A comprehensive analysis of aerodynamic flow around H-Darrieus rotor with camber-bladed profile

Abstract

Improving the H-Darrieus rotor is often followed by the investigation of the influence of the turbine’s parameter design, notably, the aspect ratio, the solidity (σ), the tip speed ratio, and the airfoil profile shape. In this work, we are interested in both the aerodynamic flows around a straight cambered blade profile and the rotor turbine wake separation of a Darrieus vertical axis wind turbine. The aim of this study is to better understand the evolution of the instantaneous torque and the generated-separated blade vortex during full rotation. Indeed, a three-dimensional computational fluid dynamics model of a vertical axis wind turbine with a straight cambered blade profile NACA4312 operating over a large range of tip speed ratio is considered. The flows are governed by Reynolds-averaged Navier–Stokes equations and the turbulence is modeled with shear stress transport formulations k-ω. This research revealed a high correlation between the evolution of the torque coefficient and the generated-separated blades vortex. In particular, a good correlation between the maximum tip vortices size and the torque coefficient peak is demonstrated.

Keywords

H-Darrieus vertical axis wind turbines cambered profiles vortex turbine wake

Introduction

In the past few years, there has been growing interest in renewable energy in order to reduce the impact of the unsustainable resources, such as fossil fuel, on environment (Balat, 2007, 2009). In fact, more attention is given toward exploration and expansion of the use of clean, renewable, and green energy. One of the promising solutions is to convert the wind’s kinetic energy to electricity form (Jha, 2013). There are two main kinds of wind turbines according to the axis of rotation, horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs). To overcome the inherent drawbacks of HAWTs (high maintainability cost, located away from urban areas, etc.), a particular attention has turned to VAWTs. VAWTs are characterized by wind potential harnesses from any direction and operating under severe turbulent flow conditions and at a low tip speed ratio (TSR). They are divided into two categories: drag-based Savonius which are well known by their better self start-up and lift-based Darrieus which provide a high performance compared to the Savonius turbine (Aslam Bhutta et al., 2012; Balat, 2009).

Although substantial amount of research has been conducted on this subject, the effectiveness of VAWT with cambered blade profiles is not yet achieved. This is mainly due to the difficulty to ascertain the flow field around blades. It should also be acknowledged that much more remains to be done to understand the interactions between blade wake, dynamic vortex stalls, and turbine wake.

Subramanian et al. (2017) have studied the effect of various symmetrical profiles’ thickness on the performance of VAWT through three-dimensional (3D) computational fluid dynamics (CFD) modeling. They have noted that thicker profiles performed better for low TSR due to the long duration of the attached wake. However, thinner profiles are advised to perform at high and with a wide range of TSR. This could be mainly attributed to the fast dissipation of the shedding vortex. Also, the effect of solidity has been studied by altering the number of blades. The authors have concluded that low-solidity turbine performs better at high TSR. However, high-solidity turbine performs better at low TSR.

Qamar and Janajreh (2017a) have investigated the effect of solidity on the performance of straight camber-bladed turbine through a two-dimensional (2D) CFD model with various chord lengths. The results have shown a low performance for lower turbine solidity on large operating range of TSR. However, high turbine solidity performed better performance at short range of TSR. They have concluded that large chord length improves the torque production. However, a change in blade number with near unit-solidity rotors results in a dispersed wake behind the rotor turbine which would penalizes wind farm setting-up.

Beri and Yao (2011a) have conducted a 2D CFD analysis in order to investigate the effect of cambered profile NACA2415 on the performance of a H-Darrieus-type VAWT. Their results reveal that cambered profiles improved the starting-up of the VAWT to the detriment of turbine performance compared to symmetrical profiles.

Hofemann et al. (2008) have studied experimentally the vortex structure with various tip-blade shapes and its evolution around a H-rotor blade using the PIV (Partical Image Velocimetry) technology. They have concluded that former tip-vortex shedding accelerate the newly shed wake. It should be noted that this effect is strongly associated to the circulation strength of the shed vortex and to the angle of attack.

Chen and Lian (2015) have numerically investigated the vortex blade interaction of H-Darrieus VAWT. They have focused on the evolution of the generated torque against various solidities. They have demonstrated that when the solidity increases, the peak torque decreases and its corresponding azimuthal angle shifted toward increasing values at low TSR. The effect of airfoil profile thicknesses is also studied, and they have found that thinner airfoils perform better than thicker ones at high TSR.

