Aerodynamic performance enhancement and computational methods for H-Darrieus vertical axis wind turbines: Review

ABSTRACT

The wind is one of the most promising green energy resources that replenishes itselves in less than a human lifetime without depleting the planet’s resources. According to the disposition of the blade concerning the shaft, wind turbine can be classified as horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT). In contrast to VAWT, HAWT covers most commercial installations around the globe. However, VAWTs became a promising alternative for areas far away from grid-connected electricity, they have certain drawbacks associated with aerodynamic performance. The present work overviews the magnitude of factors affecting the aerodynamics of typical VAWT, i.e H-Darrieus VAWT and enhancement options associated with cutting edge performance. Additionally, the accuracy of the turbine performance predicting tools through computational investigation and optimization was also assessed. Therefore, the review covered the factors that altered the turbine performance and viable enhancement options studied in the existing literature. Finally, FSI simulation was tics of materials commonly used for turbine blade manufacturing. It was determined that the computational tools employed significantly influence the accuracy of the model, and proper model selection and more experimental validations are compulsory. It was determined that the computational tools employed significantly influence the accuracy of the model, and proper model selection and more experimental validations are compulsory.

KEYWORDS:

• H-Darrieus vertical axis wind turbine
• blade element momentum (BEM)
• computational fluid dynamics (CFD)
• aerodynamic performance
• fluid-structure interaction (FSI)
• natural fiber-reinforced composite
• artificial intelligence (AI)

1. Introduction

Due to the increase in fossil fuel demand, a large amount of carbon dioxide (CO₂) is emitted into space which significantly depleted the environment. Hence, future energy embraces renewable energy resources for sustainable environmental protection and economic development. These are naturally replenished useful energy including solar, biomass, geothermal, hydro, and wind have been used. Among these resources, the wind became the primary energy opportunity for massive electricity generation. Hence, extensive research efforts have been devoted to advance sophisticated technologies to improve energy generation through the wind.

A wind turbine is a rotary machine that transforms the kinetic energy of the wind to mechanical energy in a shaft and then electrical energy in a generator. It was probably originated around 200 BC by ancient Persian (Fleming and Probert 1984; Pasqualetti, Richter, and Gipe 2004). This was a vertical axis windmill used to grind grain and to irrigate water.

According to rotational axis disposition, wind turbine design can be classified into two main categories, i.e Horizontal Axis Wind Turbine (HAWT) and Vertical Axis Wind Turbine (VAWT). In HAWTs, the rotor blades are perpendicular to the rotational axis (the shaft). Whereas the blades of VAWT are parallel to the axis of rotation. For the last few decades, the major wind energy research activities were regarding HAWT improvements. Through this installed capacity was increased from 25,000 MW to more than 200,000 MW in 10 years (from 2001 to 2010) (Bhutta et al. 2012), and it extensively growing to 564 GW in 2018 (IRENA 2019). The global wind energy council (GWEC) reports indicating an additional 355 GW of wind turbine expected to be installed in the year 2020 up to 2024 (Update 2017).

Figure 1. Characteristic of wind turbines (Ahmed and Gawad 2016).

Unlike HAWTs, VAWTs are omnidirectional and can obtain higher capacity factors in near-the-ground installations where the direction of the wind is more erratic than higher altitudes without blades yawing mechanism, generator and gearbox of the turbine can be installed at sea level which is easier for safe maintenance and the best turbine stability during a float. This leads to reduced machine complexity and better scalability to a large turbine size. Although VAWT was the first-ever machine to be used for harnessing wind energy, because of the lack of researchers’ concern it has limited installed share in the global wind energy market (Kalagi, Patil, and Nayak 2018). Yet there is an increasing VAWTs demand for small-scale energy supplies away from grid-connected sites such as rural areas and military campuses. Moreover, due to their aesthetic and silent prototype, VAWTs are also attractive for urban wind energy generation.

According to a blade design, VAWTs are classified as drag type and lift type. A drag-type design named it ‘Savonius wind turbine’ the net torque is generated wherever the imbalance of drag force blows over asymmetric blades. However, drag-type VAWTs usually have very low power and torque coefficients as compared to other wind turbines (Roy and Saha 2013). On the contrary, lift-based VAWTs named ‘Darrieus wind turbine’ reveal superior aerodynamic efficiency (see Figure 1–3) than other wind turbines (Sun et al. 2016). For this fact, lift-type VAWT becomes a renewed interest for micro to mega-scales offshore wind energy generation (Hand, Kelly, and Cashman 2021). Nevertheless, lift-type VAWT is incapable of self-starting at a low tip speed ratio (TSR) unless external auxiliary devices are provided. This is because of the complex aerodynamic nature of VAWT caused by many factors including turbine geometry, airfoil type, free stream velocity, incident angle (φ), turbine spacing, angle of attack (AoA), axis eccentricity, blades tip loss, and tip speed ratio (Mohamed, Ali, and Hafiz 2015; Naccache and Paraschivoiu 2018). These collaboratively affect the turbine self-starting characteristics (Islam, Ting, and Fartaj 2008). Hence, attempts are devoted to employing several aerodynamic performance improvement alternatives such as altering the blade profile through CFD and aeroelastic tools, using flow control systems, using high strength to weight ratio material, and so on.

Figure 2. Darrieus types VAWT design concepts (Dabachi, Rahmouni, and Bouksour 2020).

Figure 3. Lift-type VAWTs trends (Möllerström et al. 2019).

A wind turbine is a complex system consisting of several components where turbine blades form key structural elements for achieving higher power generation. For this fact, proper choice of material for its component manufacturing must be demonstrated at the beginning of wind turbine development. From the long history of a wind turbine, blades were made of wood (Howard 2017) and other local materials. However, to prolong the blade life scientists and engineers are intended to search lightweight and high-strength blade materials for modern structural applications. Among the materials, metallic fiber-reinforced composite (FRC) was superior to those of wind turbine blade designs (Beardmore and Johnson 1986; Davies and Chauchot 1999; Immarigeon et al. 1995; Thomas and Ramachandra 2018). For example, In 1956–57, the so-called Gedser wind turbine was built by Johannes Juul with a composite blade supported by steel spars, aluminum shells, and wooden ribs (Abdalrwaf 2017). This was the first long-lasting wind turbine that operates for 11 years without failure (Schubel and Crossley 2012). However, besides the advantage, synthetic fiber composites become incompatible with the environment of their end-of-life disposal. Because traditional disposal methods, i.e incinerated and landfills (Duflou et al. 2012; Kalkanis et al. 2019; Psomopoulos et al. 2019), impose significant environmental impact (Ramirez-Tejeda, Turcotte, and Pike 2017), and most recycling technologies are not yet commercialized.

This paper overviewes the studies done on the parameters that significantly affect the aerodynamic performance of Darrieus type VAWTs. Also, both conventional and unconventional performance enhancement techniques were addressed. Furthermore, opportunities regarding the turbine blade materials which can replace traditional synthetic materials such as glass and carbon fibers with their structural improvement alternatives are also highlighted. Finally, computational techniques for this type of wind turbine are thoroughly discussed, and a case study on the performance of two turbulence models flow characteristics over H-Darrieus VAWT based on the geometry of the NREL baseline turbine was presented.

2. Aerodynamic performance of H-darrieus wind turbine

The aerodynamic performance of H-Darrieus VAWT depends on different design parameters including blade pitch angle, tip speed ratio, airfoil type and configuration, number of blades, blade solidity, and others, In the following few sections, the main factors which will alter the aerodynamic performance of H-Darrieus VAWT are discussed thoroughly.

1. Pitch Angle (β)

H-Darrieus VAWT can be configured as a fixed pitch (FP) or variable pitch (VP) angle. Compared with the FP-blade, the VP-blade has a wider azimuthal zone that corresponds to higher AoA (Zhao et al. 2017) (see Figure 4). VP-VAWT design strategy is targeted to narrow the azimuthal range of poor performance (Zhao et al. 2017). The moment of turbine blades about the pivotal axis became either cycloidal or cyclic motion (Camporeale and Magi 2000; Zhao et al. 2017). The comparison of the symmetrical blade pitch design strategy of VAWT at main azimuth positions is illustrated in Table 1. FP turbines are inherent with lower power efficiency at the rated speed and higher drag coefficient which might affect the self-starting ability of the machine (Dwiyantoro and Suphandani 2017; Zhao et al. 2018). This is mainly due to large fluctuations when the turbines are in operating conditions (Zamani, Maghrebi, and Varedi 2016). In contrast, VP blade designs become handy to alleviate the turbine aerodynamic performance (Guo, Zeng, and Lei 2019; Sagharichi, Maghrebi, and ArabGolarcheh 2016), and mitigate the turbine blade from catastrophic failure during the turbines are exposed to higher wind loads (Sagharichi, Maghrebi, and ArabGolarcheh 2016). The pitching movement of the blades reduces the variation of AoA along the streamwise direction and provides a high torque coefficient (Sagharichi, Zamani, and Ghasemi 2018). This leads to the blade reducing the flow separation and offered the turbine for self-starting opportunities (Pawsey 2002). VP does not rely on avoiding stall, but optimal TSR must be high enough to maintain a low flow angle which squeezes performance out of the turbine by increasing AoA (Soraghan et al. 2013).

Figure 4. Fixed and variable pitch VAWTs configuration (Sagharichi, Zamani, and Ghasemi 2018).

Table 1. Comparison of four different pitching strategies for H-Darrieus VAWT (Zhao et al. 2017).

TurbineItems	θ (^o)	FP-VAWT	VP-VAWT Cyclic	VP-VAWT cycloidal	VP-VAWT Modified
AoA	0 (180)	0	0	0	0
	90 (270)	Maximum	Maximum	Approached to maximum	May be max
Pitch angle	0 (180)	0	0	0	0
	90 (270)	0	Maximum	Approached to max	0
Pitch angle curve			Sinusoidal	Near to sinusoidal	Combination of two trigonometric functions
Design effect			The largest growth is limited in azimuths of 90 and 270	The largest growth is limited in azimuths near 90 or 270	The largest value will distribute at four zones for two sides of 90 and 270

CFD attempts are boosted to explore VAWT performance predictions apart from analytical studies. Through these, the performance of NACA0012 airfoil on a three-bladed H-Darrieus rotor between $-7^{\circ }$ and $3^{\circ }$ pitch angle was investigated (Rezaeiha, Kalkman, and Blocken 2017a). The result showing that the optimum performance of the rotor was achieved at $-2^{\circ }$ which was a 2% higher power coefficient (C_p) than $0^{\circ }$ pitch angles. 2D CFD simulation was carried out under NACA0015 airfoil blade VAWT (Elsakka et al. 2019). Experimental investigation of NACA0015 in (Douak et al. 2018) indicates, at high TSR (λ = 7) and low TSR (λ = 1.5) of VP the torque and power coefficient were increased by 18.5 N and 0.15 respectively as compared to FP angle and provides faster start-up at low wind speed.

The comparative aerodynamic performance of both VAWT pitch angle mechanisms is illustrated in Figure 5. It implies the VP regime was successful in increasing the peak aerodynamic performance at optimal TSR by 5.4% from 0.37 to 0.39 (Soraghan et al. 2013). Nevertheless, with an off-design TSR of 2.5, the power coefficient drops by 26.7% (Elkhoury, Kiwata, and Aoun 2015). This implies that the peak in the power coefficient takes place at VP blades. The performance comparisons between FP and VP VAWT with different aerodynamic aspects are illustrated in Figure 6 to Figure 7,8. This implies that the overall performance of VAWT improved by VP design as compared to FP once (Mohamed, Ali, and Hafiz 2015; Pawsey 2002; Sagharichi, Maghrebi, and ArabGolarcheh 2016) Because the pitching mechanism maintains the blade at safe AoA and reduces the dynamic stall effect.

Figure 5. Aerodynamic simulations for the test H-Darrieus rotor operating at λ of 4.5 (Soraghan et al. 2013), a) AoA b) Induction Factor c) Tangential Force Coefficient d) Normal Force Coefficient.

Figure 6. Variation AoA vs azimuthal angle for a λ of 1.5. a) high solidity on the variable pitch (Sagharichi, Zamani, and Ghasemi 2018) b) the variation of pitch angle at different azimuth positions vs AoA (Elkhoury, Kiwata, and Aoun 2015).

When the wind velocity fluctuates the pitch of the blade would be controlled and allowed to capture the maximum amount of energy by pitching the blades at optimum pitch angles. Hence to find the desired β optimization analysis must be carried out during the blade design. The variation of Cp concerning TSR for seven different β (i.e $-{10}^{\circ },-5^{\circ },0^{\circ },4^{\circ },5^{\circ },6^{{ }^{\circ }}$ and ${10}^{\circ }$) was studied (Mazarbhuiya, Biswas, and Sharma 2020a). The result shows the turbine performance was increased with increasing the β from negative to positive values. Among all considered βs, the optimum Cp (0.27) was obtained when β $(5^{\circ })$ at $\lambda =2.4$.

