An efficient approach of unsteady flamelet modeling of a cross-flow-jet combustion system using LES

Steady flamelet models have been widely used in turbulent combustion simulations because of their simplicity, efficiency, yet physics-based nature. They are, however, unable to handle slow chemical and physical processes such as pollutant formation. Unsteady flamelet models have been shown to be able to provide accurate predictions especially for pollutants, but their implementations are usually not as straightforward as for the steady models, and additional assumptions are involved. One relatively straightforward approach of implementing the unsteady flamelet model is to tabulate the time history of unsteady flamelet solutions. This often leads to flamelet libraries of large sizes because of increased dimensions for the new physics. The purpose of this paper is to introduce a new and efficient approach of tabulating unsteady flamelet solutions in the LES of complex systems, here demonstrated in simulations of a cross-flow-jet combustion system. This approach employs Taylor series expansions to represent the time history of unsteady flamelet solutions. Compared with other approaches, the new approach retains the efficiency and simplicity benefits of steady flamelet models but possesses the accuracy of unsteady flamelet models. Various issues associated with the formulation and implementation of this approach are discussed, which include the selection of the base solution, the order of accuracy of the expansion, and the treatment of simultaneous wall heat losses and heat transfer through thermal radiation. This approach is validated in large eddy simulations of a cross-flow-jet combustion system. Good agreement with experiments is obtained for both temperature and NO concentration, as well as for major species.