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Chapter 4

Pyrolysis Rate and Smouldering Combustion Table of Contents 1. Introduction................................................................................57 2. State of the Art ..........................................................................57 3. Flaming Burning.........................................................................62 3.1 Simplified Model for the Pyrolysis Rate of Liquid or NonCharring Fuels.............................................................................62 3.1.1 Definition of the Scenario and Hypotheses .......................62 3.1.2 Pyrolysis Rate Equations .................................................63 3.1.3 Pyrolysis Rate in Open Conditions...................................66 3.2 Simplified Model for the Pyrolysis Rate of Charring Fuels.....67 3.2.1 Pyrolysis Rate Equations .................................................67 3.2.2 Temperature Distribution in the Fuel ..............................68 3.2.3 Stability of the Finite Difference Model ...........................70 3.2.4 Convective Heat Transfer.................................................70 4. Non-Flaming Combustion: Smouldering Combustion..................71 5. Flame Extinction ........................................................................71 6. Material Properties .....................................................................72


6.1 Wood .....................................................................................72 6.2 Other Materials......................................................................76 7. Parametric Study........................................................................76 7.1 Parameters in Study ..............................................................77 7.2 Reference Fire Scenario..........................................................77 7.3 Results of the Study...............................................................78 7.3.1 Height of the Compartment .............................................78 7.3.2 Material of the Partitions.................................................78 7.3.3 Ventilation Parameter......................................................78 7.3.4 Fire Area..........................................................................78 8. Graphical Method for Comparison between Fire Scenarios according to Accumulation of Mass and Pyrolysis Rate..................81 9. Conclusion ..................................................................................85


4. Pyrolysis Rate and Smouldering Combustion

1. Introduction A fuel burning in open conditions has a pyrolysis rate different from the same fuel burning inside a compartment. Two factors mainly influence this difference: • •

First, the heat radiated from the hot gases and partitions (wall, ceiling) towards the fuel surface. This factor enhances the pyrolysis rate. Second, the enclosure vents may restrict the availability of oxygen needed for combustion. This causes a decrease in the amount of fuel burnt, leading to a decrease in the energy release, which may in turn decrease the pyrolysis rate.

In this chapter, two simple models for estimating the pyrolysis rate for free burning and for compartment burning are provided. The first one is applied to non-charring materials or liquids and the second is applied to charring material such as wood. Only the model for non-charring material or liquids and the finite difference model for obtaining the temperature distribution in charring materials are implemented in OZone. Parameters such as the flame temperature and the transparency of the flame are normally unknown. For this reason the results obtained are not validated but they are used to reveal the influence of for example the material of partitions, the size of openings, the compartment geometry and the type of fuel on the estimation of the pyrolysis rate. These results obtained are used to carry out a graphical method that allows us to determine the maximum accumulation of unburnt products, the maximum pyrolysis rate and the fire duration of a fire scenario.

2. State of the Art Before continuing with this chapter, it is important to clarify the difference between the pyrolysis rate and the burning rate since these two concepts are sometimes confused. The pyrolysis rate or the mass loss rate is defined as the decomposition of fuel into gas due to heat mechanisms. The burning rate is the amount of the pyrolysis gas that becomes burnt. Even though these concepts are used to describe two distinct phenomena, both depend on factors such as fuel properties and distribution, compartment properties, ventilation conditions, temperature of the surroundings, etc. Mass loss rates have normally been measured in the past with the use of load cells, or by volumetric techniques in the case of liquid pool fires. Useful techniques for measuring heat release rates in the open were not available until a few years ago, when the principle of oxygen consumption calorimetry was. Early attempts required the direct measurement of sensible enthalpy, something which is very difficult to do correctly. The oxygen consumption principle states that, to within a small degree of uncertainty, the heat released from the

57


4. Pyrolysis Rate and Smouldering Combustion combustion of any common combustible is uniquely related to the mass of oxygen removed from the combustion flow stream. This measurement technique then requires that only the flow rate and oxygen concentration be determined, used along with the knowledge of the oxygen consumption, 13路103 [kJ] heat released per kg of oxygen consumed (Babraukas, 1986). Figure 4-1 represents in a schematic way a calorimeter using this principle. A great number of authors have employed this apparatus for obtaining the burning rate of common items normally found in fires. A good review of burning rates in open conditions is given by Babrauskas, 1986, in which items such as pools, liquid, plastics, cribs, wood pallets, upholstered furniture, mattresses, pillows, wardrobes, television sets, Christmas trees, curtains, etc. are burnt.

Figure 4-1: A diagram of an oxygen consumption calorimeter.

In Figure 4-2 (a), a fire test of a sofa is presented. The RHR at this stage is already 0.8 MW. Figure 4-2 (b) represents some test results for upholstered furniture: a sofa, a loveseat and a single chair. Other extensive reviews on burning rates in open conditions are given by the CBUF project (Sundstr枚m, 1997) and by Saquevist, 1993. They carried out RHR measurements for various items such as mattresses, plaster board, etc. and various room occupancies such as bedrooms or offices containing typical furniture. This latter database is available on the Internet web site of SP, Sweden. All the reviews above are free-burning measurements, meaning that the burning is not influenced by the surrounding environment and happens as if it were outside. In general, a given fire load burns faster and at a higher rate in a compartment than in free-burning conditions. For example, the rate of burning of an alcohol

58


4. Pyrolysis Rate and Smouldering Combustion fire in a small enclosure can be up to eight times greater than in the open (Friedman, 1975).