Lee and Lim (2015) have interested to overall parameters design that might affect the performance of VAWT. such as rotor diameter, chord length, pitch angle, etc. A 3D CFD analysis is carried out. In fact, the rotor diameter, the chord length, and the pitch angle are investigated. Their results showed that a high-solidity turbine performs better at low TSR. However, low-solidity turbine performs better at high TSR. In addition, the authors have investigated the effect of blade’s helical angle, and they have found that the power performance decreases as the helical angle increases.

Castelli et al. (2012) have conducted a sensitivity study based on variation of the number of blades in order to reduce the torque fluctuation during blades rotation.

Castelli et al. (2015) have demonstrated that increasing the helical blade angle penalizes the generated turbine performance.

Gosselin et al. (2016) have carried out a parametric analysis in which the number of blades and the aspect ratio are investigated. It showed that increasing the number of blades could smooth the power performance fluctuation and has no effect since the turbine solidity is kept constant. They have also investigated the effect of various endplates on the blade pressure distribution. They have concluded that the presence of endplates helps to uniformize its distribution and improve the VAWT efficiency.

Howell et al. (2010) have demonstrated, in their work, the close dependency of the VAWT performance to the blade surface roughness as well as to a Reynolds number threshold. Also, they have shown that the solidity has an influence on the turbine performance over particular range of TSR.

Danao et al. (2014) have studied using CFD approach the effect of periodic inlet fluctuation wind conditions on the flow fields around a H-Darrieus VAWT. In particular, the flow separation and re-attachment are more emphasized. The results showed that for a given mean TSR and fluctuation amplitude, the performance of the VAWT is slightly enhanced. However, for a mean TSR lower than the steady peak performance TSR, in steady inflow wind condition, it causes a deep stall and vortex shedding. Moreover, in the case of large fluctuation in wind speed, the turbine works in dominated drag condition.

Beri and Yao (2011b) carried out a 2D unsteady flow analysis to investigate the effect of cambered airfoil profiles on VAWT performance. It improved the benefit effect of cambered blades on the self-starting-up of the VAWT. However, the cambered blade decreases the turbine performance.

Chen and Lian (2015) have studied through 2D CFD analysis the influence of solidity on the turbine performance. They found that the blades’ vortex interactions largely depend on solidity and TSR. Their results showed that when the solidity increases the torque decreases while the azimuthal angle increases with the solidity. Furthermore, the azimuthal angle moved less at high TSR than at low TSR.

Yang et al. (2017) have investigated the influence of tip vortex on wind turbine wake through experimental and numerical approaches. They have noted that the generated vortex by support structure increases the turbulence intensity. They have studied the effect of tip vortex on the downwind region of VAWT in different spanwise positions. They have concluded that the tip vortex has a longer dissipation distance and the low-velocity region appears at the mid-area of the rotor. The maximum of torque coefficient is produced at the upstream region.

Li et al. (2016a) have been interested in the flow circulation amount and power performance acting on a two straight-bladed VAWT. A 3D CFD calculation and wind tunnel experiments based on laser Doppler velocimeter (LDV) measurement are used. They have found that the maximum induced velocity and circulations are noted at the mid-span blade and are reduced along with spanwise position. It has been rather illustrated that mean freestream wind velocity shows a large value and fluctuation at the blade tip position.

Li et al. (2016b) have studied the characteristics of flow field through 2D wind velocity measurements. For that, the authors have used an LDV system at the center of straight-bladed VAWT. They have also experimentally investigated the aerodynamic loading characteristics using multiport pressure devices. They have found that a reduced wind velocity area appeared in the internal turbine region toward the downstream region. The low wind velocity region showed an expansion trend when the TSR increased.

Several advancements have been made in the investigation on the flow field and vortices generation for VAWTs as previously mentioned. However, most of the work has been conducted over 2D CFD model because of the complexity of the flow around VAWTs and the lack of computing power machines and software technology.

Few studies have been conducted over 3D CFD. In this work, we have implemented a 3D CFD model. A thorough investigation is dedicated to explaining the physics of field flow and the vortex generation around a cambered (NACA4312) bladed turbine, in particular the influence of generated-separated vortex on the torque output at a range of TSR. Finally, the originality of this study is the establishment of a correlation between vortex generation and torque.

Problem setup

The geometrical model of the VAWT is depicted in Figure 1. It consists of two sub-domains. A stationary cuboids region including inner rotate cylindrical region which contains three cambered-blade profiles NACA4312 as well as the shaft. The support arms of the rotor blades are neglected. The dimensions of the model are selected from Qamar and Janajreh (2017a) and are given in Table 1.

