Laminar diffusion flamelet models in non-premixed turbulent combustion

Abstract

The laminar flamelet concept views a turbulent diffusion flame as an ensemble of laminar diffusion flamelets. Work relevant to the flamelet concept is spread over various fields in the literature: laminar flame studies, asymptotic analysis, theory of turbulence and percolation theory. This review tries to gather and integrate this material in order to derive a self-consistent formulation. Under the assumption of equal diffusivities a coordinate-free formulation of the flamelet structure is given. This assumption is relaxed and flow dependent effects are considered. It is shown that the steady laminar counterflow diffusion flame exhibits a very similar scalar structure as unsteady distorted mixing layers in a turbulent flow field. Therefore the counterflow geometry is proposed to be the most representative steady flow field to study chemistry models and molecular transport effects in laminar flamelets. The conserved scalar model is interpreted as the most basic flamelet structure. Non-equilibrium calculations are reviewed. The coupling between non-equilibrium chemistry and turbulence is achieved by the statistical description of two parameters: the mixture fraction and the instantaneous scalar dissipation rate. The hypothesis of statistical independence of these two parameters is discussed. Calculation methods for the marginal distributions are reviewed. It is shown how local quenching of diffusion flamelets leads to a reduction of burnable flamelets. However, there are burnable flamelets in a turbulent flame which are not reached by an ignition source. This phenomenon is described by percolation theory. Complementary approaches related to local quenching effects and connectedness are combined to derive criteria for the stabilization of lifted flames and to blow out. Further applications of the flamelet concept are reviewed and work to be done is discussed.