(a)

(b)

Figure 4-2: (a) Sofa fire. The RHR at this point is about 800kW; (b) Typical upholstered chair heat release rates The studies carried out by Kawagoe, 1958 showed that the ventilation conditions might reduce the burning in comparison to one that would occur in free-burning conditions. Kawagoe measured the rate of burning of wooden cribs contained within full-scale and reduced-scale compartments with different sized ɺ fi [kg/s], was found to ventilation openings, Figure 4-3. The burning rate, m depend strongly on the size and the shape of the ventilation opening. As one may see, the results correlate very well with the relationship, Eq. (4-1): ɺ fi = 0.09A w H w = 0.09Vf m

(4-1)

where Aw is the area of the opening in m2, Hw is the height of the opening in m, and Vf is the ventilation parameter. However, Kawagoe’s correlation is only applicable over a limited range of values of AwHw1/2 as Thomas found in 1967, Figure 4-3. Kawagoe’s correlation states that the rate of mass loss is linked to the air inflow in the compartment. This is difficult to understand, as it is known that in a confined situation the rate of pyrolysis is increased by the surrounding heat feedback. The Kawagoe’s correlation should thus only apply to wooden cribs in which the burning surface is largely shielded from the influence of the compartment. Considering that fact, Harmathy proposed the following correlation, Eq. (4-2), to distinguish this type of burning from ventilation and fuel-controlled fires (Harmathy, 1972; Thomas, 1975; Drysdale, 1999).

59


4. Pyrolysis Rate and Smouldering Combustion

Ď a g1/ 2 A w H w Ventilation control: < 0.235 A fi Ď a g1/ 2 A w H w > 0.290 A fi

Fuel control:

(4-2)

Full scale tests

Medium scale tests

Small scale tests

(a) (b) Figure 4-3: (a) Kawagoe correlation (line) and test in under-ventilated conditions (Kawagoe, 1958); (b) Fire test with fire load densities between 7.5 and 60 kg/m2 and large openings and Kawagoeâ&#x20AC;&#x2122;s correlation (dotted line), (Thomas, 1967) Other authors have tried to develop models for predicting the burning rate of materials based on mass and energy balance. Kanury, 1995 gave a general overview of the ignition of solids by thermal radiation or convection. Robert, 1970 reviewed the role of kinetics for the pyrolysis of wood and related materials. Simms, 1962 examined the role of thermal radiation in the damage done to cellulosic solids by considering the chemical and thermal histories of the material. Work on char rate in wood includes studies by Kanury, 1972, who examined the phenomenon using Arrhenius pyrolysis kinetics. A detailed study of the pyrolysis kinetics of cellulose was conducted by Suuberg et al., 1994. Chen et al., 1983 and Wichman and Atreya, 1993 have done extensive work on the ignition and burning process of wood using a pure heat conduction model to describe complex chemical kinetics for the pyrolysis of charring material. There are many other models that consist of complex computational codes that require a relatively large number of difficult-to-obtain property values to complete their predictions. Another model is the integral model of Quintiere, 1992. It is a one-dimensional pyrolysis model, which includes the processes of charring and vaporization, as well as flame and heat conduction effects. This model has been validated by Anderson, 1997 with some exact solutions. Hopkins et al., 1995 have also compared this model against experimental data for the burning of non-charring 60


4. Pyrolysis Rate and Smouldering Combustion thermoplastics. Finally, a nearly identical model for burning of a charring material was also successfully demonstrated by Moghtaderi et al., 1997 by validation using an exact numerical solution and with experimental data. Iqbal, 1994 extended the approach presented by Quintiere for a thermoplastic material under flaming conditions. Iqbalâ&#x20AC;&#x2122;s model includes flame radiative and convective effects, transient heat conduction effects and turbulent and laminar burning. In his model, the flame radiation to the pool surface is calculated by using the experimental steady-state mass loss rate results of Modak & Croce, 1977. They found flame radiation to be a dominant factor affecting the burning rate of horizontal pools, particularly for turbulent fires. However, accurate methods of predicting flame radiation in such fires are not currently available. When flames die out due to a lack of oxygen, a type of combustion known as smouldering combustion may occur. This combustion is defined as a non-flaming combustion. Only porous materials which form a solid carbonaceous char when heated can undergo smouldering. Included are a wide range of materials of vegetable origin such as paper, cellulosic fabrics, sawdust, fibreboard and latex rubber, as well as some thermosetting plastics in expanded form. Materials that can melt and shrink away from a heat source will not exhibit this model of combustion (Drysdale, 1999). Moussa et al., (1977) have examined the propagation of smouldering along horizontal, cylindrical cellulosic elements and have shown that the combustion wave has three distinct regions as shown in Figure 4-4. The first zone corresponds to the pyrolysis zone, the second is called charred the zone and the last is made of very porous residual char and/or ash. This process requires temperatures greater than 250-300ÂşC to achieve this process in most of the organic materials (Drysdale, 1999).

Virgin cellulose Zone 2 Zone 1

Zone 3

Figure 4-4: Representation of steady smouldering along a horizontal cellulose rod.

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4. Pyrolysis Rate and Smouldering Combustion As it is shown, there are many different methods for predicting the burning rate for different materials (usually plastics and wood when dealing with solid fuel). In this thesis a simplified model for predicting the pyrolysis rate of liquid and solid fuel is developed, based on the general formula shown in Eq. (4-3).

qɺ "net ɺ = m Lv " fi

(4-3)

qɺ "net is the net heat flux to the fuel used to release the volatiles; Lv is called the ɺ "fi is the pyrolysis rate, in kg/s. heat of gasification and m

3. Flaming Burning 3.1 Simplified Model for the Pyrolysis Rate of Liquid or NonCharring Fuels 3.1.1 Definition of the Scenario and Hypotheses Figure 4-5 represents a diagram of a liquid (or non-charring) fuel burning in a compartment. The thermal mechanisms that take place are: • • • •

Convection and radiation from the flame to the fuel surface. Radiation from the hot smoke. Conduction within the fuel. Radiation is not considered between the walls and the fuel.

h ( Tfl − Tv )

σε u ζ ( Tg4 − Tv4 ) Tg

ɺ m

Tfl

"

σε fl ( Tfl4 − Tv4 )

Ts =Tv y

λ

Tc Compartment

∂T ∂y

L

Fuel

Figure 4-5: Schematic burning of a liquid or non-charring fuel in a compartment.

