Lift-based offshore vertical-axis wind turbines for power generation: Current status of technology and future direction of numerical research

Abstract

The vertical-axis wind turbines (VAWTs) are regarded as the best feasible alternative for small-scale power generation due to their design simplicity, ease of installation, good self-starting ability, and independency from wind direction among others. The dilemma of limited land, low onshore wind speed, and the abundance of high-speed wind near the ocean encouraged the researchers to explore the offshore fields. As a result, the lift-based VAWTs are becoming increasingly popular for large-scale offshore wind power production as well as small-scale urban applications. In the present review article, the historical evolution of lift-based offshore VAWTs from their inception to recent advancement has been discussed. The related geometrical and aerodynamic parameters, various loadings, and numerous models utilized in the design and analysis of offshore VAWTs have also been systematically reviewed. Finally, the challenges and the future scope of numerical research have been highlighted.

Keywords

Vertical-axis wind turbines lift-based offshore wind turbines geometric parameters aerodynamic modeling structural dynamics power coefficient tip speed ratio

Introduction

The environmental impact of fossil fuels necessities the development of clean, eco-friendly, and cost-effective sources of energy to overcome greenhouse effect and fulfill the increasing demand of energy. The wind energy can be seen as an alternative that can meet those expectations. As per the Global Wind Energy Council (GWEC) report 2021 (GWEC, 2021), currently, there is 743 GW of wind power capacity installed around the world, preventing nearly 1.1 billion tons of CO₂ from being released into the atmosphere.

The wind energy is extracted by means of a system called as wind turbine. Based on their axis of orientation, the wind turbines can be categorized into (a) horizontal-axis wind turbines (HAWTs) and (b) VAWTs. Further classification of VAWTs can be done based on the driving forces, that is, whether lift-based (such as Darrieus rotor), or drag-based (Savonius rotor) turbines (Patel et al., 2024; Rathod et al., 2024; Saad and Asmuin, 2014; Talukdar et al., 2023). Because of their advantages over HAWTs, currently, the VAWTs are becoming increasingly popular. These VAWTs are characterized by their lesser noise level, self-starting characteristics, omni-directional characteristics, and their generator being located at the bottom (Jain and Saha, 2020; Shukla et al., 2023). The main disadvantage of a VAWT lies with its lesser efficiency as compared to its horizontal counterpart. The onshore wind farm has reached comparatively a mature level mainly for HAWTs (Mohan et al., 2023; Sarma et al., 2021). However, the evolutionary process has not taken place for the offshore VAWTs. Also, it is to be noted that the land topography is the major issue for the onshore wind turbines. Various terrains affect the wind direction and speed which reduces the overall performance of the onshore wind turbines.

Purpose of present study

It is worth noting that various investigations in the field of offshore VAWTs have been conducted since its inception. Few review articles have also appeared in open literature. As for instance, Hand and Cashman (2020) studied a historical development of VAWTs, while Hand et al. (2021a) reviewed the aerodynamic design and performance parameters of offshore VAWTs. On the contrary, Zhao et al. (2022) reviewed the approaches for aerodynamic performance improvement of offshore VAWTs. However, till date, there is not a single article that provides a comprehensive and systematic review on the evolution and progress of offshore VAWT technology. This paper attempts to gather and synthesize all the scholarly work related to these wind turbines to highlight the state-of-the-art research together with the challenges and future direction of research.

Historical development of VAWTs

Utilization of wind energy has been going on for centuries for different purposes like grain grinding, irrigation systems and other small-scale power generation. The lift-based Darrieus VAWT designed by Scottish academic James Blyth in Glasgow, Scotland in 1887 was the first known electricity-generating device. Charles Brush was credited with the first to attempt large-scale wind energy generating in 1887 in Ohio, USA (Matthew and Harrison, 2004). This type of turbine, consisted of vertically oriented airfoil shaped blades rotating along an axis perpendicular to the flow direction, was invented in 1920s and patented in 1931 by French engineer Georges Jean Marie Darrieus (Möllerström, 2019). The patent included both Φ-type with troposkein bent blades and straight bladed H-type (Figure 1). Until late 1960, the VAWTs was not much explored. In 1972, the very first experimental investigation had been conducted by National Research Council (NRC) of Canada. In 1977, they had established a large Darrieus wind turbine rated at 230 kW at Magdalen Islands, Qúebec, Canada (Paraschivoiu, 2002).

Figure 1.

Darrieus VAWTs: (a) Φ-type, (b) H-type.

The United States started working on the development of VAWTs around in 1970. Having conducted rigorous wind tunnel and field tests, they planned, built, and installed 500 Darrieus VAWTs with a rated capacity of over 90 MW till 1997 (Alom et al., 2021). At the same time, in the United Kingdom, a more thorough evaluation of the straight-bladed VAWT was carried out. Peter Musgrove (Musgrove, 1982) of the University of Reading invented the most ingenious prototype variable-geometry VAWT 450 (Figure 2). It had the blade reefing system to control the power production, however, when the blades were in flat position, the significant lift forces caused large bending moments on the support arms, which was a fundamental flaw in the design. To overcome this flaw, the straight-bladed (H-type) turbine was developed in 1990. The vertical-sail-type Chinese windmills are the conventional vertical-axis windmills in China and are known as the Great Windmill or the Chinese Great Windmill (Lin and Lin, 2012).

Figure 2.

The Musgrove VAWT 450 (Tjiu et al., 2015) (reproduced with permission).

After the NRC Magdalen Islands VAWTs disaster in 1978, the research and development had started declining. However, after 2005, because of its greater performance in extremely unstable multi-directional flow condition with minimal noise emissions and attractive look pulled it back to compete HAWTs. Figure 3 depicts the year-wise research papers published in the field of VAWTs. Gorlov (1995) of Northeastern University designed a new helical shaped blades called as Gorlov turbine (Figure 4). This turbine improved the self-starting characteristics but at the same time the efficiency got reduced. It was designed for hydro-power extraction but the helical shape has also been adapted for VAWTs. Till date, the drag based Savonius turbine has not been utilized in offshore applications up to that level because of its lower efficiency. The historical development of VAWTs have been presented briefly and chronologically in Table 1.

Figure 3.

Number of research papers published in the field of VAWTs (Hand and Cashman, 2020).

Figure 4.

The Gorlov helical turbine (Gorlov, 1998; Tjiu et al., 2015) (reproduced with permission).

Table 1.

Summary of the historical development of VAWTs.

Turbine	Year	Origin	Description
Persian vertical wind mill	10th century AD	By Persians	The very first type of windmill developed by the Persians to automate the tasks of grinding grain and irrigation.
First VAWT	1887	James Blyth	It was the first known electricity-generating VAWT designed in Glasgow, Scotland.
Darrieus VAWT	1920	Georges Jean Marie Darrieus	It can have both straight-bladed (H-type) as well as curved-bladed (Φ-type).
Musgrove VAWT	1982	Peter Musgrove	Its variable geometry incorporated a blade reefing mechanism to feather the blades and control the power output at high wind speeds.
Gorlov helical turbine	1995	Alexander M. Gorlov	The straight blades turned along the circumference of the rotor to form a helical shape with some helix angle of (0° < $ϕ$ < 90°).

The rise of offshore VAWTs

The complex design and high cost of energy was the challenging aspect for the expansion of the offshore HAWTs. From the economical point of view, the installation of a wind turbine in deep sea (>50 m) necessitates the platforms to be floating. Because of certain advantages of VAWTs such as lower manufacturing and maintenance cost, high energy density in farms, omni-directional, stability (because of the lower center of gravity, since the generator is installed at the bottom of the system), this type of VAWTs was seen to be preferable for the floating platforms (Shakoor, 2016) in comparison to their horizontal counterpart. It is obvious that the research of floating VAWTs is still in its primary stage. The DeepWind project was the first collaboration between 13 international organizations that were funded by the European Union’s 7th Framework Programme (EU-FP7). Its goal was to develop a floating VAWT system that could reduce the cost of wind energy. At a later stage, multiple projects such as EU-FP7 INFLOW project, Gwind, SeaTwirl AB, SKWID, Aerogenerator X proposed by UK-based NOVA (Novel Offshore Vertical Axis) project and Spinfloat project (Hand and Cashman, 2020; Parsons et al., 2011) have been executed in different countries to develop a scalable and cost effective VAWT model as shown in Table 2 (Hand and Cashman, 2020). A number of research institutions are now looking into the development of offshore floating VAWTs, especially for the large-scale applications.

Table 2.

Summary of floating offshore VAWT projects (Hand and Cashman, 2020).

Projects	Rating (MW)	Turbine configuration	Company	Origin	Status
DeepWind	5	Darrieus curved blades	DeepWind	EU (USA)	Prototype
INFLOW I	2	Helical blades	INFLOW	USA	Prototype
INFLOW II	2	Two rotors with straight blades	INFLOW	USA	Concept
Gwind	—	Helical blades	Gwind	Norway	Prototype
SeaTwirl	1	Helical blades	SeaTwirl AB	Sweden	Prototype
SKWID	0.5	Hybrid (Darrieus/Savonius)	MODEC Inc.	Japan	Prototype
Aerogenerator X	10	V-shaped	Wind Power Ltd.	UK	Concept
Spinfloat	6	Straight blades	EOLFI	France	Concept

Geometric and aerodynamic parameters of offshore VAWTs

The various design parameters associated with the offshore VAWTs are discussed in the following subsection.

