Ronald W. Yeung

Added mass and damping of a vertical cylinder in finite-depth waters

Abstract A comprehensive set of theoretical added masses and wave damping data for a floating circular cylinder in finite-depth water is presented. The hydrodynamic problem is solved by matching eigen functions of the interior and exterior problems. The resulting infinite system is solved directly and found to have excellent truncation characteristics. Added mass and damping are given for heave, sway, and roll motion, as well as coupling coefficients for sway and roll. It is shown that the heave added mass is logarithmic singular and the damping approaches a constant in the low-frequency limit. Transition of the behaviour in finite-depth water to deep water is also discussed.

Wave-interference effects on a truncated cylinder in a channel

The effects of channel walls on the hydrodynamic properties of a floating vertical cylinder are examined. An interior eigensolution under the cylinder is matched with an exterior eigensolution in a manner similar to Yeung [1]. Wave effects due to an image cylinder can be conveniently expressed in terms of the coordinates of the central cylinder by the use of Graffs theorem. The infinite array results in a slowly convergent series which has to be summed with caution. Results for the heave added mass and damping of a cylinder for several geometric configurations are obtained. Also presented in the paper are results for the diffraction of incident waves about the same cylinder. The channel walls exert an important influence on the radiation and diffraction properties, the latter to a lesser extent. Such influence is characterized by the presence of “spikes” at wave frequencies corresponding to the occurrence of symmetric transverse resonant modes in the channel. An analytical solution of a three-dimensional flapper wavemaker given in the Appendix further confirms such characteristics. In the high-frequency range, the radiation properties approach those of a single cylinder. In the low-frequency limit, they exhibit a behavior similar to that of a two-dimensional horizontal cylinder heaving in water of finite depth.

ON THE INTERACTIONS OF SLENDER SHIPS IN SHALLOW WATER

The unsteady hydrodynamic interaction of two bodies moving in a shallow fluid is examined by applying slender-body theory. The bodies are assumed to be in each others far field and the free surface is assumed to be rigid. By matched asymptotics, the inner and outer problems are formulated and a pair of coupled integro-differential equations for determining the unknown cross flows is derived. The degree of coupling is shown to be related to a bottom-clearance parameter. Expressions are given for the unsteady sinkage force, trimming moment, sway force, and yaw moment. Numerical calculations for two weakly coupled cases are presented. One corresponds to the interaction of a stationary body with a passing one, the other to the interaction of two bodies moving in a steady configuration. Theoretical results are compared with existing experimental data.

Waves generated by a moving source in a two-layer ocean of finite depth

The velocity potentials of a point source moving at a constant velocity in the upper layer of a two-layer fluid are obtained in a form amenable to numerical integration. Each fluid layer is of finite depth, and the density difference between the two layers is not necessarily small. The far-field asymptotic behavior of the surface waves and internal waves are also derived using the method of stationary phase. They show that the wave system at the free surface or at the interface each contains contributions from two different modes: a surface-wave mode and an internal-wave mode. When the density difference between the two layers is small or the depth of the upper layer is large, the surface-wave mode mainly affects the surface waves while the internal-wave mode mainly affects the internal waves. However, for large density difference, both modes contribute to the surface wave or internal wave system. For each mode, both divergent and transverse waves are present if the total depth Froude number is less than a certain critical Froude number which is mode-dependent. For depth Froude number greater than the critical Froude number, only divergent waves exist for that mode. This classification is similar to that of a uniform fluid of finite depth, where the critical Froude number is simply unity. The surface waves and internal waves are also calculated using the full expressions of the source potentials. They further confirm and illustrate the features observed in the asymptotic analysis.

Oscillation of a floating body in a viscous fluid

The nonlinear viscous-flow problem associated with the heaving motion of a two-dimensional floating cylinder is considered. It is formulated as an initial-boundary-value problem in primitive variables and solved using a finite-difference method based on boundary-fitted coordinates. A fractional-step procedure is used to advance the solution in time. As a case study, results are obtained for a rectangular cylinder oscillating at a Reynolds number of 103• The nonlinear viscous forces are compared with those of linear potential theory. An assessment on the importance of viscous and nonlinear effects is made. The solution technique is sufficiently robust that extensions to consider other single and coupled modes of motion are possible.