62


4. Pyrolysis Rate and Smouldering Combustion The author considers the following hypotheses for these types of fuels:

a) At every moment during the development of the fire, the temperature of the surface, Ts, is equal to the vaporization temperature of the fuel, Tv. b) The pyrolysis rate in open conditions is constant during the burning of the fuel. c) At time equals to zero, a linear temperature profile is assumed in the fuel. It fulfils the following boundary conditions: Ts = Tv and Ty=L = Tc = To. This temperature distribution remains unchanged during the burning and the temperature of the bottom is obtained according to the quantity of fuel evaporated. Figure 4-6 represents these hypotheses. Note that the surface of the fuel has been taken as the reference frame for the evaporation edge.

To

Tg

Ts=Tv

Ts=Tv

Tg

Ts= Tv

y y

L

Tc=T(y)

Increase of Tc

Tc=T(y)

t = 0 [sec]

Tc=To

t = 1t [sec]

t = 2t [sec]

Figure 4-6: Quadratic temperature distribution inside the fuel. Above, L is the initial thickness of the fuel in m; y is the thickness of the remaining fuel in time, expressed in m; Tg is the temperature of the hot gases in K. Ts is the surface temperature of the fuel, in K. Tfl represents the flame temperature in K. Tv is the vaporization temperature of the fuel in K. Tc is the temperature at the bottom of the fuel, in K. To is the initial temperature of the gas inside the compartment, 298 K. εu and εfl are the emissivity of gas and flame, respectivity.

3.1.2 Pyrolysis Rate Equations The pyrolysis rate of one square meter of combustible material in open conditions is given by Eq. (4-4):

ɺ = m " fi

qɺ " − qɺ "L Lv

(4-4)

63


4. Pyrolysis Rate and Smouldering Combustion where qɺ " is the heat transfer from the flame to the burning surface in kW/m2. qɺ "L corresponds to the energy transferred from the flame to the fuel surface not used directly to pyrolyse the fuel. Finally, Lv is the heat of vaporisation, normally expressed in kJ/kg. It is a measure of how much energy is needed to gasify one unit of mass of fuel. Its value depends on the temperature but it is often considered a constant. According to hypotheses a) and c) of Section 3.1.1: “Definition of the Scenario and Hypotheses”, Eq. (4-4) can be rewritten as:

ɺ = m " fi

(

qɺ "F + qɺ "Open − qɺ "L,Conduction + qɺ "L,Radiation + qɺ "L,Convection

)

Lv

 ( T − Tc (t))  σε fl Tfl4 + σε u ζTo4 −  λ v + σε fl Tv4 + σε u ζTv4 + h ( Tv − Tfl )  y(t)   ɺ "fi = m Lv

(4-5)

(4-6)

where qɺ "L,Conduction , qɺ "L,Radiation and qɺ "L,Convection correspond to the heat lost by conduction, radiation and convection, respectively. These terms are a function of the surface temperature, Ts=Tv, the ambient temperature, To, the remaining thickness of the fuel, y, and ζ is a factor that takes into account the transparency and absorptivity of the flame. If an item burns in a compartment, the temperature around the fire is not To but Tg. The pyrolysis rate of one square meter of combustible material in a compartment is defined by Eq. (4-7):

ɺ = m " fi

(

qɺ "F + qɺ "Comp − qɺ "L,Conduction + qɺ "L,Radiation + qɺ "L,Convection Lv

)

(4-7)

where the influence of the rise of temperature around the fire is included in the terms qɺ "Comp . Eq. (4-7) can be rewritten as:

 ( T − Tc (t))  σε fl Tfl4 + σε u ζTg4 (t) −  λ v + σε fl Tv4 − σε u ζTv4 + h ( Tv − Tfl )  y(t)   (4-8) ɺ "fi = m Lv It is clearly observed that for a given fire load, the burning in a compartment will be faster and at a higher rate than if the fire load burns in free-burning conditions. Figure 4-7 shows the effect of a compartment on the burning of a slab of polymethylmethacrylate carried out by Friedman in 1975.

64


4. Pyrolysis Rate and Smouldering Combustion

Figure 4-7: The effect of enclosure on the rate of burning of a slab of polymethylmethacrylate [0.76 m x 0.76 m], (Friedman, 1975). Our goal is to eliminate the flame temperature from the equations because normally it is a very difficult value to find in the literature, sometimes even impossible. For that purpose, Eq. (4-6) and Eq. (4-8) are written as Eq. (4-9) and Eq. (4-10), respectively:

 ( T − Tc (t))  σε fl ( Tfl4 − Tv4 ) −  λ v + h ( Tv − Tfl )  4 4 y(t)   + σε u ζ ( To − Tv ) ɺ "∞ = m Lv Lv (4-9)

 ( T − Tc (t))  σε fl ( Tfl4 − Tv4 ) −  λ v + h ( Tv − Tfl )  4 4 y(t)   + σεu ζ ( Tg (t) − Tv ) ɺ "fi = m Lv Lv

(4-10)

ɺ "∞ is the pyrolysis rate in free-burning conditions (see Section 3.2.3: where m “Pyrolysis Rate in Open Conditions”). This value is easily found for a significant number of fuels. Substituting Eq. (4-9) into Eq. (4-10) and after some algebra, Eq. (4-11) can then be obtained:

ɺ =m ɺ + m " fi

" ∞

σεu ζ ( Tg4 (t) − To4 ) Lv

(4-11)

Eq. (4-11) represents the pyrolysis rate of a non-charring material in a compartment as a function of the pyrolysis rate in open conditions, the gas temperature, the initial temperature in the compartment, 298K, and ζ . ζ is unknown in the literature. However, one may well say that it ranges from 0 to 65


4. Pyrolysis Rate and Smouldering Combustion 1. If a value of zero is considered, the flame does allow the radiation from the ɺ "fi = m ɺ "∞ . If a value of one is considered, smoke to pass through it and therefore m then, the pyrolysis rate will be at its maximum value. We should note that in a compartment there are two types of fire areas: the fire area that is affected by the flame and hot smoke and the fire area that is only affected by the smoke. The development above focused on the former type of area. To take into account the latter, Eq. (4-12) should be used. In this case ζ takes the value of zero.

