A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient (C_r). The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x². A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s (1976) method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.

The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics (CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.

The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(<<1), which measures the smallness of the deformation, the governing Boundary Value Problem (BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green’s integral theorem with the introduction of suitable Green’s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.

Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method (IBEM) and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground (WIG) effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a ° Angle of Attack (AoA) which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.

This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients (C_R, C_T, and C_E) for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the C_R increases with increasing wave number, kd, and with a decreasing permeable wall part, dm. The C_T follows the opposite trend. The C_E slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the C_R, while increasing the C_T. At lower values of kd, a decreasing porosity increases the C_E, but for high values of kd, a decreasing porosity reduces the C_E. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd<0.5. Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd >0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.

The unsteady performance of drag and double reverse propeller podded propulsors in open water was numerically simulated using a computational fluid dynamics(CFD) method.A moving mesh method was used to more realistically simulate propulsor working conditions, and the thrust, torque, and lateral force coefficients of both propulsors were compared and analyzed. Forces acting on different parts of the propulsors along with the flow field distribution of steady and unsteady results at different advance coefficients were compared.Moreover, the change of the lateral force and the difference between the abovementioned two methods were mainly analyzed.It was shown that the thrust and torque results of both methods were similar, with the lateral force results having the highest deviation.

A flow field around a streamlined body at an intermediate angle of incidence is dominated by cross-flow separation and vortical flow fields. The separated flow leads to a pair of vortices on the leeside of the body; therefore, it is essential to accurately determine this pair and estimate its size and location. This study utilizes the element-based finite volume method based on RANS equations to compute a 3D axisymmetric flow around a SUBOFF bare submarined hull. Cross-flow vortex structures are then numerically simulated and compared for a submarine with SUBOFF and DRDC STR bows. Computed results of pressure and shear stress distribution on the hull surface and the strength and locations of the vortex structures are presented at an intermediate incidence angle of 20°. A wind tunnel experiment is also conducted to experimentally visualize the vortex structures and measure their core locations. These experimental results are compared with the numerical data, and a good agreement is found.

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.

In this paper, a numerical study of flow in the turbulence boundary layer with adverse and pressure gradients (APGs) is conducted by using Reynolds-averaged Navier-Stokes (RANS) equations. This research chooses six typical turbulence models, which are critical to the computing precision, and to evaluating the issue of APGs. Local frictional resistance coefficient is compared between numerical and experimental results. The same comparisons of dimensionless averaged velocity profiles are also performed. It is found that results generated by Wilcox (2006) k-ω are most close to the experimental data. Meanwhile, turbulent quantities such as turbulent kinetic energy and Reynolds-stress are also studied.

In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform finite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.

The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green’s integral theorem with the introduction of appropriate Green’s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method (FVM) is applied to solve Reynolds averaged Navier-Stokes (RANS) equation. The realizable k-ε turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid (VOF) method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull’s movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattern and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull’s heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships’ movement, wave and hydrodynamics.

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji’s method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration (A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.

The numerical simulation of wake and free-surface flow around ships is a complex topic that involves multiple tasks: the generation of an optimal computational grid and the development of numerical algorithms capable to predict the flow field around a hull. In this paper, a numerical framework is developed aimed at high-resolution CFD simulations of turbulent, free-surface flows around ship hulls. The framework consists in the concatenation of “tools”, partly available in the open-source finite volume library OpenFOAM?. A novel, flexible mesh-generation algorithm is presented, capable of producing high-quality computational grids for free-surface ship hydrodynamics. The numerical frame work is used to solve some benchmark problems, providing results that are in excellent agreement with the experimental measures.

Recently, Morabito (2010) has studied the water spray phenomena in planing hulls and presented new analytical equations. However, these equations have not been used for detailed parametric studies of water spray around planing hulls. In this paper, a straight forward analysis is conducted to apply these analytical equations for finding the spray geometry profile by developing a computer program based on presented computational process. The obtained results of the developed computer program are compared against existing data in the literature and favorable accuracy is achieved. Parametric studies have been conducted for different physical parameters. Positions of spray apex are computed and three dimensional profiles of spray are examined. It is concluded that spray height increases by an increase in the speed coefficient or the deadrise angle. Ultimately, a computational process is added to Savitsky’s method and variations of spray apex are computed for different velocities. It is shown that vertical, lateral, and longitudinal positions of spray increase as the craft speed increases. On the other hand, two new angles are defined in top view and it is concluded that they have direct relation with the trim angle. However, they show inverse relation with the deadrise angle.

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.

As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics (CFD). A numerical study of one transitional flow in two-dimensional is conducted by Reynolds averaged numerical simulation (RANS) in this paper. Turbulence model plays a significant role in the complex flows’ simulation, and four advanced turbulence models are evaluated. Numerical solution of frictional resistance coefficient is compared with the measured one in the transitional zone, which indicates that Wilcox (2006) k-ω model with correction is the best candidate. Comparisons of numerical and analytical solutions for dimensionless velocity show that averaged streamwise dimensionless velocity profiles correct the shape rapidly in transitional region. Furthermore, turbulence quantities such as turbulence kinetic energy, eddy viscosity, and Reynolds stress are also studied, which are helpful to learn the transition’s behavior.

Oblique ocean wave damping by a vertical porous structure placed on a multi-step bottom topography is studied with the help of linear water wave theory. Some portion of the oblique wave, incident on the porous structure, gets reflected by the multi-step bottom and the porous structure, and the rest propagates into the water medium following the porous structure. Two cases are considered: first a solid vertical wall placed at a finite distance from the porous structure in the water medium following the porous structure and then a special case of an unbounded water medium following the porous structure. In both cases, boundary value problems are set up in three different media, the first medium being water, the second medium being the porous structure consisting of p vertical regions-one above each step and the third medium being water again. By using the matching conditions along the virtualvertical boundaries, a system of linear equations is deduced. The behavior of the reflection coefficient and the dimensionless amplitude of the transmitted progressive wave due to different relevant parameters are studied. Energy loss due to the propagation of oblique water wave through the porous structure is also carried out. The effects of various parameters, such as number of evanescent modes, porosity, friction factor, structure width, number of steps and angle of incidence, on the reflection coefficient and the dimensionless amplitude of the transmitted wave are studied graphically for both cases. Number of evanescent modes merely affects the scattering phenomenon. But higher values of porosity show relatively lower reflection than that for lower porosity. Oscillation in the reflection coefficient is observed for lower values of friction factor but it disappears with an increase in the value of friction factor. Amplitude of the transmitted progressive wave is independent of the porosity of the structure. But lower value of friction factor causes higher transmission. The investigation is then carried out for the second case, i.e., when the wall is absent. The significant difference between the two cases considered here is that the reflection due to a thin porous structure is very high when the solid wall exists as compared to the case when no wall is present. Energy loss due to different porosity, friction factor, structure width and angle of incidence is also examined. Validity of our model is ascertained by matching it with an available one.

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.

