Emiliano Renzi

Resonant behaviour of an oscillating wave energy converter in a channel

A mathematical model is developed to study the behaviour of an oscillating wave energy converter in a channel. During recent laboratory tests in a wave tank, peaks in the hydrodynamic actions on the converter occurred at certain frequencies of the incident waves. This resonant mechanism is known to be generated by the transverse sloshing modes of the channel. Here the influence of the channel sloshing modes on the performance of the device is further investigated. Within the framework of a linear inviscid potential-flow theory, application of Green’s theorem yields a hypersingular integral equation for the velocity potential in the fluid domain. The solution is found in terms of a fast-converging series of Chebyshev polynomials of the second kind. The physical behaviour of the system is then analysed, showing sensitivity of the resonant sloshing modes to the geometry of the device, which concurs in increasing the maximum efficiency. Analytical results are validated with available numerical and experimental data.

Landslide tsunamis propagating along a plane beach

A forced two-horizontal-dimension analytical model is developed to investigate the distinguishing physical features of landslide-induced tsunamis generated and propagating on a plane beach. The analytical solution is employed to study the wave field at small times after the landslide motion starts. At larger times, the occurrence of transient edge waves travelling along the shoreline is demonstrated, showing the differences with the transient waves propagating over a bottom of constant depth. Results are satisfactorily compared with available experimental data. Finally, the validity of non-forced numerical models is discussed.

Wave farm modelling of oscillating wave surge converters

A mathematical model is described to analyse the hydrodynamic behaviour of a wave energy farm consisting of oscillating wave surge converters in oblique waves. The method is a highly efficient semi-analytical approach based on the linear potential flow theory. Wave farms with a large number of such devices are studied for various configurations. For an inline configuration with normally incident waves, the occurrence of a near-resonant behaviour, already known for small arrays, is confirmed. A strong wave focusing effect is observed in special configurations comprising a large number of devices. The effects of the arrangement and of the distance of separation between the flaps are also studied extensively. In general, the flaps lying on the front of the wave farm are found to exhibit an enhanced performance behaviour in average, owing to the mutual interactions arising within the array. A random sea analysis shows that a slightly staggered arrangement can be an ideal layout for a wave farm of this device. The hydrodynamics of two flaps that oscillate back to back is also discussed.

Landslide tsunamis propagating around a conical island

An analytical forced two-horizontal-dimension model is derived to investigate landslide tsunamis propagating around a conical island lying on a flat continental platform. Separation of variables and Laplace transform are used to obtain the free-surface elevation in the whole domain and the runup at the shoreline in terms of confluent Heun functions. The main properties of these functions and their asymptotic behaviour for large parameters are investigated. Expression of the transient leading wave travelling offshore is also derived. The distinguishing physical features of landslide tsunamis propagating in a round geometry are then pointed out and compared with those of landslide tsunamis propagating along a straight coast. Analytical results satisfactorily agree with available experimental data.

Wave Power Extraction by an Oscillating Wave Surge Converter in Random Seas

This paper investigates the behaviour of a bottom hinged flap-type wave energy converter (WEC), namely the Oscillating Wave Surge Converter (OWSC), in random seas. The semi-analytical model of Renzi and Dias (2013b) for an OWSC in the open ocean is considered to analyze the performance of the device in random incident waves. The modelling is performed within the framework of a linear potential flow theory, by means of Green’s integral theorem. The resultant hypersingular integral equation for the velocity potential obtained from the above formulation is solved using a series expansion in terms of Chebyshev polynomials of the second kind.The behaviour of the device is investigated for six different sea states, generally representative of the wave climate in the North Atlantic Ocean at the European Marine Energy Centre test site. A Bretschneider spectrum is considered in order to reproduce the sea climate. The analysis is made for sea states where the spectral energy contribution from large periods, which cause excitation of body resonance of the flap — not modelled by the linear theory — is almost negligible. The power take-off damping is optimised for each individual sea state to calculate the captured power.The investigation is undertaken for two flaps of different widths, resembling the Oyster1 and the new Oyster800 version of the Oyster WEC, respectively. Comparison is made between the performances of the two converters. The effect of varying the width and the characteristic parameters of the flap on the capture factor in random seas is then discussed.The results of the analysis show that the performance of the device is fairly consistent for the sea states considered. Also an enhancement in the overall average capture factor is shown for the latest version of the wave energy conversion device.© 2013 ASME