Figure 7. Instantaneous pressure coefficient through mid-plane of an FP and VP angles VAWT at λ = 1 (Elkhoury, Kiwata, and Aoun 2015).

Figure 8. Instantaneous torque coefficients of H-Darrieus VAWT as a function of azimuth position.

2.1. Tip speed ratio (λ)

During the operation of VAWT, the speed ratio inversely varies with the AoA at each rotation. The continuous variation of AoA results in complex flow separation (Jayabalan et al. 2017) called a dynamic stall. The effect of TSR on the wake feature of these turbines is studied in Posa (2020). At high TSR, instability of the shear layer generated closer to the flow of leeward and edge ward wakes results in the inversion of freestream wind flow to the downstream direction. This is due to the presence of induction velocity through the flow direction. The influence of induction velocity is the main force that causes to vary the AoA of the rotor blade that leads to stall and reduce the performance of wind turbine (Rezaeiha, Montazeri, and Blocken 2018a). Thus, the upstream induction velocity contributed more than half of the total power produced throughout the full cycle.

Usually, the turbine solidity inversely varies with operating TSR, the rotor blades do not interact as strongly with much of the airflow passing through the volume swept out by the proceeding blades (Howell et al. 2010), which demonstrate dynamic stall which lower efficiency (Mukherjee, Jain, and Saha 2016). CFD simulation study on 0.12 solidity H-Darrieus wind turbine shows, at high TSR the flow was more attached to the blades and the AoA was limited below the static stall angle during turbine revolutions (Rezaeiha, Montazeri, and Blocken 2018b). While at low TSR as illustrated in Figure 9 the blades have gone through a deep stall in most azimuth position of the rotor. This results in a sudden drop in coefficient moment C_m as illustrated in Figure 10–13.

Figure 9. Vortex structure for lower and higher tip speed ratios at different azimuthal positions (θ) (Mukherjee, Jain, and Saha 2016).

However, high TSR minimizes the flow separation, a region of backflow that creates a greater blockage effect behind the VAWT (Parker and Leftwich 2016). In Ma et al. (2019), URANS simulation was carried out on NACA0022 airfoil blade VAWT to study stall conditions. The result shows that at high TSR, the boundary layer reattached to the blade leading edge which contributed to delay effects on the turbine. This dynamic stall effect over the turbine performance has been suppressed by a stall actuated control device (Ma et al. 2019). TSR is not a sufficient parameter to express the dynamic stall behaviors of VAWT. Particle Image Velocimetry (PIV) experiment approved that to accurately understand the flow separation around the leading edge, it is necessary to account for pitch rate effects with TSR (Buchner et al. 2018).

Figure 10. Instantaneous moment coefficient for the last turbine revolution for different tip speed ratios using various azimuthal increments (σ = 0.12) (Rezaeiha, Montazeri, and Blocken 2018b).

2.2. Type of airfoil

Usually, symmetrical NACA-series airfoils are used for VAWT blade design. However, in the modern aerodynamics of wind turbines, some enhanced airfoils become preferable. For example, the aerodynamic performance of VAWT can be improved by using readymade airfoils such as NLF and hybrid NLF-NACA 4 series for blade design (Tjiu et al. 2015a). The performance comparison of 25 different airfoils using CFD based on the URANS equation and SST k-ω turbulence modeling was studied (Mohamed, Ali, and Hafiz 2015; Mohamed, Dessoky, and Alqurashi 2019). The best five airfoils selected under investigation were LS(1)-0413, NACA63-215, NACA63-415, NACA64-415, and NACA0015. They confirmed these airfoils achieved a high lift to drag ratio with low stall conditions at high AoA when λ was between 0 and 9. Among the five airfoils, NACA63-415 and NACA64-415 show the best aerodynamic characteristics for H-Darrieus VAWT blade design (Mohamed, Ali, and Hafiz 2015). Interims of blade shape using LS(1)-0413 airfoil was 16% better performance than NACA0012 (Mohamed, Dessoky, and Alqurashi 2019).

In the recent era of VAWT blade design, S-series airfoils have become the leading inventions, For example, NREL S818 has a partial self-starting capability at low wind speed H-Darrieus rotor, beyond that when it is hybrid with H-Savonius rotor the turbine becomes fully self-starting at any wind speed and azimuth angle (Bhuyan and Biswas 2014). Similarly, replacing the symmetrical airfoil blade with S1210 airfoil at optimum blade solidity, the static torque coefficient is positive and four times higher than both cambered and non-cambered airfoils, and the maximum Cp of 0.32 is obtained for rotor solidity of 1.0 and wind speed 5.7 m/s, in which the turbine can develop standalone energy generation (Singh, Biswas, and Misra 2015). S1046 has a 26.83% higher power output coefficient and 10.87% higher efficiency than traditional symmetrical airfoils used in H-Darrieus VAWT (Mohamed 2012). A 2D CFD analysis on the H-Darrieus rotor having S815 and NACA0018 airfoils shows the stall AoA in the S815 rotor was as high as 9.95° than the NACA0018 blade and exhibited higher performance at optimal wind speed (6 m/s) (Sengupta, Biswas, and Gupta 2017). The aerodynamic performance of two different unsymmetrical airfoil blade profiles (S815 and EN0005) was compared using 3D CFD simulation for improving H-Darrieus rotor performance (Sengupta, Biswas, and Gupta 2016). It was found that the S815 blade shows a higher velocity difference between suction and pressure sides (i.e. 7 m/s which was 3 m/s higher than EN0005 blade) which reveals better influence for the rotor performance improvement. The performance of S-series airfoils was compared with NACA0015 airfoil (Cao et al. 2018). The result shows at low TSR (λ = 4) NCAA0015 revealed higher performance than S1012 airfoil. The aerodynamic performance of 24 different symmetric and asymmetric airfoils was studied using CFD based on k-ε turbulence (Hashem and Mohamed 2018). The result shows at low TSR (λ = 4) S1046 airfoil performs with the highest power and torque coefficient over other airfoils under investigation.

Figure 11. Airfoil performance evaluations, a) instantaneous rotor torque coefficient as a function of the blade at the midsection azimuth coordinate of NACA0012airfoil blade(Castelli et al. 2013) b) instantaneous best airfoils torque coefficients different family of an airfoil at 4 tip speed ratio (Mohamed, Ali, and Hafiz 2015; Mohamed, Dessoky, and Alqurashi 2019).

Figure 12. Comparative performance of NACA0015 to four S-series airfoils at different azimuth angles (Cao et al. 2018).

2.3. Number of blades (N)

Many scholars proved that the highest performance of the wind turbines was obtained at the three blades (Rezaeiha, Kalkman, and Blocken 2017a; Sunny et al. 2018). Based on the tangential force generated (Sunny et al. 2018), NACA0015 was screened as the best airfoil over all non-cambered airfoils which were supposed to design two, three, and four-bladed Darrieus wind turbines. 2D aerodynamic simulations based on the k-ε model at 10 m/s wind speed and rotor speeds of 4 rad/s, 6 rad/s, and 8 rad/s were studied. The aerodynamic performance of three blades wind turbine was increasing with the rotational speed and highest at 8 rad/s hence maximum torque. While four and two-bladed wind turbine shows moderate and lowest performance (are not efficient to provide an optimum amount of power at low wind speed) at the same aerodynamic conditions, respectively. The performance prediction of three, four, and five-bladed Darrieus type VAWT were studied at constant free stream velocity (Castelli, De Betta, and Benini 2012). The 2D-CFD result shows that the performance of the four and the five-bladed turbine was 5% and 15% respectively lower than the three-blade rotors.

2.4. Turbine solidity (σ)

When the diameter of the rotor becomes wider, the vortex wake, drags coefficient, and stress on the blade become reduced (Salman and Bdaiwi). Because the solidity of the blade significantly increases with larger rotor diameter span length as a result the optimum power coefficient decreased at higher TSR (Li et al. 2017). In Subramanian et al. (2017), the comparative effect of solidity on the performance of 1 KW VAWT of non-cambered airfoils, NACA0012, NACA0015, NACA0030, and AIR001, blades were studied using 3D-CFD simulations with transition SST and SST-k-ω turbulence model. The result shows that the NACA0012 airfoil has the highest performance at the lowest TSR (λ) under the three-bladed VAWT. And also the performance of the blades is increased with solidity and reaches the maximum value at high TSR, while the power coefficient was dropdown beyond pick point (Douak et al. 2018; Subramanian et al. 2017) because of large solidity leads to undesirable vibration.

Figure 13. The effect of solidity on Darrieus peak efficiency (Kirke and Lazauskas 2011).

2.5. Control methods employed

Controls of the wind turbine are fundamental to increase the wind power capture and reduce harsh operational conditions such as vibrations and total damage during off-design and extreme winds. Hence for regulations, active control systems are commonly used in larger HAWTs, whereas passive control systems such as blade pitching are often used in VAWTs. The blade pitch control mechanism must be designed to achieve a certain range of angles of attack during most of the cycles. The four-bar linkage mechanism controls the blade orientation related to the tangential direction to modify the angle of attack which is used to vary the blade pitch angle through the whole cycle. It allows output power up to 60% at TSR. A four-bar linkage mechanism (Kiwata et al. 2010; Sagharichi, Zamani, and Ghasemi 2018), shown in Figure 14,15, is the common passively aerated control system provided in a variable pitch VAWT. These control systems consisted of spools rotating on the cam (Sagharichi, Maghrebi, and ArabGolarcheh 2016). The pitch angle will be determined according to the eccentricity between the axis of rotation and the cam. This blade pitch control largely depends on the placement of moving rods hinged to the blades.

• For better self-starting, the blade pitch amplitude should be large enough and the moving rods hinged near the trailing edge of the blade.

• And to achieve maximum power, moving rods should be hinged near the place, where the fixed rods have been hinged to the blade.

The four-bar linkage mechanism described in Yamada et al. (2012) the performance of a variable-pitch VAWT with double tail vanes installed on the eccentric link lever which can prevent the turbine during storming wind conditions.

Figure 14. Four bar linkage mechanism in H-Darrieus wind turbine a) 2D view (Kiwata et al. 2010), and the 3D view (right) (Sagharichi, Maghrebi, and ArabGolarcheh 2016; Sagharichi, Zamani, and Ghasemi 2018).

Figure 15. Schematics of the over-speed prevention device using double tail vanes for variable pitch VAWT (Yamada et al. 2012).

Due to the aerodynamic complexity of VAWT, recently more sophisticated active control systems have emerged since mechanical braking mechanisms are not sufficient to maintain the turbine at rated power. Magnetically-suspended vertical axis wind turbine pitch control system designed by (Shuqin (2011) automatically adjust the blade angle of attack at different azimuth position and alleviate the turbine efficiency. This provides the turbine to minimize the starting torque at low wind speed and self-started. Even though the variable pitch generates higher power than a fixed-pitch VAWT configuration but is not still the optimal mechanism (Hwang et al. 2006). This can be improved by a rotary encoder to sense the azimuth position of blades separately at each time step. Figure 16 demonstrates through the pitch control system, the servo motor can transmit its rotating force directly to the blade by linkage, and the changing ratio of the blade pitch angle can be increased by shortening the linkage length (Hwang et al. 2006). This makes it possible to respond rapidly at high-speed rotation and increase the power output up to 60% higher than the fixed-pitch bladed rotor. The variable pitch controller Multilayer Perceptron-Artificial Neural Network (MLP-ANN) shown in Figure 17 proposed by Abdalrahman, Melek, and Lien (2017) which operates based on a neural network reveals a 25% higher power coefficient than conventional proportional integral derivative (PID) controlled system.

Figure 16. Sensor and actuating systems layout for individual pitch control system (Hwang et al. 2006).

Figure 17. MLP-ANN variable pitch control system (Abdalrahman, Melek, and Lien 2017).

2.6. Blade weight

Studies show a denser material used in wind turbine blades leads to a higher frictional effect on the hub bearing which results in reduced efficiency (Ozdamar, Mertcan, and Ozdamar 2018). In contrast, the turbine with lighter density blade material will be able to spin faster, creating greater force on the shaft and thus making the generator turn faster and generate more voltage for electricity production (Yee and Long). Under the condition of constant load torque, the energy efficiency of straight-bladed VAWT was almost independent of the wind cycle and the moment of inertia (Hara, Hara, and Hayashi 2012). However, under variable wind conditions, even if the frictional loss is neglected so that the higher the weight leads to the higher inertia, and more energy will be invested in acceleration and this is a loss.

