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16.2.1 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 $c$:


 \frac{\partial}{\partial t} (\rho c) + \nabla \cdot ( \rho {... ...ot \left( \frac{\mu_t}{{\rm Sc}_t} \nabla c \right) + \rho S_c (16.2-1)


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,


 c = \frac{\displaystyle{\sum_{i=1}^n} Y_i} {\displaystyle{\sum_{i=1}^n} Y_{i, \rm eq}} (16.2-2)


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:

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  16.2-1 is modeled as [ 415]


 \rho S_c = \rho_u U_t \vert\nabla c\vert (16.2-3)


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

Other mean reaction rate models exist [ 42], and can be specified using user-defined functions. See the separate UDF Manual. for details about user-defined functions.


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