Numerical and Experimental Investigation of Interactions Between Free-Surface Waves and A Floating Breakwater with Cylindrical-Dual/Rectangular-Single Pontoon

This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics(CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom(3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step.The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes(sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.

Effect of Viscosity on Free-Surface Waves in Oseen Flows

Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis. A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile. The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.

Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets

A doublet integral equation is formulated for the two-dimensional dissipative potential flow around a hydrofoil submerged below a free-water surface. The free-water surface is assumed to involve energy dissipation, and thus it is the source of damping. A doublet panel method is developed from incorporation of the dissipative Green function approach and the doublet distributions on the hydrofoil surface. Numerical computations are implemented, and the derived numerical results are in good agreement with analytic solutions and experimental measurements.

Formation of free-surface vortex and vortex suppression by rotating stopper-rod at end of tundish casting

A rotating stopper-rod technique was proposed to suppress the formation of free-surface vortex in the tundish.The large eddy simulation model coupled with volume of fluid model was developed to study the steel–slag–gas three-phase flow behavior.The critical slag entrapment height of the free-surface vortex and mass of residual steel were predicted at different rotating speeds(30,60,90 and 120 r/min)of the rotating stopper-rod.The numerical model was verified by water model experiment.The results showed that by rotating the stopper-rod in the opposite direction of the vortex above the submerged entry nozzle,the formation of vortex can be effectively disturbed and the critical height of the free-surface vortex can be reduced.Particularly for the 2nd strand,when the rotating speeds are 30,60,90 and 120 r/min,the critical height of the free-surface vortex above the 2nd strand is 7.3,4.7,6.3 and 7.4 cm,respectively.A reasonable rotating speed should be 60 r/min,which can reduce about 2 tons of residual steel.Other rotating speeds just can reduce about 1.6 tons of residual steel.

PREDICTION OF PROJECTILE PENETRATION AND PERFORATION BY FINITE CAVITY EXPANSION METHOD WITH THE FREE-SURFACE EFFECT

With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.

Large eddy simulation of free-surface flows

This paper introduces and discusses numerical methods for flee-surface flow simulations and applies a large eddy simula- tion （LES） based flee-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, dis- advantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a LES solver that employs the level set method to capture flee-surface deformation in 3-D flows is presented, as are results from two example calculations that concern com- plex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.

A RAISED PANEL METHOD BASED ON NURBS FOR FREE-SURFACE POTENTIAL FLOWS WITH FORWARD SPEED

A raised panel method based on NURBS (Non-Uniform Rational B-Splines) forfree-surface flows with forward speed is presented. In this generalized panel method, NURBS areemployed to represent the body geometry, disturbed free surface, and to express the unknown sourcestrength distribution, on the body surface and above the free surface. Compared with commonhigher-order panel methods, it has no need of adopting local coordinates. NURBS make the geometryrepresentation of the body shape and the wave pattern more precise. Raised panels above the freesurface produce less numerical dispersion error, need less CPU consumption and are helpful andcombined with collocation-point shifting up-stream, can satisfy the radiation condition numerically.By using continuous and discrete Fourier analysis, numerical errors of this method are discussedand a general expression for the errors of numerical damping and dispersion, including the effectsof the vertical distance of singularities to the free surface, the order of singularity distributionrepresented by B-splines in panels, and collocation-point shifting is derived.

FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

The free-surface waves and the flow field due to a body moving on the surfaceof an incompressible viscous fluid of infinite depth were studied analytically. The floating bodywas modeled as a normal point pressure on the free surface. Based on the Oseen approximation forgoverning equations and the linearity assumption for boundary conditions, the exact solutions inintegral form for the free-surface elevation, the velocities and the pressure were given. Byemploying Lighthill's two-stage scheme, the asymptotic representations in far field for largeReynolds numbers were derived explicitly. The effect of viscosity on the wave profiles was expressedby an exponential decay factor, which removes the singular behavior predicted by the potentialtheory.

Effect of Marangoni Number on Thermocapillary Convection and Free-Surface Deformation in Liquid Bridges

Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.

UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID

The interaction of laminar flows with free surface waves generated by submerged bodies in an incompressible viscous fluid of infinite depth is investigated analytically. The analysis is based on the linearized Navier-Stokes equations for disturbed flows. The kinematic and dynamic boundary conditions are linearized for the small-amplitude free-surface waves, and the initial values of the flow are taken to be those of the steady state cases. The submerged bodies are mathematically represented by fundamental singularities of viscous flows. The asymptotic representations for unsteady free-surface waves produced by the Stokeslets and Oseenlets are derived analytically. It is found that the unsteady waves generated by a body consist of steady-state and transient responses. As time tends to infinity, the transient waves vanish due to the presence of a viscous decay factor. Thus, an ultimate steady state can be attained.

THE HYBRID PROBLEM OF FREE-SURFACE GRAVITY SPILLWAY FLOW TREATED BY VARIATIONAL PRINCIPLES WITH VARIABLE DOMAIN: POTENTIAL fUNCTION FORMULATION

Making full use of functional variations with variable domain for handling both the free surface and unknown part of the dam wall,a family of variational principles(VPs)for the hybrid(direct-inverse)problem of free surface spillway flow under gravity is formulated in terms of the potential function Φ.This theory offers new rational and versatile ways for dam de- sign and a sound theoretical basis for numerical solution,e.g.by the finite element method (FEM).

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation.The dispersion of free-surface temperature is modelled by an advection-diffusion equation.Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure.Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations.In addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms.We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.

