An efficient coupled-mode/FEM numerical method for linear wave propagation over 3D variable bathymetry domains

© Copyright 2016 by the International Society of Offshore and Polar Engineers (ISOPE).A robust numerical algorithm for the simulation of linear water wave propagation over uneven bottom topography is developed. The solution strategy is based on a highly efficient reduction of the 3D problem to a system of partial differential equations by means of a consistent coupled mode series expansion for water wave propagation over variable seabed. The main feature of the proposed series representation is the incorporation of special terms in the vertical expansion basis, accounting for the bottom boundary condition of the varying seabed. The formulation of the 2D system follows from the variations, with respect to the expansion coefficients (functions of the horizontal plane spatial coordinates), of a suitably chosen energy functional. The resulting model is a variable coefficient system of second order, with respect to the spatial coordinates, Partial Differential Equations (PDEs). Linear triangular finite elements are employed for the solution of this PDE system offering flexibility in the discretization of complex 2D domains. The numerical method developed has been applied to several test cases yielding accurate representations of the wave field at relatively low computational cost and small execution times

Energy-Efficient Marine Engine and Dynamic Wing Evaluation Under Laboratory Conditions to Achieve Emission Reduction Targets in Shipping

There is a requirement to comply with the forthcoming IMO & EU requirements to reduce ship emissions by at least 40% in 2030 compared to the 2008 levels. Such medium-term emission reduction targets can only be achieved by introducing novel technologies into the shipping industry. The SeaTech H2020 project (seatech2020.eu) introduces two main innovations that can support the same emission reduction objectives. Those innovations consist of integrating an energy-efficient marine combustion engine with a renewable energy recovery device, i.e. dynamic wing. However, these two technologies are not evaluated in an actual environment in a selected ocean-going vessel. On the other hand, various data sets are collected from both innovations and can be used to quantify their energy efficiencies in a data science environment. Furthermore, it is expected that both innovations should interact with each other in the same data science environment as well as in the respective testing platforms, therefore more realistic vessel operational conditions can be introduced. Hence, this study introduces realistic head wave conditions in both innovations, where the dynamic wing creates adequate thrust to push the vessel forward under the same ocean wave conditions. The same thrust and ocean wave conditions have been applied to marine engine testing as the main contribution of this study. Finally, the data sets collected from the engine testing platform under its loading situations for both wave and thrust conditions of the selected ocean-going vessel are presented in this study

Active and passive pitch-controlled flapping wing propulsors; usage of the wake structure as a performance qualifier

Economic and ecological needs dictate for an ever growing need for increased efficiency, both in marine propulsion and energy saving systems. Biomimetic (flapping wing) systems, have already shown a serious potential as propulsors [1] and an even greater as a mechanism that converts energy from ship motions to thrust [2], [3]. In this paper, the problem of passively (spring loaded) or actively pitched controlled wing is formulated and solved using a free wake 3D Boundary Element Method [4]. For the spring loaded case, the unsteady BEM code is used to calculate the instantaneous forcing (i.e. pitching moment) entered in the nonlinear second order PDE in time, expressing equilibrium of moments including damping and inertia, around the pitch axis. Systematic simulations were conducted for a series of harmonically heaving wings of different aspect ratios, with the instantaneous pitch selected either passively via a spring-damper system or actively using a proper control algorithm. The results regarding developed mean thrust coefficient are presented in the form of systematic diagrams compatible with the design diagrams introduced in [1], allowing comparison of the different flapping wing propulsors. Results are also presented for the wake patterns of the different configurations, at similar propulsive conditions, revealing the connection between the propulsive effectiveness and 3D wake structure

Resonances of enclosed shallow water basins with slender floating elastic bodies

A model for the hydroelastic response of enclosed shallow water basins with floating slender plates of large span, in variable bathymetry is presented. The eigenproblem for the system's resonant behaviour is formulated in the strong and variational form. Based on the variational form, and special hydroelastic finite elements, a quadratic eigenvalue problem is derived for the eigenfrequencies and eigenmodes of the basin-floating body system. Benchmark examples, for simplified configurations, are used to study the effects of parameters like the plate's span, position, draft, mass, stiffness and depth of the basin. It is observed that the presence of the plate can alter significantly the eigenstates of the pond if the depth of the basin is relatively small, compared to the plate draft. In such cases the plate span and position play a crucial role. The hydroelastic analysis can be important even in cases where the depth increases and the upper surface elevation differences, in the presence or absence of the floating plate, appear to be less significant. This is due to the importance in accurately calculating the curvature and hence bending moments inside the plate. The proposed model could be relevant to the seiche formation analysis in reservoirs with floating photovoltaic platforms or ice-covered lakes

Shape-optimization of 2D hydrofoils using an isogeometric BEM solver

In this paper, an optimization procedure, based on an Isogeometric BEM solver for the potential flow, is developed and used for the shape optimization of hydrofoils. The formulation of the exterior potential-flow problem reduces to a Boundary-Integral Equation (BIE) for the associated velocity potential exploiting the null-pressure jump Kutta condition at the trailing edge. The numerical solution of the BIE is performed by an Isogeometric Boundary-Element Method (BEM) combining a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight parameters, the very same basis of the geometric representation for representing the velocity potential and collocation at the Greville abscissas of the knot vector of the hydrofoil's B-splines representation. Furthermore, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the Isogeometric BEM solver and an optimizer employing a controlled elitist genetic algorithm. Multi-objective hydrofoil shape optimization examples are demonstrated with respect to the criteria (i) maximum lift coefficient and (ii) minimum deviation of the hydrofoil area from a reference area

Higher-order fem for nonlinear hydroelastic analysis of a floating elastic strip in shallow-water conditions

The hydroelastic response of a thin, nonlinear, elastic strip floating in shalow-water environment is studied by means of a special higher order finite element scheme. Considering non-negligible stress variation in lateral direction, the nonlinear beam model, developed by Gao, is used for the simulation of large flexural displacement. Full hydroelastic coupling between the floating strip and incident waves is assumed. The derived set of equations is intended to serve as a simplified model for tsunami impact on Very Large Floating Structures (VLFS) or ice floes. The proposed finite element method incorporates Hermite polynomials of fifth degree for the approximation of the beam deflection/upper surface elevation in the hydroelastic coupling region and 5-node Lagrange finite elements for the simulation of the velocity potential in the water region. The resulting second order ordinary differential equation system is converted into a first order one and integrated with respect to time with the Crank-Nicolson method. Two distinct cases of long wave forcing, namely an elevation pulse and an N-wave pulse, are considered. Comparisons against the respective results of the standard, linear Euler-Bernoulli floating beam model are performed and the effect of large displacement in the beam response is studied

Evolution of surface gravity waves over a submarine canyon

The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. Yet, a spectral refraction model predicts an even larger reduction by about a factor 10, because low frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, indicating that evanescent modes and high order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles

Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field

Hydroelastic analysis of ice shelves under long wave excitation

Abstract. The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length