Two-dimensional numerical simulation and experiment on strongly nonlinear wave–body interactions

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 two-dimensional 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 floating-body freeboard is adopted in order to easily obtain water-on-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.     

Numerical simulation of violent sloshing by a CIP-based method

In this article, a new computational fluid dynamics simulation approach based on the constraint interpolation profile (CIP) method is applied to tackle the violent sloshing problem. The present study considers two-dimensional sloshing phenomena in a rectangular tank. By the proposed method, the sloshing problem is viewed as a multiphase problem that includes water and air flows. A stationary Cartesian grid is used and the free surface is solved by an interface capturing method. The CIP combined unified procedure (CCUP) scheme was adopted for the flow solver, and both the CIP scheme and the CIP conservative semi-Lagrangian with cubic interpolation polynomial (CIP-CSL3) scheme were used for interface capturing. For validation of the numerical method, a physical experiment was conducted with a rectangular tank for several frequencies and filling heights. A convergence check was first performed for the method. The numerical simulation results on violent sloshing show that the use of the CIP-CSL3 scheme as an interface capturing procedure gives much better results for the pressures and free-surface profiles than the conventional CIP scheme.     

Finite-difference simulation of green water impact on fixed and moving bodies

A numerical method was developed to predict the water impact pressure caused by green water phenomena. The density function method was employed in the framework of a locally refined overlapping grid system. The simple problem of a rectangular body placed in regular waves was considered and the simulation results were compared with tank experiments. Good agreement with experiment was shown for wave–body interactions and for the pressure values at three different positions on the body. The case of a rectangular body with a vertical wall on the deck was also considered and the comparison showed satisfactory agreement. It was demonstrated that this method could be extended to a moving body problem, in which the body was free to undergo heave, pitch, and surge motions.     

The influence of different turbulence schemes on modelling primary production in a 1D coupled physical–biological model

A one-dimensional (1D) coupled physical–microbiological model has been applied to a site in the central North Sea. The impact of the choice of the turbulence closure scheme on the modelling the primary production has been investigated.The model was run with four different parameterisations of vertical mixing of heat, momentum and dissolved and suspended matters, using M2 tidal forcing and the hourly mean meteorological forcing of 1989 to reproduce the annual thermal structure and primary production. The four mixing parameterisations are: Level 2 turbulence closure scheme [Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806; Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for geophysical Fluid problems. Rev. Geophys. Space Phys. 20 (4) 851–875] using an explicit numerical scheme [Sharples, J., Tett, P., 1994. Modelling the effect of physical variability on the midwater chlorophyll maximum. J. Mar. Res. 52, 219–238]; a version of the Level 2.5 turbulence closure scheme [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62; Ruddick, K.G., Deleersnijder, E., Luyten, P.J., Ozer, J., 1995. Haline stratification in the rhine/meuse freshwater plume: a 3D model sensitivity analysis. Cont. Shelf Res. 15 (13) 1597–1630] simplified to use an algebraic mixing length by Sharples and Simpson [Sharples, J., Simpson, J.H., 1995. Semidiurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15, 295–313], also solved explicitly; the same simplified L2.5 scheme with an implicit numerical solution and modified vertical discretisation scheme [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206]; and another version of the same scheme (but using a different algebraic mixing length) as described by Xing and Davies [Xing, J., Davies, A.M., 1996a. Application of turbulence energy models to the computation of tidal currents and mixing intensities in the shelf edge regions. J. Phys. Oceanogr. 26, 417–447; Xing, J., Davies, A.M., 1996b. Application of a range of turbulence models to the computation of tidal currents and mixing intensities in shelf edge regions. Cont. Shelf. Res. 16, 517–547; Xing, J., Davies, A.M., 1998. Application of a range of turbulence energy models to the computation of the internal tide. Int. J. Numer. Methods Fluids 26, 1055–1084]. Various model outputs at the sea surface and in depth profiles have been compared with data collected in 1989 as part of the North Sea Project [Huthnance, J.M., 1990. Progress on North Sea Project. NERC News, vol. 12, pp. 25–29, UK]. It is shown that the biological results are extremely sensitive to the small changes in the physical conditions, which arise due to the different turbulence schemes tested. The timing of the spring bloom and the maintenance of the midwater chlorophyll maximum all differ greatly between model runs, and the gross primary production varies by a factor of two from the highest to lowest results. The simplified Level 2.5 scheme, implemented using the numerical methods of Annan [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206], produces results, which give the best agreement with the available data.     