Configurations

There are mainly three different types of configurations available for VAWTs (Figure 5), viz., (a) curved-bladed, (b) straight-bladed, and (c) helical-bladed turbines. During the early stages of the development, the blades of VAWTs were primarily curved to withstand the bending stress due to high centrifugal forces encountered during operation. When the turbine is stationary, the curved blades are subjected to gravitational-induced bending strains. However, when the turbine rotates, these bending stresses become dynamic and are finally overcome by the blade centrifugal forces, which commensurate to the turbine’s rotational velocity. The diminishing diameter near the top and bottom of the turbine, where little thrust is produced, is a significant aerodynamic disadvantage of this layout (Tjiu et al., 2015). As a result, the performance of a Darrieus turbine is dependent on the blade curvature (Figure 6).

Figure 5.

Configurations of Darrieus rotor.

Figure 6.

Effect of curvature ratio (Strickland et al., 1979).

Musgrove (1982) emphasized the need of the blades being straight and upright to maximize the aerodynamic efficiency, and hence, developed a straight-bladed geometry. Furthermore, the straight-bladed turbine with its simplest geometry is easier to construct and has a better self-starting ability in comparison to the curved-bladed turbine (Apelfröjd, 2016). The necessity of horizontal struts to hold the blades is a downside of the straight-bladed turbine.

Due to the discontinuous circumferential spacing between the blades, both (straight and curved) the turbines have a variable torque output which causes a torque ripple. To overcome this problem, the helical-bladed turbine has been evolved where the blade shape has swept along the circumference of turbine (Shiono et al., 2002). The helical turbine is superior at self-starting but, the power production reduces with the reduction of helix angle. The maximum power is obtained at 90° helix angle that is, for straight-bladed configuration (Figure 7). Shiono et al. (2002) opined that “the helical-bladed water turbine is better at starting, while the straight-bladed water turbine is better in energy production.” The comparative study of the three configurations has been presented in Table 3.

Figure 7.

(a) Blade helical angle, (b) effect of helical angle on efficiency (Shiono et al., 2002).

Table 3.

Comparison of the three configurations.

Properties	Curved-bladed	Straight-bladed	Helical-bladed
Geometric simplicity	Less simple	Most simple	Complex
Manufacturing cast	Medium	Low	High
Self-starting capability	Low	Medium	High
Shaft torque ripple	High	High	Low
Struts requirement	No	Yes	Yes
Guy-cables requirement	Yes	No	No
Aerodynamic efficiencies	Medium	High	Low

Solidity

The solidity (σ) of a VAWT is defined as the ratio of the entire blade planform area (=NcH) to the swept area (=DH) of the turbine that is, σ = Nc/D (also represented as σ = Nc/R). Here, N, c, H, and D denote the number of blades, blade chord, blade height, and blade diameter, respectively. As σ of the turbine increases, the mass and manufacturing costs of the turbine will also increase. In contrast, a low σ turbine rotates at higher tip speed ratio (TSR = ωR/U_∞), which causes a high centrifugal load and a low peak efficiency of power. As a result, it is critical to choose an optimum σ that maximizes the efficiency without using excessive blade material (Islam et al., 2008a). Strickland et al. (1979) suggested an optimal σ to be in the range 0.2–0.3. As demonstrated in Figure 8, σ has a significant impact on the power coefficient (C_p) of a VAWT (Brusca, 2014).

Figure 8.

Effect of solidity on C_p of VAWT (Brusca, 2014).

Number of blades

The number of blades (N) is an important design consideration that must be balanced between blade rigidity, aerodynamic efficiency, and economic considerations. Blackwell et al. (1977) have suggested that the Reynolds number (Re) should be high as possible, and N should be kept as low as reasonably achievable. It can be seen from the expression (σ = Nc/R) that the σ is directional proportional to Shiono et al. (2000) showed that even when the σ is the same, the turbine’s performance is affected by N. They have opined that the 2-bladed turbine gives a better performance than the 3-bladed turbine, while the 4-bladed turbine performs worse. Although the increasing the number of blades reduces the torque ripple (Bedon, 2015) and improves self-starting capability (Maeda, 2015), but ultimately it increases cost of energy. Sun et al. (2014) investigated the effect of number of blades and found that the 2-bladed turbine has a higher C_p than the 3-, and 4-bladed turbines (Figure 9).

Figure 9.

Effect of number of blades on C_p at constant solidity: (a) σ = 0.10, (b) σ = 0.30 (Sun et al., 2014).

Aspect ratio

The aspect ratio (AR = H/D) is defined as the ratio of height (H) to the diameter of turbine (D). Lower AR means a higher diameter that allows the turbine to have higher chordal Re, but the blade tip losses is also increased due to the large vortex formation. According to Zanforlin and Deluca (2018) the effects of blade tip losses are more significant than the Re effects. As a result, using a large AR with long blades is more critical. Li et al. (2017) demonstrated that with the increase of AR, the C_p increases, and the optimum TSR was also increases (Figure 10). Li et al. (2014) revealed that the increasing AR increases the C_p but the structural strength of blade reaches to its limiting condition. Further increment of AR will cause the structural failure to the blade. Paraschivoiu (2002) has also found the similar results and suggested an optimum AR in the range of 1.3–1.5.

Figure 10.

Effect of AR on C_p of a VAWT with constant c/R ratio (Li et al., 2017).

Use of struts

The struts are used to attach the blades to the central shaft of the turbine. They provide stability and structural support to the blades to bear aerodynamic, inertial, and gravitational loads. However, they create hindrance to the flow and develop undesired drag forces. The drag forces are of two types, viz., (a) profile drag on the surface of struts, (b) interference drag at the joint of blade and struts. The influence of struts is shown in Figure 11, where it is clear that the turbine performance is oversensitive to the addition of support structure, especially at higher TSRs. The use of struts reduces the power outputs by 26% in comparison to the same turbine without struts (Worstell, 1981). The undesired drag can be reduced by using streamlined struts. Bachant et al. (2016) has conducted an experiment with two different struts, viz., one with cylindrical cross section and other with NACA 0012 airfoil. They have found that the streamlined struts with NACA 0012 produces considerably lower drag force. Although the losses in the strut composed of NACA 0021 airfoil were substantially smaller, they were still considered at high TSRs.

Figure 11.

Variation of C_P with TSR of the SNL 17-m turbine (without and with struts) (Worstell, 1981).

The struts are normally horizontally oriented and attached perpendicularly to the blade with T-shape joint (Islam et al., 2008a). The fairings with radius of 6% of chord length were added to the joint to reduce the flow separation and form a smooth boundary layer, which results a minimum interference drag (Gudmundsson, 2014). The horizontally supported struts can have mainly three different configurations: (a) cantilever supported, (b) simple-supported, and (c) overhang-supported (Islam et al., 2008a), as depicted in Figure 12. For minimizing the parasitic drag losses, the cantilever-support type is preferred, while the two struts with overhang-support is preferred for minimum bending moment development (Bhutta et al., 2012). The minimum bending moment occurs when the struts are joined at 20.7% of the blade span from each blade tip(Ahmadi-Baloutaki et al., 2014).

Figure 12.

The strut configurations with bending moment (Hand et al., 2021b).

Airfoils of VAWTs

Figure 13 represents a typical diagram of symmetric and asymmetric (cambered) airfoils. The cost of wind energy depends largely on the type of airfoils used in the manufacture of turbine blades. Thus, it is important to choose the right kind of airfoils for the blade design. The uncambered (symmetric) airfoils were commonly used in early VAWTs due to their superior aerodynamics and ease of manufacturing as evident in reported studies. For example, Elkhoury et al. (2015) studied multiple airfoils, including the NACA 0018, NACA 0021, and NACA 634221 airfoils, and discovered that the NACA 0018 airfoil performed better in VAWTs. Takahashi et al. (2006) has investigated various symmetric airfoils such as MEL002, NACA 0012, NACA 0020, NACA 0024, and NACA 0030 and concluded that NACA 0024 gives an optimum performance. Samanoudy et al. (2010) has investigated various symmetric and asymmetric NACA airfoils such as NACA 0024, NACA 4420, NACA 4520 where C_P was found to be higher for NACA 0024. In this consequence, Mohamed (2012) examined multiple series of symmetric and asymmetric airfoils including NACA 00××, NACA 63×××, A-series, S-series, and FX-series, respectively. Their findings indicated that the S1046 airfoil had a C_P value of 26.83% higher than the symmetric NACA airfoils. Claessens (2006) designed the DU 06- W200, a cambered airfoil specifically designed for VAWTs and found better C_P than that of NACA 0018, in the tested range of angle of attack. Wang et al. (2018) investigated the effects of maximum thickness, maximum camber, and their locations on the aerodynamic performance of a VAWT. The usage of cambered blades for VAWTs is becoming more popular as a result of recent research and enhanced production processes (Healy, 1978a; Yang et al., 2019). In the extensive study on various airfoils used in VAWTs, there is still no agreement on the best option. As a result, many more studies of specialized airfoils for their application in VAWTs need to be conducted in future (Zhao et al., 2022). A chronological development of airfoils used in VAWTs has been presented in Table 4.

Figure 13.

Airfoil nomenclature.

Table 4.

Historical development of airfoils for VAWT applications.

