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