A good understanding of aerodynamic loading is essential in the design of vertical-axis wind turbines (VAWTs) to properly capture design loads and to estimate the power production. This paper presents a comprehensive aerodynamic design study for a 5 MW Darrieus offshore VAWT in the context of multi-megawatt floating VAWTs. This study systematically analyzes the effect of different, important design variables including the number of blades, aspect ratio and blade tapering in a comprehensive load analysis of both the parked and operating aerodynamic loads including turbine power performance analysis. The number of blades is studied for two- and three-bladed turbines, aspect ratio is defined as ratio of rotor height and rotor diameter and studied for values from 0.5 to 1.5, and blade tapering is applied by means of adding solidity to the blades towards blade root ends, which affects aerodynamic and structural performance. Analyses were carried out using a three-dimensional vortex model named CACTUS (Code for Axial and Cross-flow TUrbine Simulation) to evaluate both instantaneous azimuthal parameters as well as integral parameters, such as loads (thrust force, lateral force and torque loading) and power. Parked loading is a major concern for VAWTs; thus, this work presents a broad evaluation of parked loads for the design variables noted above. This study also illustrates that during the operation of a turbine, lateral loads are on par with thrust loads, which will significantly affect the structural sizing of rotor and platform and mooring components.

In order to improve the current situation of global climate change, there is a push for more environmentally sustainable sources of energy in the power grid. As wind energy costs have come down, the opportunity to fill this need by advancing the potential of wind turbine technology is at an all-time high as a part of the initiative to reduce greenhouse gas emissions and provide greater generation by renewable sources. The wind energy community has been mostly focused on horizontal-axis wind turbines (HAWTs), but recently another type of turbine named vertical-axis wind turbines (VAWTs)

VAWTs received a significant amount of attention during the 1970s and 1980s in the USA and Canada

As wind energy is moving to deployments in deeper waters offshore, maintenance and installation procedures as well as cost trends are changing. It has also been shown that floating VAWTs have the potential to achieve a significant reduction in the cost of energy (COE) compared to floating HAWTs

In order to make VAWTs a viable candidate as a replacement for HAWTs, one must have reliable aerodynamic models and reliable predictions of aerodynamic design loads and power production. Some well-established aerodynamic models include the momentum models (single stream tube (SST) model, multiple stream tube (MST) model, double multiple stream tube (DMST) model) and vortex models

A major concern for VAWTs is cyclic aerodynamic loading throughout one revolution, which gives rise to serious issues like high root blade bending moments and fatigue

The aim of this work is to establish and better understand the aerodynamic design process of a floating 5 MW Darrieus VAWT and how the selection of various design variables affects this design process without necessarily going into the detailed explanation of how these design variables affect the flow physics. This study includes blade and tower design loads, rotor power performance, and the loads that are imparted to the floating platform and mooring system. In order to find an efficient design, we perform a comprehensive aerodynamic performance and load analysis by studying trade-offs between different, important design variables. These variables include the number of rotor blades (

Simulations are carried out using a 3D vortex-based code named CACTUS

In summary, the research objective is twofold:

Studying the impact of important design variables like the number of rotor blades (

Providing an understanding of the VAWT's cyclic loads as well as the parked loads, which are typically not investigated.

CACTUS is a 3D aerodynamic design code capable of performing an analysis of arbitrary turbine configurations

Schematic view of a two-bladed VAWT

Following the results of convergence studies, each blade in the model for a 5 MW Darrieus VAWT is represented by 10 elements, and 30 time steps are used per rotor revolution. Calculations are run for 10 rotor revolutions with free wake and with no dynamic stall model, which leads to a maximum of 0.75 % difference between the power coefficient of the last two revolutions at high tip speed ratios (TSR) and a maximum of 0.005 % difference at low tip speed ratios (TSR).

The present work presents a design study aiming to reveal the impact of different important design variables on the aerodynamic performance of VAWTs and subsequently how it affects the design of other major components of the turbine or floating system. Therefore, the parameters are systematically studied, which will provide a comprehensive picture of the influence of design parameters under various operational conditions.