On the Modelling of Tsunami Generation and Tsunami Inundation

While the propagation of tsunamis is well understood and well simulated by numerical models, there are still a number of unanswered questions related to the generation of tsunamis or the subsequent inundation. We review some of the basic generation mechanisms as well as their simulation. In particular, we present a simple and computationally inexpensive model that describes the seabed displacement during an underwater earthquake. This model is based on the finite fault solution for the slip distribution under some assumptions on the kinematics of the rupturing process. We also consider an unusual source for tsunami generation: the sinking of a cruise ship. Then we review some aspects of tsunami run-up. In particular, we explain why the first wave of a tsunami is sometimes less devastating than the subsequent waves. A resonance effect can boost the waves that come later. We also look at a particular feature of the 11 March 2011 tsunami in Japan - the formation of macro-scale vortices - and show that these macro-scale vortices can be captured by the nonlinear shallow water equations.

Analytical and computational modelling for wave energy systems: the example of oscillating wave surge converters

The development of new wave energy converters has shed light on a number of unanswered questions in fluid mechanics, but has also identified a number of new issues of importance for their future deployment. The main concerns relevant to the practical use of wave energy converters are sustainability, survivability, and maintainability. Of course, it is also necessary to maximize the capture per unit area of the structure as well as to minimize the cost. In this review, we consider some of the questions related to the topics of sustainability, survivability, and maintenance access, with respect to sea conditions, for generic wave energy converters with an emphasis on the oscillating wave surge converter. New analytical models that have been developed are a topic of particular discussion. It is also shown how existing numerical models have been pushed to their limits to provide answers to open questions relating to the operation and characteristics of wave energy converters.

Mathematical Modelling of a Flap-Type Wave Energy Converter

A mathematical model for a flap-type wave energy converter is derived in the framework of a linear inviscid potential flow theory. The wave field resulting from the interaction of an incident plane wave with the flap is determined by applying Green’s integral theorem to the fluid domain. The hydrodynamic parameters of the system are determined, allowing to solve the equation of motion of the flap and to obtain the capture factor of the device. Asymptotic analysis in the far field yields new relations between the hydrodynamic parameters of the system, which reveal the peculiarity of a flap-type device with respect to traditional point-absorber converters. Finally, comparison is made between the behaviour of the device in the open ocean and in a channel. It is shown that the effect of the channel lateral walls on the system can concur to increase its performance.Copyright

Hydroelectromechanical modelling of a piezoelectric wave energy converter

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

Oscillating Wave Surge Converters: Interactions in a Wave Farm

The hydrodynamic behaviour of a wave farm comprising of Oscillating Wave Surge Converters (OWSC) is investigated using a mathematical model based on linear potential flow theory. The developed method can analyse a large number of wave energy converters in arbitrary configurations with oblique wave incidence and considers the hydrodynamic interactions amongst all the devices. The highly efficient novel method is based on Greens Integral Equation formulation, yielding hypersingular integrals which are finally solved using Chebyshev polynomials of the second kind. Using the semi -analytical approach, some possible configurations of a wave farm are studied. In the case of an inline configuration of the OWSCs with normal wave incidence, the occurrence of a near resonant behaviour already observed for 3 flaps is confirmed. A strong wave focussing effect is observed in some special configurations comprising of a large number of such devices. In general, the flaps located on the front of the wave farm are found to exhibit an enhanced performance behaviour in average, due to the mutual interactions arising within the array. A special case of two back to back flaps, oscillating independently, is also analysed using the above approach.Copyright