Chapter 9
Ignition of the Flammable Region: Backdraft Deflagration Table of Contents
1. Introduction.............................................................................. 242 2. State of the Art ........................................................................ 242 3. Main Governing Equations for Backdraft Deflagrations............ 244 3.1 Assumptions of the Deflagration Model ............................... 245 3.2 Nomenclature of the Governing Equations........................... 246 3.3 Main Governing Equations .................................................. 249 3.4 Outflow Equation................................................................. 250 3.5 Comments............................................................................ 251 4. Fireball: Estimation of the Diameter ........................................ 252 5. Validation of the Model ............................................................ 253 6. Graphical Method for Obtaining the Fireball’s Diameter.......... 262 7. Conclusion ................................................................................ 264
9. Ignition of the Flammable Region: Backdraft Deflagration
1. Introduction When a flammable mixture is ignited, a sudden increase in volume and a violent release of energy takes place, generating high temperatures and combustion products. This process is what really happens in a backdraft deflagration. Many authors have studied explosions and vented deflagration in confined and unconfined enclosures, developing simple correlations for predicting the “reduced pressure�. However, to define a backdraft phenomenon, not only the reduced pressure reached in the compartment, which can cause structure collapse, is important, but the quantity of gas burning inside and outside the compartment also must be assessed. This section deals with a theoretical model for modelling backdraft deflagrations in compartments based on the theoretical study of vented gaseous deflagration for premixed stoichiometric mixtures examined in Grigorash. A., 2003. Combustion and thermal chemistry laws are also taken into account. Comparisons with real explosions and simple correlations are carried out for different explosion scenarios (e.g. using different shapes, volume, type of mixture).
2. State of the Art Deflagration can be defined as a sudden increase in volume and a violent release of energy, usually associated with the generation of high temperatures and combustion products. This outburst causes subsonic pressure waves in the local medium in which it occurs. Deflagration is initiated by any ignition source with weak shock potential and low energy release (in comparison with the internal energy of a mixture inside the enclosure) like a spark or hot ember placed at any point of space inside an arbitrarily shaped enclosure. Vented deflagration has been studied extensively for many years to provide understanding of the phenomenon as well as correlations that allow predicting the pressure development (Grigorash, A., et al., 2003; Razus, D. et al., 2000; Francesco, T. and Valius, J.V., 2000). These studies have shown that the evolution of a deflagration depends on the nature and state of the initial explosive mixture (i.e. its composition, initial pressure and temperature, preignition turbulence) and on the vessel characteristics (i.e. its dimension and shape, position of the ignition source, location, size, strength and shape of the vents, and presence of obstacles within the vessel). Other factors, such as the characteristics of the ignition source, may also influence the deflagration’s evolution in a compartment fire.
242
9. Ignition of the Flammable Region: Backdraft Deflagration
Yao and Pasman developed the first theory on gaseous deflagration in 1974. This theory is based on a lumped parameter called the turbulence factor, χ. To estimate the unknown in advance (the so-called turbulence factor χ), they employed the inverse problem method according to which the theoretical pressure-time curve is fit to the experimental one by adjusting of χ. The turbulence factor quantitatively describes a flame stretch, i.e. the increase of a real flame-front area at any moment during the course of deflagration with respect to the reference laminar spherical flame area. This last term refers to the surface area of a sphere to which combustion products inside the enclosure at any moment can be gathered. In general, χ varies over the time (see Eq. (9-1)). χ=
Ff (t) Fs (t)
(9-1)
Above Ff is the real flame front area and Fs is the surface area of a flame assuming a laminar spherical propagation. Since χ was the only parameter to adjust, the coincidence between theoretical and experimental pressure-time curves was poor in many cases and generalization of the experimental data was impossible at that time. Then in 1981, Molkov and Nekrasov suggested a deflagration theory with two lumped parameters, i.e. the turbulence factor χ and the generalized discharge coefficient, µ. Molkov developed his advanced lumped parameter model on the basis of a large number of examples, including all possible vessels geometries (sphere, cube, rectangle, cylinder, segment), and various sizes and positions of the ignition source. This theory gives reasonably good results for gaseous deflagration in both closed and vented enclosures for a wide range of explosion conditions. Note that the generalized discharge coefficient µ represents not only the usual discharge coefficient in a standard orifice equation. For our purposes, µ also compensates for the difference between real and calculated mass outflow rates, in particular due to the non-zero velocity of outflowing gases inside the enclosure proposed during the deduction of standard orifice equations. In 1999, a universal correlation was suggested for predicting reduced explosion pressures for an arbitrary gaseous mixture. This correlation is a function of the Bradley number, Br, developed in 1978 by Bradley and Mitcheson and the lump parameters χ and µ (see Eq. (9-2)).
