%0 Journal Article %1 pitsch1998consistent %A Pitsch, Heinz %A Peters, Norbert %D 1998 %J Combustion and Flame %K prev %N 1-2 %P 26-40 %T A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects %V 114 %X A flamelet formulation for non-premixed combustion that allows an exact description of differential diffusion has been developed. The main difference to previous formulations is the definition of a mixture fraction variable, which is not related directly to any combination of the reactive scalars, but defined from the solution of a conservation equation 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 assumptions about the Lewis numbers for chemical species. The formulation is shown to be exact if the scalar dissipation rate is prescribed as a function of the mixture fraction. Different approximations of the scalar dissipation rate that had been derived from analytic solutions for special cases are investigated by varying the diffusion coefficient of the mixture fraction transport equation. As examples, counterflow flames of hydrogen and n-heptane, which have much larger and much smaller diffusivities than oxygen and nitrogen, are considered. It is shown that the use of equal thermal and mixture fraction diffusivities yields a sufficiently well-described flame structure and is therefore recommended for the definition of the mixture fraction diffusion coefficient. Finally, the possibility of using constant species Lewis numbers has been examined. It has been found 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 oxidizer temperature.

@article{pitsch1998consistent, abstract = {A flamelet formulation for non-premixed combustion that allows an exact description of differential diffusion has been developed. The main difference to previous formulations is the definition of a mixture fraction variable, which is not related directly to any combination of the reactive scalars, but defined from the solution of a conservation equation 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 assumptions about the Lewis numbers for chemical species. The formulation is shown to be exact if the scalar dissipation rate is prescribed as a function of the mixture fraction. Different approximations of the scalar dissipation rate that had been derived from analytic solutions for special cases are investigated by varying the diffusion coefficient of the mixture fraction transport equation. As examples, counterflow flames of hydrogen and n-heptane, which have much larger and much smaller diffusivities than oxygen and nitrogen, are considered. It is shown that the use of equal thermal and mixture fraction diffusivities yields a sufficiently well-described flame structure and is therefore recommended for the definition of the mixture fraction diffusion coefficient. Finally, the possibility of using constant species Lewis numbers has been examined. It has been found 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 oxidizer temperature.}, added-at = {2013-03-21T15:13:41.000+0100}, author = {Pitsch, Heinz and Peters, Norbert}, biburl = {https://www.bibsonomy.org/bibtex/2ed97c19de9569e16ce0c6b793047974d/itv}, interhash = {567df66fee06d6f9a8510102a54c891f}, intrahash = {ed97c19de9569e16ce0c6b793047974d}, journal = {Combustion and Flame}, keywords = {prev}, number = {1-2}, pages = {26-40}, timestamp = {2014-07-31T07:46:38.000+0200}, title = {A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects}, volume = 114, year = 1998 }