1. Introduction
In the last few years, the world has seen a growing interest in environmental conservation and the engagement of socio-economic development plans based on a global vision of sustainable development. In order to reconcile the energy needs of countries with the requirements of the preservation of the environment, the international energy strategy aims to increase the share of renewable energies. According to the International Renewable Energy Agency (IRENA) [
1], “the objective set for the year 2050 is to reach 17% of the global installed offshore wind capacity (6044 GW)”.
To achieve this capacity, it is necessary to look for technological solutions for more powerful and efficient wind turbines [
2,
3,
4]. The offshore wind turbine is considered as one of many solutions, defined as a wind turbine exploiting the energy generated by the wind at sea [
5]. Consequently, the use of this type of wind turbine has significant advantages over onshore wind turbines. Indeed, at sea, the winds are particularly strong and stable, which means more power generated. Moreover, the installation of offshore wind turbines on large water bodies significantly reduces visual and noise pollution for residents [
6]. There are two types of offshore wind turbines: VAWTs and HAWTs. The vast majority of installed offshore wind power solutions are HAWTs, because of their maximum power coefficient value, approximately up to 50% of the Betz limit (59.3%) [
7]. In comparison, the VAWT procures 40%. There are also other theoretical formulas that announce a maximum power coefficient value of about 61.7% or 64% for Darrieus VAWTs. This result is due to the fact that the blades cross the airflow twice, first in the upstream phase of the rotation, and second in the downstream phase [
5].
VAWTs can be classified into two main types based on the wind velocity, efficiency desired, and utilization. The first type is a Savonius wind turbine (drag-driven family) that consists of two or more simple semicircular blades. The design of the Savonius rotor makes them unsuitable for large-scale offshore application, but it can be attractive for small-scale application as domestic wind turbines due to good starting characteristics, easy installation, and low cost [
8,
9]. The second type is Darrieus VAWTs (lift-driven family) that demonstrate good efficiency compared to Savonius wind turbines, because of their simple blade design and lower center of gravity, making them more attractive for offshore applications. The first patent for a modern Darrieus VAWT was deposited by the French inventor Georges Jean Marie Darrieus first in France in 1925, then in the United States in 1931. The patent covered two major configurations: curved non-straight blades (non-SB) and straight blades (SB), and this is illustrated in
Figure 1. There are several variations of non-SB, such as cantilevered and guy-wired versions [
10,
11]. These types of non-SB VAWTs minimize the bending moments in the blades and are more prone to the dynamic stall than SB VAWTs as demonstrated by Scheurich [
12]. In addition, SB has several variations: H-rotor, helical H-rotor, tilted H-rotor, articulating H-rotor. SB-VAWT rests better than non-SB-VAWT due to self-regulation, simple rotor geometry, absence of guy wire use, cost, etc.
Offshore wind turbine goes to deep water. According to a study conducted by the National Renewable Energy Laboratory (NREL) [
13], a floating foundation (tensioned-leg platform, spar floater, semi-submersible platform) is more cost-effective than fixed foundations (monopile, tripod, jacket frames…) from a water depth of about 60–100 m. That is why current research on offshore wind turbines is focused on F-VAWTs that have several advantages compared to F-HAWTs, such as: simple mechanism, low center of gravity, no yaw control, withstand high turbulence wind, easier maintenance, cost effectiveness, etc. [
14,
15]. These benefits have motivated several countries such as the USA, France, Sweden, and Japan to create F-VAWT design projects. Hiromichi et al. [
16] developed a new concept of F-VAWT, called FAWT. This concept used a new mechanism named “bearing swivel rollers” to support the turbine axis and help transform the torque from the turbine to the electric generator. Nakamura et al. [
17] has also developed the Savonius keel wind turbine Darrieus concept (SKWID), an improvement of the FAWT concept. In fact, it is a combination between a floating wind turbine and a Savonius water turbine. The aim of the Savonius water turbine is to provide a starting torque to overcome the inertia of the wind turbine, because the VAWT weakness is that it requires some external assistance to initiate the rotation, but Dominy et al. [
18] and Hill et al. [
19] indicated that self-starting is possible by using symmetrical airfoils under steady wind conditions for a two-blade H-rotor with fixed geometry.
The French company Nenuphar proposed two wind turbines. The first one is VertiWind [
20], which has a very high availability rate. The cost of its foundation can be reduced by optimizing the float architecture. The second one is Twinfloat [
21], which is built based on two turbines of 2.5 MW, working in a counter-rotating mode, and creating a tunnel effect between them in order to increase electricity production. Other design projects are described in [
22,
23,
24]. The aim of this paper is to propose a novel design of Darrieus-type straight-bladed F-VAWT with three-stage rotors. A DMST model was adopted in the aerodynamic modeling in order to analyze several critical parameters of VAWT, taking into consideration the turbine solidity, the number of blades, the rotor radius, and the aspect ratio. The remainder of the paper is organized as follows: the proposed design of F-VAWT with three-stage rotors is discussed in
Section 2.