In order to evaluate the relative cost of candidate rotor designs, annual energy production (AEP) must be estimated. Further, aerodynamic loads are required for iterative design of the turbine blades and platform design. As mentioned previously, CACTUS is used to perform all the necessary analysis.

For the purpose of this study, the VAWT machines are assumed to be stall-regulated, with no active power or loads control. They are also assumed to operate with a simple variable-speed controller to optimize energy capture in below-rated wind speed (region 2) of the power curve. A cut-in, cut-out and rated wind speed of 5, 25 and 15

Revolution-averaged performance for 10 revolutions at

Six Darrieus rotor designs were analyzed for the blade tapering and number of blades study, with each design incorporating a unique combination number of blades (two and three) and choice of blade tapering (

A visual representation of the tapering scheme.

Rotor design candidate summary.

The first step of the aerodynamic analysis is the development of the operational strategy as a function of wind speed. To generate the power curve, operating thrust and lateral loads of each design case, a (wind speed (WS)–RPM) schedule must be defined that is assumed to be the operational condition of the turbine. As a first step, a power coefficient

In the second stage, an RPM sweep is performed at the stall TSR to find the required RPM to produce the desired rated aerodynamic power of 5 MW at the selected rated wind speed of 15

Stage 2 and 3 of the operational strategy development.

In the third stage, the rotor RPM schedule is completely defined as a function of wind speed. The RPM is set to the minimum of the RPM giving the optimal tip speed ratio (TSR) for a given wind speed and the RPM for rated power at stall. This defines a simple variable speed control schedule that provides for optimal energy capture under the constraint that the required RPM to maintain rated power is never exceeded. An example of an RPM schedule and resulting operating TSR range is shown in Fig.

This operational strategy is used to generate all the operational loads and power information including power curves and the cyclic thrust, lateral and torque loads vs. wind speed for all the rotor design candidates. As a result the AEP can be calculated from the power curve, whereas the thrust, lateral and torque loads provide the maximum design loads and the cyclic fatigue loads used to design the turbine, the platform and the mooring system.

The impact of blade tapering, number of blades, and the aspect ratio on the performance of a turbine and their impact on the design process is discussed in detail in this section.

In this study tapering is applied to blades by adding solidity, as shown in Fig.

Tapering provided various advantages and disadvantages over conventional non-tapered blades. As tapering adds solidity to the blades it will have a higher performance coefficient (

Figure

Rotor power coefficient (

Figure

Rotor power performance analysis.

Rotor design candidate summary.

The thrust (

Rotor thrust coefficient (

Rotor lateral load coefficient (

The forces on a turbine during parked conditions at extreme wind speeds are a major load case to investigate, to ensure safe operation of the turbine. Parked loads are of increasing concern because VAWT design loads tend to be maximum for the cut-out wind speed, and the loads increase with wind speed (wind force relation) due to the absence of a pitching mechanism

Despite the importance of parked loads in VAWTs, very few studies have
been conducted on the parked load calculations of VAWTs; thus, in this
section we present parked loads for various levels of blade chord
tapering, and in subsequent sections we examine the impact of other
parameters on parked loads.

In this section, parked loads for the six design candidates will be studied to understand the effects of design variables starting with blade tapering on the parked loads. As methods like CFD will be very computationally intensive to predict parked loads, a simplified analytical method has been developed. Some of the assumptions of this study are that blade loads are calculated from measured 180

The numerical model computes the solution for a 3D Darrieus rotor, for a set of specified azimuthal positions, horizontal planes and blade elements similar to CACTUS. As a first step, the relative velocity encountered by the blade is determined assuming that the rotational component and the disturbance velocity induced by wake and bound vorticity are zero. Once the relative velocity is found, the instantaneous angle of attack (AOA) can be determined. It is to be noted that the normal and tangential vectors attached to each blade element are considered while calculating the local blade element angle of attack, and thus it is essential to include the blade curvature effects for a 3D Darrieus rotor. Once the angle of attack (AOA) at each azimuthal position for each blade element at specific horizontal planes is known, one can find the instantaneous lift-and-drag forces on the blade elements from static airfoil data. These lift-and-drag forces are resolved into normal (

Flowchart of the parked load numerical model.