ɺ "fi = m

σε u ( Tg4 (t) − Tv4 ) + h ( Tg (t) − Tv ) − λ

( Tv − Tc (t)) y(t)

(4-12)

Lv

For this area to pyrolyse, Ts must be equal to the vaporisation temperature, Tv. Note that Eq. (4-12) can be also used to simulate smouldering combustion. y can be obtained from Eq. (4-13) and Tc for hypothesis c) of Section 3.1.1: “Definition of the Scenario and Hypotheses”. ɺ" dy m = fi dt ρ

(4-13)

3.1.3 Pyrolysis Rate in Open Conditions Based on a great number of experiments carried out in open conditions, the ɺ "∞ has been defined as Eq. (4-14): pyrolysis rate at free burning, m " ɺ "∞ = m ɺ aux m ( 1 − e − kβ D )

(4-14)

ɺ "aux and kβ depend on the type liquid type. The diameter, D, is assumed where m to represent a circular configuration. Square and similar configurations can be treated as a pool of equivalent circular area. This relation is valid for liquid or non-charring fuels.

ɺ "∞ and kβ for common fuels, (Karlsson, Table 4-1 represents some values of m 2000). Another source is the SFPE Handbook of Fire Protection Engineering. Material Butane (C4H10) Benzene (C6H6) Gasoline Polypropylene (C3H6)n Polystyrene (C8H8)n PMMA

ɺ "∞ m [kg/m2s] 0.078 0.085 0.055 0.018 0.034 0.003

kβ [m-1] 2.7 2.7 2.1 ----

Table 4-1: Free-burning rate of common fuels (liquids and non-charring).

66


4. Pyrolysis Rate and Smouldering Combustion

3.2 Simplified Model for the Pyrolysis Rate of Charring Fuels 3.2.1 Pyrolysis Rate Equations Figure 4-8 represents a diagram for a charring fuel burning in a compartment. The thermal mechanisms that take place are: • • • •

Convection and radiation from the flame to the fuel surface. Radiation from the hot smoke. Conduction within the fuel. Radiation is not considered between the walls and the fuel.

σε u ζ ( Tg4 − Ts4 ) Tg

ɺ" m

Tfl

h ( Tfl − Ts )

σε fl ( Tfl4 − Ts4 )

Ts Tv

λ

Tc Compartment

∂T ∂y

y

L

Fuel

" Char

Tv

Pyrolysis plane

qɺ "Fuel Figure 4-8: Diagram of a piece of charring fuel burning in a compartment. Tg is the temperature of the hot gases, while Ts is the surface temperature of the fuel. Tfl represents the flame temperature. Tv is the vaporization temperature of the fuel. To is the temperature at the bottom of the fuel. All of these temperatures are given in K. y represents the thickness of the char. Its position is found by seeking the vaporisation temperature along the thickness of the fuel, in m. Lastly, L is the thickness in m (see Annex I). Considering a linear temperature profile for char and fuel, and knowing that the temperature at the pyrolysis plane is always Tv, the pyrolysis rate per square meter of a charring material can be expressed as Eq. (4-15):

67


4. Pyrolysis Rate and Smouldering Combustion

ɺ "fi = m

" qɺ Char − qɺ "Fuel Lv

(4-15)

" where qɺ Char − qɺ "Fuel is:

" − qɺ "Fuel = qɺ Char

λ char ( Ts (t) − Tv ) λ fuel ( Tv − Tc (t)) − y(Tv , t) L − y(Tv , t)

(4-16)

Ts(t), To(t) and y(Tv,t) can be obtained by a finite difference method explained in Section 3.2.2: “Temperature Distribution in the Fuel” as a function of the additional heat flux and the flame heat flux. However, there is a problem finding in the literature the heat flux from the flame (the flame temperature is needed for that) and the value of ζ also unknown. It is clearly observed that the char layer created between the vaporization plane and the flame acts as a shield decreasing the quantity of heat that hits the surface of vaporisation. That means that the pyrolysis rate in open conditions, ɺ "∞ , cannot be considered constant during the burning for these types of fuels m are char. Therefore the development applied to non-charring materials cannot be applied here. For using this model, these data are needed. More research is needed in this field.

3.2.2 Temperature Distribution in the Fuel The heat transfer mechanisms affecting a burning material are as follows: convection and radiation between the char and the hot smoke, radiation between the flame and the char and conduction between the char and the fuel. Conduction may also exist between the fuel and the wall. A one-dimensional finite difference method is used to obtain the temperature distribution in the fuel. The nodes are spaced evenly throughout the thickness of the fuel. Three types of different nodes are identified in Figure 4-9. One is the node on the surface of the fuel. Another is the node in contact with other nodes of the same material, i.e. wood and wood or char and char. The third one is the node in contact with other nodes of different material as occurs along the interface, i.e. wood and char. The temperature at each node is calculated at each time step using transient explicit finite difference formulae, that can be written by considering of the energy balance for each node, Eq. (4-17): Eɺ in + Eɺ out = Eɺ stored

(4-17)

68


4. Pyrolysis Rate and Smouldering Combustion qɺ in

Node I Material i Node II

qɺ store

Material ii

qɺ out

Node II

Energy balance

Temperature

Figure 4-9: Different types of nodes found in a fuel. Energy balance in a node. Using the convention that heat flows into the node under consideration, the energy balance for the nodes can be written in the finite difference formulation below. Type node I: surface node Flames above the material: Ti,1P+1 = Ti,1P +

2∆t h (Tfl − Ti,1P ) + σε fl ( Tfl4 − Ti,1P ) + cpi,1 ρi,1∆x  σε u ζ ( Tg4 − Ti,1P ) −

λ i.1 P (Ti,2 − Ti,1P ) ∆x 

(4-18)

No flames above the material: Ti,1P+1 = Ti,1P +

2∆t  λ i.1 P P 4 P h (T − T ) + σε T − T − (Ti,2 − Ti,1P ) ( ) g i,1 u g i,1  cpi,1 ρi,1∆x  ∆x 

