A comprehensive model for non-adiabatic multi-modal combustion using physically-derived reduced-order manifolds

Generally, turbulent combustion models fall into a hierarchy of model complexity based on the assumptions made about the underlying combustion processes. Models that make no assumption about the underlying combustion processes, such as Transported PDF (TPDF) methods, can model more complex combustion phenomena, specifically multi-modal combustion with heat losses, but this generality comes with increased computational cost. Manifold methods, including "flamelet"-like models, are more computationally efficient but at the cost of generality, usually restricting the combustion processes to a single asymptotic mode under adiabatic conditions and relying on one-dimensional component problems. Recent work from our group has attempted to increase the generality of manifold methods and has resulted in two-dimensional manifold equations for non-adiabatic premixed combustion, non-adiabatic nonpremixed combustion, and adiabatic multi-modal combustion. In this work, a new, more general manifold method is developed, capable of describing non-adiabatic multi-modal combustion. The approach relies on a three-dimensional manifold consisting of mixture fraction, a generalized progress variable, and a generalized enthalpy deficit parameter, which excludes the influence of mixture fraction and progress variable variations, defined on the unit cube. The governing equations for the thermochemical state on the manifold are derived, and the two-dimensional manifolds mentioned previously are shown to be recovered in appropriate limits.