Darrieus vertical axis wind turbine for power generation I: Assessment of Darrieus VAWT configurations

Darrieus vertical axis wind turbine for power generation I: Assessment of Darrieus VAWT configurations

Renewable Energy 75 (2015) 50e67 Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene Review...

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Renewable Energy 75 (2015) 50e67

Contents lists available at ScienceDirect

Renewable Energy journal homepage: www.elsevier.com/locate/renene


Darrieus vertical axis wind turbine for power generation I: Assessment of Darrieus VAWT configurations Willy Tjiu a, *, Tjukup Marnoto b, Sohif Mat a, Mohd Hafidz Ruslan a, Kamaruzzaman Sopian a a b

Solar Energy Research Insititute (SERI), National University of Malaysia, UKM Bangi, Selangor 43600, Malaysia Faculty of Industrial Technology, “Veteran” National Development University, UPN Jogjakarta 55283, Indonesia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 December 2013 Accepted 18 September 2014 Available online

This paper aims to assess the Darrieus vertical axis wind turbine (VAWT) configurations, including the drawbacks of each variation that hindered the development into large scale rotor. A comprehensive timeline is given as a lineage chart. The variations are assessed on the performance, components and operational reliability. In addition, current development and future prospects of Darrieus VAWT are presented. The Darrieus VAWT patented in France in 1925 and in the US in 1931 had two configurations: (i) curved blades and (ii) straight blades configurations. Curved blades configuration (egg-beater or phirotor) has evolved from the conventional guy-wires support into fixed-on-tower and cantilevered versions. Straight blades configuration used to have variable-geometry (Musgrove-rotor), variable-pitch (Giromill), Diamond, Delta and V/Y rotor variations. They were stopped due to low economical value, i.e. high specific cost of energy (COE). Musgrove-rotor has evolved into fixed-pitch straight-bladed Hrotor (referred as H-rotor in this paper for simplicity). H-rotor, in turn, has evolved into several variations: Articulating, Tilted and Helical H-rotors. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Darrieus VAWT H rotor Musgrove Giromill Articulating

1. Introduction During the Cold War and energy crisis in 1970s, wind turbines were recognized and developed for its potential in power generation since wind energy resource was unaffected by political and economic insecurity. Interest in developing wind energy technology had sprouted Darrieus VAWT out of the vacuum. An already known wind turbine technology for electricity generation at the time was HAWT pioneered by Poul la Cour in Denmark in 1891 [1]. Until currently, only variable-pitch Darrieus VAWT configuration known as giromill that is deemed as efficient as HAWT with coefficient of performance (CP) of about 0.5 [2,3]. For a 500 kW variablepitch giromill at mean wind site of 5.4 m/s, Darrieus VAWT power generation cost was found out to be about 18e39% less than the HAWT counterpart [2]. However, the practical implementation has been challenging for Darrieus VAWT researchers. Unlike HAWT blades which see relatively steady angle of attack (AOA) of the incoming wind, VAWT blades undergo inconsistent AOA which

* Corresponding author. SERI, Level 3, Perpustakaan Tun Sri Lanang, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia. Tel.: þ603 8921 4596; fax: þ603 8921 4593. E-mail address: [email protected] (W. Tjiu). http://dx.doi.org/10.1016/j.renene.2014.09.038 0960-1481/© 2014 Elsevier Ltd. All rights reserved.

changes rapidly between the positive and negative angles. In addition, VAWT blades encounter turbulent wind in the leeward side due to the vortices created by the blades passing through the windward side. These phenomena present Darrieus VAWT designers a complicated aerodynamic problems not experienced by HAWT blades. Darrieus VAWT was intensely investigated for about two decades, mainly at National Research Council (NRC) in Canada, Sandia National Laboratories (SNL) in the US, and The Carmarthen Bay Wind Energy Demonstration Centre in the UK. Attempts in building large scale Darrieus VAWT were carried out by Dominion Aluminium Fabricators in Canada [4], Alcoa in the US [5], and James Howden and Co., Wind Energy Group, Ltd. and VAWT, Ltd. in the UK [6]. Recent innovations on Darrieus VAWT have contributed to simpler and predictable characteristics, which improve the reliability and performance of the turbine. The innovations differ distinctively from the previous developments in the 1970se1990s, especially in terms of design complexity and the components used. 2. Evolution of Darrieus VAWT After the WWI, G.J.M. Darrieus, a French aeronautical engineer, invented a VAWT by adopting airfoil profile for the blades. He

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patented the design in France in 1925 and in the US in 1931 and put the working principle as a biomimicry of birds' wings by stating, “It is thus possible to give these blades a stream line section analogous to that of the wings of birds, that is to say, offering the minimum resistance to forward movement and capable of converting into mechanical energy the maximum available amount of energy of the fluid by means of the useful component of the traverse thrust which this section undergoes” [7]. The patent covered two major configurations: curved and straight blades as shown in Fig. 1. The curved and straight-blades configurations have evolved into several variations, as shown in Fig. 2. Curved-blades configuration has been known as egg-beater or phi-rotor due to the similar look. There are several variations of phi-rotor, such as guy-wired, fixedon-tower and cantilevered versions (details on these types are available in the following sections). Similarly, straight-blades configuration has several variations. Diamond, V/Y and delta (D) variations have been documented [8,9]. Another variation, a variable-geometry VAWT or often called Musgrove-rotor had been replaced by fixed-pitch H-rotor (referred only as “H-rotor” in this paper for simplicity). Currently, H-rotor has been actively investigated, including multi-megawatt rotor for offshore application (details on the topic are available in the Part II of this article). Furthermore, improvements on H-rotor sprout another three variations: Articulating, Helical and Tilted H-rotor. Details on Articulating and Helical H-rotor are given in the following sections, while Tilted H-rotor is given in the Part II of this article. 3. Support structures for Darrieus VAWT G.J.M. Darrieus did not mention specific support structure for his invention in the patent. However, curved-blades configuration with cable or guy wires support has been very popular due to the intense research in the US and Canada. Nevertheless, several support structures have been implemented for both curved- and straightblades Darrieus VAWTs, as shown in Fig. 3. Although the illustrations in Fig. 3 are depicted using curved-blades, it is applicable for straight-blades configuration as well. Guy wires support (A) has been widely used for phi-rotor. Guy wires cannot be readily mounted on top of the rotor shaft in straight-blades configuration without extending the rotor shaft or the use of support arms for the wires. Alternatively, a combination of cantilever support and guy wires (B) has been used for straightblades configuration. Guy wires support has been less preferable in recent years [10e12] due to several drawbacks, including increased axial load on the bearings due to wire tension in (A), vibrations induced by the rotor and the wind, and large land area required to mount the wires [2]. Fixed-on-tower (C) requires a customized