(4-19)

Type node II: nodes between different materials. +1 P TiP_ii,n = Ti_ ii,n +

2∆t  2λ ii,n +1 P (Tii,n +1 − TiP_ ii,n ) −  cpii,n +1 ρii,n +1∆x + cpi,n −1 ρi,n −1∆x  ∆x −

2λ i,n −1 ∆x

P (TiP_ ii,n − Tii,n +1 )]

(4-20)

Type node III: nodes between same material. P +1 P Ti,m = Ti,m +

2∆t  λ i,m P P P  (Ti,m −1 + Ti,m +1 − 2Ti,m )  cpi,m ρi,m ∆x  ∆x 

(4-21)

Where: • •

p indicates the current time step and p+1 indicates the next time step. i indicates one material, i.e. char and ii indicated the other, i.e. wood.

69


4. Pyrolysis Rate and Smouldering Combustion • •

n represents a node and n+1 or n-1 indicate the next or the previous node. m represents a node and m+1 or m-1 indicate the next or the previous node.

The input data for obtaining the temperature distribution are: • • • •

The conductivity, the density and the specific heat of each material. These properties can be considered constant or dependent on the temperature, see Section 6: “Material Properties”. The temperature of the gas, Tg. This is obtained according to the mass and energy balance described in Chapter 11: “Implementation in OZone”. The gas emissivity. Its value is normally considered between 0.8 and 1.0. The convective heat transfer (see Section 3.2.3: “Convective Heat Transfer”).

3.2.3 Stability of the Finite Difference Model With the set of formulas given above, mathematical problems arise when a certain relation of ∆t/∆x is surpassed. In this case, the calculation gives an error as a result. The relation between ∆t and ∆x is expressed in Eq. (4-22): ∆t ≤

(∆x)2

∆x 2α  (h + ε u σT03 ) + 1  λ 

(4-22)

Selecting a larger number of nodes will decrease both the spacing between nodes and the upper limit of the time step. This means that selecting a large number of nodes is computationally demanding both in terms of the number of temperatures to be calculated throughout the thickness of the glass and in terms of the number of times the calculations must be performed. The trade−off is in the accuracy of the calculations. Choosing a large number of nodes will provide a more accurate result.

3.2.4 Convective Heat Transfer The convective heat transfer coefficient is dependent on the temperature and on the velocity of the hot gases. Sincaglia and Barnett, 1997 propose an expression for the convective heat transfer in fire conditions: h = h min + (h max − h min )

(Tg − 300) 100

(4-23)

where the temperature of the upper layer, TU, is measured in Kelvin and the values of hmin and hmax are 5.0 and 50.0 W/m2·K respectively. This correlation describes a linear increase in the coefficient between hmin at 300K and hmax at 400K. h is capped at hmax and cannot drop below hmin (see Figure 4-10). 70


4. Pyrolysis Rate and Smouldering Combustion

60 50

h

2

W/m K

40 30 20 10 0 290

310

330

350

370

390

410

Temperature [K]

Figure 4-10: Variation of the convective heat transfer as a function of the gas temperature.

4. Non-Flaming Combustion: Smouldering Combustion Smouldering combustion is defined as combustion without flames. In open conditions, it is only possible for charring materials such as wood. However, when considering the effect of the compartment, both kinds of fuels are able to smoulder since there is an additional heat flux that can “act” as the extinguished flame. The models explained in Section 3.1: “Simplified Model for Pyrolysis Rate of Liquid or Non-Charring Fuels” and Section 3.2: “Simplified Model for Pyrolysis Rate of Charring Fuels” are applicable to simulate this type of combustion but must take into account the following considerations: • •

The heat flux from the flame is zero. The smouldering process finishes when all the fuel has been pyrolysed or when the temperature of the material is lesser than the vaporisation temperature.

5. Flame Extinction When the availability of oxygen is not enough in the compartment, the fire dies out progressively. No clear criterion has been found in the literature for determining when the fire will die out because of the lack of oxygen in the compartment. Some authors have stated that the fire dies out when the oxygen contained in the opening reaches a certain level, normally considered 12% of the

71


4. Pyrolysis Rate and Smouldering Combustion compartment volume. Other criteria used for determining if a fire will die or not, are based on Figure 4-11. The axis x represents the equivalence ratio, Eq. (4-24), and axis y represents the ratio of ventilation-controlled to well-ventilated yield. These data have been obtained from relatively small turbulent fires under controlled air and fuel supply with the solids enhanced by external radiation. Figure 4-11 shows that at roughly φ = 4, there is a transition from flaming to non-flaming conditions (Tewarson, 1995). φ represents the equivalence ratio and is explained further in Chapter 5: “Combustion Products in Fires”.

Figure 4-11: Effect of under-ventilation on yields of O2, CO2, and CO for many materials. (Tewarson, 1995). When one of these criteria is met and the flame dies out and the oxygen entering through the openings starts to accumulate in the room. This can provoke the re-ignition of flames in the compartment. A model for predicting the extinction of the flames is not developed in this thesis. Further research is needed.

6. Material Properties In this chapter the most important properties of some common materials are given. A special section is dedicated to wood.

6.1 Wood The properties of wood change as a function of the temperature. Figure 4-12 (a), (b) and (c) represent the variation of properties such as density, conductivity, and specific heat as a function of the temperature. These figures

72


4. Pyrolysis Rate and Smouldering Combustion have been taken from Eurocode 5. It is considered that from a temperature higher than 300ÂşC, the wood turns into char. Attention must be paid when the wood starts to cool since properties cannot return along the curves. This phenomenon is observed in Figure 4-14 and Figure 4-15. In spite of this temperature dependence, it is common practise to consider the properties of wood and char as constant. Table 4.2 shows the average value of the properties mentioned above as a function of the type of wood (balsa, oak, pitch pineâ&#x20AC;Ś) and its grain orientation, Figure 4-13. Another important characteristic is the vaporisation temperature. It is defined as the temperature at which the wood decomposes into gaseous fuel and char. Normal values are between 200 and 350ÂşC.

