Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes

Abstract

The dynamics of the velocity field resulting from the interaction between the atmospheric boundary layer and a wind turbine array can affect significantly the performance of a wind power plant and the durability of wind turbines. In this work, dynamics in wind turbine wakes and instabilities of helicoidal tip vortices are detected and characterized through modal decomposition techniques. The dataset under examination consists of snapshots of the velocity field obtained from large-eddy simulations (LES) of an isolated wind turbine, for which aerodynamic forcing exerted by the turbine blades on the atmospheric boundary layer is mimicked through the actuator line model. Particular attention is paid to the interaction between the downstream evolution of the helicoidal tip vortices and the alternate vortex shedding from the turbine tower. The LES dataset is interrogated through different modal decomposition techniques, such as proper orthogonal decomposition and dynamic mode decomposition. The dominant wake dynamics are selected for the formulation of a reduced order model, which consists in a linear time-marching algorithm where temporal evolution of flow dynamics is obtained from the previous temporal realization multiplied by a time-invariant operator.This article is part of the themed issue 'Wind energy in complex terrains'.

Stochastic Wake Modelling Based on POD Analysis

“…It has been shown that a few spatial modes can already capture important features of the wake flow [35][36][37][38][39]41,43,47]. In the case of a large eddy simulation of an infinite row of turbines, Andersen et al [35] found that a few modes stemming from the proper orthogonal decomposition (POD) already yield a good description of the velocity field on large spatial scales.…”

“…Furthermore, the description and inclusion of a turbulent atmospheric inflow is a very challenging task. An alternative approach, investigated by Iungo et al [41], Debnath et al [43], is to linearize the temporal evolution leading to the dynamic mode decomposition [50][51][52][53]. In this framework, the relevant weighting coefficients are all periodic.…”

“…Another dynamic approach, also followed in this work, is to analyse and model wind turbine wakes using modal decompositions [21,[35][36][37][38][39][40][41][42][43][44][45][46][47] which describe the velocity field as a linear superposition of spatial modes with time-dependent weighting coefficients. It has been shown that a few spatial modes can already capture important features of the wake flow [35][36][37][38][39]41,43,47].…”

A Reduced Order Model to Predict Transient Flows around Straight Bladed Vertical Axis Wind Turbines

“…Among other applications, ROM may be used as surrogates for prediction or as a replacement of costly solvers in optimisation routines. ROM have been proposed to represent horizontal axis turbine wakes, e.g., [9,10], but to the authors' knowledge, the present work is the first to propose a ROM for vertical axis turbines.…”

Introduction Wind farms in complex terrains: an introduction

“…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.…”