U-Oscillating Water Column in Random Waves: Modelling and Performances

2013 ◽  
Author(s):  
Giovanni Malara ◽  
Felice Arena
Keyword(s):  
Nonlinear Equation ◽  
Water Column ◽  
Wave Energy ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Equation Of Motion ◽  
Oscillating Water Column ◽  
Random Waves ◽  
Statistical Measures ◽  
Initial Boundary Value

This paper deals with the analytical modelling of an U-Oscillating Water Column (U-OWC). It is shown that this device can be adequately described by a nonlinear equation of motion including hydrodynamic memory effects. The excitation of the system, the added mass and the retardation function are derived by approximating the solution of a pertinent initial boundary value problem via eigen-function expansions of the (linear) velocity potential. Next, the performance of the system is investigated in random waves by relying on Monte Carlo simulations. The excitation of the system is synthesized from a given power spectral density. Then, the nonlinear equation of motion is numerically integrated. Pertinent statistical measures are estimated for assessing the efficiency of the U-OWC in exploiting sea wave energy. In this regard, the parameters show that the device can absorb most part of the incident wave energy. Further, the device can work in safe conditions even in quite rough sea states.

Latching Control of a Floating Oscillating Water Column Wave Energy Converter in Irregular Waves

2014 ◽  
Author(s):  
João C. C. Henriques ◽  
Juan C. Chong ◽  
António F. O. Falcão ◽  
Rui P. F. Gomes
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Rotational Speed ◽  
Phase Control ◽  
Wave Energy Converter ◽  
Irregular Waves ◽  
Oscillating Water Column ◽  
Random Waves ◽  
Energy Converter ◽  
Excitation Force

The paper concerns the phase control by latching of a floating oscillating-water-column (OWC) wave energy converter of spar-buoy type in irregular random waves. The device is equipped with a two-position fast-acting valve in series with the turbine. The instantaneous rotational speed of the turbine is controlled through the power electronics according to a power law relating the electromagnetic torque on the generator rotor to the rotational speed, an algorithm whose adequacy had been numerically tested in earlier papers. Two alternative strategies (1 and 2) for the latching/unlatching timings are investigated. Strategy 1 is based on the knowledge of the zero-crossings of the excitation force on the floater-tube set. This is difficult to implement in practice, since the excitation force can neither be measured directly nor predicted. Strategy 2 uses as input easily measurable physical variables: air pressure in the chamber and turbine rotational speed. Both strategies are investigated by numerical simulation based on a time-domain analysis of a spar-buoy OWC equipped with a self-rectifying radial-flow air turbine of biradial type. Air compressibility in the chamber plays an important role and was modelled as isentropic in a fully non-linear way. Numerical results show that significant gains up to about 28% are achievable through strategy 1, as compared with no phase control. Strategy 2, while being much easier to implement in practice, was found to yield more modest gains (up to about 15%).

Internal gravity waves in a time-varying stratification

1977 ◽  
Vol 82 (4) ◽  
pp. 609-619 ◽  
Author(s):  
Richard Rotunno
Keyword(s):  
Gravity Waves ◽  
Wave Energy ◽  
Irreversible Process ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Internal Gravity Waves ◽  
Slow Time ◽  
Time Variations ◽  
Initial Boundary Value ◽  
Inverse Proportionality

The influence of slow time variations of the Brun-Väisälä frequency N upon the energy of internal gravity waves is investigated. It is found that, when time variations in N are produced by a mean deformation field (reversible mean state), the wave energy can vary in either direct or inverse proportion, depending on the wavenumber orientation. When N changes owing to a certain type of irreversible process, the wave energy varies with only inverse proportionality.The nocturnal planetary boundary layer (NPBL) provides an example where N = N(z, t). The full initial/boundary-value problem for an N(z, t) similar to the climatological mean for the NPBL is solved.

scholarly journals On the Stability of Continuous Media

1972 ◽  
Vol 39 (2) ◽  
pp. 438-444 ◽  
Author(s):  
A. F. D’Souza
Keyword(s):  
Nonlinear Equation ◽  
Spectral Representation ◽  
Nonlinear Problems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Panel Flutter ◽  
Linearized Problem ◽  
The Stability ◽  
Initial Boundary Value ◽  
Function Matrix

The stability of a basic stationary motion is investigated. The problem is posed as an initial boundary-value problem of partial differential equations in the perturbations. The spectral representation of the Green’s function matrix for the linearized problem is obtained and employed to generate a generalized energy function which is then used for the stability investigation of linearized and certain nonlinear problems. The results are applied to the stability of linearized aerodynamic panel flutter problem and to a nonlinear equation with conic nonlinearity.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

RESEARCH OF THE IMPACT DEVICE MODEL OF THE ROD TYPE BY DIFFERENCE METHOD

2020 ◽  
pp. 73-80
Author(s):  
А.М. Слиденко ◽  
В.М. Слиденко
Keyword(s):  
Boundary Value Problem ◽  
Difference Method ◽  
Model Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cross Sectional ◽  
Impact Device ◽  
Initial Boundary Value ◽  
The Impact

Приводится анализ механических колебаний элементов ударного устройства с помощью модели стержневого типа. Ударник и инструмент связаны упругими и диссипативными элементами, которые имитируют их взаимодействие. Аналогично моделируется взаимодействие инструмента с рабочей средой. Сформулирована начально-краевая задача для системы двух волновых уравнений с учетом переменных поперечных сечений стержней. Площади поперечных сечений определяются параметрическими формулами при сохранении объемов стержней. Параметрические формулы позволяют получать различного вида зависимости площади поперечного сечения стержня от его длины. Начальные условия отражают физическую картину взаимодействия инструмента с ударником и рабочей средой. Краевые условия описывают контактные взаимодействия ударника с инструментом и последнего с рабочей средой. В качестве модельной задачи рассматривается соударение ударника и инструмента через элемент большой жесткости. Начально-краевая задача исследуется разностным методом. Проводится сравнение решений задачи, полученных с помощью двухслойной и трехслойной разностных схем. Такие схемы реализованы в общей компьютерной программе в системе Mathcad. Показано, что при вычислениях распределения нормальных напряжений по длине стержня лучшими свойствами относительно устойчивости обладает двухслойная схема The article gives the analysis of mechanical vibrations of the impact device elements using the model of the rod type. The hammer and the tool are connected by elastic and dissipative elements that simulate their interaction. The interaction of the tool with the processing medium is simulated in a similar way. An initial boundary-value problem is formulated for a system of two wave equations taking into account the variable cross sections of the rods. Cross-sectional areas are determined by parametric formulas maintaining the volume of the rods. Parametric formulas allow one to obtain various dependence types of the cross-sectional area of the rod on its length. The initial and boundary conditions reflect the physical phenomenon of the tool interaction with the processing medium, and also describe the contact interactions of the hammer with the tool. The impacting of the hammer and the tool through an element of high rigidity is considered as a model problem. To control the limiting values, the solution of the model problem by the Fourier method is used. The initial-boundary-value problem is investigated by the difference method. A comparison of solutions obtained for the two-layer and three-layer difference schemes is given. Such schemes are realized in a common computer program in the Mathcad. It is shown that the two-layer scheme has the best properties in relation to stability while calculating the distribution of normal voltage along the length of the rod

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