A CONSISTENT FLAMELET FORMULATION FOR NON-PREMIXED COMBUSTION CONSIDERING DIFFERENTIAL DIFFUSION EFFECTS

A flamelet formulation for non-premixed combustion that allows an exac t description of differential diffusion has been developed. The main d ifference to previous formulations is the definition of a mixture frac tion variable, which is not related directly to any combination of the reactive scalars, but defined from the solution of a conservation equ ation with an arbitrary diffusion coefficient and appropriate boundary conditions. Using this definition flamelet equations with the mixture fraction as the independent coordinate are derived without any assump tions about the Lewis numbers for chemical species. The formulation is shown to be exact if the scalar dissipation rate is prescribed as a f unction of the mixture fraction. Different approximations of the scale r dissipation rate that had been derived from analytic solutions for s pecial cases are investigated by varying the diffusion coefficient of the mixture fraction transport equation. As examples, counterflow flam es of hydrogen and n-heptane, which have much larger and much smaller diffusivities than oxygen and nitrogen, are considered. It is shown th at the use of equal thermal and mixture fraction diffusivities yields a sufficiently well-described flame structure and is therefore recomme nded fur the definition of the mixture fraction diffusion coefficient. Finally, the possibility of using constant species Lewis numbers has been examined. It has been hound that once an appropriate set of Lewis numbers is determined, good results are achieved over wide ranges of the parameters. such as scalar dissipation rate, pressure, and oxidize r temperature. (C) 1998 by The Combustion Institute.