The steady flamelet approach models a turbulent flame brush as an ensemble of discrete, steady laminar flames, called diffusion flamelets. The individual diffusion flamelets are assumed to have the same structure as laminar flames in simple configurations, and are obtained by experiments or calculations. Using detailed chemical mechanisms, Ansys Fluent can calculate laminar opposed-flow diffusion flamelets for non-premixed combustion. The diffusion flamelets are then embedded in a turbulent flame using statistical PDF methods.
The advantage of the diffusion flamelet approach is that realistic chemical kinetic effects can be incorporated into turbulent flames. The chemistry can then be preprocessed and tabulated, offering tremendous computational savings. However, the steady diffusion flamelet model is limited to modeling combustion with relatively fast chemistry. The flame is assumed to respond instantaneously to the aerodynamic strain, and therefore the model cannot capture deep non-equilibrium effects such as ignition, extinction, and slow chemistry (like NOx).
Information pertaining strictly to the steady diffusion flamelet model is presented in the following sections:
For general information about the mixture fraction model, see Introduction.
In a diffusion flame, at the molecular level, fuel and oxidizer diffuse into the reaction zone. Here, they encounter high temperatures and radical species and ignite. More heat and radicals are generated in the reaction zone and some diffuse out. In near-equilibrium flames, the reaction rate is much faster than the diffusion rate. However, as the flame is stretched and strained by the turbulence, species and temperature gradients increase, and radicals and heat diffuse more quickly out of the flame. The species have less time to reach chemical equilibrium, and the degree of local non-equilibrium increases.
The steady diffusion flamelet model is suited to predict chemical non-equilibrium due to aerodynamic straining of the flame by the turbulence. The chemistry, however, is assumed to respond rapidly to this strain, so as the strain relaxes to zero, the chemistry tends to equilibrium.
When the chemical time-scale is comparable to the fluid mixing time-scale, the species can be considered to be in global chemical non-equilibrium. Such cases include NOx formation and low-temperature CO oxidation. The steady diffusion flamelet model is not suitable for such slow-chemistry flames. Instead, you can model slow chemistry using one of the following:
the Unsteady Diffusion Flamelet model (see The Unsteady Diffusion Flamelet Model Theory)
the trace species assumption in the NOx model (see Pollutant Formation)
the Laminar Finite-Rate model (see The Generalized Finite-Rate Formulation for Reaction Modeling), where the turbulence-chemistry interaction is ignored.
the EDC model (see The Eddy-Dissipation-Concept (EDC) Model)
the PDF transport model (see Composition PDF Transport).
Ansys Fluent can generate multiple steady diffusion flamelets over a range of strain rates to account for the varying strain field in your multi-dimensional simulation. If you specify the number of diffusion flamelets to be greater than one, diffusion flamelets are generated at scalar dissipation values as determined by Equation 8–53.
 | (8–53) |
where 
ranges from 1 up to the specified maximum number
of diffusion flamelets, 
is the initial
scalar dissipation at the stoichiometric mixture fraction 
from Equation 8–50, and 
is
the scalar dissipation step. Diffusion flamelets are generated until
either the maximum number of flamelets is reached, or the flamelet
extinguishes. Extinguished flamelets are excluded from the flamelet
library.
By default, 1D flamelet grids are discretized by clustering a fixed number of points about the stoichiometric mixture fraction, which is approximated as the location of peak temperature. Ansys Fluent also has the option for Automated Grid Refinement of steady diffusion flamelets, where an adaptive algorithm inserts grid points so that the change of values, as well as the change of slopes, between successive grid points is less than user specified tolerances.
When using automated grid refinement, a steady solution is calculated
on a coarse grid with a user specified Initial Number of
Grid Points in Flamelet (default of 
). At convergence, a new grid
point is inserted midway between a point 
and its neighbor 
if,
 | (8–54) |
where 
is the value for each temperature and species mass fraction at grid point
, 
is a user specified Maximum Change in Value Ratio
(default of 0.5), and 
(
) are the maximum (minimum) values over all grid points.
In addition a grid point is added if,
 | (8–55) |
where the slope 
is defined as,
 | (8–56) |
In Equation 8–55 and Equation 8–56, 
is a user specified Maximum Change in Slope Ratio
(default of 0.5), 
(
) are the maximum (minimum) slopes over all grid points, and 
is the mixture fraction value of grid point 
.
The refined flamelet is reconverged, and the refinement process is repeated until no further grid points are added by Equation 8–54 and Equation 8–55, or the user-specified Maximum Number of Grid Points in Flamelet (default of 64) is exceeded.
For non-adiabatic steady diffusion flamelets, Ansys Fluent follows the approach of [62], [464] and assumes that flamelet species profiles are unaffected by heat loss/gain from the flamelet. No special non-adiabatic flamelet profiles need to be generated, avoiding a very cumbersome preprocessing step. In addition, the compatibility of Ansys Fluent with external steady diffusion flamelet generation packages (for example, OPPDIF, CFX-RIF, RUN-1DL) is retained. The disadvantage to this model is that the effect of the heat losses on the species mass fractions is not taken into account. Also, the effect of the heat loss on the extinction limits is not taken into account.
After diffusion flamelet generation, the flamelet profiles are convoluted with the assumed-shape PDFs as in Equation 8–44, and then tabulated for look-up in Ansys Fluent. The non-adiabatic PDF tables have the following dimensions:
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During the Ansys Fluent solution, the equations for the mean mixture fraction, mixture fraction variance, and mean enthalpy are solved. The scalar dissipation field is calculated from the turbulence field and the mixture fraction variance (Equation 8–45). The mean values of cell temperature, density, and species mass fraction are obtained from the PDF look-up table.