Inherently multi-phase manifold-based combustion models of liquid fuel combustion: Redefinition of mixture fraction and interfacial conditions

Manifold-based combustion models greatly improve the computational cost of reacting flow CFD by projecting the thermochemical state onto a lower-dimensional space. For nonpremixed combustion, this lower-dimensional space is the mixture fraction. While well-defined for single-phase combustion, extensions of nonpremixed manifold models to liquid fuel combustion have seen limited success. Existing approaches use a single-phase combustion model with small adjustments; these include modifications to conserve energy due to evaporative cooling and redefinition of the mixture fraction to account for the non-unity fuel mass fraction at the droplet surface. In this work, a new approach is proposed that is inherently multi-phase. The mixture fraction is redefined to be a conserved scalar with a value of unity at the gas-liquid interface (i.e., droplet surface). Boundary conditions for unity mixture fraction are derived from the fundamental governing equations of species and enthalpy at the gas-liquid interface. Numerical experiments are conducted to demonstrate the capability of the model, and pathways to implementation into CFD and extension to multi-component liquid fuels are discussed.