1 Introduction

Although the majority of ships,especially the seagoing ones,typically operate in more or less unbounded water areas and methods for estimating hydrodynamic forces in free sailing are of primary importance,not so rare are situations when the vessels approach rigid boundaries or other objects closely enough to make account for the hydrodynamic interaction absolutely necessary for adequate modeling of the behavior of these ships.These situations include sailing in canals and other restricted areas,overtaking and encountering at small lateral distances occurring in areas of intense ship traffic such as haven approach channels,lightering operations,and berthing and unberthing,entering locks.

The hydrodynamic interaction typically observed in the form of somewhat unexpected suction,repulsion,or forced yawing effects has been known to seafarers since long ago but formerly there were no urgent necessity for predicting actual values of the interaction forces and moments as good seamanship practice of avoiding close proximity maneuvers at a more or less tangible speed was sufficient.However,planning safe sea replenishment operations,some approaches to working out environmental maneuvering standards,needs of expert assessments of certain maritime accidents,and,especially,necessity of adequate reproduction of the behavior of ships on computerized bridge simulators made the hydrodynamic interaction problem important enough to trigger multiple experimental,theoretical,and numerical studies.

A rather comprehensive review of literature on the hydrodynamic interaction was presented by Sutulo and Guedes Soares(2012),and here,emphasis will be given to more recent contributions not available at the time of preparation of the cited paper.

It should be noted that in some cases,the hydrodynamic interaction is considered in a somewhat extended sense embracing also interaction related to the sea waves action with such effect as water flow in the gap between two ships moored close to each other,wave sheltering effect,and influence of interaction on ship motions in waves.These issues were discussed by Faltinsen(2011)but the present review is dealing exclusively with interaction in calm water caused by non-zero speed of advance of at least one of involved vessels or by some steady current.

1.1 Experimental Studies

There exists a large group of recent contributions dedicated mainly to experiments with scaled models although some of them are complemented with CFD modeling.One of the most sophisticated experimental studies was performed by Lataire et al.(2011)in a shallow water tank equipped with two carriages one of which was two-coordinate.Over 2000 static and dynamic tests were performed,and regression models applicable to lightering and overtaking scenarios were devised.Duffy and Renilson(2011)carried out a somewhat simpler experiment measuring loads on a moored model when another model was passing by at close distances.

4．动物感染试验。结果小白鼠注射病原菌的第四天开始死亡，死亡的小白鼠皮肤发绀，剖检肝、脾、肺、心出血，呈败血症，剖检发现注射部位有直径0.9～1.1 cm的脓肿，浓汁呈黄绿色。而对照组作的均未见死亡，从死亡的小白鼠的肝脏、重新分离到革兰氏阳性单在、呈双或链状排列的球菌。试验表明，分离的菌株对小白鼠有致病性。

Arslan et al.(2011)studied a less usual case of hydrodynamic interaction between two ships in the transverse flow which corresponds to the case of ships moored stern to pier and subject to a current along the pier.The experiment was carried out in a circulating water tunnel with cylindrical models representing the ship sections.In addition,2D computations with the code Fluent using the Smagorinsky LES model were performed demonstrating qualitative agreement of the flow fields.

Some latest studies focused on working out empiric“universal”regression models for fast estimation of the interaction forces(Chetvertakov et al.2011).

任务驱动型作文名称是张开的杰作，而其命制形式不是我国独创，它的渊源是国外的作文。比如美国SAT试题，能力上，注重考查考生的提出观点与用逻辑或数据支撑观点和严密推理的能力；内容上，“都和公共问题息息相关，或与现实问题挂钩，或探讨基本理念问题”。（《难以套题的外国高考作文》，商群《南方周末》）2015年来，任务驱动型作文材料直面公众生活领域，在任务指令下完成对材料的思辨理解，使得它的作文思维区别于以前的作文。要在思辨中将情景材料涉及的事与理论清，这就是任务驱动型作文的独到之处。

This approach was brought to perfection by Gronarz(2011)who proposed the so-called “hybrid regression”which resulted in a relatively simple algorithm for describing all interaction loads on two ships moving parallel to each other with various velocities and various length ratio values.Although,the method seems quite elegant,it is not able to embrace cases of non-parallel motion.Xu and Sun(2012)have used a novel approach approximating ship-to-ship experimental data for the overtaking and encountering parallel motion with an artificial neural network.

Sano et al.(2012)have studied experimentally interaction of a ship with the channel bank having created polynomial regressions for the interaction forces followed by a rather interesting local stability analysis.However,the used linearized mathematical model raises certain doubts:the effects of the heading and drift angles seem to be blended,and it is overlooked that at nonzero balancing parameters,the surge equation cannot be decoupled from the sway-yaw equations even in the linear approximation.Another linear regression was obtained by Ibaragi et al.(2012)for the ship-to-bank interaction,and this study seems also to suffer from mixed effects of the heading and drift.

Probably,impossibility of creation of universal multifactor regression models valid for arbitrary relative motion of interacting ship and the desire to have a very fast estimator stimulated the appearance of ultimately simple interaction models or the so-called “field theory”based on the concept of zones of higher and lower pressure around the ship’s hull(M cArthur 2011;Maxwell 2011).This concept can be useful in training as it gives a simple explanation,e.g.,for the bank suction and rejection but,obviously,it is impossible to expect reasonable quantitative predictions with such simplistic method.

1.2 Potential Codes

As long as empiric methods practically are not capable to account for all possible combinations of mutual positions and motions of interacting objects,numerical methods were considered as alternative.To be used online,a method must be sufficiently fast which can only be achieved in the case of boundary element potential algorithms.

Sutulo and Guedes Soares(2008)developed a double-body code which is based on the method of Hess and Smith(1964).Being relatively fast and flexible,the code is appropriate for online computations in ship simulators of the interaction forces for arbitrary number of ship hulls with arbitrary relative positions and motion.In the beginning,the algorithm was used only for deep waters.Later,it was extended to cover the cases of the flat bed shallow water and arbitrary shape of the bottom and banks(Zhou et al.2010).The algorithm was also combined with the maneuvering simulation code and was used to simulate motion of two ships in overtaking maneuver(Sutulo and Guedes Soares 2009).

