1. Introduction
Wind power is currently one of the most promising renewable energy sources. The year 2017 was a record year for annual installations in Europe, with 16.8 GW of additional wind power capacity installed. Wind energy remains the second largest form of power generation capacity in Europe, closely approaching gas installations. In the EU, wind energy overtook nuclear energy in 2013, hydro in 2015, and coal in 2016. In 2017, offshore installed wind power capacity represented 15.8 GW against 153 GW for onshore installations [
1]. Onshore installations are mainly built on flat terrain, making them easier to operate compared to those mounted on hilly terrain, where forecasts are more uncertain, wear and tear is greater, and maintenance and construction costs are higher. However, wind energy in mountainous regions has been making inroads in recent years and is of increasing interest to the wind-energy community.
WindForS, a wind energy research cluster in Southern Germany, aims to answer the question of how to optimize installations in complex terrains and extend their service life. In the framework of the project Wind Science and Engineering in Complex Terrain (WINSENT), a field-test site for research and industry, located behind an escarpment in the Swabian Alps, near the town of Geislingen an der Steige is setting up. The project working plan is divided into two stages: the first phase investigates the local wind flow without wind turbines where different measurement equipment is used to characterize the wind flow, such as towers equipped with anemometers, Lidar [
2], eddy-covariance stations, and an unmanned aircraft system (UAS) (see [
3,
4,
5]). The second stage will include two wind turbines with a nominal output of around 750 kW. The turbine-terrain interference will be studied in this second phase.
Characterizing the wind flow in complex terrain is more challenging compared to flat terrain. At these locations, wind flows are more complex, and they are influenced by changes in topography such as hills, escarpments, and roughness, leading to non-linear features such as high levels of turbulence, wind shear, unsteadiness, etc. Analytical models, mainly developed in the 1970s and 1980s such as the well-known Wind Atlas Analysis and Application Program (WAsP), are capable of predicting the mean wind field only in simple geometries and are suitable only for attached flow (see [
6,
7,
8,
9] and others). Modelling non-linear features of the flow became a feasible option with the help of computational fluid dynamics (CFD) solvers which retain the nonlinearity of the Navier-Stokes equations and simulate momentum, turbulence, and energy [
10]. The commonly referenced field experiment of Bolund hill, which consists of a steep hill, has been used for a blind comparison of models with different ranges of fidelity (linearized and CFD models) as reported in [
11]. One of the outcomes of this comparison was that the linearized models were not able to predict the mean flow features such as the speed-up, unlike the CFD models (see [
12] for a complete review). In [
13], the flow field over a large-scale model of the same hill was investigated experimentally and showed that the mean wind, wind shear, and turbulence level are extremely sensitive to the details of the terrain. Making the edge of the hill sharper resulted in a reduction of the estimated annual energy production by at least 50% and an increase in the turbulent level by a factor of five in the worst-case scenario. They concluded “the mean wind, wind shear, and turbulence level are extremely sensitive to the exact details of the terrain”. This shows that special attention should be paid not only to the model but also to the topography representation in complex terrains by using high-resolution topographic data and information on land use, such as the Corine land cover [
14].
The use of large eddy simulation (LES) or detached eddy simulation (DES) in complex terrain has increased in recent years. These models are superior to both steady and unsteady Reynolds averaged Navier-Stokes (RANS) as they have the advantage of providing additional information on turbulent structures and non-linear features of wind flow over complex terrain. However, the requirement of high computational resources and the challenge of obtaining proper inflow boundary conditions limits their usefulness for wind engineering studies where a fast solution is required [
10]. In addition, for wind-energy applications, the simulation often needs to be computed for different wind directions or stability conditions. Due to these constraints, RANS/URANS models are still appropriate for use as they provide a good balance between computational effort and model accuracy.
A common problem when using CFD models in a complex terrain is how to specify initial and boundary conditions. A standard way to proceed is to impose a standard logarithmic velocity profile at an inlet which is orientated perpendicular to the wind direction. Another approach is to use numerical weather prediction (NWP) models, also called mesoscale models, to provide more realistic boundary conditions for the CFD simulations. Mesoscale models, generally, have a low spatial resolution with a horizontal extent on the order of 2 km and they generally present a bias on the predicted wind speed and turbulent quantities in complex terrains due to unresolved topographic effects. In [
15], the WRF mesoscale model for the Horns Rev wind farm was applied with a horizontal resolution of 333 m and showed that the model still underestimates the power deficit due to its coarse resolution. Nevertheless, as demonstrated in [
16], much effort has been made to improve the NWP models. Coupling a mesoscale model to a microscale model (CFD), which presents a more detailed representation of the topography seems to be one of the more promising approaches for wind-energy assessment in complex terrain. Several coupling methods of mesoscale and microscale models have been developed in the last decade, and an overview of these methods can be found in [
10,
17]. One of the most common coupling methods is the one-way approach where the mesoscale model is coupled to the microscale model through the lateral boundaries at fixed times (time-slice). This approach has been successfully applied in complex terrain by several authors as [
18,
19,
20] among others.
