Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds

Abstract

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.

RANS modelling of a lifted H2/N2 flame using an unsteady flamelet progress variable approach with presumed PDF

“…We actually need a parameter giving a physical sense of the time advancement of the unsteady flamelet solution. A good candidate may be a progress variable defined as a linear combination of species mass fractions of combustion products as it has been proposed many times for the construction of tabulated chemistry manifolds based on steady flamelets [36][37][38][39]. In the present case, an immediate choice would be to define Y c as the mass fraction of water vapour: Y c = Y H 2 O .…”

“…On the other hand, when using approximated diffusion flamelets, Michel et al use a mean source term including both chemical reaction and molecular diffusion: we will denote this termẎ c (which is zero for steady flamelets where diffusion and reaction counterbalance). The principle of SFPV models is clearly detailed in [35], and such models have been introduced and used by different authors with different names: for instance FGM [36], FPI [37,38] or REDIM [39]. In SFPV models [35], the progress variable Y c -corresponding to the value of mass fractions of combustion products either in steady laminar flames or in the inert mixture (extinguished flames) -is a way to substitute the scalar dissipation rate χ in the parametrisation of the steady-flamelet models, previously expressed in terms of (Z, χ).…”

A priori investigation of PDF-modeling assumptions for a turbulent swirling bluff body flame (‘SM1’)

“…In a reduced scalar approach (e.g. FGM [12], FPI [13], REDIM [14] and ADF-PCM χ [15], flamelet -progress variable (FPV) [16]), the 'progress' of the reaction is modeled by e.g. a 'progress variable' (c [15][16][17] or sensible enthalpy [10]) or a 'reaction progress parameter' λ [18] [in [15], a third additional property, the scalar dissipation rate χ, is also considered].…”

On-demand generation of reduced mechanisms based on hierarchically extended intrinsic low-dimensional manifolds in generalized coordinates

“…[2][3][4]) have been developed and improved continuosly. Examples are the partial-equilibrium- [5] and steady-state approximations [6], the method of rate-controlled constrained equilibrium (RCCE) [7,8], computational singular perturbation (CSP) [9][10][11][12][13][14][15][16], the method of integral or invariant manifolds (MIM) [17][18][19][20], the functional iteration method (FIM) [21][22][23], flamelet generated manifolds (FGM) [24], trajectory-generated manifolds (TGLDM) [25,26], PIC-/ICE-PIC-Methods [27][28][29] and different concepts for reaction-diffusion manifolds (e.g. [30,31]).…”