Extended Shvab–Zel’dovich formulation for multicomponent-fuel diffusion flames

Abstract

In this paper an extension of the Shvab–Zel’dovich formulation is presented. This extended formulation, based on the Burke–Schumann kinetic mechanism, describes the combustion of multicomponent fuels in a diffusion flame in terms of mixture fraction and the excess enthalpy. Under the condition of Burke–Schumann kinetic mechanism, the multicomponent fuel is burned in a single flame. The model is applied to a diffusion flame generated by the burning of mixtures of n-heptane and hydrogen diluted in nitrogen in a counterflow configuration. Due to the very small ratio of the hydrogen molecular weight to the n-heptane molecular weight, small quantities of hydrogen (in terms of mass) in the mixture does not change significantly the properties related to the mass, like as the total heat released per unit of mass at the flame. However, properties related to the hydrogen mole fraction does change expressively with small quantities, like as the radiative energy loss from the hot region around the flame. The results show the flame properties as a function of the reciprocal scalar dissipation and hydrogen quantity in the mixture. It is observed that, by reducing the reciprocal scalar dissipation, the radiative energy loss decreases and by increasing the presence of the hydrogen, the sensitivity of the flame properties with the reciprocal scalar dissipation reduces. It is also revealed by the results, the effects of the potentiated preferential hydrogen mass diffusion in compositions in which nitrogen and n-heptane are the majority species, and the potentiated preferential n-heptane thermal diffusion in compositions in which nitrogen and hydrogen are the majority species, on the flame properties. Although, this work do not treat the extinction problem, the fluid dynamical results will be properly handled to provide information about the reciprocal scalar dissipation and the Liñán’s parameter necessary for future flame stability analyses.