Date of Graduation

5-2025

Document Type

Thesis

Degree Name

Master of Science in Mechanical Engineering (MSME)

Degree Level

Graduate

Department

Mechanical Engineering

Advisor/Mentor

Walters, Keith

Committee Member

Leylek, James H.

Second Committee Member

Huang, Po-Hao Adam

Keywords

Boundary Layer; Computational Fluid Dynamics; Large Eddy Simulation; Turbulence; Wall modeling

Abstract

The use of computational fluid dynamics (CFD) to test engineering designs with reduced cost and time compared to physical testing has become increasingly common in a range of industries and research fields. While numerical methods exist that can accurately solve the equations that govern the flow of fluids, these methods are computationally expensive for practical engineering problems due to the large amount of computational power needed to resolve the fluid flow over the entire range of length and time scales. Several different approaches have been introduced to address this computational cost issue, namely Reynolds-averaged Navier-Stokes (RANS) modeling and scale resolving methods. Reynolds averaging is the least computationally expensive approach, however due to assumptions made in the formulations this method also tends to be the least physically accurate as it only solves for the mean flow field. Scale resolving approaches such as Large-Eddy simulation (LES) provide more accurate results by resolving the large turbulent eddies primarily responsible for momentum and energy transfer. In free shear flows the grid resolution requirements for LES models are comparable in size to that of RANS models. However, for LES to produce accurate results for wall bounded flows by resolving even the largest eddy present in the boundary layer, the computational grid must be significantly more refined than that of RANS simulations. Hence, fully resolved LES for wall-bounded flows remain computationally expensive and are rarely used for simulation of practical engineering problems. There have been several different methods presented to mitigate the cost of modeling in the near wall region while still providing results that are comparable to fully resolving the eddies in this region.

The present work presents a new approach for wall modeling in large-eddy simulation. The wall mean resolved LES method (WMRLES) utilizes the dynamic hybrid RANS-LES (DHRL) framework to solve a RANS model in the near wall region and transition to LES further from the wall. This approach differs from other hybrid RANS-LES methods. The choice of RANS model differs as a zero-equation mixing length model is used. This does not require the solution of additional transport equations, significantly reducing computational cost. Since the transition between RANS and LES modes is affected by a physics-based blending function which is computed locally in the flow domain, prior knowledge of the flow is not required to denote RANS and LES regions prior to the simulation. Finally, WMRLES does not require the use of analytical or numerical wall functions, which are limited in their flexibility and universality for numerical simulations. The new modeling approach is developed, presented, and applied to two separate classes of problem: an attached boundary layer case represented by a fully developed channel flow and a separated shear layer case represented by a two-dimensional channel with periodic restrictions. Results are compared to available direct numerical simulation data and other wall modeling methods. The new method is found to produce results comparable to the full dynamic hybrid RANS-LES method in terms of accuracy, while using a simpler and more computationally efficient implementation.

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