Three-dimensional numerical wave tank simulations on fully nonlinear wave–current–body interactions

A finite-difference scheme and a marker-and-cell (MAC) method are used for numerical wave tank (NWT) simulations to investigate the characteristics of nonlinear wave motions and their interactions with a stationary three-dimensional body in the presence of steady uniform currents. The Navier–Stokes (NS) equation is solved in the computational domain, and the boundary values are updated at each time-step by a finite-difference time-marching scheme in the frame of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the marker–density function technique developed for two fluid layers. The incident waves are generated from the inflow boundary by prescribing a velocity profile resembling the motions of a flexible flap wavemaker, and the outgoing waves are numerically dissipated inside an artificial damping zone located at the end of the tank. Using the NS–MAC NWT, nonlinear wave and current interactions around a stationary vertical truncated circular cylinder are studied, and the results are compared with the experimental results of Mercier and Niedzwecki, a time-domain NWT based on linear potential theory, a fully nonlinear NWT, and a second-order diffraction computation. Received: July 3, 2001 / Accepted: September 25, 2001     

船舶航行时水动力系数求解二维半理论的稳定算法

给出一种基于高速细长体理论的预报排水型船在波浪上运动水动力求解的数值方法.在该理论的定解条件中,自由面条件是三维的,而控制方程和物面条件则是二维的,所以称为二维半理论.采用二维时域自由面Green函数将定解问题转化为船体切片上的积分方程,进而求解有航速下的船舶水动力问题.重点讨论了水动力计算的稳定算法.对ITTC建议的标准WIGLEY船型作了理论预报,并与DELFT大学的实验结果和用STF切片法的理论预报结果作了比较.比较结果表明,本文提出的二维半理论的预报结果与试验结果相当接近,而计算效率和切片法相当,且大大改善了理论预报的精度.     

基于SPH方法的波浪对水平板冲击的数值模拟(英文)

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.     

带自由面肥大船粘性绕流场的数值模拟

采用直接求解RANS方程的方法对带自由面的肥大型船舶的流场和阻力进行了数值计算,湍流模型选用RNGk-ε两方程模式,自由面的处理采用VOF方法.数值计算结果与已公开试验数据的定量比较相当吻合.计算结果的分析表明:文中发展的CFD计算方法可以满足于带自由面肥大型船舶快速性工程预报的要求.     

紧致插值曲线CIP方法及其应用

波浪与建筑物的相互作用过程会涉及到波浪破碎、水气掺混和结构物的动力响应等复杂过程,对数值算法提出了更高要求。文章基于紧致插值曲线CIP（Constrained Interpolation Profile）方法建立了可模拟波浪破碎、翻滚等自由面大变形流动问题的数学模型。模型以CIP方法为流场基本求解器,离散了纳维—斯托克斯（Navier-Stokes：N-S）方程,同时还以CIP方法捕捉了自由面,通过多相流理论描述了流—固—气之间的相互作用。对强非线性自由表面流动问题的典型算例溃坝问题开展了数值模拟,并通过与他人实验结果的比较验证了模型的有效性。最后开展了极端波浪对浮式结构冲击过程的模拟,准确地预测了甲板上浪和结构的动力响应等问题。     

H-adaptive Navier–Stokes simulations of free-surface flows around moving bodies

This article deals with Navier–Stokes simulations of multiphase flows around moving bodies coupled with an adaptive mesh refinement strategy. The numerical framework is considered first: the Navier–Stokes solver, the methodologies for handling multiphase flows and moving bodies, the remeshing techniques, and the adaptive procedure are explained and detailed. Then an application involving hydrodynamic impacts is presented in detail and studied to highlight the relevance of the whole global approach. Of particular interest is the accurate computation of pressure peaks arising during impacts.     