Yasukawa and Yoshida(2011)have modeled two Wigley hulls advancing at close proximity with the lifting surface vortex panel method.Effect of thickness was completely neglected.Some of the studied cases were for one of the hulls deflected by 5 or 10°.Obviously,effects of the nonzero drift angle and of the changed configuration were then blended.

十九大以来我国新时代社会主要矛盾成为研究热点，取得了很多有价值的理论成果。总体来看，集中在对主要矛盾新论断的内涵、提出过程及转化依据、化解方式、重要意义等方面的研究[1][2]。而对社会主义初级阶段新旧主要矛盾之间的关系以及其转化逻辑缺乏深入研究，对其转化的时代价值还有待挖掘。本文将着重从“变”与“不变”的视角分析新时代社会主要矛盾的特点，从理论、历史和实践三个维度探究社会主要矛盾“变”的内在逻辑，探究这一新论断对于习近平新时代中国特色社会主义思想的形成、国家治理的现代化以及全面深化改革的推进的重大意义。

Skejić et al.(2011)used the slender-body developed by Tuck and Newman(1974)for estimating interaction between a ship maneuvering around a fixed or freely drifting cargo storage facility of hexagonal shape.Qualitatively satisfactory results were obtained in spite of poor applicability of the slender-ship concept to this case.However,Xiang et al.(2011)discovered that the slender-body theory typically over predicts the interaction forces compared to the results obtained with a 3D panel code developed earlier by Xiang and Faltinsen(2010).

Van der Molen et al.(2011)estimated forces in a moored ship induced by a passing by one using a finite-Froude number panel method.

Von Graefe et al.(2015)applied the Rankine source method to the interaction between a container ship and a feeder vessel.A similar method,in a more general formulation comprising also effects caused by incoming waves was applied to two Wigley hulls in parallel motion by Yuan et al.(2015)but that study was more focused on interaction effectin the seakeeping sense.

Perspectives for preferable application of the double-body potential-flow model for modeling interaction loads were also outlined by Pinkster(2016)who suggested a multi-domain variation of the method facilitating computations in the case of complex bank and fairway configurations.In(Van Hoydonck et al.2016),the potential code ROPES was thoroughly validated for two hull forms in shallow water and with possible presence of tank walls.It was found that the code is able to predict reliably interaction forces in encounter maneuvers with certain underestimation of peak values.The latter inspired a suggestion to introduce appropriate empiric corrections.

Sutulo et al.(2012)presented a validation of the potential interaction code against experimental results that were obtained in the towing tank for a tug operating near a large vessel.The comparisons of the results corresponding only to parallel motion and equal speeds showed good agreement with experiments for the sway force and yaw moment in most cases.Large discrepancies were,however,noticed at very small distances between the ship sidewalls which were attributed to the influence of viscosity and/or wave making effects neglected by the double-body potential code.

Recently,Kadri and Weihs(2015)have revisited the slender-body theory applying it to the problem interaction of two bodies of revolution in parallel motion in unbounded fluid.The authors have compared their numerical results with classic experimental data obtained by New ton(1960).The authors focused on obtaining higher-order solutions and demonstrated that they provide better agreement with experiments.The slender-body technique may result in very fast algorithms but is not able to properly account for the specifics of shapes of interacting bodies that may become important in very close proximity.

1.3 Application of Field Computational Methods

Lately,a number of publications were dedicated to application of various CFD codes implementing the Reynolds-averaged Navier-Stokes(RANS)model.Such codes cannot be applied directly in maneuvering simulations but they are very important for acquiring better insight into the details of the flow and can serve as a substitute for physical experimentation.

Benedict et al.(2011)presented a comprehensive study emphasizing that“the implementation into simulators requires a holistic model valid for the entire range of parameter combinations”.To handle the most general cases with the CFD,the so-called overset method using overlapping grids was developed on the basis of the finite volume and level-set techniques.However,most of the results refer to the parallel motion where they were compared with the experimental data showing rather good overall(over the range of instantaneous stagger in the overtaking)agreement though very large disagreement could be present at some specific relative positions.The crossing motion case was studied only numerically using the “transformed space”,i.e.,reversing the flow around the larger vessel.

“纲要”课程的内容主要是概括近代以来中国志士仁人和人民群众为实现民族独立、人民解放、国家富强、人民富裕的历史任务而艰苦探索的历史，重点反映近代以来久经磨难的中华民族在中国共产党领导下英勇奋斗，实现了从站起来、富起来到强起来的历史性飞跃过程。“纲要”课程的这些内容与爱国主义教育基地包含的内容和承担的使命是非常契合的。

Yang et al.(2011)studied Wigley and KVLCC2 hulls by means of the commercial code FLUENT,and the RANS results were compared with those obtained with the potential flow method developed by Xiang and Faltinsen(2010).Agreement in the passing by maneuver for two identical Wigley hulls at a low Froude number was perfect.The RANS computations with the KVLCC2 forms were carried out for the Froude number values 0.037 and 0.055.Zhang and Zou(2011)have studied the interaction of two ships(KCS and Osaka types)in encountering and overtaking in a shallow canal with the code FLUENT using the layering method of dynamic meshing.The sway force and yaw moment coefficients were computed for Fn=0.04,0.08 and for various values of the canal width,relative depth,and lateral distance to the bank.

Sadat-Hosseini et al.(2011)performed CFD computations of the interaction between two tanker models(KVLCC2 and Aframax)advancing with the same speed in shallow water.The in-house RANS code CFDShip-Iowa adapted to multi-object configurations was used,and results of the computations were compared to the towing tank measurements.The overall number of grid points exceeded 8×106,and the Froude number varied from 0.046 to 0.06,i.e.,was very small but the free-surface effects,though not very significant,were captured by the level-set method.The agreement between measured and computed values was rather large and in most cases varied from 30%to 200%but it must be also noted that measured absolute values of the loads were very small for 3-4 mmodels,due to very small velocities.

