Numerical and experimental study on seakeeping performance of ship in finite water depth

Vessels operating in shallow waters require careful observation of the finite-depth effect. In present study, a Rankine source method that includes the shallow water effect and double body steady flow effect is developed in frequency domain. In order to verify present numerical methods, two experiments were carried out respectively to measure the wave loads and free motions for ship advancing with forward speed in head regular waves. Numerical results are systematically compared with experiments and other solutions using the double body basis flow approach, the Neumann-Kelvin approach with simplified m-terms, and linearized free surface boundary conditions with double-body m-terms. Furthermore, the influence of water depths on added mass and damping coefficients, wave excitation forces, motions and unsteady wave patterns are deeply investigated. It is found that finite-depth effect is important and unsteady wave pattern in shallow water is dependent on both of the Brard number τ and depth Froude number F_h.     

Numerical Study on the Vertical Water Exit of A Cylinder with Cavity

When a high-speed body with cavity passes through water-air free surface and exits water, its mechanical environment and dynamic characteristics change significantly due to the great difference in density and viscosity between water and air. With focusing on this problem, the Computational Fluid Dynamics (CFD) method is applied to perform numerical calculation on the process of this vapor-liquid-gas flow during the water exit of a high-speed cylinder, with the Volume of Fraction (VOF) multiphase flow interface-capturing techniques and the overset grid technology. After the verification and validation of the CFD model through mesh convergence study and a water-entry experiment, cavity evolution and flow characteristics including pressure and velocity distribution during the water exit are analyzed. The effects of different initial velocities on the pressure distribution and drag characteristics of the cylinder are investigated. Calculated results show that the cavity collapse during water exit causes strong pressure fluctuation on the cylinder; when the cylinder exits water enveloped in a supercavity, the pressure distribution on its wall surface and surrounding water region is relatively uniform, and the drag changes gently, and thus the cylinder has good motion stability.

     

Analysis of loads,motions and cavity dynamics during freefall wedges vertically entering the water surface

In this paper, theoretical models are developed and numerical methods are used to analyze the loads, motions and cavity dynamics for freefall wedges with different deadrise angles vertically entering the water surface at Froude numbers: 1 ≤ Fn < 9. The time evolutions of the penetration depth, the velocity and the acceleration are analyzed and expressed explicitly. The maximum and average accelerations are predicted. The theoretical results are compared with numerical data obtained through a single-fluid BEM model with globally satisfactory agreement. The evolution of the pressures on the impact side is investigated. Before flow separation, gravity and the acceleration of the wedge have negligible influence on the pressure on the impact side for large Froude numbers or small deadrise angles; with increasing the deadrise angle or decreasing Froude number, the effects of gravity and the acceleration of the wedge tend to become more important. Global loads, with the main emphasis on the drag coefficient, are also studied. It is found that for the light wedge, the transient drag coefficient has slow variation in the first half of the collapse stage and rapid variation in the last half of the collapse stage. For the heavy wedge, the transient drag coefficients vary slowly during the whole collapse stage and can be treated as constant. The characteristics of the transient cavity during its formation are investigated. The non-dimensional pinch-off time, pinch-off depth and submergence depth at pinch-off scale roughly linearly as the Froude number.     

Nonlinear wave resistance of a two-dimensional pressure patch moving on a free surface

A model problem of the flow under an air-cushion vessel is studied. Two different numerical techniques are used to determine the solution of the free-surface elevation and the wave resistance for a range of Froude number, Reynolds number, value of the pressure applied in the cushion, and depth of the water. The first numerical technique uses a velocity potential that satisfies linearized free-surface boundary conditions, whereas the second employs a finite-volume method to find a solution that satisfies the fully nonlinear free-surface boundary conditions. The results clearly show that for high Froude number and practical values of the cushion pressure, the linear-theory solution is in excellent agreement with the more exact nonlinear prediction. For lower Froude number the solution becomes unsteady, and the disagreement between the two methods is larger.     

Numerical investigation of wave elevation and bottom pressure generated by a planing hull in finite-depth water

A numerical investigation of the bottom pressure and wave elevation generated by a planing hull in finite-depth water is presented. While the existing literature addresses the free-surface deformation and pressure field at the seafloor independently, this work proposes a direct comparison between the two hydrodynamic quantities. The dependence of the pressure disturbances at the ocean floor from the waves generated at the free-surface by a planing hull is studied for several values of both the depth and hull Froude numbers. The methodology employed is Smoothed Particle Hydrodynamics (SPH), a numerical technique based on the discretization of the continuum fields of hydrodynamics through mesh-less particles. The SPH code herein chosen is initially validated against experimental data for transom-stern flow. Subsequently, numerical simulations are presented for a planing hull in high-speed regimes. The results show a direct correlation between surface wave dynamics and hydrodynamic pressure disturbances at the seafloor as the value of the Froude number is varied. This is assessed by studying the inverse dependence of the low-pressure wake angle with the Froude number and by comparison of SPH results with similar works in the cited literature.     