Figure 1.

Computational domain and boundary conditions of VAWT.

Table 1.

Geometrical parameters for CFD simulation.

Parameter	Chord	Blade span	Rotor radius	Inlet velocity	Walls conditions	No. of blade	Rotor solidity	Outlet pressure
Value (m)	0.1665	1	1.110	10	No slip	3	0.45	Zero Gauge pressure

Numerical setting

The flow around the VAWT is governed by incompressible viscous unsteady Reynolds-averaged Navier–Stokes (URANS) equations which generally reflect the conservative of mass (continuity) and momentum (1) and (2). They are solved using a couple pressure-velocity scheme and second-order spatial and temporal discretization schemes. These numerical settings are selected following the work of Rezaeiha et al. (2017). A symmetry boundary condition is taken on the wall sides of the domain. An inlet velocity U_∞ = 10 m s and a zero Gauge pressure are imposed at the inlet and outlet conditions, respectively. An interface condition is selected between the rotating rotor and the stationary domain.

The initial conditions are based on a steady single reference frame motion (SRF). The azimuth increment angle for the unsteady simulations of the turbine is taken as 0.5 which corresponds to a time step increment size of 0.0003 s. The turbine operating at a large range of TSR from 0.5 to 5 allows a flow with a chord-based Reynolds ranging from Re = 5.7 × 10⁴ to Re = 5.7 × 10⁵.

Continuity equation (incompressible flow)

\frac{\partial \bar{u_{i}}}{\partial x_{i}} = 0

(1)

Momentum equation

\frac{\partial \bar{u_{i}}}{\partial t} + \bar{u_{j}} \frac{\partial \bar{u_{i}}}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial \bar{P}}{\partial x_{i}} + ν \frac{\partial^{2} \bar{u_{i}}}{\partial x_{j}^{2}} - \bar{u_{j}^{'} \frac{\partial u_{i}^{'}}{\partial x_{j}}} + g_{i}

(2)

where $u_{i}$ and $\bar{u_{i}^{'}}$ are the mean and fluctuating velocity components in x_i-direction, respectively. $\bar{P}$ is the mean pressure. $ρ$ and $ν$ is the density and the viscosity of the air, respectively. However, using the Reynolds decomposition, there are new unknowns that were introduced such as the termed Reynolds stresses $ρ \bar{u_{i}^{'} u_{j}^{'}}$ . The Reynolds stress terms should be modeled in order to mathematically close the problem. The term $ρ g_{i}$ represents gravitational forces. We have adopted the shear stress transport (SST) k-ω model, which is more accurate and reliable for a wider class of flows (e.g. adverse pressure gradient flows, airfoils). Two transport equations are associated with the standard SST k-ω model as:

Turbulence kinetic energy equation

\frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{i}} (ρ k u_{i}) = \frac{\partial}{\partial x_{j}} (Γ_{k} \frac{\partial k}{\partial x_{j}}) + G_{k} - Y_{k} + S_{k}

(3)

Specific dissipation rate equation

\frac{\partial}{\partial t} (ρ ω) + \frac{\partial}{\partial x_{i}} (ρ ω u_{i}) = \frac{\partial}{\partial x_{j}} (Γ_{ω} \frac{\partial ω}{\partial x_{j}}) + G_{ω} - Y_{ω} + S_{ω}

(4)

In these equations, G_k represents the generation of turbulence kinetic energy due to mean velocity gradients. G_ω represents the generation of ω. $Γ_{k}$ And $Γ_{ω}$ represent the effective diffusivity of k and ω, respectively. $Y_{ω}$ and $S_{ω}$ represent the dissipation of k and ω due to turbulence.

Grid strategy

As shown in Figure 2, the VAWT is composed of a rotating rotor with a diameter of 1.5 times the turbine diameter and a static domain with dimensions of (20D length × 3D width × 3D height). To capture the transient flow around the rotating blades, a sliding mesh is adopted to model the interface between the two sub-domains.

Figure 2.

Grid independency of torque coefficient solution.

The aspect ratio is defined as

A R = \frac{D i a m e t e r \times R o t o r D e p t h}{D o m a i n W i d t h \times D o m a i n H e i g h t} = \frac{H}{9 D} = 5 %

(5)

A blockage ratio with 5% ensures that the flow acceleration due to the symmetry condition on the side boundaries has insignificant impact on the calculated aerodynamic performance (Rezaeiha et al., 2017).

