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Publication# Subfilter-scale fluxes over a surface roughness transition. Part II: Evaluation of large-eddy simulation models

Abstract

The ability of subfilter-scale (SFS) models to reproduce the statistical properties of SFS stresses and energy transfers over heterogeneous surface roughness is key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. In this study, several SFS models are evaluated a priori using experimental data acquired downwind of a rough-to-smooth transition in a wind tunnel. The SFS models studied include the eddy-viscosity, similarity, non-linear and a mixed model consisting of a combination of the eddy-viscosity and non-linear models. The dynamic eddy-viscosity model is also evaluated. The experimental data consist of vertical and horizontal planes of high-spatial-resolution velocity fields measured using particle image velocimetry. These velocity fields are spatially filtered and used to calculate SFS stresses and SFS transfer rates of resolved kinetic energy. Coefficients for each SFS model are calculated by matching the measured and modelled SFS energy transfer rates. For the eddy-viscosity model, the Smagorinsky coefficient is also evaluated using a dynamic procedure. The model coefficients are found to be scale dependent when the filter scales are larger than the vertical measurement height and fall into the production subrange of the turbulence where the flow scales are anisotropic. Near the surface, the Smagorinsky coefficient is also found to decrease with distance downwind from the transition, in response to the increase in mean shear as the flow adjusts to the smooth surface. In a priori tests, the ability of each model to reproduce statistical properties of the SFS stress is assessed. While the eddy-viscosity model has low spatial correlation with the measured stress, it predicts mean stresses with the same accuracy as the other models. However, the deficiency of the eddy-viscosity model is apparent in the underestimation of the standard deviation of the SFS stresses and the inability to predict transfers of kinetic energy from the subfilter scales to the resolved scales. Overall, the mixed model is found to have the best performance.

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Large eddy simulation

Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer. The simulation of turbulent flows by numerically solving the Navier–Stokes equations requires resolving a very wide range of time and length scales, all of which affect the flow field.

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The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square metre, or pascal-seconds. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion.

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In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers.

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