Centrifuge study on the runout distance of submarine debris flows

ABSTRACT

In this paper, a series of mini-drum centrifuge experiments on motion of submarine debris flow, which are able to correctly reproduce the self-weight stresses and gravity-dependent processes, are presented. These tests were performed using artificial submarine clay with high water content, from 93 to 149%. The extremely low shear strength made the debris material behave as idealistic lubricating material when it was deposited, resulting in a linear relationship between water content and runout distance of strongly coherent debris flow. On the other hand, the dilation of the flow body and hydroplaning was observed for weakly coherent debris flow, which further increased the mobility of flow body. A densimetric Froude number Fr_d was used to indicate the threshold of hydroplaning, which occurs if the Fr_d is greater than 0.2. Finally, two simple analytical models based on prototype debris flow under 1?g condition was used to validate the experiment results, which further prove the effects of soft marine clay on the high mobility of submarine debris flow. On the other hand, when the water content exceeded 120%, the experiment results deviated from the analytical solution due to the effects of hydroplaning.     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.     

Scarifying and fingering surfaces of plunging jets

The local surface deformation resulting from the oblique impact of a columnar water jet has been computed, using a three-dimensional large eddy simulation, as a model of the overturning jet of a breaking wave. The emergence of the secondary jet from the front face of the initial jet has been examined and the organisation of the vortices within the jet characterised. As the secondary jet emerges, the vorticity field becomes unstable under the action of the strong shear beneath the jet surface and pairs of longitudinal counter-rotating vortices stretched along the direction of the jet projection are formed. The presence of these longitudinal vortex pairs creates convergent surface flows, resulting in the formation of longitudinal scars on the rear face of the projecting jet. Following significant growth of the scars on both its upper and lower surfaces, the jet decouples into fingers. The lateral widths of the longitudinal vortices provide a minimum measure of the finger size. A horizontal Froude number Fr_h, representing a measure of strength of horizontal shear in a gravity-dominated impacting flow is defined, which characterises the organisation of the longitudinal vortices occurring in the shear flow, and the resultant formation of scars and fingers. For higher Fr_h, stronger longitudinal vortices and deeper scars are formed at longer lateral intervals, enhancing the fingering process during the splashing event. Fundamental features of material transport in the vicinity of the surface of jets (e.g. gas transfer across a sea surface) are related to the entrainment of surface fluid by the longitudinal vortices, and is thus also characterised by Fr_h.     

CFD, system-based and EFD study of ship dynamic instability events: Surf-riding, periodic motion, and broaching

CFD and system-based simulation are used to predict broaching, surf-riding, and periodic motion for the ONR Tumblehome model, including captive and free model test validation studies. CFD shows close agreement with EFD for calm water resistance, static heel (except for sway force and yaw moment), and static drift (except for roll moment). CFD predictions of static heel in following waves also compare well with EFD except for surge force, sway force, and pitch angle. Froude-Krylov calculations of wave-induced surge force in following waves provides good agreement for high Froude number, but significantly overestimates for Froude number less than 0.2. On the other hand, CFD successfully reproduces the reduction of the wave-induced surge force near Froude number 0.2, probably because CFD can capture the 3D wave pattern. CFD free model simulations are performed for several speeds and headings and validated for the first time for surf-riding, broaching, and periodic motions. System-based simulations are carried out based on inputs from EFD, CFD, and Froude-Krylov for a dense grid of speeds and headings to predict the instability map, which were found to produce fairly similar results.     

Interaction of uniform current with a circular cylinder submerged below an ice sheet

The problem of a uniform current passing through a circular cylinder submerged below an ice sheet is considered. The fluid flow is described by the linearized velocity potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The Green function due to a source is first derived, which satisfies all the boundary conditions apart from that on the body surface. Through differentiating the Green function with respect to the source position, the multipoles are obtained. This allows the disturbed velocity potential to be constructed in the form of an infinite series with unknown coefficients which are obtained from the boundary condition. The result shows that there is a critical Froude number which depends on the physical properties of the ice sheet. Below this number there will be no flexural waves propagating to infinity and above this number there will be two waves, one on each side of the body. When the depth based Froude number is larger than 1, there will always be a wave at far upstream of the body. This is similar to those noticed in the related problem and is different from that in the free surface problem without ice sheet. Various results are provided, including the properties of the dispersion equation, resistance and lift, ice sheet deflection, and their physical features are discussed.     

