Back to the programme printer.gif Print

Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Aerodynamics and rotor design' taking place on Wednesday, 12 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Guoying Feng Vrije Universiteit Brussel, Belgium
Guoying Feng (1) F P Tim De Troyer (1) Mark C. Runacresa (1)
(1) Vrije Universiteit Brussel, Brussel, Belgium

Printer friendly version: printer.gif Print

Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Ms. Guoying has been working in wind industry for almost 7 years. She is currently a researcher at Vrije Universiteit Brussel and involved in the project ‘Hydroformed blades for meshes of vertical axis wind turbines’. She got her Ph.D degree in wind energy technology in Inner Mongolia University of Technology in China. She spent one year studying wind turbine measurement in Risoe National Laboratory in Denmark. Her research is focused on small wind turbine technology and application.


Optimising land use for wind farms of vertical axis wind turbines


Compared to horizontal axis wind turbines (HAWTs), vertical-axis wind tur- bines (VAWTs) exhibit a different behaviour when built in tight arrays [1, 2]. Dabiri proposed the idea of closely spaced counter-rotating VAWT pairs [1]. Based on field tests and simple calculations they found that the array efficiency of VAWTs could be 5 -10 times higher than existing wind farms. In this research we build a model based on a free vortex model and empirical wake models. The goal is to investigate the main impact factors to power density of wind farms of VAWT pairs.


The wind farm power density is defined as the electrical power generated by the wind farm divided by its footprint area. The power of each VAWT pair is calculated using a free vortex model. The effective flow velocity on each turbine, which is influenced by the wake of upwind turbines, is calculated using Jenson’s wake model and by considering multiple wake effects. The proposed wind farm simulation model takes into account the detailed geometry of VAWTs and influence of upwind turbines on downwind turbines.

1. Free vortex model

A free vortex model has been used for the aerodynamic simulation of one VAWT [3, 4, 5] and the interference of two VAWTs [6]. A turbine is reduced to its blades, and each blade is divided into a number of segments. These segments are then linked to the aerodynamic coefficients via a bound vortex, and to the wake via a free vortex. One advantage of the vortex model is that it calculates the wake, so that it can be used to study the interference between neighbouring turbines.

2. Single wake model

We use Jensen’s wake model [7]. This model considers the wake after the turbine as being turbulent, and its velocity as a function of the downwind distance of the wind turbine. It assumes that the wake expands linearly in both horizontal and vertical direction, as shown in Figure 1.

Figure 1: Schematic of VAWT wake model

3. Multiple wake effects

When multiple turbines lie upwind from the turbine of interest, the individual wakes must be combined. The multiple wake model used here is similar to the one in [8] and [9]. The model considers the shadowed areas of the upstream wind turbines. This shadowing is a measure of the degree of overlap between the area spanned by the wakes and the area swept by the turbine experiencing shadowing, as shown in Figure 2.

Figure 2: Schematic of partial shadowing

Although Jenson’s wake model was developed for HAWTs, based on the similarity of the wake velocity profiles of VAWTs [5] and HAWTs [10] and the ‘actuator disk’ assumption of the model [7], it is assumed here to be capable of approximating the wake of VAWT arrays.

Main body of abstract

Using the proposed methodology, the power performance of VAWT pairs are analysed first. Then the sensitivity of power density to following parameters are investigated:

• wind direction
• turbine height-diameter-ratio
• turbine spacing

We assume that all turbines are equal with parameters as in Table 1.
Table 1: Basic parameters of the VAWT used for simulation

1. Performance of VAWT pairs

To demonstrate the power enhancement of two counter-rotating turbines, the power output of a clockwise-rotating turbine was calculated at multiple positions around the azimuth of a counter-clockwise-rotating turbine. Sixteen different orientations of the turbines are investigated as shown in Figure 3. The corresponding normalized power coefficients obtained at a tip-speed ratio of 3.5 are shown in red. It turns out that the power output of turbine pairs is higher than two isolated VAWTs. So the close proximity of two counter-rotating VAWTs improves their power output relative to the turbines in isolation. Similar results have been obtained by field tests [1].

Figure 3: Plot of normalized power coefficient of turbine CW1 at a tip speed ratio λ=3.5 versus relative position of CW1 to CCW1. Black and blue circles indicate two turbines, arrows indicate the rotational direction.

The turbulence behind a turbine pair reduces when the power coefficient of the turbine increases, as shown by Frandsen [11]. Furthermore, based on the similarity of VAWTs with cylinders and studies on two counter-rotating cylinders [12], it is possible that two counter-rotating VAWTs suppress unsteady vortex shedding. This lower turbulence intensity has two effects. On the on hand, horizontal flow velocity will be less reduced by the turbines. On the other hand, less vertical kinetic energy will be entrained in the wake of the turbines. The future work will demonstrate which one has the dominant effect on the performance of downwind turbines.

2. Sensitivity analysis to wind farm power density

2.1 Wind direction

The impact of wind direction on power density of wind farms is investigated and compared between wind farms using single turbines and turbine pairs, as shown in Figure 4. The power density of wind farms using VAWT pairs could be 5 – 10 times higher than existing wind farms, which is restricted to 2 – 3 W/m2 in practice [13]. The results also indicate that the advantages of using VAWT pairs largely depends on the wind direction distribution of the potential site.

