# Combustion Reaction

When considering combustion, one can rely on the following combustion parameters of materials [5, 6]:

• Y ($O_2$) - oxygen consumption, [kg/kg]
• Y ($CO_2$) – carbon dioxide emission, [kg/kg]
• Y ($CO$) – carbon monoxide emission, [kg/kg]
• Y ($HCL$) – hydrogen chloride emission, [kg/kg]
• D ($m$) – smoke generating capacity, [Np·m²/kg]
• ∆H – calorific value, [kJ/kg]

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Further in the Combustion Reaction section, all the quantities whose value is known at the time of mention are highlighted in bold.

Usually, FDS does not use all of these parameters unchanged to simulate combustion. Also, a number of other parameters are required that are not present in the available reference books. Accordingly, it is necessary to convert the known parameters to the parameters required for simulation with FDS.

FDS6 allows to define a “simple” combustion reaction by setting the chemical formula of the fuel. In this case, the fuel must consist only of carbon, hydrogen, oxygen and nitrogen atoms:

This method can be used for reactions without the hydrogen chloride emission (e.g., paper burning). However, it is not suitable for reactions with the hydrogen chloride emission (e.g., car burning).

For combustion reactions with the emission of hydrogen chloride (and any other products), FDS6 uses a different approach: instead of specifying the exact chemical formula of the fuel, only the molar mass of the fuel, the amount of oxygen required for fuel combustion, and the amount of combustion products obtained are set. This method is also suitable for describing combustion reactions without the hydrogen chloride emission and, therefore, is used in Fenix+ 3 when preparing the input file for FDS for all reactions.

The combustion reaction can be represented as follows:

where:

• Fuel – fuel;
• Air – combustion air
• ϑ(Air) – amount of air required for fuel combustion
• Products – combustion products

Air is a mixture of gases, the main components of which are nitrogen (78.084 vol%) and oxygen (20.9476 vol%). When modeling, we assume that the volume fraction of nitrogen is 79%, and oxygen is 21%:

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or

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Since {width=15%} equation (18) takes the following final form:

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Equation (19) can be rewritten as:

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Combustion products are the same as in formula (14) with the addition of hydrogen chloride:

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As a result, the combustion reaction is as follows:

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Thus, to set the combustion reaction, it is necessary to determine the amount of oxygen Y ($O_2$) and the amount of each combustion product: Y ($CO_2$), Y ($H_2$O), Y ($CO$), Y ($Soot$), Y ($HCl$) and Y ($N_2$).

From the law of conservation of the number of atoms, we get that:

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The rest of the quantities are found as follows:

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where:

• Y ($O_2$) – oxygen consumption (unit of meas.: [kg/kg])

• Y ($CO_2$), Y ($CO$), Y ($HCl$), Y ($H_2$O), Y ($Soot$) – emission of carbon dioxide, carbon monoxide, hydrogen chloride, water and soot, respectively (unit of meas.: [kg/kg])

• W ($Fuel$) - molar mass of the fuel. Often it is not known exactly, since the combustible content is a complex mixture of substances (for example, “Administrative rooms, classrooms of schools, universities, polyclinic offices”). Therefore, usually, either ~87 g/mol (for wood, fabrics) or ~104 g/mol (for plastic, rubber) is taken as the value.

• W ($O_2$), W ($CO_2$), W ($CO$), W ($H_2$O), W ($HCl$), W ($Soot$) – molar mass of oxygen, carbon dioxide, carbon monoxide, water, hydrogen chloride, and soot, respectively (unit of meas.: [g/mol]). The values of these constants are presented in Table P1.1 of Appendix 1.

The release of water Y (**$H_2$**O) is determined from the law of conservation of mass:

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The emission of soot Y ($Soot$) (27) can be justified by considering the procedure for determining the smoke-developed index:

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where:

• V – measuring chamber capacity

• L – light beam path length in a smoky environment

• m – sample weight

• $T_0$, $T(min)$ – the values of the initial and final light transmission, respectively.

On the other hand, the intensity of light passing through the smoke the distance L decreases in accordance with the following law:

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where:

• K – light extinction coefficient (optical smoke density)

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where:

• $K_m$ – mass extinction coefficient (unit of meas.: m²/kg). The default FDS value for this parameter is 8700 m²/kg – a typical value for wood and plastic combustion.

• $PY(Soot)$ – smoke density

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As a result, equation (28), taking into account (29) – (31), is transformed as follows:

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From equation (32) we find equation (27).

