## 7.8. The Flamelet Model

The flamelet concept [37] for non premixed combustion describes the interaction of chemistry with turbulence in the limit of fast reactions (large Damköhler number). The combustion is assumed to occur in thin sheets with inner structure called flamelets. The turbulent flame itself is treated as an ensemble of laminar flamelets that are embedded into the flow field.

The Flamelet model is a non equilibrium version of the classical “Burke-Schumann” limit. It adds new details to the simulation of combustion processes compared to other common combustion models for the price of the solution of only two scalar equations in the case of turbulent flow. An arbitrary number of intermediates may be specified as long as their laminar chemistry is known.

The main advantage of the Flamelet model is that even though detailed information of molecular transport processes and elementary kinetic reactions are included, the numerical resolution of small length and time scales is not necessary. This avoids the well-known problems of solving highly nonlinear kinetics in fluctuating flow fields and makes the method very robust. Only two scalar equations have to be solved independent of the number of chemical species involved in the simulation. Information of laminar model flames are pre-calculated and stored in a library to reduce computational time. On the other hand, the model is still restricted by assumptions like fast chemistry or the neglecting of different Lewis numbers of the chemical species.

The coupling of laminar chemistry with the fluctuating turbulent flow field is done by a statistical method. The PDF used can in principle be calculated at every point in the flow field by solving a PDF transport equation as shown by Pope and many others. The most often mentioned advantage of this method is that the nonlinear chemical source term needs no modeling. Even though the method avoids some modeling that is necessary if using moment closure, it still requires modeling of some of the most important terms, in particular, the fluctuating pressure gradient term and the molecular diffusion term. If combustion occurs in thin layers as assumed here, the molecular diffusion term is closely coupled to the reaction term and the problem of modeling the chemical source term is then shifted towards modeling the diffusion term.

However, there is no source term in the mixture fraction equation, which is the principal transport equation in the Flamelet model. Therefore, a presumed beta-PDF, which is a commonly accepted choice, is used here. Additionally, this avoids the extremely large computational efforts of calculating the PDF in 3D with a Monte Carlo method.

The following list outlines the assumptions made to derive the Flamelet model:

- Fast Chemistry

- Unity Lewis numbers for all species,

- Combustion is in the Flamelet Regime

- Two feed system, that is, fluid composition at boundaries must be pure “fuel,” pure “oxidizer” or a linear blend of them.

- Diffusion flames. For premixed or partially premixed combustion, the Flamelet model can be combined with a model for reaction progress. For details, see Burning Velocity Model (Premixed or Partially Premixed).

Fluid properties, including temperature and density, are computed from the mean composition of the fluid in the same way as for other combustion models, such as the Eddy Dissipation model.

The Flamelet model as implemented in CFX can be applied for non-adiabatic configurations. The only limitation is that changes in the composition of the fluid due to different temperature and pressure levels are not accounted for. However, the effect of heat loss and pressure on density and temperature is taken into account. For heat losses occurring in many combustion devices, the influence of heat losses on composition is sufficiently small to be neglected.

In a large number of industrial combustion devices, pure non-premixed combustion is less present than premixed or partly premixed combustion. In CFX, a model for premixed and partially premixed combustion is available, which involves the Flamelet model as a sub-model. For details, see Burning Velocity Model (Premixed or Partially Premixed).

Release 18.2 - © ANSYS, Inc. All rights reserved.