generator for a particular tower since the generator stator coils are mounted on the tower's stationary shaft, while generator rotor are attached to the lower hub of the rotor shaft. In addition, the stationary shaft diameter to height ratio is preferably about 0.01e0.02 [13]. Cantilevered-rotor (D) has been used with great success. It has several advantages compared to other types due to its simplicity in manufacturing and maintenance. The components manufacturing is flexible since the drivetrain is not embedded into the rotor and stator assemblies as in (C). In addition, the drivetrain is detachable for simpler onsite maintenance [14]. Among these four types, cantilevered-rotor will most likely be dominant in future Darrieus VAWT development. 4. Tailored airfoils for Darrieus VAWT Airfoils used for commercial Darrieus VAWTs are usually based on the airfoils used in aviation industry. The most common profiles used are the symmetrical NACA airfoils [2,12,15], with thickness usually ranges from 12% (NACA 0012) to 21% (NACA 0021). Some manufacturers camber the airfoils in order to capture more energy at either side of the rotor [16,17]. However, no significant difference in the performance has been reported as compared to the Darrieus VAWT with symmetrical airfoil, since cambering the airfoil causes an increase of tangential force in one half, but decreases the force in the other half of the swept region [18]. SNL found that a way to improve the performance was by designing airfoils specifically tailored for Darrieus VAWT [19]. They argued that standard aviation airfoils are not intended for Darrieus VAWT since the operating regime of a VAWT blade is very different from an airplane blade, which can be summarized in Table 1 [20]. Summary of the intended tailored airfoil characteristics by SNL compared to the experimental results obtained are shown in Table 2 [20]. The tailored airfoil exhibits more reliable turbine operation via better tip speed ratio (TSR) range cut-off near the peak CP condition over the standard NACA 4-series, and is implemented on variable-speed turbine [21]. The tailored airfoil is employed at the transition and equatorial sections to provide overspeeding regulation. While for the root sections at which the TSR is lower than the equatorial section, standard NACA 4-series is used. This is due to the customized natural laminar flow (NLF) airfoils by SNL have sharp leading edge, which make them more suitable for high TSR. The root sections in a phi-rotor experience higher AOA, so that the rounded leading edge of standard NACA 4-series airfoils performs better. The combination reduces the COE and increases the turbine reliability and lifetime [21]. Based on the results by SNL, future Darrieus VAWT blades should use the combination of standard NACA 4-series and NLF

Fig. 1. Original illustrations by G.J.M. Darrieus in 1931 patent: curved blades (left) and straight blades (right). Annotations in the figure: (a) ¼ blades, (e) ¼ supporting plates, (f1) and (f2) ¼ hubs, (f) and (g) ¼ rotor shaft [7].


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Fig. 2. Timeline of Darrieus VAWT development.

airfoils for phi-rotor and whole NLF airfoils for H-rotor. Fortunately, standard NLF airfoils like NACA 65-series look similar to the SAND airfoils. Therefore, with the help of modern analytical software, various NLF airfoils can be investigated for use as Darrieus VAWT blades. Fig. 4 shows the comparison of SAND airfoils to NACA 65series. Standard symmetrical NACA 4-series are represented as dotted lines to serve as the comparison baselines. A recent investigation using computational fluid dynamic (CFD) has been performed on 20 shape of airfoils listed in Table 3 along with the simulation results [22]. Unfortunately, the author neither

included symmetrical NACA 65-series nor SAND airfoils in the simulation. Fig. 5 shows Selig S 1046, the best performing airfoil in the simulation with CP of 0.4051. The simulation, however, was neither optimized for certain TSR nor Reynolds number. The author simulated several rotor solidities between 0.1 and 0.25 with TSR ranges from 2 to 10. The S 1046 has a similar trailing edge shape to the NLF airfoils shown in Fig. 4. The leading edge is also slightly sharper than the standard NACA 4-series, but it is not as sharp as the NLF airfoils. However, the main difference between S 1046 and SAND/NACA65-series is the location of the thickest point. S 1046

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Fig. 3. Types of support structures for curved- and straight-blades Darrieus VAWTs.

Table 1 Operating conditions of a Darrieus VAWT blade and an airplane blade.

Table 3 List of airfoils simulated with the corresponding CP [22].


Blades of a Darrieus VAWT

Blades of an airplane



Operate in unsteady conditions; oscillate between positive and negative AOA twice per revolution, which are often exceeding ±90 . Encounter stall frequently, especially in strong wind.

Operate in nearly steady conditions at near zero AOA.



Reynolds number (Re)

Between a few hundred thousand and a few million.

Encounter stall only in unusual operating conditions. Usually between three and thirty million.

0010 0015 0018 0021 6312

CP max Airfoil

CP max Airfoil CP max Airfoil

CP max

0.2345 0.2947 0.2964 0.2679 0.1290

0.1711 0.2772 0.2469 0.2541 0.2130

0.2074 0.1639 0.2961 0.3311 0.3576

NACA 63415 NACA 63418 AH93W174 AH93W215 AH94W301

AG18 S 809 S 9000 S 1046 S 1014

0.0123 0.3428 0.1696 0.4051 0.2769

FX66S196 FX77W256 FX71L150 FXL142 FXLV152

5. Egg-beater or phi (4) rotor 5.1. History of phi-rotor

has the thickest point similar to NACA 4-series at about 30% of chord from the leading edge, while the NLF airfoils' thickest point is at 50% (except for SAND 0015/47, which is at 47% from the leading edge).

Table 2 Comparison between actual and intended characteristics of SAND airfoils. Requirements of tailored-airfoil

Actual characteristics of tailored-airfoil

Increase the maximum CP (higher power generation). Force blade stall at a wind velocity closer to the maximum CP (Over-speed and power regulation in strong winds). Allow the turbine to operate at higher rotational speed (higher power generation and lowering the cost of direct-drive generator).

Modest value of maximum CP. - Low drag at low AOA, and high drag at high AOA. - Sharp stall. Higher operational speed is achieved by using low thickness/chord ratio.