Much better agreement was reached by Simonsen et al.(2011)who applied the commercial code Star CCM+for studying interaction between a tanker ship and a tug in deep water using an unstructured grid in coarse(1.8×106 cells),medium,and fine(8.9×106 cells)variants.The isotropic k-ε/k-ω SST turbulence model with wall functions was used.Satisfactory and even good agreement with the tank data was demonstrated for parallel motion and also for the tug’s relative heading 20°,bow inwards.It must be noted that in some cases,much better agreement was reached with the coarse grid than with more refined ones,which probably is related to the fact that monotone convergence over the grid refinement was not quite certain.

Zou and Larsson(2012)studied interaction between an Aframax tanker and a KVLCC2 type ship using the finite volume RANS solver XCHAP.Only the case of parallel center planes and equal velocities was considered.The wave making was neglected,and the double-body model was used.Not only the hulls but also the rudders and propellers were modeled with the overall number of cells reaching 5.5×106.The computed results were validated against available independent computational and experimental data.While the agreement with the CFD results obtained at the Iowa University is always good,this is much less so when it goes about comparison with the tank data:the discrepancies in the sway force and yaw moment reached 100%and even more.Nikushchenko et al.(2012)have presented data about interaction forces and moments in parallel steady motion computed for two Wigley hulls using three commercial codes:ANSYS Fluent(data presented for the surge force only),NUMECA FINE/Marine,and Star CCM+.The agreement between results obtained with different codes varied from quite good to relatively large(30%-50%)discrepancies depending on the component and on relative position of the hulls.Some development of these studies for the KCS container ship in overtaking maneuver at relatively high(up to 0.26)values of the Froude number and using different turbulence models was presented by Nikushchenko and Zubova(2015).

Fonfach et al.(2011)used commercial CFD codes to model the flow between the same tug and tanker forms as studied in(Sutulo et al.2012)using four different flow models with viscous or inviscid fluid and with or without wavemaking.In that study,viscous flow was modeled for the full-scale Reynolds numbers.The obtained data showed that,likely,account for the free-surface effects is more important than that of viscosity.However,it must be emphasized that in general,the results of the cited reference are harder to assess and discuss as computations were performed using two different commercial codes with different grids and different turbulence models so that effects of those factors were mixed with the effect of the flow model per se.In addition,viscous computations were performed for the full scale that made comparisons with the tank experimental data less meaningful.In many cases,iterative convergence was not achieved.As result,the conclusions,presented there,even if they happened to be correct,must be viewed as uncertain let alone any quantitative assessments.

In the paper by Sian et al.(2016)interaction of an LNG carrier with a ship of Series 60 hull was studied in a towing tank and with the commercial CFD code Fluent V15 for the case of parallel overtaking motion in a shallow canal was considered.The SST k-ωturbulence model was used,and all reported computations were performed with 2M cells.The experimental and numerical results showed satisfactory agreement with some under-prediction(from slight to moderate)of the sway force and some over-prediction for the yaw moment while data for the surge force were only presented for few cases.In the contribution(Toxopeous and Bhawsinka 2016),interaction effects on a full-bodied ship entering a lock were predicted using the in-house CFD code ReFRESCO,validated with the scaled-model experimental data and compared with predictions obtained with the in-house double-body potential flow code ROPES.In the CFD modeling,a combined sliding and deforming grid approach was used but the free-surface effects were neglected as the maximum Froude number 0.026(or 0.091 when based on the water depth)was considered small enough for application of the rigid-wall condition.The SST k-ωturbulence model was applied and wall functions were used for modeling the flow close to the hull surface.Two grids with 1.6 and 4.6 M cells were applied.The panel method computations were performed using 1650 panels on the hull and 2091 panels on the lock walls.Agreement with the experimental data was demonstrated to vary from reasonable to good,especially at smaller time steps.Refinement of the grid in RANS computations improved agreement for the surge force but worsened it for the sway force.The potential flow model in most cases heavily under predicted the magnitudes of the sway force and of the yaw moment.

Yuan and Incecik(2016)described results of application of the in-house potential flow method MHydro.Unlike many other potential interaction codes,this code accounts for wavemaking effects applying the linear steady flow free-surface condition which is quite adequate for the ship-bank interaction but much less so for the overtaking maneuver with substantial difference of velocities of the interacting ship.Comparisons with tank data,two CFD codes and the double-body potential code ROPES did not show any definite patterns.For instance,while the code MHydro predicts the sway interaction force better than other codes,it fails to predict the yaw moment.

A very comprehensive attempt to investigate capabilities of various interaction prediction methods was undertaken by Van Hoydonck et al.(2015)who compared tank results for a KVLCC2 model with those obtained with the CFD codes Re FRESCO and ISIS-CFD and with the potential code ROPES mentioned in the previous subsection.The Froude number was 0.055,and the Reynolds number was 1.5×106(model scale).In some ReFRESCO computations,not only the hull but also the rudder and the propeller(on the body force level)were modeled.The overall number of cells varied from 2.9 to 34.7M cells.Even for the finest grid,no interaction convergence was achieved with oscillating deviations reaching 6.6%in sway interaction force,and for the yaw moment,these deviations were even much larger than the average value.Also,practically,no convergence over the grid density was reached,especially for the surge force.Most of computations with the code ISIS-CFD were carried out for 16M cells.The grid convergence studies carried out for four grids with the number of cells varying from 5 to 29.7 M showed better trends than in the case of ReFRESCO but uncertainty at 16M cells is not quite excluded.Comparisons between experimental responses and those obtained with various codes look rather disappointing in the sense that no one of the codes was able to predict reliably all components,and the divergences are often significant reaching 50%,100%,and even 200%.Also,it must be noted that the observed influence of the propeller was substantially stronger than could be predicted with the potential flow method(Sutulo and Guedes Soares 2012).

