demonstrated in the following paragraph of this paper, the smoke flow rate has been upper limited, due to the finite dimensions of the tunnel. The definition of a limiting value of Q will allow in the following paragraphs, to calculate an analytical expression of vca, relying only on the dynamic interactions among the different flows. The obtained relation for vca can directly be correlated to the geometric characteristics of the tunnel.
Limiting Smoke Flow Rate As tunnel dimensions are finite, the smoke flow rate in _ f can not exceed a particular characteristic case of fire, m _ fl . In order to value, here defined as ‘limiting flow’, m
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evaluate this flow, reference is made to Figure 5, where is depicted a plane tunnel, characterized by a rectangular section A ¼ DH, with a central fire at steady-state conditions. The following regions can be identified in Figure 5: . an acceleration region where, due to density difference with respect to external air, smoke accelerates until it attains the velocity vz; . a compression – expansion region, located near the tunnel ceiling, where the smoke firstly slows down while at the same time it is compressed, secondly it is subjected to expansion, with subsequent acceleration and at last move towards the tunnel ends, under a velocity vb. A cautious estimate of the limiting flow of the smoke can be obtained under the following hypotheses: (1) mechanical energy conservation during the transformations to which the smoke is subjected as time goes on (compression, expansion, kinetic energy variation, speed direction variation); (2) smoke particles during the acceleration phase cover the maximum distance. The former hypothesis is in connection with the kinetic energy maximum of the smoke out of the tunnel and correspondingly with the maximum smoke flow, at the given exit section: 2Ab ¼ 2DHb, the latter implies that smoke velocity is maximum, once the buoyancy force gets fixed, i.e., the smoke density rf and, therefore, the smoke temperature Tf are constant.
Figure 5. Fire and smoke schematization in a plane tunnel, at steady-state conditions, without longitudinal ventilation.
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The validity of previous hypotheses is strictly verified under the following conditions: . a very short tunnel, so that energetic dissipations (fluid– fluid and fluid –wall frictions) are really negligible; . combustion starting at ground level, for example due to an hydrocarbon pool fire occurring immediately. Under these conditions, with the hypothesis of uniform smoke temperature, the smokes gains kinetic energy, connected with its buoyancy thrust. This can be expressed as 1 2 H Hb rf vz ¼ (ra rf )g 2 2
Then, from equation (16), one can obtain a 0.94. More f ¼ 28:5 kg kmol1 , thus confirming the over, it results M f ffi Ma . It must be remarked that in previous hypothesis M case of combustion with excess of air, a is more proximate f is nearly equal to Ma . to 1 and M The velocity of air entrained from outside, in connection with the limit smoke flow rate, can be calculated by means of the expression
val ¼ (10)
_ al ð1=2Þm ð1=2Þa0:77ra A(gH)1=2 ¼ ra ð1=3ÞHD ra ð1=3ÞA
ffi 1:16a(gH)1=2
(17)
23
In equation (10), ra ffi 1.2 kg m is the air density at standard ambient conditions, while (H 2 Hb)/2 represents the average length of distance available for the acceleration of the ascending smoke. For equation (10) one can write vz ¼ ½(r 1)g(H Hb )1=2
(11)
where r¼
ra Tf ffi rf Ta
(12)
f ffi Ma ffi Equation (12) results under the assumption M f and Ma represent the mean 29 kg kmol21, where M molar mass of the smoke and of the air, respectively. On the basis of mechanical energy conservation, can be derived that vb ¼ vz and, subsequently, the mass flow rate of the smoke can be calculated as _ f ¼ 2Ab rf vb ¼ 2 m
ra DHb ½(r 1)g(H Hb )1=2 r
(13)
Equation (13) shows that the maximum value of the smoke flow rate is attained in connection with the conditions Hb ¼ (2/3) H and r ¼ 2 (Tf 596 K), as follows pffiffiffi 4 3 _ fl ¼ m r A(gH)1=2 ffi 0:77ra A(gH)1=2 9 a
(14)
An analogous limit fresh air flow rate corresponds to the limit smoke flow rate, as follows _ al ¼ am _ fl m
(15)
We can write
a¼
_a _a 1 m m ¼ ¼ _ c 1 þ ½ðMc =Ma Þ ð_nc =_na Þ _f m _a þm m
(16)
_ c is the fuel mass burning per time unit. where m From a practical viewpoint, a is a coefficient slightly lower than 1. In fact, for example, in case of stoichiometric combustion of hexane, the overall equation is 2 C6 H14 þ 19 O2 ! 12 CO2 þ 14 H2 O
comparable with the ones of the critical velocity presented in the previous paragraph. However, in order to provide positive smoke control, avoiding the smoke to exit at one end of the tunnel and providing clean air upstream of the fire, it is necessary to adopt a forced ventilation system. Given this argument, the model has to be modified, considering the main effects of the activation of the ventilation system on the smoke flow, which, as depicted in Figure 6, are: . the momentum of the advecting smoke column involving a longitudinal component; . drag effect between the air conveyed by the ventilation system and the backlayering. The development of the predictive model is presented in the next section. The main hypothesis the model is built upon is the uniformity of smoke temperature and, consequently, of its density (obviously smoke density is equal to backlayering density rb ¼ rf). An indication of the mean value and distribution of the smoke temperature in case of fire can be established making reference to Table 1, in which are presented the results from this study and from different researchers on fires in tunnels at a variety of scales, from small laboratory rigs, to full size tunnels. In the former case, the maximum temperatures of the ascending smoke are not particularly severe, in connection with values of the fire heat release rate by far lower than the ones allowed in the given tunnel. In any case, experimental results obtained from Wu and Bakar (2000) by means of accurate temperature measures in the acceleration region, are of particular interest to the purpose of the present study. Empirical evidence showed that as Q increases, the flame tends to extend to the full tunnel height, so that smoke temperature and density become more and more uniform, thus validating the hypothesis previously assumed in this study. A quantitative indication of the uniformity of the acceleration smoke region can be obtained from Table 2, in which are reported: . smoke temperature at the fuel pool level and at the tunnel ceiling; . values of the parameter (r 2 1)1/2, directly correlated to vz, according to equation (11); . the ratio rpv, which drops as Q increases, thus indicating a condition of uniformity of the chemico-physical properties, in the considered region.