Fig. 4. Tailored airfoil by SNL (left) [20] and standard NACA 65-series (right).

Darrieus VAWT had experienced a vacuum period for about four decades when South and Rangi of the NRC of Canada reinvented the phi-rotor design in 1968 [23]. The local community called it “RangiSouth Wind Turbine” [24], being unaware it was previously invented by Darrieus. Thereafter, Darrieus VAWT caught the interests of many researchers [25e38], and various dynamic analysis on the performance were formulated, including blade momentum, vortex, and finite-difference models. Unfortunately, not long after the investigations into phi-rotor gained momentum, several machines experienced problems in the drivetrain, control system and brakes. The failure started with the first large scale phi-rotor of 224 kW manufactured by Dominion Aluminium Fabricators under NRC supervision in Magdalen Islands, Canada [4]. The machine crashed to the ground in 1978, a year after its operation. In the US, Alcoa built several phi-rotors under SNL supervision, including the 12.8 m, 17 m and 25 m diameter with generating capacity of 30e60 kW, 60e100 kW and 300e500 kW, respectively. However, similar fate with the turbine in Magdalen Islands, turbines built by Alcoa had various problems. The 12.8 m turbine collapsed in 1980 when the rotor column vibrated and buckled due to over-speed. The 25 m turbine crashed in 1981 when software error in the controller failed to actuate the brake in strong winds [5]. The last and biggest phi-rotor built by SNL was called “Test Bed” with rotor diameter of 34 m, which was operational in 1988. The rotor had a swept area of 955 m2 and height-to-diameter ratio of 1.25. It achieved 500 kW rated power at 37.5 rpm in mean velocity

Fig. 5. Selig S 1046 airfoil in comparison with standard NACA 0017 airfoil [22].


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of 12.5 m/s. The peak CP of 0.409 was obtained at TSR of 6.34 [39]. Abundant data on large scale phi-rotor as well as the “Test Bed” are available at SNL website. However, the largest Darrieus VAWT in the world was a phi-rotor built in Canada with rated power of 4 MW, rotor height of 96 m and diameter of 64 m. Construction of the phi-rotor called Eole began in 1982, and was completed in 1988. However, the Eole was mostly operated in reduced speed, and the power output was limited to 2.5 MW to ensure longevity [40]. The turbine was successfully operated for 5 years until 1993 when it was damaged during a storm [41]. Repairing the damage was deemed too costly since the whole rotor needed to be dismantled. Instead, the Eole was utilized as a tourism icon to show the achievement of Canadian wind energy sector in attempting large scale Darrieus VAWT. The “Test Bed” inspired FloWind Corp. to commercially market Darrieus VAWT under auspices of SNL and NREL. Extended heightto-diameter ratio was developed with the blades made of composite materials. Until the 1995, FloWind had installed more than 800 Darrieus VAWTs in the Altamont and Tehachapi passes in California [41]. However, despite the successful operation of the turbines, the company went bankrupt in 1997 due to production fleet financing could not be obtained. Thereafter, VAWT was out-offavor and virtually all government sponsors on VAWT research were terminated [8]. Until recently, fixed-on-tower and cantilevered phi-rotors have gained popularity. The new designs utilize tubular tower, and does not use guy wires. The designs offer simpler and more reliable system than the conventional guy-wired phi-rotor. 50 kW fixed-ontower rotors are developed by ArborWind in collaboration with Johnson System, Inc. (JSI) [10]. The target markets include rural use, large industrial, farm and green houses. Large scale fixed-on-tower phi-rotor with power rating of 200 kW has been attempted by McKenzie Bay International, Ltd. (MKBY) in collaboration with Clean Green Energy, LLC. (CGE) [11]. However, high cost prohibits the commercialization of the rotor. Instead, smaller cantilevered versions of 20e65 kW are currently developed [11]. A 60 kW cantilevered phi-rotor is also developed by VAWTPower Management, Inc. (VMI) in cooperation with the US Department of Agriculture Conservation and Production Research Laboratory and SNL of the US Department of Energy (DOE) [12]. VMI stated that the design is an innovation of the earlier concepts developed by SNL, NRC of

Canada, Alcoa, Agway, the National Rural Electric Cooperatives Association, FloWind and Vawtpower, Inc [12]. In addition, SNL provides technical assistance and instruments to measure the rotor performance. Furthermore, new interest in Darrieus VAWT for multi-megawatt offshore wind power generation has granted SNL $4.1 million from the US DOE. The project was started in 2012, and will be completed in 2017. 5.2. Assessment on phi-rotor Rotor illustration and the components of guy-wired phi-rotor in the early 1970s development are shown in Fig. 6a and b, respectively [42]. Two and three-bladed rotors were manufactured, and were structurally enhanced with struts forming “X” sign. The struts were detrimental because they added costs, and lowered the performance due to parasitic drag and turbulent flow formed by them. The struts were eliminated in the following designs since the troposkein blades were able to withstand stresses in high rotational speed. The phi-rotor was supported by guy cables mounted at the top of rotor shaft to the ground at equally-spaced angles. Thrust bearings were used at the top and bottom of the rotor, enabling it to rotate freely. Mechanical brake was mounted at the bottom of rotor shaft to ensure safe operation in strong winds. Torque sensors via flexible couplings were utilized to monitor anomalies in the system and to regulate the generators power. The early design of guy-wired phi-rotor exhibited many disadvantages due to complex arrangements as well as mechanical losses in the components. In the development, researchers at SNL examined the guy-wired phi-rotor design more thoroughly and made several conclusions, such as: (i) two-blade design is more cost-effective than the original three-blade design, (ii) struts should be kept short or possibly eliminated since they add parasitic drag and cost, and (iii) the blade airfoil shape should be tailored for VAWT application [40]. In addition, the brake system had been positioned directly below the rotor lower hub in order not to obstruct maintenance work on other components while keeping the rotor stationary, and to prolong the gearbox lifetime since braking force was not transmitted through the gearbox. The guy-wired phi-rotor blades were manufactured via standard extrusion method using aluminum alloy, which were then

Fig. 6. Three-bladed DOE/Sandia 17-m guy-wired phi-rotor. (a) Photograph [79] and (b) major components illustration [42].