A comparison of the numerical simulation has been performed where the results are compared with

Parked load comparison with existing literature.

There are applicable standards in extreme meta-ocean condition like the 50- and 100-year return periods. As International Electrotechnical Commission (IEC) prefers 50-year return periods for extreme design conditions; in this work the parked loads are calculated using a site-specific 50-year return period having a 10 min average wind speed of 30.94

We now examine the rotor thrust and lateral parked loads for different blade chord tapering with results shown in Fig.

Parked thrust load (

Parked lateral load (

Increasing the solidity or tapering(

The number of blades is an important design consideration, which significantly affects the aerodynamic performance of a VAWT because a change in the number of blades will significantly affect the forcing frequency of the cyclic aerodynamic loads. Further, the number of blades may cause a change in solidity, Reynolds number, blade wake interaction, stall behavior, etc. The effect of changing the number of blades on aerodynamic forces generated in VAWTs and the performance coefficients will be discussed in this section. This work investigates the impact of the number of blades on the steady and cyclic turbine loads including thrust loads, lateral loads, parked loads and power ripple effects of Darrieus turbines.

The influence of the number of blades on VAWT aerodynamics has been studied previously in detail; however, most studies have focused primarily on VAWTs with straight blades, which are known as H-VAWTs.

To demonstrate the impact of the number of blades on turbine performance, the power coefficient (

Power coefficients (

Figure

Rotor thrust coefficient (

We now turn our attention to cyclic aerodynamic load variations, where the thrust and lateral load profiles for two- and three-bladed turbines are shown in Fig.

Thrust load (

To demonstrate the effect of the number of blades on parked loads, it is important to show the orientation of loads to wind direction. The dependence of parked (thrust and lateral) loads on number of blades is demonstrated in Figs.

Maximum and minimum of parked thrust (

The change in cyclic load amplitude has been quantified according to previous sections. For

As the solidity is kept constant for the number of blades study, the chord value along the blade span decreases for three-bladed rotors, which causes a reduction of the blade structural stiffness. This reduction in stiffness might lead to deflection and fatigue issues, which can be counteracted by a structural redesign of the blade. This structural redesign usually results in a heavier blade to due increased spar cap thickness or adding more carbon to the blade composite layup

As noted, there are multiple parameters affecting the performance of a VAWT. Thus far, we have examined solidity including solidity changes through variable chord tapering and the impact of the number of blades. We now turn our attention to the impact of aspect ratio (AR) and its effect on aerodynamic performance and loading. The effect of the changing rotor aspect ratio (AR) on the aerodynamic forces generated by a VAWT and the performance coefficients will be discussed in this section. As changes in aspect ratio (AR) affect the aerodynamics of a VAWT especially for Darrieus configurations, it is important to study the change in performance and loads. For this study, aspect ratio is defined as the ratio between the rotor height (

The effect of aspect ratio on VAWT performance has been investigated previously through both experiments and numerical simulation and mostly for H-type VAWT rotors. The effect of changing the aspect ratio on H-type VAWTs has been studied by

The effect of aspect ratio on H-type VAWTs also has been studied using a 3D panel method by

Despite these studies of AR for H-type VAWT rotors, no similar studies of aspect ratio impacts on aerodynamic loads and power performance have been performed for Darrieus-type VAWT rotors. In the following sections, we employ the CACTUS code in a 3D analysis of these aerodynamic effects for a change in aspect ratio similar to the prior studies for variable blade chord tapering and number of blades shown in prior sections.

It can be seen from the literature that different non-dimensional parameters can give us erroneous perceptions regarding the effect of aspect ratio on rotor performance; therefore, in this study the aspect ratio has been varied in such a manner that the rotor diameter (

Figure

Power coefficient (

As seen from the figure, the peak of the power coefficient increases with the increase in aspect ratio (

Maximum power coefficient (

This increase in power coefficient with aspect ratio (AR) can be attributed to blade curvature effects. As a low-

Individual blade power coefficient (

The effect of increasing the aspect ratio (AR) on the thrust and lateral loads is studied in this section. Figure

Thrust coefficient (

Lateral load coefficient (

Because parked loads are a major load case in designing VAWTs

Parked rotor thrust load (

Parked rotor lateral load (

As seen in this section, increasing the turbine aspect ratio significantly affects the power and loads of a turbine. It is important to carefully select the design aspect ratio of the turbine as a high aspect ratio value will lead to greater power production but will also result in significantly higher parked and operating loads. Aspect ratio will also affect the rotor center of gravity, which in turn affects the floating platform stability.

