First Research Meeting 2024

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The first meeting will be held on Tuesday 4 June 2024 at the Plymouth COAST Laboratory. If you would like to attend the meeting, please register by sending an email to h.alemi-ardakani@exeter.ac.uk

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University of Plymouth, COAST Laboratory:

Flexible responsive systems in ocean wave energy.

 

This meeting will be devoted to recent advances in flexible wave energy converters. Topics will include:  Wave basin model tests for WEC systems with deformable materials. Experimental results, their analysis and comparison with theoretical models. New numerical models used in COAST Laboratory. New technological advances for wave energy converters with deformable and flexible components. Representatives of WECs stakeholders, relevant industry companies and academics leading research projects in the field, will be invited to this meeting.

 

 

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Theme: Flexible Responsive Systems in Ocean Waves

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Date: Tuesday 4 June 2024, 10:00 – 16:40

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Venue: Room BGB 402, School of Engineering, Computing and Mathematics, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK

 

 

Timetable

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10:00–10:30 Prof. Emiliano Renzi (Northumbria University)

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Modelling and design of flexible plate wave energy converters

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10:30–11:00 Prof. Richard Porter (University of Bristol)

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Wave power from a large closely-spaced array of bottom-hinged paddle converters

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11:00–11:30 Dr. Raphael Stuhlmeier (University of Plymouth)

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Deterministic wave forecasting with corrected nonlinear dispersion

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11:30–12:00 Dr. Simone Michele (University of Plymouth)

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Flexible offshore floating plates in water waves

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12:00–13:30 Lunch and Discussion

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13:30–14:00 Dr. Siming Zheng (Zhejiang University)

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Hydrodynamic performance of a U-shaped oscillating water column consisting of a flexible bottom-standing front wall

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14:00–14:30 Prof. Alistair Borthwick (University of Plymouth)

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Flexibly mounted cylinder in waves

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14:30–15:00 Dr. Kang Ren (University of Southampton)

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Surface wave interaction with floating elastic plates in channels

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15:00–15:30 Coffee Break

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15:30–16:00 Prof. M. Reza Alam (University of California, Berkeley)

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Wave Energy Extraction from an Actuated Seabed-Mounted Flexible Carpet: Linear and Nonlinear Analysis

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16:00–16:30 Prof. Deborah Greaves (University of Plymouth)

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The FlexWave project

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Titles and Abstracts

Emiliano Renzi (Northumbria University)

Modelling and design of flexible plate wave energy converters

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We discuss developments in hydrodynamic modelling of wave energy converters that use flexible plates. We present models for both submerged and floating elastic plates, examining how hydroelasticity and power take-off (PTO) damping contribute to harnessing energy from incoming waves. A piezoelectric plate converter is modelled through a hydro-electromechanical approach that incorporates linearised potential flow theory and integrates piezoelectric and circuit dynamics. Additionally, we explore an alternative hydrodynamic model that includes a floating elastic plate attached to a dissipative PTO system, with both theoretical and experimental analyses. We also explore preliminary results on the impact of a variable wave field on wave energy generation.

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Richard Porter (University of Bristol)

Wave power from a large closely-spaced array of bottom-hinged paddle converters

 

We consider a wave energy farm design consisting of a large number of thin buoyant paddles extending through the depth and hinged at the sea bed. The paddles are arranged in a doubly-periodic manner consisting of a finite number of identical rows, each row assumed to extend indefinitely to infinity. Each paddle is attached to its own damper and spring, allowing power to be generated through its pitching motion. Unlike previous studies into absorbing paddle arrays, we envisage compact arrays consisting of narrow devices arranged across a large number of rows. The calculation of the wave power is performed using a mathematical approach which exploits the periodicity of the array. Specifically, we show how the solution throughout the domain of the array is expressed in terms of a single set of eigenmodes that result from a suitably-defined periodic cell problem so that the matching to the solution in the domains either side of the array results in a low-order system of equations. The method used in this study is exact within the setting of linearised water wave theory and has all of the advantages of classical low-frequency multi-scale homogenization without the low-frequency restriction. It may also be regarded as a natural extension of the well-known wide-spacing approximation without the large separation restriction. Whilst we place a focus on the mathematical approach to the problem, we will also show a range of results to illustrate the performance of this proposed wave energy converter design. The work was jointly undertaken with Dr Jin Huang as part of an EPSRC-funded project into metamaterial-inspired wave energy converters.

 

 

 

Raphael Stuhlmeier (University of Plymouth)

Deterministic wave forecasting with corrected nonlinear dispersion

 

Deterministic wave forecasting aims to provide a wave-by-wave prediction of the free surface elevation based on measured data. Such information about upcoming waves can inform marine decision support systems, control strategies for wave energy converters, and other applications. Unlike well-developed stochastic wave forecasts, the temporal and spatial scales involved are modest, on the order of minutes or kilometres. Due to the dispersive nature of surface water waves, such forecasts have a limited space/time horizon, which is further impacted by the effects of nonlinearity. I will discuss the application of the reduced Zakharov equation, and simple frequency corrections derived therefrom, to preparing wave forecasts. Unlike procedures based on solving evolution equations (e.g. high order spectral method), such corrections entail essentially no additional computational effort, yet show marked improvements over linear theory.