(a) Temperature-specific heat relationship for wood and char

(b) Temperature-conductivity relationship for wood and char

(c) Temperature-density ratio relationship for softwood with an initial moisture content of 12 % Figure 4-12: Properties of wood according to Eurocode 5.

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4. Pyrolysis Rate and Smouldering Combustion

Species

Redwood Red oak Douglas fir Maple

Grain orientation

Average density [kg/m3]

Tignition [ºC]

Thermal conductivity [W/mK]

Specific heat [J/kg K]

Along Across Along Across Along Across Along Across

354 328 753 678 502 455 741 742

375 204 304 275 384 258 354 150

0.19 0.85 0.44 0.86 0.23 0.80 0.35 2.08

3200 7400 3100 3200 2200 4000 2500 7100

Table 4-2: Properties of different types of wood according to the grain orientation.

Incident heat flux parallel to grain

Across grain

Along grain

Figure 4-13: Simple grain configuration, Quintiere, 2000. Figures 4-14 and 4-15 show an example of temperature distribution for a piece of wood with constant properties for char and wood and the properties proposed by Eurocode 5 when only submitted to a gas temperature TU. The density of the wood in both cases is 500 kg/m3. The piece of wood simulated according to Eurocode 5 contains 12% moisture. The piece of wood simulated with constant properties does not contain moisture and is defined as follows: • • •

Char: 200 kg/m3, 0.09 W/mK and 1600 J/kgK. Wood: 500kg/m3, 0.23 W/mK and 2200 J/kgK. εu = 1.0.

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4. Pyrolysis Rate and Smouldering Combustion 1050 Node Node Node Node Node Node Node Node Node Node TU

900 750

[C]

600 450 300

1 2 3 4 5 6 7 8 9 10

Influence of water

150 0 0

500

1000

1500

2000

2500

3000

3500

Time [s]

Figure 4-14: Temperature distribution. Properties of wood: Eurocode 5. 1050 Node Node Node Node Node Node Node Node Node Node TU

900 750

[C]

600 450

1 2 3 4 5 6 7 8 9 10

300 150 0 0

500

1000

1500

2000

2500

3000

3500

Time [s]

Figure 4-15: Temperature distribution. Properties of wood: Constant. 600

500 Node 1

400

[kg/m3]

Node 2 Node 3

300

Node 4

200

100

0 0

500

1000

1500

2000

2500

3000

3500

Time [s]

Figure 4-16: Density distribution. Properties of wood: Eurocode 5.

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4. Pyrolysis Rate and Smouldering Combustion 600

500 Node 1

400

[kg/m3]

Node 2 Node 3

300

Node 4

200

100

0 0

500

1000

1500

2000

2500

3000

3500

Time [s]

Figure 4-17: Density distribution. Properties of wood: Constant.

6.2 Other Materials A list of some other common fuels is given in Table 4-3.

Fuel

Density

Cellulose Polyethylene Polystyrene Polyurethane foams PMMA Nylon 66

Variable 940-970 1100 Variable (20) 1190 1200

Heat capacity 1.3 1.3-2.3 1.2 1400 1420 1.4

Thermal conductivity Variable 0.44 0.11 0.034 0.19 0.4

Table 4-3: Density, specific heat capacity and thermal conductivity of common fuels.

7. Parametric Study The aim of this section is to assess the influence, using OZone calculations, of a modification of the value of one of the parameters listed in Section 7.1: “Parameters in Study”. This influence is shown in the pyrolysis rate. From a reference fire scenario, defined in Section 7.2: “Reference Fire Scenario”, a single parameter is modified whereas all other parameters remain unchanged.

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4. Pyrolysis Rate and Smouldering Combustion

7.1 Parameters in Study The parameters and the range of variation are: • • • •

The height of the fire scenario, from 3.0 m to 6.0 m. The ventilation parameter defined as V.F = Aw(Hw)0.5, from 0.35 to 1.84. The floor area, from 9.0 m2 to 81.0 m2. In this study, the floor area is considered to be the fire area. The material of the partitions of the compartment (see Table 4-4).

Material of the partitions

Abbrev.

Normal Weight Concrete Middle Weight Concrete Lightweight Concrete Normal Brick (11.0 cm) + Gypsum Board (1.0 cm) Heavy Brick Light Perforated Brick Normal Brick Heavy Wood Normal Wood

NWC MWC LWC NB + GB HB LB NB HW NW

Unit mass [kg/m3] 2300 1800 1600 1600 900 2000 700 1600 720 450

Conduct. [W/mK] 1.6 1.15 0.8 0.7 0.25 1.2 0.15 0.7 0.2 0.1

Spec. heat [J/kgK] 1000 1000 840 840 1000 1000 840 840 1880 1113

Table 4-4: Properties of the material of the partitions: unit mass, conductivity and specific heat

7.2 Reference Fire Scenario The fire scenario is defined as follows: • • • • •

Dimensions of the compartment: 3.0m x 3.0m x 3.0m. Dimensions of the opening: 1.0 m x 1.0 m. (V.F = 1) Fire load: 511 MJ/m2 and RHRf: 250 kW/m2, fire area = 9.0 m2. No gas species were considered in the calculation except the quantity of total unburnt mass. Only the quantity of the unburnt and burnt gas and air is computed. Partitions of the compartment: o Thickness: 12.0 cm. o Material: unit mass 720 kg/m3; conductivity 0.2 W/mK; specific heat 1880 J/kgK.

• Burning material properties: o o o o

ɺ "∞ equal to 0.018 kg/m2s. Non-charring material with m Stoichiometric ratio: 1.27 Combustion heat: 17.5 MJ/kg. Combustion efficiency factor: 0.8.

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4. Pyrolysis Rate and Smouldering Combustion The simulations were carried out assuming an NFSC design fire and the model for non-charring materials described in Section 3.2: â&#x20AC;&#x153;Simplified Model for Pyrolysis Rate of Liquid or Non-Charring Fuelsâ&#x20AC;?. Loss by conduction has not been considered. Îś is considered to be 1.0.