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bent conforming troposkein shape [5]. As implemented in the “Test Bed”, a blade was divided into three sections: root, transition and equatorial section. The sections were equipped with extruded NACA 0021 (1.22 m chord), SNL 0018/50 (1.07 m chord) and SNL 0018/50 (0.91 m chord) airfoil profiles, respectively [39]. SNL code denoted natural laminar flow airfoils developed by Sandia for use on Darrieus VAWT [21]. There seemed to be no standardization in the naming of the tailored airfoils, for example, SNL 0018/50 might be referred to as SAND 0018/50 or SANDIA 0018/50. Nevertheless, the codes for airfoil thickness and thickest location remain the same. Fig. 7a and b shows the “Test Bed” with illustrations on the blade sections and geometry. Upper root section was longer than the lower one in order to maintain the shape under bending stress due to gravitational loading. The airfoil profile tailored to a particular section of a blade serves two purposes: structural strength and aerodynamic performance. Different propelling forces between the root and equator section would cause localized edgewise bending on a blade of uniform dimension from the root to the equator section. This edgewise bending is insignificant for small scale rotor, but for large scale rotor like the “Test Bed” it would be detrimental. Thus, in order to minimize the fatigue, airfoil chord dimension was altered, so that the propelling force would be more uniform from the root to the equator. In addition, the chord of the root section was made thicker for the same purpose of reducing fatigue due to bending, and also to compensate for lower TSR and higher AOA. Fig. 8a and b shows typical components of a guy-wired phi-rotor based on the “Test Bed”. Generally, the major components consist of the following:  rotor assembly (rotor column, upper and lower hubs, and blades),  shaft assembly (interconnection shaft, brake disk and caliper, rubber isolator, and torque sensor),  base structures (gearbox, generator, foundations, and ground equipment station), and rotor support structures (support stands, upper and lower rotor bearings, guy wires and tensioners).


VMI has been testing VP100 (shown in Fig. 9a) since 2006, which is a three-bladed cantilevered phi-rotor with 60 kW rating. The total structure is about 23.7 m tall, while rotor height and diameter are 13.5 m and 15 m, respectively. The blades use NACA 0015 profile with 0.35 m chord length, 0.053 m chord thickness and 0.0053 m wall thickness [12]. The blades were made of extruded aluminum alloy, which were bent into troposkien shape. The blades were then fitted with two hinges at the ends, which were epoxied into position. The hinges allow vibration in the rotor assembly without stressing the aluminum blades, which is an innovation of the rotor. VP100 is connected to vertical gearbox and generator considering the 1200 rpm generator used in the system [14], while the rotor speed is only 62.4 rpm [12]. The high rotational speed of generator suggests that a speed increaser is used in the system. The main reason of using a combination of a speed increaser and a generator is to get the reliability improvement over a multi-stage gearbox, while keeping the cost reasonably below a direct-drive generator [43]. Fig. 9b shows an artist's impression of the major components of the VP100. Maintenance work demonstration on the VP100 showed that it takes only four hours to replace the 800 pounds (363 kg) generator without using crane as in typical HAWT maintenance. In addition, only hand tools and light jacks are used in the process since the generator is placed on the ground. VMI claims that the VP100 maintenance cost is much lesser than the HAWT counterpart, since the use of crane adds thousands to tens of thousands of dollars in the servicing cost of the wind turbine [14]. MKBY and CGE successfully installed a 200 kW fixed-on-tower phi-rotor in Ishpeming, Michigan in 2010, after having installation problems in the previous year. A troposkien blade was deformed when lifted by a crane, which prompted for redesigning the core structure of the blade. In the next attempt, a frame was constructed to hold a blade while being lifted by a crane to be assembled to the rotor shaft. However, the turbine has not been a satisfaction, primarily due to the high cost in manufacturing. In addition, the installation was too expensive and complex [11]. Fig. 10a and b shows the 200 kW and its major components description, respectively. The turbine has an outer (rotor) shaft which rotates around an inner (stationary) shaft. The stationary

Fig. 7. The “Test Bed”. (a) Photograph [40] and (b) Blade geometry [39].


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Fig. 8. (a) General view and (b) drivetrain view of the “Test Bed” [40].

Fig. 9. A 60 kW cantilevered phi-rotor by VMI. (a) The VP100 photographed during operation [80] and (b) an artist's impression of major components of the VP100.

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Fig. 10. The 200 kW cantilevered phi-rotor by MKBY and CGE. (a) Photograph of the rotor in operation [11] and (b) major components illustration of the rotor [13].

shaft functions as the holding post for the rotor assembly as well as foundation post. Truss structure is used for additional foundation support for the whole system. MKBY and CGE are currently developing cantilevered phi-rotor called “Wind-e20”, which is scheduled for completion in 2013. Wind-e20 is the 20e65 kW version based on the improvements on the 200 kW model [11]. Wind-e20 has several unique features, including remote-controlled foldable blades for safety in strong winds, typically above 38 m/s. The blades are made of straight sections with joints that are powered by hydraulic pumps, so that during strong winds the hydraulic actuator pulls the blades close to the shaft, similar to the closing of an umbrella. In addition, the blades are equipped with airbrakes, particularly at the equatorial section. The airbrake movement is electronically controlled depending on the wind velocity [44]. Fig. 11 shows an artist's impression of the major components and the blades position during normal operation (right) and folded in strong winds (left). In another development, ArborWind in collaboration with JSI have been manufacturing 50 kW fixed-on-tower phi-rotor similar to the 200 kW model used by MKBY and CGE. However, the turbine built by ArborWind and JSI does not include a ground-mounted stationary shaft, and the blade is not manufactured in multiple small sections. The lack of fully extended stationary shaft reduces cost in trade off with higher bending stress on the shaft mounted on the truss structure. In addition, a fixed blade further reduces cost on the hydraulic pumps and complexity in the manufacturing. Considering the troposkien shape of the blade, it is able to withstand centrifugal force in strong winds. The goal is to produce a specific COE between 9 and 12 cents per kWh [10]. Fig. 12a and b shows the commercial prototype of the 50 kW and its major components, respectively.