Investigators	Airfoil(s)	Description
Healy (1978b)	NACA 00xx, Gö	The influence of airfoil thickness and camber on VAWT performance
Sheldahl and Klimas (1981)	NACA 00xx	Full 360° airfoil angle of attack wind tunnel tests
Migliore (1983)	NACA 00xx, NACA 6-series, WSU 0015	Natural laminar flow type airfoils were investigated
Klimas (1984)	SAND 0015/47, SAND 0018/50, SAND 0021/50	Design and analysis of the SNL SAND airfoil family
Berg (1990)	SAND 0015/47, SAND 0018/50, SAND 0021/50	Robustness of SAND airfoils to roughness
Galbraith et al. (1992)	GUVA 10	Stall regulated turbine airfoil design
Claessens (2006)	DU 06-W-200	Developed to improve aerodynamic performance and structural strength
Islam et al. (2007)	Many airfoil	Self-starting of small-scale turbines
Danao et al. (2012)	NACA 0012, NACA 0021, NACA 5522, LS0421	Effect of airfoil thickness and camber
Ferreira and Geurts (2014)	DU 12-W-262	Genetic optimization of airfoil design with focus on lift-to-drag ratio
Bedon et al. (2016)	WUP 1615	Genetic performance optimization of an airfoil by 2D URANS
Zamani et al. (2016)	J-DU 06-W-200	J-shaped airfoil to improve the starting torque
Lin et al. (2016)	NACA 0015	Higher C_P with tubercle trailing edge
Wang and Zhaung (2017)	NACA 0018	Leading-edge serrations for higher C_P at low TSRs
Wang et al. (2018)	NACA 0018	Improvement if leading edge serrations using Taguchi’s method
Ma et al. (2018)	NACA 0018	Airfoil optimization using genetic algorithm
Zhu et al. (2018)	NACA 0021	Passive flow control techniques
Song et al. (2019)	NACA 0015	Effect of airfoil leading edge radius
Lositaño and Danao (2019)	NACA 0025	Effect of cambered tubercle leading edge
Bianchini et al. (2019)	NACA 0021	Airfoil design improvement using Gurney flaps
Zhong et al. (2019)	NACA 0018	Dynamic stall control using a leading-edge rod
Rezaeiha et al. (2019)	NACA 0018	Impact of leading-edge slot suction
Mohamed et al. (2020)	NACA0018 Slotted airfoil	To delay flow separation at high angles of attack and thereby improving C_P at low TSR.
Raul and Leifsson (2021)	PARSEC airfoil	To delay dynamic stall over an airfoil
Francis et al. (2021)	MCO-1, MCO-2, MCO-3, MCO-4, MCO-5, MCO-6, MCO-7, MCO-8, MCO-9, MCO-10, MCO-11	Developed from standard airfoils like DU06-W-200-dt, NACA0012h-sa, S822, and S823 and exhibit better performance and good start-up capacity
Ahmed et al. (2022)	NACA 0018	VAWT with guided vane has 26% higher power output than the one without guide vane.
Sun et al. (2023)	NACA 4418	In turbulent condition, the self-starting characteristics of the VAWT is improved with the use of NACA 4418
Ghafoorian et al. (2024)	NACA 0010, NACA 0012, NACA 0018, and NACA 0021	The optimum stagger angle for the configurations with NACA0021 and NACA0018 was found to be 45°, while with NACA0010 and NACA0012, the optimum was 30°

Reynolds number

The Reynolds number (Re) is an essential aerodynamic characteristic, and it must be taken into account while designing the wind turbines. The influence of Re on the performance of 2-m SNL turbine were explored by Blackwell et al. (1976). They have demonstrated that the increase of Re improves the C_P of the turbine in the tested range of TSRs. Also, with the increase of Re, the optimal TSR was found to be decreasing (Figure 14). Similar results were also reported by Battisti et al. (2016) and Bachant et al. (2016). When the turbine works in a turbulent flow regime, Lohry and Martinelli (2016) found the maximum C_P to occur at around the same TSR in the tested range of Re. A high blade Re also has a beneficial influence on the turbine’s ability to self-start, however, this leads a longer blade chord length in the design (Rossetti and Pavesi, 2013).

Figure 14.

Effect of Reynolds number on VAWT performance (Blackwell et al., 1976).

Wake effect for wind farm layout

In general, the wake effect will significantly decrease the wind velocity and increase the turbulence intensity of downstream wind turbines (Rodrigues et al., 2015). Also, the upstream wind turbines can significantly decrease the length scale of the atmospheric streams and can produce added turbulence intensity in the wake region, resulting by about 5%–15% upsurge in the fatigue loads of downstream ones (Cao et al., 2022). Cao et al. (2022) have also proposed a multi-objective wind farm layout optimization framework considering both the power generation and the distribution of turbulence intensity in a wind farm. On the contrary, Yang et al. (2019) studied the wake effect on the wind farm layout using a simulated annealing algorithm. The proposed technique prohibited wake effect concentration on specific turbines by making the wake effect levels uniform.

Performance parameters of offshore VAWTs

There are mainly two parameters upon which performance of a turbine can be described: (a) torque coefficient (C_Q), and (b) power coefficient (C_p). The mathematical description of both the parameters are presented in equations (1) and (2) (Su et al., 2021; Talukdar et al., 2023).

C_{Q} = \frac{Q_{torque}}{\frac{1}{2} {ρ U}_{\infty}^{2} AR}

(1)

C_{P} = \frac{Q_{torque} ω}{\frac{1}{2} {ρ U}_{\infty}^{3} A}

(2)

In equations (1) and (2), Q_torque, U_∞, and ρ represent the generated torque, free-stream velocity and fluid density, respectively. On the contrary, ω, A, and R represent the angular velocity, rotor swept area, and the rotor radius, respectively.

Having reviewed the parameters involved with the offshore VAWTs, the optimum or suggested values/configurations of respective parameters are represented in Table 5.

Table 5.

Optimum parameters of offshore VAWTs from literature review.

Investigators	Parameters	Optimum value
Strickland et al. (1979)	Solidity ( $N c / R$ )	0.2–0.3
Musgrove (1982)	Configuration	Straight-bladed
Galbraith et al. (1992)	Optimum TSR ( $λ_{o p t}$ )	3–4
Shiono et al. (2000)	Number of blades	2–3
Paraschivoiu (2002)	Aspect ratio (H/D)	1.3–1.5
Claessens (2006)	Blade airfoil profile	DU 06-W-200
Islam et al. (2008a)	Strut orientation (joint)	Horizontal (T-shape joint)
Bhutta et al. (2012)	Strut per blade	2
Gudmundsson (2014)	Blade-strut connection design	Faired joint
Gudmundsson (2014)	Fairing fillet radius	0.06c
Ahmadi-Baloutaki et al. (2014)	Strut positions	0.207H (from each blade tip)
Bachant et al. (2016)	Struts cross section	Streamlined airfoil
Xu et al. (2023)	Suitable design scheme for large-scale VAWTs	Installation of one or more levels of turbine arrays on a single platform.
Kuang et al. (2023)	Effectiveness of horizontally and vertically staggered arrangements	Vertically staggered arrangement significantly improves the performance

Loads on offshore VAWTs

The various loads acting on the offshore VAWTs are elaborated in the following subsections

Wind force

The wind force is a static load that induces the static displacement to the system (i.e. floating offshore VAWTs). It can be evaluated by equation (3) (Blusseau and Patel, 2012):

F = 4 \frac{1}{2} {ρ U}_{\infty}^{2} C_{D} S

(3)

where F is the wind force in the wind’s direction, ρ is the air density, U_∞ is the wind speed, C_D is the drag coefficient over VAWT column, and S is the frontal area of the VAWT system.

Aerodynamic forces

Aerodynamic forces cause the rotation of the turbine to harvest energy from the wind. There are two important aerodynamic forces that act on a turbine blade, viz., drag, and lift forces. Drag force acts on the blade in the direction of the relative flow, while lift force acts perpendicularly to the relative flow of wind (Manwell, 2009). Usually, the force of the lift is stronger than the drag and this causes the turbine to spin for a Darrieus turbine. The drag forces generally reduce the efficiency of the turbine. Further, the self-starting capability of the lift-based VAWTs are lesser as compared to the drag-based VAWTs due to the unfavorable angles of attack and dynamic stall at low TSR. An illustration of lift and drag forces on a typical H-type VAWT is presented in Figure 15, where F_LF_DF_N and F_T represent the lift, drag, normal and tangential forces, respectively. Further, W and α represent the relative flow velocity and angle of attack, respectively.

Figure 15.

Aerodynamic forces applied on blades (2D).

Gyroscopic forces

The gyroscopic effect of the spinning turbine rotor is very much significant. Shīlovskīĭ (1924) defines the gyroscopic effect as follows: any couple, apparently tending to incline the axis of a rotating body in a given direction, actually causes an inclination of the axis in a plane perpendicular to that given direction. Every system with a spinning component experiences the gyroscopic effect. This effect experienced by floating platform due to its motion with degrees of freedom (DOF), as illustrated in Figure 16. The gyroscopic effect becomes incredibly influential as the moment of inertia or rotational speed of the rotating element increases. A more detailed discussion on the gyroscopic effects and consideration during modeling has been done by Blusseau and Patel (2012).

Figure 16.

Various modeling used in the analysis of offshore VAWTs.

Hydrostatic forces

The hydrostatic forces are defined as $F = C' x (t)$ where $C'$ is the hydrostatic restoring stiffness matrix, and x(t) is the displacement of body (Borg and Collu, 2015). The hydrostatic forces are the result of buoyancy forces. The buoyant forces caused by displacement of water due to the submerged support structure which give rise to hydrostatic forces. Hydrostatic forces are nonzero only in the heave, roll, and pitch DOFs because the buoyancy force always works vertically upwards. The linear and nonlinear approaches are used to calculate the hydrostatic forces. The linearized technique may appropriately describe the hydrostatic forces, if the support structure displacements are minimal compared to its characteristic length, as the water plane area does not change much over time. On the other hand, if a floating wind turbine experiences large-amplitude vibration there may be considerable variations in hydrostatic stiffnesses over time, a nonlinear approach needs to be preferred (Philippe et al., 2014).

Viscous damping forces

In the formulation of the damping phenomena, the source of damping force is modeled as a function of the volume, shape, and velocity of an object traversing through a real fluid with viscosity (Rao, 2011). Most of the hydrodynamic models are developed for potential flow. As a result, the fluid that interacts with the support structure is inviscid. Therefore, it is necessary to consider a simple viscous model inside a coupled dynamics model to have more realistic model to accurately depict the hydrodynamic forces operating on the floating VAWT. Few approaches have been made such as linear viscous damping and quadratic viscous damping and Morison viscous drag which are reported by Borg and Collu (2015).