Br =
Av V2 / 3
co 1 − 1/ γ b Suo E o − 1 − 1/ γ u
(9-2)
243
9. Ignition of the Flammable Region: Backdraft Deflagration
During the last two decades, different methods for analysing gas explosions (deflagrations) have been developed. The most important, for theoretical approaches, are either CFD models or the so-called multi-zone models. Gas explosions based on multi-zone models are easier to use than CFD models and predict with accuracy the pressure-time profiles in vessels with simple geometries. Both of these models make use of a number of adjustable parameters tuned against large sets of experiments data. The computational fluid dynamics (CFD) technique has been employed intensively for deflagration modelling. Unfortunately, the CFD approach cannot be free from lumped parameters. Gas explosion predictions based on CFD codes are able to predict very accurately the evolution in time and space of deflagration. However, for practical purposes it can be an excessively sophisticated and time consuming, even impracticable approach for large and complex geometries. Nevertheless, there are still good prospects for CFD in the future, owing to rapid progress in computers and computational techniques. At present, it seems that technical standards for gas explosions will not include computational methods on a level higher than simple empirical or semiempirical rules. Three reasons exist for this (Molkov et al., 1999): • • •
More sophisticated methods based on computational fluid dynamics are not yet generally accepted among experts. Until now, only preliminary attempts have been made to standardise CFD computer codes. The explosion guidelines and standards are intended to be used by a widespread community of practical engineers and not just by a limited number of experts.
Therefore, simpler equations are often used to solve gas explosions. These equations have a validity restricted to certain limits, such as the characteristic parameters for the vessel, the vents and the explosive mixture. However, as mentioned before, a simple correlation is not enough for a good analysis or prediction of a backdraft deflagration; parameters other than pressure are needed.
3. Main Governing Equations for Backdraft Deflagrations The main governing equations for deflagration are taken from a model developed by Grigorash, A., 2002. These equations allow for the calculation of the pressure evolution as well as the mass consumption inside the compartment at every moment in time during the deflagration. Based on this development (see Annex V), we have obtained four more equations in order to get more accurate results in terms of mass consumption and mass expulsion through the vents of the enclosure. These equations are given in Section 3.4: “Outflow Equations”.
244
9. Ignition of the Flammable Region: Backdraft Deflagration
All of these equations rely on conservation laws (mass, volume, energy), the ideal gas state equation, and the standard orifice equations for calculating the of mass flow rate for subsonic and sonic regimes of outflow. Definitions of the terms used in the equations are given in Section 3.1: “Assumption of the Deflagration Model” and in Section 3.2: “Nomenclature of the Governing Equations”. It is important to remark that these derivation equations are applicable for well-stirred scenarios with single or multiples vents.
3.1 Assumptions of the Deflagration Model Backdraft deflagrations are initiated by an ignition source with low energy release. The ignition source may reside inside a compartment of arbitrary shape, volume V [m3], with the ratio of the longest overall dimensions to the shortest one not more than 6:1 (Molkov et al, 2000). For greater ratios, pressure nonuniformity and wave effects could become important. An initial pressure, pi, and an initial temperature, Tui, expressed respectively in Pa and K, are assumed for the scenario. In general, obstacles can be distributed throughout the enclosure. A well-stirred mixture is assumed within in the compartment. For future reference in this section, the mixture just before ignition is defined by the subscript “u”. This mixture can include unburnt and burnt gas species and oxygen. The burning of the mixture “u” is identified by the sub-script “b”. This mixture includes the combustion products released in the combustion (see Figure 9-1).
Flame front area
Combustion products
CO
mb
mu
H2O CO2
CH4 Flame propagation
Figure 9-1: Unburnt mass consumption and burnt mass generation in the deflagration.
A premixed flame propagates from the point of ignition throughout the mixture at condition of changing in time the temperature of the unburnt mixture Tu(t) and pressure p(t) with burning velocity Su(Tu, p). The flame front area Ff(t)
245
9. Ignition of the Flammable Region: Backdraft Deflagration
changes in time, as does the burning velocity and the density of the unburnt gas ρu. The Mach number for the flame velocity is defined as M = Su/cu, where cu is the speed of sound in the medium of propagation. Normally, its value does not exceed about 0.1. Therefore, it is assumed that pressure changes in time but remains uniform throughout the space of the enclosure. The flamelet model of turbulent combustion is assumed for the conversion of fresh gases into combustion products. Because deflagration duration is short enough in comparison to the typical time needed for heat transfer from hot gases to walls and obstacles, the adiabatic approach to this phenomenon is employed. The difference between the calculated adiabatic isochoric complete combustion pressure and the experimental one is roughly 10% (Kumar, Dewit & Greig, 1989). Hence the decision could be adopted that the compression and expansion of gases comply with the adiabatic equation T/p1-1/γ = cte. The specific heat ratios of unburnt (γu) and burnt (γb) gases are constant during deflagration. The molecular masses of unburnt (Mu) and burnt (Mb) gases are constant as well. Vents may appear as single or multiple units. They are considered inertia-free, m = 0.0 [kg]. A latching pressure (static activation pressure) pv may be used to prevent the vent from opening until the target pressure is reached. Since the vents are inertia-free, the vent opens instantaneously when pv is reached. pv will serve as the atmospheric pressure for openings already in open position.
3.2 Nomenclature of the Governing Equations The terms used in the governing equations below will now be defined. π is the dimensionless pressure. It is expressed by Eq. (9-3), where i is the initial state, p is the pressure, in Pa, and pi is the initial pressure in the enclosure, also in Pa.