3. Performance enhancement options

The aerodynamic performance of H-Darrieus VAWT can be enhanced through the conventional design or by employing new approaches such as:

• Geometric alteration such as new airfoil (Bhuyan and Biswas 2014; Mohamed 2012; Mohamed, Ali, and Hafiz 2015), optimum blade shapes (Lositaño and Danao 2019; Wang, Wang, and Zhuang 2018), employing flow augmentation devices (Kim and Gharib 2014, 2013; Wong et al. 2017);

• Employing advance and efficient materials and manufacturing methods, such as light composite and natural fiber reinforced composites materials (Hamdan and Mustapha 2017; Kalagi, Patil, and Nayak 2018);

• Utilize advance flow control devices and schemes such as vortex generators (Gao et al. 2015; Wang et al. 2017), variable pitch (Abdalrahman, Melek, and Lien 2017; Hwang et al. 2006; Kiwata et al. 2010);

3.1. Thick airfoil blades

A blade’s thickness can influence the performance of VAWT. Usually, symmetrical NACA-series airfoil blades are more streamlined characteristics that accelerate flow separations. However, thicker airfoils provide a better stall at high solidity turbine, improve the structural strength of the blade with an increase in the dead weight of the rotor. Airfoil with the least thickness provides high lift to drag ratio (Jahanmiri, Shooshtaryrezvany, and Nirooei 2016). At the same geometric AoA NACA0012 aerofoil performs better than the NACA0022 (Danao, Qin, and Howell 2012). The thickness effects of four symmetrical airfoils (NACA0012, NACA0015, NACA0018, and NACA0022) were investigated (Reddy and Kumar 2014). It was confirmed that NACA0025 reveals the best performance over the other one. This could be the effect of the blade’s interaction with the large vortices generated by other blades during rotation. A typical thickness effect of 126 airfoils was studied at low TSR (Tirandaz and Rezaeiha 2021). Among these, NACA0018 to NACA0024 became optimal airfoils for VAWT blades with increasing the maximum thickness from 18%c to 24%c when a slit λ was declined from 3 to 2.5. Also, the H-Darrieus rotor with asymmetrical airfoil, NACA 63–415 with a relative maximum thickness of 0.3, blade maximizes C_P at low wind speed (6.0 m/s) and low λ (2.4) (Mazarbhuiya, Biswas, and Sharma 2020b).

3.2. Helical blades

Due to adverse dynamic pressure gradients, high flow separations have occurred from the tips of the rotor blade. Hence, blade tip optimization alleviates the stall AoA which vanishes the flow separation. In this regard, The 2D CFD simulation was done for performance enhancements of H-Darrieus VAWT with trailing edge blade twists angles ($0^{\circ }$ upto $3^{\circ }$) (Mazarbhuiya, Biswas, and Sharma 2020c). It was confirmed that the rotor blade at a $1^{\circ }$ twist angle reveals the maximum C_P (0.171) at low wind speed (6 m/s) and TSR (2.4). The 2D-CFD H-Darrieus rotor with a ${30}^{\circ }$ blade twist angle at a trailing edge up to 10% of the chord was studied (Gupta and Biswas 2010). The result shows an approximate self-starting of the rotor was obtained for blade azimuth position of ≥90° with the operating wind velocity of 9 m/s at chord Reynolds number of 6.125 × 10⁴. A similar investigation was conducted while 3D geometry with a two-bladed rotor (Biswas and Gupta 2014). It attributed delayed stall AoA ($5^{\circ }$ higher than untwisted) which accelerates the flow on the suction side and produces non-zero lift higher than untwisted one.

3.3. Blade leading edge serrations

Leading-edge serration effectively reduces the boundary layer flow separation and is allowed to accelerate the flow from the pressure side to the suction side of the slot (Mohamed et al. 2020). It improves the power outputs of VAWTat low TSR (Lositaño and Danao 2018a; Wang and Zhuang 2017). It was applied in the H-Darrieus rotor with NACA0018 blade and the flow separation was reduced through the grooved section and the power coefficient was 18.3% higher than the baseline blade (unserrated NACA0018 blade) (Wang, Wang, and Zhuang 2018). However, this method was also implemented in a 5 KW H-Darrieus with NACA0025 airfoil blade against a massive vortex flow and leads to poor performance (Lositaño and Danao 2019). A serrated blade in a VAWT generates high turbulence instead of containing or decreasing it as was presumed (Lositaño and Danao 2018). Hence the concept of leading-edge serration is somehow a contradicted idea and needs more investigation.

3.4. Turbine twin configuration

The performance can also be maximized by optimizing the H-Darrieus turbine configuration through a wind farm. The effects of twin configuration on VAWT studied in Peng et al. (2020) maximize the C_Pavg by 13% than standalone once. Performance of clusters of two, three, and nine co-and counter-rotating VAWT turbines in parallel and oblique configurations were studied using CFD at low TSR (2.6) (Shaaban, Albatal, and Mohamed 2018). The result shows in the two turbine parallel clusters with counter-rotating turbines achieved 16% higher performance than stand-alone, while in the three and nine turbine cluster only one turbine was counter-rotating and reveals 30% and 28% higher performance than the standalone turbine configuration respectively. And also the configurations of the turbines’ cluster, Figure 18, affect the turbine performance (Shaaban, Albatal, and Mohamed 2018). CFD simulation result shows configuration represented in Figure 18,19 c has a better average C_P at the low spacing between the turbines. Even though, the highest C_P was less than that of the single isolated turbine by 3.1%.

Figure 18. Staggered arrangement of H-Darrieus turbine in a wind farm a) flow domain b) all turbines rotating in the same direction c) One turbine counters rotating.

3.5. Employing flow augmentation devices

Placing the H-Darrieus turbine in the convergent duct can increase the upstream wind speed near the blades (de Santoli et al. 2014). According to the CFD investigation carried out between 2 m/s and 12 m/s inlet wind speed, the result shows 32.2% and 30% wind speed enhancement respectively in the middle of the duct. Similarly, the power generated at 8 m/s and 15 m/s was maximized by 125% and 30%, respectively. The reason for low speed and power amplification at high wind speed was due to higher pressure loss at a corresponding flow. Placing a straight plate deflector upstream side of the H-Darrieus turbine enhances efficiency (Kim and Gharib 2014, 2013). This significantly increases the streamwise local wind velocity which leads to upgrade the angular speed of the rotor while the change of angle of attack was minimized from the no-deflector case. Providing flow augmentation devices such as duct, stator, diffuser, and guide vanes can increase the incoming wind speeds which significantly improve the performance of the turbine (Wong et al. 2017). Most of these devices are installed at the upwind side of the turbine and used as shields to reduce the negative torque created on the VAWT, guide the flow to a better angle of attack, increase the wind velocity towards the turbine blade. The blades are configured as cantilever support with or without guy wire at the top of the main tower, while the aerodynamic braking system is mounted near to the ground on the support bar (Tjiu et al. 2015b). Cyclonical surface wind lens configuration of S1046 airfoil blade with a diffuser significantly improves the performance of VAWT than traditional orientations (Hashem and Mohamed 2018).

3.6. Smart rotor and control schemes

When the turbine spins, the angles of attack (AoA) change continuously and each blade generates its maximum power at the front and rear side of the cycle. This is highly experienced in resonance which leads the turbine to pulse. Due to this reason, an active controlling system such as a braking system is used to regulate the H-Darrieus turbine from a long time spinning. The influence of upwind pressure around the leading edge was larger than the downwind effect on the trailing region of the blade (Li et al. 2016). This can be reduced by spanwise extension of the turbine blade, designing a more streamlined support structure and arms, and by extending the rotor diameter with a variable pitch blade (Arab et al. 2017). Active pitch controlling systems such as multilayer perceptron artificial neural network (MLP-ANN) individual blade pitch controller provide 25% output power enhancement than constant pitch operated turbines (Abdalrahman, Melek, and Lien 2017). The automatic optimization platform (VBPAOP) control system generated in Li et al. (2018) improved the self-starting capability.

3.7. Blade materials

Wind turbine blades are the most important and expensive part of wind turbine components (Mishnaevsky et al. 2017). These parts are exposed to diversified load conditions such as gravitational forces, dynamic-wind force, and cyclic load (Thomas and Ramachandra 2018), which sever the structural dynamics of the rotor blade (Hameed, Afaq, and Shahid 2015). For this reason, lightweight and high-strength materials must be considered during the structural development process to meet the structural requirements of the blade (Muzammil et al. 2019; Park 2016; Tarfaoui, Shah, and Nachtane 2019). To capture high energy and assure low starting speed, employing light-weighted blades can easily rotate and harness the incoming wind speed to the required form of energy. And to protect from any structural damage, typical blade materials must have high stiffness and yield strength. For this fact, proper choice of material for its component manufacturing was demonstrated at the beginning of the history of wind energy development. In the ancient era, wood was considered a common wind turbine blade material (Howard 2017). However, due to the nature of high moisture absorption woods are poor in structural performance. Hence, this section highlights the wind turbine blade materials used in the previous era and the future replacement opportunities for the novel blade design.

Figure 19. Key elements to be considered during wind turbine blade materials selection (Zangenberg, Brøndsted, and Koefoed 2014).

3.7.1. Synthetic materials

According to the origin, wind turbine blade materials can be categorized as synthetic and natural composites. Among synthetic materials aluminum alloy, glass fibers, and carbon fiber composites are widely used materials for wind turbine blade applications (Kalagi, Patil, and Nayak 2018). Aluminum alloy has a better strength-to-weight ratio than glass fiber and carbon fiber (Nader and Jendoubi 2018). The comparative performance of straight-bladed VAWT made from Aluminium and the Alumide blade was studied in (Neville 2019). The results show that Alumide blade turbine produces higher torque than Aluminium once. Due to its characteristics including low density, high strength-to-weight ratios, and modulus-to-weight ratios, the fiber-reinforced composite (FRC) materials are superior to those of metallic materials (Beardmore and Johnson 1986; Davies and Chauchot 1999; Immarigeon et al. 1995; Thomas and Ramachandra 2018). The glass-reinforced composites (GRC) have better mechanical properties, good corrosion resistance, high-temperature tolerance, ease of manufacture, and favorable cost (Eker, Akdogan, and Vardar 2006). There are three fundamental ways that carbon fiber may be used in wind turbine blade designs bulk replacement of load-bearing fiberglass materials, selective reinforcement, and cost attractiveness (Veers et al. 2003). Besides the advantages, synthetic fiber composites become incompatible with the environment of their end-of-life disposal. Because traditional disposal methods, i.e incinerated and landfills (Duflou et al. 2012; Kalkanis et al. 2019; Psomopoulos et al. 2019), impose significant environmental impact (Ramirez-Tejeda, Turcotte, and Pike 2017), and most recycling technologies are not yet commercialized. Hence, attempts are exploring a lignocellulosic material that can replace synthetic composites with better strength and affordable wind energy generation.

3.7.2. Natural Fiber Reinforced composites (NRFC) materials

Thermo-mechanical properties, surface treatment, moisture absorption, fibers attachment, availability, durability, and overall cost are the most important screening approaches for natural reinforced fiber composite (NRFCs) during the selection of them for specific structural applications (Lotfi et al. 2019). In the previous few decayed NFRCs are becoming suitable for high purpose structural applications buildings, marines, vehicle component designs (Binici, Aksogan, and Demirhan 2016; Boumhaout et al. 2017; Bravo et al. 2018; Florentin et al. 2017; Hallonet et al. 2019; Hamdan et al. 2014; Yoo et al. 2019). Because of superior performance in terms of temperature resistance, endurance, long-lasting, and cost attractiveness. Ashby (Ashby 2008) investigations illustrated in Figure 20, the relative performance of various natural fibers compared with manmade synthetic fibers which are frequently used in structural applications. It showed that some plant fibers such as hemp, flax, and jute have better tensile strength than E-glass and steel wire. This is due to the relatively low hydrophobic nature of the fiber.

Figure 20. Comparison of the position of natural fibers against synthetic fibers concerning specific tensile strength and stiffness (Ashby 2008).

Studies show natural reinforced fiber composite (NRFC) materials can also replace structural components like a blade. Flax and bamboo reinforced composite materials are dominant in wind turbine blade manufacturing industries. In Setiawan, Al Gifari, and Hamidah (2018), a handmade HAWT blade from bamboo having an average tensile strength of 284.4 MPa starts rotation at 4.6 m/s wind speed, while a standard glass fiber reinforced (GFR) blade is required 4.7 m/s to begin rotation. However, vibration and dynamic instability were observed as drawbacks of the bamboo blade at high wind speed. NRFC blade made from hemp fibers laminated in vinyl ester resin had have resisted the structural impact subjected to low wind speed (Boria et al. 2019). The comparative damage pattern of the blade subjected to the lightning strike of flax fiber and glass fiber VAWT blade was studied in (Mat Daud, Mustapha, and Adzis 2018). Their microscopic visual result indicates, when both blades were got a lightning strike, flax fiber shows some peeling and some surface breakage while the glass fiber blade experienced burnet. However, a considerable weight and volume of flax are needed than E-glass to pass the same structural requirements (Blanchard and Sobey 2019). Hence, physical treatment and other treatment processes are essential to enhance the mechanical properties of natural fibers.