Obliquely incident water wave scattering by an uneven channel-bed in the form of a small bottom undulation in a two-layer fluid is investigated within the frame work of three-dimensional linear water wave theory. The upper fluid is assumed to be bounded above by a rigid lid, while the lower one is bounded below by a bottom surface having a small deformation and the channel is unbounded in the horizontal directions. Assuming irrotational motion, perturbation technique is employed to calculate the first-order corrections to the velocity potentials in the two fluids by using Fourier transform approximately, and also to calculate the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that the reflection coefficient is an oscillatory function of the ratio of twice the component of the wave number along x-axis and the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large.

This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algorithm’s cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model (IMM) algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for engineering applications.

In the present study, a new approach is applied to the cavity prediction for two-dimensional (2D) hydrofoils by the potential based boundary element method (BEM). The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by the use of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code (FLUENT). Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.

An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0? to 22.5?. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.

This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method (BEM). Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes (1) vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, (2) liquid droplets or column impact as well as wave impact on a body, (3) similarity solution of an expanding body. It covers two dimensional (2D), axisymmetric and three dimensional (3D) cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.

This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The obtained difference non-linear coupled equations are solved by Newton’s method and satisfactory results were achieved. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.

Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace’s equation by a method based on Green’s integral theorem with the introduction of appropriate Green’s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.

This paper investigates mathematical modelling of response amplitude operator (RAO) or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency ( ) varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.

To solve the problems concerning water entry of a structure, the RANS equations and volume of fluid (VOF) method are used. Combining the user-defined function (UDF) procedure with dynamic grids, the water impact on a structure in free fall is simulated, and the velocity, displacement and the pressure distribution on the structure are investigated. The results of the numerical simulation were compared with the experimental data, and solidly consistent results have been achieved, which validates the numerical model. Therefore, this method can be used to study the water impact problems of a structure.

The higher-order boundary element method is applied to the numerical simulation of nonlinear waves radiated by a forced oscillating fully submerged vertical circular cylinder. In this time-domain approach, the mixed boundary value problem based on an Eulerian description at each time step is solved using the higher order boundary element method. The 4th-order Runge–Kutta scheme is adopted to update the free water surface boundary conditions expressed in a Lagrangian formulation. Following completion of the numerical model, the problems of radiation (heave) of water waves by a submerged sphere in finite depth are simulated and the computed results are verified against the published numerical results in order to ensure the effectiveness of the model. The validated numerical model is then applied to simulate the nonlinear wave radiation by a fully submerged vertical circular cylinder undergoing various forced sinusoidal motion in otherwise still conditions. The numerical results are obtained for a series of wave radiation problems; the completely submerged cylinder is placed in surging, heaving and combined heave-pitching motions with different drafts, amplitudes and frequencies. The corresponding numerical results of the cylinder motions, wave profiles, and hydrodynamic forces are then compared and explained for all the cases.

In order to study the effects of geometric parameters of the rudder on the hydrodynamic performance of the propeller-rudder system, the surface panel method is used to build the numerical model of the steady interaction between the propeller and rudder to analyze the relevant factors. The interaction between the propeller and rudder is considered through the induced velocities, which are circumferentially averaged, so the unsteady problem is translated to steady state. An iterative calculation method is used until the hydrodynamic performance converges. Firstly, the hydrodynamic performance of the chosen propeller-rudder system is calculated, and the comparison between the calculated results and the experimental data indicates that the calculation program is reliable. Then, the variable parameters of rudder are investigated, and the calculation results show that the propeller-rudder spacing has a negative relationship with the efficiency of the propeller-rudder system, and the rudder span has an optimal match range with the propeller diameter. Futhermore, the rudder chord and thickness both have a positive correlation with the hydrodynamic performance of the propeller-rudder system.

On March 26, 2010 an underwater explosion (UWE) led to the sinking of the ROKS Cheonan. The official Multinational Civilian-Military Joint Investigation Group (MCMJIG) report concluded that the cause of the underwater explosion was a 250 kg net explosive weight (NEW) detonation at a depth of 6?9 m from a DPRK “CHT-02D” torpedo. Kim and Gitterman (2012a) determined the NEW and seismic magnitude as 136 kg at a depth of approximately 8m and 2.04, respectively using basic hydrodynamics based on theoretical and experimental methods as well as spectral analysis and seismic methods. The purpose of this study was to clarify the cause of the UWE via more detailed methods using bubble dynamics and simulation of propellers as well as forensic seismology. Regarding the observed bubble pulse period of 0.990 s, 0.976 s and 1.030 s were found in case of a 136 NEW at a detonation depth of 8 m using the boundary element method (BEM) and 3D bubble shape simulations derived for a 136 kg NEW detonation at a depth of 8 m approximately 5 m portside from the hull centerline. Here we show through analytical equations, models and 3D bubble shape simulations that the most probable cause of this underwater explosion was a 136 kg NEW detonation at a depth of 8m attributable to a ROK littoral “land control” mine (LCM).

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid, is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate. In such a two-layer fluid there exist waves with two different modes, one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface. An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes. Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes. One special type of bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.

Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching. The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation, the boundary conditions on the free surface and on the sea bed. The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls. In the paper, the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy’s law. Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant. Wave loading on the outer and inner cylinder is presented in the numerical results.

The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here. The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate. Using the Green’s function technique, from this boundary condition, the normal velocity of the plate is expressed in terms of the difference between the velocity potentials (unknown) across the plate. The two ends of the plate are either clamped or free. The reflection and transmission coefficients are obtained in terms of the integrals’ involving combinations of the unknown velocity potential on the two sides of the plate, which satisfy three simultaneous integral equations and are solved numerically. These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.

Nowadays, there are many studies conducted in the field of marine hydrodynamics which focus on two vessels traveling and floating in sufficiently close proximity to experience significant interactions. The hydrodynamic behavior of parallel moving ships in waves is an interesting and important topic of late. A numerical investigation has been carried out for the prediction of wave exciting forces and motion responses of parallel moving ships in regular waves. The numerical solution was based on 3D distribution technique and using the linear wave theory to determine the exciting forces and ship’s motion. The speed effects have been considered in the Green function for more realistic results. The numerical computations of wave exciting forces and motion responses were carried out for a Mariner and Series 60 for the purpose of discovering different Froude numbers and different separation distances in head sea conditions. Based on the numerical computations, it was revealed that the sway, roll and yaw have a significant effect due to hydrodynamic interaction.

In this research, a commercial CFD code “Fluent” was applied to optimization of bulbous bow shape for a non ballast water ships (NBS). The ship was developed at the Laboratory of the authors in Osaka Prefecture University, Japan. At first, accuracy of the CFD code was validated by comparing the CFD results with experimental results at towing tank of Osaka Prefecture University. In the optimizing process, the resistances acting on ships in calm water and in regular head waves were defined as the object function. Following features of bulbous bow shapes were considered as design parameters: volume of bulbous bow, height of its volume center, angle of bow bottom, and length of bulbous bow. When referring to the computed results given by the CFD like resistance, pressure and wave pattern made by ships in calm water and in waves, an optimal bow shape for ships was discovered by comparing the results in the series of bow shapes. In the computation on waves, the ship is in fully captured condition because shorter waves, λ/Lpp<0.6, are assumed.