τ represents dimensionless time. It is given by Eq. (9-4), where Sui is the laminar velocity for the initial state expressed in m/s, a is the radius of the spherical vessel of equal volume, in m, and t is the time expressed in s. p pi S τ = t ui a π=
(9-3)
(9-4)
ε is the overall thermokinetic exponent. γu is the adiabatic exponent (ratio of specific heats, cp/cv) for the unburnt mixture. γb is the adiabatic exponent (ratio of specific heats) for burnt mixture. These values may be found in the literature. 246
9. Ignition of the Flammable Region: Backdraft Deflagration
nu is the relative mass of unburnt mixture inside the enclosure given by Eq. (95). nb is the relative mass of burnt mixture inside the enclosure (see Eq. (9-6)). mu and mb represent the mass of the unburnt and burnt mixtures, respectively, in kg. mu mi mb nb = mi nu =
(9-5) (9-6)
Aj(t) is the fraction of the cross-section area of vent occupied by burnt gas and Fj(t) is the vent area of the vent j, in [m2]. To distinguish between the unburnt and burnt gas flows, the fraction of the area Fj(t) of a vent occupied by burnt gas during outflow at any moment is denoted by Aj(t). So, the unburnt gases occupy (1- Aj(t)) fraction of Fj(t). In the most general case of vented deflagration, only unburnt and burnt gases flow out from the vent at the beginning of venting, A = 0. After that, joint outflow of unburnt and burnt gases takes place. Figure 9-1 shows the evolution in time of Fj(t) as a function of the pressure reached during the deflagration. Since the vents are assumed to be inertia-free only two positions are possible: totally opened or closed. 2.25 2.00
2 [m ] [m2]
1.75 1.50
Initially opened
1.25
Initially closed
1.00 0.75 0.50 Static activation pressure = 2 bars
0.25 0.00 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
Pressure [bar]
Figure 9-2: Evolution in time of F as a function of the pressure reached during a deflagration. At the end of the process, the outflow has to be accomplished by burnt gases only, A = 1. One exception is the case of ignition in close proximity of a relatively small vent, when burnt gases occupy the whole of the vent crosssection from the very start of the venting, A = 1. Molkov, 1996, analysed motion pictures of vented deflagrations by various authors and showed that, in general, A = r2 is a reasonable estimate of the joint outflow.
247
9. Ignition of the Flammable Region: Backdraft Deflagration
Three values for A are proposed according to the position of the ignition source relative to the vent: • • •
If the ignition source is very close to the vent, then A = 1. If the ignition source is very far from the vent, then A = 0. If the ignition source is in the middle of the enclosure, then A = r2.
Note that the estimate A = r2 gives unsatisfactory results when the maximum deflagration pressure is comparable to the vent release pressure (static activation pressure), pv. R is the outflow parameter. R Σ is the outflow contribution. Z is the auxiliary quantity and W is the transient venting parameter (see Section 4.3: “Main Governing Equations”). Ei is the combustion product expansion coefficient at initial condition (see Eq. (9-7)); cui is the speed of sound in unburnt gas at initial conditions. It is defined in Eq. (9-8), in m/s. Rgas is the universal gas constant, equal to 8314.41 J/K·kmol; Tui is the temperature of the unburnt gas at initial conditions, in K; Mui is the molecular mass of unburnt mixture at initial conditions, expressed in kg/kmol; V is the volume of the enclosure, in m3.
σ is the relative density of the gases. σu for unburnt gases is given by ρu/ρi and σb for burnt gases is given by ρb/ρi; ρu and ρb are the density of unburnt and burnt gases, respectively, in kg/m3. ρi is the initial density of unburnt gases, expressed by Eq. (9-9), in kg/m3. Ei =
ρui ρbi
γ R T cui = u gas ui Mui m ρi = i V
(9-7) 0.5
(9-8) (9-9)
As mentioned before, µ and χ are the generalized discharge coefficient for the vent and the turbulence factor (Eq. (9-10)), respectively. χ=
Ff (t) Fs (t)
(9-10)
where Ff is the real flame front area and Fs is the surface area of a flame assumed to display a laminar spherical propagation. Note that in the ideal case of laminar spherical flame propagation, the turbulence factor is constant during the course of deflagration and takes a value of 1.0.
248
9. Ignition of the Flammable Region: Backdraft Deflagration The ratio χ/µ is called the deflagration-outflow-interaction number. Molkov et al., 2000 derived an equation for χ/µ by fitting the calculated pressure-time curves to the experimental data from various authors (Eq. (9-11)).
(1 + 10V1/ 3 ) (1 + 0.5Brβ ) χ = α µ 1 + πv
0.4
(9-11)
The empirical coefficients for hydrocarbon-air mixture are α= 1.75 and β = 0.5, and those for hydrogen-air mixtures are α = 1.00 and β = 0.8.
3.3 Main Governing Equations The main governing derivative equations for gaseous deflagrations in a compartment are given in Eq. (9-12), Eq. (9-13) and Eq. (9-14). They represent the rate of the dimensionless pressure defined as π = p/pi, the rate of the relative mass of unburnt (nu = mu/mi) and burnt (nb = mb/mi) mixture inside the enclosure. χ ( τ ) Zπ dπ = 3π dτ
ε+1/ γ u
(1 − n π
)
−1/ γ u 2 / 3
u
π1/ γ u
γ − γb nu − u γu
− γ u WR Σ
(9-12)
2/ 3 dn b = 3 χπε+1/ γu (1 − n u π−1/ γu ) − R b W∑ A jµ jFj / ∑ µ jFj dτ
(9-13)
2/ 3 dn u = 3 χπε+1/ γ u (1 − n u π−1/ γ u ) + R u W∑ (1 − A j ) µ jFj / ∑ µ jFj dτ
(9-14)
W, Z and RΣ are defined as follows in Eq. (9-15), Eq. (9-16) and Eq. (9-17). W=
cui ∑ µ jFj
( 36πo )
1/ 3
γ ( γ − 1) Z = γ b E i − u b π γ b ( γ u − 1) RΣ = Ru
(9-15)
V 2 / 3Sui γ u 1−γ u γu
+
γb − γu γu − 1
∑ (1 − A ( τ ) ) µ F ( τ ) + R ∑ µ F ( τ) j
j
j
j
j
π1/ γ u − n u ∑ A j ( τ ) µ jFj ( τ ) b nb ∑ µ jFj ( τ )
(9-16)
(9-17)
Ru and Rb, known as the outflow parameters, are given by Eq. (9-18) and Eq. (9-19).
