ECFM Models with LES

Using the ECFM-3Z or ECFM-CLEH model in conjunction with any LES turbulence model activates a new equation for modelling the subgrid scale (SGS) flame surface density.

$T_{res}$ is the resolved transport:

$T_{sgs}$ is the unresolved transport plus the molecular diffusion term:

$P$ is the laminar propagation (where $n$ is the unit vector normal to the flame front):

$S_{res}$ is the resolved tangential strain:

$C_{res}$ is the resolved curvature:

$C_{sgs}$ is the unresolved curvature:

where $\beta$ and $c^{*}$ are model constants. ${\mathrm{\Sigma }}_{lam}$ is the laminar part of the flame surface density:

$S_{sgs}$ is the unresolved tangential strain:which is a function of the non-dimensional parameters $\frac{{\hat{u}}^{\prime }}{S_l},\frac{\hat{\mathrm{\Delta }}}{{\delta }_l}$ where the ^ symbol indicates the combustion filter size: the species, enthalpy and flame surface density equations are filtered at this filter size inside the flame. The Intermittent Turbulent Net Flame Stretch (ITNFS) function $\mathrm{\Gamma }$ in Eqn. (3899), models the effect of flame wrinkling by all vortices and is a function of the unresolved turbulence scales. Colin et al. [810] showed that vortices smaller than the turbulent flame brush $l_t$ are unable to wrinkle the flame. Therefore, it is necessary that the input values for $\mathrm{\Gamma }$ are filtered with a filter greater than or equal to $l_t$ . In other words, $\mathrm{\Delta }\approx l_t$ .

Near the walls, the flames are quenched by $$\begin{gathered} q_{wall \\ } \end{gathered}$$ :where $q_w$ is the wall quenching factor and $f_v$ is the Van Driest damping function (see Eqn. (1389)).