A new approach for a non-viscosity one-equation large eddy simulation (LES) subgrid stress model is presented. The new approach uses a tensor coefficient obtained from the dynamic modeling approach of Germano (1991) and scaling that is provided by the sub-grid kinetic energy. Mathematical and conceptual issues motivating the development of this new model are explored. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES. These conditions are examined for traditional dynamic Smagorinsky modeling (i.e. zero-equation approaches) and the one-equation sub-grid model of Ghosal et al. (1995). It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strain-rate to estimate the sub-grid stresses scale poorly with filter level leading to significant errors in the modeling of the sub-grid scale stress. The poor scaling in traditional LES approaches can result in not only weak models but also can cause non-realizability of the sub-grid stresses. A better scaling based on the sub-grid kinetic energy is proposed that leads to a new one-equation non-viscosity model that does satisfy the solvability conditions and maintains realizability. The transport equation for the sub-grid kinetic energy is closed using series formulations of Bedford and Yeo (1993) instead of the more traditional viscosity based gradient transport approaches. Both integral and algebraic formulations of the new one-equation non-viscosity model are presented. The resolved and sub-grid kinetic energies are shown to compare well to a DNS simulation of decaying isotropic turbulence.
LES models were also implemented into the combustion and spray simulation code KIVA. Traditional LES models were tested by comparing computational results to experimental data. The one-equation viscosity model of Menon (1996) was found to compare well to experimental data. This LES model was used in conjunction with a probability density function (PDF) combustion model to simulate the diesel combustion process of the Caterpillar 3400 engine. The engine simulation results were in good agreement with experimental data.