In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders. The fluid was considered to be inviscid and irrotational. Therefore, the Helmholtz equation was used as a governing equation. The boundary element method (BEM) was adopted to discretize the relevant equations. Open boundaries were used in far fields of the study domain. Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them. Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders, ka and kd on forces and trapped modes. The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data. The comparisons confirm the accuracy of the model. The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders. Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0. Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.

In this paper, various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified -transformation. Based on this new numerical algorithm, a numerical study on a regularly and randomly excited container in vertical direction was conducted utilizing four different cases: The first case was performed utilizing a 2D container with regular excitations. The next case examined a regularly excited 3D container with two different initial conditions for the liquid free surface, and finally, 3D container with random excitation in the vertical direction. A grid independence study was performed along with a series of validation tests. An iteration error estimation method was used to stop the iterative solver (used for solving the discretized governing equations in the computational domain) upon reaching steady state of results at each time step. In the present case, this method was found to produce quite accurate results and to be more time efficient as compared to other conventional stopping procedures for iterative solvers. The results were validated with benchmark results. The wave elevation time history, phase plane diagram and surface plots represent the wave nonlinearity during its motion.

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method (FDM) and finite element method (FEM) was developed to analyze the fluid structure interaction (FSI) problem. The FDM, in which the Constraint Interpolation Profile (CIP) method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting (THINC/SW) scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary (IB) method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.

In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104 < Re<1.54×106. The calculations were performed by means of solving the 2-D Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with a turbulence model. The calculated results, produced flow structure drag and lift coefficients, as well as Strouhal numbers. The findings were in good agreement with previous published data, which also supplied us with a good understanding of the flow across cylinders of different high Reynolds numbers. Meanwhile, an effective measure was presented to control the lift force on a cylinder, which points the way to decrease the vortex induced vibration of marine structure in future.

Under the background of the energy saving and emission reduction, more and more attention has been placed on investigating the energy efficiency of ships. The added resistance has been noted for being crucial in predicting the decrease of speed on a ship operating at sea. Furthermore, it is also significant to investigate the added resistance for a ship functioning in short waves of large modern ships. The researcher presents an estimation formula for the calculation of an added resistance study in short waves derived from the reflection law. An improved method has been proposed to calculate the added resistance due to ship motions, which applies the radiated energy theory along with the strip method. This procedure is based on an extended integral equation (EIE) method, which was used for solving the hydrodynamic coefficients without effects of the irregular frequency. Next, a combined method was recommended for the estimation of added resistance for a ship in the whole wave length range. The comparison data with other experiments indicate the method presented in the paper provides satisfactory results for large blunt ship.

A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green’s second identity to the potential functions and appropriate Green’s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.

In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length (CSCL) iteration and cavity shape for fixed cavitation number (CSCN) iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.

The quarter-circular caisson breakwater (QCB) is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.

Numerical simulation is investigated to disclose how propeller boss cap fins (PBCF) operate utilizing Reynolds-averaged Navier–Stokes (RANS) method. In addition, exploration of the influencing mechanism of PBCF on the open water efficiency of one controllable-pitch propeller is analyzed through the open water characteristic curves, blade surface pressure distribution and hub streamline distribution. On this basis, the influence of parameters including airfoil profile, diameter, axial position of installation and circumferential installation angle on the open water efficiency of the controllable-pitch propeller is investigated. Numerical results show: for the controllable-pitch propeller, the thrust generated is at the optimum when the radius of boss cap fins is 1.5 times of propeller hub with an optimal installation position in the axial direction, and its optimal circumferential installation position is the midpoint of the extension line of the front and back ends of two adjacent propeller roots in the front of fin root. Under these optimal parameters, the gain of open water efficiency of the controllable-pitch propeller with different advance velocity coefficients is greater than 0.01, which accounts for approximately an increase of 1%-5% of open water efficiency.

Offshore observation platforms are required to have great ability to resist waves when they are operating at sea. Investigation on the motion characteristics of the platforms in the sea can provide significant reference values during the platform design procedure. In this paper, a series of numerical simulation on the interaction of a triple-hulled offshore observation platform with different incident waves is carried out. All of the simulations are implemented utilizing our own solver naoe-FOAM-SJTU, which is based and developed on the open source tools of OpenFOAM. Duration curves of motion characteristics and loads acting on the platform are obtained, and a comparison between the results of the amplitude in different incident waves is presented. The results show that the solver is competent in the simulation of motion response of platforms in waves.

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

The most complicated component in cavitating flow and pressure distribution is the flow in the cavity closure line. The cavitating flow and pressure distribution provide critical aspects of flow field details in the region. The integral of pressure results of the hydrodynamic forces, indicate domination in the design of a supercavitating vehicle. An experiment was performed in a water tunnel to investigate the pressure characteristics of the cavity closure region. Ventilation methods were employed to generate artificial cavity, and the ventilation rate was adjusted accordingly to obtain the desired cavity length. An array of pressure transducers was laid down the cavity closure line to capture pressure distribution in this region. The experimental results show that there is a pressure peak in the cavity closure region, and the rise rate of pressure in space tends to be higher in the upwind side when the flow is non-axisymmetric. The transient pressure variations during the cavity formation procedure were also present. The method of measurement in this paper can be referenced by engineers. The result helps to study the flow pattern of cavity closure region, and it can also be used to analyze the formation of supercavitating vehicle hydrodynamics.

The numerical prediction of added resistance and vertical ship motions of one ITTC (International Towing Tank Conference) S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SJTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions (heave and pitch motions) with four very different wavelengths ( ) in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.

Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure (Yan and Ma, 2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)’s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.

Sloshing of liquid can increase the dynamic pressure on the storage sidewalls and bottom in tanker ships and LNG careers. Different geometric shapes were suggested for storage tank to minimize the sloshing pressure on tank perimeter. In this research, a numerical code was developed to model liquid sloshing in a rectangular partially filled tank. Assuming the fluid to be inviscid, Laplace equation and nonlinear free surface boundary conditions are solved using coupled FEM-BEM. The code performance for sloshing modeling is validated against available data. To minimize the sloshing pressure on tank perimeter, rectangular tanks with specific volumes and different aspect ratios were investigated and the best aspect ratios were suggested. The results showed that the rectangular tank with suggested aspect ratios, not only has a maximum surrounded tank volume to the constant available volume, but also reduces the sloshing pressure efficiently.

This paper presents a study on the numerical simulation of planing crafts sailing in regular waves. This allows an accurate estimate of the seas keeping performance of the high speed craft. The simulation set in six-degree of freedom motions is based on the Reynolds averaged Navier Stokes equations volume of fluid (RANSE VOF) solver. The trimming mesh technique and integral dynamic mesh method are used to guarantee the good accuracy of the hydrodynamic force and high efficiency of the numerical simulation. Incident head waves, oblique waves and beam waves are generated in the simulation with three different velocities (Fn =1.0, 1.5, 2.0). The motions and sea keeping performance of the planing craft with waves coming from different directions are indicated in the flow solver. The ship designer placed an emphasis on the effects of waves on sailing amplitude and pressure distribution of planing craft in the configuration of building high speed crafts.