In the present paper, the WINSENT test site is studied by means of numerical simulations along with UAS data. We confine the study to a neutral stratification case.
Section 2 presents the physical model with its validation, while
Section 3 presents the parametric study. The parametric study is conducted with the help of a design of experiment (DoE) method applied to a two-dimensional case. This study intends to assess the sensitivity of our model results for different parameters and predict their effect on some relevant variables for wind turbines.
Section 4 gives an overview of the test site and the measurement system, while
Section 5 presents the model which uses the one-way coupling approach. The same section compares simulation results against UAS measurements.
Section 6 draws a summary and discusses the limitation of the model and possible future improvements.
3. Design of Experiments (DoE) Study
After verifying the capability of the model to reproduce the flow features in the ABL, the next step was to identify primary contributors to the wind flow at the WINSENT test site. One of the main features of the test site is an escarpment covered by heterogeneous vegetation. The two planned test wind turbines, with a hub height of 75 m and a rotor diameter of 50 m will be installed approximately 200 m downstream of the forested escarpment and will be directly influenced by the canopy. Finding the impact of the forest height and density (which varies seasonally as the foliage grows and develops) on the wind flow can be assessed using a DoE approach. Combining CFD simulations with a DoE can be used to accurately rank the importance of the design parameters in a study [
32] and can significantly reduce, for a real test site, the amount of simulated case and computational time. In our study, the influence of three parameters (namely the slope of the escarpment α, the LAI, and the forest height H) on the horizontal velocity, the flow inclination angle, and the turbulent kinetic energy at different locations, corresponding to the future position of the turbines was investigated.
Table 3 lists the three parameters and their assigned values.
In order to apply the DoE, a simplified test case was defined as shown in
Figure 3. The test case represents a simplification of the test site in two dimensions. We consider a
high escarpment and the slope α to be of 15° or 30°, corresponding to a West and West-North-West wind direction. The escarpment is covered by a forest (green block in
Figure 3).
In the real case, the separation between the forest and the ground is not as sharp, but rather shows a smooth transition. Several studies in the literature on the flow over an escarpment, including wind tunnel, full-scale and simulations exist [
33,
34,
35]. However, none of these studies presents results for a vegetated escarpment.
At the inflow, an empirical power law is used to describe the vertical wind profile as in [
22]:
where
μ(
z) is the average streamwise velocity at height
z.
μ(
zr) = 6
is the reference wind speed at the reference height
and
is the power law exponent. This exponent depends on the surface roughness and the thermal stability parameter α. A value of 0.14 is taken as we assume the neutral case in this DoE study. It is worth mentioning that such a wind profile is an idealized one and is rarely found in a hilly complex terrain. However, our DoE study aims to assess the impact of modelling assumptions for a vegetated escarpement on certain parameters of interest and is not conducted in order to obtain the exact profiles at our specific test site with complex terrains.
We define the speed-up ratio
as being the mean wind speed at a height
z above the ground divided by the mean wind speed of the undisturbed flow at the same height:
Similarly, we define
as the speed-up ratio for the turbulent kinetic energy as:
Speed-up ratio profiles for the wind speed downstream of the escarpment along
and
are presented in
Figure 4. All the possible configurations of variables listed in
Table 3 were simulated, and, additionally, the case of an escarpment with no canopy was simulated. The case without forest allows one to distinguish between the effect caused by the slope of the escarpment and the canopy.
Figure 4 reveals the influence of the canopy, particularly up to
above ground level (agl.). At
, i.e., at the crest, the speed-up ratio shows a reduction in the velocity due to the drag effect generated by the forest, whereas for the case with no canopy, a strong acceleration of the flow can be seen. This effect is still perceptible
downstream of the escarpment (at position
). The same observation was made in the work of [
33]. There, a wind tunnel investigation of the flow over several escarpment shapes with a slope of 2:1 (26.7°) and 4:1 (14.0°) was performed. It was found that the region of influence of the escarpment persists
(
being the escarpment height) downstream of the crest. The largest speed-up ratios were found close to the ground and decreased with increasing height for all cases. The location of the maximum moved upward as the flow proceeded downstream. The inclusion of a forest along the escarpment deflected the position of the maximum speed-up ratio S to higher altitudes. At L
1, the position of the maximum of
located between
and
agl. with no canopy model, and between
and
agl. for the cases with a canopy. The maximum values of S, for a slope of 30°, are higher than in the case of 15°. For example, at
, a maximum value of 1.33 and 1.26 was reached with a slope of 30° and 15°, respectively. This effect was reduced
downstream of the crest, where a maximum of 1.27 and 1.24 was reached. For the same forest height (blue vs. red lines), as expected, a higher deceleration of the flow, i.e., lower value of
was observed for an
of 5 instead of an
of 2. All the positions, except the crest position, show an acceleration of the flow at the relevant heights for a wind turbine (between
and
agl.).
