Modelling turbulent boundary layer flow over fractal-like multiscale terrain using large-eddy simulations and analytical tools

Abstract

In recent years, there has been growing interest in large-eddy simulation (LES) modelling of atmospheric boundary layers interacting with arrays of wind turbines on complex terrain. However, such terrain typically contains geometric features and roughness elements reaching down to small scales that typically cannot be resolved numerically. Thus subgrid-scale models for the unresolved features of the bottom roughness are needed for LES. Such knowledge is also required to model the effects of the ground surface ‘underneath’ a wind farm. Here we adapt a dynamic approach to determine subgrid-scale roughness parametrizations and apply it for the case of rough surfaces composed of cuboidal elements with broad size distributions, containing many scales. We first investigate the flow response to ground roughness of a few scales. LES with the dynamic roughness model which accounts for the drag of unresolved roughness is shown to provide resolution-independent results for the mean velocity distribution. Moreover, we develop an analytical roughness model that accounts for the sheltering effects of large-scale on small-scale roughness elements. Taking into account the shading effect, constraints from fundamental conservation laws, and assumptions of geometric self-similarity, the analytical roughness model is shown to provide analytical predictions that agree well with roughness parameters determined from LES. This article is part of the themed issue ‘Wind energy in complex terrains’.

scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

“…The sinusoidal elements all have the same aspect ratio 1. The multiscale roughness implementation is similar to that in Yang & Meneveau (2017), although in that study square roughness elements were adopted and positioned randomly. The size of the largest roughness element is used as the reference scale, R 1 = 0.1.…”

“…At the second and third generation, we have the rough elements size as R n+1 = 2 −n R n . No roughness elements of intermediate sizes are included, and the roughness height spectrum is thus discrete (Yang & Meneveau 2017). Figure 1 gives an overview of the computational domain and the roughness elements.…”

Introduction Wind farms in complex terrains: an introduction

“…The roughness height is usually the leading scaling parameter, but the roughness distribution and size also have a significant impact [3,4]. Forests are a typical example since the foliage and tree density affect their permeability to the boundary layer, so that some gusts could sweep inside the forest and be ejected at a later stage.…”

“…This theme issue of the Philosophical Transactions of the Royal Society A mainly builds on presentations [2][3][4][5][6][7][8][9][10][11] made at the EUROMECH Colloquium 576, Wind Farms in Complex Terrain, which took place at KTH Royal Institute of Technology in Stockholm, Sweden, over 3 days in June 2016. The main focus of the Colloquium was the various issues related to complex terrains, mainly from the aerodynamic, meteorological and noise-propagation points of view.…”

“…The topics include wind statistics on both the micro-and macro-scale level [2], the effect of surface roughness on the description of boundary-layer flow physics [3,4], the effect of complex terrain on sound propagation [5], as well as various strategies for modelling the flow field around wind turbines [6][7][8] and wind farms [9][10][11].…”