As well as shock wave and bubble pulse loading, cavitation also has very significant influences on the dynamic response of surface ships and other near-surface marine structures to underwater explosive loadings. In this paper, the acoustic-structure coupling method embedded in ABAQUS is adopted to do numerical analysis of underwater explosion considering cavitation. Both the shape of bulk cavitation region and local cavitation region are obtained, and they are in good agreement with analytical results. The duration of reloading is several times longer than that of a shock wave. In the end, both the single computation and parallel computation of the cavitation effect on the dynamic responses of a full-scale ship are presented, which proved that reloading caused by cavitation is non-ignorable. All these results are helpful in understanding underwater explosion cavitation effects.

Ship hull form of the underwater area strongly influences the resistance of the ship. The major factor in ship resistance is skin friction resistance. Bulbous bows, polymer paint, water repellent paint (highly water-repellent wall), air injection, and specific roughness have been used by researchers as an attempt to obtain the resistance reduction and operation efficiency of ships. Micro-bubble injection is a promising technique for lowering frictional resistance. The injected air bubbles are supposed to somehow modify the energy inside the turbulent boundary layer and thereby lower the skin friction. The purpose of this study was to identify the effect of injected micro bubbles on a navy fast patrol boat (FPB) 57 m type model with the following main dimensions: L=2 450 mm, B=400 mm, and T=190 mm. The influence of the location of micro bubble injection and bubble velocity was also investigated. The ship model was pulled by an electric motor whose speed could be varied and adjusted. The ship model resistance was precisely measured by a load cell transducer. Comparison of ship resistance with and without micro-bubble injection was shown on a graph as a function of the drag coefficient and Froude number. It was shown that micro bubble injection behind the mid-ship is the best location to achieve the most effective drag reduction, and the drag reduction caused by the micro-bubbles can reach 6%–9%.

The problem of oblique wave (internal wave) propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green’s integral theorem suitably with the introduction of appropriate Green’s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples (having the same wave number) shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to . These theoretical observations are supported by graphical results.

A computer code based on the double-body potential flow model and the classic source panel method has been developed to study various problems of hydrodynamic interaction between ships and other objects with solid boundaries including the seabed. A peculiarity of the proposed implementation is the application of the so-called “moving-patch” method for simulating steady boundaries of large extensions. The method is based on an assumption that at any moment just the part of the boundary (“moving patch”) which lies close to the interacting ship is significant for the near-field interaction. For a specific case of the flat bottom, comparative computations were performed to determine optimal dimensions of the patch and of the constituting panels based on the trade-off between acceptable accuracy and reasonable efficiency. The method was applied to estimate the sway force on a ship hull moving obliquely across a dredged channel. The method was validated for a case of ship-to-ship interaction when tank data were available. This study also contains a description of a newly developed spline approximation algorithm necessary for creating consistent discretizations of ship hulls with various degrees of refinement.

Computational fluid dynamics (CFD) plays a major role in predicting the flow behavior of a ship. With the development of fast computers and robust CFD software, CFD has become an important tool for designers and engineers in the ship industry. In this paper, the hull form of a ship was optimized for total resistance using CFD as a calculation tool and a genetic algorithm as an optimization tool. CFD based optimization consists of major steps involving automatic generation of geometry based on design parameters, automatic generation of mesh, automatic analysis of fluid flow to calculate the required objective/cost function, and finally an optimization tool to evaluate the cost for optimization. In this paper, integration of a genetic algorithm program, written in MATLAB, was carried out with the geometry and meshing software GAMBIT and CFD analysis software FLUENT. Different geometries of additive bulbous bow were incorporated in the original hull based on design parameters. These design variables were optimized to achieve a minimum cost function of “total resistance”. Integration of a genetic algorithm with CFD tools proves to be effective for hull form optimization.

The computational fluid dynamics (CFD) method is used to numerically simulate a propeller wake flow field in open water. A sub-domain hybrid mesh method was adopted in this paper. The computation domain was separated into two sub-domains, in which tetrahedral elements were used in the inner domain to match the complicated geometry of the propeller, while hexahedral elements were used in the outer domain. The mesh was locally refined on the propeller surface and near the wake flow field, and a size function was used to control the growth rate of the grid. Sections at different axial location were used to study the spatial evolution of the propeller wake in the region ranging from the disc to one propeller diameter (D) downstream. The numerical results show that the axial velocity fluctuates along the wake flow; radial velocity, which is closely related to vortices, attenuates strongly. The trailing vortices interact with the tip vortex at the blades’ trailing edge and then separate. The strength of the vortex shrinks rapidly, and the radius decreases 20% at one diameter downstream.

In this research, liquid sloshing behavior in a 2-D rectangular tank was simulated using ANSYS-FLUENT software subject to single or multiple-coupled external excitations (such as sway coupled with roll, and sway and roll coupled with heave). The volume of fluid (VOF) method was used to track the free surface of sloshing. External excitation was imposed through the motion of the tank by using the dynamic mesh technique. The study shows that if the tank is subjected to multiple coupled excitations and resonant excitation frequencies, liquid sloshing will become violent and sloshing loads, including impact on the top wall, will be intensified.

In order to provide instructions for the calculation of the propeller induced velocity in the study of the hull-propeller interaction using the body force approach, three methods were used to calculate the propeller induced velocity: 1) Reynolds-Averaged Navier-Stokes (RANS) simulation of the self-propulsion test, 2) RANS simulation of the propeller open water test, and 3) momentum theory of the propeller. The results from the first two methods were validated against experimental data to assess the accuracy of the computed flow field. The thrust identity method was adopted to obtain the advance velocity, which was then used to derive the propeller induced velocity from the total velocity field. The results computed by the first two approaches were close, while those from the momentum theory were significantly overestimated. The presented results could prove to be useful for further calculations of self-propulsion using the body force approach.

Planing vessels are applied widely in civil and military situations. Due to their high speed, the motion of planning vessels is complex. In order to predict the motion of planning vessels, it is important to analyze the hydrodynamic performance of planning vessels at high speeds. The computational fluid dynamic method (CFD) has been proposed to calculate hydrodynamic performance of planning vessels. However, in most traditional CFD approaches, model tests or empirical formulas are needed to obtain the running attitude of the planing vessels before calculation. This paper presents a new CFD method to calculate hydrodynamic forces of planing vessels. The numerical method was based on Reynolds-Averaged Navier-Stokes (RANS) equations. The volume of fluid (VOF) method and the six-degrees-of-freedom equation were applied. An effective process was introduced to solve the numerical divergence problem in numerical simulation. Compared with experimental results, numerical simulation results indicate that both the running attitude and hydrodynamic performance can be predicted well at high speeds.

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.

In an atrocious ocean environment, the lateral propulsion hole could potentially be partly out of water and capture an air cavity. Bubbles would form when the captured air cavity escapes underwater and they may affect the performance of the sonar. The common commercial computational fluid dynamics software CFX was adopted to calculate the ambient flow field around the lateral propulsion hole generated by a moving vessel. The oscillation of the spherical bubble was based on the Rayleigh-Plesset equation and its migration was modeled using the momentum equation. The radiated noise of the oscillating bubble was also studied. The aim is that the results from this paper would provide some insight into corresponding fluid and acoustic study.

