Unified Manifold-Based Approach to Modeling Combustion-Affected Turbulence

Abstract

Turbulent combustion is characterized by nonlinear, multi-scale interactions of turbulence and combustion and is significantly important in practical combustion systems. Predictive computational models must capture such interactions in a complete and physically accurate way. The turbulence dynamics can be significantly affected by combustion heat release when the combustion-induced dilatation dominates the turbulence-induced strain, which occurs in regions of low Karlovitz number in turbulent premixed combustion. At low Karlovitz number, foundations of conventional turbulence models developed for non-reacting flows become invalid. Typical zone-conditioned approaches presume a zero Karlovitz number and are not appropriate for finite Karlovitz numbers in the presence of mean shear. This dissertation aims to investigate the detailed physical processes by which combustion heat release affects turbulence and develop an integrated modeling framework that generally accounts for the influence of combustion on turbulence. To model flames at any finite Karlovitz number, a manifold-based approach that relies on conditionally averaging the momentum transport equation with respect to a progress variable has been developed. Conventional turbulence modeling approaches based on traditional unconditional averaging are limited in accurately capturing combustion heat release effects since they must capture both the direct influence of combustion heat release on turbulence and the flame dynamics. Conditioning on a flame structure variable introduces information about the local flame structure, and the flame dynamics are embedded into the conditioning. The conditional momentum transport equation includes numerous unclosed terms that evolve in both physical and phase spaces and show fundamentally different behaviors at low and high Karlovitz numbers. In this dissertation, closure models for those unclosed terms are developed and validated against Direct Numerical Simulation databases of spatially-evolving turbulent premixed planar jet flames at low and high Karlovitz numbers. Each of the models considers the relative contributions of combustion heat release and turbulent shear to account for their finite-rate competition at finite flame thickness. The models are shown to capture the influence of combustion heat release on turbulence including the correct conditional dependence. Finally, the counter-gradient-transport behavior of the scalar flux at low Karlovitz number is predicted in a posteriori analysis.