 

 

 

Siming Zheng (Zhejiang University)

Hydrodynamic performance of a U-shaped oscillating water column consisting of a flexible bottom-standing front wall

 

We propose a concept of U-shaped oscillating water column (UOWC) device consisting of a flexible bottom-standing front wall. The deflection of the flexible wall could bring benefits for wave power absorption. To evaluate the hydrodynamic performance and predict the wave power absorption of the flexible UOWC, a theoretical model based on the linear potential flow theory and the Galerkin approximation method is developed. For some examined flexible UOWCs, three peaks of the frequency response of the maximum wave power capture efficiency are observed, in which two are related to the resonant frequencies of the oscillating water column and the 1st natural mode of the flexible wall, respectively, and one could be related to wave near-trapping. The flexibility of the flexible bottom standing front wall is found to be a key factor affecting the performance of the device. As the dimensionless flexibility increases, the three peaks of the efficiency wave frequency curve move towards large frequencies and a large bandwidth of high efficiency is achieved.

 

 

 

Alistair Borthwick (University of Plymouth)
 

Flexibly mounted cylinder in waves

This talk will examine the response of a small-diameter, initially vertical cylinder to loading from regular waves in a laboratory flume. The cylinder was mounted by means of a helical spring to the bed of the flume. Free vibration tests were used to evaluate the dynamic characteristics of cylinder in air and water. Local force and displacement time series were measured for a series of wave tests. Analytical load-response model will be derived based on the linearized form of the modified Morison equation and a harmonic lift equation. The model indicates the relative importance of key dimensionless parameters such as the mass ratio, frequency ratio, damping ratio, wave depth parameter, surface Keulegan-Carpenter number (SKC = UmsT/D where Ums is the maximum water particle velocity at still water level, T is wave period, and D is cylinder diameter), surface reduced velocity (SV r = Ums/fnD where fn is the natural frequency in water), etc. A numerical model will also be presented based on a finite-difference solution of the equations of motion. In-line and transverse force and displacement time histories will be compared, and drag, inertia, and lift force coefficients evaluated. It is found that for local Keulegan-Carpenter number KC > 14, the force coefficients depend on the orbital shape parameter (the ratio of vertical to horizontal first harmonic water velocity components), whereas for KC < 14, the ratio of wave frequency to natural frequency has a major influence on the force coefficients. Dominant frequencies are identified through spectral analysis. Although the study was originally undertaken in the late 1980s, the combination of analytical, numerical, and experimental techniques remain valid in assessing hydro-elastic structural responses to wave loading.

 

 

 

Kang Ren (University of Southampton)

Surface wave interaction with floating elastic plates in channels

 

The interaction between surface waves and a finite rectangular floating plate in a channel is considered analytically, while the location of the plate is not restricted. The mathematical model is based on the linear velocity potential flow theory for the fluid and the Kirchhoff–Love plate theory for the plate. The problem is converted into an integral equation through using the Green function. The second order singularity associated with a body with no thickness is treated with the Dirac delta function. The developed scheme is used for case studies of various edge constraints. Extensive results are provided for the hydrodynamic forces acting on the plate and the wave reflection and transmission coefficients. The effects of wave frequency, channel width, plate length, and edge conditions are analysed, and their physical implications are highlighted. Significant findings comprise the highly oscillatory nature of force curves, influenced by the natural frequencies of the channels and the length of the plate, and substantial effects of edge conditions and the plate position on the results.

 

 

 

Reza Alam (University of California, Berkeley)

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Wave Energy Extraction from an Actuated Seabed-Mounted Flexible Carpet: Linear and Nonlinear Analysis

 

Abstract: TBC

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Simone Michele (University of Plymouth)

Flexible offshore floating plates in water waves

We first present a theoretical model of the hydrodynamic behaviour of a two-dimensional floating flexible plate of variable flexural rigidity connected to the seabed by a spring/damper system. Decomposition of the response modes into rigid and bending elastic components allows us to investigate the hydroelastic behaviour of the plate subject to monochromatic incident free-surface waves of constant amplitude. We show that spatially dependent plate stiffness affects the eigenfrequencies and modal shapes, with direct consequences on plate dynamics and wave power extraction efficiency. We also examine how plate length and Power Take-Off (PTO) distribution affect the response of the system. Then we extend the theory to the case of wave energy converters comprised of three-dimensional, floating, compound rectangular plates in the open sea. The hydrodynamic problem is solved by means of Green’s theorem and a free-surface Green’s function. We first analyse the case of a single rectangular plate and validate our model against experimental results from physical model tests undertaken in the COAST laboratory at the University of Plymouth. Then we extend our theory to complex shapes and arrays of plates and examine how the geometry and PTO coefficient affects the consequent absorbed energy.
 

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Deborah Greaves (University of Plymouth)

The FlexWave project

FlexWave seeks to improve the design, manufacture and survivability of flexible WECs. It will investigate intelligent design concepts to explore whether types of rubber, composites and polymers can be effective in improving performance, reliability and reduce costs compared to current available materials. Testing will also include how materials hold up against extreme storms and sea conditions, which present a significant challenge to existing WEC designs. The project will unite experts in hydrodynamics, materials and deployable structures and conduct extensive design analysis and numerical modelling simulations of flexible fabric WECs, alongside physical tests in the COAST Laboratory. The researchers will also work closely with the advisory board and wider industry to ensure any technology developed can be applied in real-world settings.

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For any enquiries, please contact Hamid Alemi Ardakani.