5.3. Shape of the phi-rotor blade In the early development, phi-rotor was hailed for its advantage of using troposkein blades, which took the shape of a jumping rope enduring high centrifugal force. Therefore, the blades could be made slender, light and low cost via relatively simple extrusion manufacturing method [5]. However, phi-rotor performance varies depending on the blade curvature as shown in Fig. 13 [23]. Efficiency is influenced by the length of the relatively straight section at the equator to the rotor height [45], which is denoted by ze/H. Therefore, SNL neither used ideal troposkien, catenary nor parabola shapes for the phi-rotor due to the curvature effect. Instead, SNL used straight-line for the top and bottom parts and circular arc-shape for the middle of the rotor [19]. The reason behind such configuration is to increase the ze/H ratio while still having the ability to endure centrifugal force. In addition, blade curvature is affected by the H/D ratio. In term of H/D ratio, pure troposkien shape has the H/D ratio of about 0.9, while the “Test Bed” had the H/D ratio of 1.25. Furthermore, Paraschivoiu [23] suggested that future phi-rotor will use extended height-todiameter (EHD) with H/D ratio between 1.3 and 1.5, which makes the ze/H ratio closer to unity. However, the trade-off in increasing the H/D and ze/H ratios is the increment in operational bending stresses since the shape has become nontroposkien [8]. 5.4. Disadvantages of phi-rotor Recent innovations by MKBY and CGE, ArborWind and JSI, and VMI have demonstrated significant advantages of the fixed-ontower and cantilevered phi-rotor over the conventional guywired phi-rotor, while still using the acclaimed fatigue-free


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section may experience much higher wind than the lower section near the ground surface, which causes uneven lift force produced across the blades length that contributes to instability, bending and torsion stress on the blades [46e48]. On the other hand, straight-bladed configuration type has the flexibility in adjusting the swept-area. Rotor height and diameter can be independently adjusted to suit particular design. In addition, H-rotor type is mostly mounted on a tower, which further reduces uneven wind velocity variation.  Gravity-induced bending stress on the blades

Fig. 11. An artist's impression of the Wind-e20 and its major components.

troposkien blades. Nevertheless, the phi-rotors are the product of lessons learned in the guy-wired phi-rotor, which was the most extensively investigated design among the Darrieus VAWT variations. Based on the failures in the design, several disadvantages of phi-rotor, especially the guy-wired type, are such as:  High axial load on support bearings due to rotor assembly and guy-wires.

In phi-rotor, gravity-induced bending stress is the force to deform the troposkien shape due to the blades own weight. For a small-scale phi-rotor less than 100 kW, gravitational loading on the blades may be neglected with respect to centrifugal force. However, weight of the blades becomes significant in large rotor since the length of a typical phi-rotor blade is three times a HAWT blade with the same swept area and solidity [40]. When the rotor is stationary, the bending stress on the blade is static. However, when the rotor starts to rotate, the static bending stress becomes dynamic and is overcome by centrifugal force depending on the rotational speed of the rotor. The bending stress oscillates in accordance with the centrifugal force, which is affected by wind velocity, turbulence and wake effect at the downwind side. Paraschivoiu [23] and Sutherland et al. [8] mentioned that gravity-induced stress is related to rotor height-to-diameter (H/D) ratio. Lower H/D ratio leads to greater gravitational stresses, but the type of airfoil can be tuned to minimize gravity and radial aerodynamic influences. This is the reason why the “Test Bed” was equipped with thicker root section than the equatorial section, and upper root was longer than the lower one, i.e. to maintain blade shape when the rotor is stationary as well as sustaining stresses endured by the blades in motion. Gravity-induced bending stress is less vulnerable for straightbladed configuration since the blades are shorter and have lower bending moment, i.e. the blades are more rigid at the same chord length and thickness as a phi-rotor blades. In addition, they are positioned vertically and are suspended by support arm(s), so that they are not subjected to constant bending stress due to gravity. Support arm is the component which endures gravity-induced bending stress, and it can be made stronger and tapered from the shaft to the blade.  Wake due to large rotor column

Tare and zero-wind losses are relatively small and can be neglected compared to the total power produced [39]. Tare loss is the power loss due to bearing friction of a rotor without the blades attached, while zero-wind loss is the friction loss with the blades attached and spun at no wind. However, a recent report released by SNL in 2012 stated that the bearings, especially the bottom support bearing must be designed to support both the rotor weight and downward force due to the wires tension. Therefore, the required high capacity of the support bearings can contribute significantly to the capital cost of the turbine [8].

The rotor column of a phi-rotor needs to sustain high tension produced by guy wires as well as cyclic torque produced by the blades, so that buckling strength is the most important aspect of a rotor column requirement [23]. However, large rotor column extending across the height causes blades in leeward position to suffer from turbulent flow region known as wake, especially in large-scale rotor. A wake not only reduces performance, but also causes vibration on the blades and support structures. Fig. 14 shows the vortices and wakes generated by the blades and rotor column of a typical Darrieus VAWT [23].

 Uneven wind velocity across rotor height  Rotor height limitation The swept-area of phi-rotor is bound by the troposkien shape and is determined by rotor height-to-diameter (H/D) ratio. With the tendency to use higher H/D ratio in order to get higher equatorial section [23], rotor height increases more than the increment in rotor diameter. For large-scale on-land phi-rotor which is located on the ground, the effect of uneven wind velocity is more severe due to terrain roughness. The rotor's upper

Despite the low cost and simplicity in supporting a phi-rotor, guy wires have a drawback of instability over a long distance, including the catenary effect. In addition, guy wires also endure intermittent rotor and wind forces which make them vibrate and oscillate. The oscillation frequency and operating mode of guy wires were studied extensively in order to avoid resonances with

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Fig. 12. A 50 kW cantilevered phi-rotor manufactured by Arborwind and JSI: (a) Photograph [10] and (b) artists impression of the major components.

rotor vibration [47]. Therefore, it is difficult to build a very tall rotor equipped with guy wires in order to take advantage of higher altitude winds.  Large footprint to mount guy-wires.

Since guy-wires are fixed above the rotor assembly, large land area is required for anchoring them. This restricts the implementation of phi-rotor at limited and utilized area, such as in farming land. In addition, the use of guy-wires is not practical for offshore application. Nevertheless, higher H/D ratio phi-rotor requires smaller footprint. 6. Variable geometry VAWT (Musgrove-rotor) 6.1. History of Musgrove-rotor Variable geometry Darrieus VAWT or also known as Musgroverotor was invented by Peter Musgrove, a British aeronautical engineer in the mid-1970s [49]. The rotor was a modification of the straight-blades Darrieus VAWT by employing blades reefing

Fig. 13. CP of phi-rotor in respect to curvature ratio [23].

Fig. 14. Vortices and wakes of a typical Darrieus VAWT [23].


