9.2.1 Propagation of the Flame Front

In many industrial premixed systems, combustion takes place in a thin flame sheet. As the flame front moves, combustion of unburnt reactants occurs, converting unburnt premixed reactants to burnt products. The premixed combustion model thus considers the reacting flow field to be divided into regions of burnt and unburnt species, separated by the flame sheet.

The flame front propagation is modeled by solving a transport equation for the density-weighted mean reaction progress variable, denoted by $c$:

where
	$c$	=	mean reaction progress variable
	Sc $_t$	=	turbulent Schmidt number
	$S_c$	=	reaction progress source term (s $^{-1}$)

The progress variable is defined as a normalized sum of the product species,

where
	$n$	=	number of products
	$Y_i$	=	mass fraction of product species $i$
	$Y_{i, \rm eq}$	=	equilibrium mass fraction of product species $i$

Based on this definition, $c=0$ where the mixture is unburnt and $c=1$ where the mixture is burnt:

• $c=0$: unburnt mixture

• $c=1$: burnt mixture

The value of $c$ is defined as a boundary condition at all flow inlets. It is usually specified as either 0 (unburnt) or 1 (burnt).

The mean reaction rate in Equation  9.2-1 is modeled as [ 391]

where
	$\rho_u$	=	density of unburnt mixture
	$U_t$	=	turbulent flame speed

Many other models for turbulent flame speed exist [ 36], and can be specified using user-defined functions. More information about user-defined functions can be found in the separate UDF Manual.