Extreme coastal events require careful prediction of wave forces. Recent tsunamis have resulted in extensive damage of coastal structures. Such scenarios are the result of the action of long waves on structures. In this paper, the efficiency of vegetation as a buffer system in attenuating the incident ocean waves was studied through a well controlled experimental program. The study focused on the measurement of forces resulting from cnoidal waves on a model building mounted over a slope in the presence and absence of vegetation. The vegetative parameters, along with the width of the green belt, its position from the reference line, the diameter of the individual stems as well as the spacing between them, and their rigidity are varied so as to obtain a holistic view of the wave-vegetation interaction problem. The effect of vegetation on variations of dimensional forces with a Keulegan-Carpenter number (KC) was discussed in this paper. It has been shown that when vegetal patches are present in front of structure, the forces could be limited to within F*?1, by a percentile of 92%, 90%, 55%, and 96%, respectively for gap ratios of 0.0, 0.5, 1.0, and 1.5. The force is at its maximum for the gap ratio of 1.0 and beyond which the forces start to diminish.

The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method (MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.

A set of parametric stress analyses was carried out for two-planar tubular DKT-joints under different axial loading conditions. The analysis results were used to present general remarks on the effects of the geometrical parameters on stress concentration factors (SCFs) at the inner saddle, outer saddle, and crown positions on the central brace. Based on results of finite element (FE) analysis and through nonlinear regression analysis, a new set of SCF parametric equations was established for fatigue design purposes. An assessment study of equations was conducted against the experimental data and original SCF database. The satisfaction of acceptance criteria proposed by the UK Department of Energy (UK DoE) was also checked. Results of parametric study showed that highly remarkable differences exist between the SCF values in a multi-planar DKT-joint and the corresponding SCFs in an equivalent uni-planar KT-joint having the same geometrical properties. It can be clearly concluded from this observation that using the equations proposed for uni-planar KT-connections to compute the SCFs in multi-planar DKT-joints will lead to either considerably under-predicting or over-predicting results. Hence, it is necessary to develop SCF formulae specially designed for multi-planar DKT-joints. Good results of equation assessment according to UK DoE acceptance criteria, high values of correlation coefficients, and the satisfactory agreement between the predictions of the proposed equations and the experimental data guarantee the accuracy of the equations. Therefore, the developed equations can be reliably used for fatigue design of offshore structures.

This paper numerically investigates the influence of separation variation of the outriggers on the hydrodynamic performance of a high speed trimaran (HST) aiming at improving its applicability in diverse realistic disciplines. The present investigation was performed within the framework of the 2-D slender body method (SBM) by calculating the resistance of three symmetric trimaran series moving in a calm free surface of deep water. Each trimaran series comprises of 4681 configurations generated by considering 151 staggers (?50%≤α≤+100%), and 31 separations (100%≤β≤400%) for 81 Froude numbers (0.20≤Fn≤1.0). In developing the three trimaran series, Wigley?-st, AMECRC?-09, and NPL?-4a models were used separately for both the main and side hulls of each individual series models. A computer macro named Tri-PL? was created using the Visual Basic for Applications?. Tri-PL? sequentially interfaced Maxsurf? then Hullspeed? to generate the models of the three trimaran series together with their detailed hydrostatic particulars, followed by their resistance components. The numerical results were partially validated against the available published numerical calculations and experimental results, to benchmark the Tri-PL? macro and hence to rely on the analysis outcomes. A graph template was created within the framework of SigmaPlot? to visualize the significant results of the Tri-PL? properly.

Based on a volume of fluid two-phase model imbedded in the general computational fluid dynamics code FLUENT6.3.26, the viscous flow with free surface around a model-scaled KRISO container ship (KCS) was first numerically simulated. Then with a rigid-lid-free-surface method, the underwater flow field was computed based on the mixture multiphase model to simulate the bubbly wake around the KCS hull. The realizable k-ε two-equation turbulence model and Reynolds stress model were used to analyze the effects of turbulence model on the ship bubbly wake. The air entrainment model, which is relative to the normal velocity gradient of the free surface, and the solving method were verified by the qualitatively reasonable computed results.

An innovative hydrodynamic theory and numerical model were developed to help improve the efficiency, accuracy, and convergence of the numerical prediction of wave drift forces on two side-by-side deepwater floating bodies. The wave drift forces were expressed by the double integration of source strength and the corresponding Green function on the body surface, which is consistent with the far field formula based on momentum conservation and sharing the advantage of near field calculations providing the drift force on each body. Numerical results were validated through comparing the general far field model and pressure integral model, as well as the middle field model developed using the software HydroStar.

The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow. Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank. The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests.

A new approach that models lift and drag hydrodynamic force signals operating over cylindrical structures was developed and validated. This approach is based on stochastic auto regressive moving average with exogenous (ARMAX) input and its time-varying form, TARMAX. Model structure selection and parameter estimation were discussed while considering the validation stage. In this paper, the cylindrical structure was considered as a dynamic system with an incoming water wave and resulting forces as the input and outputs, respectively. The experimental data, used in this study, were collected from a full-scale rough vertical cylinder at the Delft Hydraulics Laboratory. The practicality of the proposed method and also its efficiency in structural modeling were demonstrated through applying two hydrodynamic force components. For this purpose, an ARMAX model is first used to capture the dynamics of the process, relating in-line forces provided by water waves; secondly, the TARMAX model was applied to modeling and analysis of the lift forces on the cylinder. The evaluation of the lift force by the TARMAX model shows the model is successful in modeling the force from the surface elevation.

A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid (VOF) method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio B/D was shown to have significant influence on the non-dimensional transverse wave force.

In this work, Green-Naghdi (GN) equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level (higher than 4) equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth . Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.

It is hypothesized that steady anguilliform swimming motion of aquatic animals is purely reactive such that no net vortex wake is left downstream. This is versus carangiform and tunniform swimming of fish, where vortex streams are shed from tail, fins, and body. But there the animal movements are such to produce partial vortex cancellation downstream in maximizing propulsive efficiency. In anguilliform swimming characteristic of the eel family, it is argued that the swimming motions are configured by the animal such that vortex shedding does not occur at all. However, the propulsive thrust in this case is higher order in the motion amplitude, so that relatively large coils are needed to produce relatively small thrust; the speeds of anguilliform swimmers are less than the carangiform and tunniform, which develop first order thrusts via lifting processes. Results of experimentation on live lamprey are compared to theoretical prediction which assumes the no-wake hypothesis. Two-dimensional analysis is first performed to set the concept. This is followed by three-dimensional analysis using slender-body theory. Slender-body theory has been applied by others in studying anguilliform swimming, as it is ideally suited to the geometry of the lamprey and other eel-like animals. The agreement between this new approach based on the hypothesis of wakeless swimming and the experiments is remarkably good in spite of the physical complexities.

