On the generalisation of the mixture fraction to a monotonic mixing-describing variable for the flamelet formulation of spray flames

International audienceSpray flames are complex combustion configurations that require the consideration of competing processes between evaporation, mixing and chemical reactions. The classical mixture- fraction formulation, commonly employed for the representation of gaseous diffusion flames, cannot be used for spray flames due to its non-monotonicity. This is a consequence of the presence of an evaporation source term in the corresponding conservation equation. By addressing this issue, a new mixing-describing variable, called effective composition variable η, is defined to enable the general analysis of spray-flame structures in composition space. This quantity combines the gaseous mixture fraction Zg and the liquid-to-gas mass ratio Z. This new expression reduces to the classical mixture-fraction definition for gaseous systems, thereby ensuring consistency. The versatility of this new expression is demonstrated in application to the analysis of counterflow spray flames. Following this analysis, the effective composition variable η is employed for the derivation of a spray-flamelet formulation. The consistent representation in both effective-composition space and physical space is guaranteed by construction and the feasibility of solving the resulting spray-flamelet equation in this newly defined composition space is demonstrated numerically. A model for the scalar dissipation rate is proposed to close the derived spray-flamelet equations.The laminar one-dimensional counterflow spray flamelet equations are numerically solved in the η-space and compared to the physical-space solutions. It is shown that the hysteresis and bifurcation characterizing the flame structure response to variations of droplet diameter and strain rate are correctly reproduced by the proposed composition-space formulation