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Fig. 15. An experimental model of Musgrove-rotor [50]. Fig. 17. The VAWT-450 Musgrove-rotor [6].

mechanism to prevent the rotor from over-speeding in strong winds. The turbine consisted of two sets of straight blades supported on a horizontal beam similar to the shape of an “H” letter. The horizontal beam, also taking the shape of an airfoil, was in turn supported by a tower at the middle of the beam. The drivetrain and generator were located at the base of the tower. Each set of the blades consisted of two equal portions feather-able about the horizontal beam, for which in reefed position they took the shape of a double-arrow “4”, thus reducing the swept area as well as the lifting force of the blades tangential to the radial line of the rotor. The rotor was operational in the wind velocity of up to 30 m/s. Fig. 15 shows the installation of an early experimental model of Musgrove-rotor [50], while Fig. 16 shows the major components diagram [49]. Musgrove-rotor had similar components to the guy-wired phirotor. However, Musgrove-rotor was equipped with two stages of speed increaser (upper and lower gearbox) as shown in Fig. 16. The consideration of using multi-stage gearbox is to reduce the number of poles needed for the generator, therefore, reducing the cost of generator. Transformer was used to step-up the AC voltage before injecting it into transmission lines on electricity grid system. Promising results in the early development made the UK government financially supported the scaling-up of Musgrove rotor in the late 1970s [51]. The first large scale Musgrove rotor was completed in 1986 by VAWT Ltd., and was named VAWT-450 (based on the swept area of 450 m2). It had rotor diameter of 25 m and rated power of 130 kW at 11 m/s wind velocity. Fig. 17 shows the VAWT450 in reefed position. Several Musgrove rotors with 100 kW capacity were also built by VAWT Ltd. on Isles of Scilly and Sardinia [6]. 6.2. Assessment on Musgrove-rotor Manufacturing process of straight blades is simpler than curved blades. However, the main disadvantages of variable geometry

VAWT were the unnecessarily complex design of reefing mechanism, large concrete structure and high cost in building the turbine. In addition, the Musgrove-rotor consisted of many components which hindered its cost-effectiveness. Despite the disadvantages, after learning that there was a rotational speed limit of the fullyextended blades, Musgrove-rotor development was terminated and shifted to H-rotor. 7. Giromill or cycloturbine 7.1. History of giromill Another variant of straight-blades Darrieus VAWT is giromill or also known as cycloturbine. The term “giromill” was constructed from two words: cyclogiro and windmill coined by MCAIR, which developed cyclogiro airborne vehicle and adapted it to the version of the windmill [52]. It was developed in the US around 1976, at about the same time of Musgrove-rotor in the UK. Giromill is a Hrotor with variable-pitch, so that wind's AOA to the blade is maintained relatively constant at certain negative angle for one half and certain positive angle for the other half of revolution at certain wind velocity. The pitching method include mechanical and electrical actuators, such as using a cam and push-rod mechanism [53], hydraulic mechanism, and DC motor connected to a blade pivot axis via a timing belt [52]. After the successful feasibility study, a three-bladed precommercialization prototype giromill was built in 1980 under funding from US DOE. Fig. 18a and b shows the MCAIR giromill [40] and its components description [54], respectively. The giromill had a diameter of 58 ft (17.7 m) and rotor height of 42 ft (12.8 m), which produced constant power of 40 kW at 8.9e17.9 m/s wind velocity. The drivetrain concept was similar to the Musgrove-rotor, except for the placement of the brake disc and the single stage gearbox utilized on the giromill. However, despite the successful development of MCAIR giromill, the US government chose a two-bladed downwind HAWT with similar power rating. The decision was based on higher annual energy generation and lower COE. 7.2. Assessment on giromill

Fig. 16. Major components of Musgrove-rotor [49].

A giromill is able to achieve maximum CP of 0.5 [3,52], which is more efficient than other Darrieus VAWT variations presented in this paper. Although variable-pitch mechanism in giromill shows higher performance than fixed-pitch Darrieus VAWT, the

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Fig. 18. The MCAIR 40 kW prototype giromill. (a) The 40 kW giromill during testing [40] and (b) components of the giromill [54].

mechanism is costly. Complexities of the pitch-change system and support structures for changing the pitching angle reliably over the service time make the giromill not cost effective and have prevented it from being manufactured in large-scale basis. 8. H-rotor 8.1. History of H-rotor Despite its simplicity, H-rotor was developed later than Musgrove and giromill rotors although it was mentioned in the original Darrieus patent. Experience gained from the VAWT-450 showed that the reefing mechanism in Musgrove design was unnecessary because passive stall of the airfoils in vertical position during strong wind naturally prevented the blades from over-speeding. Thus, another turbine was built as a H-rotor by VAWT Ltd. in 1988 and was named VAWT-850 which had rated power of 500 kW and rotor diameter of 38 m [55]. Fig. 19 shows the VAWT-850, whose connection of support bar and blades was simpler than the Musgrove-rotor at the background. The turbine was completed in August 1990 and was tested until February 1991 when one of the blades broke due to an error in the fiberglass blades manufacturing process [56]. Current large scale H-rotor is developed by Vertical Wind AB, a wind energy research company based in Sweden in collaboration with Uppsala University. After successful initial investigations on 2 kW and 12 kW prototypes [57,58], the company produced a large scale turbine of 200 kW [59,60]. The production of a 200 kW Hrotor was started in October 2009, and has been operational since April 2010. Fig. 20a and b shows the rotor and an artist's impression on the major drivetrain components, respectively. The structural concept of the H-rotor is similar to the giromill built by MCAIR. However, the H-rotor developed by Vertical Wind is much simpler

since the rotor does not have wind detection and blade pitching mechanism as well as a gearbox. Vertical Wind AB also reported that fewer moving parts compared to conventional wind turbines gives higher availability and reliability as well as lower maintenance cost. The company claims that direct-drive generator provides excellent cost efficiency since it is placed on the ground, and hence, does not need to be optimized for the weight and size. In addition, costs related to gearbox failure are eliminated. Furthermore, the H-rotor is quieter than a HAWT of similar size. The success story was received enthusiastically by the Swedish Energy Authority, E.ON and Falkenberg Energy, for which four turbines will be installed there [61].

Fig. 19. The VAWT-850 fixed-pitch H-rotor with the VAWT-450 Musgrove-rotor in the background [6].