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions. Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering. However, difficulties can still be found in some particular problems. In the following study, the LDQ was applied to solve the Sod shock tube problem. This problem is a very particular kind of problem, which challenges many common numerical methods. Three different examples were given for testing the robustness and accuracy of the LDQ. In the first example, in which common initial conditions and solving methods were given, the numerical oscillations could be found dramatically; in the second example, the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example; in the third example, the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity, causing the numerical oscillations to nearly disappear in the process of calculation. The numerical results presented demonstrate the detailed difficulties encountered in the calculations, which need to be improved in future work. However, in summary, the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.

In the present paper, the effect of a small bottom undulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated. A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order. The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth. This is a well known problem whose solution is available in the literature. From the second boundary value problem, the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation, by employing Green’s integral theorem. For a patch of sinusoidal ripples at the sea bottom, the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number. It is observed that resonant interaction of the wave generated, with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated, approaches unity. Also it is found that the resonance increases as the length of the barrier increases.

Various water wave problems involving an infinitely long horizontal cylinder floating on the surface water were investigated in the literature of linearized theory of water waves employing a general multipole expansion for the wave potential. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation (for non-oblique waves in two dimensions) or two-dimensional Helmholz equation (for oblique waves) satisfying the free surface condition and decaying rapidly away from the point of singularity. The method of constructing these wave-free potentials is presented here in a systematic manner for a number of situations such as deep water with a free surface, neglecting or taking into account the effect of surface tension, or with an ice-cover modelled as a thin elastic plate floating on water.

A numerical approach was performed to predict the propagation and transformation of nonlinear water waves. A numerical wave flume was developed based on the non-periodic high-order spectral (HOS) method. The flume was applied to analyze the effect of wave steepness and wavelength on the propagation of nonlinear waves. The results show that for waves of low steepness, the wave profile and the wave energy spectrum are stable, and that the propagation can be predicted by the linear wave theory. For waves of moderate steepness and steep waves, the effects associated with the interactions between waves in a wave group become significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position.

A numerical model was established for simulating wave impact on a horizontal deck by an improved incompressible smoothed particle hydrodynamics (ISPH). As a grid-less particle method, the ISPH method has been widely used in the free-surface hydrodynamic flows with good accuracy. The improvement includes the employment of a corrective function for enhancement of angular momentum conservation in a particle-based calculation and a new estimation method to predict the pressure on the horizontal deck. The simulation results show a good agreement with the experiment. The present numerical model can be used to study wave impact load on the horizontal deck.

The motion of the fins and control surfaces of underwater vehicles in a fluid is an interesting and challenging research subject. Typically the effect of fin oscillations on the fluid flow around such a body is highly unsteady, generating vortices and requiring detailed analysis of fluid-structure interactions. An understanding of the complexities of such flows is of interest to engineers developing vehicles capable of high dynamic performance in their propulsion and maneuvering. In the present study, a CFD based RANS simulation of a 3-D fin body moving in a viscous fluid was developed. It investigated hydrodynamic performance by evaluating the hydrodynamic coefficients (lift, drag and moment) at two different oscillating frequencies. A parametric analysis of the factors that affect the hydrodynamic performance of the fin body was done, along with a comparison of results from experiments. The results of the simulation were found in close agreement with experimental results and this validated the simulation as an effective tool for evaluation of the unsteady hydrodynamic coefficients of 3-D fins. This work can be further be used for analysis of the stability and maneuverability of fin actuated underwater vehicles.

For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh. In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method. Then artificial compressibility method, dual time-stepping technique and Roe’s approximate Riemann solver are adopted in the numerical scheme. Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.

The Reynolds-averaged Navier-Stokes (RANS) method, along with the Fluent software package, was used to study the steady and unsteady interaction of propellers and rudders with additional thrust fins. The sliding mesh model was employed to simulate unsteady interactions between the blades, the rudder and the thrust fins. Based on the numerical results, the pressure distribution on the propeller and the efficiency of the fins were calculated as a function of the attack angle. The RANS results were compared with results calculated by the potential method. It was found that the results for the potential method and the RANS method have good consistency, but they yield maximum efficiencies for the fins, and thus corresponding attack angles, that are not identical.

Applications of computational fluid dynamic (CFD) to the maritime industry continue to grow with the increasing development of computers. Numerical approaches have evolved to a level of accuracy which allows them to be applied for hydrodynamic computations in industry areas. Hydrodynamic tests, especially planar-motion-mechanism (PMM) tests are simulated by CFD software –FLUENT, and all of the corresponding hydrodynamic coefficients are obtained, which satisfy the need of establishing the simulation system to evaluate maneuverability of vehicles during the autonomous underwater vehicle scheme design stage. The established simulation system performed well in tests.

In this paper, the effects of forward speed on the lateral vibration of a slender structure in an infinite fluid are considered. By equating the bending stress of the structure with the hydrodynamic force acting on it, the equation which governs the fluid-structure interaction of a slender structure both vibrating and moving in water is obtained. Numerical results show that the influence of forward speed on the vibration of a slender structure in water is significant. It behaves like damping, reducing both natural frequencies and responses significantly.

This paper presents an improved unstructured grid immersed boundary method. The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain. The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain. The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS (volume of solid) method. A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph. The method is verified with flow past oscillating cylinder.

Fish are able to make good use of vortices. In a complex flow field, many fish continue to maintain both efficient cruising and maneuverability. Traditional man-made propulsion systems perform poorly in complex flow fields. With fish-like propulsion systems, it is important to pay more attention to complex flow fields. In this paper, the influence of vortices on the hydrodynamic performance of 2-D flapping-foils was investigated. The flapping-foil heaved and pitched under the influence of inflow vortices generated by an oscillating D-section cylinder. A numerical simulation was run based the finite volume method, using the computational fluid dynamics (CFD) software FLUENT with Reynolds-averaged Navier-Stokes (RANS) equations applied. In addition, dynamic mesh technology and post processing systems were also fully used. The calculations showed four modes of interaction. The hydrodynamic performance of flapping-foils was analyzed and the results compared with experimental data. This validated the numerical simulation, confirming that flapping-foils can increase efficiency by absorbing energy from inflow vortices.

In this paper, two novel numerical computation methods are introduced which have been recently developed at Research Institute for Applied Mechanics ( RIAM ), Kyushu University, for strongly nonlinear wave-body interaction problems, such as ship motions in rough seas and resulting green-water impact on deck. The first method is the CIP-based Cartesian grid method, in which the free surface flow is treated as a multi-phase flow which is solved using a Cartesian grid. The second method is the MPS method, which is a so-called particle method and hence no grid is used. The features and calculation procedures of these numerical methods are described. One validation computation against a newly conducted experiment on a dam break problem, which is also described in this paper, is presented.

Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-factorization method for calculating (LCEs) Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.

The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.

Smoothed particle hydrodynamics (SPH) is a Lagrangian meshless particle method. It is one of the best method for simulating violent free surface flows in fluids and solving large fluid deformations. Dam breaking is a typical example of these problems. The basis of SPH was reviewed, including some techniques for governing equation resolution, such as the stepping method and the boundary handling method. Then numerical results of a dam breaking simulation were discussed, and the benefits of concepts like artificial viscosity and position correction were analyzed in detail. When compared with dam breaking simulated by the volume of fluid (VOF) method, the wave profile generated by SPH had good agreement, but the pressure had only reasonable agreement. Improving pressure results is clearly an important next step for research.