Section 3 shows general mathematical expressions for the aerodynamic analysis of straight-bladed VAWT.
Section 4 is devoted to the DMST model, while
Section 5 presents the results and discussion. Lastly,
Section 6 concludes the paper.
2. Floating Darrieus-Type Wind Turbine with Three-Stage Rotors
In this section, a new design of Darrieus F-VAWT with three-stage rotors is shown in
Figure 2. The rotors will have a straight-blade configuration, as it has been shown to demonstrate a higher aerodynamic performance and be self-regulating in all wind velocities in comparison to other possible VAWT configurations [
25]. The concept allows having a higher height in order to benefit from the stronger winds. The three rotors of the wind turbine rotate independently around the fixed shaft, unlike conventional VAWTs where the rotor and shaft rotate at the same time, causing the increase of the inertia and the torque applied to the shaft [
26], and create problems in the self-starting of the turbine. In addition, by reducing the number of bearings, the axial and radial forces exerted on the shaft are minimized, as well as the related manufacturing cost, compared to the rotating shaft, due to the simple geometric specifications and because our solution does not need much tolerance interval precision [
27]. In this design, three permanent-magnet synchronous motors (PMSMs) can be used with different powers depending on the rotor radius, wind velocity, and the height where each rotor is located. The float used is a semi-submersible tri-float type. We are also considering the introduction of connection beams to support the VAWT and increase its stability. Moreover, by using aerodynamic airfoils for turbine supporting arms (or struts), we can avoid the problem of decreasing the aerodynamic efficiency of the turbine. Ahmadi-Baloutaki et al. [
28] demonstrated that it is necessary to adopt an aerodynamic airfoil for struts, and when two struts per blade are used at intermediate location of 21% and 79% along the blade length, the bending stress distribution along the blade is reduced.
Figure 3 illustrates one rotor stage of F-VAWT. A mechanism consisting of a pivot (screw-nut) is introduced in the middle of the two blades, which is automatically actuated by a small electric motor and a lever in the shape of a parallelogram. The latter is attached to the end of both blades. When turning the screw, the lever moves with the help of the two sliding links and exerts a force on the two blades that allows us to increase the diameter. On the other hand, when the screw rotates in the opposite direction, the diameter will be reduced. This new mechanism aims to change the diameter of the wind turbine automatically according to the wind speed, and it solves the problem of starting a large VAWT rotor.
4. Double Multiple Stream Tube Model
In the literature [
25], many aerodynamic models for VAWT have been proposed, such as double multiple stream tube (DMST), multiple stream tube (MST), vortex, cascade, and panel. Each of them has its advantages and disadvantages, and
Table 1 gives a comparison of the aerodynamic models according to important criteria such as complexity and computational time. Therefore, it is necessary to find a compromise between the validity of the results, the problem complexity, and the computational effort, depending on the objectives fixed. The model chosen for this work is the DMST developed by Paraschivoiu [
32] in 1981. This model combined the MST model with the double actuator disk theory (see
Figure 6a) to predict the performance of VAWT. The advantages of this model can be seen through the fact that it is relatively simple to implement and gives better correlation between calculated and experimental results [
25]. However, the major drawback of this model is to give over prediction of power for a high solidity turbine, and there appears to be a convergence problem for the same type of turbine, especially in the downstream side and at the higher tip speed ratio [
29].
As shown in
Figure 6b, the rotor’s area is divided into a set of adjacent parallel stream tubes. The calculation is performed separately for the upwind and downwind half cycles, and the blade element theories and the momentum conservation are used for calculating the aerodynamic forces acting on the blades, which then makes it possible to calculate the torque and the power generated.
For the upstream half-cycle
For the downwind half-cycle
where, at the downwind side, the induction factor
and the induced velocity
.
Once the new relative wind speed and angle of attack are determined to use the new induction factor, the torque coefficient, thrust coefficient, and power coefficient could be obtained. Equating the forces given by momentum equations to those defined by blade element theory:
where the upwind function
is given by:
Thus, the power coefficient for the upwind half of the turbine is obtained by:
where A = 2hR is the turbine swept area
The downwind part of the rotor is evaluated in the same manner, and finally, by the summation of the power coefficients of the two half-cycles, the total power coefficient of the rotor can be found.
4.1. QBlade Simulation Tool
QBlade is used as an open source framework for the design and aerodynamic simulations of the wind turbines. In a recent paper by Nachtane et al. [
33] QBlade solver was used to predict the hydrodynamic performance of a new hydrofoil named NTSXX20. QBlade utilizes the blade element momentum (BEM) method for the simulation of HAWTs, and a double multiple stream tube (DMST) model for the VAWTs performance. The XFOIL code is integrated seamlessly into QBlade based on the viscous-inviscid coupled panel method to generate 2D airfoil coordinates for blade design, airfoil lift, drag coefficients, and 360° polar extrapolation for turbine simulations [
34].