Sea/ocean current forces

Due to the relative flow with the water generated by sea/ocean currents, a moored floating structure might endure tremendous loading. Because the amplitude and direction of current speed might change over spatial and temporal based on site circumstances, proper current velocity profiles should be incorporated during coupled model simulations, as required by design standards like DNV-RPC205 (Veritas, 2010).

Several aerodynamic and hydrodynamic loads have been discussed in Section “Performance Parameters of Offshore VAWTs.” All of them have their own influence such as gyroscopic effect, mooring line tension, and others on the system (i.e. floating offshore VAWTs). The aerodynamic forces cause rotation of the turbine rotor and other forces have an impact on the mooring line mechanism. Hence, all of these loads need to be considered while design and modeling of the VAWTs system.

Dynamic modeling of offshore VAWTs

All the models that are used in the analysis of offshore VAWTs can be presented as shown in Figure 16. Some of these models are briefly discussed below.

Structural dynamic modeling

The most basic dynamic model of a body (i.e. floating offshore VAWT) is to treat the body as a single rigid body with a point mass and inertial properties. The next approach would be dividing the system into a number of rigid bodies (for example, dividing VAWT into platform, tower, and blades) and then analyze the forces acting on interconnections between these rigid bodies. For a more reliable model, it is essential to incorporate the flexibility of slender components like tower and blades, using a linear modal representation (Jonkman, 2007). These models have drawbacks in that they are linear and are not applicable for large-amplitude displacements and deflections (Cordle, 2010). To describe the structural behavior of a floating offshore VAWT under a coupled model of dynamics more precisely, additional discretization and the use of various model approaches are necessary. The multibody formulation and the finite element approach are the two basic methodologies in this area which are discussed in the later sections.

Aerodynamic modeling

The Blade Element Momentum (BEM) model, Cascade model, Vortex model, and Panel model are the most commonly used aerodynamic modeling for the VAWTs. In the early design of floating VAWTs, computational fluid dynamics (CFD) methods such as Reynolds–averaged Navier–Stokes (RANS) was not very common due of their high computational cost (Borg et al., 2014a).

Blade element momentum (BEM) model

In this model, the forces applied on the turbine blades are equated to the streamwise loss of momentum throughout the turbine. Templin (1974) proposed a model in which the VAWT is represented as a single stream tube running through an actuator disc and the momentum equations are applied to it. Later, Strickland (1975) has proposed a multiple stream tube model, in which the flow through the actuator disc is divided into a multiple independent identical stream tubes. Each streamtube and the blade parts that are passing through it are therefore subjected to the momentum equation. The double-multiple streamtube (DMST) model (Paraschiviou, 1981) is more sophisticated approach, which has the highest agreement with experimental data for lightly loaded, low-solidity rotors at lower TSRs. This model, in addition to having several streamtubes, also executes momentum calculations independently for the downwind and upwind half-cycles of the rotor. This allowed for the study of more complicated geometry while maintaining the numerical precision (Shires, 2013).

Cascade models

The cascade model for the aerodynamic analysis of VAWTs was first proposed by Hirsch and Mandal (1987). In this model, the rotor blades are supposed to be placed on a planar surface and the gap between blades is equal to rotor circumferential length divided by the number of blades (Figure 17).

Figure 17.

Cascade model configuration (Dixon et al., 2008).

Mandal and Burton (1994) made an improvement in above proposed model by incorporating flow curvature and dynamic stall. These changes improved the model’s ability to effectively simulate the flow and loading characteristics encountered by a VAWT in practice, allowing for local blade force estimates and produced power that were more in line with the study’s experimental results, for low and high σ rotors as well as higher TSRs (Islam et al., 2008b).

Vortex model

In this model, the flow is assumed to be inviscid. The aerofoil blades are divided into several parts, and each of these parts are being substituted by a bound vortex filament (lifting line) (Sarma et al., 2021). Vortices are released with each time step, and they have an impact on the blade’s induced velocity (Figure 18). Larsen (1975) was the first to suggest two-dimensional (2D) vortex models for VAWTs, and later, Fanucci and Walter (1976), Holme (1976), and Wilson (1980) also proposed 2D models. Many assumptions have been made in these models, including high TSRs, lightly laden rotors, short angles of attack to avoid stalling, which limits these models up to a particular set of applications. Strickland et al. (1979) provided the first three-dimensional (3D) model. Strickland et al. (1981) integrated the effects of pitching circulation, dynamic stall, and increased mass. When instantaneous blade forces and near-wake velocities were compared to experimental results, a good correlation was observed. In this consequence, several investigators came up with various approaches to modify the model such as; Cardona (1984), Vandenberghe and Dick (1987), Beyer et al. (2012), and Ponta and Jacovkis (2001). According to Ilin et al. (2012), although the vortex model does not considerably enhance power estimations in comparison to momentum models, it forecasts the blade loads very precisely, which is more important for coupled dynamics of floating VAWTs.

Figure 18.

Depiction of vortex elements with progression of shed vortices (Strickland et al., 1979).

Panel models

This method assumes the flow to be inviscid and the 3D surface of the blade discretizes into several panels, as illustrated in Figure 19. An element such as a source or doublet is put with a predetermined strength on each panel, and the Laplace equation for the inviscid and incompressible flow is then computed. This approach has been widely used in naval hydrodynamics and aviation aerodynamics (Erickson, 1990). Dixon et al. (2008) was the first to propose a 3D panel approach for VAWTs, which was later verified by Dixon (2009) and Ferreira et al. (2010). This model was proposed to examine and comprehend the formation of a VAWT’s near wake and tip vortices. Since the model has assumption that the flow is inviscid, viscous phenomena like stalling are not taken into account. As a result, a boundary layer approach like the lag entrainment approach must be included (Green et al., 1977).

Figure 19.

Panel discretization of a blade section and the wake roll up (Borg et al., 2014a; Flow Solutions Ltd, NEWPAN, 2013).

From the literature review of models used for the aerodynamic analysis of offshore VAWTs, some observations have been made which are represented in Table 6.

Table 6.

Comparative study of aerodynamic models.

Characteristics	BEM model	Cascade model	Vortex model	Panel model
Complexity	Low-medium	Low-medium	Medium-high	High
Implementation	Easy-medium	Easy-medium	Medium	Hard
Flexibility	Low	Low-medium	Medium-high	High
Computational cost	Low	Low	Medium-high	Medium-high
Simulate any aerofoils	No	No	No	Yes
Emphasize rotor-wake	No	No	Yes	Yes
Multiple rotor interactions	No	No	Limited	Yes
Emphasize unsteady conditions	Limited	Limited	Yes	Yes
Power prediction capability	Good	Good	Better	Better
Instantaneous blade forces prediction capability	Low	Low	High	High

Mooring line modeling

Mooring lines serve as a station keeping mechanism for floating offshore VAWTs. They allow them to retain their position on the sea surface and also providing stability to platform under adverse conditions. In offshore turbines, three main types of mooring lines are often employed: (a) catenary mooring, (b) inclined tensioned mooring, and (c) vertical tensioned mooring lines as illustrated in Figure 20. The first one is free-hanging chains or wires that connect a floating platform to seabed anchors at some distance. The second one is taut elastic lines attached vertically or at an inclination to the floating platform, which maintain it to its position using their elasticity (Borg et al., 2014b). The modeling that are used for the analysis of the above mooring lines are discussed below.

Figure 20.

Three main types of mooring lines (Borg et al., 2014b).

Linear force–displacement–velocity model

The linear force-displace-velocity model is the most basic model expressed in equation (4). The mooring stiffness (K) is generally a function of elasticity of mooring line and the direction of mooring line forces, whereas mooring damping (C) is a result of structural and hydrodynamic damping in the mooring system. Although this approach is not particularly efficient, it may be utilized for the preliminary study of the anchored floating platform as it sufficiently describes the features of the system under global movements. The use of a nonlinear force-displacement-velocity equation (5) can give better description of characteristics of the mooring lines, as in this approach, K and C are a function of the degree-of-freedom of platform motion (Borg et al., 2014a, 2014b).

F_{mooring} (t) = C . \overset{\cdot}{x} (t) + K . x (t)

(4)

F_{mooring} (t) = C (x) . \overset{\cdot}{x} (t) + K (x) . x (t)

(5)

Quasi-static model

The quasi-static model is a modified form of linear force-displacement-velocity model. It is an analytical formulation of mooring line loads and is often used for catenary mooring line systems (Jonkman, 2009). This model may consider elastic stretching, buoyant forces, and seafloor friction, but it ignores the mooring wires’ inertia, hydrodynamic, and elastic damping. This method has been used in various researches, but it may produce disappointing results under specific loading conditions, and therefore, the nonlinear dynamic model is preferred (Cordle, 2010). The multi-segmented, quasi-static model (Masciola et al., 2013) is an extension of the quasi-static model. This model is applicable to numerous configurations of mooring lines in 3D space, but each mooring line segment must lie inside a 2D plane. The associated forces and movements at the mooring line-platform connection can be addressed using spatial transformations by applying the quasi-static model to each of these segments.

Multibody model

The inertial features of the mooring lines are considered in this model. This model is also known as Lumped Mass Method (LMM). In this method, each mooring line is divided into a number of stiff or flexible parts and each part is interconnected by a spring-damper system as shown in Figure 21 (Matha et al., 2011). All the internal, external, and inertial forces are formulated at each of the nodes with the assumption of dynamic equilibrium which results a set of differential equations (Kurian et al., 2013). The multibody approach has the benefit of employing the same basic mathematics that defines structural dynamics which allows for the usage of common simulation modules. This will result more efficient and resilient, as well as insure a quick result (Borg et al., 2014a, 2014b). This technique is highly appealing since it can tolerate large-amplitude, hydrodynamic drag forces and 3D movements while not being too computationally costly. But the torsional stiffnesses and structural damping are not incorporated in this approach (Kreuzer and Wilke, 2003).

