Framework Of Potential Flow Theory Research Articles

Wave-Current Interaction Effects on the OC4 DeepCwind Semi-Submersible Floating Offshore Wind Turbine

In order to investigate the hydrodynamic performances of semi-submersible type floating offshore wind turbines (FOWTs), particularly the effect of body-wave-current interaction, the OC4 FOWT is considered in the presence of co-existing regular wave and uniform current fields. The wind loads are not considered at this stage. The problem is treated in the framework of potential-flow theory in the frequency domain, assuming waves of small steepness, and the solution is obtained by using a perturbation expansion method for the diffraction potential with respect to the normalized current speed. Analytical and numerical formulations have been used to treat the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for the derivation of the associated perturbation potential. The hydrodynamic loads were obtained after evaluating the pressure field around the multi-body configuration using three different computer codes. The results from the three computer codes compare very well with each other and with the numerical predictions of other investigators. Finally, the mean second-order drift forces are calculated by superposing their zero-current values with the corresponding current-dependent first-order corrections, with the latter being evaluated using a ‘heuristic’ approach.

Second-order wave loads on a floating bridge of T-type cross section

An analytical model for the complete second-order wave loads on a floating bridge of T-type cross section is established within the framework of potential flow theory. The first-order problem is solved using the matched eigenfunction expansion method (MEEM). Meanwhile, the second-order wave loads are divided into two distinct parts which are computed separately. The first part is dependent on the quadratic products of the first-order velocity potential and its derivative. It has been evaluated through two different ways. One is based on a direct pressure integration, i.e., a near-field method. To ensure a high accuracy of the computation, a local expansion is applied to determine the spatial derivative of the first-order velocity potential at a sharp corner. The other is based on the momentum conservation over a control volume. The effect of the control surface location on the computation has been discussed. In addition, the two proposed methods have been applied to both the time-independent wave-load component as well as the second-harmonic component, respectively. The second part of the complete second-order wave loads is due to the second-order velocity potential. It is evaluated based on an indirect method by introducing an auxiliary potential. Detailed numerical investigation is then conducted. The influence law of the sectional geometric parameters on the second-order wave loads is investigated. The numerical results reveal that the cantilever plate imposes an apparent protection effect on the inner web beam. Such effect gets obviously enhanced as the section net width or section height decreases or as the plate width or draft increases.

Oblique wave trapping by a permeable wall breakwater connected with thick surface porous layer

ABSTRACT The reflection of surface gravity waves by a vertical wall breakwater connected with a thick surface porous layer is analysed under the framework of potential flow theory. The thick surface porous layer is placed within the confined space available between the vertical permeable wall and the impermeable seawall. The analytical investigation is progressed by creating the hidden water chamber beneath the surface porous layer. The Matched Eigenfunction Expansion Method (MEEM) is used based on the continuity of velocity and pressure along with orthogonal mode-coupling relation. The hidden water chamber will be helpful to enhance the trapping of incident wave energy and also to reduce the quantity of construction material. The present study results are well agreed with the results available in the literature when a hidden water chamber is absent. The effect of permeable wall porosity, thick surface layer porosity, angle of wave contact, depth of the surface porous layer, thickness of the permeable wall, and hidden chamber spacing on wave reflection against incident wave properties and breakwater physical properties are studied. A comparative study is performed between three different types of porous breakwaters to investigate the integrity of the proposed breakwater. The minor value of wave reflection and gradual reduction of fluid force experienced by the rigid wall is achieved due to the presence of a surface layer, which maximises the incident wave damping, as most of the wave energy propagates near the free surface.

Numerical Investigation on Higher-Order Harmonic Waves Induced by a Submerged Inclined Plate

In this paper, a two-dimensional time-domain numerical flume has been established to model and investigate nonlinear interactions between nonlinear surface waves and a submerged inclined thin plate. The model solves the Laplace equation and the fully nonlinear free surface boundary conditions within the framework of potential flow theory based on the high-order boundary element method. The mixed Euler–Lagrangian method is applied to update the water surface at each time step, and the fourth-order Runge–Kutta method for time stepping. A so-called four-point method was employed to separate the second-order harmonic free and bounded wave that has the same wave frequency but different wave celerity in front of and behind the submerged plate. It is found that the amplitude of the second-order harmonic free wave increases with the inclination angle of the submerged plate, and the level/amount of the increase is larger for a larger wave steepness. In addition, the amplitudes of both the second-order reflected and transmitted waves are found to increase with the wave steepness, and their empirical relationships are derived for potential use in practical engineering.