249
9. Ignition of the Flammable Region: Backdraft Deflagration
1/ 2
2 γ p 2 / γ p ( γ+1) / γ R= πσ a − a γ − 1 p π p π i i
(9-18)
and γ+1 γ−1 2 R = γ πσ γ + 1
1/ 2
(9-19)
for subsonic regime and sonic regime, respectively. The transition from the subsonic to the sonic regime of discharge happens when the pressure exceeds the critical value of:
p π≥ a pi
1 + γ γ /( γ−1) 2
(9-20)
The unburnt and burnt values for R and the critical pressure are obtained from Eq. (9-20) and Eq. (9-18) or Eq. (9-19) by substituting the unburnt and burnt values of γ and σ into these equations. Further details about the development of Grigorash’s model can be found in Annex V.
3.4 Outflow Equation The other four equations obtained based on the development of Grigorash’s model that allow us to calculate the following points are given by Eq. (9-21)-(922), Eq. (9-23) and Eq. (9-24): •
•
The quantity of unburnt gas that becomes consumed in the enclosure during the deflagration is defined by Eq. (9-21). Analogically, the equation representing the quantity of burnt gas generated in the combustion can be obtained by Eq. (9-23). The quantity of unburnt and burnt gas that exits the enclosure (through the vents) in the course of time is defined by Eq. (9-22) and Eq. (9-24), respectively.
For unburnt gas: 2/3 dn u→b = 3χπε+1/ γ u (1 − n u π−1/ γu ) dτ
(9-21)
dn u→v = −3R u W ∑ (1 − A j ) µ jFj / ∑ µ jFj dτ
(9-22)
250
9. Ignition of the Flammable Region: Backdraft Deflagration
For burnt gas: 2/3 dn b←u = 3χπε+1/ γ u (1 − n u π−1/ γu ) dτ dn b→v = −3R b W ∑ A jµ jFj / ∑ µ jFj dτ
(9-23) (9-24)
Where nu→b is the relative mass of unburnt gas that becomes consumed; nb←u is the relative mass of burnt gas generated in combustion; nu→v and nb→v are respectively the relative mass of unburnt and burnt gases expelled through the vents.
107000 106000 (mB,mU->,mB->) [kg]
105000
[Pa]
104000 103000 102000 101000 100000
0.12
1.24
0.1
1.2
0.08
1.16
mB mU-> mB-> mU
0.06
1.12
0.04
1.08
0.02
1.04
0
0
0.01
0.02 Time [s]
(a)
0.03
0.04
(mU)[kg]
Figure 9-3 represents the typical pressure, mass consumption and the (burnt and unburnt) mass expelled out during the deflagration’s evolution.
1 0
0.01
0.02
0.03
0.04
Time [s]
(b)
Figure 9-3: (a) Typical pressure evolution (b) mass consumption and generation of unburnt mass (mU) and burnt mass (mB), respectively; unburnt (mU->) and burnt (mB->) mass expelled. Simulated in OZone.
3.5 Comments In order to solve a backdraft deflagration using the equations explained above, it is necessary to provide the following input data: • •
The initial temperature, pressure and density of the mixture. The gas species, the specific heat ratio and the molecular weight of the gas species, as well as the burning velocity of the mixture.
251
9. Ignition of the Flammable Region: Backdraft Deflagration •
The compartment shape and vent characteristics (volume, vent areas, static activation pressures). The compartment is considered to be a sphere with the same volume as the model.
The initial conditions of the main governing equations and the outflow equations at the beginning of the integration, τ = 0, are: • • •
The pressure in the enclosure is equal to pi, so π = 1. Nothing has burnt yet, so nu = 1 and nb = 0. Nothing has gone out, so nu→b = nb←u = nu→v = nb→v= 0.
At any given moment of time, a number of dimensional deflagration parameters can be obtained: • • • • • • • •
The time of the explosion in seconds: t = τa/Sui. The current pressure, in Pa, in the enclosure: p = πpi. The current burning velocity in m/s: Su = Suiπε. The current radius, in m, of the imaginary spherical flame: rb = r a. The current temperature, in K, inside the compartment: Tu = Tuiπ(γu-1)/ γu. The current mass of unburnt and burnt gases mass; nu=mu/mi and nb=mb/mi. The current quantity of mass becoming consumed or generated: nu→b = mu→b /mi and nb←u = mb←u/mi, The current quantity of mass expelled through the vents: nu→v = mu→v/mi and nb→v = mb→v/mi.