Figure 21.

Multibody representation (Matha et al., 2011).

Finite-element method

More precise dynamic models may be created using the finite-element method (FEM), although the finer discretization and more sophisticated mathematical description of the mooring lines may result to an expansive computational model, which is extremely undesired for floating offshore wind turbines. Kurian et al. (2013) explained that interpolation functions are used in the FEM to determine an internal system state in terms of mooring line nodal displacements in a generalized coordinate system. The motion of each mooring line member may thus be determined by utilizing these interpolation functions to the given kinematic relations, as well as dynamic equilibrium. Although FEM has computationally costly algorithms, it enables for the study of systems having significant bending and torsional stiffnesses.

From the simple force–displacement relation to the nonlinear finite element model, a series of more sophisticated mooring line models were discussed in Subsection “Gyroscopic forces.” The benefits and drawbacks of each model were explored. There was also a discussion of the trade-offs between computing efficiency and model quality. The force–displacement–velocity model is the simplest approach, calculating only global mooring system static forces, whereas using the multibody formulation or finite element method allows for detailed dynamic analysis of individual mooring lines and their interactions with the environment. The observations made from the literature review about the models used for mooring lines system analysis are represented in Table 7.

Table 7.

Comparative study of mooring line models.

Characteristics	Linear force-displacement-velocity model	Quassi-static model	Multi-body model	Finite-element model
Complexity	Low	Low	Low-medium	High
Computational cost	Low	Low	Low-medium	High
Implementation	Easy	Easy-medium	Easy-medium	Medium-hard
Incorporate nonlinearities	Very limited	Limited	Yes	Yes
Accuracy	Low	Medium	High	High
Individual mooring line analysis	No	Yes	Yes	Yes

Coupled dynamic modeling

A floating wind turbine system is subjected to loads from various sources including aerodynamics, structural dynamics, hydrostatics and hydrodynamics, mooring line dynamics, and control dynamics, as depicted in Figure 22.

Figure 22.

Various loads acting on a 2-bladed VAWT mounted in a semi-submersible support structure (Borg and Collu, 2015).

There are two approaches to formulate all of these loads: (a) frequency-domain modeling, and (b) time-domain modeling (Philippe et al., 2011). Frequency-domain analysis may be an essential tool in the initial stages of design because it is computationally efficient and less expensive. It is very useful to determine the natural frequencies of the system, which are a major design factor because it should be outside the range of frequencies where significant wave energy is located to reduce platform motion response and loads. It has a few significant drawbacks that restrict its application in detailed design. It cannot handle the nonlinear dynamics and also unable to catch transient events such as start-up and shut-down activities, which are important in the design of a floating wind turbine. The time-domain model is preferred to investigate the transient and nonlinear dynamics of floating wind turbines. The Morison equation (Morison et al., 1950) and the Cummins equation (Cummins, 1962) are the two major theories used for the time-domain hydrodynamic modeling. The primary disadvantages of this models are that they are computationally more costly than frequency-domain simulations, and usually require data input from frequency-domain simulations to establish the time-domain model. A more detailed discussion of both the approaches has been done by Borg and Collu (2015).

Numerical investigation on offshore VAWTs

Various researchers investigated the offshore VAWTs using various models and commercial software in order to study and modify the performance of the turbines. The numerical studies and their findings are shown in Table 8.

Table 8.

Summary of numerical investigations of off-shore VAWTs.

Researchers	Model	Software	Findings
Blusseau and Patel (2012)	Double-multiple stream tube model	MATLAB	• The gyroscopic motion greatly amplifies the peak amplitude in roll whatever the wave direction. • The aerodynamic forces induce large static displacements in surge, sway, and yaw.
Paulsen et al. (2013)	FEM	ANSYS	• A rotor with stall control and pultruded GRP blades, considerable weight and load reductions on the rotor are proven.
Siddiqui et al. (2015)	Realizable k − ε turbulence model	ANSYS Fluent	• Increasing turbulence intensity from 5% to 25% reduces wind turbine performance by around 23%–42% when compared to no turbulence in the incoming wind field.
Lei et al. (2019)	IDDES (SST k − ω turbulence model)	CFD software STAR-CCM+	• The wind turbine’s wake profiles can be dramatically altered by pitching and surging motion, and the extent of these alterations becomes more apparent in downwind.
Dabachi et al. (2020)	Double-multiple stream tube model	Q-blade software	• The C_P falls as the variable radius of the turbine increases, however, the mechanical power provided by the rotor increases.
Hand et al. (2021b)	Analytical and FEA model	ANSYS Mechanical	• The analytical methodology proved to be a quick and accurate method for computing the composite blade strain distribution.
Su et al. (2021)	IDDES (SST k − ω turbulence model)	CFD software STAR-CCM+	• Under platform pitch movements, an averaged net C_P enhancement of roughly 1.5%–15% could be attained, and that the variation of aerodynamic loads increased.
Hansen et al. (2021)	SST k − ω turbulence model	CFD software STAR-CCM+	• When the second rotor is located three turbine diameters downstream and at an angle of 60° to the wind direction, the pairs of VAWTs produced 15% more power than the isolated VAWT. • When three turbines were connected in series, the power production was 3% higher as compared to two turbines connected in parallel.
Gatlewar et al. (2021)	—	Pro-E, ANSYS	• The structure steel is found to be suitable material for rotor blade of VAWTs application.
Kuang et al. (2022)	IDDES	CFD software STAR-CCM+	• For moderate and high TSRs, the enclosed type basic diffuser with curved inner surface may greatly increase the C_P of the VAWT.
Ardaneh et al. (2022)	SST k − ω turbulence model	ANSYS Fluent	• A pitch angle of −2° gives better than zero pitch angle for a three-part-blade VAWT.
Xu et al. (2023)	Navier–Stokes solver based on FVM	In house developed solver SuperMan	• Large-scale VAWT is feasible based on aerodynamic performance. • With a consistent reduced frequency, large-scale VAWTs can improve their C_P.
Zhang et al. (2024)	SST k − ω turbulence model	STAR-CCM+ version 13.06	• At low solidity (i.e. 0.1) and moderate TSR (i.e. 3.5), periodic pitch motion results in a 16.42% improvement in the C_P for the full-scale VAWT.

Challenges with offshore VAWTs

In the course of the developing offshore VAWTs, the researchers have experienced multiple challenges which are summarized below.

Early VAWTs used symmetric airfoils because the blade surface alternated between the suction and pressure sides. According to recent research, cambered airfoils improve the performance of VAWTs. Even though various studies on airfoils have been undertaken, there is no agreement on the ideal series of airfoils for use in VAWTs.

The wind gathering device (WGD), augmentation-guide-vane (AGV), diffuser, and flat plate deflector (FPD) are only a few of the several types of power augmentation devices that have been invented. These devices are used to concentrate wind energy. The use of a flow augmentation device can result in an increased aerodynamic efficiency. However, these devices have a number of severe limitations, including a high initial cost, bulky in size, and a complicated design, which have kept them from being commercially viable.

Variable pitch (VP) methods can help VAWTs to enhance their self-starting capability and power production, as well as reduce torque oscillation and function as an aerodynamic brake. However, VP approaches necessitate the use of additional devices, like a yaw system, in order to complete pitching; this adds to the complexity of VP technology. Pitching needs be developed for the intended range of TSR in order to improve the self-starting ability at lower TSR, and increase the peak efficiency at higher TSRs.

Different stages of design necessitate models of varying complexity, and there is no “one-size-fits-all” model that can be utilized throughout the design process. Establishing an effective coupled model of dynamics with a code that offers stable interfaces between modules and is flexible enough to incorporate future notions is a major challenge in this field of research. As realized from the literature review, modeling floating wind turbines requires an integrated approach that considers the interactions between various parts of the system.

Due to the higher difficulties of turbine maintenance in comparison to onshore turbines, higher reliability is essential for the offshore wind turbines. The gearbox of a wind turbine, in particular, is a critical part, accounting for nearly 20% of HAWT malfunctions. Although the direct drive technology eliminates the need for a high-maintenance gearbox and allows for direct attachment of the driveshaft to the generator, when compared to a standard geared generator, the direct drive generator is heavier and bigger. This is not a major issue for the VAWT as it is positioned at the bottom. As a heavier setup is no more desired, hence, there could be some alternative with high reliability and lightweight.

The past numerical studies have mainly focused on increasing the VAWT’s aerodynamic efficiency, whereas little emphasis paid to enhance the turbine’s passive dynamic stall characteristics. This is critical for large-scale VAWTs as they are regulated at high wind speeds using stall-regulation. Some of the dynamic stall models such as Beddoes–Leishman model, ONERA model, and Gormont model have been proposed by the researchers. The Gormont model, originally designed for helicopter rotor applications, is now commonly utilized in VAWT BEM models since it is simpler to apply and has proven to be accurate. However, it has been observed that it overestimates the effects of dynamic stall. Some investigators have proposed a damping coefficient to achieve the high accuracy but still need to have a better alternative to model the effects of dynamic stall more accurately.