Numerical investigation on evaluating nonlinear waves due to an air cushion vehicle in steady motion by a higher order desingularized boundary integral equation method

The problem of nonlinear ship waves generated by an air cushion vehicle is studied and modelled in the framework of potential flow theory. A higher order desingularized boundary integral equation method (HODBIEM) using Rankine source is developed. A stationary iterative method is adopted to solve the nonlinear free surface which is discretized into the inner area disturbed by cushion pressure and the outer undisturbed area. Techniques for numerical implementation are described in detail. To save computing time, grid density and domain size are refined.Both straight-ahead and yawed cases are considered for validations. Wave-making resistance versus various speeds in deep and shallow water are calculated for straight-ahead vehicles. The resistance curves obtained by HODBIEM agree well with results of nonlinear CFD simulations. The linear theory predicts higher peak value of resistance than nonlinear methods. The experimental data fit at low Froude number but deviate from numerical predictions when exceeding primary hump speed. Effects of speed and water depth are analyzed by wave patterns and wave profiles. Resistance, side force and yaw moment are calculated at Fn = 0.533 for drift angle from 0° to 90°. Satisfactory results are given by present method. Details about wave patterns and wave angles are discussed.

Semi-analytical study on an integrated-system with separated heaving OWC and breakwater: Structure size optimization and gap resonance utilization

To complement the topic on the integration of Oscillating Water Column (OWC) device with breakwater structures, a novel integrated system composed of an offshore heaving OWC device and a floating stationary breakwater with a certain length of gap between each other is proposed. Under the framework of potential flow theory, corresponding theoretical model is established and solved by decomposing the boundary-value problems into one wave scattering component and two radiation components. Apart from the examinations concentrating on the influences from the geometrical configuration of the breakwater, the gap distance between the OWC device and the breakwater is changed in a broad range to identify its effects on the interested hydrodynamic performance. It is found that for a specific wave frequency, when the gap distance is well-tuned against the wave length to satisfy the condition of sloshing mode happening inside the gap, power extraction efficiency is much likely to achieve its maximum extent. In this way, the optimization in terms of gap distance is proved to be effective in enhancing wave power capturing within a wider range of wave conditions.

Inclusion of a pitching mid-wall for a dual-chamber oscillating water column wave energy converter device

The concept of a dual-chamber oscillating water column (OWC) device consisting of a pitching mid-wall (restrained by an angle spring stiffness) is proposed and the corresponding theoretical model is established under the framework of potential flow theory. By employing the matched eigenfunction method along the common interfaces in terms of the velocity and pressure continuity, the present model can be numerically solved. A numerical strategy of successive approximation is utilized to determine the optimal turbine parameters for the optimal energy extraction. Some potential influential factors, including the linear density, installed location and draft of the mid-wall, chamber breadth and angle spring stiffness, are explored to analyze their impacts on the power extraction performance. It is found that the mid-wall in the dual-chamber structure with a relatively larger linear density and smaller draft is more beneficial for energy extraction. Under the condition that the dual-chamber structure is designed with a relatively wider size, an asymmetry configuration with a narrower front but a wider rear chamber is more recommended. In addition, a relatively smaller angle spring stiffness is advisable due to the occurrence of more satisfactory peak efficiency.

THEORETICAL METHOD OF THE OPTIMUM DESIGN OF A SUPERCAVITATING PROPELLER BLADE WITH SPOILER MOUNTED ON THE TRAILING EDGE

This paper presents theoretical design method to obtain 2-D optimum section with spoiler mounted on the trailing edge of a supercavitating propeller blade. Matched Asymptotic Expansions (MAE) is applied to determine the geometry of profile and cavity shape in the framework of potential flow theory. The blade section is of wedge-like shape and the opened cavity closure scheme is adopted. A typical section, on which the optimum blade design will be based, is singled out among the best individual sections from root to tip. The spoiler length of each hydrofoil section resulting from MAE method are finalized with CFD method so as to consider viscous effect under the same lift condition, others hydrofoil geometries being kept constant. The hydrodynamic performances of all blade sections being designed on the basis of the resulting typical section from linearized method are finally predicted with CFD method.

Semi-analytical study on the wave power extraction of a bottom-seated oscillating water column device with a pitching front lip-wall

A bottom-seated oscillating water column (OWC) device with a front lip-wall which is allowed to oscillate in a pitching mode is explored under the framework of potential flow theory. By utilizing the matched eigenfunction method and employing the continuity conditions along the adjacent common interfaces, the theoretical model can be transformed into a set of linear equations. Some potential influential factors, including the linear density (ρs) and draft (d) of the front lip-wall, the chamber breadth (b) and the imposed angle spring stiffness (K), are examined to study their effects on the wave power extraction performance. The results show that the inclusion of a pitching front lip-wall can effectively expand the frequency bandwidth of high-efficiency, especially under the geometry condition of a relatively larger front lip-wall draft and larger chamber breath. In addition, the examination of different spring stiffness K demonstrates that it is more beneficial for the energy extraction when K is designed as a relatively lower value or even set to 0.