In order to generate modern and efficient VAWT rotor designs, one needs to understand the design space and the variables affecting the aerodynamic design space of a VAWT. However, to capture the effect of one design variable on the turbine performance, it is important to isolate the effect of that particular design variable so we can reach proper conclusions. In this work a comprehensive and systematic study of the effect of blade tapering (

In this study, a mid-fidelity 3D vortex model named CACTUS (which has been validated with experimental data) has been used to carry out all the analysis. Both two- and three-bladed turbines have been studied for different blade chord tapering schemes (

Some of the highlights of the present study are listed as follows.

Blade chord tapering impacts

As tapering has been applied to the blades by adding solidity, the power coefficient (

With an increase in tapering, the maximum operating RPM to produce a rated power of 5 MW also decreases, and the lower RPM leads to higher torque, which will increase the cost of the drivetrain.

As for turbine loads, there is an increase in thrust coefficient with increasing

We also see similar trends for parked loading too. With an increase in

Number of blades impacts

The effect of the number of blades on the power coefficient has been studied both at low and high wind speeds to observe the effect of Reynolds number on trends since changing the number of blades directly affects the chord-to-radius ratio (

As the solidity is kept constant for both two-bladed and three-bladed rotors for a particular

Adding one blade to 2B turbines significantly affects the range of the load profiles or the ripple effect. For example, when one blade is added to a 2B (

Similar trends are also seen for parked load variation. There is a massive reduction in the range of both thrust and lateral parked loads for the three-bladed rotor in comparison to the two-bladed rotor. It is important to note that the magnitude of parked loading on a three-bladed turbine is independent of the incoming wind direction, which is in direct contrast to a two-bladed turbine. So parked loading on a two-bladed turbine can be significantly reduced through an optimal parking operational strategy.

Aspect ratio impacts

The effect of changing aspect ratio (AR) has been quantified for

With an increase in aspect ratio, the power coefficient, thrust coefficient and peaks of lateral load coefficient increase.

A similar trend is observed for parked loads too, where the peak of thrust and lateral loads increases with an increase in aspect ratio.

The findings in this work provide a better understanding of the effect of blade chord tapering, rotor aspect ratio, and number of blades on the power, thrust, lateral, and parked loads and shed light on some important load conditions which are usually overlooked, namely VAWT parked loads and the cyclic lateral (side-to-side) loading components. In future studies, to better quantify the effects of these design variables, the analysis should be coupled with a levelized cost of energy (LCOE) analysis. This can be really insightful as a small change in a single parameter will change the cost of energy as other variables are also affected – for example, to see if the cost of adding an extra blade is lower than the savings it would lead to or if opting for a turbine with higher

The code is available in the public CACTUS GitHub repository (

The data that support the findings of this study are available on reasonable request from the corresponding author (D. Todd Griffith).

This work was performed during the MS of MSS under the supervision of DTG as part of an Advanced Research Projects Agency–Energy (ARPA-E)-funded project named A Low-cost Floating Offshore Vertical Axis Wind System. MSS and DTG contributed to the analysis and interpretation of the data, and the manuscript was prepared by MSS with the help of DTG.

The contact author has declared that neither they nor their co-author has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The research presented herein was funded by the US Department of Energy Advanced Research Projects Agency–Energy (ARPA-E) under the ATLANTIS program with the project title A Low-cost Floating Offshore Vertical Axis Wind System and with award no. DE-AR0001179. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of ARPA-E. The authors are grateful for the support of the ARPA-E program and staff, as well as the project team.

This work was funded by the US Department of Energy Advanced Research Projects Agency–Energy (ARPA-E) (grant no. DE-AR0001179).

This paper was edited by Gerard J. W. van Bussel and reviewed by Claudio Balzani and one anonymous referee.