7.3 Results of the Study 7.3.1 Height of the Compartment Increasing the height of the compartment decreases the average gas temperature of the compartment and, consequently, the external heat flux affecting the surface of the fuel is lesser. That causes a lower pyrolysis rate, Figure 18 (b). Furthermore, increasing the height also increases the volume of the compartment and obviously the mass fraction of unburnt gas is reduced, Figure 18 (a).

7.3.2 Material of the Partitions The influence of thermal inertia. quantity of heat temperature falls

the material of the partitions on the pyrolysis rate is due to A material with higher thermal inertia transfers a higher from the compartment to the exterior and therefore, the gas lower, Figure 4-19 (a) and (b).

7.3.3 Ventilation Parameter Increasing the ventilation parameter allows a higher quantity of air to enter the compartment. Therefore, the burning rate increases, releasing a higher quantity of heat and the average gas temperature rises as well as the external heat flux affecting the surface of the fuel. This causes a higher accumulation of mass and a higher pyrolysis rate, Figure 4-20 (a) and (b).

7.3.4 Fire Area Two areas must be taken into account in order to understand the results of this section, namely the fire area that is burning (presence of flames) with oxygen entering the compartment and the fire area that is not burning (no presence of flames) but is able to pyrolyse when it reaches its vaporisation temperature. Therefore, having a bigger fire area implies being able to have a higher pyrolysis rate, Figure 4-21 (a) and (b). On the other hand, increasing the fire area means increasing the volume of the compartment. Therefore, more time is needed for the fire area that is not burning to reach the vaporisation temperature and start to pyrolyse.

78


4. Pyrolysis Rate and Smouldering Combustion In all these figures, a jump can be readily observed in both mass fraction and the pyrolysis rate. This jump occurs when the fire area that does not burn reaches the vaporisation temperature. 0.5

50 H = 3m

40

H = 3m

0.4

H = 4m

Mass fraction [%]

H = 4m H = 5m H = 6m

H = 5m

20

0.2

10

0.1

0

0

0

500

1000

1500

2000

2500

H = 6m

0.3

[kg/s]

30

0

3000

500

1000

1500

2000

2500

3000

Time [s]

Time [s] (a)

(b)

Figure 4-18: (a) Mass fraction of unburnt products and (b) pyrolysis rate for a compartment of height = 3, 4, 5 and 6 m.

0.5

60

N. wood L. brick H. wood NB + Gb N. brick L.W.concrete M.W. concrete H. brick N.W. concrete

N. wood L. brick

50

0.4

H. wood

Mass fraction [%]

N.B + Gb

40

N. brick M.W. concrete

30

H. brick N.W. concrete

20

[kg/s]

0.3

L.W. concrete

0.2

0.1

10 0

0 0

500

1000

1500

Time [s]

(a)

2000

2500

3000

0

500

1000

1500

2000

2500

3000

Time [s]

(b)

Figure 4-19: (a) Mass fraction of unburnt products and (b) pyrolysis rate for a compartment build of different materials. 79


50

0.5

40

0.4

V.F = 1.84 V.F = 1

30

V.F = 0.53

0.3 V.F = 1.84 V.F = 1

20

[kg/s]

Mass fraction [%]

4. Pyrolysis Rate and Smouldering Combustion

V.F = 0.53

V.F = 0.35 0.2

V.F = 0.35 10

0.1

0

0 0

500

1000

1500

2000

2500

3000

0

Time [s] (a)

500

1000

1500

2000

2500

3000

Time [s] (b)

Figure 4-20: (a) Mass fraction of unburnt products and (b) pyrolysis rate for a ventilation parameter of 0.35, 0.53, 1 and 1.83.

70

0.8

60

0.7

Afi = 25 m2 Afi = 49 m2

0.6

50 Afi = 9 m2

40

Afi = 25 m2 Afi = 49 m2

30

Afi = 81 m2

0.5

[kg/s]

Mass fraction [%]

Afi = 9 m2

0.4 0.3

Afi = 81 m2

20

0.2

10

0.1

0

0

0

1000

2000

3000

4000

Time [s]

(a)

5000

6000

0

1000 2000 3000 4000 5000 6000

Time [s]

(b)

Figure 4-21: (a) Mass fraction of unburnt products and (b) pyrolysis rate for a different value of fire area 9, 25, 49, 81 m2.

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4. Pyrolysis Rate and Smouldering Combustion

7.3.3 Summary of the Study The results of the study are summarized in Table 4-5.

Height Ventilation parameter Fire area Thermal inertia

⇑ ⇑ ⇑ ⇑

Mass fraction [%] ⇓ ⇑ ⇑ ⇓

Pyrolysis rate [kg/m2] ⇓ ⇓ ⇑ ⇓

Fire duration [s] ⇑ ⇓ ⇑ ⇑

Table 4-5: Summary of the results of the parametric study

8. Graphical Method for Comparison between Fire Scenarios according to Accumulation of Mass and Pyrolysis Rate Taking the results obtained in the parametric study from the previous section, a method for comparing fire scenarios can be elaborated concerning the accumulation of unburnt mass and maximum pyrolysis rate. For this purpose the maximum pyrolysis rate, the maximum mass fraction of unburnt products accumulated in the compartment and the fire duration of the simulations of the previous section is summarized in the tables below.

Height [m] 3 4 5 6

Pyrolysis ratemax [kg/s] 0.32 0.29 0.26 0.25

Unburnt mass fractionmax [%] 39 34 31 27

Fire duration [s] 1500 1620 1740 1860

Table 4-6: Maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the height of the compartment. Ventilation Pyrolysis ratemax Factor [kg/s] 1.84 0.49 1.00 0.32 0.53 0.18 0.35 0.12

Unburnt mass fractionmax [%] 33 39 42 43

Fire duration [s] 1080 1500 2400 3480

Table 4-7: Maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the ventilation factor.