4. Fireball: Estimation of the Diameter The unburnt gases expelled from the compartment may ignite. If that happens a fireball is created. The dimension of the fireball diameter can be estimated: • •
Assuming a spherical volume. Using the ideal law of gases.
By arranging this equation, the fireball diameter, DFball, is given by Eq. (9-25).
DFball = 2· 3
3·m u→ v R·T 4·P·π·MWu
(9-25)
where R is the universal gas constant, 0.082 atm·l/molK. T is the temperature of the mixture when burning. An approximate value can be taken as 1573 K. P is the atmospheric pressure, in atm; MWu is the molecular weight of the mixture, in g/mol; m u → v is the mass of the initial mixture in the compartment that has been expelled, in kg; π is the 3.1416 and DFball is the diameter of the fireball in m.
252
9. Ignition of the Flammable Region: Backdraft Deflagration
DFball DFball
Figure 9-4: Fireball diameter.
5. Validation of the Model The validation of the model is carried out by comparing the reduce pressure reported in Razus, D., 2001. He compared several simple correlations for gas deflagrations using real tests. By comparing his studies, we can see, on one hand, the accuracy of the model in predicting pressure development and on the other hand, how accurate the model is relative to existing ones. The simple correlations are listed below. Their expressions and validity are commented on in detail in Annex V.
• • • • • • • •
NFPA. Simpson. Runes 1 and Runes 2. Bradley 1 and Bradley 2. Cubbage. Rasbash. Yao. Molkov 1 and Molkov 2.
The tests used to compare these correlations were carried out with three types of fuel-air mixtures: methane, propane and hydrogen-air mixtures. All of these are in stoichiometric fuel-air concentration. Other conditions of the tests are:
• • • • • • •
Enclosure volume from 0.03 to 200 m3. Enclosure shapes: cubes, rectangular, cylindrical profile ducts. Different values of discharge coefficients. Vent diameters from 0.1 to 2.0 m. Various static activation pressures of vents, from 1.1 to 1.5 bars. Various locations of the ignition sources (centre, near vent, rear). An initial temperature and pressure of 298 K and 1 bar.
253
9. Ignition of the Flammable Region: Backdraft Deflagration
The input data for the simple correlations and the simulations are summarized in Table 9-1. Eq. (9-11) is used in order to obtain χ in simulations. For future reference, the term OZone is used to designate to the results obtained by the model. A more detailed list of the characteristics of each explosion scenario is given in Table 9-2, Table 9-3 and Table 9-4 for the methane-air mixture, for the propane-air mixture and for hydrogen -air mixture, respectively. The results from the simple correlations and OZone are listed in Table 9-5, Table 9-6, Table 9-7 for the methane-air mixture, for the propane-air mixture and for the hydrogen-air mixture, respectively.
Fuel-air mixture CH4-Air 9.5% C3H8-Air 4.0% H2-Air 29.5%
Sui [m/s] 0.44
Cd (discharge coefficient)
Eo
γu
γb
0.60
cui [m/s] 353
7.48 1.380 1.18
0.46
0.65
339
7.90 1.365 1.25
2.77
0.60
408
7.29 1.400 1.25
Table 9-1: Summary of data used in simulations.
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Conc. (%) 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 10.0
V (m3) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.95 0.95 49.1 33.5
As (m2) 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 5.5 5.5 88.3 67.5
Shape Cube Cube Cube Cube Cube Cube Cube Cube Cube Cube Cube Cylinder Cylinder ? Rectang.
D or l 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.92 0.92 2.51 2x 3.1
L
Ignition
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.43 1.43 9.92 5.4
Centre Centre Centre Centre Centre Centre Centre Centre Centre Centre Centre Centre Centre ? Centre
Av (m2) 0.16 0.36 0.10 0.10 0.10 0.20 0.20 0.20 0.30 0.30 0.30 0.05 0.10 3.46 2.57
Pstat 0.50 0.50 0.10 0.20 0.50 0.10 0.20 0.50 0.10 0.20 0.50 0.32 0.16 0 0
Table 9-2: Conditions of various experiments for vented deflagrations (METHANE-AIR).
254
9. Ignition of the Flammable Region: Backdraft Deflagration
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Conc. (%) 4.0 4.0 4.0 4.0 4.0 4.05 4.45 4.8 4.8 4.8 4.8 4.8 5.0 5.0 5.25 5.25
V (m3) 1.0 1.0 1.0 203.8 203.8 11.0 30.4 0.65 0.65 0.65 0.65 0.65 0.029 0.76 35 35
As (m2) 6.0 6.0 6.0 219 219 28.3 64 2.86 2.86 2.86 2.86 2.86 0.56 5.0 65.5 65.5
Shape
D or l
L
Ignition
Cube Cube Cube Rectang. Rectang. Cylinder Rectang. Cylinder Cylinder Cylinder Cylinder Cylinder Cylinder Cube Rectang. Rectang.
1.0 1.0 1.0 4.52 4.52 2.0 4.2 0.91 0.91 0.91 0.91 0.91 0.25 0.913 2.8 2.8
1.0 1.0 1.0 9.95 9.95 2.5 1.72 1.09 1.09 1.09 1.09 1.09 0.58 0.91 4,47 4.47
Centre Centre Centre ? ? Rear Centre Centre Centre Centre Centre Centre Centre Centre Vent Centre
Av (m2) 0.20 0.40 0.60 21.58 17.3 1.36 0.58 0.018 0.018 0.032 0.073 0.099 0.034 0.29 1.0 1.0
Pstat 0.10 0.10 0.10 ? ? 0.05 0.4 0.65 0.65 0.72 0.86 0.86 0.10 0 0 0
Table 9-3: Conditions of various experiments for vented deflagrations (PROPANE-AIR).
