A control-orientated analytical model for a cyclorotor wave energy device with N hydrofoils

Abstract

We present a new analytical model from which a model-based controller can be derived for a cyclorotor-based wave energy converter (WEC). Few cyclorotor-based WEC concepts and models have previously been studied and only one control strategy for the entire wave cancellation has been tested. Our model is derived for a horizontal cyclorotor with N hydrofoils and is suitable for the application of various control algorithms and the calculation of various performance metrics. The mechanical model is based on Newton’s second law for rotation. The cyclorotor operates in two dimensional potential flow. This paper modeled the velocity field in detail around the turbine with N hydrofoils by explaining each velocity term and estimated the generated torque using two methods (point source method and thin-chord method). The developed model is very convenient for control design, using the power take off torque and hydrofoil pitch angles as control inputs. The authors of this work have derived new, exact analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time and increase the accuracy of the results. The new equations also provide useful insight into the nature of the associated variables, and are successfully validated against the results of physical experiments and numerical calculations previously published by two independent research groups. Representation of hydrofoils as both a point source and a thin chord were analysed, with both models cross-validated for the case of free rotation in monochromatic waves.

Some Fundamental Results for Cyclorotor Wave Energy Converters for Optimum Power Capture

“…This note provides, within the fidelity of the model [9] employed, conclusive evidence that a time-varying rotational rate profile for a cyclorotor optimally captures wave power and that it is important to focus on the converted (shaft) energy metric, rather than using wave cancellation as a surrogate measure. However, the results presented are calculated by the model in [9], which has some approximations in relation to the potential (theory) wave model employed, using a representation of the foil as the point source and use of the approximate lift and drag coefficients from [12]. These approximations may affect the relative balance between shaft power and wave cancellation, since the model does not consider complex hydrodynamic effects such as added mass, dynamic drag losses and generation of the vortices caused by the rapid changes in rotational speed.…”

“…In order to compute the optimal rotational rate profile, we use the validated model [9]- [11] of a cyclorotor, with the following specifications, proposed in [5]: two hydrofoils NACA0015 [12] with chord length C = 5 m, operational radius R = 6 m, and a distance y 0 = −12 m between the still water level (SWL) and rotor centre (see Fig. 1).…”

“…5(b)). The difference in the shaft power and wave cancellation metric values is primarily due to the fact that, when maximising shaft power, tangential force needs to be maximised (2) (with attack angle optimised at 15°) while, for wave cancellation, circulation needs to be optimised (9). In addition, the use of a variable rotational rate is also detrimental to wave cancellation.…”

“…In this study, a cyclorotor-based WEC is simulated with the use of point-source model presented and validated in [9]- [11]. In order to provide some indication of the connection between cyclorotor rotational velocity and tangential force, the principal model equations are briefly presented.…”

“…In order to provide some indication of the connection between cyclorotor rotational velocity and tangential force, the principal model equations are briefly presented. The model [9] essentially considers rotation in two-dimensional potential flow, and includes radiation effects and viscous losses. Linear monochromatic Airy waves are used as input to the cyclorotor.…”