Physically-derived reduced-order manifold-based modeling for multi-modal turbulent combustion

Abstract Turbulent combustion models can be divided into two broad classes: models that make no assumption about the underlying combustion processes and models that constrain the underlying combustion processes to some a priori presumed reduced-order manifold. The former class of models, including the Transported PDF (TPDF) approach and the Linear Eddy Model (LEM), is by nature more general but comes at increased computational cost. The latter class of models, including “flamelet”-like models and Conditional Moment Closure (CMC), is computationally more efficient albeit with the need to assume something about the underlying combustion processes a priori, traditionally limiting combustion processes to a single asymptotic mode. In this work, a new turbulent combustion model is developed that breaks this inherent trade-off and enables a computationally efficient description of multi-modal combustion. The model is constructed by first postulating that all (adiabatic, isobaric, two-stream) combustion processes can be described with a two-dimensional space whose coordinates are a mixture fraction and a generalized progress variable. The governing equations for the species mass fractions and temperature are then projected onto this two-dimensional manifold through a coordinate transformation to provide the evolution equations for the thermochemical state on the manifold; this approach results in an equilibrium manifold formulation. An explicit transport equation for the generalized progress variable is derived through the choice of a (set of weighted) arbitrary reference species and the functional dependence of the reference species on the generalized progress variable. The approach can accommodate both unity Lewis numbers and differential diffusion without issue. The mode of combustion is encoded into three scalar dissipation rates (the mixture fraction dissipation rate, the generalized progress variable dissipation rate, and the cross-dissipation rate), and the asymptotic modes of combustion are recovered under appropriate limits. However, the relative ease at which the nonpremixed limit is recovered depends on the reference species. Alternatively, the evolution of the thermochemical state on the manifold can be derived by conditionally filtering (or averaging) the governing equations with respect to the manifold coordinates, resulting in a non-equilibrium manifold formulation. Simplification of the non-equilibrium manifold formulation to the equilibrium manifold formulation reveals the implicit assumptions inherent to the equilibrium manifold formulation. A new solver PDRs is developed for solving the manifold equations, and example solutions demonstrate the ability of the model to describe general multi-modal combustion phenomena as the scalar dissipation rates are varied including not only the asymptotic modes of combustion but also partially premixed and stratified premixed combustion coupled or uncoupled with autoignition. The paper concludes with a discussion of open challenges for integrating the model with Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) approaches.