No. 1 2
Conc. (vol %) 29.6 29.6
V (m3) 0.95 0.95
As Shape (m2) 5.5 Cylinder 5.5 Cylinder
D or l 0.92 0.92
L
Ignition
1.43 1.43
Centre Centre
Av (m2) 0.20 0.30
Pstat 0.075 0.135
Table 9-4: Conditions of various experiments for vented deflagrations (HYDROGEN-AIR).
255
No
Exp. values
Calculated values NFPA
Simpson
Runes 1
Runes Bradley Bradley 2 1 2
Cubbage
Rasbash
Yao
Molkov 1
Molkov 2
OZone
1
2.40
---
2.27
1.41
5.61
2.56
2.69
1.19
1.27
1.67
1.41
1.19
1.47
2
1.64
---
1.47
1.08
1.91
1.7
1.61
1.09
1.16
1.13
1.11
1.05
1.15
3
2.40
5.93
2.23
2.04
12.8
3.17
2.66
1.31
1.33
2.72
2.16
1.53
2.15
4
3.19
---
2.43
2.04
12.8
3.17
3.15
1.31
1.34
2.72
2.07
1.49
2.06
5
2.95
---
3.24
2.04
12.8
3.17
4.03
1.31
1.39
2.72
1.88
1.40
2.04
6
1.8
2.23
1.53
1.26
3.95
2.34
1.70
1.16
1.17
1.43
1.38
1.17
1.41
7
2.48
---
1.62
1.26
3.95
2.34
1.91
1.16
1.19
1.43
1.35
1.16
1.39
8
2.11
---
1.96
1.26
3.95
2.34
2.28
1.16
1.23
1.43
1.29
1.13
1.36
9
1.43
1.55
1.32
1.12
2.31
2.01
1.42
1.10
1.12
1.19
1.20
1.09
1.22
10
1.77
---
1.38
1.12
2.31
2.01
1.54
1.10
1.13
1.19
1.19
1.09
1.27
11
1.59
---
1.59
1.12
2.31
2.01
1.77
1.10
1.18
1.19
1.15
1.07
1.24
12
3.00
---
4.79
2.84
21.9
4.31
6.47
1.57
1.62
6.78
4.32
2.51
3.37
13
2.00
---
2.63
1.46
6.22
3.04
2.77
1.28
1.31
2.45
2.15
1.53
2.26
14
1.12
1.89
1.55
1.02
1.24
2.19
---
1.13
1.13
1.31
1.82
1.38
1.48
15
1.15
1.94
1.55
1.06
1.69
2.22
---
1.14
1.14
1.33
1.79
1.36
1.49
Table 9-5: Comparison of calculated reduced explosion pressure with experimental data from different literature sources for stoichiometric METHANE-air mixtures (pressure in bars).
No
Exp. values
Calculated values NFPA
Simpson
Runes 1
Runes 2
Bradley 1
Bradley 2
Cubbage
Rasbash
Yao
Molkov 1
Molkov 2
OZone
1
2.25
2.82
1.74
11.6
125
2.43
1.79
1.17
1.19
1.53
1.22
1.19
1.85
2
1.40
1.46
1.26
3.64
31
1.69
1.33
1.09
1.10
1.13
1.07
1.07
1.30
3
1.14
1.20
1.14
2.17
14.3
1.31
1.2
1.06
1.07
1.06
1.04
1.04
1.16
4
1.03
1.21
1.16
1.01
1.12
1.32
---
1.06
1.06
1.06
---
---
1.25
5
1.06
1.33
1.22
1.02
1.19
1.49
---
1.07
1.07
1.09
---
---
1.36
6
1.09
1.88
1.85
1.06
1.72
2.11
1.39
1.12
1.13
1.25
1.27
1.24
1.53
7
1.70
---
9.19
11.85
124
4.56
7.78
1.63
1.69
8.13
4.41
3.23
6.67
8
6.22
---
37
16.1
171
5.56
13.7
1.9
2
15.5
6.14
3.62
6.02
9
6.31
---
37
16.1
171
5.56
13.7
1,9
2
15.5
6.14
3.62
6.02
10
6.59
---
7.10
5.75
55
4.05
7.39
1.51
1.61
5.56
2.71
2.49
5.23
11
4.14
---
4.86
1.94
11.6
2.73
3.47
1.22
1.35
1.90
1.40
1.35
2.75
12
3.75
---
1.35
1.51
6.74
2.39
2.68
1.17
1.29
1.49
1.24
1.21
2.46
13
1.19
1.55
1.35
1.25
1.28
1.83
1.38
1.09
1.11
1.16
1.04
1.03
1.16
14
1.05
1.60
1.28
1.10
2.10
1.91
---
1.10
1.10
1.17
1.09
1.08
1.34
15
1.75
9.70
3.41
1.72
9.18
3.47
---
1.38
1.38
3.51
3.23
2.79
5.20
16
2.37
9.70
3.31
1.72
9.18
3.47
---
1.38
1.38
3.51
3.23
2.79
5.20
Table 9-6: Comparison of calculated reduced explosion pressure with experimental data from different literature sources for stoichiometric PROPANE-air mixtures (pressure in bars).