Shevchuk et al.(2016)have performed a thorough numerical study of the flow between the ship hull and the bottom of a shallow canal with an in-house CFD code based on the OpenFoam software.In particular,it was found that at very small underkeel gaps the boundary layers on the hull and on the bottom are fused which leads to an additional pressure drop and intensifies the squat.Besides the more or less usual RANS modeling,a hybrid(RANS+LES)closure was applied with a much finer grid(13 instead of 4M cells)and then self-sustained motions of the ship in heave and pitch caused by the unsteady flow separation were captured.However,that does not change substantially the time averaged values of the sinkage and trim.

下面比较两种算法的时间和空间复杂性.在保证两种方法具有相同计算精度的情况下，通过不断增大系统模型状态的数量，统计算法的执行时间和消耗的内存空间.图5给出了两种安全性验证算法时间和空间随系统状态数增大的变化趋势.

Rattanasiri et al.(2014)applied the commercial code ANSYS CFX to a less common problem of hydrodynamic interaction between several autonomous underwater vehicle operating in tight formations.Numerical results were compared to experimental ones,and special attention was paid to effects of alteration of resistance and to possible gains that can be achieved on optimized configurations.The presented review of the published results rather clearly demonstrates that so far,in spite of considerable efforts,it has not been possible to obtain definite and crisp estimates of possible discrepancies between predictions of hydrodynamic interaction loads obtained with various methods,and the performed comparative studies are not sufficient and must be continued.

如果GB/T 17281-2016中规定的方法是和GB/T 13610-2014中所规定的方法一起使用，应把GB/T 13610-2014得到的未归一化结果与GB/T 17281-2016得到的结果相结合，体现在一个测试报告中。戊烷作为架桥组分时，样品气中碳数为n(6≤n≤16)的i组分摩尔分数按式(4)计算。

The Turbulence suppression model allows the user to mimic the effect of transition from the laminar to turbulent flow if the location of transition is known priori while the γ -Reθ model is determining that location automatically and therefore is used more often.In all variants,the SST model requires a finer mesh with an increased number of mesh cells around the surface to capture the viscous sublayer effects which result in a significantly larger computation time.It was found that while the force/moment coefficients obtained with various turbulence models varied insignificantly,the speed of iterative convergence turned out rather different(Fig.4)with somewhat better behavior for the k-ε model which pre-determined the final choice as the required computations are very time consuming.

2 Ship Models and Interaction Configuration

Computations of the interaction forces were performed on two ships:a smaller tug model(designated as ship 1 or tug)and alarger tanker model(ship 2 or tanker)at the scale 1:25.The main characteristics of the vessels in two scales are presented in Table 1 and their hull forms are outlined in Fig.1.

Considered were two values of the water depth given in Table 2,and corresponding to the conditions of the tank tests is described in(Sutulo et al.2012),where also all necessary details about the experimental setup are given.Two ship lengths are presented in Table 1,the length overall(o.a.),and the length between perpendiculars(p.p.).

所罗门群岛地震（MW6.2）于2003年6月12日发生在太平洋地区的所罗门群岛附近，震源深度185km。该地区的地质构造非常复杂（Mann and Taira，2004），而且我们没有发现对于此事件的任何详细论述的文章。因此，不能将我们的结果与以前的研究作比较。我们确定的震源椭球很细长，沿单一的主轴延长，表明破裂为单向扩展。平均破裂速度被认为有3.2km／s的现实值（表2）。此外，因为它合理地高于零，我们可以认为扩展是单边的。剩余的二阶矩参数汇总于表2和图7所示。

The axes Cxyz were linked to each ship with the x-axis pointing forward,y-axis—to the starboard,and the z-axis—downwards.The origin was defined as the intersection of the centerplane,midship plane,and waterplane.The both centerplanes were remaining parallel in the present study,and the position of the tug relative to the tanker was described by location of the origin of the tug’s frame in the body axes of the tanker,i.e.,by its longitudinal stagger ξand the signed lateral distance ηbetween the centerplanes which is always negative for a tug located at the port side from the tanker.

The dimensionless values for the forces and moments are presented in Fig.10 for the depth H1 and in Fig.11 for the depth H2 in the form of graphs as functions of the relative lateral distance η′.Besides,the isolated symbols corresponding to four different flow models and to the experimental data,presented are solid lines representing the data obtained withthe panel method.The results for the viscous flow with free surface are presented with error bars representing the maximum and minimum force or moment values present on the final interval of the iterative convergence plots.Similar error bars are not shown for the case of inviscid flow with the free surface in order to not congest the graphs too much,although in those cases,the iterative convergence was even more difficult to achieve,likely,because of the absence of natural dissipation.It should be emphasized that the thus estimated uncertainty caused by poor iterative convergence is probably exaggerated as the physical flow itself can keep oscillatory character which is probably typical for flows in narrow gaps with the wavemaking effects,and in such cases time-averaged values must be taken as estimates anyway.Although the authors do not possess experimental time histories,this is indirectly confirmed by the fact that absence of iterative convergence was also observed by Van Hoydonck et al.(2015).

Due to specifics of the interaction configuration characterized by a large difference in the dimensions of the interacting ships,the interaction forces of surge X,sway Y,and the interaction yaw moment N,were only computed for the smaller ship(tug).Each interaction force was obtained as the difference between its total values obtained in presence and in absence of the interacting large ship.All the forces and moments were non-dimensionalized as:where ρ is the water density,A=is the reference area,∇is the ship displacement,and L is the length between perpendiculars.The subscripts 1 and 2 here and further correspond to the tug and tanker respectively.

1) SST k-ω model without transition model(fully turbulent)

No results for the loads in heave,roll,and pitch are presented in this paper as,first,they are less important in interaction scenarios,and,second,the authors did not possess any experimental data for them.