3.7.3. Mechanical properties of natural fibers

Properties of the composites materials depend on various factors, such as type of resin, the origin of the fiber, fiber orientation, manufacturing technique, crystalline index and crystallite size of the fiber, chemical functional groups existing in the fiber, volume and weight fraction of fiber added into the composite, as well as fiber condition (raw or surface treated) (Sanjay et al. 2018), and fiber orientation, pressure, cooling speed, temperature and post-curing duration (Cadu et al. 2018) are the major decisive parameters affecting the mechanical properties of the fibers. Unidirectional and cross-ply laminates of flax /Elium fiber and flax/epoxy orientation were investigated under 100 KN loading conditions (Cadu et al. 2018; Haggui et al. 2019). The result indicates that unidirectional composite resin articulation provided higher energy dissipation, a higher life cycle, and comparative stiffness degradation than cross-play orientations (Haggui et al. 2019). The tribological behavior of unidirectional flax/polypropylene composite material using, glass fibers as a benchmark was investigated in (Chegdani et al. 2017). They used the nanoindentation technique and scratch test under loading conditions. And they conclude as the load increase, dynamic friction coefficient of glass fiber increase while flax fiber reduced, and supplementary behaviors of flax/polypropylene correspond to viscoelasticity/plasticity significantly reduce friction coefficient.

3.7.4. Moisture absorption of NRFCs

The fatigue behavior of uniaxial flax/epoxy composite specimen subjected to 100 kN before and after 23 days immersed in a water bath was studied in Jeannin et al. (2019). Their experimental result shows that

• Due to water absorption, the thickness and width are increased by 10% and 3% respectively.

• The stiffness of the aged specimen was reduced by 64% and 25% than saturated and dried specimens respectively.

• The tensile strength was decreased by 26.5% and 30.3% during saturated and after drying of the specimen.

• Hydrothermal aging reduces static rigidity and strength while the fatigue resistance increased with aging and the water absorption can be limited by using coating the specimen.

The hydrophilic property of unidirectional hemp/epoxy reinforcements in a humid environment ranging from 9% to 98% RH (relative humidity) at a constant temperature, moisture absorption, and its effect on mechanical behavior has been studied in Réquilé et al. (2019). Their result shows; 13% reduction of the tangent modulus, longitudinal stiffness reduced, 6.2 ± 1.3 GPa to 3.5 ± 1.2 GPa while despite moisture content the tensile strength was significantly increased and is optimum at 75% RH (3% moisture content).

Also, the orientations of fiber/fiber or fiber/resins are the main cause of moisture absorptions which results in a degradation in the composite structure. The energy absorption intensity and damage resistance capability of hybrid jute/ natural rubber bio-composite materials subjected to low-velocity impact under different layering were studied (Mahesh, Joladarashi, and Kulkarni 2019). They conclude that energy absorption and damage resistance of depended on the fiber orientation and plys order in the composite.

3.7.5. Matrixes properties and selection criteria

High moisture absorption, non-uniformity, lower mechanical strength, and matrix in compactness are the major drawback of natural fibers in a structural application (Yıldızhan et al. 2018). These can be significantly reduced by using proper reinforcement (Davoodi et al. 2011). The common reinforcement compounds used for bio-composites laminate are epoxy, polyester, vinyl ester, etc. Similar to the fiber selection requirements; load resistance, thermal creep, chemical composition are the important characters to select a resistant matrix to protect bio-composite materials from structural failures (Lotfi et al. 2019). The comparative energy absorption of Kevlar bio-composite materials using rubber and epoxy matrix under high-velocity loading conditions was studied in (Khodadadi et al. 2019). Finally, it was concluded that the epoxy matrix has the lowest reinforcement factor which leads to the lowest ballistic energy absorption, weak load resistance than low hardness (LH), and high hardness (HH) rubber matrix. In contrast, the ballistic absorption of HH matrix was; 19 % and 9 % for two layers, 41 % and 21 % for four layers higher than neat and LH fabrics, respectively. Hence high-quality matrix allowed a better composite interfacial interactions.

3.7.6. Specimen preparation methods of NFRC

The bonding strength between the fiber/matrix pulls out the model influenced by physical dimensions such as fiber length, the thickness of the adhesive layer, diameter, and elastic modulus of fiber and risen (Lau et al. 2018). The common specimen manufacturing techniques used in NRFC are spray layup, hand layup, compression moldings, injection molding, filament winding (McGregor et al. 2017; Sanjay et al. 2018), compression and hand layup molding is used for fabricating woven fabrics, while spray layup and injection molding are used for short fibers manufacturing (Lau et al. 2018). In wind turbine blades manufacturing, the blade should follow the standard airfoil profile patterns, and spanwise extensions are provided to have a desired blade size. Wind Empowerment association is highly promoting local manufacturing of small wind turbine blades from NRFC (Latoufis et al.) commonly used for rural electrifications because of the low cost of fabrication and environmentally friendly. Some modern researchers introduced a new mode of blade manufacturing; light resin transfer molding (LRTM) was used to fabricate flax/unsaturated polyester resin blades (Shah, Schubel, and Clifford 2013).

3.8. Non-Conventional performance enhancement of Darrieus VAWT

In the modern aeronautical industry, airplane wings are designed with additional aerodynamic structures such as slats and flaps on the leading and trailing edge of the wings respectively. These structures significantly improve the lift force of the blast without affecting the dead weight of the wings. Similarly, researchers coming up with the concept of flaps to solve the self-starting problems of H-Darrieus VAWT at low TSR (El Baz et al. 2013). The effect of the inside (Gurney) and streamline flaps on straight blade H-type VAWT was investigated by (Xu et al. 2011). The result shows Gurney flap allows a 4% higher power coefficient than the reference NACA0015 blade turbine when TSR was 3.5.

Another alternative recently emerged to enable H-Darrieus WT to self-start and the high power coefficient is to hybrid with another VAWT such as Savonieus (Bhuyan and Biswas 2014). This is due to the dynamic stall suppressed by the inside Savonieus rotor and provides starting torque at low TSR (Liu, Yu, and Zhu 2019). The comparative investigation is illustrated in Figure 21, the static torque coefficient of the hybrid system was 15 times higher than alone of three-bladed H-type VAWT (Mohamed 2013), getting a quick start. However, the flow penalty may happen when its size becomes larger. The second hybrid system is related to other sources of energy such as solar systems. The wind-solar hybrid system technology is becoming a very interesting research area for mega-scale energy generations such as power plants and grid integrated utilities. These are used for stand-alone energy generations or hybrid energy obtained from the source connected to the DC system and stored in a battery. In Bhuvaneswari and Rajeswari (2013), a hybrid H-type VAWT with an evacuated tube collector was used for the power plant. However, a lack of research is available regarding solar hybrid efficiency enhancement and self-starting issues of H-type VAWT.

Figure 21. H-Darrieus-Savonieus Hybrid WT performance (Mohamed 2013). a) Static torque coefficient and hybrid system. b) Torque coefficients for an individual and hybrid turbine.

4. Computational methods for Darrieus vertical axis wind turbine

With growing interest in wind energy harvesting offshore as well as in the urban environment, vertical axis wind turbines (VAWTs) have recently received renewed interest. On the contrary, the complex aerodynamics around these wind turbines hindered and limited the options to enhance the aerodynamic performance. Hence, a comprehensive understanding of the aerodynamics of these VAWT and the relations among several parameters is a vital step.

Fluid flow around the wind turbine is governed by Navier-Stokes equations, which comprised the continuity equation and conservation of momentum equations along each coordinate. As for wind turbine application, the flow pattern is categorized as low Mach flow, nearly 0.1 (Ageze, Hu, and Wu 2017a; Hansen et al. 2006); thus the incompressible flow models suit well. Therefore, the governing equations will be;

(1) $\left.\begin{array}{c}\frac{\mathrm{\partial }\left(\mathrm{u}\right)}{\mathrm{\partial }\mathrm{t}}+\left(\mathrm{u}\cdot \mathrm{\nabla }\right)\bar{\mathrm{V}}=-\frac{1}{\rho }\mathrm{\nabla }\mathrm{p}+\frac{\eta }{\rho }{\mathrm{\nabla }}^2\mathrm{u}+\frac{{\mathrm{F}}_{\mathrm{x}}}{\rho }\\ \frac{\mathrm{\partial }\left(\mathrm{v}\right)}{\mathrm{\partial }\mathrm{t}}+\left(\mathrm{v}\cdot \mathrm{\nabla }\right)\bar{\mathrm{V}}=-\frac{1}{\rho }\mathrm{\nabla }\mathrm{p}+\frac{\eta }{\rho }{\mathrm{\nabla }}^2\mathrm{v}+\frac{{\mathrm{F}}_{\mathrm{y}}}{\rho }\\ \frac{\mathrm{\partial }\left(\mathrm{w}\right)}{\mathrm{\partial }\mathrm{t}}+\left(\mathrm{w}\cdot \mathrm{\nabla }\right)\bar{\mathrm{V}}=-\frac{1}{\rho }\mathrm{\nabla }\mathrm{p}+\frac{\eta }{\rho }{\mathrm{\nabla }}^2\mathrm{w}+\frac{{\mathrm{F}}_{\mathrm{z}}}{\rho }\end{array}\right\}$(1)

(2) $\mathrm{\nabla }.(\bar{V})=0$(2)

where: $\bar{V}=u\hat{i}+v\hat{j}+w\hat{k}$: velocity vector, $\rho$: air density, $p$: pressure, $\eta$: kinematic viscosity, and $\bar{F}=F_x\hat{i}+F_y\hat{j}+F_z\hat{k}$ body force vector.

However, as the flow approaches the incompressible limit, it is very difficult to solve the flow equations. To alleviate this numerical difficulty to solve incompressible N-S equations, two common remedies are available: preconditioning and artificial compressibility (Hansen et al. 2006). Applying the latter method, the artificial compressibility term will be added to the continuity equation and results (Equation 3(3) $\frac{\mathrm{\partial }p}{\mathrm{\partial }t}+{\mathrm{a}}^2(\mathrm{\nabla }.\bar{V})=0$(3) ), pressure-based, or pressure corrected continuity equation as (equation 3(3) $\frac{\mathrm{\partial }p}{\mathrm{\partial }t}+{\mathrm{a}}^2(\mathrm{\nabla }.\bar{V})=0$(3) ), with $a$ is a pseudo speed of sound.

(3) $\frac{\mathrm{\partial }p}{\mathrm{\partial }t}+{\mathrm{a}}^2(\mathrm{\nabla }.\bar{V})=0$(3)

Finally, Equations (1 to 3) will be solved to determine the flow characteristic. Pressure-based coupled solver provides merit of faster solution convergence rate as compared to the segregated algorithm, aside from its high memory requirement.

Therefore, based on these relations, computation methods to study and optimize VAWT and the cutting edge method and techniques will be reviewed. The computational method for a wind turbine can be categorized as the Blade Element Momentum method, lifting line, panel and vortex models, generalized actuator disc models, and Navier Stokes based solvers; each theory possesses pros and cons (Ageze, Hu, and Wu 2017a).

The key procedures of all computational models to predict performance are described as (Islam, Ting, and Fartaj 2008; Kumar et al. 2017a).

• Calculation of local relative velocities and AoA at different TSRs and azimuthal positions;

• Calculations of the ratio of induced to free stream velocity $(V_{i\mathrm{\infty }}/V_{\mathrm{\infty }})$ considering the wake instruction between the blades;

• Suitable model selection

• Mathematical expressions of normal and tangential forces;

• Pre-stall airfoil characteristics’ for the attached regime at different Reynolds numbers;

• Post-stall model for stall development and fully stalled regimes;

• Finite aspect ratio consideration;

• Dynamic stall model to account for unsteady effects;

• Flow curvature model’ to consider the circular blade motion

4.1. Blade Element Momentum (BEM) theory

Frequently, the BEM method is used for modeling horizontal axis wind turbines and was originally introduced by Glauert H (G. H., Airplane propellers 1963). The theory is based on a one-dimensional classical momentum theory in which forces are distributed continuously in the azimuth direction (Li et al. 2014). However, the performance characteristics of VAWT using the BEM model accounting stream tube models also has been the most popular approach to studying its aerodynamics because of their usefulness for giving rough but reasonably accurate performance predictions (Mohammed et al. 2019). Hence, this theory is the best-validated model for the performance predictions of both curved and straight bladed VAWTs (Bedon, Castelli, and Benini 2013,Hilewit et al., 2498-2509, 2019; Saber, Attia, and El Gamal 2015). Generally, BEM models can be classified into two categories. i.e cascade model and vortices model. Each of these models has strengths and weaknesses which are presented in this section.