Figure 4: Power density of wind farms (composing of 7 VAWTs and 7 VAWT pairs) varies with turbine spacing and wind direction. ‘dir_ave’ indicates the average over all wind directions examined here.

2.2 Turbine height-diameter-ratio

Since Jenson’s wake model was originally designed for HAWTs and only considers two dimensional wake, the velocity deficit is a function of rotor diameter. In other words, the power density of wind farms using turbines with higher H/D (and thus higher power), is higher than those using turbines with smaller H/D. For instance, the power density of wind farms using turbines with H/D=4 would be 4 times higher than those using turbines with H/D=1, assuming the same efficiency for both turbines. However, this is not true for very large wind farms, for which the vertical kinetic energy flux can’t be omitted.

2.3 Turbine spacing

Figure 5 shows the impact of turbine spacing on power density of wind farms with variable size. For the same number of turbines, smaller turbine spacing means smaller footprint area of wind farms, which contributes to higher power density in general. However, smaller turbine spacing will causes a bigger velocity deficit on downwind turbines and consequently less total power production of the wind farm. Recent field tests indicate that the velocity recovery behind VAWTs is faster than HAWTs [1, 2].

Figure 5: Power density of wind farms with various sizes and densities, composing of VAWT pairs

Comparing with an estimated power density 18 W/m2 based on a field test [1], our simulation results are low. One reason is that the field test was per- formed on an array of 4 VAWTs, and thus the power losses due to the wake is smaller. Nevertheless, the power densities of all wind farms examined here are higher than existing wind farms. These results indicate the great potential of optimising land use by using VAWTs.


Compared with HAWTs, VAWTs have great potential regarding to maximizing land use. The results of this research indicate that the power density of wind farms using VAWTs could be much higher than existing wind farms. Our main findings can be summarized as follows:

• There are two potential advantages using VAWT pairs, one is enhanced power performance for each turbine, which has been investigated by a vortex model simulation here and field test [1]. Another is less energy dissipation in the wake and consequently smaller velocity deficit for downwind turbines, which has been analysed based on Betz theory, but still needs further confirmation.

• Larger turbine H/D contributes to higher power density. For small wind farms, most of the energy extracted by turbines comes from in front of the wind farm. Similar to HAWTs, the required spacing for velocity recovery is mainly relying on turbine diameter. So one can increase the power density of wind farms by using turbines with large H/D. However, the higher power density needs to be balanced with the negative structural impacts caused by increased height.

• The wind direction distribution at potential sites has crucial influence on the power production of wind farms using turbine pairs. For a pair of closely-spaced counter-rotating VAWTs, the power reduction is only significant when one turbine is directly downstream of the other.

• Turbine spacing has a significant impact on power density of wind farms using VAWT pairs. Smaller size and smaller turbine spacing in general contribute to higher power density. Recent field tests indicated that the velocity recovery behind VAWTs is faster than HAWTs [1, 2]. Nevertheless, more intensive investigation still needed.

Learning objectives
• To increase the power density of wind farms using VAWTs
• To understand how closely spaced counter-rotating VAWTs can have a better power performance than
individual turbines
• To predict the aerodynamic interference of VAWTs in proximity using a free vortex model
• To assess the main impact factors on the power density of VAWT farms.

[1] John O Dabiri. Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays. Jour- nal of Renewable and Sustainable Energy, 3:043104, 2011.
[2] Matthias Kinzel, Quinn Mulligan, and John O Dabiri. Energy exchange in an array of vertical-axis wind turbines. Journal of Turbulence, 13(1), 2012.
[3] JH Strickland, BT Webster, and T Nguyen. A vortex model of the dar- rieus turbine: an analytical and experimental study. Journal of Fluids Engineering, 101:500, 1979.
[4] Sandeep Gupta. Development of a time-accurate viscous Lagrangian vor- tex wake model for wind turbine applications. PhD thesis, University of Maryland, College Park, Md, 2006.
[5] Carlos Simão Ferreira. The near wake of the VAWT. PhD thesis, PhD thesis, Technische Universiteit Delft, 2009.
[6] PR Schatzle, PC Klimas, and HR Spahr. Aerodynamic interference between two darrieus wind turbines. In Wind Energy Conference, volume 1, pages 8–13, 1980.
[7] Niels Otto Jensen. A note on wind generator interaction. Technical Report Risø-M-2411, Risø National Laboratory, Roskilde, Denmark, 1983.
[8] Tales G do Couto, Bruno Farias, Alberto Carlos GC Diniz, and Marcus Vinicius G de Morais. Optimization of wind farm layout using genetic algorithm.
[9] F González-Longatt, P Wall, and V Terzija. Wake effect in wind farm performance: Steady-state and dynamic behavior. Renewable Energy, 39(1):329–338, 2012.
[10] LJ Vermeer, Jens Nørkær Sørensen, and A Crespo. Wind turbine wake aerodynamics. Progress in aerospace sciences, 39(6):467–510, 2003.
[11] Sten Tronæs Frandsen et al. Turbulence and turbulence-generated structural loading in wind turbine clusters. Risø National Laboratory, 2007.
[12] Andre S Chan, Peter A Dewey, Antony Jameson, Chunlei Liang, and Alexander J Smits. Vortex suppression and drag reduction in the wake of counter-rotating cylinders. Journal of Fluid Mechanics, 679(1):343–382, 2011.
[13] David MacKay. Sustainable Energy-without the hot air. UIT Cambridge, 2008.