Derivation and Evaluation of a Multi-regime Spray Flamelet Model

The formulation of a comprehensive flamelet model to consider detailed chemical reaction mechanisms in the simulation of turbulent spray flames is a very challenging task due to the inherent multi-regime structure of spray flames. Non-premixed, premixed, and evaporation-controlled combustion regimes may be found in a single spray flame. Recently, attempts have been made to extend classical single regime flamelet models to more complex situations, where at least two combustion regimes coexist. The objective of this work is to develop a framework in which two-regime flamelet models can be described and combined in order to advance the development of a comprehensive flamelet model for turbulent spray flames. For this purpose, a set of spray flamelet equations in terms of the mixture fraction and a reaction progress variable is derived, which includes the evaporation, characterizing the spray flames, and which describes all combustion regimes appearing in spray flames. The two-regime and single regime flamelet equations available in the literature are retrieved from these multi-dimensional spray flamelet equations as special cases. The derived set of spray flamelet equations is then used to evaluate structures of laminar ethanol/air spray flames in the counterflow configuration in order to determine the significance of different combustion regimes. The present study concerns spray flames with no pre-vaporized liquid in the oxidizing gas phase, and it is found that only non-premixed and evaporation-controlled combustion regimes exist, so that premixed effects may be neglected. Moreover, an exact transport equation for the scalar dissipation rate is derived, which explicitly takes spray evaporation and detailed transport into account. This equation is then used to evaluate assumptions commonly adopted in the literature. The results show that the spatial variation of the mean molecular weight of the mixture may be neglected in the formulation of the mixture fraction, but it may be significant for its scalar dissipation rate. The assumption of unity Lewis number may lead to non-physical values of the scalar dissipation rate of the mixture fraction, whereas the use of a mass-averaged diffusion coefficient of the mixture is a good approximation for the spray flames under investigation.