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

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

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

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

Finite element simulation of long wave impact on floating breakwaters with variable stiffness

The hydroelastic response of flexible, floating breakwaters is a subject of interest for coastal engineering applications. In this study, a higher order hydroelastic finite element is applied to the simulation of floating breakwaters of variable stiffness undergoing long wave impact. The main aim is the evaluation of breakwater efficiency in terms of transmitted and reflected wave characteristics. It is established that, for the wave-lengths examined, the maximum amplitude and wave-length of the transmitted pulse are strongly dependent on the breakwater stiffness. Finally it is shown that for case of a periodic stiffness profile the transmitted energy is minimised when the modulation wavelength is comparable to the wavelength of the incoming excitation

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

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

HYDRODYNAMIC ANALYSIS OF FLOATING BODIES IN GENERAL BATHYMETRY

ABSTRACT A hybrid technique, based on the coupled-mode theory developed b