Article

# Analytical Modeling of a Cyclorotor in Hovering State

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## Abstract

In the paper it is proposed and described in detail a mathematical model that is able to assist in the design of cycloidal rotors. The method is formulated on a semi-empirical way including unsteady aerodynamic effects that are based on first principles. It is able to predict the overall generated thrust and the power required by the operation of the cycloidal rotor. The model also includes a kinematic package that can provide an instantaneous design and animation of the cycloidal rotor under different regimes of operation. For validation it was addressed three different rotor configurations where it was varied several rotor parameters, namely: pitch amplitude; pitching axis location; blade chord; airfoil thickness; phase angle of eccentricity. It was shown that the proposed model is able to provide a good estimation of thrust and power when compared with the experimental data from these different sources, showing that the semi-empirical approach could be applied in a more general way.

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... The dynamic pitching provided by the four-bar linkage mechanism is expressed by the following equations [13]: ...
... This mechanism, which has proved well for cyclogyros used in aeronautical propulsion [13][14][15][16][17][18], is simple, reliable, and has the ability to self-adjust the turbine dynamics as a function of the rotating speed of the rotor and also on the direction and magnitude of the incoming wind. It is noted that the system kinematics also allows for an asymmetric pitching schedule of the blades, which could be beneficial since the frontal area of the rotor operates at a different angle of attack than the rear region. ...
... To this end, data for a cyclogyro of similar dimensions as the wind turbine, operating in propulsion mode (V wind ¼ 0), are used. This configuration, here denominated IAT21-L3 rotor, was analyzed as a part of an European research project, which aimed to develop the cyclogyro technology as a mean of propulsion for small and medium size aircraft [13,18,[20][21][22][23]. It is obvious that the results obtained for the IAT21-L3 rotor do not faithfully represent the features of a VAWT, since in propulsion mode energy is being provided and not extracted from the flow. ...
Article
In this paper, four key design parameters with a strong influence on the performance of a high-solidity variable pitch vertical axis wind turbine (VAWT) operating at low tip-speed-ratio (TSR) are addressed. To this aim, a numerical approach, based on a finite-volume discretization of two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) equations, on a multiple sliding mesh, is proposed and validated against experimental data. The self-pitch VAWT design is based on a straight-blade Darrieus wind turbine with blades that are allowed to pitch around a feathering axis, which is also parallel to the axis of rotation. The pitch angle amplitude and periodic variation are dynamically controlled by a four-bar linkage system. We only consider the efficiency at low and intermediate TSR; therefore, the pitch amplitude is chosen to be a sinusoidal function with a considerable amplitude. The results of this parametric analysis will contribute to define the guidelines for building a full-size prototype of a small-scale wind turbine of increased efficiency. [DOI: 10.1115/1.4032794]
... The airfoils depict an increase in C p with t/c as seen through Fig. 19(b), and this observation suggests that for a given k, upon increasing the blade thickness, the performance of the rotor seems to be promising. Apart from this, they have also examined the effect of b through a controlled pitching mechanism as suggested by Leger et al. 94 Their findings suggest that using the proposed pitching mechanism, the rotor generates a relatively higher torque compared to fixed b while operating a low k. Furthermore, it is to be noted that the rotor with six blades produces a higher torque compared to lesser number of blades. ...
... 59 At low k, the pitching mechanism for VAWT generates higher torque. 94 ...
Article
The utility of small wind turbines (SWTs) covering horizontal and vertical-axis types as off-grid, standalone, and decentralized energy supplement systems has gained market attention. Such turbines primarily operate at low Reynolds number ( Re) and low tip speed ratio ( λ) conditions. Under such circumstances, the design, development, and testing of SWTs have become a tedious task, mainly due to the lack of precise aerodynamic knowledge of SWT. The present article reviews the fundamental aspects of SWT, including airfoil selection criteria, blade design, and aerodynamic improvement through passive flow control and augmentation techniques. The article also reports several classes of potential airfoils that can be employed in the design of SWTs. The airfoils considered operate mainly in the range of Re = 0.3 x 10 ⁵ to 3 x 10 ⁵ and λ = 0.5 to 6. Besides the classical approach, the article showcases the prospects of several bioinspired profiles/shapes that are meant for SWTs operating at low Re and λ conditions. Towards the end, various design constraints and applicability of SWTs are summarized.
