Numerical and experimental study on a 2-D floating body under extreme wave conditions (original) (raw)
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A CIP-based numerical simulation of freak wave impact on a floating body
A two-dimensional (2-D) multi-phase fluid flow model is proposed to investigate freak wave impact on a floating body. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based finite-difference method on a fixed Cartesian grid system. The free surface/interface boundary is captured by a Volume of Fluid (VOF)-type scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW), which is more accurate than the original THINC scheme. Physical experiments are performed for validation. Series of images of the impact events from high speed camera are recorded; wave elevations along the wave flume and impact pressure have been measured. Fairly good agreements are obtained from the qualitative and quantitative comparisons between numerical results and laboratory data regarding to distorted free surfaces and large amplitude body motions. Numerical solutions for the velocity field and pressure contour in the vicinity of the floating body are also presented for detailed analysis. Some discrepancies were observed for the predicted peak pressure. The effects of grid resolution on body motions and impact pressure are performed for error analysis. The comparison of the numerical results and measured data reveals that the proposed CIP-based model is capable of reproducing the nonlinear dynamics of the floating body for applications.
Two-dimensional numerical simulation and experiment on strongly nonlinear wave–body interactions
Journal of Marine Science and Technology, 2009
A constrained interpolation profile (CIP)-based Cartesian grid method for strongly nonlinear wave-body interaction problems is presented and validated by a newly designed experiment, which is performed in a twodimensional wave channel. In the experiment, a floating body that has a rectangular section shape is used. A superstructure is installed on the deck and a small floatingbody freeboard is adopted in order to easily obtain wateron-deck phenomena. A forced oscillation test in heave and a wave-body interaction test are carried out. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in this paper. The CIP scheme is applied in the Cartesian grid-based flow solver. New improvements of the method include an interface-capturing method that applies the tangent of hyperbola for interface capturing (THINC) scheme and a virtual particle method for the floating body. The efficiency of the THINC scheme is shown by a dam-breaking computation. Numerical simulations on the experimental problem for both the forced oscillation test and the wave-body interaction test are carried out, and the results are compared to the measurements. All of the comparisons are reasonably good. It is shown, based on the numerical examples, that the present CIP-based Cartesian grid method is an accurate and efficient method for predicting strongly nonlinear wave-body interactions.
A Cip Based Numerical Simulation Method for Extreme Wave-Boby Interactions
2003
Numerical simulation of the floating body motion in rough seas is a challenging subject. The main difficulty is that the topology of free surface may be largely distorted or broken up, which makes it impossible to apply the conventional numerical method such as the potential-flow based method by BEM. As there is a growing interest in the extreme wave-body interactions such as slamming, water on deck, wave impact by the green water and capsizing due to large-amplitude waves, development of new CFD simulation methods for the seakeeping researches is therefore required. Recently several challenging works have been made by the finite difference method in which the free surface is treated by VOF method (Greco et al., 2002), and by the particle method (Sueyoshi and Naito, 2001). Some preliminary results have been shown, but still many difficulties should be cleared before performing an engineering computation. The particle method requires very large computation time and memory and it is d...
Numerical Study of Interaction Between Waves and Floating-Body by MPS Method
2015
In the present study, interaction between regular waves and free roll motion of a 2D floating body is investigated by our in-house particle solver MLParticle-SJTU based on modified Moving Particle Semi-Implicit (MPS) method. Numerical wave tank is developed to calculate the interaction between waves and floating body, including wave-maker module and free roll motion module. The comparison between the numerical wave elevation and analytical solution shows that the MLParticle-SJTU can provide acceptable accuracy of wave making. Roll motion and force acting on the floating body in waves are in good agreement with experimental results. Profiles of the wave surface surrounding floating body are presented.
A Time-Domain Nonlinear Simulation Method for Wave-Induced Motions of a Floating Body
Journal of the Society of Naval Architects of Japan, 1998
A nonlinear calculation method based on the Mixed Eulerian Lagrangian method is presented for wave-induced motions of a 2-D floating body. Attention is placed on an effective calculation of the hydrodynamic force associated with the temporal derivative of the velocity potential in Bernoulli's pressure equation. Unlike other existing methods, the acceleration field can be computed simultaneously with the velocity field, which contributes greatly to reduction of the computation time. By use of Green's second identity, the new method is explained as an extension from the mode decomposition method, and close relations between the two methods are emphasized. Computations are performed for a wall-sided model and a flared model, and numerical results of the waves at upwave and downwave positions and the body motions (sway, heave, and roll) are compared with corresponding experiments. The overall agreement is very good, confirming validity of the present method. Discussion is also made on the parametric oscillation in roll, observed for the flared model. ing attention in the seakeeping and ocean engineering research. Recently, great interest is placed on effects of the body geometry above the sea level, for which no information has been given by conventional linear theories. For this kind of research, the so-called Mixed Eulerian Lagrangian (MEL) method, initiated by Longuet-Higgins & Cokelet1), is the most promising in the framework of the potential flow. The MEL method has been studied by many researchers ; recent references in this context are Cao et al.2), Tanizawa3),4), Kashiwagi5), Wu & Eatock Taylor6), and others cited therein. However, simulations of the wave-body interaction were not so successful, because of the difficulty in precise evaluation of the temporal derivative of the velocity potential, •Ýƒ³/•Ýt-ƒ³t, appearing in Bernoulli's pressure equation. The simplest way of evaluating ƒ³t is to use a backward finite-difference scheme in time. However, it is known that this scheme makes a solution inherently unstable, resulting in the breakdown of computations.
