Numerical modelling of a 1.5 MW tidal turbine in realistic coupled wave–current sea states for the assessment of turbine hub-depth impacts on mechanical loads

This paper considers hub-depth impacts on mechanical loads for a tidal turbine operating in realistic coupled wave–current sea states. A novel medium-fidelity actuator-line CFD model for simulating tidal turbine non-steady hydrodynamic rotor load responses in the presence of turbulence, shear, and surface waves is developed. The model is validated using tank testing data from a lab-scale turbine. The validated model is then upscaled, to a power rating of 1.5 MW, and simulated in realistic wave–current conditions consistent with those of the MeyGen site. Mean torque and thrust are found to increase with turbine hub height, and the presence of waves is shown to increase mean torque and thrust values by up to 22% and 11%, respectively. The effect on standard deviations and maximum values for these variables is more pronounced, with increases of up to 2500% and 1700% in signal standard deviations, and up to 80% and 30% in maximum values for torque and thrust, respectively. The presence of longer period waves is also shown to reduce mean torque levels, while the corresponding standard deviations and maximum values remained relatively unchanged. In such circumstances, the turbine is operating with an undesirable combination of low-power and high-fatigue. Tidal turbine hub loading characteristics and sensitivities, in the context of the operational loads which subsequently enter the drivetrain and turbine support structure, are also analysed. The magnitude of out-of-plane rotor moments are found to increase with the hub height and wave height. Complex flow interactions are shown to play an important role in this context, leading to what is termed “wave-driven moment-type dominance” effects. Overall, both the rotor location and wave composition are found to significantly impact the turbine’s rotor mechanical load response

Radiation Force Modeling for a Wave Energy Converter Array

The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, , of the radiation force transfer function matrix

Control of a Point Absorber using Reinforcement Learning

This work presents the application of reinforcement learning for the optimal resistive control of a point absorber. The model-free Q-learning algorithm is selected in order to maximise energy absorption in each sea state. Step changes are made to the controller damping, observing the associated penalty, for excessive motions, or reward, i.e. gain in associated power. Due to the general periodicity of gravity waves, the absorbed power is averaged over a time horizon lasting several wave periods. The performance of the algorithm is assessed through the numerical simulation of a point absorber subject to motions in heave in both regular and irregular waves. The algorithm is found to converge towards the optimal controller damping in each sea state. Additionally, the model-free approach ensures the algorithm can adapt to changes to the device hydrodynamics over time and is unbiased by modelling errors.The authors would like to thank the Energy Technology Institute and the Research Council Energy Programme for funding this research as part of the IDCORE programme (grant EP/J500847) as well as the Engineering and Physical Sciences Research Council (grant EP/J500847/1). In addition, Mr. Anderlini would like to thank Wave Energy Scotland for sponsoring his Eng.D. research project

Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure

Large floating structures, such as liquefied natural gas (LNG) ships, are subject to both internal and external fluid forces. The internal fluid forces may also be detrimental to a vessel’s stability and cause excessive loading regimes when sloshing occurs. Whilst it is relatively easy to measure the motion of external free surface with conventional measurement techniques, the sloshing of the internal free surface is more difficult to capture. The location of the internal free surface is normally extrapolated from measuring the pressure acting on the internal walls of the vessel. In order to understand better the loading mechanisms of sloshing internal fluids, a method of capturing the transient inner free surface motion with negligible affect on the response of the fluid or structure is required. In this paper two methods will be demonstrated for this purpose. The first approach uses resistive wave gauges made of copper tape to quantify the water run-up height on the walls of the structure. The second approach extends the conventional use of optical motion tracking to report the position of randomly distributed free floating markers on the internal water surface. The methods simultaneously report the position of the internal free surface with good agreement under static conditions, with absolute variation in the measured water level of around 4 mm. This new combined approach provides a map of the free surface elevation under transient conditions. The experimental error is shown to be acceptable (low mm-range), proving that these experimental techniques are robust free surface tracking methods in a range of situations