COMBUSTION
V.M.GREMYACHKIN Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
Modern buildings are faced inside by wood and plastic plates which are very dangerous in case of buildings firing. There are two stages in wood or plastic plates combustion.
First stage is volatile materials burning out and the second stage is the combustion of carbonized materials which are formed after volatile components burned out. The second stage of the face plates combustion is the most dangerous because of combustion temperature is highest in this stage. Besides, the carbonized materials at high temperature can interact with carbon dioxide and steam but not only with oxygen. In this case the gaseous fuels (mixture of carbon oxide and hydrogen) may be formed what is very dangerous for fire development. These circumstances made the investigations of carbonized materials combustion very important for the simulation of fire development in modern buildings.
The most investigations deal with char particles combustion [1–4] for what the kinetics of carbon interaction with different reactances is determined. Here we shall consider the carbonized material plates combustion what is more important for buildings fire consideration.
Let’s have a plate of porous char and the gas layer over char surface having the thickness δ. On the external boundary of the gas layer the temperature and the composition of the gas phase are known:
.
Let us consider the diffusive equations in form of carbon, oxygen and hydrogen atoms conservation and the heat transfer equation in form of the full enthalpy conservation
(1) (2) (3) (4)
where mj, and nj, and lj are the numbers of carbon, oxygen and hydrogen atoms in molecules and is the elimination flux of heat from char surface, and
are the flows of substances and heat.
Also the next equations are considered
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(5) (6) (7) taking into consideration that the sum of relative mass concentrations is unit; the alteration of mass flow is associated with rate of carbon consumption; the existing of gas flow in porous char media is associated with pressure gradient by Darcy’s law.
It is necessary also to consider the equations of chemical reactions kinetics of char interaction with reactances.
It can be assumed that all chemical reactions proceed in diffusive regime [5–6] on the char surface and in the thin flame over the char surface. This diffusive model demands nothing the kinetic data for utilization. Such model rather well describes the combustion of liquid hydrocarbon fuels droplets, when only the homogeneous chemical reactions take place. However, this model is not able to describe the complex regularities of char combustion.
If the equations of all chemical reactions kinetics are considered [7–8], the most common theoretical model takes place. However, the equations in this model are nonlinear and very complex for solution. The big volume of information received in a result of these equations numerical solution are very hard to analyze. The lack of real kinetic data is also considerable hard for utilization of this model.
The estimations [9] show that in case of carbon combustion in air, as in case of liquid droplets combustion the homogeneous reactions transfer from diffusive to kinetic regimes for carbon particles size about a few microns only. However, the heterogeneous chemical reactions proceed in kinetic regime. Thus it can be assumed that the heterogeneous chemical reactions proceed in kinetic regime but the homogeneous chemical reactions proceed in diffusive regime in process of char combustion and gasification.
It is necessary to note that the temperature of liquid droplets is limited by boiling temperature of liquid fuels which is rater low. Because the homogeneous reactions in case of liquid droplets combustion can proceed only in the thin flame where the temperature is maximum. The temperature of char particles may be very high. In this case the homogeneous chemical reactions can take place in gas phase everywhere but not only in the thin flame front.
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If the homogeneous reactions proceed in diffusive regime, when the chemical reaction rate is significantly more reactances flows, the chemical equilibrium in gas phase must take place as the process of chemical reaction proceedng is the process of chemical equilibrium establishment. The conditions of chemical equilibrium give the additional equations [10]
(8) where Kj are the equilibrium constants of substances formation from elements.
If the heterogeneous reactions proceed in diffusive regime the equilibrium between solid and gas phases must take place also. In this case the partial pressure of carbon vapor must be equal to partial pressure of satiation carbon vapor inside the char. If the heterogeneous reactions proceed in kinetic regime it is necessary to get the kinetic equation for rate of carbon consumption
(9) where zej are the equilibrium concentrations of reactances at the char surface and γj are the rate constants of the corresponding heterogeneous chemical reactions.
The boundary conditions for case of char plate combustion and gasification may be written in form
Besides, it is necessary to determine the conditions on the char surface also. Such conditions must be uninterruption of the temperature, the gas components concentrations and the gas flow velocity.
It is necessary to mark that the theoretical model includes consideration of char porous structure from which the penetration K and internal char surface S are depended.
The considering theoretical model of char plate combustion and gasification in a mixture of gaseous reactances arbitrary composition and temperature is able to determine:
(1) the char burning out rate in dependence on environment gas temeperature and composition;
(2) the distributions of the temperature, pressure and reactances concentrations in gas phase and inside porous char;
(3) the surface temperature of char and elimination flux from the char surface;
(4) the distribution of the carbon consumption rate inside char which depends on temperature, pressure and reactances concentrations;
(5) the rates of the individual reactances formation (consumption) including hydrogen and carbon oxide formation.
REFERENCES
1. Laurendau N.M., Progress in Energy and Combustion Sciences 4:221–270 (1978) 2. Dutta S.,Wen C.Y., Belt R.J., Ind. Eng. Chem. Process Des. Dev. 16:20–28 (1977)
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3. Chin G., Kimura S., Tone S., Otake T., Ind. Chem. Eng. 23:105–120 (1983) 4. Smith I.W., Combust. Flame 14:237–248 (1979)
5. Gloving A.M., Pesochin V.R., Tolmachev I.Y., Physica goreniya i vzriva 18(No 2): 28–35 (1982)
6. Libby P.A., Blake T.R., Combust. Flame 36:139–169 (1979)
7. Hitrin L.N., Physics of Combustion and Explosion, MGU, Moscow, 1957, p. 337–411.
8. Srinevas B., Amundson R.N., AIChE Journal 26:487–496 (1980)
9. Gremyachkin V.M., Schiborin F.B., Physica goreniya i vzriva 27(No 5):67–73 (1991)
10. Thermodynamic properties of individual substances (Ref., V.P.Glushko,Ed.), Nauka, Moscow, 1978.
11. Lee S., Angus J.C., Edwards R.V., Gardner N.C., AIChE Journal 30:583–593 (1984) 12. Gremyachkin V.M., Roschina L.M., Physica goreniya i vzriva 26(No5):63–67 (1990)
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