3 Problem Formulation

3.1 Computational Domain

The finite computational domain has the shape of a parallelepiped(Fig.3)whose transverse section and location of the hulls corresponded to the actual tank layout and had longitudinal extensions:2.5L2 to the front of the larger ship and 4L2 behind it.The depth was defined equal to H1 or H2(depending on the case)in model scale from the undisturbed free surface.In the case of the deformable free surface handled with the two phase flow model,the air layer extended 0.1L2 up from the still water-free surface.The width of the domain was always 8 m which is not arbitrary but is the actual width of the towing tank used in the tests described in(Sutulo et al.2012).Also,exactly as it was in the tank tests,the transverse location of the smaller ship was in the central longitudinal plane of the domain or tank while the larger model was shifted in the lateral direction to set the required distance|η|between the centerplanes of the ship hulls.

3.2 Governing Equations,Turbulence Model and Boundary Conditions

The standard Reynolds-averaged Navier-Stokes equations were applied in the whole computational domain and used for the both flow phases:

where t is the current time;Fi are components of the volumetric force which is only here represented by the vertical gravity force; are the components of the averaged fluid velocity;xi are the Cartesian coordinates;ρ is the water or air density; is the averaged pressure;and are the turbulent stresses disappearing when the inviscid fluid model is considered and the momentum equation becomes the Euler equation.

Obviously,this equation must be complemented with the continuity equation

and with the closing equations representing the turbulence model.

Although the review presented in the Introduction indicates that the SST k-ω turbulence model was preferred by most researchers,no solid explanations of this choice for interaction problems were presented.That is why,an auxiliary comparative study performed for the smallest water depth H1 and lateral distance ξ′=1.36 with account for the deformable free surface with the following turbulence models:

Computations were carried out for two different speed values as shown in Table 3,where standard definitions for the Froude number based on the ship length and water depth H are used,i.e.,andrespectively with g being the magnitude of the gravity acceleration.

2)SST k-ω model with the Turbulence Suppression transition model

3)SST k- ω model with the γ -Reθtransition model

4)k-ε model

建筑自身除了可以向使用者传达一定的信息以外，还可以引导使用者的行为。正如布莱恩·劳森所说，“一个房子不仅给人们提供遮蔽，而且我们还期望它看上去像一个房子，从而也告诉了我们的来访者举止应该如何[26]。”西区是接待宾客的区域，深柳堂、方形水池与临池别馆中心对齐，隔岸呼应。临池别馆的屋顶与庭园大门的屋顶结合，使面宽与深柳堂相等，形成方正整齐的格局。临池别馆的用地不在庭园的区域，而是缩进了门厅的用地里，拉宽了与深柳堂之间的空间尺度，也使西区空间更加明亮。方正整齐的空间格局和明亮宽敞的空间营造了严肃与端庄的空间氛围。东区作为休闲观赏区，通过曲折多变的走道以及高矮参差的树木，营造了轻松自由的环境气氛。

As result,it was decided to revisit one of the scenarios considered earlier and perform thorough comparative computations with the recognized commercial code Star CCM+.Although the scenario covers the cases studied in(Sutulo et al.2012)and(Fonfach et al.2011),the present study is quite independent and original and is aiming at obtaining more credible data on relative importance of accounting for wavemaking and viscous effects in interaction load prediction.Special attention was paid to appropriate choice of computational domains and grids,to selection of a single turbulence model,and to convergence studies.At each interaction configuration,CFD computations were performed for four possible combinations formed by accounting or non-accounting for viscosity and wavemaking.In addition,experimental and panel method data are also shown for comparisons.To avoid any ambiguities,it should be taken into account that through the present paper,the term “Free Surface case”means the case when the actual kinematic and dynamic boundary conditions on the free surface are met and the wavemaking effects are modeled.This is opposed to the “Rigid Wall”case when the non-penetration(and free-slip when the viscosity is present)condition is applied on the free surface of the fluid and all wavemaking is neglected.The main purpose of the study is to try to demonstrate relative importance of purely inertial forces(provided by the double-body potential theory)and of influence of viscosity and wavemaking in problems of hydrodynamic interactions.

Hence,the main set of computations was performed using the k-ε turbulence model described by:

五轮山井田隶属贵州省毕节地区纳雍县，北边与坪山井田为邻，东边过水公河向斜轴与补作勘查区相邻，西边与加戛背斜南西翼南段相毗邻，面积43.94 km2。井田煤层埋藏较浅，煤层原生结构完整，含气量高，煤层气资源丰富，平均资源丰度 8.04亿m3/km2，可采资源丰度2.63亿m3/km2，远远高于全国平均水平，勘探开发潜力巨大[14-16]。因此，分析了该区主采煤层8号煤层含气量的分布特征及地质影响因素，为五轮山井田煤层气勘探与开发试验提供地质依据。

and

where k is a turbulent kinematic energy;ε is a turbulent dissipation rate;μ is the fluid viscosity;μt is the dynamic turbulent viscosity,S ij is a component of a fluid element deformation rate,with i,j=1,2,3,and σk,σε,C1ε,C2ε are the model constants,as presented by Versteeg and Malalasekra(2007).

As the considered problem was steady,the reversed flow was modeled with the following boundary conditions:

Analysis of results turned out not very easy as the character of agreement/disagreement between various flow models is rather different for different force/moment components,various lateral distances,and even for various water depths.

·Outlet plane:pressure equal to the hydrostatic pressure in the water domain and atmospheric pressure in the air;

·Bottom and sidewalls:the non-penetration condition and zero shear stresses;

·Air-water separation surface:the non-penetration condition for the rigid-wall model(RW)or the velocity and pressure continuity otherwise;

·Hull surface:no-slip condition(zero velocity)for the viscous fluid model and non-penetration condition for the inviscid fluid.

Of course,in computations with the inviscid fluid,the turbulent stresses vanishes,and the RANS(1)reduce to the Euler equations,and part of the boundary conditions are simplified accordingly.

