Flamelet models

The results reproduced from Ref. [28] and presented in Figure 7.1.9 show that the internal structure of the "flamelets" within the studied flames displays strong departures from both unstretched laminar flamelet and stretched counterflow flamelets. Figure 7.1.9 supports the picture of the perturbed flamelet model recently introduced in Ref. [29]. In this model, depending on the local value of the ratio of laminar flame thickness and... 

A. Mura, F. Galzin, and R. Borghi 2003, A unified PDF-flamelet model for turbulent premixed combustion. Combust. Sci. Technol. 175 (9) 1573-1609. 

Qualitative comparison of the inclined structure of thin layers of high scalar dissipation in a piloted CH4/air jet flame as revealed by (a) mixture fraction imaging, (b) LES with a steady flamelet library (a and b are adapted from Kempf, A. Flemming, F., and Janicka, ]., Proc. Combust. Inst, 30, 557, 2005. With permission.), and (c) LES with unsteady flamelet modeling. (Adapted from Pitsch, H. and Steiner, H., Proc. Combust. Inst., 28, 41, 2000. With permission.)... 

At present, there exists no completely general RANS model for differential diffusion. Note, however, that because it solves (4.37) directly, the linear-eddy model discussed in Section 4.3 can describe differential diffusion (Kerstein 1990 Kerstein et al. 1995). Likewise, the laminar flamelet model discussed in Section 5.7 can be applied to describe differential diffusion in flames (Pitsch and Peters 1998). Here, in order to understand the underlying physics, we will restrict our attention to a multi-variate version of the SR model for inert scalars (Fox 1999). 

The governing equation for the flamelet model is then found starting from a change of variables 113... 

In almost all reported applications of the flamelet model, f and x have been assumed to be independent so that the joint PDF can be written in terms of the marginal PDFs ... 

Figure 5.20. The flamelet model requires the existence of unmixed regions in the flow. This will occur only when the mixture-fraction PDF is non-zero at = 0 and = 1. Normally, this condition is only satisfied near inlet zones where micromixing is poor. Beyond these zones, the flamelets begin to interact through the boundary conditions, and the assumptions on which the flamelet model is based no longer apply.

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. 

Thus, the flamelet model is applicable only in regions of the flow where fluctuations are large, i.e, the variance must satisfy... 

As shown in Fig. 5.20, such regions normally occur only near the inlet zones where micromixing is poor. Further downstream, interaction between flamelets will become significant, and the assumptions on which the flamelet model is based will no longer apply.117 Reactors with recirculation zones are also problematic for flamelet models. For these reactors, partially reacted fluid is brought back to mix with the feed streams so that the simple non-premixed flow model no longer applies. 

This is rarely done in practice. For example, all commonly used models ignore possible effects of chemical reactions on the scalar-mixing process. Compare this with the flamelet model, where mixing and reactions are tightly coupled. 

This model is consistent with (6.67), and can be seen as a multi-variate version of the IEM model. The role of the second term (eC 1) is simply to compensate for the additional diffusion term in (6.91). Note that, like with the flamelet model and the conditional-moment closure discussed in Chapter 5, in the FP model the conditional joint scalar dissipation rates ( ap ip) must be provided by the user. Since these functions have many independent variables, and can be time-dependent due to the effects of transport and chemistry, specifying appropriate functional forms for general applications will be non-trivial. However, in specific cases where the scalar fields are perfectly correlated, appropriate functional forms can be readily established. We will return to this question with specific examples below. 

Peters, N. (1984). Laminar diffusion flamelet models in non-premixed turbulent combustion. Progress in Energy and Combustion Science 10, 319-339. 

This combustion model benefits from the low calculation time and memory usage of a flamelet model and is thought to improve the accuracy of gas-phase species and temperature predictions due to the use of a reaction progress variable. Moreover, turbulence-chemistry interactions are taken into account in a physical way. 

The use of laminar flamelet combustion models within FDS have been studied by Yang et al. [42] and Kang and Wen [43], Unfortunately, the performance or advantage over the simple flame-sheet model in large-scale fire simulation was not demonstrated in these studies. In full-scale calculations, the mixture fraction and temperature fields close to the flame sheet have overshoots, caused by the second-order transport scheme. It is still unclear how the laminar flamelet models that require both second and first moments of the local mixture fraction field could work in this situation. 

Yang, R., Weng, W.G., Fan, W.C., and Wang, Y.S. Subgrid scale laminar flamelet model for partially premixed combustion and its application to backdraft simulation. Fire Safety Journal, 2005. 40(2), 81-98. 

J.M. Duclos, D. Veynante and T. Poinsot, A Comparison of Flamelet Models for Premixed Turbulent Combustion, Comb, and Flame 95 (1993) 101. 

A 2-D CFD model has been set up using FLUENT4.5 in a joint EU JOULE project with FLUENT and ALSTOM. As turbulence models the k- model and Reynolds Stress model (RSM) have been applied. As chemistry models a chemical equilibrium model has been applied and on the other hand two models describing finite reaction chemistry, i.e. the laminar flamelet model and the reaction progress variable model. The comparison between experiments and the numerical results from the three chemistry models show that the chemical equilibrium model is sufficient to predict the combustion of LCV gas at elevated pressures, since deviation from chemical equilibrium is small due to the fast reactions. Hence no improvements are expected and have been observed from kinetically limited models. The RSM with constants Cl and C2 in the pressure-strain term proposed by Gibson and Younis [17] seems to yield the best predictions, however, the influence of the type of turbulence model (RSM or k- e) on the species concentrations and temperature predictions is not very large. 

Liew, S.K., Bray, K.M.C. and Moss, J.B. (1984), A stretched laminar flamelet model of turbulent non-premixed combustion. Combust. Flame, 56, 199. 

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