Future research direction of offshore VAWTs

The limitation of land areas and the higher wind’s kinetic energy near sea-areas motivated mankind to go for the offshore application to increase the power production through wind turbines. The necessity to maximize offshore wind resources in order to meet renewable energy goals has driven offshore wind turbines farther into the deeper ocean, where floating support foundations are more cost-effective than fixed support foundations. Although the HAWTs have matured in offshore applications, the VAWTs have drawn more attention among researchers nowadays. The design simplicity, easy installation, high packing factor, and scalability are the major driving factor. Kinzel et al. (2012) observed that for a single operating VAWT, the flow velocity required four rotor diameters behind the turbine to reach 95% of the freestream velocity; whereas, for a HAWT, the downwind flow required approximately fourteen rotor diameters to reach 95% of the upwind velocity. As a result, a high energy density can be achieved in farms with VAWTs. Professor Iakovos Tzanakis’ research shows that the VAWT design is far more efficient than traditional turbines in large scale wind farms, and when set in pairs, the VAWTs increase each other’s performance by up to 15%, furthermore, when three turbines were placed in series, the power production was increased additionally by 3% over a pair (Hansen et al., 2021). Professor Tzanakis comments: “This study evidences that the future of wind farms should be vertical. Vertical axis wind farm turbines can be designed to be much closer together, increasing their efficiency and ultimately lowering the prices of electricity. In the long run, VAWTs can help accelerate the green transition of our energy systems, so that more clean and sustainable energy comes from renewable sources.” Since the offshore VAWTs are in the premature stage of development, lots of future research scope are opened to the investigators. A few of them are listed below:

There is still a conflict among the researchers about an optimum airfoil series for VAWTs, hence, a dedicated investigation needs to be done to develop the specific airfoil. It is recommended to use asymmetrical airfoil with an optimum angle of attack to minimize the dynamic stall.

The augmentation devices are beneficial but have multiple limitations such as high initial cost, large size, and complexity. Rigorous research is required to overcome these issues.

The helical-bladed turbine has several advantages such as high self-starting capability, less torque ripple, and produce a more consistent power output. But it produces a lesser C_P that needs to be optimized with further research.

Dynamic stall is a common occurrence that significantly reduces the performance of VAWTs. To overcome the effects of dynamic stall, an investigation should be there holistically.

The effect of varying solidity along the VAWT’s vertical axis on the blade’s aerodynamic qualities would be particularly interesting to investigate.

The VAWT’s blades might benefit from a geometrical spanwise twist, which could improve the aerodynamic performance of VAWTs by reducing the negative torque and increasing the lift force.

Conclusion

Although VAWTs exhibit lower aerodynamic performance than HAWTs, floating VAWTs have attracted more attention from researchers due to their various inherent advantages over HAWTs in offshore applications. This review paper discusses the historical development of lift-type VAWTs from their inception to recent development. The related parameters, various loadings, and the various models which are used to analyze the offshore VAWTs have also been discussed in this paper. The challenges and future research scope of offshore VAWTs have been addressed. The deployment of VAWTs in the offshore wind sector has opened up new possibilities for the VAWT, especially for large deployments. Although large-scale VAWT aerodynamics investigation is still in its infancy, several research institutions are now looking at the development of offshore floating VAWTs. Many of the investigators have hardly tried to improve the efficiencies of the VAWTs wind farms at a large scale by developing different configurations and have succeeded up to a significant level. In the present review work, these studies are reviewed and summarized together with the future scope of research.

Footnotes

Appendix

Acknowledgements

The authors of this study express their sincere gratitude to all the authors of classical and popular papers, reports, text books, and theses that formed the framework of this review study. A list of these has been included in the reference section, and the authors apologize if due recognition to any source has been left out inadvertently. The authors sincerely thank the Elsevier, Amsterdam, Netherlands, for giving the copyright permission to reproduce two images/figures. During the period of this study, the scholarship extended to the first author by the Indian Institute of Technology Guwahati, India, is gratefully acknowledged.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ujjwal K. Saha

References

Ahmadi-Baloutaki

Carriveau

Ting

(2014) Straight-bladed vertical-axis wind turbine rotor design guide based on aerodynamic performance and loading analysis. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 228(7): 742–759.

Ahmed

Hani

Gamal

, et al. (2022) A novel VAWT passive flow control numerical and experimental investigations: Guided vane airfoil wind turbine. Ocean Engineering 257: 111704.

Alom

Saha

Dewan

(2021) In the quest of an appropriate turbulence model for analyzing the aerodynamics of a conventional Savonius (S-type) wind rotor. AIP Journal of Renewable and Sustainable Energy 13(2): 023313-1–023313-10.

Apelfröjd

Eriksson

Bernhoff

(2016) A review of research on large scale modern vertical-axis wind turbines at Uppsala University. Energies 9(7): 1–16.

Ardaneh

Abdolahifar

Karimian

SMH

(2022) Numerical analysis of the pitch angle effect on the performance improvement and flow characteristics of the 3-PB Darrieus vertical-axis wind turbine. Energy 239(D): 122339.

Bachant

Wosnik

Gunawan

, et al. (2016) Experimental study of a reference model vertical-axis cross-flow turbine. PloS One, 11(9): 1–20.

Battisti

Benini

Brighenti

, et al. (2016) Normalized performance and load data for the DeepWind demonstrator in controlled conditions. Data in Brief 8: 1120–1126.

Bedon

De Betta

Benini

(2016) Performance-optimized airfoil for Darrieus wind turbines. Renewable Energy 94: 328–340.

Bedon

Paulsen

Madsen

, et al. (2015) Computational assessment of the DeepWind aerodynamic performance with different blade and airfoil configurations. Applied Energy 185(2): 1100–1108.

10.

Berg

(1990) Customized airfoils and their impact on VAWT (Vertical-Axis Wind Turbine) cost of energy. No. SAND-90-1148C; CONF-9009107-1, Sandia National Labs, Albuquerque, NM.

11.

Beyer

Matha

Sebastian

, et al. (2012) Development, validation and application of a curved vortex filament model for free vortex wake analysis of floating offshore wind turbines. In: 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Nashville, TN, 9–12 January.

12.

Bhutta

MMA

Hayat

Farooq

, et al. (2012) Vertical-axis wind turbine - a review of various configurations and design techniques. Renewable and Sustainable Energy Reviews 16(4): 1926–1939.

13.

Bianchini

Balduzzi

Di Rosa

, et al. (2019) On the use of gurney flaps for the aerodynamic performance augmentation of Darrieus wind turbines. Energy Conversion and Management 184: 402–415.

14.

Blackwell

Sheldahl

Feltz

(1976) Wind tunnel performance data for the Darrieus wind turbine with NACA 0012 blades. No. SAND-76-0130, Sandia National Labs, Albuquerque, NM.

15.

Blackwell

Sullivan

Reuter

, et al. (1977) Engineering development status of the Darrieus wind turbine. Journal of Energy 1(1): 50–64.

16.

Blusseau

Patel

(2012) Gyroscopic effects on a large vertical-axis wind turbine mounted on a floating structure. Renewable Energy 46: 31–42.

17.

Borg

Collu

(2015) Offshore floating vertical-axis wind turbines, dynamics modelling state of the art. Part III: Hydrodynamics and coupled modelling approaches. Renewable and Sustainable Energy Reviews 46: 296–310.

18.

Borg

Shires

Collu

(2014a) Offshore floating vertical-axis wind turbines, dynamics modelling state of the art. Part I: Aerodynamics. Renewable and Sustainable Energy Reviews 39: 1214–1225.

19.

Borg

Collu

Kolios

(2014b) Offshore floating vertical-axis wind turbines, dynamics modelling state of the art. Part II: Mooring line and structural dynamics. Renewable and Sustainable Energy Reviews 39: 1226–1234.

20.

Brusca

Lanzafame

Messina

(2014) Design of a vertical-axis wind turbine: How the aspect ratio affects the turbine’s performance. International Journal of Energy and Environmental Engineering 5(4): 333–340.

21.

Cao

Gao

, et al. (2022) Wind farm layout optimization to minimize the wake induced turbulence effect on wind turbines. Applied Energy 323: 119599.

22.

Cardona

(1984) Flow curvature and dynamic stall simulated with an aerodynamic free-vortex model for VAWT. Wind Engineering 8(3): 135–143.

23.

Claessens

(2006) The design and testing of airfoils for application in small vertical-axis wind turbines. Master of Science Thesis, Department of Aerospace Engineering, Delft University of Technology, The Netherlands.

24.

Cordle

(2010) Enhancement of design methods and standards. UpWind deliverable D4.3.6. WP4: Offshore Foundations and Support Structures, UpWind.

25.

Cummins

(1962) The impulse response function and ship motions. In: Symposium on ship theory. Institut fur Schiffbau, Universitat Hamburg.

26.

Dabachi

Rahmouni

Bouksour

(2020) Design and aerodynamic performance of new floating H-Darrieus vertical-axis wind turbines. Materials Today: Proceedings 30(4): 899–904.

27.

Danao

Qin

Howell

(2012) A numerical study of blade thickness and camber effects on vertical-axis wind turbines. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 226(7): 867–881.

28.

Dixon

Simao Ferreira

Hofemann

, et al. (2008) A 3D unsteady panel method for vertical-axis wind turbines. In: Proceedings of the European wind energy conference and exhibition, pp. 1–10. Brussels: EWEA.

29.

Dixon

(2009) The near wake structure of a vertical-axis wind turbine. Master’s Thesis, TU Delft, Netherlands.

30.

Elkhoury

Kiwata

Aoun

(2015) Experimental and numerical investigation of a three-dimensional vertical-axis wind turbine with variable-pitch. Journal of Wind Engineering and Industrial Aerodynamics 139: 111–123.

31.

Erickson

(1990) Panel methods - An introduction. NASA TP-2995. NASA, CA.

32.

Fanucci

Walter

(1976) Innovative wind machines: The theoretical performance of a vertical-axis wind turbine. In: Proceedings of the vertical-axis wind turbine technology workshop, vol. 3, pp. 61–95. USA: Sandia Laboratories.

33.

Ferreira

Hofemann

Dixon

, et al. (2010) 3D wake dynamics of the VAWT: Experimental and numerical investigation. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, FL, 4–7 January.

