In order to reduce the computational cost of flame simulations, several methods have been developed during the last decades, which simplify the description of the reaction kinetics. Most of these methods are based on partial-equilibrium and steady-state assumptions, assuming that most chemical processes have a much smaller time scale than the flow time scale. These assumptions, however, give poor approximations in the ‘colder’ regions of a flame, where transport processes are also important. The method presented here, can be considered as a combination of two approaches to simplify flame calculations, i.e. a flamelet and a manifold approach. The method, to which we will refer as the Flamelet-Generated Manifold (FGM) method, shares the idea with flamelet approaches that a multi-dimensional flame may be considered as an ensemble of one-dimensional flames. The implementation, however, is typical for manifold methods: a low-dimensional manifold in composition space is constructed, and the thermo-chemical variables are stored in a database which can be used in subsequent flame simulations. In the FGM method a manifold is constructed using one-dimensional flamelets. Like in other manifold methods, the dimension of the manifold can be increased to satisfy a desired accuracy. Although the method can be applied to different kinds of flames, only laminar premixed flames are considered here. Since the major parts of convection and diffusion processes are present in one-dimensional flamelets, the FGM is more accurate in the ‘colder’ zones of premixed flames than methods based on local chemical equilibria. Therefore, less controlling variables are sufficient to represent the combustion process. Test results of one and two-dimensional premixed methane/air flames show that detailed computations are reproduced very well with a FGM consisting of only one progress variable apart from the enthalpy to account for energy losses.

Flamelet based chemical reduction techniques are very promising methods for efficient and accurate modeling of premixed flames. Over the years the Flamelet Generated Manifold (FGM) technique has been developed by the Combustion Technology Group of Eindhoven University of Technology. Current state-of-the-art of FGM for the modeling of premixed and partially-premixed flames is reviewed. The fundamental basis of FGM consists of a generalized description of the flame front in a (possibly moving) flame-adapted coordinate system. The basic nature of the generalized flamelet model is that effects of strong stretch in turbulent flames are taken into account by resolving the detailed structure of flame stretch and curvature inside the flame front. The generalized flamelet model, which forms the basis on which FGM is built, is derived in Part I. To be able to validate numerical results of flames obtained with full chemistry and obtained from FGM, it is important that the generalized flamelet model is analyzed further. This is done by investigating the impact of strong stretch, curvature and preferential diffusion effects on the flame dynamics as described by the local mass burning rate. This so-called strong stretch theory is derived and analyzed in Part I, as well as multiple simplifications of it, to compare the strong stretch theory with existing stretch theories. The results compare well with numerical results for flames with thin reaction layers, but described by multiple-species transport and chemistry. This opens the way to use the generalized flamelet model as a firm basis for applying FGM in strongly stretched laminar and turbulent flames in Part II. The complete FGM model is derived first and the use of FGM in practice is reviewed. The FGM model is then validated by studying effects of flame stretch, heat loss, and changes in elements, as well as NO formation. The application to direct numerical simulations of turbulent flames is subsequently studied and validated using the strong stretch theory. It is shown that the generalized flamelet model still holds even in case of strong stretch and curvature effects, at least as long as the reaction layer is dominated by reaction and diffusion phenomena and not perturbed too much by stretch related perturbations. The FGM model then still performs very well with a low number of control variables. Turbulent flames with strong preferential diffusion effects can also be modeled efficiently with an FGM model using a single additional control variable for the changes in element mass fractions and enthalpy. Finally FGM is applied to the modeling of turbulent flames using LES and RANS flow solvers. For these cases, the flame front structure is not resolved anymore and unresolved terms need to be modeled. A common approach to include unresolved turbulent fluctuations is the presumed probability density function (PDF) approach. The validity of this FGM-PDF approach is discussed for a few test cases with increasing level of complexity

In the recently introduced flamelet-generated manifold (FGM) method the ideas of the manifold and the flamelet approach are combined: a manifold is constructed using one-dimensional (1D) flamelets. In this paper the effect of flame stretch on the accuracy of the FGM method is investigated. In order to isolate the effect of flame stretch, premixed methane/air counterflow flames are simulated. In the case of unit Lewis numbers, a 1D manifold is sufficient to model the main effects of flame stretch. A manifold with two progress variables reproduces the results computed using detailed kinetics almost exactly. When non-unit Lewis numbers are used, the enthalpy and element composition of the burnt mixture change, which may influence the mass burning rate significantly. If these composition changes are included in the manifold using one additional controlling variable, the results agree well with detailed computations.