Development of a hybrid particle-mesh method for simulating free-surface flows

In this work the feasibility of a numerical wave tank using a hybrid particle-mesh method is investigated.Based on the fluid implicit particle method（FLIP）a formulation for the hybrid method is presented for incompressible multiphase flows involving large density jumps and wave generating boundaries.The performance of the method is assessed for a standing wave and for the generation and propagation of a solitary wave over a flat and a sloping bed.A comparison is made with results obtained with a well-established SPH package.The tests demonstrate that the method is a promising and attractive tool for simulating the nearshore propagation of waves.

Application Progress of Computational Fluid Dynamic Techniques for Complex Viscous Flows in Ship and Ocean Engineering

Complex flow around floating structures is a highly nonlinear problem,and it is a typical feature in ship and ocean engineering.Traditional experimental methods and potential flow theory have limitations in predicting complex viscous flows.With the improvement of high-performance computing and the development of numerical techniques,computational fluid dynamics(CFD)has become increasingly powerful in predicting the complex viscous flow around floating structures.This paper reviews the recent progress in CFD techniques for numerical solutions of typical complex viscous flows in ship and ocean engineering.Applications to free-surface flows,breaking bow waves of high-speed ship,ship hull-propeller-rudder interaction,vortexinduced vibration of risers,vortex-induced motions of deep-draft platforms,and floating offshore wind turbines are discussed.Typical techniques,including volume of fluid for sharp interface,dynamic overset grid,detached eddy simulation,and fluid-structure coupling,are reviewed along with their applications.Some novel techniques,such as high-efficiency Cartesian grid method and GPU acceleration technique,are discussed in the last part as the future perspective for further enhancement of accuracy and efficiency for CFD simulations of complex flow in ship and ocean engineering.

Study on Transient Gap Resonance with Consideration of the Motion of Floating Body

In this paper, the transient fluid resonance phenomenon inside a narrow gap between two adjacent boxes excited by the incident focused waves with various spectral peak periods and focused wave amplitudes is simulated by utilizing the open-sourced computational fluid dynamics software, Open FOAM. The weather-side box is allowed to heave freely under the action of waves, and the lee-side box keeps fixed. This paper mainly focuses on how both the spectral peak period and the focused wave amplitude affect the free-surface amplification inside the gap, the motion of the weather-side box, and the wave loads(including the vertical and the horizontal wave forces) acting on both boxes.For comparison, another two-box system with both boxes fixed is also considered as a control group. It is found that the motion of the weather-side box significantly changes the characteristics of the transient gap resonance, and it would cause that the fluid resonant period becomes 1.4-1.6 times that of the two-box system with both boxes fixed.All the concerned physical quantities(i.e., the free-surface amplification in the gap, the motion of the weather-side box, the wave loads) are found to closely depend on both the spectral peak period and the focused wave amplitude.

Extension of the Frequency-Domain pFFT Method for Wave Structure Interaction in Finite Depth

To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform （pFFT） method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Tocplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.

High Resolution Ship Hydrodynamics Simulations in Open Source Environment

The numerical simulation of wake and flee-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.

Numerical Study on Flow Around Modern Ship Hulls with Rudder-Propeller Interactions

Reducing the fuel consumption of ships presents both economic and environmental gains. Although in the past decades,extensive studies were carried out on the flow around ship hull, it is still difficult to calculate the flow around the hull while considering propeller interaction. In this paper, the viscous flow around modern ship hulls is computed considering propeller action. In this analysis, the numerical investigation of flow around the ship is combined with propeller theory to simulate the hull-propeller interaction. Various longitudinal positions of the rudder are also analyzed to determine the effect of rudder position on propeller efficiency. First, a numerical study was performed around a bare hull using Shipflow computational fluid dynamics(CFD) code to determine free-surface wave elevation and resistance components.A zonal approach was applied to successively incorporate Bpotential flow solver^ in the region outside the boundary layer and wake, Bboundary layer solver^ in the thin boundary layer region near the ship hull, and BNavier-Stokes solver^in the wake region. Propeller open water characteristics were determined using an open-source MATLAB code Open Prop, which is based on the lifting line theory, for the moderately loaded propeller. The obtained open water test results were specified in the flow module of Shipflow for self-propulsion tests. The velocity field behind the ship was recalculated into an effective wake and given to the propeller code that calculates the propeller load. Once the load was known, it was transferred to the Reynolds-averaged Navier-Stokes(RANS) solver to simulate the propeller action. The interaction between the hull and propeller with different rudder positions was then predicted to improve the propulsive efficiency.

Linear inversion-imaging method based on joint primary refl ected waves and surface-related multiples

In marine seismic exploration,especially in deep-water and hard ocean-bottom cases,free-surface multiples are strongly developed.Compared with primary waves,the wider illumination aperture of the multiples is beneficial for high-resolution seismic imaging.In this study,by introducing a new compound source composed of primaries and free-surface multiples and by ignoring internal multiples,we derive a new linearized forward problem(free-surface-multiple prediction model)under a weak-scattering assumption(i.e.,first-order Born approximation).On the basis of the new linearized problem,we propose a joint inversion-imaging method by simultaneously using the primaries and free-surface multiples under the general framework of least square inversion.To eliminate the crosstalk artifacts introduced by the cross-correlation of multiples with different orders,we prove that the crosstalk artifacts can be gradually eliminated during the inversion if a proper step length is selected.Synthetic-andfield-data tests demonstrate the effectiveness of the proposed method.

Unsteady Spillway Flows by Singular Integral Operators Method

The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.