## 7.13. Extended Coherent Flame Model (ECFM)

The Extended Coherent Flame Model (ECFM) shares the framework for premixed or partially premixed combustion with the Burning Velocity Model (BVM). Transport equations are solved for mean mixture fraction (Equation 7–32), variance of mixture fraction (Equation 7–33) and for either reaction progress (Equation 7–41) or weighted reaction progress (Equation 7–45).

In order to describe the intensity and the location of the reaction zone the flame surface density is introduced, which is defined as the area of flame surface per unit volume. The physical units are that of an inverse length (for example, [1/m]). The reaction source in Equation 7–41 or Equation 7–45 is defined in terms of flame surface density as:

| (7–70)

The flame surface density is calculated by solving a transport equation:

| (7–71)

The source terms and their physical meanings are as follows:

- Flame surface production by turbulent stretch

  | (7–72)

- Flame surface production by mean flow dilatation

  | (7–73)

- Thermal expansion and curvature

  | (7–74)

- Destruction due to consumption

  | (7–75)

where the typical (default) values for and are 1.6 and 1.0, respectively.

Note that the production term and the destruction term are formulated in terms of the volumetric reaction progress , in contrast to the specific reaction progress (Favre-average):

| (7–76)

The flame surface density is a volumetric quantity, i.e. flame surface area per unit volume. In order to be able to use the generic machinery for solving transport the specific flame surface density, , is introduced as an auxiliary variable:

| (7–77)

which can be rewritten as

| (7–78)

The specific flame surface density is the flame surface area per unit mass. Rewriting Equation 7–71 in terms of leads to:

| (7–79)

The volumetric transport Equation 7–71 and the specific transport Equation 7–79 are equivalent. The specific form has the advantage that it has the same structure as other transport equations, which are also in specific form, and therefore Equation 7–79 may be solved using the same discretization schemes and numerical algorithms. The flame surface density becomes a dependent variable and is calculated according to Equation 7–77.

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