We study turbulent flow over surfaces with varying roughness scales, using large eddy simulation (LES). The goal is to use LES results to formulate effective boundary conditions in terms of effective roughness height and blending height, to be used for RANS. The LES are implemented with the dynamic Smagorinsky model based on the Germano identity. However, as is well-known, when this identity is applied locally, it yields a coefficient with unphysically strong fluctuations and averaging is needed for better realism and numerical stability. The traditional approach consists of averaging over homogeneous directions, for example horizontal planes in channel flow. This requirement for homogeneous directions in the flow field and the concomitant inability to handle complex geometries renders the use of this model questionable in studying the effect of surface heterogeneity. Instead, a new version of the Lagrangian dynamic subgrid-scale (SGS) model  is implemented. A systematic set of simulations of flow over patches of differing roughness is performed, covering a wide range of patch length scales and surface roughness values. The simulated mean velocity profiles are analyzed to identify the height of the blending layer and used to measure the effective roughness length. Extending ideas introduced by Miyake  and Claussen , we have proposed a simple expression for effective surface roughness and blending height knowing local surface patch roughness values and their lengths . Results of the model agreed well with the LES results when the heterogeneous surface consisted of patches of equal sizes. The model is tested here for surfaces with patches of different sizes.
Applications of the Lagrangian Dynamic Model in LES of Turbulent Flow Over Surfaces With Heterogeneous Roughness Distributions
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Bou-Zeid, E, Meneveau, C, & Parlange, MB. "Applications of the Lagrangian Dynamic Model in LES of Turbulent Flow Over Surfaces With Heterogeneous Roughness Distributions." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 2, Parts A and B. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 291-298. ASME. https://doi.org/10.1115/HT-FED2004-56127
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