Figure 7 shows the different modules and types of analysis (shown inside the dotted square) that can be performed by Qblade for aerodynamic simulation.
4.2. QBlade Validation
In order to show the validity of this software, the Qblade was compared with the experimental and computational results of Raciti Castelli et al. [
35] with various TSRs. The comparison of the power coefficient versus TSR results from the QBlade with experimental and numerical results are shown in
Figure 8. It can be observed that the general trend of the experimental plot was captured by the Qblade where the quantitative differences (presented in
Table 2) are found to be the largest for the highest TSR equal to 2.21. The observed deviations may be explained by the uncertainties associated with the experimental data, e.g. boundary conditions, the blade surface roughness, the wake-blade interaction. Also, the effect of blade-spoke connection on the
of the turbine is known to be more significant in higher TSRs [
36]. As well as Qblade overestimates the
at high TSRs due to the dynamic stall effects are not considered, which is difficult to predict because the angle of attack
change rapidly and the turbulence generated. Another source of error is from the extrapolation of the initial data obtained from XFOIL as the airfoil characteristics are required for 360°. Regarding the extrapolation, Montgomerie [
37,
38] and Viterna [
39] are the most widely used methods. The Montgomery method is founded on the assumption as a thin plate, whereas the Viterna method is formulated on the basis of the potential flow theory. Extrapolated values provide a good estimate if the initial limited data are obtained from experiments. However, in this case, the initial data is over predicted by Xfoil which can further extend the high lift/drag ratio error for other angles of attack. Furthermore, the Montgomery and Viterna methods are intended for static airfoils, and do not consider the unsteady effects. The airfoil characteristics calculated from the Xfoil assume that the flow is laminar, but in fact, VAWT airfoils face a turbulent and unstable incoming flow, and it becomes worse in the downstream side, where the blade operates entirely in wake for a high solidity turbine [
40].
Table 2 presents percent differences between numerical and experimental results of the power coefficient. The relative deviation between the numerical and experimental results is given by the equation:
4.3. Input Parameters Used for the Aerodynamic Simulation
The most common profiles used for commercial Darrieus VAWTs are the symmetrical NACA profiles [
10]. The blade airfoil will consist of a symmetrical four-digit NACA 0015 which has a maximum thickness of t/c = 15% and a 0% maximum camber. A study was conducted at the University of Windsor in Canada analyzing the performance of several airfoils for Darrieus VAWT [
41]. Of all the airfoils tested, the NACA0015 performed the best performance.
Figure 9a gives a comparison between the four aerodynamic profiles in terms of coordinates. To assess the aerodynamic efficiency of each possible VAWT design, the power coefficient Equation (16) will be used.
Table 3 outlines the input parameters used for the performance curves for different aerodynamic profiles, and
Table 4 gives the physical proprieties of air used for aerodynamic simulation. As shown in
Figure 9b, aerodynamic profile NACA 0015 presents the best aerodynamic efficiency compared to other aerodynamic profiles.
Figure 10 depicts the lift and drag coefficients of a NACA0015 airfoil at R
e = 10
6.
In the following, we have used this profile for the parametric study of the VAWT rotor.
The objective of this study is to carry out a parametric study by the DMST method, in order to show the interest of a stepped rotor with variable radius, and to determine the aerodynamic behavior of the rotor during the design phase, which then makes it possible to perform a structural analysis of the design.
6. Conclusions
This paper presents a new design of F-VAWT with three-stage rotors. Three electrical generators can be used with different powers depending on the rotor radius, wind speed, and the height where each rotor is located. In fact, this configuration of three stage rotors helps to optimize power and solve the problem of turbine self-starting. The result of the performance curve of Qblade software was validated by comparison with experimental and numerical results, and it shows a good prediction of the rotor performance. Moreover, the aerodynamic profile NACA 0015 is employed for aerodynamic simulations, because this profile gives the best aerodynamic efficiency compared to other aerodynamic profiles, as well as being the most common profiles used for commercial Darrieus VAWTs. An investigation of several influential geometric parameters of VAWT has been taken into account, including solidity, number of blades, rotor radius, aspect ratio, wind velocity, and rotor height. Thus, numerical results obtained by the aerodynamic simulations identify a low solidity turbine (σ = 0.3), offering the best aerodynamic performance. A two-blade design is recommended to minimize the rotor weight, reduce the problem of starting the turbine, and lower the cost. In addition, we can integrate a mechanism that allows varying the rotor radius according to the wind speed available by using a two-bladed design. These findings also indicate the interest of a variable AR and wind velocity, as when these parameters increased, the aerodynamic performance will be improved as well.