4.1.1. Cascade model

The aerodynamic characteristics of each blade are calculated independently by considering AoA and local Reynolds number in the azimuth of upwind and downwind rotor position (Batista et al.). This model can readily account for the integrated effect of WT parameters such as high solidity, high TSR, blade pitch, flow curvature, and aspect ratio at the same time (Kumar et al. 2017a)(see Figure 22). The Cascade model reasonably predicts the blade aerodynamic force and wakes effect, but it is poor consideration of the dynamic stall effect (Hirsch and Mandal 1987).

Figure 22. Cascade model of Darrieus VAWT (Kumar et al. 2017a).

4.1.2. Vortex model

During the turbine rotation, vortex-blade interaction may be attached or detached characteristics. This mainly depends upon the AoA, solidity, and TSR and it has a significant contribution to the performance of VAWT (Chen and Lian 2015). The vortexes of WT are mainly originated due to the turbine structures such as support, shaft, blades flow instructions, and other sub-components. The trailing vortex originating in the region of azimuth angle −90° < θ < 90° has a longer dissipation distance at high TSR and a more significant impact on the wake of WT (Yang et al. 2017). Due to the complex flow behaviors of VAWT, it is not an easy task to capture the vortex effect by using wind tunnel experiments (Yang et al. 2017). Instead of that, CFD and analytical methods are vital to predict the reasonable effect of the vortex on the turbine wake. The intensity of bound vortices shed vortices and trailing vortices of FP and VP straight blade VAWT are presented in Figure 23 b. Except for two azimuth positions of the rotor ($0^{\circ }$ and ${180}^{\circ }$), bond vortices of blades were higher than the other twos vortices. This indicates that bound vortices with VP configurations revealed higher lift force than other own vortices and FP cases of vortices (Zhao et al. 2019).

The vortex model assumed the flow to be incompressible and inviscid. In this model, the vortex filaments substitute the blades and the vortices in the wakes of blades are calculated by considering blade profile coefficients, relative flows, and AoA (Batista et al.). Several vortex methods i.e. blob vortex (constant vortex generating time interval close to the trailing edges of the blade) (Zannetti, Gallizio, and Ottino 2007), vortex filament method (the blades are divided into the number of segments along their span) (Zhao et al. 2019), and the strength of vortices filaments are reduced along the span and generate trailing vortices (Zhao et al. 2019). To increase the computational effort of the vortices model, the dynamic stall model of the blades was adopted to calculate the lift and drag coefficients (Dyachuk and Goude 2015). Hence, this model was effectively incorporating the effect of flow curvature and the dynamic stall effect of VAWT.

Figure 23. Schematics of vortices model. a) Vortex model filaments in straight-blade (Griffith et al. 2018). b) Strength of different vortices of FP and VP H-Darrieus VAWT (Zhao et al. 2019).

4.1.3. Stream Tube Models

Stream tube (ST) model is a modified actuator disc theory that effectively accounts for 3D effects such as aspect ratio and dynamic stalls of aerodynamic devices (see Figure 24). However, due to uniform flow assumptions, this model is inferior accuracy at high rotor σ and λ (Kumar et al. 2017b). ST model assumptions include:

• Irrational and incompressible upstream flow,

• The flows over the entire disc are uniform in-stream tube model.

Figure 24. Single-stream tube model (Kumar et al. 2017a).

ST models can be classified as single stream tube and Multiple Stream Tube (MST) and Double Multiple Stream Tube (DMST) Models.

Single Stream Tube Model: This model considers the change in kinetic energy between the upstream and downstream wind as the useful power extracted from the wind. In this model, as shown in Figure 24, the rotor is represented as an actuator disk inside a stream tube (Templin 1974).

Multiple Stream Tube (MST) Model: An improved version of the single-stream tube model was introduced in Wilson and Lissaman (1974). The swept volume of the turbine was divided into multiple parallel stream tubes as shown in Figure 25 which are aerodynamically independent. The blade element and the moment theory are applied for each stream tube. Rotor power and torque are obtained by averaging the values from each stream tube.

Figure 25. Multiple stream tube model (Kumar et al. 2017a).

Double Multiple Streamtube (DMST) Model: DMST model developed by Paraschivoiu (Paraschivoiu 1988) divides the rotor into upwind and downwind half considering different induction factors (i.e $a$ and $a^{\prime }$) along each half of the tandems respectively (see Figure 26). This model is a combination of MST model and double actuator disk theory which incorporates both momentum and BEM theory (Ayati et al. 2019; Manwell, McGowan, and Rogers 2010). DMST model is the most accurate and optimized model which accounts for the aerodynamic characteristics of VAWT having high σ and low λ (Meana-Fernández et al. 2018).

Figure 26. Double multiple stream tube models (Kumar et al. 2017a).

Previous studies focus only on operation at the optimal tip speed ratio and there is a lack of analysis of exploiting pitching for any other control objective (Soraghan et al. 2013) and there are almost no aerodynamic prediction models publically available for VAWTs with pitching blades (Soraghan et al. 2013). A DMST model permits active pitch blade control (Soraghan et al. 2013). This is the better numerical model to predict the aerodynamic performance of VAWT considering the blades’ tip-loss at low Reynolds number and TSR (Kumar et al. 2017a). It predicted the Cp by 23.1% and 21.8% when Re 1.4 × 10⁵and Re 2.6 × 10⁵ respectively which cannot be achieved in wind tunnel models. BEM relayed the post-stall prediction results with incidences between ${10}^{\circ }$ and ${30}^{\circ }$, superimposition of 10% wind fluctuation which allows overcoming the dead band and the rotor achieved self-start (Rossetti and Pavesi 2013). In parallel, it was predicted the effect of streamline divergence and relative flow curvature, and the vortices intensity effect at low TSR on the blade using 2D and 3D-CFD analysis respectively. DMST and CFD analysis was used for the performance comparison of the NACA0018 airfoil blade with that of movable airfoil blade at 70% of the cord length away from the leading edge (Beri and Yao 2011). They conclude that in CFD lift force generated in the modified blade was a better performance of the turbine at a lower tip speed ratio (< 1) and starts to rotate, and DMST reveals high starting torque or low Cp at low TSR.

4.1.4. Enhanced BEM

The original Blade Element Momentum method was developed with simplified assumptions and assumed a quasi-static/steady flow condition. On contrary, the flow characteristics around actual vertical axis wind turbines tend to be complex and unsteady, therefore additional models have to be included such as wind shear, tip loss factor, dynamic wake/inflow, and dynamic stall.

4.2. Dynamic stall

When the incoming free stream wind is getting strike to straight bladed Darrieus WT, the induced velocity is distributed along the length of the blades (spanwise), blade profile downwind components, and passing through the equator. Thus air passing through the rotor flow towards the tip of blades, and the stream tube passing to the blade tips consequently transfer less moment to the airfoil than those passing at the equator (Paraschivoiu, Desy, and Masson 1988). Over the last two decades experimental investigation has been done to understand the dynamic stall characteristics in various aeronautic machines such as helicopters (Carr 1988), and H-Darrieus WT (Brochier et al. 1986). Now a days the advancement of flow visualization devices such as PIV tends to extend the dynamic stall prediction phenomena (Ferreira et al. 2007). However, due to the complexity of dynamic stall behaviors in VAWT, experimental results are inconsistent and lack accuracy, for this reason, attempts are devoted to CFD simulations. While advanced models are required to account for wake interaction to the blades (Richter et al. 2011), that may scarify too much computational cost. In Almohammadi et al. (2015), straight bladed H-Darrieus WT, the trailing vortex and leading vortex are formed close to the trailing edge and leading edge respectively and propagated towards each other. Consequently, the two vortexes are merged and formed one larger shed vortex. Hence, the instantaneous lift coefficient shows a large difference in the upwind and downwind sides of VAWT blades (Qin et al. 2011). This indicates due to the presence of a dynamic stall the power extracted from downwind side became lower than the upwind side.

4.3. Tip loss factor

According to finite wings theory (Abbott and Von Doenhoff 1959), the tip vortices of aerodynamic structures such as airplane wings and WT blades are generated by the pressure difference created between the upper and bottom surface of the blade. Thus, the tendency to trailing vortices from the blade tip, or any point in the blade where flow circulation varied (Zhao et al. 2018), thereby reducing the effective blade’s length (Balduzzi et al. 2017). The effect may less significant when the turbine aspect ratio is smaller AR < 1. However, for medium AR > 1 (Zanforlin and Deluca 2018), and high AR ≥ 6 VAWT (Li and Calisal 2010) the tip loss effect on the blade reached 10 % and less than 5% respectively. Similarly, due to the severe influence of tip loss, the torque coefficients become smaller along the blade up span (Jiang et al. 2020). As illustrated in Figure 27 a, the vortex at the top tip of the blade is higher and dropped down along the bottom tip. And the corresponding torque coefficients are also presented in Figure 27b. The loss of blade tip can be reduced by bending the blade tips at a certain angle (Li 2019).

Figure 27. H-Darrieus blade vortex. a) flow streamlines in the tip region, skin friction lines, and z velocity component on the blade suction surface (Balduzzi et al. 2017). b) instantaneous torque at different blade sections (Jiang et al. 2020).

4.3.1. Comparison of hydrodynamic models

To investigate the accuracy of hydrodynamic models Ferreira et al. (Ferreira et al. 2014) presented a blind comparison of six different models using the analytical method. The models are the Multiple-Stream tube Model (MST), the Double-Multiple Stream tube Model (DMST), the Actuator Cylinder model (extension of the actuator disc model), the U2DiVA code (Unsteady Two-Dimensional Vortices Aerodynamics model), the ARDEMA2D code (based on vortex model), and the CACTUS code (code for axial and cross-flow turbine simulation, a 3D vortex code). To check the accuracy of these models they used different test cases of several TSR, rotor solidity, and fixed pitch angles, included heavily loaded rotors, in inviscid flow. Then evaluating the effect of TSR and solidity on the C_p, assuming these models should give a consistent value of C_{p under} similar conditions. They used different cases, case A used was at the condition of TSRs of 2.5, 0.5, and 7, solidity (σ) of 0.04, 0.005, and 0.14, and the evaluation criterion was power C_p and torque coefficients (CT). Based on the CP value the models showed good agreement between each other except the MST which showed a deviation from the other models as shown in Table 2,3.

Table 2. Strength and weakness of different analytical models (Batista et al.; Hirsch and Mandal 1987; Islam, Ting, and Fartaj 2008).

Models	Strengths	Limitations
Cascade	No-solution convergence problem Can predict any range of turbine parameters	High computational time Poor in accounting Dynamic stall effect
Vortex	Effectively account flow dynamic stall Have a good agreement with correlation to experimental data.	Expensive computational cost
SST	Very fast prediction	Insufficient predictions for highly loaded VAWT Disagreement with experimental data
MST	Fast computational time Reasonable computations for lightly loaded VAWT	Convergence problem Increasing computational time Disagreement with the field test result
DMST	Offer good agreement with experimental data	Increasing computational time Convergence problems Poor tip loss Consideration Over predictions for high solidity and at high TSR VAWT

Table 3. Accuracy comparison of aerodynamic models (Ferreira et al. 2014).

Models	CT	CP
MST	0.92	0.55
DMST	0.87	0.6
Actuator Cylinder	0.89	0.59
U2DiVA	0.89	0.56
CACTUS	0.86	0.57
ARDEMA2D	0.92	0.63

4.4. Computational Fluid Dynamics (CFD) models

CFD applications developed from the aerospace industry which employs potential flow solvers, to alleviate their limitation, and the use of unsteady Euler solvers emerged. As the computing power grows, the application of full Reynolds Averaged Navier Stokes equations including viscous effects applied for helicopter rotor computations, later on, the full Navier Stokes (NS) computations of wind turbine rotor aerodynamics was presented in Ageze, Hu, and Wu (2017b). NS solver originally developed from an aerospace code solving compressible equations, intended for high speed aerodynamic in subsonic and transonic regimes; apparently, this nature of the code is not compatible with wind turbine application, because of low Mach numbers around the roots of the blades. As the flow approaches the incompressible limit, it is very difficult to solve the compressible flow equation. Two remedies have been suggested by Ageze et al. (Ageze, Hu, and Wu 2017b): the first one is preconditioning that changes the eigenvalues of the system of the compressible flow equations by pre-multiplying the time derivative by a matrix. The second method is an artificial compressibility method in which an artificial sound speed is introduced to allow standard compressible solution methods and schemes to be applied for incompressible flows. This method has many merits such as ease of implementation of overlapping grids as the compressible codes, and the main limitation is the problem to enforce incompressibility in transient computations without the need for a huge amount of sub-iterations and the problem of determining the optimum artificial compressibility parameter. The method is well suited for solving nearly incompressible problems often experienced in connection with wind energy. In connection with steady-state problems, the method can be accelerated using local time-stepping, while the method using global time-stepping still is well suited for transient computations.