Influence of the seagrass,Zostera marina L., on current flow

A salt-water flume was used to describe the mechanics of current flow around an articial Zostera marina meadow. Shear velocity and roughness height were positively correlated with seagrass surface area, and were positively/negatively correlated with current velocity. Current velocity intrusion into the meadow before diminution and maximum reduction (both at the 2 cm height line) proceed by factors of 1·25 and 2·07 cm into the meadow per cm s^?1 of current velocity, respectively.Froude number was correlated with mean bending angle of the canopy as a whole. Maximum bending had occurred with Froude = 1, but most bending had taken place by Froude = 0·4, a velocity of 40–50 cm s^?1 in this experiment.The meadow edge is the most dynamic zone of a seagrass meadow in regard to current flow. Bending of the shoot canopy is a mechanism for re-direction of current flow and in-canopy reduction of current velocity. Meadow dimensions may be regulated by scouring processes in different hydraulic regimes. Shoot bending and subsequent in-meadow current velocity reduction are mechanisms that affect self-shading and photosynthetic capabilities as well as providing habitat stability.     

Stationary waves in the flow of a homogeneous fluid with vertical shear of the velocity

A plane problem of free stationary gravitational waves in a horizontal current with vertical shear of the velocity is studied in the linear statement. The determination of the parameters of waves is reduced to the solution of the Sturm–Liouville boundary-value problem. For some vertical distributions of current velocity, we obtain analytic solutions. We propose a numerical algorithm for finding the parameters of waves. On the basis of the performed analysis, we establish the possibility of existence of stationary surface waves in currents for certain ranges of the Froude number. As the Froude number decreases, the waves become shorter, which leads to a faster attenuation of waves disturbances with depth. Under the actual conditions, the waves are short and suffer the influence of shear currents only in the subsurface layer of the ocean.     

URANS investigation of the interaction between the free surface and a shallowly submerged underwater vehicle at steady drift

An axisymmetric underwater vehicle (UV) at a steady drift angle experiences the complex three-dimensional crossflow separation. This separation arises from the unfavorable circumferential pressure gradient developed from the windward side toward the leeward side. As is well known, the separated flow in the leeward side gives rise to the formation of a pair of vortices, which affects considerably the forces and moments acting on the UV. In this regard, the main purpose of the present study is to evaluate the role of the leeward vortical flow structure in the hydrodynamic behavior of a shallowly submerged UV at a moderate drift angle traveling beneath the free surface. Accordingly, the static drift tests are performed on the SUBOFF UV model using URANS equations coupled with a Reynolds stress turbulence model. The simulations are carried out in the commercial code STARCCM+ at a constant advance velocity based on Froude number equal to F_n = 0.512 over submergence depths and drift angles ranging from h = 1.1D to h = ∞ and from β = 0 to β = 18.11°, respectively. The validation of the numerical model is partially conducted by using the existing experimental data of the forces and moment acting on the totally submerged bare hull model. Significant interaction between the low-pressure region created by the leeward vortical flow structure and the free surface is observed. As a result of this interaction, the leeward vortical flow structure appears to be largely responsible for the behavior of the forces and moments exerted on a shallowly submerged UV at steady drift.     

A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

Viscous free surface effect on coastal embankment hydrodynamics

A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

Performance analysis of 3D hydrofoil under free surface

The purpose of the present paper is to develop a potential-based panel method for determining the steady potential flow about three-dimensional hydrofoil under free surface. The method uses constant-strength doublets and source density distribution over the foil body surface and thereby Dirichlet-type boundary condition is used instead of Neumann-type condition. On the undisturbed free surface source density is used to meet the free surface condition that is linearised in terms of double-body model approach and is discretised by a one-side, upstream, four-point finite difference operator. After solving the doublets on the foil and sources on the free surface, the numerical results of pressure, lift and resistance coefficients and also wave profiles can then be calculated for different Froude number and depth of submergence to demonstrate the influence of free surface and aspect ratio effects on performance of the hydrofoil.     

一种新型三维水流数值模型

以不可压缩流体的N-S方程为基本控制方程,用快速粒子level set方法(FPLS)追踪自由表面,提出了一种新的三维水流数值模型。在自由表面处应用虚拟压力法来封闭压力泊松方程,同时用速度等值外插的方法构造自由表面外侧的虚拟速度分布。通过模拟水波振荡、水柱崩塌、水滴滴落和空箱注水过程证明了模型的有效性。