Definition of a flamelet

The basic physical model is that of fast reactions occurring in thin quasi-one-dimensional reaction sheets with thickness less than the size of the smallest eddies in the flow. As discussed in Section 5.5, this picture will be valid for non-isothermal one-step reactions when the reaction rate constant k (T) is near zero at the ambient temperature, but very 

Given the thinness of a diffusion flamelet, it is possible to neglect as a first approximation curvature effects, and to establish a local coordinate system centered at the reaction interface. By definition, x is chosen to be normal to the reaction surface. Furthermore, because the reaction zone is thin compared with the Kolmogorov scale, gradients with respect to X2 and X3 will be much smaller than gradients in the x direction (i.e., the curvature is small).112 Thus, as shown in Fig. 5.18, the scalar fields will be locally onedimensional. 

more generally, to one-step reactions with a relatively weak dependency on T. This may occur in combusting flows where the adiabatic temperature rise is small for example, in a rich flame near extinction. 

Flamelet wrinkling will be caused by vorticity, which is negligible below the Kolmogorov scale. 

By definition, on the fuel side of the reaction zone f = 0, while on the oxidizer side f = 1. As illustrated in Fig. 5.19, when moving across the reaction zone from fuel to oxidizer the mixture fraction increases monotonically. 

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Because x appears as a parameter in the flamelet model, in numerical implementations a flamelet library (Pitsch and Peters 1998 Peters 2000) is constructed that stores T( , x ) forO < < 1 in a lookup table parameterized by ( ), (4, 2),and x - Based on the definition of a flamelet, at any point in the flow the reaction zone is assumed to be isolated so that no interaction occurs between individual flamelets. In order for this to be true, the probabilities of finding f = 0 and f = 1 must both be non-zero. 

Parametric investigations of turbulent combustion are based on the definition of a reduced flame radius 7 l (0 that corresponds to the slope of the pressure - t time curve. When the chemical reaction is localized in narrow flamelets (see. Borgi diagram. Fig. 1.4), the spherical volume of radius 7 l (0 is close to the balanced turbulent combustion products volume. For this case, the pressure ratios P = P t) obtained experimentally during the time of burning are used for calculating / l (0-The turbulent flame velocity 5t (often designated as Ut) can be denoted by... 

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