A GHOST CELL BASED IMMERSED BOUNDARY METHOD FOR WALL-MODELED LARGE-EDDY SIMULATIONS

Abstract

Turbulence is one of the most important unsolved problems in classical physics as it strongly affects skin friction and heat transfer rates and, thus, the performance of aerospace systems. Due to the high cost associated with flight and wind tunnel tests, there exists an ever-increasing demand for computational tools for engineering analysis. Hence, accurately predicting turbulent flows around aerospace vehicles is crucial for lowering safety factors, achieving optimal performance, and for the development of novel designs.

However, simulating turbulent flows around complex geometries is a challenging task, especially for off-design conditions, where the flow may not be fully attached to the vehicle surface, e.g., close to stall conditions. A key challenge is that resolving all relevant turbulent scales is computationally intractable in a day-to-day engineering environment even with currently available computing hardware. For these complex turbulent flows, higher-fidelity simulation approaches, such as large eddy simulation (LES), are employed as they are able to provide the desired accuracy. In recent years, with the advancement of simulation methodologies and the accessibility of modern computer hardware, there has been a growing consensus within the Computational Fluid Dynamics (CFD) community that higher-fidelity turbulent flow simulations (including DES and wall-modeled LES, or WMLES) will be used more frequently complimenting lower-fidelity CFD approaches, such as Reynolds Averaged Navier-Stokes (RANS) approaches, which are generally accurate enough at more benign flow conditions. While conventional wall-resolved LES approaches are still significantly more expensive than RANS-based methods, WMLES can provide accurate turbulent flow predictions at a fraction of the cost compared to direct numerical simulations (DNS) or wall-resolved large-eddy simulations (WRLES). This is achieved by modeling only the large-scale flow structures as in conventional LES and in the vicinity of the wall, where most of the grid points are concentrated in WRLES, a wall model is utilized to account for the very small near wall flow structures. All aforementioned CFD approaches, i.e. RANS, LES, and DNS, rely on the creation of high-quality body-fitted grids that can be a time-consuming task depending on the geometric complexity of the fluid system being analyzed. The use of immersed boundary methods (IBM) on Cartesian grids can completely eliminate the manual mesh generation process, thus, reducing the overall time-to-solution.

This dissertation assesses the viability of an unconventional simulation approach eliminating the time-consuming mesh generation approach by combining the IBM with WMLES. It was shown that in cases where the Cartesian grid is not aligned with the immersed boundary, the details of the numerical scheme, \textit{i.e.}, the order of accuracy, boundary treatment, \textit{etc.} play an important role in obtaining accurate solutions. Schemes with higher orders of accuracy lead to reduced numerical errors in the vicinity of the boundary providing better solutions. Furthermore, a physics informed boundary operator was used to provide a better representation of the mean flow in the near-wall region by using the gradient from the wall-model solution. A series of test cases are used to demonstrate the capabilities of this method for real-world applications and provide comparisons with conventional body-fitted results.