4.4.1. CFD flow domain

CFD study is also quite sensitive to the flow domain size (the ratio of the side length of flow domain to turbine diameter). Chen et al. (Chen et al. 2016) studied the effect of flow domain on CFD accuracy of vertical axis wind turbine, five different ratios (i.e. 10, 15, 20, 25, and 30) were compared. Figure 28 demonstrates the effect of the flow domain ratio on the C_T, from the figure it can be seen that the C_T value of the rotor is relatively stable when the computational domain ratio is larger than 15.

Figure 28. The flow domain ratio effects on the turbine torque coefficient (Ferreira et al. 2014).

4.4.2. Turbulence modeling

Flow around the wind turbine can be fairly considered as turbulent and so including the effect of turbulence in the flow model is mandatory. Several turbulence models are available, such as the Spalart-Allmaras model, two equations k-ϵ model and k-ω model, Reynolds stress model, Detached Eddy Simulation (DES), Large Eddy Simulation (LES) model, and others (Ageze, Hu, and Wu 2017a).

The main shortcoming in CFD modeling is the selection of the meshing accuracy, physical model, and turbulence model which results in conflicts and confusing output (Mohamed, Ali, and Hafiz 2015). Hence, detailed understandings of CFD points are essential to obtain meaningful results. RANS turbulence model reduces computational time and cost, however, it is not an efficient tool to couture the turbulence intensity caused by adverse pressure gradient (Lanzafame, Mauro, and Messina 2014) and considered Reynolds stress tensor proportional to the strain rate tensor which is an invalid computational model for highly accelerated and curvature flow (Mohamed, Ali, and Hafiz 2015). Hence, k-ε, kω, SST- kω, LES, and hybrid LES are enhanced RANS tools to developed turbulence modeling in wind turbine and other aerodynamic performance studies. All turbulence models have similar transport equations for turbulent kinetic energy (k) and turbulent dissipation rate (ε), while in the eddy simulation turbulence model, the Prandtl numbers governing the turbulent diffusion and dispassion rate (Ghasemian, Ashrafi, and Sedaghat 2017). The k-ε turbulence model is the most common turbulence model used in industrial applications. It can solve the turbulence kinetic energy (k) and turbulence dissipation rate (ε) based on the RANS equation. The renormalization group (RNG) k-ε turbulence model handle some gaps observed in the k-ε turbulence model (Yakhot and Orszag 1986), which make it more reliable than the standard k-ε model (Ghasemian, Ashrafi, and Sedaghat 2017), while the Realizable k-ε turbulence model provides superior performances for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, recirculation and non-reliance on assumed relationships between Reynolds stress tensor and stress rate tensor (Hashem and Mohamed 2018; Mohamed, Ali, and Hafiz 2015) the major differences of this families are the determination of C_µ for the standard k-ε model is not constant (Mohamed, Ali, and Hafiz 2015). The main problems observed in these models are not efficient to compute near-wall boundary flow with adverse pressure gradients.

When the flow is in the transitional region transitional SST turbulence model corresponds to time step independence became significant (Subramanian et al. 2017). The freestream inflow which is far away from the wall boundary is used the formulated SST k-ω turbulence model which can accurately be calculated for the separation (Li et al. 2017). Hence, SST k-ω turbulence model can achieve good results because of its capability of capturing proper behavior in the near-wall layers or shear stress transports of the fluid and separated flow regions (Castelli, De Betta, and Benini 2012). The three combined models, k-ε and SST k-ω are essential turbulence models to consider both near walls and far wall-flow conditions, The standard k-ε and SST k-ω properly resolve near-wall boundary conditions and the flow separation formed by a free stream inflow far away from the walls respectively (Li et al. 2017) with an acceptable computational cost and reasonable accuracy (Almohammadi et al. 2013; Nobile et al. 2011; Spentzos et al. 2005), however it takes too much computational time and high computational space.

4.4.3. Comparison of hydrodynamic models and CFD with experiment

To evaluate the accuracy of hydrodynamic models presented in section 2.3 and CFD (SST k-ω turbulence model) (Delafin et al. 2017) studied the comparison of low-order aerodynamic models and RANS CFD for full-scale 3D vertical axis wind turbines. They used a DMST model a free-wake vortex model, and SST k – ω turbulence model, and compared the result with a 17 m vertical axis wind turbine field-tested by SNL. Their result showed among comparisons of the three numerical models SST k–ω turbulence model gives better accuracy than the other hydrodynamics models which can give a fairly good prediction of the turbine CP. However, predictions at low and high tip speed ratios do not have the same level of accuracy.

Figure 29. CFD model comparison of power coefficient C_P as a function of TSR and experimental studies results used for H-Darrieus VAWT.

Hence, here the robustness of these models compared to each other is illustrated in Figure 29,30. The unique feature of the SST k-ω model over k-ε is allowing reliable power coefficients (Cp) at low TSR (λ) Ma et al (Ma et al. 2018). In contrast, the Realizable k-ε model used in M.R.Castelli et al. (Castelli, Englaro, and Benini 2011) over predicted the performance and disagreed with experimental and other numerical results.

4.5. Structural models for darrieus VAWT

The structural models will determine the dynamic response of the system for the aerodynamic load. The earliest works tend to use linear beam theories with homogenous properties. As the design of VAWT blades becomes more flexible and increasing its size, classical beam theory may be sufficiently incapable of a model the structural dynamic of the turbine, contrary to the fact that the utilization of more nonlinear beam theory with less assumption is demanded (Ageze, Hu, and Wu 2017b). Besides the beam theory (linear or nonlinear) and elements (shell or beam elements) to be employed, there are three frequent discretization methods to model the structural dynamics of the wind turbine (Ageze, Hu, and Wu 2017b), that is, modal reduction approach, multibody dynamics (MBD), and finite element methods (FEM).

4.5.1. Finite Element Method (FEM) studies in H-Darrieus VAWT

FEM analysis was used in composite blades based on the shell element discretization method which effectively determines the accumulation of ice, mechanical, and hydro-thermal loads (Kong, Bang, and Sugiyama 2005). The strain stress characteristics of four different lay up of 1.2 MW blades were studied in Lanting (2012). Their result shows, [0°/±60°/90°] lay-up sequence became the optimal orientation. The centrifugal forces acting on the glass fiber-epoxy blade was evaluated using FEM (Hameed, Afaq, and Shahid 2015). The orientation of Glass fiber-Epoxy layers [45°/90°/0°/−45°] with varying thickness of each layer was chosen for the best design of straight blade of a VAWT which reduced the values of both maximum stresses and maximum deflections when compared with Aluminum blade. This method is also used in composite VAWT for fatigue and ultimate strength analyses under normal and extreme wind conditions (Lin, Xu, and Xia 2019). Experimental validation of the FEM thermoplastic composite sandwiched 5 KW straight blade design meets the required performance criteria at extreme wind load cases (Brown and Brooks 2010).

The upper FEM studies are carried on synthetic and metallic wind turbine blade materials, while this method is also implemented in advanced blade materials such as NFRC. In Park (2016), the structural analysis of the 1 KW flax/ epoxy wind turbine blade was performed and compared with the glass fiber/epoxy blade. The results confirmed an acceptable structural safety of flax-reinforced structures at extreme loading conditions. The comparative structural analysis of aluminum alloy, glass fiber, and hemp fiber composite blades has been investigated at 11 m/s wind speed (Elalaoui 2019). The result shows constant stress of 49.92 MPa, and the maximum deflections of hemp fiber were lowest and which beneficial than the two-bladed materials due to their low weight and cost. Bamboo fiber-reinforced has a superior ability to resist wind attacks than GRF blade, which the three-layer structures i.e. outer, middle, and inner skins combinations suppress blade vibration and static loading when the flow reaches the dangerous velocity (Meng and Sun 2017).

Figure 30. Structural analysis platform of vertical axis wind turbines (VAWTs) (Lin, Xu, and Xia 2019).

4.5.2. Modal approach

When VAWT works in a natural environment, the loads are complicated and variable. The freestream wind load, elasticity force, and inertia forces are applied on the blades of a wind turbine can make the blade and tower deform and oscillate (Feng et al. 2018). These lead to the damage of the wind turbine when the exciting force approaches the natural frequency of the turbine. The flap-wise, edgewise, extensional, and torsional deformations vibration analysis of troposkein shape blade has been characterized under stationary and rotating conditions in Hakeem Saleh (2017). The effects of wind speed and shear on the modal response of the lift type VAWT to azimuth position are mainly due to excitation being applied to the tower rather than to the blades and struts (Kusnick and Adams 2012). In some other shapes of the blade of VAWT, the blade resonance may be significant for the structural response. This may improve by introducing new materials such as woods that have low density and high yield strength (Yi and Teoh 2018). The modal analysis of straight-bladed H-Darrieus WT shown in Figure 31 a was done (Afzali, Kapucu, and Feeny 2016). The natural frequency of the rotor can be expressed in equation (4)(4) ${\omega }_{nq}=\sqrt{\frac{EI}{m}\left(\frac{\pi }{2a}\right)-{\mathrm{\Omega }}^2}=\sqrt{{{\omega }_o}^2-{\mathrm{\Omega }}^2}$(4) .

(4) ${\omega }_{nq}=\sqrt{\frac{EI}{m}\left(\frac{\pi }{2a}\right)-{\mathrm{\Omega }}^2}=\sqrt{{{\omega }_o}^2-{\mathrm{\Omega }}^2}$(4)

The turbine response as a function of rotor speed at different blade position length ‘a’ are illustrated in the Figure 31 b, the primary resonance of the turbine occurred at the point where the natural frequency is equal to the rotor speed which the undamped natural frequency. When the rotor reached the critical angular speed the system becomes unstable. Therefore, to increase the natural frequency of the system ${\mathrm{\Omega }}_{oprational}\ll {\omega }_n$ must be satisfied (Afzali, Kapucu, and Feeny 2016).

Figure 31. Modal analysis of straight-bladed H-Darrieus WT. a) blade deflection b) natural frequency.

4.5.3. Multibody Dynamics (MBD) Method

The multi-body design approach helps to parameterize different elements of VAWT such as blade mass, the mass of the arms, the size of the tower and optimize the size of linkage mechanisms used for blade pitch controls (Chougule and Nielsen) which are described in sections 2.6 and to specify the characteristics of the generator coupled to other elements of the turbine (Rishmany et al. 0000). The effect of the twisted blade turbine system on the mast has been discretized based on a simplified multi-degree of freedom (MDOF) (Verkinderen and Imam 2015). Taking the mass of the rotating element into account, ignoring the stiffness, and considered the turbine as a static structure, the stiffness of the mast was characterized under the height of 3 m, 6 m, 9 m, and 15 m. The response of 15 m masts for the first three modes and the system coupled natural frequencies for different mast lengths are presented (Verkinderen and Imam 2015) in Figure 32 a and b respectively. The dynamic behavior of the tower and blades of 5 MW H-type floating VAWT has been studied using multi-body kinematics and dynamics analysis (Deng et al. 2020). It was determined that the elasticity of the blade and tower has little effect on the dynamic response of the floater. The blade responses are mainly affected by aerodynamic whereas the tower response includes both aerodynamic and wave frequency.

Figure 32. Multi-body dynamics of typical VAWT (Verkinderen and Imam 2015). a) FE model of 15 m mast and first three mode shapes. b) Mast, turbine and coupled system natural frequencies for different mast lengths.

4.6. Artificial Intelligence (AI) method

AI is an imitation of human cognitive processes to create intelligent machines that can simulate human thinking capability and behavior in which machines can execute tasks smartly. It applies superimposed concepts such as machine learning (ML), deep learning (DL), ensemble deep learning (EDL), and many more techniques to understand and solve the actual problem. Whereas, ML is the subset of AI that allows machines to learn from data without being programmed explicitly or assisted by domain expertise. It includes the ability to learn and train a model based on the data and ML algorithms respectively and then evaluate performance to predict the desired output.

In the last few decades, AI was applicable with advanced search engine referral systems (such as YouTube, Amazon, and Netflix), human speech understanding (such as Siri or Alexa), self-driving cars (such as Tesla), and high-level competitive game systems such as chess and Go and the machines became more efficient (Chatterjee 2020). Know a day AI also became a promising approach in energy sectors (Bose 2017). Because the nature of turbines tends to be complex to increase the power output, next-generation wind energy industries require AI-based system design and monitoring to operate machines efficiently and consistently (Chen et al. 2021) which includes structural health monitoring (Reddy et al. 2019), design and optimization (Jayabalan et al. 2017), wind turbine performance predictions (Papathanassiou, Kladas, and Tegopoulos 2001), load and price estimation (Negnevitsky, Mandal, and Srivastava 2009), fault detections and monitoring (Saenz-Aguirre et al. 2019; Stetco et al. 2019), system control and sustain energy output (Saenz-Aguirre et al. 2019), etc. Hence, wind turbine designers and engineers must consider multi‐objective optimization algorithms that are essential to identify a trade‐off curve that reveals the weaknesses, anomalies, and rewards of certain targets (Chehouri et al. 2016).

