Máquinas eólicas de eje vertical
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Parametros del rotor Savonius. Introducción.

1 Introduction.

When a wind site is chosen to install wind machines in order to produce electricity, it is expected to extract the maximum possible energy from the wind. The choice of an "aerogenerator" should be done via this sole criterion.
Wind turbine are generally designed for a nominal working point, i.e. for a given velocity of the wind which is obviously linked to an attended delivered power. Consequently, the notion of the produced energy, for example for a whole year, is often forgiven; the notion of installed power, or that of installed power per square-meter of cross wind, are generally preferred. This idea incites the operators to prefer wind machines of higher efficiency for the equipment of wind sites.

The choice of a wind machine is obviously based on its energetic performances. To simplify our presentation, we have drawn the working curves of main conventional wind turbines (figure 1). These curves, extracted from the monograph of Wilson and Lissaman [1], give the power coefficient Cp , ratio of the aerodynamic power of the turbine to the power of the incident wind, as a function the speed ratio l. l is also called the velocity coefficient and is equal to the ration of the tip peripheral speed to the wind velocity.

The power coefficient is directly linked to the global efficiency of a wind machine.
The curves of figure 1 show that the fast running horizontal axis wind machines (two- or three-bladed airscrew) have incontestably the best efficiencies. Consequentely, theses machines are systematically chosen for the equipment of wind sites. On an other hand, the Savonius rotor [2], which is a slow running vertical axis wind machine (l » 1.0)
has a rather poor efficiency : Cp » 0.2.

The studies dealing with the performances of Savonius rotors are numerous and various. The reader can refer to Le Gourrières handbook [9] for a clear and a complete description of the expected performances of such a rotor.

Some of these studies present global experimental results issued from measurements in situ. For different values ofthe wind velocity, the power coefficient is given. Neverthless, it is difficult to compare these results because of the differences in the geometry and dimensions of the rotors, in the experimental conditions or moreover in the Reynolds numbers.

Some studies have been carried out in wind tunnels [10, 11, 12, 13, …]. Generally, the global performance of a rotor, derived from the conventional Savonius rotor, is presented but no parametric study was really realized. The flow, which is greatly non-stationary, is very complex: the aerodynamic studies are rare and old, and do not permit the prediction of the energetic behaviour of the rotor. Sometimes, some visualisations of the flow in and around the rotor are proposed, but with a poor description of the physical phenomena. However, Chauvin et al. [10] give a precise description of the aerodynamics of the conventional Savonius rotor, obtained by pressure measurements on the paddles.

Numerical simulations have also been carried out on this kind of rotors. These studies include static or dynamic modelling. Neverthless, the results suffer from a lack of a global description of the rotor. Aldoss et al. [15] used the discrete vortex method to predict the flow around a pair of coupled Savonius rotors. They suggested the reason few numerical studies had been successful was due to the “complexity of the flow pattern about the rotor and to the separation of the flow from the blade surfaces”.

Fujisawa [11] carried out a study comparing experimental results with a numerical study also using the discrete vortex method. He concluded that the numerical calculations were adequate to “predict the basic features of the variation in flow fields with rotor angle”. However, the reproduction of the flow field around a stationary rotor was poor, and Fujisawa supposed that it was due to false assumptions used in the calculations [11]. He suggested that the assumption that the flow was strictly bidimensional was incorrect, and that the separation of flow at the blade tips was not well modelled.

Kawamura et al. [16] investigated numerically the running performance of the rotor, using a domain decomposition method. Two computational domains are used and connected to each other. One domain contains the rotating rotor and the other one contains the fixed walls; both domains have common overlapping regions. The running performance of the Savonius rotor, such as the torque coefficient, is obtained for various tip speed ratios. The effects of the walls on the running performance is also investigated. It is found that the power coefficient can be sensibly raised.

Using a specific comparison method, namely the L-sigma criterion, Menet et al. [3, 4] have shown that despite its poor efficiency, the Savonius rotors are in fact more resistant to mechanical stresses than all fast running wind turbines. Under theses circumstances, the corresponding delivered power is largely superior to that of any fast running wind machine, in the case of using the same intercepted front width of wind, and the same value of the maximal mechanical stress on the paddles or the blades. It is clear that, considering the L-sigma criterion, the Savonius rotor is a better wind machine than all the fast running horizontal axis wind turbines. In fact, the Savonius rotors can be considered to be high productivity and low technicality wind machines. It is probably the reason why they are often used for water pumping, especially in poor countries and in isolated sites [5, 6].

The design of a Savonius rotor is in fact very simple. The whole rotor turning around a vertical axis is composed of two vertical half-cylinders, as shown in figure 2. The movement is due of the difference between the drag on the advancing paddle and the drag on the other one.

Noticing the undisputable advantages, in terms of performances and mechanical behavior, a prototype of Savonius rotor, designed for measurements in situ, has been built up [7, 8]. The study carried out on this prototype showed that the main problem for the production of "wind electricity" is the design of the generator. This previous consideration constitutes a good justification for additional studies about this kind of rotor.

Through an exhaustive investigation, the influence of geometrical parameters on the efficiency is presented in the second section. In the third section, a numerical approach is used to complete this investigation. Available experimental data are compared to numerical results in order to validate the simulation. The aim is to show the influence of the geometrical parameters on the flow structures in order to increase the efficiency of the Savonius
rotors.