34.

Ferreira

Geurts

(2014) Aerofoil optimization for vertical-axis wind turbines. Wind Energy 18(8): 1371–1385.

35.

Francis

Ajayi

Ojo

(2021) Development of a novel airfoil for low wind speed vertical-axis wind turbine using QBlade simulation tool. Fuel Communications 9: 100028.

36.

Flow Solutions Ltd, NEWPAN (2013) Available at: http://www.flowsol.co.uk/products/newpan/ (accessed 20 September 2013).

37.

Galbraith

Coton

Dachun

(1992) Aerodynamic design of vertical-axis wind turbines. Technical report, University of Glasgow, UK.

38.

Gatlewar

Mandavgade

Kanojiya

, et al. (2021) Material selection for rotor blade of vertical-axis wind turbine. Materials Today: Proceedings 46(17): 8489–8493.

39.

Gorlov

(1995) Unidirectional helical reaction turbine operable under reversible fluid flow for power systems. US Patent 5,451,137.

40.

Gorlov

(1998) Development of the helical reaction hydraulic turbine. Final technical report, July 1, 1996–June 30, 1998 (No. DOE/EE/15669-T1), Northeastern University, Boston, MA.

41.

Green

Weeks

Brooman

JWF

(1977) Prediction of turbulent boundary layers and wakes in compressible flow by a Lag-entrainment method. R&M no. 3791, Aeronautical Research Council, London.

42.

Gudmundsson

(2014) General Aviation Aircraft Design: Applied Methods and Procedures, 1st edn. Oxford: Butterworth-Heinemann Publication.

43.

Ghafoorian

Mirmotahari

Wan

(2024) Numerical study on aerodynamic performance improvement and efficiency enhancement of the Savonius vertical axis wind turbine with semi-directional airfoil guide vane. Ocean Engineering 307: 118186.

44.

GWEC (2021) Global wind energy council report 2021. Wind Global Council Energy, 1–61. Available at: www.gwec.net (accessed 26 January 2022).

45.

Hand

Cashman

(2020) A review on the historical development of the lift-type vertical-axis wind turbine: From onshore to offshore floating application. Sustainable Energy Technologies and Assessments 38: 100646.

46.

Hand

Kelly

Cashman

(2021a) Aerodynamic design and performance parameters of a lift-type vertical-axis wind turbine: A comprehensive review. Renewable and Sustainable Energy Reviews 139: 1–30.

47.

Hand

Kelly

Cashman

(2021b) Structural analysis of an offshore vertical-axis wind turbine composite blade experiencing an extreme wind load. Marine Structures 75: 1–13.

48.

Hansen

Mahak

Tzanakis

(2021) Numerical modelling and optimization of vertical-axis wind turbine pairs: A scale up approach. Renewable Energy 171: 1371–1381.

49.

Healy

(1978a) The influence of blade camber on the output of vertical-axis wind turbines. Wind Engineering 2(3): 146–155.

50.

Healy

(1978b) The influence of blade thickness on the output of vertical-axis wind turbines. Wind Engineering 2(1): 1–9.

51.

Hirsch

Mandal

(1987) A cascade theory for the aerodynamic performance of Darrieus wind turbines. Wind Engineering 11(3): 164–175.

52.

Holme

(1976) Contribution to the aerodynamic theory of the vertical-axis wind turbine. In: Proceedings of the international symposium on wind energy systems, Cambridge, UK, pp. 55–71.

53.

Ilin

Dumitrescu

Cardos

, et al. (2012) A free wake method for performance prediction of VAWT. In AIP conference proceedings, College Park, Maryland, USA, vol. 1479, issue 1, pp. 1635–1638.

54.

Islam

Fartaj

Carriveau

(2008a) Analysis of the design parameters related to a fixed-pitch straight-bladed vertical-axis wind turbine. Wind Engineering 32(5): 491–507.

55.

Islam

Ting

Fartaj

(2007) Desirable airfoil features for smaller-capacity straight-bladed VAWT. Wind Engineering 31(3): 165–196.

56.

Islam

Ting

DSK

Fartaj

(2008b) Aerodynamic models for Darrieus-type straight-bladed vertical-axis wind turbines. Renewable and Sustainable Energy Reviews 12(4): 1087–1109.

57.

Jonkman

(2007) Dynamics modeling and loads analysis of an offshore wind turbine. NREL/TP-500-41958, NREL, Golden, CO.

58.

Jonkman

(2009) Dynamics of offshore floating wind turbines - model development and verification. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology 12(5): 459–492.

59.

Jain

Saha

(2020) The state-of-the-art technology of H-type Darrieus wind turbine rotors. ASME Journal of Energy Resources Technology 142(3): 030801.

60.

Kinzel

Mulligan

Dabiri

(2012) Energy exchange in an array of vertical-axis wind turbines. Journal of Turbulence 13(1): 1–13.

61.

Klimas

(1984) Tailored airfoils for vertical-axis wind turbines. In Proceeding of intersociety energy conversion engineering conference, no. conf-840804, research org., ?Sandia National Labs, Albuquerque, NM.

62.

Kreuzer

Wilke

(2003) Dynamics of mooring systems in ocean engineering. Archive of Applied Mechanics 73(3): 270–281.

63.

Kuang

Chen

, et al. (2022) Wind-capture-accelerate device for performance improvement of vertical-axis wind turbines: External diffuser system. Energy 239(B): 122196.

64.

Kuang

Katsuchi

Zhou

, et al. (2023) Strategy for mitigating wake interference between offshore vertical-axis wind turbines: Evaluation of vertically staggered arrangement. Applied Energy 351: 121850.

65.

Kurian

Yassir

, et al. (2013) Nonlinear dynamic analysis of multi-component mooring lines incorporating line-seabed interaction. Research Journal of Applied Sciences, Engineering and Technology 6(8): 1428–1445.

66.

Larsen

(1975) Summary of a vortex theory for the Cyclogiro. In: Proceedings of the 2nd US national conferences on wind engineering research, USA. Colorado State University V-8-1.

67.

Lei

Bao

, et al. (2019) Investigation of wake characteristics for the offshore floating vertical-axis wind turbines in pitch and surge motions of platforms. Energy 166: 471–489.

68.

Karri

Wang

(2014) Three-dimensional numerical analysis on blade response of a vertical-axis tidal current turbine under operational conditions. Journal of Renewable and Sustainable Energy 6(4): 1–10.

69.

Maeda

Kamada

, et al. (2017) Effect of rotor aspect ratio and solidity on a straight-bladed vertical-axis wind turbine in three-dimensional analysis by the panel method. Energy 121: 1–9.

70.

Lin

Bai

, et al. (2016) Performance analysis of vertical-axis-wind-turbine blade with modified trailing edge through computational fluid dynamics. Renewable Energy 99(C): 654–662.

71.

Lin

(2012) Structure and motion analyses of the sails of Chinese great windmill. Mechanism and Machine Theory 48: 29–40.

72.

Lohry

Martinelli

(2016) Unsteady Reynolds-averaged Navier–Stokes simulation of crossflow rotors, scaling, and blockage effects. AIAA Journal 54(12): 3828–3839.

73.

Lositaño

ICM

Danao

LAM

(2019) Steady wind performance of a 5 kW three-bladed H-rotor Darrieus vertical-axis wind turbine (VAWT) with cambered tubercle leading edge (TLE) blades. Energy 175: 278–291.

74.

Lei

Han

, et al. (2018) Airfoil optimization to improve power performance of a high-solidity vertical-axis wind turbine at a moderate tip speed ratio. Energy 150: 236–252.

75.

Maeda

Kamada

Murata

, et al. (2015) Effect of number of blades on aerodynamic forces on a straight-bladed vertical-axis wind turbine. Energy 90: 784–795.

76.

Mandal

Burton

(1994) The effects of dynamic stall and flow curvature on the aerodynamics of Darrieus turbines applying the cascade model. Wind Engineering 18(6): 267–282.

77.

Manwell

Mcgowan

Rogers

(2009) Wind Energy Explained: Theory, Design and Application. Oxford: John Wiley & Sons Limited.

78.

Masciola

Jonkman

Robertson

(2013) Implementation of a multi-segmented, quasi-static cable model. In: 23rd international offshore and polar engineering conference, Anchorage, AK, June 2013.

79.

Matha

Schlipf

Cordle

, et al. (2011) Challenges in simulation of aerodynamics, hydrodynamics, and mooring-line dynamics of floating offshore wind turbines. In: Proceedings of the international offshore and polar engineering conference, Maui, HI, June 2011.

80.

Migliore

(1983) Comparison of NACA 6-series and 4-digit airfoils for Darrieus wind turbines. Journal of Energy 7(4): 291–292.

81.

Mohamed

(2012) Performance investigation of H-rotor Darrieus turbine with new airfoil shapes. Energy 47(1): 522–530.

82.

Mohamed

Ibrahim

Etman

, et al. (2020) Numerical investigation of Darrieus wind turbine with slotted airfoil blades. Energy Conversion and Management 5: 100026.

83.

Mohan

Alom

Saha

(2023), Role of optimization and soft-computing techniques in the design and development of futuristic Savonius wind turbine blades: A review. Wind Engineering 47(3): 722–744.

84.

Möllerström

Gipe

Beurskens

, et al. (2019) A historical review of vertical-axis wind turbines rated 100 kW and above. Renewable and Sustainable Energy Reviews 105: 1–13.

85.

Morison

Johnson

Schaaf

(1950) The force exerted by surface waves on piles. Journal of Petroleum Technology 2(5): 149–154.

86.

Musgrove

(1982) A review of UK wind energy activities. International Journal of Solar Energy 1(2): 145–160.

87.