The unit of measurement for the smoke-developed index is [m²/kg]. In some textbooks [Np·m²/kg] is used as the unit of measurement. Neper (Np) is a dimensionless logarithmic unit of measurement of the ratio of two quantities. Its use only emphasizes the “physical essence” of the smoke-developed index and does not lead to a change in the numerical value. Therefore, the smoke-developed index values expressed in [m²/kg] and [Np·m²/kg] are the same.

Thus, in order to convert the combustion parameters of materials into the parameters that are required for FDS, the following steps must be sequentially performed:

• Determine Y($_Soot$) by formula (27).

• Determine Y($H_2O$) by formula (26).

• Determine the chemical reaction coefficients by formulas (25.1 – 25.6).

• Determine Y($N_2$) by formula (24).

Let’s consider an example of converting known material parameters into parameters required for FDS.

Let us do this using the example of a typical “Car” fire load. Let us use the following fire load parameters:

• Inferior calorific value (∆H): 31700 kJ/kg
• Smoke generating capacity ($D_m$)): 487 Np·m²/kg
• Oxygen consumption (Y($O_2$)): 2,64 kg/kg;
• Carbon dioxide emission (Y($CO_2$)): 1,295 kg/kg;
• Carbon monoxide emission (Y($CO$)): 0,097 kg/kg;
• Hydrogen chloride emission (Y($Hlc$)): 0,0109 kg/kg;
• Molar mass of the fuel (W($Fuel$)): 104,3233 g/mol.

In FDS, the combustion reaction is represented by several SPEC groups defining each reaction component and one REAC group. In this case, the combustion reaction will be represented by the following groups:

1. &SPEC ID=‘OXYGEN’ LUMPED_COMPONENT_ONLY=.True./
2. &SPEC ID=‘NITROGEN’ LUMPED_COMPONENT_ONLY=.True./
3. &SPEC ID=‘CARBON DIOXIDE’ LUMPED_COMPONENT_ONLY=.True./
4. &SPEC ID=‘CARBON MONOXIDE’ LUMPED_COMPONENT_ONLY=.True./
5. &SPEC ID=‘HYDROGEN CHLORIDE’ LUMPED_COMPONENT_ONLY=.True./
6. &SPEC ID=‘WATER VAPOR’ LUMPED_COMPONENT_ONLY=.True./
7. &SPEC ID=‘SOOT’ LUMPED_COMPONENT_ONLY=.True./
8. &SPEC ID=‘Avtomobil’ MW=104.3233/
9. &SPEC ID=‘AIR’ BACKGROUND=.True. SPEC_ID(1:2)
=‘OXYGEN’,‘NITROGEN’ VOLUME_FRACTION(1:2)=1,3.7619/
10. SPEC ID=‘PRODUCTS’ SPEC_ID(1:6)=‘SOOT’,‘CARBON
DIOXIDE’,‘CARBON MONOXIDE’,‘HYDROGEN CHLORIDE’,‘WATER
VAPOR’,‘NITROGEN’ VOLUME_FRACTION(1:6)
=0.535241224739138, 3.06976160828912, 0.361275400659048,0.031187456220273,12.6304974369969, 32.3786545368201/
11. &REAC FUEL=‘Avtomobil’ HEAT_OF_COMBUSTION=31700 SPEC_ID_NU (1:3)=‘Avtomobil’,‘AIR’,‘PRODUCTS’ NU(1:3)=-1,-8.60699501231296,1/

The first seven SPEC groups describe the “elemental” components of the reaction. Since these are “standard” components, the properties of which are already included in FDS, there is no need to specify any additional parameters for them except LUMPED_COMPONENT_ONLY.

The LUMPED_COMPONENT_ONLY=.True. parameter value means that this component can only be used in a “complex” component – in a mixture.

The SPEC ID=‘Avtomobil’ group represents a fuel for which only molar mass is specified.

The SPEC ID=‘AIR’ group represents air composed of oxygen and nitrogen (see formula (21)). Since it is present at all points of the simulated space, let us set the BACKGROUND parameter to .True.

The SPEC ID=‘PRODUCTS’ group represents the combustion products and their amount in the reaction.

The REAC group actually reflects formula (20).

The SPEC_ID_NU parameter lists all the components involved in the combustion reaction: fuel, air and reaction products.

The NU parameter lists the amount of each reaction component corresponding to the enumeration in the SPEC_ID_NU parameter. Components with a “-” sign are consumed during the reaction, and those with a “+” are highlighted.