Theoretical analysis on hydrodynamic performance for a dual-chamber oscillating water column device with a pitching front lip-wall

For the sake of extracting wave energy over a broader range of wave frequencies, dual-chamber OWC devices are more beneficial than the single-chamber one. In this paper, the concept of a dual-chamber OWC device with a pitching front lip-wall is proposed and by utilizing the matched eigenfunction method along the adjacent interfaces, present theoretical model developed under the framework of potential flow theory can be numerically solved. To determine the optimal turbine parameters combination of front and rear chamber for the optimal wave power extraction efficiency, a numerical method of successive approximation is employed. Parameters, including lip-wall drafts, installed location of mid lip-wall and angle spring stiffness are changed to explore effects on the hydrodynamic performance. It is found that when the device is designed with an asymmetry structure configuration, i.e., narrow front but wide rear, is more desirable and the optimal breadth ratio is 3:7. There exists a medium lip-wall draft condition which can satisfy stable operation and efficient performance simultaneously by including the pitching motion of front lip-wall. In addition, a relatively smaller spring stiffness (within the range of 105) is more recommended as the pitching motion of lip-wall can be adequately utilized to obtain a more satisfactory energy efficiency curve.

Local Enhancements of the Mean Drift Wave Force on a Vertical Column Shielded by an Exterior Thin Porous Shell

The wave interaction with a vertical column shielded by an exterior porous shell is studied within the framework of potential flow theory. The structures are fixed rigidly at the sea bottom. The interior cylinder is impermeable, and the exterior shell is slightly porous and thin. Additionally, the exterior shell is assumed to have fine pores, and a linear pressure drop is adopted at the porous geometry. The mean drift wave force on the system is thereby formulated by two alternative ways, based respectively on the direct pressure integration, i.e., the near-field formulation, and the application of the momentum conservation theorem in the fluid domain, i.e., the far-field formulation. The consistency of the two formulations in calculating the mean drift wave force is assessed for the present problem. Numerical results illustrate that the existence of the porous shell can substantially reduce the mean drift wave force on the interior column. It also appears that the far-field formulation consists of a conventional part as well as an additional part caused by the energy dissipation through the porous geometry. The mean drift wave force on the system is dominated by the first part, which resembles that on an impermeable body. Local enhancements of the mean drift wave force are found at some specific wave frequencies at which certain propagation modes of the fluid satisfy a no-flow condition at the porous shell.

A study on the added resistance of a catamaran advancing in waves considering variations of both operating and geometric parameters

ABSTRACT The study focuses on the analysis of the added resistance of a catamaran advancing both in regular waves and in a seaway. The numerical simulation has been carried out within the framework of potential flow theory by using a three dimensional, linear, Rankine source-based Boundary Element Method (BEM) and a Near-Field approach based on pressure integration for the first-order motions and the second-order longitudinal force prediction, respectively. A preliminary validation and verification study on both a mono-hull and a catamaran is proposed. A systematic analysis of the effect of some relevant operating and geometric parameters on the added resistance performance of a catamaran in waves is presented. Variations of the operating and geometric parameters include the advancing speed, the encounter angles from head to beam waves, the hull static trim and the demi-hulls separation. The trends of the added resistance pseudo-RAO are discussed in the light of the comparison against the reference design condition highlighting possible worse and optimal configurations.

A frequency-domain hybrid HOBEM for motion responses and added resistance of ships sailing in head and oblique waves

A hybrid higher-order boundary element method (HOBEM) within the framework of potential flow theory in frequency domain is developed for solving ship hydrodynamic problems with forward speed. The method introduces a wall-sided artificial control surface to decompose the fluid domain into two subdomains, one encompassing the ship and the other on the outside. To guarantee the radiation condition at infinite for any frequency, the translating-pulsating Green's function method with singularities distributed on the control surface is used in the outer domain. The panel integrals of the Green's function are evaluated by a robust and efficient semi-analytical scheme. In the inner domain, the Rankine panel method (RPM) is adopted, and the steady flow effects are considered in the free surface and body surface conditions. The integral equation imposed on the inner boundaries is discretized and solved by a numerical approach of HOBEM based on bi-quadratic isoparametric elements. By imposing the continuous conditions of velocity potential and its normal derivative on the control surface, the solutions in the two domains are matched and a coupled equation system is formulated for the velocity potential on boundaries. Through the calculations of radiation and diffraction forces on a mathematical ship model, the present method is proved to have good mesh convergence, and satisfactory results can be obtained in a relatively small computational domain.The present hybrid HOBEM is applied to evaluate the hydrodynamic responses of ships sailing in head and oblique waves. Numerical simulations are first conducted on the free motions of two slender ships (i.e., a modified Wigley hull and a non-wall-sided S175 containership) in head waves. By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating Green's function method and RPM, it is found that the present method is of better stability and accuracy, especially for the non-wall-sided ship. Then further investigations are conducted on the wave-induced motions and added resistance of S175, a newer container ship KCS and a full formed bulk carrier S-Cb84 with different forward speeds and heading angles. In all cases, the numerical results obtained by the present method are satisfactory in comparison with the experimental data.