... A European Union project entitled "CROP" was developed with the intention to work on aerodynamic efficiency, optimizations and designing the most promising configurations of cyclorotors as propulsion systems. Under this project, Leger et al. [17][18][19] made detailed analytical studies to detect the optimal mechanical dimensions under specific operating conditions. Their model was able to compute the dynamic and kinematic behavior of a UAV-scale cyclorotor operating at hover. ...
Article
The present study demonstrates an improved performance of cycloidal rotors by actively controlling the pitching oscillations and rotational speeds. The computational fluid dynamics (CFD) coupled with artificial neural network (ANN) were the methodologies used in the optimization analysis for the hover-state operation rather than the take-off mode under ground effects [1]. The former is carried out to obtain numerical predictions at various operating conditions for an UAV-scale cyclorotor. The oscillating-rotating blades and the corresponding flowfield is computed unsteadily along the complete circular trace for performance considerations. From CFD simulations, the optimum operational state is predicted for a 30∘ and 500 (rpm) pitch angle and rotating speed, respectively. On a second step, by training the ANN with the CFD database at various operating conditions and parameters, the ANN was then capable of analyzing the optimum states for operating at different conditions. The pitching oscillation schedule is then optimized for each rotational speed by using ANN and for each azimuthal location over the traversing trace. This will imply to perform on-board control in active mode for the blades, rather than assigning constant pitching oscillations for all operating states. This active control concept showed to be a potential approach to enhance the cyclorotor efficiency by 12 percent in average.
... A European Union project entitled "CROP" was developed with the intention to work on aerodynamic efficiency, optimizations and designing the most promising configurations of cyclorotors as propulsion systems. Under this project, Leger et al. [17][18][19] made detailed analytical studies to detect the optimal mechanical dimensions under specific operating conditions. Their model was able to compute the dynamic and kinematic behavior of a UAV-scale cyclorotor operating at hover. ...
Article
The present study demonstrates an improved performance of cycloidal rotors by actively controlling the pitching oscillations and rotational speeds. The computational fluid dynamics (CFD) coupled with artificial neural network (ANN) were the methodologies used in the optimization analysis for the hover-state operation rather than the take-off mode under ground effects [1]. The former is carried out to obtain numerical predictions at various operating conditions for an UAV-scale cyclorotor. The oscillating-rotating blades and the corresponding flowfield is computed unsteadily along the complete circular trace for performance considerations. From CFD simulations, the optimum operational state is predicted for a 30◦ and 500 (rpm) pitch angle and rotating speed, respectively. On a second step, by training the ANN with the CFD database at various operating conditions and parameters, the ANN was then capable of analyzing the optimum states for operating at different conditions. The pitching oscillation schedule is then optimized for each rotational speed by using ANN and for each azimuthal location over the traversing trace. This will imply to perform onboard control in active mode for the blades, rather than assigning constant pitching oscillations for all operating states. This active control concept showed to be a potential approach to enhance the cyclorotor efficiency by 12 percent in average.
... The Cycloidal Rotor Optimized for Propulsion (CROP) project (CROP 2013b), a project under the European Union FR7 framework license, held cyclorotors as the optimizing target. Leger et al. (2015Leger et al. ( , 2016 studied the different operating principles of a cyclorotor at a hovering state using an analytic approach. Furthermore, in another numerical work, they predicted the presence of threedimensional effects, tip leakage, and main flow structure considerations when equipped with endplates (Xisto et al. 2014b). ...
... The blade numerical domain exchange information with the rotor domain through a sliding mesh as well as the rotor and the environment domains. Each blade region moves according to Eq. (3) [33] which describes the blade pitch angle variation [ ] imposed by the mechanical system shown in Fig. 6. ...
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