The development of optimal control strategies for cyclorotor wave energy converters (WECs) is at an early stage. In this paper, we present new methods and solutions for optimal pitch and/or rotational velocity control strategies for different configurations of cyclorotor-based WECs, in both monochromatic and panchromatic waves. The cyclorotor is modelled with the use of an approximate two-dimensional mathematical model, where hydrofoils are approximated as point source vortices in potential waves. The goal of the developed control strategy is to determine the optimal velocity profile, and/or pitch angle variations, for maximum energy conversion, in terms of generated mechanical shaft power. The solutions, obtained with the use of spectral methods, show a clear benefit in using a variable velocity for cyclorotors with either one or two hydrofoils, in monochromatic waves, with a typical increase in energy capture of 30-40%, while the optimal pitching did not significantly increase the value of the absorbed wave energy. We also present control results for panchromatic waves, assuming all the properties of incoming wave packages, within a 10 second time interval, are known. The obtained solutions have shown significant benefit in joint optimal pitch and velocity control, especially in the case of panchromatic waves. It has been also shown that successful implementation of cyclorotor control strategies requires optimal configuration of the static characteristics of the cyclorotor. In conclusion, we discuss the optimal control benefits and highlight problems which must be solved for further successful development of these control strategies.

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.

We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal coordinate due to the gradual variation of duct width. Such a model admits an analytical solution of the problem in hand, and we calculate the scattering coefficients as functions of incident wave frequency for all possible cases of sub-, super-, and transcritical currents. For completeness we study both cocurrent and countercurrent wave propagation in accelerating and decelerating currents. The results obtained are analyzed in application to recent analog gravity experiments and shed light on the problem of hydrodynamic modeling of Hawking radiation.

The analytical study of long-wave scattering in a canal with a rapidly varying crosssection is presented. It is assumed that waves propagate on a stationary current with a given flow rate. Due to the fixed flow rate, the current speed is different in the different sections of the canal, upstream and downstream. The scattering coefficients (the transmission and reflection coefficients) are calculated for all possible orientations of incident wave with respect to the background current (downstream and upstream propagation) and for all possible regimes of current (subcritical, transcritical, and supercritical). It is shown that in some cases negative energy waves can appear in the process of waves scattering. The conditions are found when the over-reflection and over-transmission phenomena occur. In particular, it is shown that a spontaneous wave generation can arise in a transcritical accelerating flow, when the background current enhances due to the canal narrowing. This resembles a spontaneous wave generation on the horizon of an evaporating black hole due to the Hawking effect.

Cyclorotor-based wave energy converters (WECs) present a relatively new and innovative paradigm for wave energy harvesting. Their operational principle is based on the generation of lift forces on the rotating hydrofoils due to their interaction with wave-induced circulation of water particles. As a result, relatively little is known about their optimal operation. To date, cyclorotor device performance has been measured by the power of waves radiated by the WEC, while a constant rotational velocity, consistent with the wave frequency, is employed. In this note we show (a) that variation of the cyclorotor velocity within the incoming monochromatic wave period significantly increases the generated mechanical power, while (b) optimising wave cancellation is at odds with the maximisation of shaft power. To optimise shaft power, the letter adopts a multi-harmonic solution for variable cyclorotor rotation rate, inspired by methods developed in other WEC domains.