No
Exp. values
Calculated values NFPA
Simpson
Runes 1
Runes 2
Bradley 1
Bradley 2
Cubbage
Rasbash
Yao
Molkov 1
Molkov 2
OZone
1
2.25
---
3.47
30.7
56.2
4.89
5.22
1.71
1.73
10.1
4.46
3.00
2.06
2
1.40
---
1.99
14.2
25.5
3.93
4.17
1.48
1.50
5.05
2.63
2.15
1.65
Table 9-7: Comparison of calculated reduced explosion pressure with experimental data from different literature sources for stoichiometric HYDROGEN-air mixtures (pressure in bars).
9. Ignition of the Flammable Region: Backdraft Deflagration
Figure 9-5 to Figure 9-7 compare the results obtained with OZone (large black circles), the simple correlations and the experimental values (large red squares).
7
7
5 4 3
6
Rasbash 5
Molkov1
1
1
0
0
2
3
4
5
6
7
8
9
Molkov2 Ozone
3
2
1
Yao
4
2
0
Cubbage
[bar]
6
[bar]
Exp Values
Exp Values NFPA Simpson Runes1 Bradley1 Bradley2 Ozone
0
10 11 12 13 14 15 16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Case number
Case number
(a)
(b)
Figure 9-5: Methane-air mixture; (a) Experimental values, NFPA, Simpson, Runes1, Bradley1, Bradley2 and OZone. (b) Experimental values, Cubbage, Rasbash, Yao, Molkov1, Molkov2, OZone. 17.5
40
Exp Values 35
15
Cubbage
Simpson
30
Rasbash
Runes1
12.5
Yao
Bradley1
25
Molkov1
10
Bradley2 20
[bar]
[bar]
Exp Values
NFPA
Ozone
Molkov2 7.5
Ozone
15
5
10
2.5
5 0
0 0
1
2
3
4
5
6
7
8
9
Case number
(a)
10
11
12
13
14
15
16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Case number
(b)
Figure 9-6: Propane-air mixture; (a) Experimental values, NFPA, Simpson, Runes1, Bradley1, Bradley2 and OZone. (b) Experimental values, Cubbage, Rasbash, Yao, Molkov1, Molkov2, OZone.
259
9. Ignition of the Flammable Region: Backdraft Deflagration 35
12
Exp Values
Exp Values 30
Simpson
Cubbage
10
Rasbash
Runes1 25
Bradley1
Yao
8
Bradley2
Molkov1 [bar]
[bar]
20
Ozone
6
Molkov2
15
Ozone
4 10
2
5
0
0 0
1
2 Case number
(a)
3
0
1
2
3
Case number
(b)
Figure 9-7: Hydrogen-air mixture; (a) Experimental values, NFPA, Simpson, Runes1, Bradley1, Bradley2 and OZone. (b) Experimental values, Cubbage, Rasbash, Yao, Molkov1, Molkov2, OZone. A more convenient examination of the calculated results could be made by means of Figure 9-8-(a) to Figure 9-10-(a), which present the value S/ni, where S is the sum of the relative deviation δI (see Eq. (9-25)) between the calculated and the experimental reduced pressure and ni is the number of considered experimental points for a certain fuel-air mixture, plotted for the equations studied.
p − pexp δi = 100 calc pexp
(9-25)
These diagrams have been drawn up using sets of data for methane, propane and hydrogen. Note that the hydrogen-air system has to be examined with care, since it contains only 2 sets of data. In all diagrams, the results obtained from Eq. (9-25), Runes 2, have been excluded aside, since they provide exceedingly large deviations. Figure 9-8-(b) and Figure 9-9-(b) represent the reduced pressure obtained in the OZone versus the reduced pressure obtained in real tests.
260
9. Ignition of the Flammable Region: Backdraft Deflagration
40
4.00
30
3.50
20
3.00
[bar]-OZone
S/ni
10 0 -10 -20
2.50 2.00 1.50
-30
1.00
-40
0.50
-50
0.00
Cu
bb
ag
e Ra
sb
as
h M
olk
ov
2 Ru
ne
s1
Oz
o
ne M
o lk
ov
1
Y
ao Si
m
ps
on a Br
dl
ey
2 a Br
dl
ey
1
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
[bar]-Exp results
(a) (b) Figure 9-8: Methane-air mixture: (a) Average deviation of the simple correlation and OZone. (b) OZone vs. Tests. 120
7.5
100
6.0
[bar]-OZone
80
S/ni
60 40 20
4.5 3.0
0
1.5
-20 -40
PA
s1 ne
l ey
Ru
ad Br
0
1.5
NF
2
o
e
Ya
1
Oz
l ey
ov
ad Br
o lk M
on
1
2 ov
as
o lk M
sb
bb Cu
Ra
ag
e
h
0.0 3
4.5
6
7.5
[bar]-Experimental values
(a) (b) Figure 9-9: Propane-air mixture: (a) Average deviation of the simple correlation and OZone. (b) OZone vs. Tests. 1200 1000
S/ni
800 600 400 200 0
o
s1 ne Ru
2
Ya
ley
Br
ad
ley
1
1 Br
o lk M
ad
ov
2 ov o lk
ps
on M
m
on
e Si
as
Oz
sb Ra
Cu
bb
ag
e
h
-200
(a) Figure 9-10: Hydrogen-air mixture: (a) Average deviation of the simple correlation and OZone. No graphic has been made for (b) since it contains only 2 sets of data.