The computational grid for the VAWT consists of unstructured grid and includes a boundary layer grid near the walls. The first cell height adopted for this simulation is such that the maximum Y⁺ value is equal to 1 (Y⁺ = 1). So, the wall distance is y = 0.027 mm as calculated by

y = \frac{y^{+} μ}{ρ u_{*}}

(6)

with $u_{*}$ is the friction velocity and µ the dynamic viscosity.

Before starting, in general, any CFD analysis, it is strongly recommended to study the independency of the numerical results to the grid cell number. We have considered three different grid cells, each grid is almost refined of twice the former one as reported in Table 2.

Table 2.

Grid independence test for the unsteady simulation.

Grid	Number of cells
Grid 1	4,278,995
Grid 2	9,777,636
Grid 3	16,754,217

From Figure 2, it is clear that the torque coefficient result of the VAWT became invariable against the cells number from Grid 2. Thus, we adopted mesh 2 to conduct the computational analysis of H-Darrieus VAWT.

The number of cells in each grid part of the VAWT is presented in Table 3.

Table 3.

Grid information of the VAWT.

	Cells	Type
Domain	1,341,268
Rotor	8,636,368
All domain	99,777,636

Data processing method

The simulation was carried out considering a range of TSR from λ = 1.5 to λ = 5. It is well known that the optimum value for cambered airfoil is situated between these chosen values (Qamar and Janajreh, 2017b). The TSR is calculated as follows

λ = \frac{R \cdot ω}{U_{\infty}}

(7)

where $ω$ is the angular velocity, R is the rotor radius, and U_∞ is the incoming wind speed. The results were computed to determine the coefficient of torque and performance, C_T and C_P, respectively, which are given in equations (8) and (9)

C_{T} = \frac{T}{\frac{1}{2} \cdot ρ \cdot U_{\infty}^{2} \cdot R [2 R \cdot H]}

(8)

C_{P} = \frac{T \cdot ω}{\frac{1}{2} \cdot ρ \cdot U_{\infty}^{3} \cdot [2 R \cdot H]}

(9)

The swept rotor area is (2R·H) where H is the unit depth. The solution was allowed to run and reach to consistent/stable state, and the average torque (T) was evaluated over two consistent revolutions of the turbine.

Results and discussion

Moment results

Figure 3 shows the variations of the instantaneous torque coefficient versus azimuth angle of each blade as well as the resultant torque of the three rotor’s blades at TSR = 2.5. It is clearly shown, from the resultant torque coefficient, that the turbine experience, during full rotation, a positive torque with a pitch angle equal to zero. This is known to be very beneficial for self-starting turbine. This result was in line with those obtained by Qamar and Janajreh (2017a).

Figure 3.

Instantaneous torque coefficient of each blade and rotor blades.

The azimuth angle peaks, experienced by each blade, are presented in Table 4. The maximum torque values are attained when the angle of attack reached a value close to the dynamic stall angle (Castelli et al., 2011; Ferreira, 2009). We noted that the two remaining blades experience the same torque coefficients as the first one expect are periodically phase shifted of 120°.

Table 4.

Azimuth angle of maximum torque.

	Blade position	Azimuth angle peak	Region
Blade 1	120	345	Downwind-windward
Blade 2	240	225	Downwind-leeward
Blade 3	0	105	Upwind

Blade 3 is initially localized at azimuth angle θ = 0°, and the torque coefficient peak is situated at azimuthal angle θ = 105° at the upstream region. The maximum torque value is obtained during the upwind revolution of the turbine and for an azimuthal position where blades are experiencing a very high relative angles of attack (Figure 4).

Figure 4.

Instantaneous torque variation of on blade (blade 3).

It is also noticed from Figures 3 and 4 that cambered profile performed positive torque coefficient with lower values in the downwind region compared to upstream. Cambered profiles provide more advantages than the symmetrical profile, in particular at zero pitch angle. This is in agreement with the work of Qamar and Janajreh (2017a).

The variation in the torque coefficient (C_m) as the blade moves is certainly related to the physics of the flow field around blades and to the strong variation in the angle of attack particularly at low TSR.

A good correlation is observed between the evolution of generated blades vortex and torque coefficient. In fact, Figure 5 depicts the variation in the instantaneous torque coefficient against TSR. We could see from this figure the effect of TSR at both upwind and downwind regions on the torque. At low TSR (λ = 1.5), the turbine performs at too narrow upwind zone and a positive torque output. However, at the downwind region, the turbine experiences a greater torque compared to higher TSR. Otherwise, at high TSR (λ = 5), the turbine produces a negative torque at downwind zone, and at the upwind zone, torque output is much smaller than others due to lower TSR.

