Fire Simulation for Engineers/FDS/Combustion

...then gas phase combustion reaction is set up via the REAC namelist group

Combustion is not pyrolysis

A common source of confusion in FDS is the distinction between gas phase combustion and solid phase pyrolysis.

Pyrolysis is the decomposition or transformation of a compound caused by heat that produce the gaseous fuel. It is the first chemical reaction that occurs in the burning of many solid fuels, like wood, cloth, paper, and plastic.

Gas phase combustion refers to the exothermic chemical reactions between the gaseous fuel and oxygen accompanied by the production of heat and light in the form of flames.

So solid phase pyrolysis refers to the generation of fuel vapor at a solid or liquid surface, while the visible flames are not due to combustion of the solid fuel itself, but rather of the gases released by its pyrolysis.

Prescribing a fire

In FDS, a fire is a particular boundary condition applied to a surface bounding the flow field. There are two ways of designating a fire:

Demonstration of difference between combustion and pyrolysis

• The first is to specify an heat release rate on a surface; this is the same as prescribing a well defined burner. How to do this is described in detail in Section [sub:Prescribing-an-HRR].

• The other is to specify thermophysical properties of fuel materials and to let them pyrolyze. In this case the burning rate of the fuel depends on the net heat feedback to the surface. This approach is explained in Section [sec:Burning-properties-of-solids] for solid fuels and in Section [sec:Burning-properties-of-liquids] for liquids.

Both burners and pyrolyzing materials inject the calculated quantities of gaseous fuels in the flow field. In a realistic fire scenario, there may be various types of gaseous fuels originating from the various burning objects in the building and injected into the flow field.

Modeling gas phase combustion, REAC

Ignition

Once injected into the flow field, the gaseous fuels mix with air and burn. There is no need to prescribe an ignition source: the combustion model assumes that fuel gas and oxygen burn on contact. We can imagine that every grid cell hosts a virtual spark plug, that initiates combustion when temperature and local ratio of fuel gas and oxygen are appropriate (See Figure media:FlameExtinctionCriteria.png).

CombustionAndPyrolysisInMatch

Burning

The burning process releases heat and smoke.

Whereas there can be many types of combustibles in an FDS fire simulation, one only gaseous fuel can be simulated by FDS. In general, you should set the chemistry of the modeled burning gaseous fuel to coincide with the actual predominant burning gaseous fuel.

This model simplification is due to computational cost: it is expensive to solve transport equations for multiple gaseous fuels.

FDS adjusts automatically the burning rates of solids and liquids to account for the difference in the heats of combustion of the various combustibles. If the stoichiometry of the burning material differs from the global reaction, the heat of combustion of each burning material is used to ensure that an equivalent amount of fuel is injected into the flow domain from the burning object.

FDS can describe the gas phase reaction in two ways.

By default, a so-called mixture fraction model is used to account for the evolution of the fuel gas from its surface of origin through the combustion process.

The alternative is what is referred to as the finite-rate approach, where all of the individual gas species involved in the combustion process are defined and tracked individually. This is a costlier and more complicated approach than the mixture fraction model.

This manual covers the mixture fraction model only, as it is simpler and commonly employed for engineering level problems.

When the mixture fraction model is applied, a set of scalar variables, $Z_{i}$ , represent the state of the combustion process from pure fuel $(\sum Z_{i}=1)$ to pure air $(\sum Z_{i}=0)$ .

FDS provides two types of mixture fraction model:

Two-parameter mixture fraction model: the first parameter $(\mathrm {Z} _{1})$ is the mass fraction of unburned fuel and the second $(\mathrm {Z} _{2})$ is the mass fraction of burned fuel, as for example the mass of the combustion products that originated as fuel. FDS uses the two-parameter model by default.

Three-parameter mixture fraction model: this combustion model simulates a two-step chemical reaction with three parameters. The first step of the reaction is the oxidation of fuel to carbon monoxide and the second step the oxidation of carbon monoxide to carbon dioxide. The three mixture fraction components for the two step reaction are unburned fuel $(\mathrm {Z} _{1})$ , mass of fuel that has completed the first reaction step $(\mathrm {Z} _{2})$ , and the mass of fuel that has completed the second reaction step $(\mathrm {Z} _{3})$ . See Section [sec:CO-production-in-u-fires] to understand why and how to use the three-parameter model.

The mass fractions of all of the major reactants and products of combustion – as fuel, $\mathrm {O} _{2}$ , $\mathrm {CO} _{2}$ , $\mathrm {H} _{2}$ $\mathrm {O}$ , $\mathrm {N} _{2}$ , $\mathrm {CO}$ and soot – can be derived from the mixture fraction parameters by means of state relations: a set of pre-tabulated functions of the mixture fraction parameters, $\mathrm {Z} _{i}$ . In other words, the values of $\mathrm {Z} _{i}$ in any given mesh cell determines the mass fraction of all the gases listed.

The stoichiometry of the predominant gas phase combustion reaction is prescribed in the input file by one only REAC namelist group: the specified parameters are used to generate the table associating the mass fractions with $Z_{i}$ . FDS defaults to propane combustion if no REAC line is entered.

In the mixture fraction model, each reaction is assumed to be of the form:

$\mathrm {} \mathrm {\mathrm {\mathrm {C} _{x}\,\mathrm {H} _{y}\,\mathrm {O} _{z}\,\mathrm {N} _{v}\,Other_{w}} +\nu _{O_{2}}O_{2}} \rightarrow$ $\mathrm {\rightarrow \nu _{CO_{2}}CO_{2}+\nu _{H_{2}O}H_{2}O+\nu _{CO}CO+\nu _{soot}Soot+\nu _{N_{2}}N_{2}+\nu _{H_{2}}H_{2}+\nu _{other}Other}$

You need only specify the chemical formula of the fuel along with the yields of $\mathrm {CO}$ , soot, and $\mathrm {H} _{2}$ , and the amount of hydrogen in the soot, $\mathrm {H} _{frac}$ . For completeness you can specify the $\mathrm {N} _{2}$ content of the fuel and the presence of other species. FDS will use that information internally to determine the amount of combustion products that are formed.