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4. Pyrolysis Rate and Smouldering Combustion

Fire area 9 25 49 81

Pyrolysis ratemax [kg/s] 0.32 0.47 0.54 0.58

Unburnt mass fractionmax [%] 39 56 63 66

Fire duration [s] 1500 3060 5340

Table 4-8: Maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the fire area.

Material NW LB HW NB+GB NB LWC MWC HB NMC

Pyrolysis ratemax [kg/s] 0.43 0.39 0.32 0.28 0.24 0.23 0.2 0.19 0.18

Unburnt mass fractionmax [%] 53 48 39 33 27 26 21 19 17

Fire duration [s] 1140 1200 1500 1500 1800 1860 2040 2100 2280

Table 4-9: Maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the ventilation factor. It is possible to normalize the tables above with the respective values obtained in the reference case defined in Section 7.2: â&#x20AC;&#x153;Reference Fire Scenarioâ&#x20AC;?. To that end, the table below represents this transformation.

Height [m] 3 4 5 6

Pyrolysis ratemax [%] 0.0 -9.3 -18.7 -21.8

Unburnt mass fractionmax [%] 0 -12.8 -20.5 -30.7

Fire duration [%] 0 8.0 16 24

Table 4-10: Difference in % of the maximum pyrolysis rate, the maximum mass fraction of unburnt products accumulated in the compartment and the fire duration as a function of the height of the compartment.

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4. Pyrolysis Rate and Smouldering Combustion

Ventilation Pyrolysis ratemax Factor [kg/s] 1.84 53.1 1.00 0.0 0.53 -43.7 0.35 -62.5

Unburnt mass fractionmax [%] -15.3 0.0 7.6 10.2

Fire duration [s] -28 0.0 60 132

Table 4-11: Difference in % of the maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the ventilation parameter.

Fire area 9 25 49 81

Pyrolysis ratemax [kg/s] 0.0 46.8 68.7 81.2

Unburnt mass fractionmax [%] 0.0 43.5 61.5 69.2

Fire duration [s] 0.0 104 256 ---

Table 4-12: Difference in % of the maximum pyrolysis rate, maximum mass fraction of unburnt products accumulated in the compartment and fire duration as a function of the fire area.

Material NW LB HW NB+GB NB LWC MWC HB NMC

Pyrolysis ratemax [kg/s] 34.3 21.8 0.0 -12.5 -25 -28.1 -37.5 -40.6 -43.7

Unburnt mass fractionmax [%] 35.8 23.1 0.0 -15.3 -30.7 -33.3 -46.1 -51.2 -56.4

Fire duration [s] -24 -20 0 0 20 24 36 40 52

Table 4-13: Difference in % of the maximum pyrolysis rate, the maximum mass fraction of unburnt products accumulated in the compartment and the fire duration as a function of the material

These data can be represented in a graphical way as shown in Figure 4-22 (a), (b), (c) and (d). These figures are used to compare different fire scenarios built with different materials, different window sizes, different volume and different fire area with regards to the quantity of unburnt mass accumulated and the pyrolysis rate.

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4. Pyrolysis Rate and Smouldering Combustion 150

60 40

125

Duration

100

20

Duration

75 50

[%]

[%]

0 -20

25

Pyrol

UMF

0

-40

-25

-60

UMF

-50

-80

Pyrol

C M

B

0.2 0.4 0.6 0.8

1.2 1.4 1.6 1.8

2

Ventilation parameter [Aw(Hw)^0.5]

(a)

(b) 40

250 225

Duration

30

200

20

175

Duration

10 [%]

150 [%]

1

N

H

B LW C M W C

N

H W N B + G B

LB

N W

-75

125 100

0

-10

Pyrol

Pyrol

75

-20

50

UMF

25

-30

0

-40 0

9

18

27

36

45

54

Fire area [m2]

(c)

63

72

81

UMF

3

3.5

4

4.5

5

5.5

6

Height [m]

(d)

Figure 4-22: UMF: Relative Unburnt Mass Fraction accumulated in the compartment; Pyrol: Maximum pyrolysis rate; Duration: Duration of the fire.

An example of application of this method is the determination of which scenario is more at risk for backdraft to occur or merely the estimation of the risk of having backdraft in a compartment. Note that backdraft is intimately linked with the quantity of unburnt gas accumulated in the compartment just after the opening. Chapter 12 shows an example of an application of this method for a building fire.

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4. Pyrolysis Rate and Smouldering Combustion

9. Conclusion A fuel burning in open conditions has a different pyrolysis rate from the same fuel burning inside a compartment, e.g. the burning rate of burning of an alcohol fire in a small enclosure can be up to eight times greater than in the open. To take this effect into account, a simple model that describes the pyrolysis process for fuels burning in a compartment has been developed. The development of a simple model is justified considering that, practically speaking, it is impossible to know the exact amount, type and distribution of the different fuels present in a fire compartment. Therefore, it is not worthwhile to develop a very complex model for predicting the pyrolysis rate in compartments that takes into account parameters such as the humidity of the fuel, the porosity, etc., when generally no one knows which kinds of fuels are present in the compartment. On one hand, it has been explained that parameters such as the flame temperature and Îś are normally unknown. For this reason the model has not been validated. On the other hand, taking a reference case it is possible to evaluate the influence of parameters such as the height of the compartment, the fire area, the ventilation parameter and the materials of the partitions on the pyrolysis rate, on the accumulation of unburnt mass and on the duration of the fire. A graphical method based on these results has been developed with the aim of comparing and evaluating the fire duration, the accumulation of unburnt mass and the maximum pyrolysis rate of different fire compartments. This method can be used for evaluating the risk of having backdraft in a building and can help the fire fighter to know which scenario has a lower probability of ending in backdraft (tactical fire-fighting). Chapter 12 shows an example of that. Still, further studies are needed in the field of flame extinction, flame temperature, re-ignition of flames and Îś .

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4. Pyrolysis Rate and Smouldering Combustion

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4 pyrolysis rate and smouldering