Developments of Efficient Numerical Methods for Combustion Modeling with Detailed Chemical Kinetics

Abstract

Combustion modeling with detailed chemical kinetics has been challenging for decades. Even with the availability of supercomputing capability at petascale and beyond, direct numerical simulation (DNS) with detailed chemical kinetics remains infeasible. The major difficulty of utilizing detailed chemistry in combustion modeling comes from the high dimensional, nonlinear, and stiff ODE system which governs chemical reactions. Additionally, detailed calculations of transport properties at local thermodynamic conditions also consume significant computation powers and make combustion modeling with detailed chemistry prohibitive. In this study, advanced numerical methods are developed to improve the efficiency of combustion modeling from three aspects. (1) A correlated dynamic adaptive chemistry (CO-DAC) method is developed to provide on-the-fly chemical reductions with negligible computational costs, so that the ODE system can be significantly simplified by locally reduced chemical mechanisms. (2) A correlated dynamic adaptive chemistry and transport (CO-DACT) method is presented. It performs detailed calculations of the mixture-averaged model in correlated groups according to similarities of thermodynamic states in phase space. Redundant calculations of transport properties can be avoided in the CO-DACT method, which improves the computational efficiency of detailed transport properties by 2 orders of magnitude. (3) An adaptive analytical Jacobian (AAJ) method is proposed to apply locally reduced mechanisms in an analytical Jacobian method with sparse matrix solver. The computational cost of the analytical Jacobian method is reduced by half with the adaptive chemistry. More importantly, the AAJ method is stable, so that it can utilize large integration time steps to accelerate overall simulations. Moreover, a multi-scale adaptive reduced chemistry solver (MARCS) is developed by integrating the CO-DACT and AAJ methods into a multi-dimensional full-speed fluid solver to perform efficient combustion simulations in practical geometries. The advanced numerical methods developed are demonstrated to be efficient, accurate, and robust. They extend the capability of high-fidelity combustion simulations with detailed chemistry and transport. Finally, numerical studies of the dynamics and ignition to flame transitions in stratified mixtures are conducted to investigate the knocking-like acoustic wave formations at NTC (negative temperature coefficient) conditions. It is found that n-alkanes with rich low temperature chemistry promote knocking formations in stratified mixtures.