Wim Munters

Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows

In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%–15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method’s advantages are illustrated for the simulation of a developing wind-farm boundary layer.

Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms

A major challenge in turbulence-resolving flow simulations is the generation of unsteady and coherent turbulent inflow conditions. Precursor methods have proven to be reliable inflow generators but are limited in applicability and flexibility especially when attempting to couple boundary-layer dynamics with large-scale temporal variations in the direction of the inflow. Here, we propose a methodology that is capable of providing fully developed turbulent inflow for time-varying mean-flow directions. The method is a generalization of a concurrent precursor inflow technique, in which a fully developed boundary-layer simulation that uses periodic boundary conditions is dynamically rotated with the large-scale wind direction that drives the simulation in the domain of interest. The proposed inflow method is applied to large-eddy simulations of boundary-layer flow through the Horns Rev wind farm when subjected to a sinusoidal variation in wind direction at the hourly time scale.

An optimal control framework for dynamic induction control of wind farms and their interaction with the atmospheric boundary layer

Complex turbine wake interactions play an important role in overall energy extraction in large wind farms. Current control strategies optimize individual turbine power, and lead to significant energy losses in wind farms compared with lone-standing wind turbines. In recent work, an optimal coordinated control framework was introduced (Goit & Meyers 2015 J. Fluid Mech. 768, 5–50 (doi:10.1017/jfm.2015.70)). Here, we further elaborate on this framework, quantify the influence of optimization parameters and introduce new simulation results for which gains in power production of up to 21% are observed. This article is part of the themed issue ‘Wind energy in complex terrains’.

Effect of wind turbine response time on optimal dynamic induction control of wind farms

In this work, we extend recent research efforts on induction-based optimal control in large-eddy simulations of wind farms in the turbulent atmospheric boundary layer. More precisely, we investigate the effect of wind turbine response time to requested power setpoints on achievable power gains. We do this by including a time-filtering of the thrust coefficient setpoints in the optimal control framework. We consider simulation cases restricted to underinduction compared to the Betz limit, as well as cases that also allow overinduction. Optimization results show that, except for the most restrictive underinductive slow-response case, all cases still yield increases in energy extraction in the order of 10% and more.

A framework for optimization of turbulent wind-farm boundary layers and application to optimal control of wind-farm energy extraction

A PDE-based optimization framework is presented that allows optimization of turbulent wind-farm boundary layers. It consists of a state-of-the-art large-eddy simulation code that allows the time-resolved simulation of the three-dimensional turbulent flow in the atmospheric boundary layer, together with the adjoint (backward) sensitivity equations to this nonlinear system of PDEs (i.e. the incompressible Navier-Stokes equations). Both the forward and the backward system are efficiently parallelized for supercomputing, and are combined with state-of-the-art gradient-based optimization methods. We use this tool to investigate the use of optimal coordinated control of wind-farm boundary-layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators and their energy extraction is dynamically regulated in time so as to optimally influence the flow field. Earlier work on wind-farm optimal control in the fully developed regime (Goit & Meyers 2015, J. Fluid Mech. 768, 550) is discussed, and extended towards wind farms in which inflow effects are important.

Optimal dynamic induction and yaw control of wind farms: effects of turbine spacing and layout

Turbine wake interactions in wind farms result in decreased power extraction in downstream rows. This work investigates dynamic induction and yaw control of wind farms for increased total power extraction. Six different wind farm layouts are considered, and the relative benefits of induction control, yaw control, and combined induction–yaw control are compared. It is found that optimal control significantly increases wind-farm efficiency for virtually all cases, and that the most profitable control strategy between yaw and induction control depends on the effective farm layout as seen by the flow, and hence the mean wind direction.