CFD enhancements for supersonic combustion simulation with VULCAN

The progress made toward incorporating advanced, high-fidelity computational fluid dynamics (CFD) schemes into the VULCAN high-speed combustion simulation code is reported in this paper. The enhancements include better LES models, the capability to use high-order discretization schemes and the allowance for the simulation of combusting two-phase flows involving liquid fuel sprays. Regarding LES, we have successfully implemented, as baseline, Vreman's relatively high accurate approach and Menon's proposal, which involves the solution of an evolution equation for the sub-grid scale kinetic energy. Ideally, Vreman's formula can perform consistently without the need for any artificial wall-damping function, while Menon's LES model allows for non-equilibrium between sub-grid kinetic energy production and dissipation rates, and provides a natural measure of the sub-grid turbulence intensity. Several problems, both canonical and realistic, were used to validate the calculations. The results suggest the need to use high-order schemes to obtain accurate LES results. The baseline LES models were used in this exploratory work and advanced features such as the dynamic evaluation of several model constants, as in Genin and Menon (Genin, F. and Menon, S., "Simulation of Turbulent Mixing Behind a Strut Injector in Supersonic Flow," AIAA Journal, Vol. 48, No. 3, pp. 526-539), are currently being added, subsequent to our basic understanding of the baseline schemes. Several high-order schemes based on the weighted essentially non-oscillatory (WENO) approach, some of which are new, were also implemented in VULCAN during this investigation and have been rigorously validated. Variants of the Sirignano (Sirignano, W.A., "Current status of spray combustion modeling," AIAA-2003-4784, 2003) two-phase models were used as the baseline for the two-phase flow implementation, with promising results for mixing and combustion in supersonic jet cross flow. However, the demonstration of two-phase flows in this paper is limited to the subsonic models so that additional work is indicated for liquid fuel injection in supersonic gas flows.