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Fig. 20. A 200 kW H-rotor by Vertical Wind. (a) Photograph of the H-rotor [60] and (b) artist's impression on the main components of the rotor.

8.2. Assessment on H-rotor In the 1970se1980s, glass-fiber reinforced plastic (GFRP) was not common for being used as Darrieus VAWT blades. Until Musgrove and MCAIR started developing straight-bladed configuration, it was found out using aluminum via extrusion method was not suitable for H-rotor blades due to cyclic flapwise bending stress. Therefore, the recent straight-bladed Darrieus VAWT configurations use GFRP and carbon fiber composites similar to the HAWT blades, which is able to sustain continuous cycles of edgewise and flapwise bending stress during the blades service life. By the use of GFRP and carbon fiber composite, the benefit of stress-enduring troposkien-shaped aluminum blades for phi-rotor is compensated by the stress-enduring composite materials for H-rotor blades. In addition, the aerodynamic drag caused by struts or support arms in H-rotor is also compensated by the increased performance of the rotor, since blade equatorial portion-to-rotor height (ze/H) ratio becomes unity, as described earlier. The H-rotor program in UK was terminated after the failure of VAWT-850 due to the prohibitively high cost in building the concrete tower and support structure [6]. Similarly in the US, H-rotor was not attempted by the government despite successful tower and drivetrain components installation in the giromill program. Current development by Vertical Wind in the Sweden has improved the designs of H-rotor by Musgrove in the UK and giromill by MCAIR in the US. However, cyclic torque in large scale, especially in multi-megawatt range, requires investigations into strong and light-weight rotor shaft, since an extended rotor shaft is prone to vibration and fatigue, primarily due to torsional stress on the shaft. A retrospective analysis by SNL in 2012 stated that H-rotor has a high potential for cost-effective offshore wind power generation

[8]. In particular, support bar of a H-rotor can be used as an aerodynamic braking system in strong winds, which has been a major concern in Darrieus VAWT design. Airbrake system has been a standard aerodynamic brake for commercial airplanes, which deploy extended flaps during landing. In sport cars, aerodynamic braking system has been used in conjunction with mechanical brake to provide higher deceleration rate by deploying the rear spoiler upward. Therefore, H-rotor has a potential to embed similar aerodynamic braking system on the support bar cost-effectively, without modifying the blades. 9. Helical H-rotor 9.1. History of helical H-rotor H-rotor was modified into another variant in which the blades were twisted along the perimeter to form helical shape. Surprisingly, the modification was intended as a water turbine since the inventor, Professor A.M. Gorlov of Northeastern University, is an expert in hydro power. The invention was granted US Patents no. 5,451,137 & 5,451,138 on 19th September 1995. Although the turbine was originally designed as a water turbine, the disclosed patents stated that it could be used for hydro-pneumatic, hydro, wind and wave power systems [62,63]. Fig. 21aec show the comparison of Helical H-rotor for water and wind turbines. The main difference between them is that the water turbine has a much higher solidity, which is the ratio of blades coverage area to turbine swept area. The hydrofoil's chord of the Gorlov water turbine blades is made longer and thicker in order to increase the structural strength. In addition, the rotating speed is reduced, so that the chance of cavitation is minimized. Furthermore, the Gorlov water turbine rotates much slower than the

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QuietRevolution and Turby wind turbines, which is beneficial to the marine lives. The QR5 turbine shown in Fig. 21b is manufactured by Quiet Revolution in the U.K [64]. The rotor size is 5.5 m (H) by 3.1 m (D), and has a rated power of 8.5 kW at 16 m/s wind velocity. The cut-in and cut-out wind velocities for the turbine are 5.5 m/s and 26 m/s, respectively. The turbine employs state-of-the-art components, which include carbon fiber composites for the rotor assembly and direct-drive permanent magnet generator. Another helical H-rotor shown in Fig. 21c is developed by Turby BV, a Dutch manufacturer which produces 2.5 and 10 kW turbines [15]. The company has been cooperating with Delft Technical University to produce the


turbine. Similar to the QR5, the Turby blades are manufactured using carbon fiber aramide composite. In addition, direct-drive permanent magnet generator is also used. Turby has an overall CP of 0.3 from the wind power to electricity. It utilizes NACA 0018 profile for the blades, and is operated at TSR of about 3. The cut-in and cut-out wind velocities of the turbine is 4 m/s and 19 m/s, respectively, while the rated power is reached at 13 m/s [65]. 9.2. Assessment on helical H-rotor Helical H-rotor improves the performance of H-rotor by distributing a blade profile along the perimeter of the rotor

Fig. 21. Helical H-rotor for: (a) water turbine (Gorlov Helical Turbine) [81], (b) and (c) are wind turbines by QuietRevolution [64] and Turby [15], respectively.


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Fig. 22. Geometry of the modeled Darrieus VAWTs: (a) H-rotor, (b) Phi-rotor and (c) Helical H-rotor [67].

uniformly, and thus, making the swept area as well as blade sections constant to the wind at all instances of turbine rotation. Therefore, rotor torque fluctuation is significantly reduced when the helical shape covers a full 360 rotation. Benefits of having regular torque include better power output regulation and reduced cyclic stress on the drivetrain. In addition, noise is reduced and slightly higher effective chord is obtained [66]. Currently, helix design is getting popularity not only because of better performance, but also for the esthetic value, in which modern elegant design harmonizes the elements in the space. Comparison of Helical H-rotor to H-rotor and phi-rotor has been done [67,68]. Fig. 22 shows modeled geometry of H-rotor, phi-rotor and helical H-rotor. The rotors were modeled with 3 blades spaced equally at 120 using symmetrical NACA 0015 with chord-to-radius at mid-span of 0.15, aspect ratio of 20 and TSR of 5. The modeled rotors performance is shown in Fig. 23 where torque fluctuation varies three times every rotation. The graphs show that a phi-rotor has the most fluctuation with variation of about 0.3 CP, followed by H-rotor with 0.2 CP, and the least fluctuation is achieved by the helical H-rotor with variation of about 0.03 CP. However, despite the benefits gained, true helical blades are more expensive to manufacture.