Supervisory Control and Data Acquisition (SCADA) is a hardware system used to collect and store high-resolution 10-minute average or one-minute snapshot records of wind farm conditions. It allows AI techniques for analyzing the data’s dependencies among various physical sensors (Viharos et al. 2010) through three main steps i.e data-acquisition, pre-processing, machine learning, and finally diagnostic and action can be carried out (Chandrasekhar et al. 2021). SCADA systems can be used for both monitoring as well as controlling industrial systems remotely and provides an efficient way for industries to gather and analyze data in real-time (Eriksson 2020). This system has been utilized for collecting and storing data from wind farm operations (Martinez et al. 2019). To manage power consumption and turbine efficiency, the system may be integrated with turbine control systems to detect downtimes. However, SCADA is mostly used for wind farm label application which needs very expensive system cost. And in most case the system focus monitoring and diagnostics of with limited turbine components such as pitch angle, gearbox, and generator which may not sensitive enough to reflect the change in the WT health state (Liu et al. 2019). Hence advanced AI methods such as deep learning (DL) and ensemble deep neural network (EDNN) are supplemented with SCADA to build accurate fault detection models (Liu et al. 2019).

Usually, artificial neural network (ANN) algorithms are used to optimize wind turbine components such as airfoil blades (Mortazavi, Soltani, and Motieyan 2015; Ribeiro, Awruch, and Gomes 2012) and overall enhancement of aerodynamic performance of the wind turbine (Casás et al. 2005). ANN was proposed by (Brahimi 2019) as a powerful tool to predict the wind speed associated with input layers and hidden layers. The result shows as compared to weather research and forecasting (WRF) this scheme was more flexible interims of accuracy and computational time. The comparative performance of support vector regression (SVR), regression tree (RT), random forest (RF), and ANN was studied for predicting wind energy production (Buturache and Stancu 2021). Their result represents ANN delivers an MAE that is 20% smaller than RF, 35% smaller than SVR, and 59% smaller than RT. While its main drawback was the larger training time and computational power invested during the process of determining the best combination of parameters. Ensemble ML was incorporated on 1.5 MW aerostructure simulations of generic HAWT (Clifton et al. 2013). It was confirmed that the regression tree method predicts power output with two to three times more accuracy than the industry-standard power curve method, and may be useful for the estimation of power output with a limited input variable (i.e. hub height wind speed, turbulence intensity, and wind shear). The ANN model was developed by (Siavash et al. 2021) to establish a relation between inputs (wind speed and duct angle) and outputs (rotor angular speed and power) variables. The result was found to possess better performance than the regression model for both turbine power curve and rotor speed estimation.

ANN, AI based VAWT design, developed by S.Teksin et al. (Teksin, Azginoglu, and Akansu 2022) illustrated in Figure 33–36 has five inputs (AoA, D, V_∞, c and, resistance), 10 hidden layers, and one output (the voltage). They were tested each learning algorithms 50 times and the results of these 50 experiments were averaged. It was seen that according to Bayesian regularization regression algorithm analysis, the best performance was obtained with 35 hidden neurons. ANN was developed by K.Ziane et al. (Ziane et al. 2021) predicts fatigue life of GFRC blade under extreme environmental conditions (dry and wet). ANN with Cuckoo Search algorithm was pointed out that the better than the backpropagation and particle swarm optimization algorithms in terms of the blade fatigue life prediction because of its simplicity in using mathematical models, as well as its ability to adjust weights without determining a gradient. In some advanced levels of computation, the outputs of one may be considered as the parts of inputs layer for the development of AI, for example, the deflection of GFRC wind turbine blade specimen was simulated using ABAQUS (Supeni et al. 2014). The results obtained from the investigation, a load applied and the current was used as inputs to generate an ANN-based design tool for predicting the number of wires needed to restore the original shape of the blade.

Figure 33. The architecture of ANN (Teksin, Azginoglu, and Akansu 2022).

Most the reviewed research articles in this sections are the subset of AI (i.e. ML), while in some case they used interchangeably and it may be confusion behind their deference. While the main drawback of AI-based studies is the optimal number of hidden layers (neurons) can be obtained by several trials which are time-consuming during the training process rather than computational cost.

4.7. Fluid-Structure Interaction (FSI) and aeroelasticity of darrieus VAWT

The concept of aeroelasticity is a developed tool in the aviation industry since 1947 as introduced by A.R. Collar, and its application for wind turbine design and analysis begins as late as 1976 by Friedmann (Friedmann 1976). However, its application in VAWT simulation is very limited. Aeroelasticity study the fluid-structure interaction interactions of a flexible and moving body. In classical aeroelastic methods, the fluid and structure interaction is treated separately and uncoupled, ignoring the interaction among these domains (Marshall and Imregun 1996). As the computing power improved, several integrated approaches developed including inherent fluid-structure coupling. As the fidelity requirement of the analysis increases to include explicit details such as turbulence and wave loadings (Owens, Griffith, and Murray 2014), nonlinear composite layered blades, and large deformation (Owens and Griffith), the application of strong fluid-structure coupling is necessary. However, on the contrary, computational efficiency with small compromise on accuracy is also another route of coupling demands, such as introducing a reduced-order model (Ferrari 2012).

Flutter or dynamic aeroelastic instability can be a fundamental design consideration for lift-generating structures under aerodynamic loads (Owens and Griffith). This coupling of aerodynamic forcing with a structure’s natural modes can lead to large amplitude diverging motion. Hence, the fluid-structure interaction (FSI) simulation tool for turbine performance studies, combines blades’ structural dynamics and the flow around them. This requires the computation of both the velocity and pressure fields in the fluid domain, simultaneously with the stress and strain fields in the structural domain (MacPhee and Beyene 2013). It uses nonmatching discretization of the interface between the fluid and structure subdomains which interpolates the traction and kinematic simulation data was essential for aerodynamics and structural mechanics modeling approaches than the FEM model (Bazilevs et al. 2015) and helps to predict structural deflections of blade materials caused by wind flow (Castelli et al. 2013). This technique was implemented in 1.2 KW VAWT for the validation self-starting of field test data. Even though these techniques are quite preferable to the individual FEM or CFD system, limited researches are done for vertical axis wind turbines.

Figure 34. Typical Aeroelastic (FSI) based tool.

There are two main FSI solution approaches (MacPhee and Beyene 2013):

• The first is segregated (one-way coupling) fluid-structure solvers and transfers information between the two until convergence is reached. This is numerically unstable while it allows cheaper computation.

• The second is a monolithic (two ways coupling) solver which simultaneously solves for the fluid and structural domains and these are robust FSI simulation approaches.

The FSI simulation technique is one of the novel performance prediction methods used in modern mega-scaled wind turbine composite blades. The 5 MW baseline HAWT symmetric fiber glass/epoxy composite blade was considered at 11.4 m/s wind speed and angular velocity of 12.1 rpm, rotor using FSI modeling technique (Bazilevs et al. 2011). The critical stress component of the entire blade at 0.7 s was observed in σ₂₂ (0’ fiber orientation) and the maximum stress along the front and rear of the blade was 22.63 MPa and −19.84 MPa respectively. The corresponding flap and edgewise deflections were 6 and 0.3 m respectively.

Similarly, some researchers applied FSI for VAWT analysis. FEM coupled with vortices filament for an aeroelastic structural dynamic of a troposkien blade was presented (Fereidooni, Nitzsche, and Matida 2014). The aeroelastic responses of the morphing design concept of the VAWT blade passively control the pitch angle and enhance the self-starting capability of the rotor (MacPhee and Beyene 2016). This model saves simulation data to mitigate the loss attributed to vortices loading and blade stall in the region of poor airfoil lift while it is an expensive computational cost. VAWT with an active control system, coupled aero-hydro-servo-elastic simulations have been performed on individual pitch-controlled VAWT (Vlasveld et al. 2018). The result illustrated that the dynamic load acting on the rotor was reduced due to the control system employed.

FSI model becomes the preliminary effort for a better understanding of H-Darrieus WT for components elastic deformations and self-starting issues of the turbine (Bazilevs et al. 2014). The transient response of this system at inflow wind speed was 11.4 m/s and considers three initial rotor speeds: 0 rad/s, 4 rad/s, and 12 rad/s. The result shows at 4 rad/s values of angular speed became more linearized, the lift force was higher, the rotor naturally accelerated and the tower tip displacement during this cycle was about 0.10–0.12 m. This allows promising for VAWT to self-start.

Figure 35. Typical System coupling. a) one-way coupling (Wang et al. 2015) (the left side one) b) Two-way coupling (Rafiee, Tahani, and Moradi 2016), (the right side one).

FSI simulation was carried on a 1.2 KW Darrieus baseline wind turbine at 11.4 m/s and 4 rad/s inflow wind speed and the initial rotor speed respectively (Bazilevs et al. 2015). The rotor and struts were made of aluminum, and the tower was made of steel. The result shows that as the rotor spins, the structure was not too flexible and the amplitude of tip displacement became approximately 12 cm. Additionally, the rotor speed increased gradually with time step and eventually reaches the speed necessary for efficient operation. For a better understanding and more multi-perspective consideration of turbine blades, modern researchers coming up with sophisticated BEM-FSI coupling simulations. This was done in (Lee, Jhan, and Chung 2012) for fiber-reinforced plastic (FRP) composite turbine blades to enhance the optimal performance, designed power capacity at 10 and 25 m/s was 1.3 and 1.66 MW, of a HAWT turbine. Hence BEM result with FSI consideration shows 13.3% and 17% power output delay. To mitigate these design loss they three important measure has been taken i.e. twisting the blade geometry, pitch angle control correction, and adjusting fiber orientation. A synthetic coupling, DMST model-Vortex theory, approach was utilized to investigate the aeroelastic characteristics of H-Darrieus blade considering both stall and post effects (Shams, Molaei, and Mirzavand 2019). The result shows that due to the presence of stall and lift force reduction, nonlinear aerodynamics predict the elastic torsion at higher flow velocities to be smaller than the value predicted by linear aerodynamics in which static stall reduces the blade torsion.

5. FSI simulation (Case study)

In this section, the FSI simulation of Darrieus Vertical Axis Wind Turbine was done to compare the accuracy of a numerical model. In the following few paragraphs, to demonstrate the effect of coupling choice, turbulence model, and other parameters, a simple case study will be discussed considering a bidirectional (two-way) fluid-structure coupling.

The FSI simulation is targeted at a 1.2 KW Darrieus type VAWT baseline wind turbine developed by NREL, extracted from open-source Q-blade software under FAST simulation. The rotational speed of the rotor was specified to 21.56 rad/s and the details of rotor geometry are described in Table 4 However, to reduce the computational time the turbine components such as arms and shaft were ignored and the geometrical parameters were scaled down to one-third (1/3) of the actual dimensions.

Figure 36. Boundary conditions and computational domain. a) top view b) isometric view.

5.1. Results

1. Mesh Independence

A full 3D coupled simulation was applied to the Darrieus VAWT rotor disregarding the shaft and blade arms. The objective of the study was to compare the accuracy of turbulence models’ on VAWT performance predictions and structural performance of the blade materials under the same boundary conditions prescribed in Table 4. To study the intensity of flow reached over the turbine blades, Realizable k-ε and SST k-ω turbulence models have been used.

Table 4. Simulation Parameter.

Parameter	Value	Parameter	Value
Number of blades	3	Air velocity (m/s)	11.2
Blade length (m)	6.1	Turbulence model	SST k-ω and Realizable k-ε
Blade cross-section	S1046	Flow /structural solver	ANSYS fluent/Mechanical 2020R2
Chord (m)	0.07	Fluid-structure domain Coupling	Two-ways/bidirectional
Rotor radius (m)	0.51m	Type of simulation	Unsteady
Blade Material	Aluminum Alloy and E-glass fiber reinforced epoxy composites

To examine the accuracy of the computational model, the mesh sensitivity study was performed on the base model before implementing the couple simulation. The simulation domain was discretized into the rotating and stationary sub-grid, Figure 37, compliant with the dynamic mesh technique. The stationary domain has the dimensions of 15 m, 3 m, and 5 m along with streamwise, vertical, and spanwise directions respectively, and illustrated in Figure 38. To capture intermediate flow characteristics from the system boundary, an interface was created between the fixed and rotating sub-domain. The aerodynamic mesh settings were established with the three mesh alternatives i.e coarse, medium, and fine. The size of elements of the rotor and stationary sub-domain was 10 mm and 60 mm respectively. To have a better quality of results, the element size of each blade path was put into 50 divisions. Finally, the mesh convergence was achieved with 1,354,412 nodes and 1,270,000 elements in all conserved variables as shown in Figure 39–41.

Figure 37. Model mesh.

Figure 38. Model grid Independence.