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Figure 6. Model representation of the smoke flow, under forced longitudinal ventilation conditions.
Critical Velocity In order to obtain an analytical expression of the critical velocity, reference is made to the already-mentioned Figure 6, displaying . fuel pool extending to an area equal to DLp; . section 0 corresponding to the entrance of fresh air, forced by the ventilation system; . section 1 where fire starts: according to Wu and Bakar (2000) we assume that backlayering can not extend upstream of this section; . section 2, that is crossed by the ascending smoke column towards one side and by the backlayering towards the opposite side (in Figure 6, it is reproduced only the horizontal component of the smoke velocity, v2); . section 3, partially occupied by the smokes spreading towards the tunnel end downwards of the fire; . the most significant variables of the different flows.
Table 1. Main parameter and experimental results obtained in this study and by other researchers and calculated value of maximum critical velocity (vca,max). Q H D (kW) (m) (m)
Tunnel Wu (2) This study Memorial (4) Eureka (5)
1 2 3
3 7.5 15 1.5 104 105 105
0.25 0.25 0.25 0.20 6.5 6.5 5.5
A (m2)
T (K)
0.25 500 0.0625 0.25 700 0.0625 0.25 800 0.0625 0.30 0.05 600 7.0 46 600 7.0 46 900 6.2 34 1100
As already remarked, the main hypothesis the model is built upon is the uniformity of the chemico-physical smoke properties (in particular, temperature and density). We assume, as well, that the progressive reduction of the backlayering height is connected to the smoke entrainment by the fresh air. Making reference to the volume control between sections 2 and 3, the momentum balance can be written as follows _ m2 )v2 ¼ m _ f vb m _ b2 vb _f þm (m
(18)
assuming that drag effect at the tunnel ceiling is negligible and that vb ¼ vz, with vz resulting from equation (11). Defining as A2 and Ab2 the subsections of section 2 where the opposite flows extend, by definition it must arise A2 þ Ab2 ¼ A
(19)
_ b2 m _f þm _ b2 _a m m þ ¼ rb v 2 rb v b ra v a
(20)
vc vca,max (m s21) (m s21) 0.48 0.56 0.60 0.65 2.5 3.0 2.8
0.78 0.78 0.78 0.70 4.0 4.0 3.7
Table 2. Elaboration of experimental results from Wu and Bakar (2000). Tunnel
_ g TFv Q (kW) (K)
Wu (2) 1 2 3
3 7.5 15
TFp (K)
400 800 600 900 700 1000
(rv 1)1=2 (rp 1)1=2 0.59 1.01 1.16
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1.30 1.42 1.53
rpv ¼ ½(rp 1)= (rv 1)1=2 2.2 1.4 1.3
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By combining equations (18) and (20), also taking into account equations (12) and (16), one obtains (remembering that rb ¼ rf) va ¼ vb
_ b2 _f m a m a 1b ¼ vb _ b2 _ f þ 3m rm r 1 þ 3b
(21)
where b is the smoke fraction bringing about backlayering: b¼
_ b2 m _f m
(22)
As it results Ab2 ¼ A ¼A
_ b2 ra va _ b2 a 1 b m m ¼A r _ a rb v b _ f r 1 þ 3b am m b(1 b) 1 þ 3b
(23)
one can write Hb2 ¼ H
Ab2 b(1 b) ¼H 1 þ 3b A
(24)
Assuming that Hb Hb2, equation (11) yields a conservative estimate of vb
(1 b)2 vb ¼ ðr 1ÞgH 1 þ 3b
maximum values of the critical velocity (vca, max), calculated by means of the model here presented, under the condition a ¼ 1. It must be noticed that a fairly good agreement is always verified between the calculated values (vca, max) and the experimental values (vc) of the critical velocity obtained in each experiment in connection with the most severe tested fires, in terms of thermal power. As already reported, the minimum constraint for a safe intervention or evasive actions does not inevitably correspond to vanishing of backlayering. The safety constraint can be expressed as follows: the back flow must not extend upstream of the fire, i.e., making reference to Figure 6, the backlayering must stop at section 1. Assuming a linear decrease with x of the smoke mass flow rate in the backlayering, x being the upstream distance from the origin fixed at section 2, yields _ b2 f rb vb Dx _b ¼ m m
where f is the entrainment constant of smoke into the fresh air flow. The distance at which backlayering is zero can be calcu_ b ¼ 0, in the form lated from equation (29), imposing m xe ¼
_ b2 Ab2 H b(1 b) m ¼ ¼ f 1 þ 3b f rb vb D fD
(30)
One can also write (see Figure 6)
1=2 (25)