Paraschiviou

(1981) Double-multiple stream tube model for Darrieus wind turbines. In Second DOE/NASA wind turbines dynamics workshop, NASA CP-2186, Cleve-land, OH, pp. 19–25.

88.

Paraschivoiu

(2002) Wind turbine design: With emphasis on Darrieus concept. Montreal, Canada: Presses Internationales Polytechnique.

89.

Parsons

Chatterton

Brennan

, et al. (2011) Carbon Brainprint case study - Novel offshore vertical-axis wind turbines. Technical report, Cranfield University, UK.

90.

Patel

Alom

Saha

(2024) Aerodynamic analysis of a 2-stage elliptical-bladed Savonius wind rotor: Numerical simulation and experimental validation. International Journal of Green Energy 21(1): 102–115.

91.

Paulsen

Madsen

Hattel

, et al. (2013) Design optimization of a 5 MW floating offshore vertical-axis wind turbine. Energy Procedia 35: 22–32.

92.

Philippe

Babarit

Ferrant

(2014) Aero-hydro-elastic simulation of a semi-submersible floating wind turbine. ASME Journal of Offshore Mechanics and Arctic Engineering 136(2): 1–8.

93.

Philippe

Babarit

Ferrant

(2011) Comparison of time and frequency domain simulations of an offshore floating wind turbine. In: International conference on offshore mechanics and arctic engineering, Rotterdam, The Netherlands, 19–24 June, pp. 589–598.

94.

Ponta

Jacovkis

(2001) A vortex model for Darrieus turbine using finite element techniques. Renewable Energy 24(1): 1–18.

95.

Matthew

HCG

Harrison

(2004) Oxford Dictionary of National Biography. Oxford: Oxford University Press.

96.

Rao

(2011) Mechanical Vibrations, 5th edn. Singapore: Pearson Ed Asia.

97.

Rathod

Saha

Kulkarni

(2024) Bioinspired fluid dynamic designs of vertical axis turbines: State-of-the-art review and the way forward. ASME Journal of Fluids Engineering 146(9): 090801.

98.

Raul

Leifsson

(2021) Surrogate-based aerodynamic shape optimization for delaying airfoil dynamic stall using kriging regression and infill criteria. Aerospace Science and Technology 111: 106555.

99.

Rezaeiha

Montazeri

Blocken

(2019) Active flow control for power enhancement of vertical-axis wind turbines: Leading-edge slot suction. Energy 189: 1–33.

100.

Rossetti

Pavesi

(2013) Comparison of different numerical approaches to the study of the H-Darrieus turbines start-up. Renewable Energy 50: 7–19.

101.

Rodrigues

Pinto

Soleimanzadeh

, et al. (2015) Wake losses optimization of offshore wind farms with moveable floating wind turbines. Energy Conversion and Management, 89: 933–941.

102.

Saad

MMM

Asmuin

(2014) Comparison of horizontal-axis wind turbines and vertical-axis wind turbines. International Organization of Scientific Research Journal of Engineering 4: 27–30.

103.

Samanoudy

Ghorab

AAE

Youssef

(2010) Effect of some design parameters on the performance of a Giromill vertical axis wind turbine. Ain Shams Engineering Journal 1: 85–95.

104.

Sarma

Jain

Mukherjee

, et al. (2021) Hybrid/Combined Darrieus–Savonius wind turbines: Erstwhile development and future prognosis. ASME Journal of Solar Energy Engineering 143(5): 050801.

105.

Shakoor

Hassan

Raheem

, et al. (2016) Wake effect modeling: A review of wind farm layout optimization using Jensen’s model. Renewable and Sustainable Energy Reviews 58: 1048–1059.

106.

Shukla

Alum

Saha

(2023) Spline-bladed Savonius wind rotor with porous deflector: A computational investigation. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44: 444.

107.

Sheldahl

Klimas

(1981) Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical-axis wind turbines. No. SAND-80-2114, Sandia National Labs, Albuquerque, NM.

108.

Shīlovskīĭ

(1924) The gyroscope: Its practical construction and application, treating of the physics and experimental mechanics of the gyroscope, and explaining the method of its application to the stabilization of monorailways, ships, aeroplanes, marine guns, etc. E. & FN Spon, Limited, London.

109.

Shiono

Suzuki

Kiho

(2002) Output characteristics of Darrieus water turbine with helical blades for tidal current generations. In: 12th International offshore and polar engineering conference, Kitakyushu, Japan, May 2002.

110.

Shiono

Suzuki

Kiho

(2000) An experimental study of the characteristics of a Darrieus turbine for tidal power generation. Electrical Engineering in Japan 132(3): 38–47.

111.

Shires

(2013) Development and evaluation of an aerodynamic model for a novel vertical-axis wind turbine concept. Energies 6(5): 2501–2520.

112.

Siddiqui

Rasheed

Kvamsdal

, et al. (2015) Effect of turbulence intensity on the performance of an offshore vertical-axis wind turbine. Energy Procedia 80: 312–320.

113.

Song

Zhu

, et al. (2019) Numerical investigation on the effects of airfoil leading edge radius on the aerodynamic performance of H-rotor Darrieus vertical-axis wind turbine. Energies 12(19): 1–14.

114.

Strickland

(1975) Darrieus turbine: A performance prediction model using multiple streamtubes (No. SAND-75-0431). Albuquerque, NM: Sandia National Labs.

115.

Strickland

Webster

Nguyen

(1979) Vortex model of the Darrieus turbine: An analytical and experimental study. ASME Journal of Fluids Engineering 101(4): 500–505.

116.

Strickland

Webster

Nguyen

(1981) A vortex model of the Darrieus turbine: An analytical and experimental study. No. SAND81-7017, Sandia National Labs, Albuquerque, NM.

117.

Chen

, et al. (2021) Aerodynamic performance assessment of φ-type vertical-axis wind turbine under pitch motion. Energy 225: 120202.

118.

Sun

Liu

Peng

(2023) Power performance and self-starting features of H-rotor and helical vertical axis wind turbines with different airfoils in turbulence. Energy Conversion and Management 292: 117405.

119.

Sun

Wang

, et al. (2014) Aerodynamic performance and characteristic of vortex structures for Darrieus wind turbine. I. Numerical method and aerodynamic performance. Journal of Renewable and Sustainable Energy 6(4): 1–12.

120.

Takahashi

Hamada

Takashi

(2006) Numerical and experimental studies of airfoils suitable for vertical-axis wind turbines and an application of wind-energy collecting structure for higher performance. Journal of Wind Engineering 108: 327–330.

121.

Talukdar

Kulkarni

Chatterjee

, et al. (2023) Vertical-axis hybrid turbines as wind and hydrokinetic energy harvesters: Technological growth and future design strategies. Sadhana 43(3): 178.

122.

Templin

(1974) Aerodynamic performance theory for the NRC vertical-axis wind turbine. No. N-76-16618, LTR-LA-160, National Aeronautical Establishment, Ottawa, ON.

123.

Tjiu

Marnoto

Mat

, et al. (2015) Darrieus vertical-axis wind turbine for power generation I: Assessment of Darrieus VAWT configurations. Renewable Energy 75: 50–67.

124.

Vandenberghe

Dick

(1987) A free vortex simulation method for the straight bladed vertical-axis wind turbine. Journal of Wind Engineering and Industrial Aerodynamics 26(3): 307–324.

125.

Veritas

(2010) Recommended practice DNV-RP-C205: Environmental conditions and environmental loads. DNV, Norway.

126.

Wang

Shen

, et al. (2018), Investigation on aerodynamic performance of vertical-axis wind turbine with different series airfoil shapes. Renewable Energy 126: 801–818.

127.

Wang

Zhuang

(2017) Leading-edge serrations for performance improvement on a vertical-axis wind turbine at low tip-speed-ratios. Applied Energy 208: 1184–1197.

128.

Wang

Zhuang

(2018) Improvement of the aerodynamic performance of vertical-axis wind turbines with leading-edge serrations and helical blades using CFD and Taguchi method. Energy Conversion and Management 177: 107–121.

129.

Wilson

(1980) Wind–turbine aerodynamics. Journal of Wind Engineering and Industrial Aerodynamics 5(3–4): 357–72.

130.

Worstell

(1981) Aerodynamic performance of the DOE/Sandia 17-m-diameter vertical-axis wind turbine. Journal of Energy 5(1): 39–42.

131.

(2023) Feasibility analysis of aerodynamic characteristics for vertical-axis turbines in offshore: A comprehensive analysis on scale and design of wind system. Ocean Engineering 285(Part 2): 115406.

132.

Yang

Kwak

Cho

, et al. (2019) Wind farm layout optimization for wake effect uniformity. Energy 183: 983–995.

133.

Zamani

Maghrebi

Varedi

(2016) Starting torque improvement using J-shaped straight-bladed Darrieus vertical-axis wind turbine by means of numerical simulation. Renewable Energy 95: 109–126.

134.

Zanforlin

Deluca

(2018) Effects of the Reynolds number and the tip losses on the optimal aspect ratio of straight-bladed vertical-axis wind turbines. Energy 148: 179–195.

135.

Zhang

Chen

, et al. (2024) Full-scale vs. scaled aerodynamics of 5-MW offshore VAWTs under pitch motion: A numerical analysis. Applied Energy 372: 123822.

136.

Zhao

Wang

, et al. (2022) A review: Approaches for aerodynamic performance improvement of lift-type vertical-axis wind turbine. Sustainable Energy Technologies and Assessments 49: 1–21.

137.

Zhong

Guo

, et al. (2019) Dynamic stall control on a vertical-axis wind turbine aerofoil using leading-edge rod. Energy 174: 246–260.

138.

Zhu

Hao

, et al. (2018) A critical study on passive flow control techniques for straight-bladed vertical-axis wind turbine. Energy 165: 12–25.