Experimental investigation of a land-based dual-chamber OWC wave energy converter

Extensive investigation on wave energy converters (WEC) that convert wave power into electricity is required to improve competitiveness of wave energy, one of the most promising renewable energy resources. Better hydrodynamic performance should enable wave devices to compete favorably with conventional power plants in the near future. In this study the hydrodynamic performance of a land-based dual-chamber Oscillating Water Column (OWC) device is investigated experimentally, with emphasis on its overall performance and respective performance of the two sub-chambers of the system. The effects of the chamber breadth and the barrier wall draft on the hydrodynamic efficiency, the free surface elevation and the air pressure inside the chambers are investigated over a wide range of wave periods with a constant wave amplitude. Numerical simulations using fully nonlinear numerical wave tanks (NWTs) within the framework of potential flow theory are also carried out to cross-check the results, and help to further understand the experimental observations. It is found that both the maximum efficiency and the range of wave frequencies that leads to a higher rate of wave energy absorption, i.e. the effective frequency bandwidth, increase in the dual-chamber OWC system when compared to an equivalent typical single-chamber OWC device. The overall efficiency of the system is found to be insensitive to the variation of the sub-chamber breadth, while the efficiency of the two sub-chamber increases with its breadth when the total chamber breadth is kept the same. Additionally, the hydrodynamic efficiency is found to decrease with increasing barrier wall draft. The rear chamber (i.e., on the landward side) outperforms the front chamber (i.e., on the seaward side) for most of the wave frequencies investigated in this study, especially for the wave frequency that is at or close to the resonance frequency of the system.

Radiation of waves by a cylinder submerged in water with ice floe or polynya

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.

On energy arguments applied to the hydrodynamic impact force

The hydrodynamic impact problem is investigated within the framework of potential-flow theory. The vertical load acting on the rigid body is derived based on either momentum or energy conservation, and using the concept of added mass together with a homogeneous Dirichlet condition for the potential on the free surface as usually done to model an impact problem. It is demonstrated that the use of this simplified dynamic free-surface condition, instead of the fully nonlinear one, has a direct influence on the computation of the loads. In particular, the equivalence of momentum and energy analysis is in general not recovered. The situation is then highlighted by performing an asymptotic analysis of the two-dimensional blunt-body asymmetric impact problem. The asymptotic solution is given explicitly and validated through comparisons with experimental results. The energy distribution is then studied. It is shown that the contradiction between momentum and energy analysis can be removed, provided that the flux of energy through the jets is taken into account in the energy balance. If the simplified free-surface condition is indeed valid in the far-field, nonlinear terms must be retained near the body, in the spray-root domains. To leading order, the energy distribution during the gravity-free inertia stage does not depend on the blunt-body shape. The general analysis based on momentum or energy conservation suggests that this result also applies for arbitrary body shape as soon as a homogeneous Dirichlet condition can be applied as a dynamical free-surface boundary condition. In this case, and for a constant vertical impact velocity, half the work performed by the body would seem to be transferred to the fluid as kinetic energy within the spray.

New insight into the generation of ship bow waves

The generation of ship bow waves is studied within the framework of potential flow theory. Assuming the ship bow to be slender, or thin, a pattern of the flow is derived using the method of matched asymptotic expansions. This method leads to the determination of three different zones in which three asymptotic expansions are performed and matched. To first order with respect to the slenderness parameter, the near-field flow appears to be two-dimensional in each transverse plane along the bow. However, it is demonstrated that three-dimensional effects are important in front of the ship and must be taken into account in the composite solution. This leads to a three-dimensional correction to be added to the two-dimensional solution along the ship. The asymptotic approach is then applied to explain the structure of the bow flow in connection with experimental observations and numerical simulations.

Flow in a stratum in the case of pumping from an imperfect well near a basin

A study is made of the three-dimensional stationary problem of the flow of ground water to a well of the type of a point sink in a stratum of unbounded thickness in one direction. The stratum is bounded at the top by the bottom of the basin and a stratum of impermeable ground. The problem is investigated in the framework of potential flow theory based on Darcy's law [1, 2], and the solution is obtained in the form of quadratures.