261
9. Ignition of the Flammable Region: Backdraft Deflagration
As one may observe, the results are relatively accurate. The maximum average deviation of OZone is 20%, obtained for the propane-air mixture. The minimum average deviation is for the hydrogen-air mixture.
6. Graphical Method for Obtaining the Fireball’s Diameter The following figures represent the fireball diameter for stoichiometric methane, propane and hydrogen mixtures. They are a function of the volume of the compartment and the vent area. The input data for each fuel are shown in Table 9-1. A is taken as r2. The vent area is open, so the static activation pressure is equal to atmospheric pressure. The range of variation of the vent area and the compartment volume is:
• •
Vent area: from 1.0 m2 to 4.0 m2. Compartment volume: from 1.0 m3 to 500 m3.
12
120 4m2
100
3m2
90 Unburnt mass [kg]
10 Fireball diameter [m]
110
4m2 3m2 2m2 1m2
8
6
4
2m2
80
1m2
70 60 50 40 30
2
Hydrogen
0
20 10
Hydrogen
0 0
50 100 150 200 250 300 350 400 450 500
Volume [m3]
(a)
0
50 100 150 200 250 300 350 400 450 500 Volume [m3]
(b)
Figure 9-11: (a) Fireball diameter and (b) Unburnt mass expelled as a function of the compartment volume and vent area (stoichiometric mixture of hydrogen).
262
9. Ignition of the Flammable Region: Backdraft Deflagration
200
12
4m2
180 10
3m2
160
8 4m2 3m2 2m2 1m2
6
4
Unburnt mass[kg]
Fireball diameter [m]
2m2 1m2
120 100 80 60 40
Methane
2
140
20 0
Methane
0 0
50 100 150 200 250 300 350 400 450 500
0
50 100 150 200 250 300 350 400 450 500
Volume [m3]
Volume [m3]
(a)
(b)
Figure 9-12: (a) Fireball diameter and (b) Unburnt mass expelled as a function of the compartment volume and vent area (stoichiometric mixture of methane). 160
12
1m2
140
10
2m2 3m2
8
6
4m2 3m2 2m2 1m2
4
Unburnt mass [kg]
Fireball diameter [m]
120
4m2
100 80 60 40
2
Propane
20
Propane
0
0 0
50 100 150 200 250 300 350 400 450 500
Volume [m3]
(a)
0
50 100 150 200 250 300 350 400 450 500 Volume [m3]
(b)
Figure 9-13: (a) Fireball diameter and (b) Unburnt mass expelled as a function of the compartment volume and vent area (Stoichiometric mixture of propane).
263
9. Ignition of the Flammable Region: Backdraft Deflagration
Based on the previous figures, the following conclusions can be drawn:
• • •
The greater the vent area is, the greater the diameter of the fireball. The greater the compartment volume is, the greater the fireball diameter. For the same conditions, methane causes larger fireballs than propane, and propane causes larger fireballs than hydrogen.
7. Conclusion A model for simulating deflagrations in fire compartments has been developed and implemented in OZone. Even if only single vent scenarios have been simulated, the model is also valid for scenarios with multiple vents. Each vent can differ from the other vents in size, but they must have the same static activation pressure. The model is able to predict:
• • •
•
The evolution in time of pressure, burning speed of the unburnt gases, the Mach number, etc. All of these can be calculated for any initial pressure and temperature in the enclosure. The quantity of unburnt gas that becomes consumed inside the enclosure, and analogously, the unburnt gas generated. The quantity of unburnt and burnt gas expelled through the vents during the deflagration as well as the quantity of unburnt and burnt gases that remain inside the enclosure. Obtaining the quantity of initial unburnt mass flowing out through each vent is essential for evaluating the power and size of a potential fireball. The energy released inside and outside the enclosure due to combustion.
Validation using 33 stoichiometric vented deflagration explosions has been carried out. Specifically, three types of stoichiometric mixtures have been validated: methane, hydrogen and propane. A well-stirred situation is given in all of the real vented deflagrations. The model correlates very well with this kind of scenario. Based on the results obtained, the average deviation for hydrocarbon is below 20% for the reduced pressure. Comparison with backdraft experiments has not been carried out in this section. This will be done in Chapter 10: “Energy Release in Backdraft Phenomenon”. The results of the model have been used to elaborate a graphical method that allows us to obtain the fireball diameter as a function of compartment volume and vent area. This method has been elaborated for three stoichiometric mixtures (methane, propane and hydrogen) and assuming a well-stirred situation in the compartment. The aim of the method is to provide an estimation of the fireball that can be useful for fire fighters. An application of that is seen in Chapter 12: “Application: Fire in a Building”.
264
9. Ignition of the Flammable Region: Backdraft Deflagration
This chapter is intimately linked to Chapter 10. In fact, the output data of this model is used to obtain the energy release inside and outside the compartment, i.e. the mass expelled will be used to obtain the energy released in the fireball. Future research must be focused on the development of a model that allows for simulating deflagrations of non stoichiometric mixtures and in poorly-stirred situations.
265
9. Ignition of the Flammable Region: Backdraft Deflagration
266