Wind energy is one of the fastest growing sources of sustainable energy production. As more wind turbines are coming into operation, the best locations are already becoming occupied by turbines, and wind-farm developers have to look for new and still available areas—locations that may not be ideal such as complex terrain landscapes. In these locations, turbulence and wind shear are higher, and in general wind conditions are harder to predict. Also, the modelling of the wakes behind the turbines is more complicated, which makes energy-yield estimates more uncertain than under ideal conditions. This theme issue includes 10 research papers devoted to various fluid-mechanics aspects of using wind energy in complex terrains and illustrates recent progress and future developments in this important field.
This article is part of the themed issue ‘Wind energy in complex terrains’.
Investments in renewable energy sources are growing substantially in all parts of the world, and wind energy is one of the main contributors to the growth of electrical power capacity. According to the International Energy Agency  the installed power has more than doubled between 2010 and 2015, up to more than 430 GW, which means that several hundred thousand turbines are converting wind to electrical energy. In some smaller countries wind energy contributes up to 40% of the electric power production, whereas in larger countries the growth of installed power in absolute terms is substantial, without yet reaching such high percentages of the total electricity production. Optimal locations (based on high and steady wind velocities and low turbulence levels) are usually on-shore, near the coastline. However, such locations are often found in areas that are densely populated and the development of wind energy in such locations is often constrained by acceptance issues by nearby residents. Therefore, other locations for deployment of wind farms are sought, such as off-shore sites where winds are known to be strong and turbulence levels low. However, the cost of installing wind farms off-shore can be typically 100% higher than on-shore, due to higher costs for both foundations and connections to the electric grid. Also maintenance costs are higher for turbines off-shore than for corresponding turbines on-shore.
The remaining alternative for a massive deployment of wind turbines is complex terrain. With complex terrain, we mean features of the Earth's surface that influence the wind in the atmospheric boundary layer (ABL) through terrain topology and/or roughness effects (figure 1). Historically, these have been avoided because of the harsher wind conditions (both lower wind speeds and higher turbulence intensity are expected), but are now becoming more appealing from the wind industry's point of view due to the lack of better alternatives.
This theme issue of the Philosophical Transactions of the Royal Society A mainly builds on presentations [2–11] 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.
This introduction gives an overview of the current status of fluid-dynamics research areas that relate to flow over complex terrain and also introduces the papers that are included in this theme issue. The topics include wind statistics on both the micro- and macro-scale level , the effect of surface roughness on the description of boundary-layer flow physics [3,4], the effect of complex terrain on sound propagation , as well as various strategies for modelling the flow field around wind turbines [6–8] and wind farms [9–11].
2. Issues and research topics
We divide this section into three subsections, where each is relevant for the theme of this issue. References are also given for the relevant articles in this theme issue, but some other areas are also touched upon.
(a) The atmospheric boundary layer over complex terrains
Characterization of the wind resource is of utmost importance in every wind-energy project since wind is the ‘fuel’ of wind turbines. However, the quantification of the wind resource at a certain site is rather complex, because it is associated with a multitude of phenomena taking place at different spatial and temporal scales. Wind is first generated from pressure-gradient forces at a global level, providing the geostrophic wind observed at high altitudes. As the ground is approached, friction forces become important: here the ground is perceived as a blocking surface that is absorbing momentum.
Close to the ground, micro-scale effects such as terrain shape and surface roughness become important and affect the wind significantly. One can define the ABL as the lower region of the atmosphere where friction, turbulence and mixing are intense, and further identify a subregion called the roughness sublayer where the flow is strongly distorted by the presence of terrain and roughness (usually such a region is two to three times the roughness height, although it is hard to generalize such an estimate). Therefore, the wind is generated by pressure gradients (planetary time scale) that are affected by friction (meso-scale effect) and by roughness close to the ground (micro-scale effect). Wind turbines placed in complex terrains are expected to operate just above the roughness sublayer in an environment that is highly turbulent. This makes the prediction of the instantaneous wind very challenging even on a statistical level.
Let us consider the engineering problem of estimating the wind resource for a given terrain. The terrain elevation and the roughness characteristics are now becoming available from several research efforts worldwide. But what is their effects on the available wind? Nobody would be able to answer this question without field experiments or, at least, model results . It is well known that the characteristics of the ABL vary depending on the geographical location, time of day and year (neglecting variations that take place on the climate scale, approx. 30 years), so that data measured over 1 or 2 years might not be sufficient to characterize with sufficient accuracy the available wind. It is useful to remember that, since the power output of a turbine scales with the cube of the inflow velocity, an error of 1% in velocity will lead to an error of 3% in power or, equivalently, an error of 0.5 m s−1 will lead to an error of 15% in the produced power output if the mean wind speed is given as 10 m s−1.