A 2D+T VOF fully coupled formulation for the calculation of breaking free-surface flow

We present the results of simulations obtained with a free-surface flow solver based on the following method. The free surface is simulated by the volume-of-fluid interface capturing method. This code solves the Navier–Stokes equations using a finite-volume method adapted to a structured or unstructured mesh. The system is constructed using a fully coupled approach. This global approach allows the simulation of complex flow as a breaking or merging wave. Moreover, with the use of a 2D+T decomposition, it is possible to simulate three-dimensional steady flow.     

重叠网格在船舶CFD中的应用研究

文章采用RANS方法和重叠网格计算了带自由液面的船舶绕流问题。计算网格采用重叠网格的型式,自由液面的模拟采用单相Level-Set方法,Reynolds应力采用k-ω模型,采用体单元有限差分方法和PISO算法求解RANS方程。文中简要描述了重叠网格和单相Level Set自由液面模拟方法的数学模型及求解。通过对S60单体船型约束模和自由模型采用重叠网格的数值求解及与试验结果的比较表明该重叠可较好地模拟带自由液面船舶自由态绕流问题。另采用重叠网格对一简单的双体船和三体船进行了数值求解,计算结果也表明重叠网格和单相Level-Set方法可较好地模拟带自由液面的船舶绕流问题。     

Changes in apparent oxygen removal in the Baltic proper deep water

By developing a steady state diagnostic model for a stratified deep-water mass, one is able to quantify both the mass flows and apparent oxygen removal in the Baltic proper deep water. The model is based on continuity of the assumed conservative observable volume, salinity and temperature. Second degree polynomials are fitted to observed vertical profiles of temperature as well as oxygen concentration to give a functional correspondence with the used spatial variable salinity. These relations are used in the model that calculate the water flows, oxygen flows and oxygen removal during four periods between 1959 and 1997. The model forms a boundary value problem, which is solved with a finite difference scheme. The model seems to give reasonable estimates of the flows. The oxygen removal is mainly balanced by inflow of oxygen with incoming water. The oxygen consumption is 4–8 μl O₂ l⁻¹ day⁻¹, which corresponds to a degradation of organic matter in the range 30–60 g C m⁻² year⁻¹.     

Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier–Stokes computations

A spherical and a nonspherical bubble dynamics models were developed to study cavitation inception, scaling, and dynamics in a vortex flow. The spherical model is a modified Rayleigh–Plesset model to account for bubble slip velocity and for nonuniform pressures around the bubble. The nonspherical model is embedded in an unsteady Reynolds-averaged Navier–Stokes code with appropriate free-surface boundary conditions and a moving chimera grid scheme around the bubble. The effect of nonspherical deformation and bubble/flow interaction on bubble dynamics is illustrated by comparing spherical and nonspherical models. It is shown that nonspherical deformations and bubble/flow interactions are important for an accurate prediction of cavitation inception. The surface-averaged pressure-modified Rayleigh–Plesset scheme is a significant improvement over the conventional spherical model, and is able to capture the volume changes of a bubble during its capture. It is also a fast scheme for studying scaling. In a preliminary study, the scaling effects on cavitation inception were examined using two different Reynolds numbers owing to two different chord lengths. The nuclei-size effect on the prediction of cavitation inception was also studied, and its important effects are highlighted.     

带全附体潜艇尾流场的数值预报研究

本文在人工可压缩性方法得到的不可压缩守恒型Navier-Stokes方程的基础上，引入高精度的三阶基本无振荡格式（ENO）及通量分裂形式的LU分解方法，对某潜艇模型全附体的尾流场进行了数值模拟，取得与实验基本一致的结果。     

