skip to main content

Title: Wave-by-Wave Control of a Wave Energy Converter with Deterministic Wave Prediction
This paper discusses wave-by-wave near-optimal control of a wave energy device in irregular waves. A deterministic propagation model is used to predict the wave elevation several seconds into the future at the device location. Two prediction approaches are considered. The first is based on a time series being measured over an advancing time window at a particular up-wave location. This approach is here utilized in long-crested irregular waves. The second approach uses successive snapshots of wave elevation measurements over an up-wave area. This approach is found more convenient for multi-directional waves, and is here applied in a bi-directional wave irregular wave field. A small, heaving vertical cylinder reacting against a deeply submerged (i.e. assumed to undergo negligible oscillations) mass is studied under wave-by-wave control. The non-causal feedforward control force required for optimum velocity under a swept-volume constraint is based on the past, current, and predicted wave elevation at the device. Results for time-averaged converted power and displacement/force maxima are obtained for a range of irregular wave conditions. Also presented in addition are energy conversion results with a feedback-alone control force using a multi-resonant control technique.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
European Wave and Tidal Energy Conference
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Phased arrays have been a cornerstone of non-destructive evaluation, sonar communications, and medical imaging for years. Conventional arrays work by imparting a static phase gradient across a set of transducers to steer a self-created wavefront in a desired direction. Most recently, space-time-periodic (STP) phased arrays have been explored in the context of multi-harmonic wave beaming. Owing to the STP phase profile, multiple scattered harmonics of a single-frequency input are generated which propagate simultaneously in different directional lanes. Each of these lanes is characterized by a principal angle and a distinct frequency signature that can be computationally predicted. However, owing to the Hermitian (real) nature of the spatiotemporal phase gradient, waves emergent from the array are still bound to propagate simultaneously along up- and down-converted directions with a perfectly symmetric energy distribution. Seeking to push this boundary, this paper presents a class of non-Hermitian STP phased arrays which exercise a degree of unprecedented control over the transmitted waves through an interplay between gain, loss, and coupling between its individual components. A complex phase profile under two special symmetries, parity-time (PT) and anti-PT, is introduced that enables the modulation of the amplitude of various harmonics and decouples up- and down-converted harmonics of the same order. We show that these arrays provide on-demand suppression of either up- or down-converted harmonics at an exceptional point—a degeneracy in the parameter space where the system’s eigenvalues and eigenvectors coalesce. An experimental prototype of the non-Hermitian array is constructed to illustrate the selective directional suppression via time-transient measurements of the out-of-plane displacements of an elastic substrate via laser vibrometry. The theory of non-Hermitian phased arrays and their experimental realization unlock rich opportunities in precise elastoacoustic wave manipulation that can be tailored for a diverse range of engineering applications. 
    more » « less
  2. This study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.

    more » « less
  3. We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed $c$ to the wind friction velocity $u_*$ from $c/u_*= 2$ to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness $ak$ from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. The wall friction Reynolds number is 720. The novel fully coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent surface elevation is in quantitative agreement with that computed from the surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. Intermittent and localised airflow separation is observed for steep waves with small wave age, but its effect on setting the phase-averaged pressure distribution is not drastically different from that of non-separated sheltering. We find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. In addition, the history of wind wave coupling can affect the wave form drag, due to the wave crest shape and other complex coupling effects. The normalised wave growth rate we obtain agrees with previous studies. We make an effort to clarify various commonly adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical and experimental results, as we revisit this longstanding problem with new numerical evidence. 
    more » « less
  4. Wave energy converters typically use various control methods to extract energy from ocean waves. The objective of the control system is to optimize the energy extraction process, taking into account the dynamics of the system and the wave conditions. The task of deriving the optimal control laws of wave energy converter arrays for regular and irregular waves using the Pontryagin minimum principle was previously investigated in the literature. The result is a combination between the singular arc and bang-bang control laws. For irregular waves, some complexity arises due to the radiation state-space representation, which requires ignoring the hydrodynamic coupling terms related to the added mass and radiation-damping coefficients; this reduces the computational complexity of the control force but adversely affects the solution's accuracy. Also, the derived control laws are specific to a particular wave condition. Recently, the optimal control of a flexible buoy wave energy converter was derived using the convolution representation for the radiation force. In this work, the optimal control laws of flexible buoy wave energy converters are modified to simulate wave energy converter arrays; then, the results are compared to those obtained by dropping the hydrodynamic radiation coupling terms. Although using a convolution representation adds computational complexity to the optimal control problem, it generates an equation that is generic to any wave condition, can be used with any wave spectrum, and provides an expression for the switching condition. 
    more » « less
  5. Abstract

    In strong winds, air flow detaches from the ocean surface in the lee of wave crests and creates a low‐pressure zone on the wave’s leeward face. The pressure difference between the wave’s rear and front face modulates the momentum input from wind to waves. Numerical wave models parameterize this effect using a so‐called sheltering coefficient. However, its value and dependence on wind speed are not well understood, particularly with background swell waves. To bridge this gap, we conducted laboratory experiments with winds up to Category 4 hurricane force blown over various mechanically generated wave conditions (pure wind sea, mixed waves with directional spreading, and monochromatic unidirectional waves) and measured the wind, waves, and stress at a sufficient frequency to resolve wind‐wave variability over the long‐wave phase. We analyze the results in the context of Jeffreys’s sheltering theory and find two regimes: (a) from low‐to‐moderate wind forcing (10 m s−1 < U10 < 33 m s−1), the aerodynamic sheltering increases with wind speed, consistent with previous studies; (b) in hurricane conditions (U10 > 33 m s−1), the aerodynamic sheltering decreases with wind at a rate depending on wave state. Further, we isolate the short wind waves from the longer paddle waves and find that the aerodynamic sheltering by longer waves leads to a phase‐dependent variability of the short wind‐waves’ local steepness, which is evidenced by the sheltering coefficient’s value derived from wind and wave measurements. Our results emphasize the need for further measurements of aerodynamic sheltering and improving its representation in models.

    more » « less