Green-Naghdi (G-N) theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by “levels” where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fully nonlinear shallow water waves.

In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.

A finite volume algorithm was established in order to investigate two-dimensional hydrodynamic problems. These include viscous free surface flow interaction with free rigid bodies in the case of large and/or relative motions. Two-phase flow with complex deformations at the interface was simulated using a fractional step-volume of fluid algorithm. In addition, body motions were captured by an overlapping mesh system. Here, flow variables are transferred using a simple fully implicit non-conservative interpolation scheme which maintains the second-order accuracy of implemented spatial discretisation. Code was developed and an appropriate set of problems investigated. Results show good potential for development of a virtual hydrodynamics laboratory.

The authors designed three different front profiles for supercavitating vehicles based on cavity theory and the Granville streamlined equation are designed. Experiments were done using these front profiles in the Northwestern Polytechnical University high-speed water tunnel. The experiments indicated that the critical volume of gas required for supercavitation is affected by the axial distribution of the front-end’s slope. The experimental data showed critical gas flow rates required for the three designs were less than mod-1, with the greatest decrease 24%. The experimental results also showed the supercavitation generation speeds of the models were faster than mod-1 by up to 32.4%. This verifies that the front profile of a supercaviting vehicle effects supercavity generation speed and critical gas flow rates. The smaller the changes in axial distribution of pressure, the higher the supercavity generation speed. The smaller the changes in curvature distribution of axial, the smaller the critical gas flow rates.

Revetments of concrete frame tetrahedrons are being used more and more in river engineering in China. Due to their complex geometry, it is difficult to measure the velocity fields inside them using traditional measurement methods. This limits understanding of their mechanics, potentially leading to suboptimal solutions. A 3-D hydrodynamic model based on the commercial computational fluid dynamics (CFD) code, Fluent, was developed to predict velocity fields and drags. The realizable k-ε model was adopted for turbulent closure of the Reynolds averaged Navier Stokes (RANS) equations. The study demonstrates that the numerical model can effectively supplement experimental studies in understanding the complex flow fields and mechanics of concrete frame tetrahedron revetments. Graphs showing the drag coefficient CD versus Reynolds number Re and lift coefficient CL versus Reynolds number Re were produced.

A new numerical method was developed for predicting the steady hydrodynamic performance of ducted propellers. A potential based surface panel method was applied both to the duct and the propeller, and the interaction between them was solved by an induced velocity potential iterative method. Compared with the induced velocity iterative method, the method presented can save programming and calculating time. Numerical results for a JD simplified ducted propeller series showed that the method presented is effective for predicting the steady hydrodynamic performance of ducted propellers.

Demand for high-speed marine vehicles (HSMVs) is high among both commercial and naval users. It is the duty of the marine vessel’s designer to provide a hull and propulsion system that diminishes drag, improves propulsive efficiency, increases safety and improves maneuverability. From the propulsor side, surface piercing propellers (SPPs) should improve performance. Unlike immersed propellers, behavior of the SPP is affected by depth of immersion, Weber number and shaft inclination angle. This paper uses a practical numerical method to predict the hydrodynamic characteristics of an SPP. The critical advance velocity ratio is derived using the Weber number and pitch ratio in the transition mode, then the potential based boundary element method (BEM) is used on the engaged surfaces. Two models of three and six-bladed SPPs (SPP-1 and SPP-2) were selected and some results are shown.

The thrust coefficients and propulsive efficiency of a two-dimensional flexible fin with heaving and pitching motion were computed using FLUENT. The effect of different locations of the pitching axis on propulsive performance was examined using three deflexion modes which are respectively, modified Bose mode, cantilever beam with uniformly distributed load and cantilever beam with non-uniformly distributed load. The results show that maximum thrust can be achieved with the pitching axis at the trailing edge, but the highest propulsive efficiency can be achieved with the pitching axis either 1/3 of the chord length from the leading edge in modified Bose mode, or 2/3 of the chord length from the leading edge in cantilever beam mode. At the same time, the effects of the Strouhal number and maximal attack angle on the hydrodynamics performance of the flexible fin were analyzed. Parameter interval of the maximum thrust coefficient and the highest propulsive efficiency were gained. If the Strouhal number is low, high propulsive efficiency can be achieved at low , and vice versa.

The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape function. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.

The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency. Keywords: frequency-domain Green function; numerical approximation; Gaussian integral

This paper presents the survey and assessment of the estimation techniques on hydrodynamic impact. The description and definition of hydrodynamic impact are presented, and the categorization of prediction techniques and the difficulties are discussed. Analysis theories and numerical simulation techniques are reviewed and the characteristics of those theories and approaches are analyzed. The efforts are made to pinpoint the advantages and disadvantages. Recommendations for further research and development are made.

A mathematical model of podded propulsors was established in order to investigate the influence of fins. The hydrodynamic performance of podded propulsors with and without fins was calculated, with interactions between propellers and pods and fins derived by iterative calculation. The differential equation based on velocity potential was adopted and hyperboloidal panels were used to avoid gaps between surface panels. The Newton-Raphson iterative procedure was used on the trailing edge to meet the pressure Kutta condition. The velocity distribution was calculated with the Yanagizawa method to eliminate the singularity caused by use of the numerical differential. Comparisons of the performance of podded propulsors with different fins showed that the thrust of propeller in a podded propulsor with fins is greater. The resistance of the pod is also reduced because of the thrust of the fin. The hydrodynamic performance of a podded propulsor with two fins is found to be best, the performance of a podded propulsor with one fin is not as good as two fins, and the performance of the common type is the worst.

Experiments on the two-degree-freedom vortex-induced vibration (VIV) of a flexibly-mounted, rigid, smooth cylinder were performed at MIT. The research reported here is an analysis of the cylinder’s trajectories. System identification methods were used to derive a best Fourier representation for these motions and to parse these motions into symmetric and asymmetric behaviors. It was postulated that the asymmetric behavior was due to distortions caused by the free surface and bottom used at the test facility, and that the symmetric behavior is representative of deepwater VIV. Further application of systems identification methods was used to associate the symmetric behavior and test conditions to a traditional vortex street model. These models were analyzed for their ability to predict details of VIV trajectories.

The hydrodynamic characteristics of a rigid, single, circular cylinder in a three dimensional, incompressible, uniform cross flow were calculated using the large-eddy simulation method of CFX5. Solutions to the three dimensional N-S equations were obtained by the finite volume method. The focus of this numerical simulation was to research the characteristics of pressure distribution (drag and lift forces) and vortex tubes at high Reynolds numbers. The results of the calculations showed that the forces at every section in the spanwise direction of the cylinder were symmetrical about the middle section and smaller than the forces calculated in two dimensional cases. Moreover, the flow around the cylinder obviously presents three dimensional characteristics.

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.