3.3 Computational Grid

The final meshes adopted for the present study were generated after a number of comparative computations,and they were of the same type as adopted in Wnęk and Guedes Soares(2015).Although in general,inviscid flow computations allow much coarser grids than the full RANS modeling,in this particular study,it was decided to apply as similar grids as possible in all flow models to exclude the factor of approximation of the hull surfaces.The finally adopted hexahedral mesh counted around 0.65×106 cells for the inviscid flow without free surface and 0.9×106 cells when the viscosity was accounted for.In the inviscid flow case,the same mesh was kept except that denser prismatic layers were removed in the vicinity of the hull.Also,in the case of wavemaking computations when the two-phase flow was modeled,the meshes were somewhat larger counting about 1.6×106 cells for inviscid flow and about 2.3×106 cells for viscous one because of additional meshing above the undisturbed free surface.The exact number of cells also somewhat depended on the lateral distance between the two hulls.In the viscous flow cases,14 prismatic layers on the surface of the tug hull were generated with the first layer’s thickness proportional to the dimensionless wall distance y+ ≈1,and the so-called “all-y+wall treatment”option(STARCCM+User Manual 2014)was activated which is emulating the wall-function approach for coarse meshes and is resolving the viscous sublayer for fine meshes The mesh was also refined in the free-surface region(Figs.5 and 6).

Table 4 presents some results of the mesh refinement convergence study for the viscous two-phase flow for the smaller depth H1,dimensionless longitudinal stagger ξ′=0.014,and for the dimensionless lateral distance|η′|=1.47.The mesh size was being reduced until the convergence was captured with reasonable certainty.Unfortunately,it turned out impossible to reach rather definite convergence for the smallest distance|η′|=1.36 with the available resources which makes estimates for smallest distances less certain.However,in view of rather poor results of the grid convergence study presented in(Van Hoydonck et al.2015)for even much finer grids,this is not surprising and indicates that the interaction problem is especially sensitive to the grid refinement and studies in that direction must continue.

3.4 Time-Domain Convergence Studies and General Remarks

The code Star CCM+was applied in this study in the unsteady mode presuming settling of the final steady regime.For the purpose of the time-domain convergence studies,simulations corresponding to the 40 s duration with the time step 0.01 s(selected after preliminary tests)and with ten iterations for each step were carried out.The minimum convergence criterion of 1.0×10-4 relative error for all scalars was easily fulfilled in all the cases with the rigid flat-free surface and all forces of interest attained steady values.Typically,convergence was reached after 20,000 iterations;however,in some cases 40,000 iterations turned out necessary(Figs.7 and 8).

In the case of deformable free-surface simulations for viscid and inviscid flow two-phase flow,the convergence was more difficult to achieve.Values of the forces only stabilized sufficiently after more than 50,000 iterations(Fig.8)and even more for some cases.

The most serious convergence difficulties were met at the larger depth H2,when the smaller model was located in the wake of the larger one(Fig.9).Apparently,the main cause of poor decay of oscillations was the almost one-dimensional propagation of induced waves in the shallow water.Those waves have wavelengths comparable to the length of the larger ship and contain a lot of energy generated by the impulsive start of the ships.

他的脚离我的头只有几英寸远，我理应去安慰他，我本应该主动去安慰他才对，因为我从小就是受这种教育长大的。相反，我觉得那样做很恶心。看起来那么强壮的人，不应该表现得这么脆弱。为什么他不能像其余人一样悄悄地哭呢？

All computations were carried out for model-scale values of the Reynolds number as indicated in Table 3 The used hardware was represented by a cluster with 8 CPUs,Intel®Xeon®E5420,4 cores each,clock frequency 2.50 GHz and with 16GB of RAM available.

4 Results

4.1 Interaction Forces

All CFD computations were performed for exactly the same conditions for which experimental values were available and also they were carried out for the isolated tug which was necessary to get the pure interaction loads.It is,however,clear that due to the flow symmetry,the own load was non-zero for only the surge component.

笔者认为热奈特对于戏拟的定义较为准确和全面：“戏拟是对一篇文本改变主题，但保留风格的转换。”(萨莫瓦约,2003:47)戏拟是后现代派作家常用的一种写作手法。他们通过对传统的叙事模式、技巧；历史人物、事件；经典作品中的人物、主题等进行模仿，使其变得荒诞、可笑，以达到对历史、传统、经典进行讽刺和否定的目的。

The following nondimensional position parameters will be used further:where the subscript 2 means the ship number associated with the tanker.It is clear that ξ′=0 when the midship planes of the both vessels coincide,and ξ′=1 means that the midship of the tug coincides with the fore perpendicular of the tanker(Fig.2).

全文的详细阅读完成之后，语言和内容基本上过关，这时候需要回过头来细看文章的篇章组织，感受文章的结构之美。这个环节充分利用建构主义教学的协作会话理念，由学生分组讨论完成结构分析和各部分大意归纳，并选派代表将小组意见表述在黑板上。在本人的教学实践中，各个小组由于对课文有较为全面的理解，都给出了自己合理的结构分析，并概括了各部分大意。各组的结构分析并不完全一致。

While the graphs provide general view of the dependence of the interaction forces on the lateral distance,they are difficult to analyze in detail,and the same responses are duplicated in the form of bar charts presented in Figs.12,13,and 14.Data corresponding to various flow models are marked as follows:“RW”means “Rigid Wall”which corresponds to the non-penetration and free-slip condition on the undisturbed free surface without any wavemaking(double-body approximation);“FS”means“Free Surface”which is deformable and modeled with the two-phase flow with wavemaking.It is also marked(directly or with the acronym “IF”)whether the fluid was assumed to be inviscid(i.e.,the Euler equations were modeled)or the viscosity was accounted for and RANS equations served as the governing equations(acronym“VF”).Experimental and panel method data are taken from(Sutulo et al.2012).It should be noted that while the experimental results had been obtained in the towing tank with the lateral dimensions corresponding to the computational domain described above,the panel method computations had been performed for the horizontally unbounded fluid.It is,however,obvious that for the present interaction configuration(see Fig.3),the influence of the tank walls that could have been accounted for by placing fictitious series of hulls at appropriate distances could only be insignificant that can be roughly estimated extrapolating the plots on Figs.10,11,and 12.