2. Model Validation

In this section, the self-starting characteristics of straight-bladed VAWT described in Table 4 were investigated using FSI simulation. The simulation was carried out at realistic operating conditions reported in the table, and the air density and viscosity are set to 1.23 kg/m³ and $1.78\times {10}^{-5}$ kg/ms respectively.

Figure 39. Torque generated in FSI simulation.

Figure 40. Aerodynamic model comparisons.

Blade structural performance

Keeping all the turbine blades fixed at both ends and under the unsteady-state coupled analysis of blade materials, the performance of aluminum alloy is very high than the synthetic composite blade (i.e. Glass epoxy). The FSI structural response was investigated by setting the structural time step 10 seconds coupled with the k-ε turbulence model and within 1 second system time interval. The maximum total deformations have occurred on the blade which was perpendicular to the inlet of boundary condition. The maximum total deflection of aluminum alloy and Epoxy_Eglass_UD is approximately 0.0642 mm and 0.691 mm respectively. These indicate that composite E-glass are more deformable and maybe failed at stormwind conditions, while aluminum alloy allows wind load resistance. Similarly, under similar conditions. Hence, the maximum strain of aluminum alloy wind turbine is 5.545x10⁻⁶[m/m] and the maximum strain of Epoxy_Eglass_UD turbine blade is 4.287 × 10^–4 [m/m].

Figure 41. Total deformation contour. a) Epoxy_Eglass _UD blades b) Aluminum Alloy blades.

3D aerodynamic and fluid-structure instruction of H-Darrieus VAWT simulation has been carried out. The study compares the two most frequent turbulent models (i.e. k-ε and SST k-ω) used in aerodynamic studies. The result shows SST k-ω turbulence model is more reliable than the k-ε model interims of predicting the moment coefficients (Cm) of the turbine. This is because of the robustness of SST k-ω by computing near-wall and far-wall flow boundary conditions with adverse pressure gradients. In steady-state FSI analysis, the performance of the two commonly used blade materials (Epoxy_Eglass_UD and Aluminum alloy) has been compared. The result demonstrates Epoxy_Eglass_UD has larger total deformations and higher strain which may cause larger failures at stormwind conditions. Except for computational expensiveness, full-scale transient FSI simulation is a more accurate analysis to understand the action-reaction response of the fluid and the turbine structural component may have an accurate aerodynamic prediction.

So many parametric and design modifications of H-Darrieus WT with performance prediction methods are summarized in Table 5. In general, most of the authors targeted enhancing the power output of the turbine especially for enabling the turbine self-starting. Analytical, numerical, and combined methods of performance prediction are including in touch. Interim of predictions, each separate method may have their merit and demerit; combine forms such as FSI analysis provide an outstanding effort to multi-dimensional considerations in the complex aerodynamics of the turbine. Analytical models: stream tube model (STM), multiple stream tube models (MSTM), and double multiple stream tube models (DMST) and CFD models: k-ε, k-ω, and SST k-ω are the usual tools for H-Darrieus wind turbine aerodynamics study. In turn, the coupling system (FSI) becomes a mandatory and necessary tool for the high fidelity study of VAWTs. But very expensive computational costs and time consuming nature may the special drawback of this method.

Table 5. Parametric studies of H-Darrieus wind turbine Summary

Selected Airfoil	N	C	D	H	λ	U	TM	Findings	Reference
NACA0018	3	0.1	0.4	0.3	< 3	3-12	BEM	DMST model predicts negative Cp at a low aspect ratio (<1.2) and Re below 2 × 105 which cannot obtain in an experiment.	[146]
NACA0015	3	0.152	5			6	BEM	Turbulence wind allows the wind turbine to self-start at low Re and TSR than constant wind.	[168]
NACA0018	3	0.2	4		0.25-5	4	BEM	Blade shape modification (flexible tip), DMST result shows that the turbine generates negative torque for the lower tip speed ratios.	[169]
S1046	3	0.035	1.3	1	2-8	9	Realizable k-ε	S1046 airfoil with the presence cyclonical of wind lens the CP was augmented by +0.00135 than open NACA0015 airfoil H-Darrieus turbine.	[252]
NACA0018	3	0.2	0.8	0.8	0.4-1.5	7	SST k-ω	The power coefficient was improved with the maximum and minimum growth rate of 26.82% at 0.9TSR and 9.02% at 1.5TSR respectively	[195]
NACA0025	3	0.86	1.03	1	2.58	9	SST k-ω	The three-bladed H-rotors were 5% and 15% higher Cp than four and five-bladed rotors respectively.	[62]
S1046	3	0.07	2	1		5	SST k-ω	S1046 was the highest performance Cp 38.5% at 4.3 TSR over other airfoils and can use for wide range of applications.	[52]
NACA0015	2	0.25	1.7	1	2.29	7	SST k-ω	At 140 AoA and 11.90 pitch angle, 20% higher performance at variable pitch than fixed pitch.	[38]
S1046	3	2	1	0.1	2-9	5	SST-k-ω	NACA63415 & NACA64415, shows higher performance (high lift to drag ratio) and large operating ranges over S1046 and others 23s	[12]
NACA0018	2	0.06	1	1	4.5	9.3	U-T-SST	Flow separation was minimum for low solidity high aspect ratio VAWT,	[253]
NACA0015	3	0.42	2.7	3	1-2.5		T-SST	NACA0030 attained higher CP at low TSR, 2blade has higher CP than 3blade VAWT b/c higher solidity leads to large vortex interaction	[65]
NACA0015	3	0.06	1	1	4	7	U-T SST	The Cp was increased by 6.6% at -20 and The change in pitch angle literature the instantaneous loads of the blade.	[37]
NACA0012	3	0.086	1.03	1.03	-	9	SST k-ω	GRF–blade deformations, The inertial contributions of different values of shell thickness were higher than the aerodynamic deformation and maximum at the trailing edge than the leading edge.	[60]
NACA0015	2	0.2225	1.7	1.02	2.29	7	k-ε, SST	The Spanwise pressure effect was higher at the blade tip, and the maximum blade performance was obtained at z/(H/2)=0 which is 50% higher CT than other locations.	[254]
NACA0018	3	0.0246	1.7	1	2-2.5	10	SST-k-ω	Individual variable pitch control system boosted the power coefficient by 25% than the conventional fixed pitch H-d turbine	[71]
NACA0021	2	0.3	3	1.2	2.5	˂10	k-ε-expt.	Aspect ratio and CP were maximum as H/D was higher and the induced drag and spanwise backflow became reduced, hence power performance is improved.	[64]
-	4	0.25	1.70	2	1.2	6	k-ε,SST k-ω	The flow separation was higher at the trailing edge in the upstream regions of 90° < θ < 180, b/c an AoA becomes smaller and its variation range also narrower with the increase of TSR.	[190]
NACA0018	2	0.06	1	-	4.5	9.3	k-ε, SST k-ω	At optimal TSR, the upwind flow has 50% contributions which inherently increase the unsteady nature of H-D, hence introducing flow control methods can improve significant power enhancements. eg, introducing a variable speed controller, a turbine rotating at 65.1rad/s by 4m/s improved up to 168%.	[44]
NACA0012	1	1	-	-	-	Re=	FSI	Under 0-200 AoA, The performance of flexible airfoil blade without the use of pitch control became 4.2% higher than the rigid blade.	[241]
NACA0015	3	0.4	2.5	3	1.25	6	FSI	Flexible (Morphing) blade VAWT provide 9.6% higher power coefficient than fixed blade at the maximum Young’s modules (0.5MPA) for case study sample	[245]
DU06W200	3	0.127	1.168	6		11.4	FRI	The rotor in the 4rad/s case was promising to self-start, and the range of the tower tip displacement during the cycle was about 0.10–0.12m.	[247]

Where: N, C, D, H, σ, λ, U, and TM, U-T, and expt. represents, number of blade, camber(m), rotor diameter(m), highlight(m), solidity, tip speed ratio, upwind velocity(m/s), turbulence model unsteady-transitions and experiment, respectively.

6. Conclusion

Often, VAWT has a potential advantage such as omnidirectional and it can be installed anywhere if desired wind resource is available. This helps to reduce the turbine investment cost and a better energy alternative for the sites away from grid-connected electricity i.e rural areas, schools, telecommunications, military comps, health centers, research centers, etc. However, in the real fact, VAWT is not largemouth applicable in grid-connected power generation, the machine is not start-up unless an auxiliary device is supplemented to the system. The main reason behind it is that the aerodynamic nature of VAWT is too complex and affected by different parameters. With a comprehensive understanding of both structural and aerodynamics investigations, the authors give deep insight on the performance enhancement options such as using efficient airfoils, VP-blade design, optimizing the blade shape, employing flow augmentation device, allowing control methods, hybrid with other types of turbine, etc. Similarly, the influence of blade materials regarding environmental and the turbine performance aspect was also reviewed. Furthermore, the accuracy of conventional and advanced computational methods has been devoted to exploring concerning to the gross efficiency enhancement and technical means of self-startup opportunities. For example, analytical methods (BEM, MSTM, DMST), CFD (k-ε, k-ω, SST kω, LES), and advanced computational methods (FSI and AI) have been reviewed. Additionally, an FSI simulation was done on 2 KW NREL baseline VAWT to compare the structural performance of the two commonly used wind turbine blade materials (glass fiber and aluminum alloy) and the accuracy of the two turbulence models (k-ε and SST kω). These all attempts grasp multi-perspective overviews on the aerodynamics of VAWT performance enhancement. Finally, the authors are pointed out the following few critical research gaps and concepts that may shed light for future researchers

• Even though several investigations have been done for H-Darrieus VAWT performance enhance, its self-starting is one of the most critical issues which limit the turbine applications. Because several studies are based on numerical predictions which may have less accuracy and wind tunnel and field test experimental validations are compulsory.

• H-Darrieus VAWT is only limited to small-scale applications; however, the turbine has promising opportunities which are mentioned in this study to enable stand-alone and grid-connected electricity generation.

• Studies show variable pitch (VP) blade designs are better than fixed pitch (FP) once however the details of pitch control methods and the significant elevation of performance enhancements are not quantified.

• Leading-edge serration of the blade is considered as one of the performance enhancement alternatives in this investigation. However, some contradicting ideas are observed between different researchers at the same objectives.

• High fidelity simulation may be difficult or even impossible using CFD methods such as FSI and LES while very expensive computational cost and time. Therefore advanced methods such as AI schemes are promising computational methods in terms of computational cost, accuracy, and stability.

• AI-based aeroelastic analysis of wind turbine and system control concepts is very essential as mentioned earlier. However, there is a lack of AI-based research in the aerodynamics of H-Darrieus VAWT that may robust tool concerning turbine blade optimization, aerodynamic performance predictions, and system control.

• The structural performance of any aerodynamic device depends on the physical and mechanical properties of the components. Physically most wind turbine blades are exposed to several adverse environmental conditions. However in fact due to corrosion of the synthetic blade (blades made from metals) cause catastrophic structural failure.

• Since most recycling technologies are not yet commercialized, traditional end-of-life disposal methods i.e incinerated and landfills of synthetic composite blades yields high environmental depletion

• Even if, research efforts are emerged with shifting synthetic turbine blade material with biodegradable fiber-based composites, high moisture absorption characteristics minimize the turbine blade standard physical requirements. This may a sophisticated method of fiber physical modification, composite manufacturing, and blade manufacturing method.

• The aeroelastic and morphing characteristics of natural reinforced composite (NRFC) blades in H-Darrieus VAWT with VP-configuration are not investigated.

Nomenclatures

AoA Angle of attack

AR Aspect ratio

BC Before Christ

BEM Blade element momentum

CFD Computational fluid dynamics

DES Detached Eddy Simulation

DC Direct current

DMST Double multiple stream tube

FEM Finite element method

FP Fixed pitch

FRC Fiber-reinforced composite

FSI Fluid-structure interaction

GPA Giga Pascal

GRF Glass-reinforced fiber

GW Giga watt

HAWT Horizontal axis wind turbine

KN Kilo newton

LES Large Eddy Simulation

MST Multiple stream tube

MW Megawatt

NREL National renewable energy laboratory

NRFC Natural reinforced fiber composite

NS Navier Stoke

SNL Sandia National Laboratories

SST Shear stress transport

ST Stream tube

TSR Tip speed ratio

URANS Unsteady Reynolds averaged Navier Stoke

VAWT Vertical axis wind turbine

VP Variable pitch

WT Wind turbine

Symbols

Cm Moment coefficient

Cp Power coefficient

C_T Instantaneous torque coefficient

cn Normal force coefficient

ct Tangential force coefficient

α Angle of attack

β Pitch angle

λ Tip speed ratio

φ Incident angle

θ Azimuth angle

σ Rotor solidity

a Upstream induction factor

a’ Downstream induction factor

2D Two-dimensional

3D Three-dimensional

Disclosure statement

No potential conflict of interest was reported by the author(s).