A ghost-fluid method for large-eddy simulations of premixed combustion in complex geometries

Large-eddy simulation of premixed combustion is a computational challenge, because complex diffusion and reaction processes often occur in very thin layers. The interaction of these processes with turbulence determines the main properties of the flame brush, such as its burning velocity or its thickness. In turbulent flows, the large vortices wrinkle the flame brush and increase its surface, while the small scales may penetrate into the flame brush and increase its thickness. In both cases, the turbulence leads to an increase in the burning velocity. This feature has to be captured by the combustion model. Even if the turbulent scales increase the flame thickness, the flame brush remains difficult to resolve on LES meshes. Numerically, the premixed flame brush is very close to an interface, but its non-zero thickness must be taken into account to represent the proper flame-turbulence interactions. In state-of-the-art combustion models, the issue of thin flames is overcome in very different ways. The Thickened-Flame model (TFLES) (Colin et al. 2000) artificially thickens the flame brush and the source terms in the species, and energy equations are corrected to recover the right burning velocity. The thickening factor that is needed to resolve the flame on a usual unstructured mesh is of the order of 20. This factor can be decreased slightly if naturally thicker quantities are used to represent the flame. This is the case in flame surface density approaches (Boger et al. 1998), but the thickening factor remains large. Instead of transporting reacting scalars, the flame can also be described using a flamelet hypothesis. That is, the reaction zone in the flame is considered to retain a laminar structure. The problem is then reduced to finding the position of the thin reaction layer. This is the principle of the G-equation model (Williams 1985; Peters 2000) in which a level set technique is used to track accurately the flame front. The displacement velocity of the level set is usually given by a model based on asymptotic analysis or experimental correlations (Peters 2000; Pitsch 2002). Then the level set has to be coupled to the Navier-Stokes solver by imposing the temperature profile in the flame brush. Often, Navier-Stokes solvers are not able to deal with large density and momentum gradients, and the imposed temperature profile has to be resolved on more than one, typically on the order of five cells. In all the described models, the flame brush is more or less thickened, and the interactions with the smallest resolved scales are modified. The proposed method overcomes this artificial thickening using a numerical method that better couples the level set technique and the Navier-Stokes solver. This method is based on the Ghost-Fluid Method (GFM) (Fedkiw et al. 1998), which tracks discontinuities without introducing any smearing or numerical instabilities. While the original GFM has been developed to track infinitely