高校的资产管理机构为国有资产的一级管理机构，由相应的主管校长负责，实现既管资产，又管事务，兼管人员的统一。高校国有资产管理处独立行使国有资产出资者的权利，依法对相应的国有资产进行监督管理。其主要职责有：（1）加强日常国有资产管理，对国有资产的安全、完整性，相应的保值增值进行监督监管；（2）制订相关的高校国有资产的规章制度，依法行使指导监督权力；（3）依法对下级部门负责人进行任免，考核。设立相应的奖惩制度，完善有关的激励、约束机制。（4）代表学校向校办企业派遣监事人员；（5）统筹负责学校国有资产的产权相关工作，制订相应的融资、发展规划。

·Inlet plane:the incoming homogenous flow velocity as defined in Table 3;undisturbed free surface;

4.1.1 Surge Force

First of all,remarkable is the fairly good agreement between results obtained with the panel method and with the CFD code for the IF+RW flow model.It must be noticed that the applied version of the panel method tends to provide somewhat biased results for the surge force while capturing the qualitative behavior(Sutulo and Guedes Soares 2016).In theory,the responses could be identical as in both cases,the fluid was perfect and the wavemaking was absent.The observed difference can be partly explained by a much finer discretization in the field method but also by accounting for the tank sidewalls while in the panel method computations,the fluid was assumed unbounded in the horizontal plane.On the other hand,finite distances of the inlet and outlet boundaries do not exactly correspond to the absence of such boundaries in the panel method.

Accounting for the viscosity and/or wave making always improved the agreement with experimental data,especially at closer lateral distances but separate influence of these two factors looks more complicated.Although it could be expected that the most realistic flow model accounting for both viscosity and the wavemaking,this does not happen in all the cases:often the perfect fluid model provides better agreement although the differences caused by viscosity are not so large.But rather certain is that neglecting the wavemaking effects makes the agreement worse.In particular,relatively large magnitudes of the surge force at close distances are caused by the flow blockage mainly caused by wave making although also to some extent—by viscosity.Of course,neither the panel method,nor the IF+RW field method are able to capture this effect.

4.1.2 Sway Force

Agreement between the panel method and the CFD computation without viscosity and wavemaking is again good.Some difference at the smallest lateral distance is certainly caused by a relatively small number of panels.For relative lateral distances greater than 1.4 agreement is good for all data although account for the wave making and viscosity gives better agreement with the experiment.At smaller distances,however,the methods neglecting wavemaking are not able to capture the drop of the suction force and even its transition to repulsion.Obviously,ever increasing suction at unlimited approach is theoretically correct for the pure potential flow without free-surface effects but it has always been clear that in real fluid,the flow will be sooner or later blocked,the suction will disappear,and the zone of the higher pressure in the fore part of the hull will result in repulsion.This should happen even in the absence of the free surface and wavemaking effects but the results presented here show ed decisive role of the wavemaking.Although sometimes the full RANS model VF+FS gave better agreement than the model IF+FS,in other cases,the observed agreement was even worse.However,it must be taken into account that at smaller lateral clearances,the uncertainty of the RANS computations is higher as long as the grid convergence was not achieved.Apparently,viscous blocking without free surface should also come into the effect but it will likely happen at much smaller gaps than explored here.There is also little doubt that a panel method with account for the actual free surface boundary condition would also provide fair prediction of the sway force inversion effect.

4.1.3 Yaw Moment

The interaction yaw moment near a much larger vessel results from differences in the suction/repulsion loads on the fore and aft parts of the ship in concern.As result,the observed differences between data provided by various methods and flow models are here larger than for the sway force but the sign inversion effect at small lateral distances is not present.Results for the smaller depth H1are rather peculiar showing unexpectedly large divergences between the panel method and the IF+RW model.Also,the trend shown in the latter case is very different from that provided by all remaining data.The initial guess that some occasional confusion happened,was not confirmed,and the same phenomenon was present in absolutely independent computations by Fonfach et al.(2011).So far,it has not been possible to obtain absolutely clear explanation of such anomalous behavior but,apparently,this interaction configuration was especially sensitive to free-surface effects,which are expected to be the most pronounced in the gap between the vessels,although such effects exist over all domain.A better agreement observed for the panel method should be rather viewed as occasional,caused by some error cancelation effects.This hypothesis is somewhat confirmed by the fact that for the larger depth such anomalies are much less pronounced.

Furthermore,despite a rough overall agreement between various flow models,account for the viscosity is not always beneficial from the view of closeness to empiric data and although in most cases it increases the absolute value of the yaw moment,sometimes the effect is reversed.Besides,increased uncertainty caused by insufficient grid convergence at small lateral gaps mentioned above,it can be supposed that this is the effect of inherent uncertainties of the RANS technique dependent on specific turbulence models whose effectiveness and adequacy have not been exhaustively explained.

Summing up,it can be stated that the disagreement between the most physically adequate VF+FS computational model and the experimental data is substantially higher than presented by Simonsen et al.(2011)who noticed the largest discrepancies for the sway force.However,those computations were performed for an apparently simpler deep water case and for the sinkage,trim,and heel of the tug taken from the experiment while these data were not available to the authors of the present contribution.

4.2 Pressure,Velocity,and Free-Surface Elevation Distributions

Dynamic pressure contours on the tug corresponding to the minimum lateral clearance and to two values of the two different longitudinal staggers ξ′=0.014 and ξ′=0.62 are shown in Fig.15.

The magnitude of dynamic pressure on the tug was also higher when the model is located in the larger perturbations of the flow at longitudinal stagger.