Figure 5.

Variation of the instantaneous torque coefficient versus TSR.

The current zero pitched camber-bladed CFD model was validated with results of the 2D CFD model carried out by Qamar and Janajreh (2017c). As seen in Figure 6, the current model overestimates the numerical 2D CFD baseline. As we know, a 2D CFD, in general, overestimates the performance of the turbine due to the failure to take into account the tip losses and the 3D effect (Abdalrahman et al., 2017; Durrani et al., 2011). At high TSR, the power curve trend is compared well with the two CFD models. The optimum power coefficient is obtained at λ = 2.9. It is clear that the turbine experiences a better performance at large range of moderate TSR.

Figure 6.

Power coefficient versus TSR.

To study the generated-separated vortex and to better understand the flow fields around blades during their rotation, we have considered three clip-planes placed along spanwise direction at three z-positions: z = 0 (mid-blade), z = –0.5 (lower end), and z = 0.5 m (top end). Four vortices Q-criterion intensity have been used (5, 20, 50, and 100) and five azimuthal positions: 10°, 35°, 60°, 85°, and 110° as depicted in Figure 7.

Figure 7.

Clip planes spanwise positions.

Figure 8(a) and (b) shows that blade 3 interacts with a large attached vortex to blade 1 at azimuth angle range from 10° to 35°. Both the tip and the mid-blades are characterized with low intensity (M5-20, T5-20). Thus, when blade 3 moves toward the azimuth angle 28°, it experiences a little negative torque as depicted in Figure 9. The lowest torque coefficient value seen at θ = 28° is reached when blade 3 yields a stretched-separated vortex with high-intensity level (TS50 and MS50) at both middle- and top-end blades.

Figure 8.

Vorticity contour plots in clip plane: (a) mid-plane iso-surfaces and (b) tip-plane iso-surfaces.

Figure 9.

Torque output decreasing phase and correlation with generated-separated vortex.

As soon as blade 3 leaves the blade 1 wake interaction (low intensity level: M5 and T5), it starts creating a stretched-attached vortex with moderate and high intensity at both mid-blade and tip blade. Accordingly, the torque coefficient started to increase until reaching the torque coefficient peak at azimuth angle 104°. It is clear from Figure 10 that the high torque is due to the generated vortex with different intensity levels. At the middle plane, a stretched vortex is generated and remains attached to blade 3 for a long duration. However, at the tip blade, we observe a large vortex and not stretched with high intensity.

Figure 10.

Torque output increasing phase and correlation with generated-separated vortex.

From the torque coefficient peak, as we can see from Figure 11, a sequence of vortex separation is observed at the mid-blade (MS5-20), beginning from azimuth angle 110°, 130°, and 155°, respectively. The separated vortex has a moderate intensity level (MS5-20) but extended along the blade span, which could explain the torque coefficient drop.

Figure 11.

Torque output decreasing phase and correlation with generated-separated vortex.

At the azimuth angle ranging from 175° to 195°, we noted that the torque coefficient became negative. From Figure 12, we can see that blade 3 interacts with a dense separated vortex with a moderate intensity at both mid-blade and top blade. It can also be noted that the lowest value of torque coefficient is related to the separated tip vortex with high intensity TS50 and TS100.

Figure 12.

Lowest generated torque output at azimuthal angle 195°.

The torque coefficient return to increase from the azimuth angle 195° (Figure 13), and these could be attributed to the stretched vortex generated at tip blade with high intensity. Also, we can see that the blade leaves vortex interaction region at the mid-blade.

Figure 13.

Torque output increasing phase and correlation with generated-separated vortex.

However, the torque coefficient slightly decreases from 250° and is mainly due to the dragged wake being attached to blade 3 at mid-blade (M5). It is clear from Figure 11 that the rotor turbine performs a less positive torque output at the downwind than the upwind region. It can be explained from Figure 6 that the mid-blade has a short attached vortex at downwind region.

Figure 14 shows the 2D velocity contour plot of the turbine where we can see the asymmetric wake of the turbine. It is clear that the blades wake is moved toward the rotor inside during the rotor revolution. The wake behind the rotor is characterized by a low velocity. A large wake region is dragged by the shaft rotor.

Figure 14.