The species implicitly defined by FDS when doing a mixture fraction calculation for gas phase combustion are as follows:

Mixture fraction species
fuel, oxygen, nitrogen, water vapor, carbon dioxide, carbon, monoxide, hydrogen, soot, other

Note that these species are identified by a lowercase name, and are not to be confused with the species identified by uppercase names defined by the SPEC namelist groups. See Section [sec:CO2-and-co2] for further discussion.

The table below lists some of the parameters that may be prescribed on the REAC line. Note that the various *YIELD are for well-ventilated, post-flame conditions. There are options to predict various species yields in under-ventilated fire scenarios, but these special models still require the post-flame yields for CO, soot and any other species listed in the table.

Parameter	Type	Description	Unit	Default
ID	String	Identifier
C	Real	Number of carbon atoms in the fuel		3
H	Real	Number of hydrogen atoms in the fuel		8
O	Real	Number of oxygen atoms in the fuel		0
N	Real	Number of nitrogen atoms in the fuel		0
OTHER	Real	Number of other atoms in the fuel		0
MW_OTHER	Real	Average molecular weight of OTHER defaults to $\mathrm {N} _{2}$	g/mol	28
CO_YIELD	Real	The fraction of fuel mass converted into carbon monoxide	kg/kg	0
H2_YIELD	Real	The fraction of fuel mass converted into hydrogen	kg/kg	0
SOOT_YIELD	Real	Fraction of soot from the fuel. The fraction of fuel mass converted into smoke particulate.	kg/kg	0.01
SOOT_H_FRACTION	Real	Atom fraction of hydrogen in soot		0.1
HEAT_OF_COMBUSTION	Real	The amount of energy released per unit mass of fuel consumed	kJ/kg
EPUMO2	Real	Energy per unit mass oxygen. If the heat of combustion is not explicitly specified, it is calculated as: consumed $\mathrm {O} _{2}\times$ EPUMO2	kJ/kg	13100
IDEAL	Logical	Adjust for minor product yields		.FALSE.
VISIBILITY_FACTOR	Real	Visibility parameter		3
MASS_EXTINCTION_COEFFICIENT	Real	Visibility parameter	m²/kg	8700

IDEAL is a logical value indicating whether or not the EPUMO2 or HEAT_OF_COMBUSTION values represent values for complete combustion (.TRUE.) or for incomplete combustion (.FALSE.). If IDEAL=.TRUE., then FDS internally adjusts the resulting heat of combustion to account for products of incomplete combustion specified in CO_YIELD, H2_YIELD, and SOOT_YIELD.

A few sample REAC lines are given here, the values are for demonstration only:

 &REAC ID='methane', C=1., H=4. /
 &REAC ID='ethylene', C=2., H=4., SOOT_YIELD=0.05 /
 &REAC ID='propane', SOOT_YIELD=0.01, C=3., H=8.,
     HEAT_OF_COMBUSTION=46460., IDEAL=.TRUE. / 
 &REAC ID='propane', SOOT_YIELD=0.01, C=3., H=8.,
     HEAT_OF_COMBUSTION=46124., IDEAL=.FALSE. /
 &REAC ID='wood', SOOT_YIELD=0.02, O=2.5, C=3.4, H=6.2,
     HEAT_OF_COMBUSTION=17700 /
     Ritchie, et al., 5th IAFSS
 &REAC ID='polyurethane', SOOT_YIELD=0.1875, CO_YIELD=0.02775,
     C=1.0, H=1.75, O=0.25, N=0.065, OTHER=0.002427, MW=27.,
     HEAT_OF_COMBUSTION=25300., IDEAL=.TRUE. /
     Polyurethane flexible foam (means) from
     Tewarson SFPE Handbook 3rd ed,
     SFPE handbook table 3-4.14, p. 3-112.

CO production in under-ventilated fires

An algorithm has been implemented that computes the gas phase combustion as a two step reaction and that predicts the formation and destruction of CO. This algorithm is used when the parameter CO_PRODUCTION is set to .TRUE. on the MISC line:

&MISC CO_PRODUCTION=.TRUE. /

Even though the algorithm predicts CO formation and its eventual oxidation at elevated temperature, it cannot predict the post-flame yield of CO. For example, within a flashed over compartment, the algorithm predicts the elevated CO levels, but it cannot predict the CO concentration of the exhaust gases that exit the flaming region. Thus, even if using this model, you must specify the CO_YIELD that is expected of a well-ventilated fire.

Note that when active, this algorithm requires the use of three parameters for the mixture fraction instead of the two parameters used when it is disabled and will therefore increase run times and memory usage accordingly. If the simulation you are performing will not result in an under-ventilated fire, then there will be little if any benefit to enabling the CO production algorithm.

Flame extinction

FlameExtinctionCriteria

Modeling suppression of a fire due to the introduction of a suppression agent like $CO_{2}$ or water mist, or due to the exhaustion of oxygen within a compartment is challenging because the relevant physical mechanisms occur at length scales smaller than a single mesh cell.

Flames are extinguished due to lowered temperatures and dilution of the oxygen supply. A simple suppression algorithm has been implemented in FDS that attempts to gauge whether or not a flame is viable at the fuel-oxygen interface.

The default values for the limiting oxygen index and the critical flame temperature are 15% (volume fraction) and 1427 °C, respectively as shown in Figure media:FlameExtinctionCriteria.png.