Figure 5 presents the results for the speed-up ratio for the turbulent kinetic energy speed,
. Speed-up ratio profiles for the turbulent kinetic energy are highly dependent on the canopy height and the
. The crest position (
shows a maximum turbulent kinetic energy occurring near the top of the canopy and decaying rapidly above the forest. At position
, the high turbulence levels indicate that the wake generated behind the crest was not dissipated. However, the case without forest seems to be almost recovered and suggests that the changes in the turbulent kinetic energy were only due to the canopy. In general, the turbulent kinetic energy levels increased with the slope angle of the escarpment, but also with the forest height.
The results of the DoE on the 2D escarpment are shown in
Figure 6,
Figure 7 and
Figure 8. The DoE method was applied at two points,
and
, located at different altitudes (
,
and
agl.) on the lines
and
. The absolute effects of each factor, listed in
Table 3, on the horizontal velocity, the inclination angle and the turbulent kinetic energy were evaluated. A similar behaviour for the horizontal velocity (
Figure 6) and the flow inclination angle (
Figure 7) can be seen: the main variability in the response is dominated by the slope of the escarpment. This becomes even more evident for the flow inclination angle. The effect of the forest height
or the leaf area index
remains small relative to the slope, except for the lowest positions at
agl., where the forest height parameter can exceed the same absolute value as the angle (
Figure 6). Generally, as we go further downstream of the escarpment (
vs.
), the effect for the three parameters becomes smaller. The response for the turbulent kinetic energy
was different. The forest height, followed by the
, was as important as the slope at lower levels. All the effects were then dissipated at
agl.
Considering a turbine hub-height of 75
and the top of the rotor blade located at 100
agl., this parametric study shows that the primary contributor was generally the angle, i.e., for the test site, the wind direction. The forest height
and
play a significant role only at 50
agl. This is in accordance with the results from
Figure 4, where the main differences for all the configurations were only perceptible in the lower levels. For the simulations of the WINSENT test site, described in
Section 4.1, a sensitivity analysis using the same parameter values will be conducted.
6. Summary and Conclusions
This study aimed to assess whether or not our model can reproduce relevant features of the flow. The results show the potential of the proposed model based on the Boussinesq approximation and considering the Coriolis effect. The implementation of a limited version of the model has been successfully applied to predict the Leipzig experiment profiles. The limited model consists of reducing Cμ to 0.0256 and to make the production of ε as a function of height. The Coriolis force introduces a velocity component v perpendicular to the direction of the geostrophic wind and causes a turning in the wind. The limiting effect successfully reproduces the Leipzig profile by generating a surface wind turned value close to the experimental one, while the standard k-ε model obtains about half the limited value.
In the second step, we analyzed the flow on a 2D case of the escarpment. The focus was to understand the impact of the slope of the escarpment, the forest height, and the leaf area density on the horizontal velocity, the flow inclination angle, and the turbulent kinetic energy at turbine-relevant heights. A DoE was applied to the simulation results and showed that the primary contributor is the slope of the escarpment, i.e., for the test site, the wind direction. For the wind speed, it was found that the forest height and LAI plays a minor role in comparison to the slope of the escarpment. However, for the turbulent kinetic energy, we showed that the LAI and canopy height is as important as the escarpment slope.
In the final step, the simulations were performed on the WINSENT test site. The aim of the study was to evaluate the accuracy of a modified version of k-ε model in complex terrain. A validation against UAS measurements was performed. For the computation, the boundary conditions were derived from the mesoscale COSMO-DE model. Despite the low resolution of the COSMO-DE model, the one-way coupling method works well in complex terrain. The microscale model captures the varying pattern in the test site, such as the deceleration of the wind speed, the upward flow, and the increased turbulent kinetic energy in the lower levels. Generally, a good agreement was found in the lower levels (75 and 125 agl.) but discrepancies between the simulated results and the UAS measurements were found at upper levels. While the model shows enhanced absolute turbulent values in the lower altitudes, the measurements could not confirm the location of this maximum due to a low vertical resolution. Measurement campaigns with low flight heights, down to 20 are planned and will confirm or disprove the region of high turbulences. A remark on the stability should be mentioned. The assumption of an almost neutral ABL in our study was considered by checking the potential temperature profiles from UAS measurements (between 50 and 300 above the ground). This is also true at those levels, but only measurements near the ground could confirm the flow stratification. However, we have to recognize that it was likely a convective ABL and we should acknowledge that limitation in the paper. Additional measurement systems, such as Lidar, an eddy-covariance micro-meteorological station, and a tower equipped with an anemometer are going to be installed permanently on the test site, a few meters on the upwind and downwind side of the escarpment. This will also enable the attainment of values in lower levels and further valuable data for characterizing the flow and its stratification at the WINSENT test site.
The thermal stratification has a large impact on the vertical wind profile and turbulence levels. Therefore, different thermal stratification cases will be conducted in future studies when the complete measurement set up will be running. For a better comparison of UAS measurements and simulation results, the one-way coupling method with only one time step will be replaced by transient outputs from a mesoscale model.