# 4.12.3. Flamelet Combustion Model

The use of a flamelet-based combustion model requires generation of a flamelet table, in which details of the fire chemistry have been precomputed. See Tabulated Material Properties for more details on how to generate a flamelet-based model for a particular simulation scenario.

This flamelet model encapsulated in the table will contain a number simplifications of the physics in order to make the problem tractable. A common simplification, for example, is that the scenario is decomposable into a single, fixed oxidizer state (commonly called a “stream”) and a single, fixed fuel state. The additional states would require a different flamelet model to be constructed, resulting in a different table, and more transport equations to be described in fuego. For example, a second mixture fraction would need to be solved if an extra inlet with a diluted mixture of heptane was added to a previously pure heptane fire problem.

## 4.12.3.1. Equations describing flamelet-based fire scenarios

An example set of an equations to solve for a flamelet case is

    # Sierra > Fuego Procedure > Fuego Region
    Begin Solution Options
      Activate Equation Mixture_Fraction
      Activate Equation Enthalpy
      Activate Equation Conserved_Enthalpy
      Activate Equation Progress_Variable
      Activate Equation Turbulent_Kinetic_Energy

      Begin Turbulence Model Specification
        Turbulence Model = KSGS
      End

      ...

    End

Note

The buoyancy reference state will still need to correspond to the flamelet reference values, usually air with zero heat loss.

No specific options are required in solution options for the flamelet model, other than specifying an appropriate set of equations. Options describing the flamelet are defined in the table creation process and in the Tabulated Material Properties section of the input file. Equations you may want to solve:

> - `Mixture_Fraction` - Necessary for all flamelet models. Solves transport of the first fuel mixture fraction when using a flamelet combustion model. With a soot model, it’s common to add a sink term to the equation representing carbon leaving the gas-phase and becoming soot, see Aksit-Moss SNL soot model.

> - `Enthalpy` - Solves conservation for `enthalpy` and activates a post-processor utility to compute `temperature` after each solve. Radiative heat loss due to gas radiation and soot can be added as well, using MPMD Radiation for radiative heat loss. Wall heat loss can be included in two forms. If the temperature of the wall is somewhere between the temperature of a fully burning or fully extinguished flame, then an enthalpy defect heat loss model can capture the heat loss (or gain, potentially) due to the wall. If this is not the case, then a boundary heat loss model would need to be added.

> - `Conserved_Enthalpy` - Solves transport for conserved enthalpy—in other words, the enthalpy without loss terms. This equation is part of the heat loss model used by the table. For an enthalpy defect model, the difference between the enthalpy and conserved enthalpy is used a measure of the integrated heat loss that a fluid parcel has undergone. This can also be used with the boundary heat loss model to describe temperature changes in the reference states of the flamelet model. These two models can also be combined to describe both effects in a “5-dimensional” model, see Nonadiabatic Property Table Generation. It’s important to understand which heat loss effects are encapsulated in the underlying flamelet model as some physical effects may not be able to be captured with the simpler heat loss model. More complicated heat loss models maybe prohibitively expensive and less frequently used.

> - `Progress_Variable` - Solves transport of an arbitrary scalar quantity. Source terms can be attached to this equation to model for instance the number density and mass fraction of soot in the Aksit-Moss SNL soot model. Note that these progress variables are meant to be only weakly coupled with the flow and chemistry, modeling relatively slowly evolving quantities like soot or NOX. This is a different (but related) definition of progress variable compared to what is used in a flamelet-progress variable combustion model.

> - `Turbulent_Kinetic_Energy` - Solves the transport equation for the subgrid turbulent kinetic energy, with closure models for higher degree moment terms. This is part of the large-eddy simulation modeling suite and is not necessary for a flamelet calculation. This equation specification is also used to describe to overall turbulent kinetic energy in a RANS context. An algebraic model like Smagorinsky can also be used to avoid solving this equation, with modeling implications.

> - `Scalar_Variance` - Solves the transport equation for the subgrid scalar variance, with closure models for higher degree moment terms. An algebraic model is used if this equation is not solved. In a RANS context, this equation will instead model the overall scalar variance.

## 4.12.3.2. Boundary condition modifications

Additional boundary conditions are needed for each extra transport equation being solved, except for the enthalpy and conserved enthalpy pair of equations. For those equations, it is only necessary to specify the temperature and the equivalent enthalpy defect and boundary heat loss will be computed given the current or reference composition of the gas at the boundary. An example Inflow boundary condition would be

    Begin inflow boundary condition on surface surface_4
        x_velocity = 0.0
        y_velocity = 0.0
        z_velocity = 0.1
        mixture_fraction = 1.0
        scalar_variance = 1.0e-6
        turbulent_kinetic_energy = 1.0e-6
        temperature = 300.0
        progress_variable soot_moles_per_mass = 0.0
        progress_variable soot_mass_fraction = 0.0
    End