xe ¼ (H Hb )
Combining equations (25) and (21) results in (r 1)1=2 1 b2 va ¼ a (gH)1=2 r (1 þ 3b)3=2
(29)
¼H (26)
_ b2 _f m v2 (1 þ b)2 m ¼H _ b2 _b þm vz 1 þ 3b m
1 b2 1 þ 3b
(31)
By comparing equations (30) and (31), one obtains Hence, the fresh air velocity depends on the parameters a, r and b, respectively, linked to the stoichiometric, thermal and fluid-dynamic characteristics of the combustion process. In particular, in backlayering absence (b ¼ 0) and under the condition r ¼ 2, equation (26) yields the maximum value of the critical velocity va ¼ vca, max ¼
a (gH)1=2 2
(27)
Considering, as an example, the already studied hexane (a ¼ 0.94), results in vca, max ffi 0:47(gH)1=2
(28)
i.e., a value that is comparable with the ones available in literature and presented in paragraph ‘Critical ventilation limitations’ of this paper. RESULTS AND DISCUSSION Table 1 summarizes the experimental results obtained in this study and by other researchers, together with main experimental parameters adopted in full-scale and laboratory tests. The last column of the same table reports the
b¼
f 1f
(32)
Equation (32) allows obtaining, as a function of the entrainment constant f, the value of b in connection of which backlayering becomes zero, just in the tunnel section where the fire starts. Generally speaking, the value of f is to be obtained on experimental basis. However, under the hypothesis that backlayering is comparable to a plane jet (Kunsch, 2002). According to Rulkens et al. (1983), we can assume that f ¼
AR ffi 0:01–0:04 4
(33)
Complete stoichiometric combustion of hexane yields 2C6 H14 þ 19 O2 ! 12 CO2 þ 14 H2 O then, from equation (16), we obtain a 0.94. Table 3 shows, as a function of different values of the entrainment constant f : . the corresponding values of b, according to equation (32);
Trans IChemE, Part B, Process Safety and Environmental Protection, 2005, 83(B5): 443–451
ROAD TUNNEL FIRES USING HAZMAT Table 3. Calculation of model parameters f 0 0.01 0.04 0.1
b
vca (gH)1=2
0 0.01 0.04 0.11
0.47 0.45 0.40 0.30
. the values of the reduced critical velocity vca (gH)1=2 , obtained by means of equation (26), in connection with a ¼ 0.94 (hexane), r ¼ 2 and the previously obtained values of b. It can be observed that the calculated values of vca (gH)1=2 are in good agreement with the ones presented in paragraph ‘Critical ventilation limitations’, from different researchers, when f is in the range 0– 0.1. The presence of adequate and well-designed ventilation provides a decisive tactical advantage when tackling fires from hazardous materials in road- and rail-tunnels. In fact, the possibility of fighting a tunnel fire, at relatively close range, is strictly connected to the provision of forced ventilation system enabling free access from the upstream side, also allowing a safe exit way for persons involved. The approach proposed in this study allows obtaining the values of the critical velocity vca by means of equation (26), once given realistic values of the parameter f (and therefore of b). The model was validated, over a large range of fire sizes, by experimental runs carried out on a laboratory scale and by large-scale data obtained by different researchers. A fairly good agreement was verified with both laboratory-scale measurements and large-scale fire trials, so the model can be used with a good degree of confidence for the prediction of the critical ventilation velocity for a tunnel. Overall, the general model outlined here, if compared with the existing ones in literature, appears of easier application in designing a forced ventilation system to control the movement of smoke from fires. Moreover, its application can be easily extended, by proper arrangements, to geometrical conditions different from the ones studied here e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels.
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ACKNOWLEDGEMENTS This research was supported in part by the MIUR (Ministry of Instruction, University and Research, Rome)—D.M. n. 235 Uff. VIII/2001. The manuscript was received 13 August 2004 and accepted for publication after revision 28 January 2005.
Trans IChemE, Part B, Process Safety and Environmental Protection, 2005, 83(B5): 443–451