Even considering the wind from a statistical point of view, it is clear that many parameters should be accounted for, such as varying geostrophic wind, density stratification, surface roughness (sea, farmland, forest, urban, etc.) and terrain type (flat, hilly and mountainous). These local conditions affect the boundary-layer velocity profile and the turbulence characteristics of the approaching wind.
Roughness effects have been studied in laboratories for a long time because of their importance in engineering situations: roughness increases the pumping losses in pipe systems as well as the friction drag on ships, aeroplanes and wind-turbine blades, for instance. Therefore, there is a massive body of engineering literature about the boundary-layer characteristics over many kinds of roughness (sand grain, mesh and discrete cubes, for instance).
The ground below the ABL is almost always rough in a fluid-dynamics sense, although the degree and character of the roughness may differ substantially. 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 sweep–ejection cycle is also observed in boundary layers over smooth surfaces, but it contributes even more significantly to turbulence production and transfer over canopies.
One problem related to the assessment of a specific site for a wind-energy project is how to determine the wind speed. Today a typical site is evaluated based on wind measurements using one or a few towers equipped with cup anemometers, which is still the industry standard to measure wind speed. Recently, such measurements have been complemented with sonic anemometers as well as remote sensors . Measurements are typically carried out over a period of 1 year or longer in order to characterize the site (followed by long-term corrections to account for climate effects). Cup and sonic anemometers are usually calibrated under steady conditions in wind tunnels, where the flow direction is well known and the turbulence level is low. However, in a complex-terrain situation none of these conditions are usually fulfilled (the turbulence level is high and the lateral wind velocity may be quite large), which may make the original calibration of the anemometers invalid. This implies that caution must be used when analysing field experimental data, especially from measurements in complex terrains. Sound propagation  can be investigated after characterization of the velocity field. Here, the terrain roughness and topology, as well as the incoming boundary layer, in terms of both its velocity distribution and turbulence, are importance parameters.
(b) Wind-turbine aerodynamics
Wind-turbine aerodynamics was limited to the description provided by general momentum theory and vortex theory for most of the twentieth century. However, such theories do not take into account how the velocity shear, turbulence intensity and length scales of the ABL affect the response of the turbine. There are few experiments where local effects have been measured on wind turbines and where such measurements have been correlated to simultaneous ABL measurements. New possibilities arise when large-eddy simulation (LES) can be used together with modelling of the turbine, an approach taken in , where such computational data are compared with unique full-scale experiments.
In the last 30 years, there has been a sudden increase in the number of studies dedicated to the fluid dynamics of wind-turbine wakes, pushed by the growth of computational resources and by the introduction of new experimental techniques. While the wake was formerly treated as a simple momentum deficit, it is now known that the near wake of a wind turbine is a complicated vortex system characterized by vortex sheets released by the blades that tend to agglomerate to the tip as well as the root. Tip vortices spiral downstream of the turbine and represent the leading feature observed behind isolated wind turbines. Near the turbine they can be seen as the demarcation between the wake and the undisturbed flow. In low-turbulence situations, the tip vortices have a coherent spiralling pattern that is up to three to four turbine diameters downstream of the rotor plane. It is known that they are convectively unstable, so that they act as noise amplifiers: in a moderate- to high-turbulence environment (such as the one encountered over complex terrains), there is evidence that the tip vortices break down and disintegrate close to the rotor plane. After such a breakdown, a transition stage takes place where the original vortex system becomes disorganized and chaotic, and further downstream a turbulent wake is observed.
The turbulent wake stage is important for wind-farm performance: here the momentum deficit created behind the turbine decays in the streamwise direction (theoretically as a power law of the downstream distance) as well as the turbulence (which has its maximum intensity in the transition region). In a wind farm, the streamwise distance between turbines may be of the order of four to eight turbine diameters, corresponding to the initial region of wake decay, and is strongly affected by the turbine loads, by the wake receptivity to the external atmospheric perturbations and by the transition scenario. The characterization of the transitional wake is indeed of crucial importance in order to estimate the wind available to the next turbines as well as to design new control strategies.
Our current understanding of turbine wakes comes from experiments, simulations and theoretical models of various complexities. Simplified vortex models were first developed by Joukowsky and Prandtl a century ago, and were later supported by experimental data and (more recently) by high-accuracy numerical simulations. While direct numerical simulations are still limited to low Reynolds numbers, LESs are becoming a viable tool to perform numerical experiments able to enhance our current understanding [6,7]. There are still several issues regarding the modelling of the environmental turbulent field (such as surface boundary and inflow conditions), and of the turbines (such as the actuator disc and actuator line models, all motivated by the need to avoid the simulation of the blade boundary layer to reduce the computational cost), but progress is rapid and new results are expected in the coming years.