The transient heaving motion of floating eylinders

SummaryThe transient heave response of a freely floating cylinder with given initial conditions is obtained by a simultaneous time-domain solution of the fluid-motion and rigid-body dynamics problems. Volterras method is used to derive the integral equation associated with the fluid motion. It is shown that the unit initial-velocity response is simply the time-derivative of the unit initial-displacement response multiplied by one half of the infinite-fluid virtual mass of the cylinder. Numerical evaluation of integrals related to the unsteady waterwave Green function is facilitated by expressing them in terms of the complex error function. Results for the transient motion of semi-circular, triangular, and rectangular cylinders are presented and discussed. Experimental measurements for the case of a semi-immersed circular cylinder agree excellently with the theoretical calculations.

Design, Analysis, and Evaluation of the UC-Berkeley Wave-Energy Extractor

This paper evaluates the technical feasibility and performance characteristics of an ocean-wave energy to electrical energy conversion device that is based on a moving linear generator. The UC-Berkeley design consists of a cylindrical floater, acting as a rotor, which drives a stator consisting of two banks of wound coils. The performance of such a device in waves depends on the hydrodynamics of the floater, the motion of which is strongly coupled to the electromagnetic properties of the generator. Mathematical models are developed to reveal the critical hurdles that can affect the efficiency of the design. A working physical unit is also constructed. The linear generator is first tested in a dry environment to quantify its performance. The complete physical floater and generator system is then tested in a wave tank with a computer-controlled wavemaker. Measurements are compared with theoretical predictions to allow an assessment of the viability of the design and future directions for improvements.

Nonlinear free-surface flow at a two-dimensional bow

Unsteady free-surface flow at the bow of a steadily moving, two-dimensional body is solved using a modified Eulerian-Lagrangian technique. Lagrangian marker particles are distributed on both the free surface and the far-field boundary. The flow field corresponding to an inviscid, double-body solution is used for the initial condition. Solutions are obtained over a range of Froude numbers for bodies of three different shapes: a vertical step, a faired profile and a bulbous bow. A transition Froude number exists at which the bow wave begins to overturn and break The value of the transition Froude number depends on the bow shape. A stagnation point is observed to be present below the free surface during the initial stage of the wave formation. For flows occurring above the transition Froude number, the stagnation points remains trapped below the free surface as the wave overturns. Below the transition Froude number, the stagnation point rises to the surface as the crest of the transient bow wave moves upstream and away from the body.

Nonlinear Model Predictive Control Applied to a Generic Ocean-Wave Energy Extractor

This paper evaluates the theoretical application of nonlinear model predictive control (NMPC) to a model-scale point absorber for wave energy conversion. The NMPC strategy will be evaluated against a passive system, which utilizes no controller, using a performance metric based on the absorbed energy. The NMPC strategy was setup as a nonlinear optimization problem utilizing the interior point optimizer (IPOPT) package to obtain a time-varying optimal generator damping from the power-take-off (PTO) unit. This formulation is different from previous investigations in model predictive control, as the current methodology only allows the PTO unit to behave as a generator, thereby unable to return energy to the waves. Each strategy was simulated in the time domain for regular and irregular waves, the latter taken from a modified Pierson–Moskowitz spectrum. In regular waves, the performance advantages over a passive system appear at frequencies near resonance while at the lower and higher frequencies they become nearly equivalent. For irregular waves, the NMPC strategy leads to greater energy absorption than the passive system, though strongly dependent on the prediction horizon. It was found that the ideal NMPC strategy required a generator that could be turned on and off instantaneously, leading to sequences where the generator can be inactive for up to 50% of the wave period.

Multihull and Surface-Effect Ship Configuration Design: A Framework for Powering Minimization

The powering issue of a high-speed marine vehicle with multihulls and air-cushion support is addressed, since there is an often need to quickly evaluate the effects of several configuration parameters in the early stage of the design. For component hulls with given geometry, the parameters considered include the relative locations of individual hulls and the relative volumetric ratios. Within the realm of linearized theory, an interference-resistance expression for hull-to-hull interaction is first reviewed, and then a new formula for hull-and-pressure distribution interference is derived. Each of these analytical expressions is expressed in terms of the Fourier signatures or Kochin functions of the interacting component hulls, with the separation, stagger, and speed as explicit parameters. Based on this framework, an example is given for assessing the powering performance of a catamaran (dihull) as opposed to a tetrahull system. Also examined is the wave resistance of a surface-effect ship of varying cushion support in comparison with that of a base line catamaran, subject to the constraint of constant total displacement.