Figure 16 presents the velocity distribution around the tug model at the midship section of the hull for the smaller depth H1 and for the depth Froude number Fn H=0.188.The left side of the figure shows velocity distributions for the inviscid flow with the free surface,while the right side corresponds to the viscous flow.In both cases,the velocity field is changing similarly with changes of the lateral separation of the ship models.The largest velocity magnitude(0.7 m/s)near the midship of the tug model was observed at inviscid flow for lateral separation η′=1.47.It can be noticed that,as should be expected,the velocity near the hull is higher in the inviscid flow.Distribution of shear stresses in the viscous flow is presented in Fig.17.

Figure 18 presents the velocity distribution around the tug at the midship section of the hull for the larger depth H2 and for the depth Froude number Fn H=0.25.In this case,the longitudinal stagger is also larger ξ′=0.62,and the tug is located closer to the bow of the tanker;the velocity near the hull of the tanker starts to increase.In this case,larger magnitudes of the velocity are more visible also for a higher lateral distance η′=1.47.

Figure 19 shows velocity distribution on the free surface in the viscous flow for two values of the longitudinal stagger ξ.It is seen that perturbations of the flow are more pronounced in the second case with a larger stagger.This is also confirmed by Fig.20 where the velocity vector fields are shown.The free--surface elevation contour plots(Fig.21)also show larger deformations of the free surface in the second case.

An interesting observation was made in the gap between the two ship models for inviscid flow with free surface.Figures 22 and 23 present the wave profile between the two models and close to the tug with the distance 0.004 m from the hull corresponding to the mid-distance between the sidewalls.

Comparison of wave profiles was made for three different lateral separations of ship models η′=1.36,1.47,1.97.In the case with a smaller depth H1 and staggerξ′=0.014(Fig.22),a sharp profile of the wave was generated for all three lateral separations of the ships and high wave frequency was observed.The case η′=1.47 is characterized by the largest distances between the crests and troughs.

At a larger depth H2 and stagger ξ′=0.62(see Fig.23),the wave spatial frequency somewhat decreased what could be expected.Likewise,more visible is the relation between the elevation of the wave above the free surface and the distance between two ship models.The wave elevation decreases together with the increase of lateral separation of the ships.Expectedly,larger elevations of the free surface were traced at smaller water depth.At the same time,the largest descent of the water level was observed at a larger depth,and in both cases,this happened at the intermediate lateral clearance.The latter is probably related to some local resonance phenomena.

In general,it can be stated that the interaction flow is of rather complex character,and the role of nonlinear effects seems to be significant.This explains,at least qualitatively,certain observed“irregularities”in the influence of the viscosity and wavemaking effects on the estimated values of the interaction forces and moments.At the same time,it is now clear that detailed investigation of these phenomena requires much more extensive computations with simpler geometric forms.At the same time,the data already obtained can be helpful in estimating possible uncertainties related to adaptation of this or that flow model and in selecting degree of simplification appropriate in various applications.

5 Conclusions

A CFD study of interaction forces using various flow models for a small tug ship moving parallel to a larger vessel in shallow water has been carried out,and the resulting estimates of the forces and moment were also compared with the model test data and results obtained with the panel code developed earlier.The overall impression is that the ship-to-ship interaction problem is more challenging than most other problems related to the flow around a single ship hull,and the difficulties grow as the lateral clearance decreases.A number of authors discovered difficulties in reaching iterative and grid convergence using even commonly acknowledged and reliable commercial codes.The present study has generally confirmed those findings indicating that the problem still needs rather extensive and thorough investigation.The authors have made an attempt to study such factors as the fluid viscosity and gravitational waves which may or may not be in effect in various hydrodynamic models of the ship-to-ship interaction.Unfortunately,besides a more or less obvious conclusion about importance of the free-surface effects,it turned out that no definite general recommendations about application of different flow models could be worked out yet.Meanwhile,the following specific conclusions can be drawn from analysis of the results:

1.There exists an overall rough agreement between the results obtained with different methods and flow models at least at relatively large lateral distances between the sidewalls of interacting ships.

2.Differences between the results obtained with the panel method and the same flow model(perfect fluid and non-deformable free surface)implemented with the commercial CFD code typically did not have qualitative character and in most cases remained moderate and corresponding to the expected accuracy difference.The disagreement was more pronounced for the yaw moment especially at smaller water depth where anomalous results of the field method were registered.

3.The inviscid rigid wall flow models substantially under predict the magnitude of the surge interaction force for all lateral distances.While accounting for viscosity somewhat improves the agreement,rather the free surface effects are here decisive for reliable prediction.

4.Inversion of the sign of the interaction sway force happening,however,at horizontal clearances,which,however,are too small to be of practical significance,is only correctly captured by the “true free surface”flow models.

5.The viscous flow model with the rigid wall-free surface is of the least interest in studies of surface ships interactions as being very heavy computationally fails to capture many effects and does only lead to insignificant accuracy improvements compared to perfect fluid methods.

6.Account for the free-surface effects is always beneficial for improvement of the interaction force predictions at least when the exact free-surface boundary conditions are fulfilled.As the flow in the gap between the sidewalls may be of highly nonlinear character,it is unclear how adequate a flow model with the linearized free-surface condition will be and additional studies are required.

7.Account for viscosity in the free-surface flows in most cases further improves predictions but likely this not very certain improvement can be sacrificed in favor of possibly much faster calculations in the perfect fluid.This conclusion may,however,become not correct in the case of nonparallel centerplanes not considered here.

8.Poor iterative convergence with the free-surface flow models can probably reflect possible macroscopic unsteadiness of the real flow in narrow gaps,and this effect deserves special attention in the future.

In general,in spite of difficulties revealed in the present study,reliable CFD codes can serve as valuable tool for exploring intricacies of the hydrodynamic interaction between surface ships in close proximity.

Funding Information The study was performed within the project PTDC/EMSTRA/5628/2014 “Maneuvering and moored ships in ports—physical and numerical modeling,”funded by the Portuguese Foundation for Science and Technology(FCT).The first has been financed by FCT under contract number SFRH/BD/67070/2009.

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