National Laboratory since 2009. The rotor has a diameter of 10 ft (3 m) and height of 7 ft (2.1 m). The working principle of the wind turbine is based on gimbal or swashplate-like mechanism, in which the blades are free to oscillate or tilt around the rotor hub, i.e. the articulation point. Elastomeric dampeners are used to prevent the blades from over-tilting. Linkages are connected from the hub to the blades, so that pitch angles are altered depending on which blade is being pushed by the wind. Fig. 24 shows an illustration of the 1.5 kW articulating Hrotor with annotation on its major components. Pitch-control via

10. Articulating H-rotor Another recent variation of Darrieus VAWT is the articulating Hrotor developed by Blackhawk Project, LLC. The wind turbine concept is based on a helicopter rotor that adjusts automatically to the wind pressure, so that vibration and mechanical stresses are reduced. Bruce Boatner, who invented the articulating H-rotor in 2006, is an engineer and helicopter pilot. The articulating H-rotor received US Patent no. 7,677,862 on 16th March 2010 [69]. Currently, Blackhawk, LLC is testing TR-10, a prototype model of 1.5 kW at the Center For Advanced Energy Studies (CAES), Idaho

Fig. 23. Power coefficient variations of a typical phi (4) rotor, H-rotor and helical Hrotor [67].

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Fig. 24. An illustration of the 1.5 kW prototype by Blackhawk, LLC [82].

articulating motion allows the turbine to self-start at light winds despite of having low solidity, higher torque during operation, as well as for aerodynamic braking. Another advantage of articulating motion is that the blades swiftly adapt to the wind force, thus reducing vibration as often occurs in stiff and fixed blades. The feature is highly advantageous for urban application, where the wind is more turbulent. 11. Fish-schooling formation The effort to study Darrieus VAWT in array configuration has been bio-inspired by the nature. Migrating birds and fishes show that they have more stamina in traveling farther as a group. By positioning themselves precisely at certain coordinates, the animals are able to gain from the vortices shed by the animals ahead.


This phenomenon has been investigated for wind turbine application, and has been shown to be beneficial for vertical axis configuration. A recent investigation [70] using stereoscopic particle image velocimetry (PIV) shows the wake and vortices formed by a two-bladed H-rotor clearly. The H-rotor dimensions are 1 m rotor diameter, 1 m rotor height and 0.06 m NACA 0018 chord length, which rotates at TSR of 4.5 in a wind stream velocity of 9.3 m/s. The PIV images show the fast wake recovery of the H-rotor, in which after only 1.5 rotor diameter distance downwind, the cycloidal wake is no longer detectable and is replaced by large vortical structures due to the roll-up of co-rotating small vortices [70]. The utilization of these vortices is the basis of VAWT fishschooling formation. Darrieus VAWT has an advantage in turbulence compared to the HAWT, so that they can be formed into arrays to harness more power in a given area. In limited area of urban population, this arrangement would be advantageous. Unlike HAWTs that experience higher fatigue and performance loss when positioned close to each other [71e74], Darrieus VAWTs wind farm study suggested slight reduce (or even increase in some cases) in performance depending on the array configurations [75]. For a clustered turbines, Darrieus VAWT pairs at downwind position recover the efficiency to within 5% of an isolated turbine at four diameter spacing, while HAWTs require 15-20 diameter spacing [76]. Similar phenomenon has been observed for Savonius VAWT [77,78]. However, research on the topic is still very scarce, and large Darrieus VAWT cluster such as in a typical HAWT wind farm has not been performed to observe the large-scale wake effects on the pairs formation. Nevertheless, the studies showed the potential of small inter-turbine spacing in Darrieus VAWT to reduce the size and impacts of wind farm. Fig. 25a and b shows a biomimicry configuration of Darrieus VAWT wind farm based on wake vortices of fish schooling studied by Weihs in 1975 [75]. Both acw vortex (anticlockwise) and cw vortex (clockwise) represent dipoles of wake vortices formed by the school. The dipoles position are used as the placement of Darrieus VAWTs. The distances between the dipoles are indicated by 2a, 2b and 2c. 2a is the downstream distance of two vortices in the same line; 2b is the lateral distance between acw and cw vortex of a particular fish; and 2c is the distance between two adjacent fishes

Fig. 25. Biomimicry of a Darrieus VAWT wind farm to vortices pattern formed by a school of swimming fishes, where: (a) Wake vortices of schooling fish and (b) proposed Darrieus VAWT wind farm configuration [75].


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Fig. 26. Performance of two-closely spaced H-rotors. Normalized CP is showed in respect to: (a) incoming angle of the wind and (b) TSR [76].

[75]. However, it was found that adjacent turbines with the same rotational direction tend to reduce the performance of the pair. On the other hand, the performance is generally unaffected by counterrotating turbines. Investigation into a single pair of H-rotors is shown in Fig. 26a. The H-rotors (indicated by two counter-rotating circles) are spaced at 1.65 rotor diameter. The red/bold line is the normalized CP at all angle, except for some angle range which have been omitted due to inconsistent wind flow below 15 min. The three circles surrounding the H-rotors are normalized power indicators at 0.5, 1.0 and 1.5, respectively from the smallest circle. The investigation showed that at certain angle, the average power generated by both turbines is less than that of an isolated turbine. However, at other angles the average power of the pair is higher than that of an isolated. Overall, the average power generated by the pair at all angles is slightly better than an isolated turbine as shown in Fig. 26b. The figure indicates that slower turbine rotation benefits the pair in a trade-off with more critical speed regulation. The vertical dashed-line is the designed operating TSR of the H-rotors [76]. 12. Conclusion Darrieus VAWT had experienced ups and downs since the invention in 1920s. Several variations on both curved- and straightblades configurations have been investigated. Current development shows that guy-wired rotor is getting less popular due to many disadvantages, while cantilevered-rotor using tubular or truss structure is becoming more dominant for both curved- and straight-blades configurations. The reliability of cantilevered-rotor has ignited new interest in Darrieus VAWT both in small and large scale. Novel variations have emerged to provide better performance and lower COE. Darrieus VAWT has produced several variations, most notably Helical H-rotor. In addition, investigations into clustered Darrieus VAWT have been currently taking place, which show promising results over an HAWT wind farm. Acknowledgment The authors would like to acknowledge the Ministry of Science, Technology and Innovation (MOSTI) e Malaysia, for sponsoring this project under the PRGS/1/11/TK/UKM/03/2 grant. References [1] Hau E. Wind turbines: fundamental, technologies, application, economics. 2nd ed. Berlin: Springer-Verlag Berlin Heidelberg; 2006.

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