2D Velocity contour plot at mid-blade.

This figure ensures us that the chosen dimensions of the CFD model do not influence the flows around the rotor turbine. The blockage of the turbine is not significant on the flow fluid.

Figure 15 depicts the iso-surface wake in 3D. We can clearly see that the camber-bladed turbine generates a non-symmetric wake which could be beneficial in turbine farms. A separation node is observed behind the rotor from which a detached wake can be observed far away the rotor turbine.

Figure 15.

3D velocity iso-surface of the rotor wake.

Shifted tip vortices of camber-bladed profile

From Figure 16, we can observe that a large positive z-velocity iso-surfaces is generated by the top tip-blade at the upwind region. However, the generated negative z-velocity iso-surfaces is handled by the low tip-blade. It should be noted that the size of vortex generated at the downwind region either by the top tip or low tip is much smaller than the upwind generated ones. This explains the correlation between the size of the tip vortex and the produced torque.

Figure 16.

Z-velocity iso-surface at top and lower tip blade.

When the size of tip vortex is large, the rotor blades yielded a high positive torque. Another phenomenon that draws our attention is the part that might cause the creation of the positive z-velocity vortex and switched when blade moves from upwind to downwind zone. That is, at the upwind, the vortex is generated by the suction side (extrados) and at the downwind the vortex is generated by the pressure side (intrados) of the tip blade. However, for negative z-velocity the vortex is generated by the pressure side (extrados) at upwind and by the suction side (intrados) at the downwind. This implies that for studying a VAWT with cambered-blade profile, we should study the whole turbine in 3D CFD.

Figure 17 illustrates the developpement of a large sheet wake with low velocity at the inboard side of the rotor. It can be observed that the blades penetrate and interact with the generated sheed wake, when they move towards downwind.

Figure 17.

Sheet velocity iso-surface blade and blade wakes.

The wake attached to mid-blade is created before the tip vortex. The large attached vortex is observed at azimuth angle range from 105° to 130° which proves our above discussion. A separated vortex is also shown after the mid-blade wake shedding. The wake size of blade 3 has a growing trend when it moves toward the angle of 130° which explains the maximum torque value. The attached wake to mid-blade has long duration than tip blade one. The tip vortex separation is performed in earlier stage. As seen from Figure 17, the torque drop explained earlier can be related to the tip vortex shedding and to the complex flow blades wake-interaction of following blades. We can note that the sheet iso-surface has a shedding node beyond the rotor turbine.

Conclusion

This work is based on numerical high-fidelity unsteady CFD analysis of H-Darrieus with straight camber-bladed profile using the URANS solver. A sliding mesh method is used to handle the rotation of the rotor blades. The SST k-ω turbulence model is used as the turbulence closure. Grid independency analysis is presented.

Due to the complex flow phenomenon around blades and flow shedding, we have proposed a fine grid and a boundary layer was taken into account close to the blade wall. Comparisons are made with available numerical data.

It is found that the power performance increases with the increase in TSR at low TSRs. At high TSRs, the power performance drops dramatically to become a resistive power. It demonstrated that vortex and blade interactions have a pronounced impact on the turbine performance.

The numerical results reveal, despite the zero pitched blade angle, the most interesting features which is the self-starting turbine improvement of camber-bladed VAWT at low TSR with high solidity compared to symmetrical blade profile. The turbine experiences a positive torque coefficient through blades’ rotation.

A correlation between the evolution of the produced torque coefficient and the generated-separated vortex is established based on qualitative comparison. It demonstrated that the shape and size of vortex heavily affect the torque production. The generated tip vortex is delayed relative to the mid-blade vortex. However, the tip vortex separation is performed in earlier stage. The present results state that studying camber-bladed profile requires to take the whole turbine model due to the non-symmetrical phenomenon between top-tip and low-tip blades. This is attributed to the switched phenomenon from upwind to downwind.

The main results of this work state that the vortex shedding and the blades-wake interaction decrease the torque production. Large and extended vortex caused a high torque generation. A switched tip-blade vortex generation zone (positive and negative z-vorticity) is observed between upwind and downwind regions and also between top and bottom of the rotor turbines. The wake attached to the mid-blade has long duration than the tip blade wake.

Footnotes

Declaration of conflicting interests

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

Funding

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

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Blocken

(2017) Effect of pitch angle on power performance and aerodynamics of a vertical axis wind turbine. Applied Energy 197: 132–150.

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Subramanian

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Sivanandan

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26.

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