Large Eddy Simulation of Wall-bounded Turbulent Flows Using Discontinuous Spectral Element Method

The objective of the present dissertation is to develop numerical tools and techniques that facilitate the high-fidelity simulations of the air flow within ramp-cavity combustors using a discontinuous spectral element method. The supersonic turbulent reacting flow within the ramp-cavity combustor is a multi-scale, multi-physics, complex flow. The concurrent presence of shocks, turbulence, and reaction, as well as their interactions, make the simulation of such a flow one of the most challenging ones in the field of computational fluid dynamics. There have been efforts to simulate such a flow using low-order numerical schemes such as finite volume and finite difference, but a high-order method that is capable of dealing with the entire physics of the flow is highly desired. Spectral element methods provide high accuracy, are flexible with complex geometries, and can be efficiently parallelized. The focus of the present work is on the turbulence aspect of the flow. A new explicit modal filtering procedure is introduced, implemented, and tested for use in large eddy simulations without any sub-grid scale model. The method is tested for isotropic turbulence and turbulent flow in a channel, and accurate mean and fluctuation statistics are obtained comparing with direct numerical simulation. The computational overhead of the proposed method is less than 3% (compared to 45% for dynamic Smagorinsky model). Moreover, a sensor that improves the performance of the standard Smagorinsky model for separating flows is developed, implemented, and tested for a backward-facing step configuration. The error of the prediction of the reattachment length is reduced from 18.4% to 0.5% by applying the proposed sensor. The near-wall spatial resolution requirement for direct numerical simulations of wall-bounded turbulent flows is also studied in detail. It is shown that the near-wall resolution requirement strongly depends on the approximation order; for an approximation order of P = 7, eight grid points within y+ = 10 is sufficient for accurate statistics, while for an approximation order of P = 2, even having 11 points within y+ = 10 results in inaccurate statistics. Preliminary steps are also taken towards the simulations of turbulent supersonic flows. Large-eddy simulations of non-reactive turbulent supersonic flow in a ramp-cavity combustor with fuel injector are presented.