Reynolds-averaged Navier–Stokes (RANS) simulations do not give detailed physical information and are better suited for industrial applications, where the detailed physics is of less interest. RANS simulations can, however, be a good tool to investigate the complex flow features that are taking place, e.g. at the blades, such as unsteady separation and dynamic stall, as long as LESs remain too computationally expensive.
Another possible approach to study wind-turbine aerodynamics is provided by reduced-order models (ROMs), where only the leading features of the flow, measured in an experiment or observed through a simulation (such as LES), are synthesized into a simplified tool . The output of the synthesis part provides some physical understanding of the flow, while the application of a ROM as a state estimator decreases by several orders of magnitude the cost of active control methods, as the instantaneous simulation is avoided and everything is reduced to a system of ordinary differential equations in time. At the moment, these are not yet implemented in practice, but the idea is recent and its readiness level is constantly increasing.
(c) Wind-farm modelling
A wind farm is a cluster of wind turbines distributed over a certain area with the goal of maximizing the power obtained for a given investment. This often means that one wants to maximize the power density (namely the power obtained per unit surface area), a constraint suggesting that the turbines should be placed as close together as possible. However, it is known that turbines placed too close to each other tend to interact, with the result that the average power production of the turbines decreases significantly. From many wind-farm studies and field data, it has been found that the optimal distance should be around five to seven turbine diameters in the streamwise direction, although the optimum depends on the turbulence level of the ABL, the roughness, the terrain conditions and the thrust force imposed by the turbines.
Wind farms have received attention only recently with dedicated experiments and simulations. A number of LESs have been carried out that provide good insight into the power-extraction process and the momentum transfer taking place in the wind-farm internal boundary layer [9,10]. The description obtained from studies on single turbines must be extended since several wakes may simultaneously interact, making the flow highly complex.
Similar to turbulent boundary layers over rough surfaces, we are still only able to understand the flow over wind farms statistically, while there is clear pressure from the industry to enhance the understanding of the wake-interaction phenomenon and how that affects the loads experienced by the turbines. For instance, it has been observed that wind farms extract most of the energy in the first row facing the wind, while the subsequent rows extract more or less the same amount of energy: this observation implies that energy is transferred not only horizontally (as one might expect from general momentum theory at first glance) but also vertically through the action of turbulent transport in the wind-farm internal boundary layer. No studies have investigated such an aspect, and it is expected that this will open new modelling possibilities and improve our current methods for the energy-yield estimation. Any model that does not account for this energy-transfer mechanism will fail in predicting the power output of large farms.
LESs of wind farms are still done only at research level (due to the prohibitive computational cost), while RANS simulations remain the preferred industrial tool. However, many industries use even simpler tools that do not account for wind turbines in the simulation at all, but model their behaviour as a momentum deficit with a prescribed wake field. These wake models are particularly useful during the planning and optimization phase of a wind-farm project, since they are fast (the turbines are introduced in post-processing only), although they have several drawbacks: wake models prescribe the wake behaviour through the use of empirical parameters that are not known a priori and depend on the atmospheric turbulence and incoming shear, for instance. For a wind farm, the wake superposition must also be modelled, and, although several such models do exist, there is even less confidence in their correct behaviour, making the energy-yield estimation quite uncertain.
While RANS simulations appear as the only option left that accounts for proper wake behaviour, the computational cost limits their use in the wind-energy industry. Linearized models, i.e. models where the nonlinear terms in the Navier–Stokes equations are neglected , are a possible cost-effective alternative since the calculations can be made quickly, but of course with less accuracy than for RANS. Many of the industrial tools existing today are already based on linearized methods combined with wake models, but cannot account for complex phenomena, such as flow separation, and are rarely used for unsteady simulations.
The energy yield quantification is expected to become worse if a farm is placed in a complex terrain since the wakes are expected to change due to the externally imposed pressure gradient generated by the terrain topology. There is indeed need for new experiments and high-quality simulations of wind farms placed over complex terrains in order to develop new simplified models and knowledge to design future wind farms.
As discussed above, wind energy over complex terrains is an active research area still in its infancy. Several research activities are currently ongoing through experimental, numerical and theoretical modelling as well as field observations, borrowing methods from other branches of fluid mechanics, meteorology, turbulence research and control theory. Many relevant studies have been collected together in the present theme issue, which gives an overview about some of the currently important topics.
P.H.A. and A.S. wrote the manuscript and were responsible for the editing of this theme issue of Phil. Trans. R. Soc. A.
The authors declare that they have no competing interests.
This work was funded by STandUP for Wind. The Swedish Research Council (VR) is acknowledged for support of the invited speakers to the Colloquium and EUROMECH for general support.
We acknowledge all the participants in the EUROMECH Colloquium 576 and especially those who have contributed to the current theme issue.
One contribution of 11 to a theme issue ‘Wind energy in complex terrains’.
- Accepted January 3, 2017.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.