**1. Introduction**

Vertical axis wind turbines (VAWTs) are typically characterized by lower wind energy-conversion efficiency than commonly used horizontal axis wind turbines (HAWTs). However, they are often favored in micro power generation due to their simple design, a possibility to locate a generator near the ground, and to accept the wind blowing from different directions [1,2]. They are quieter and safer than small-scale HAWTs and, thus, suitable for applications in urbanized areas [3–5].

A vertical axis wind turbine, referred to as the Savonius turbine, was invented by S.J. Savonius [6]. In the top view, it resembles the letter "S" with two typically semi-cylindrical blades, often slightly overlapping. Its primary advantage lies in simple and, thus, cheap and robust design [7,8]. Similar to other VAWTs, Savonius turbines are independent of the wind direction. However, contrary to Darrieus wind turbines, they are characterized by a high starting torque for selected rotor positions. They are classified as drag-driven turbines and operate at low rotational speeds, with tip speed ratios not exceeding 2, which makes them safer than HAWTs at strong winds [9]. They perform well at low wind speeds most often encountered close to the ground and they are characterized by a low level of noise emission. Thus, Savonius turbines are suitable for application in urbanized areas [3].

Unfortunately, the primary disadvantage of Savonius turbines is their low efficiency. Typically reported values of the power coefficient for designs with semi-cylindrical blades fall

within the range *Cp* = 0.15–0.20 [7,10,11]. Therefore, this kind of turbine in its basic configuration is not usually a reasonable alternative when compared to other types of wind turbine. Nonetheless, owing to their advantages, Savonius turbines were subject to numerous investigations aimed at increasing their efficiency. Many works were focused on the search for optimal dimensions of geometrical parameters of rotors. The influence of the number of blades, overlap ratio, aspect ratio, end plates and other factors was studied both with experimental and numerical methods. Results of those investigations were presented in numerous papers, which further were summarized in thorough reviews [7,12].

Many studies were focused on modifications of the blade shape or an application of additional elements to direct the air flow towards blades. The replacement of conventional semi-cylindrical blades by more sophisticated shapes allowed one to increase the Savonius turbine performance significantly, with maximal values of the power coefficient up to *Cp* = 0.25–0.30. A substantial part of the research concentrates on two-dimensional (2D) thin blade configurations, i.e.,: Bach, Benesh, elliptical and spline [11,13,14]. Airfoil shape blades were studied in [15,16]. Optimization methods were also applied in order to search for an optimal blade shape in [16–19], taking advantage of 2D simplifications in numerical simulations. Three-dimensional (3D) blade arrangements with twisted or helical blades were tested as well. In this case, it was possible to reduce static and dynamic torque variations for different angular positions of the rotor with respect to the incoming wind, however, no significant improvement was reported as far as the turbine performance is considered [12,14].

Different augmentation systems can be used to change the wind flow path around and in the Savonius rotor. Its power output was increased by 20% up to 50% if the turbine rotor was equipped with flat plate deflectors [18,20,21], v-shaped deflectors [22] or a combination of flat and circular deflectors [23], shielding the returning blade and reducing its negative moment. A similar effect was achieved if the wind was directed towards the advancing blade with a curtain-deflector system [24], self-adjusting conveyor-deflector curtains [15], a system of adjustable shielding plates for twin rotors [9] or even a rectangular guide-box tunnel surrounding the rotor [25]. A comprehensive summary of different augmentation systems with the power coefficient exceeding considerably *Cp* = 0.3 can be found in [11,26]. However, a disadvantage of such approaches consists in larger dimensions of the turbine, an increase in the complexity of its geometry and dependence on the wind direction.

An idea of the Savonius turbine with a variable geometry of blades is proposed in order to enlarge the projected area of the advancing blade (increase the positive moment) and, at the same time, to diminish the area of the returning blade (decrease the negative moment). Elaborate two-dimensional (2D) computational fluid dynamics (CFD) simulations were performed to assess the output power gain for different arrangements of blade deformations.

The deformations of blades in this case were determined with a structural solver and then the geometry was transferred to a fluid solver for the aerodynamic analysis. This approach is referred to as the fluid-structure interaction (FSI). The FSI is a very wide concept of solvers coupling in order to obtain high-fidelity numerical solutions. Solvers can be one-way coupled once the data, i.e., loads from the fluid acting on the wall, are transferred to the structural solver where stress and strains are determined [27,28]. Another example of one-way coupling takes place where the deformation of the structure influences the flow structure and loads determined in the fluid solver. The most advanced method, called the two-way FSI, requires co-simulation between computational fluid dynamics and structural mechanics. Both CFD and structural solvers are coupled and synchronized to attain converged solutions. The two-way FSI is applied to highly dynamical systems as in the case of the aeroelastic response analysis [29] or whenever the structure is flabby [30]. The FSI strategy is typically used in horizontal axis wind turbines (HAWTs). It is also used in the analysis of vertical axis wind turbines (VAWTs), e.g., in the case of an H-rotor [31,32], but no reference reporting an analysis of the Savonius-based turbine is known to the authors. It is due to much lower blade loads than in the case of lift-driven HAWTs or VAWTs.

Idea of the Savonius Rotor with Deformable Blades

An idea of the novel turbine with a variable geometry of blades is shown in Figure 1 for subsequent phases of the rotor revolution [33]. Shapes of the blades made of a flexible material change constantly during its rotation. This is achieved by guiding the outer edges of the blades (tips marked as dots in the color of the blades) along the guide ring (red) placed eccentrically with respect to the rotor shaft. Rods attached to the outer edges of the blades can move linearly with respect to sliders, which are fixed to the shaft. The rode–slider mechanisms, marked by a red dashed line, are applied at the top and bottom of the turbine and they transfer the torque generated by the blades to the shaft. The inner edges of the blades are also attached to the rotor shaft.

**Figure 1.** Principle of the turbine operation.

The phases 90◦ and 270◦ presented in Figure 1 illustrate the maximal deformation of the blades. If the extended, advancing blade is located in such a way that its concave side is exposed to the wind and, simultaneously, the wind blows at the convex side of the contracted, returning blade, one can expect that the turbine will be driven with the wind energy more efficiently than in the case of both blades having the same, fixed shape. This implies that the turbine needs to be properly located with respect to the incoming wind. Therefore, the guide ring needs to change its position by rotation around the axis of the base of the turbine, which is coaxial with the rotor shaft axis, marked as a black X in Figure 1. The guide ring mechanism has to be equipped with an aerodynamic or mechanical system in order to adjust its position with respect to the wind direction. The turbine generator is fixed to the frame and a gear or a transmission has to be applied to transfer the mechanical energy from the turbine blades.

The additional mechanisms make the design of the proposed turbine more complex than the original Savonius. However, they consume a part of the energy generated by the turbine. Thus, all elements need to be carefully designed to be resistant and efficient. The present study focuses on the aerodynamic performance of a novel, efficient design but neither mechanical losses due to friction nor energy losses due to blade deformations are considered. Thus, one must bear in mind that the overall performance of the turbine will depend on the mechanical design and that a portion of energy will be consumed by the system itself.