Numerical Boundary Element Computation of Submerged Body-Surface Wave Interaction
A simple method to solve potential flow problem of submerged body-surface wave interaction is presented. The equation governing flow below the surface is Laplace equation. The boundary condition on the body is of Neumann type, while on the free surface the nonlinear dynamic free surface condition has to be satisfied. In addition, farfield and radiation condition, which determine the behavior of wave going to infinity, have to be satisfied. Taking advantage of potential flow model, then Green Identity is used to transform the problem of Laplace equation with nonlinear boundary condition into 'a nonlinear problem in its boundary. To satisfy the nonlinear dynamic free surface condition, Newton iteration is employed. The scheme for relaxation is obtained by expanding the nonlinear dynamic free surface condition obtain correction terms to the velocity potential. Truncation up to linear terms results in a simple scheme. Since the dynamic condition is valid on the unknown location of the free surface, in each iteration step the position of the free surface where the equation is applied, is corrected using Bernoulli equation. In this manner, dynamic free surface condition is satisfied exactly at the collocation points. Results for two and three dimensional nonlifting problem are presented as examples.
Nonlinear-wave effects on fixed and floating bodies
Journal of Fluid Mechanics, 1982
A numerical method for calculating the interaction of steep (nonlinear) ocean waves with large fixed or floating structures of arbitrary shape is described. The interaction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident waveform approaching it. The development of the flow, together with the associated fluid forces and structural motions, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral-equation method based on Green's theorem. A few results are presented for two reference situations and these serve to illustrate the effects of nonlinearities in the incident waves.
Journal of Computational Physics, 2021
A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to H/λ = 0.2 (H is the crest-to-trough wave height and λ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior of the model in situations at and beyond the limits of its formal application domain. Though effects associated with viscosity and flow separation manifest experimentally, the NWT proves able to capture the main features of the wave-structure interaction and associated loads.
Numerical study on interaction of a solitary wave with the submerged obstacle
Ocean Engineering, 2018
The extremely nonlinear interaction between waves and marine structures is one of most challenging problems in ocean engineering. In this study, the propagation of a solitary wave over a submerged vertical obstacle is investigated by a developed two-dimensional multi-phase viscous model. The constrained interpolation profile (CIP) based on Cartesian grid method is introduced to solve the Navier-Stokes equations, and free surface is captured accurately by the Tangent of Hyperbola for INterface Capturing (THINC) scheme. First, the free surface motions and velocity fields of a solitary wave interacting with a submerged obstacle are simulated. The present calculations fit fairly well with the measurements through whole wave propagation over the submerged obstacle. Second, the corresponding vorticity fields are calculated to illustrate characteristics of vortex generation and evolution. Third, wave forces acting on the submerged obstacle are calculated, and the results agree well with existing computations. Finally, the effectiveness of the submerged obstacle as a targeted breakwater is estimated by evaluating the reflection and transmission coefficients. The presented computations confirm that the CIP-based Cartesian grid method is capable of reproducing strongly nonlinear interaction of a solitary wave with the submerged obstacle and performing predictions of comprehensive flow-field information accurately.
A Generalized 3D Numerical Wave Tank for Practical Wave-Structure Interactions in Steep Waves
This paper presents development of a practical tool for wave-structure interactions based on a 3D numerical wave tank concept but with certain approximations in the treatment of the associated hydrodynamic problems of radiation and diffraction. The solution is in time domain and the method is versatile; it can incorporate influence of many subcomponents of a complex offshore platform, making it suitable for routine industry applications particularly for initial design stages. However, despite the simplified treatment of the interaction hydrodynamics, long-duration simulation of nonlinear interactions for a completely unrestrained floating body in a steep incident wave-field in general proves difficult as the solution tends to diverge. This problem is found to be associated with the evaluation of exact FK force on the instantaneous wetted surface rather than the relatively more complex and time-consuming interaction-hydrodynamic calculations. Some form of horizontal restraint is foun...