Stationary laminar flamelet model

Generally, near the stoichiometric surface, both terms in (5.268) are large in magnitude and opposite in sign (Peters 2000). A quasi-stationary state is thus quickly established wherein the accumulation term on the left-hand side is negligible. The stationary laminar flamelet (SLF) model is found by simply neglecting the accumulation term, and ignoring the time dependency of x(f, t)  

given an appropriate form for /(f), the SLF model can be solved to find 7(f) with boundary conditions 7(0) = 7(1) = 0.116 Note that if, SV(0, f) = 0, the SLF model admits the solution 7(f) = 0, which corresponds to a non-reacting system (i.e., flame extinction ). Likewise, when /(f) Sy(Y, f), the solution will be dominated by the diffusion term so that 7(f) 0. In the opposite limit, the solution will be dominated by the 

114 This procedure is similar to the one discussed in Section 5.4 for equilibrium chemistry where the spatial information is contained only in the mixture fraction. 

115 In this equation, Y should be replaced by the conditional expected value of Y given f = f However, based on the structure of the flamelet, it can be assumed that the conditional PDF is a delta function centered at T(f, r). 

116 The SLF model generates a two-point boundary-value problem for which standard numerical techniques exist. 

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