1 Copyright © 2004 by ASME Proceedings of HT-FED2004: 2004 ASME Heat Transfer/Fluids Engineering Summer Conference July 11-15, 2004, Charlotte, North Carolina, USA HT-FED2004-56127 APPLICATIONS OF THE LAGRANGIAN DYNAMIC MODEL IN LES OF TURBULENT FLOW OVER SURFACES WITH HETEROGENEOUS ROUGHNESS DISTRIBUTIONS Elie Bou-Zeid Department of Geography and Environmental Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University Charles Meneveau Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University Marc B. Parlange Department of Geography and Environmental Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University ABSTRACT 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 [1] 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 [2] and Claussen [3], we have proposed a simple expression for effective surface roughness and blending height knowing local surface patch roughness values and their lengths [4]. 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. INTRODUCTION Flows over surfaces with abrupt changes in surface roughness and heterogeneous roughness distributions occur in a wide range of engineering applications involving turbulent flows and in the environment (Atmospheric Boundary Layer flow). Consequently, the effect of variability in surface roughness on boundary layers continues to be the subject of numerous studies [5-9]. These studies attempt to understand and quantify the flow disturbances caused by the roughness change. In addition, a parameterization of the effect of heterogeneity is often desirable; for example, numerical simulations that cannot resolve the heterogeneity scale need to model its effect on resolved scales. Analytical and experimental techniques have been traditionally used to tackle the heterogeneity problem. More recently, numerical techniques, particularly Large-Eddy Simulation, has become increasingly popular as a tool for a physical understanding of the dynamics of the blending phenomena over heterogeneous surfaces [9-15]. This paper continues this previous body of work by using LES, with a new generation model for subgrid-scale stresses, to test a new parameterization for heterogeneous surfaces at high Reynolds numbers. LARGE EDDY SIMULATION AND THE LAGRANGIAN DYNAMIC SGS MODEL Large Eddy Simulation assumes that the largest eddies contain most of the energy and are responsible for most of the transport of momentum and scalars. LES consists of solving the Navier-Stokes equations with eddies smaller than the filter size excluded, whereas eddies larger than the filter size can be resolved [16]. The spatial filtering of the Navier-Stokes