Comparison of CFD and EFD for the Series 60 C B= 0.6 in steady drift motion

 This paper presents comparisons of computational and experimental fluid dynamics results for boundary layers, wakes, and wave fields for the Series 60 C _B= 0.6 ship model in steady drift motion. The numerical method solves the unsteady Reynolds-averaged Navier–Stokes and continuity equations with the Baldwin–Lomax turbulence model, exact nonlinear kinematic and approximate dynamic free-surface boundary conditions, and a body/free-surface conforming grid. The experimental and computational conditions, i.e., Froude numbers of 0.16 and 0.316 for the experiments, and Froude numbers of 0 and 0.316 for the computations, allow comparisons of low and high Froude number results, respectively, which allows an evaluation of Froude number effects and validation of the computational fluid dynamics at both low and high Froude numbers. This article gives an overview of this numerical approach, and the computational conditions and uncertainty analysis are described. Results are presented for the wave and flow fields, with emphasis on the important flow features of drift- and wave-induced effects in comparison with the experiments. Finally, conclusions from the present study are given, together with recommendations for future work. Received: August 31, 2001 / Accepted: March 25, 2002     

Time-domain numerical and experimental analysis of hydroelastic response of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a pontoon-type, very large floating structure (VLFS) edged with the perforated plates, non-perforated plates or their combination anti-motion device both numerically and experimentally. A direct time domain modal expansion method, taking amount of the time domain Kelvin sources in hydrodynamic forces, in which the fluid flows across the perforated anti-motion plate by applying the Darcy's law, is applied to the fluid–structure interaction problem. A quarter of numerical model is built based on the symmetry of flow field and structure in hydrodynamic forces, and special care is paid to the rapid and accurate evaluation of time domain free-surface Green functions and its spatial derivatives in finite water depth by using interpolation–tabulation method. Using the developed numerical tools and the model tests conducted in a wave basin, the response-reduction efficiency of the perforated plates is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. As a result of the parametric study, the porosity 0.11 is selected as the optimal porosity, and the relationship between the porosity and the porous parameter is developed by using the least-squares fitting scheme. After simulation and verification, the dual anti-motion plates which are the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS, are designed for more wave energy dissipation and added damping. Considering variation of the water depths in offshore, discussion on the effectiveness of these anti-motion devices at different water depths is highlighted.     

A dissipative free-surface approach for an underwater body in a uniform stream

A dissipative free-surface approach is applied to the potential flow problem with respect to a hydrofoil in a two-dimensional uniform stream. A dissipative source-based panel method is developed for a NACA foil problem with its trailing edge being a stagnation point, and also for a symmetric Joukowski foil problem with its trailing edge being a non-stagnation point. To facilitate the understanding of the further application of the dissipative free-surface approach, an underwater mathematical body model is presented. Numerical simulation with respect to the body in a three-dimensional uniform stream is provided from an analytic formulation obtained by the dissipative free-surface technique.     

Two-dimensional numerical simulation of water splash phenomena with and without surface tension

Two-dimensional numerical analyses were conducted and analyzed to simulate water splash produced by free falling object models starting from the resting position. The equilateral prism-shaped object models were allowed to fall onto the free surface of the water. The moving-particle semi-implicit (MPS) method was used to solve the unsteady Navier-Stokes equation for incompressible fluid flows with and without the surface tension effect. Froude numbers of 0.75, 1.0, and 1.25 were used with different model sizes for the entry velocity at the free surface. Splashes obtained by numerical computation closely agreed with the experimental results. The surface tension force, the Froude number, and the Weber number were found in these calculations to play major roles in determining various types of splash shapes. Model size was found to influence splash phenomena, even if the Froude number remained the same. The dependencies on these two nondimensional numbers and the fundamental law of similarity on water splash with and without the surface tension effect were thoroughly investigated in this research. Several two-dimensional numerical simulations are presented in this article to describe the hydrodynamic behaviors of water splash with and without the surface tension effect.     

船模阻力数值水池试验不确定度评估

文章针对水面船模阻力数值水池试验,开展了不确定度分析与评估研究。不确定度分析中,验证方法和流程基于正交设计和方差分析方法,确认方法和流程基于统计推断理论。以水面船标模DTMB5415为对象,进行了船模阻力数值水池试验不确定度分析评估的实例计算,给出了对数值试验结果有重要影响的试验因素和交互作用以及各类不确定度分量的大小,并提出了降低船模阻力数值试验不确定度的建议。