Accurate modeling and simulation of autonomous underwater vehicle (AUV) is essential for autonomous control and maneuverability research. In this paper, a mini AUV? “MAUV-Ⅱ” was researched and the nonlinear mathematic model of the AUV in spatial motion was derived based on momentum theorem. The forces acting on AUV were resolved to several modules which were expressed in matrix form. Based on the motion model and combined with virtual reality technology, a motion simulation system was constructed. Considering the characteristic of “MAUV-Ⅱ”, the heading control and depth control were simulated by adopting S-surface control method. A long distance traveling simulation experiment based on target planning was also done. The simulation results show that the “MAUV-Ⅱ” has good spatial maneuverability, and verify the feasibility and reliability of control software.

Direct time-domain simulation of floating structures has advantages: it can calculate wave pressure fields and forces directly;and it is useful for coupled analysis of floating structures with a mooring system. A time-domain boundary integral equation method is presented to simulate three-dimensional water wave radiation problems. A stable form of the integration free-surface boundary condition (IFBC) is used to update velocity potentials on the free surface. A multi-transmitting formula (MTF) method with an artificial speed is introduced to the artificial radiation boundary (ARB). The method was applied to simulate a semi-spherical liquefied natural gas (LNG) carrier and a semi-submersible undergoing specified harmonic motion. Numerical parameters such as the form of the ARB,and the time and space discretization related to this method are discussed. It was found that a good agreement can be obtained when artificial speed is between 0.6 and 1.6 times the phase velocity of water waves in the MTF method. A simulation can be done for a long period of time by this method without problems of instability,and the method is also accurate and computationally efficient.

In order to respond the discredit on the design wave standard and to recommend new consideration on design wave parameters, based on the long-term distribution of statistic characteristics of waves and the short-term probability properties of sea state defined by giving the return period, the calculation of the return period, the height, the period, and the oceanic wave parameters of the design wave and the forecasting methods are discussed in this paper. To provide references for the operation reliability of floating structures in the extreme sea state, the method of determining the design wave parameters is resurveyed. A proposal is recommended that the design wave, which can be either significant wave with 500-year of the return period, or the maximum wave with 1/N of exceeding probability, 100-year of the return period, can be applied in the engineering design practice.

A combination of methods was developed that can determine hydrodynamic forces on a planing hull in steady motion. Firstly, a potential-based boundary-element method was used to calculate the hydrodynamic pressure, induced resistance and lift. Then the frictional resistance component was determined by the viscous boundary layer theory. Finally, a particular empirical technique was applied to determine the region of upwash geometry and determine spray resistance. Case studies involving four models of Series 62 planing craft were run. These showed that the suggested method is efficient and capable, with results that are in good agreement with experimental measurements over a wide range of volumetric Froude numbers.

A meshless numerical simulation method, the moving-particle semi-implicit method (MPS) is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses panicles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of panicles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method (ICCG), the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.

Underwater cylindrical shell structures have been found a wide of application in many engineering fields,such as the element of marine,oil platforms,etc.The coupled vibration analysis is a hot issue for these underwater structures.The vibration characteristics of underwater structures are influenced not only by hydrodynamic pressure but also by hydrostatic pressure corresponding to different water depths.In this study,an acoustic finite element method was used to evaluate the underwater structures.Taken the hydrostatic pressure into account in terms of initial stress stiffness,an acoustical fluid-structure coupled analysis of underwater cylindrical shells has been made to study the effect of hydrodynamic pressures on natural frequency and sound radiation.By comparing with the frequencies obtained by the acoustic finite element method and by the added mass method based on the Bessel function,the validity of present analysis was checked.Finally,test samples of the sound radiation of stiffened cylindrical shells were acquired by a harmonic acoustic analysis.The results showed that hydrostatic pressure plays an important role in determining a large submerged body motion,and the characteristics of sound radiation change with water depth. Furthermore,the analysis methods and the results are of significant reference value for studies of other complicated submarine structures.

This research is intended to provide academic reference and design guidance for further studies to determine the most effective means to reduce a ship’s resistance through an air-cavity.On the basis of potential theory and on the assumption of an ideal and irrotational fluid,this paper drives a method for calculating air cavity formation using slender ship theory then points out the parameters directly related to the formation of air cavities and their interrelationships.Simulations showed that the formation of an air cavity is affected by cavitation number,velocity,groove geometry and groove size.When the ship’s velocity and groove structure are given,the cavitation number must be within range to form a steady air cavity.The interface between air and water forms a wave shape and could be adjustedby an air injection system.

Accurate hydrodynamic calculations for semi-submersibles are critical to support modern rapid exploration and extraction of ocean resources.In order to speed hydrodynamic calculations,lines modeling structures were separated into structural parts and then fitted to Non-uniform Rational B-spline(NURBS).In this way,the bow and stern section lines were generated.Modeling of the intersections of the parts was then done with the universal modeling tool MSC.Patran.Mesh was gererated on the model in order to obtain points of intersection on the joints,and then these points were fitted to NURBS.Next,the patch representation method was adopted to generate the meshes of wetted surfaces and interior free surfaces.Velocity potentials on the surfaces were calculated separately,on basis of which the irregular frequency effect was dealt with in the calculation of hydrodynamic coefficients.Finally,the motion response of the semi-submersible was calculated,and in order to improve calculations of vertical motion,a damping term was affixed in the vertical direction.The results show that the above methods cangenerate fine mesh accurately representing the wetted surface of a semi-submersible and thus improve the accuracy of hydrodynamic calculations.

A numerical model of a coupled bubble jet and wall was built on the assumption of potential flow and calculated by the boundary integral method. A three-dimensional computing program was then developed. Starting with the basic phenomenon of the interaction between a bubble and a wall, the dynamics of bubbles near rigid walls were studied systematically with the program. Calculated results agreed well with experimental results. The relationship between the Bjerknes effect of a wall and characteristic parameters was then studied and the calculated results of various cases were compared and discussed with the Blake criterion based on the Kelvin-impulse theory. Our analyses show that the angle of the jet’s direction and the pressure on the rigid wall have a close relationship with collapse force and the bubble’s characteristic parameters. From this, the application range of Blake criterion can be determined. This paper aims to provide a basis for future research on the dynamics of bubbles near a wall.

To simulate two-dimensional free-surface flows with complex boundaries directly and accurately, a novel VOF (Volume-of-fluid) method based on unstructured quadrilateral mesh is presented. Without introducing any complicated boundary treatment or artificial diffusion, this method treated curved boundaries directly by utilizing the inherent merit of unstructured mesh in fitting curves. The PLIC (Piecewise Linear Interface Calculation) method was adopted to obtain a second-order accurate linearized reconstruction approximation and the MLER (Modified Lagrangian-Eulerian Re-map) method was introduced to advect fluid volumes on unstructured mesh. Moreover, an analytical relation for the interface’s line constant vs. the volume clipped by the interface was developed so as to improve the method’s efficiency. To validate this method, a comprehensive series of large straining advection tests were performed. Numerical results provide convincing evidences for the method’s high volume conservative accuracy and second-order shape error convergence rate. Also, a dramatic improvement on computational accuracy over its unstructured triangular mesh counterpart is checked.