Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

Numerical investigation of local scour below a vibrating pipeline under steady currents

Local scour below a vibrating pipeline under steady current is investigated by a finite element numerical model. The flow, sediment transport and pipeline response are coupled in the numerical model. The numerical results of scour depths and pipeline vibration amplitudes are compared with measured data available in literature. Good agreement is obtained. It is found that pipeline vibrations cause increases of scour depth below the pipeline. The scour pit underneath a two-degree-of-freedom vibrating pipeline is deeper than that under a pipeline vibrating only in the transverse flow direction. The effects of water depth are also investigated. The present numerical result shows that water depth has weak effect on the scour depth. However it does affect the time scale of the scour. The shallower the water depth is, the less time it requires to reaches the equilibrium state of scour. It is found that the vibration forces vortices to be shed from the bottom side of the pipeline. Then vortex shedding around a vibrating pipeline is closer to the seabed than vortex shedding around a fixed pipeline. This contributes to the increase of the scour depth.     

往复流作用下海底管道局部冲刷机制数值模拟

基于开源的计算流体力学模式REEF3D,建立了海底管道局部冲刷水槽数值模型,在验证单向流实验结果的基础上,进一步对往复流作用下的海底管道局部冲刷机制进行了研究,并作对比分析。研究表明,总体上往复流对管道所在海床的局部冲刷规模比单向流弱。当流向改变后,原先下游的堆积区转变成上游,优先受到冲刷,并填充到管道下方的冲刷坑,同时使水流在管道下方的作用减弱。这种回填过程使短周期下的往复流作用需要更长的冲淤平衡时间。在回填与冲刷的共同作用下,上下游的冲刷坑坡度会因流向变化而变化。     

应用切割单元法对海底管道局部冲刷数值模拟

采用SIMPLEC算法的有限体积法,求解非定常流动的N-S方程,采用k-ω紊流模型,通过模拟均匀无粘性推移质的冲刷和淤积,得到海底管道由搁置在海床上的状态变为悬跨状态这一过程的管道周围局部海床冲刷情况,建立了海底管道局部冲刷的二维数值模型。海底管道从搁置在底床上到冲刷悬空的过程中,管道周围的空间产生了拓扑变化,这给采用贴体网格并在计算过程中进行网格重构的传统方法带来了很大困难,而采用切割单元法,把物体轮廓从静止的背景直角坐标结构化网格中切割出去,计算过程中不需要传统意义的网格重构过程。数值模型预测的海底管道周围局部冲刷结果与Mao的物理模型实验实测结果及Liang和Cheng等的数值模拟结果符合较好,验证了模型的准确性。     

Numerical modeling of the arctic ocean deepwater formation: Part I. Idealized study

In this study the capability of numerical models to transport anomalously dense bottom waters from the areas of their generation on the shelf to deepwater areas is considered. These numerical models have a number of mechanisms that are favorable for this transport, but unrelated directly with the real physics of that motion. A more accurate account of the resupply of oceanic deep waters requires either a very fine resolution for the numerical model or an efficient parametrization. Two such parametrizations are proposed in this study. The first is based on amplified lateral diffusion exchange if slope instability exists. The second is related to an additional procedure allowing dense waters to leak under waters of lesser density along a shelf slope with their displacement to higher layers. The first parametrization is shown to be less efficient because it leads to a significant interaction between anomaly waters and ambient waters and to a quick loss of their original features. The second procedure is more preferable because it leads to a significant resupply of dense deep waters at the expense of dense waters generated at a distance significantly far from the shelf break. With the help of the given parametrization, during a numerical experiment these waters can be transported considerable distances away from their place of generation to the shelf boundary and deepwater areas of the ocean with a slight change in their original density characteristics.     

桩周局部冲刷三维数值模拟

用数值模拟手段研究桩周冲刷越来越引起人们的重视.基于OpenFOAM开源CFD软件,采用VOF方法处理自由水面,通过动网格技术考虑床面地形随时间的变化,构建起桩周局部冲刷的动态三维数学模型.其中,通过改进沙滑模型以修正当生成的剖面坡度超过泥沙休止角时造成的模拟失真,同时克服数值计算的不稳定性.计算结果和水槽实验资料对比分析,二者符合较好.     

基于IDDES方法的冲刷地形海底管道绕流数值模拟

近年来,海底管道对于近海油气工业中碳氢化合物的运输十分重要,预测海底管道周围水动力特征对于研究管道损坏机理具有重要意义。基于Spalart-Allmaras改进延迟分离涡模拟(improved detached eddy simulation,简称IDDES)湍流模型,利用开源OpenFOAM求解器计算单管冲刷过程中4个特征阶段管道周围水动力特征。在数值模拟中先计算了无圆管时均匀来流充分发展后的流场,依据该流场中进口流速分布设定有管道时的边界层及进口边界条件。通过将最终模拟结果与前人试验数据及数值模拟结果进行对比,表明了该模型计算结果相对于k-ε模型及LES模型更加贴合试验结果,验证了定义边界层方法的可靠性及IDDES模型在预测管道周围流场的适用性。模型计算结果显示,随着冲刷坑深度的逐渐增加,管道下游回流区会经历一个大幅缩减又逐渐扩大的过程,且逐渐关于圆管中心所在水平线对称;通过对不同冲刷阶段尾涡形态的分析表明,冲刷前期并没有涡脱产生,中期已经有产生涡脱的趋势,后期出现了明显的且较为稳定的涡脱。     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

Design of a prototype ocean current turbine—Part I: mathematical modeling and dynamics simulation

The “C-Plane” is a submerged variable depth ocean current turbine that is tethered to the sea floor and uses sustained ocean currents to produce electricity. As part of the development of a $\frac{1}{30}$th scale physical model of the C-Plane, a mathematical model and dynamics simulation of the prototype was developed and is presented in this paper. This three-dimensional mathematical model represents the C-Plane as a rigid body with moveable control surfaces that is moored with three linear elastic cable elements. Gravitational, buoyancy, hydrodynamic, cable, gyroscopic, and inertial forces are included and a PC-based dynamics simulation is created. The simulation demonstrates that the C-Plane is stable and capable of changing depth in all expected operating conditions. The C-Plane prototype can fly level from a height of 3 to 6 m using the configuration suggested in this paper. The maximum ascent rates of the C-Plane with a water speed of 0.3 m/s are 0.015 m/s when the pitch is fixed at 0° and 0.030 m/s when the pitch is fixed at 4°. The maximum descent rates of the C-Plane are 0.018 m/s when the pitch is held at 0° and 0.031 m/s if the pitch is held at −4°.     

Numerical modelling of flow around coastal structures and scour prediction

The nearshore circulation and the wave characteristics are important parameters, which control coastline morphology. The interaction of nearshore circulation with coastal structures, modify the wave characteristics and seabed topography, often resulting in scour near the foundation of the structures. This paper deals with the numerical prediction of nearshore circulation induced due to wave setup in the nearshore region with and without the structure [(i) structure resting on seabed (ii) structure raised above the seabed]. It is also helps understand the deficiencies in studying the coastal characteristics by describing the flow field due to the wave velocity potential alone. Comparison of the results of both nearshore circulation and the wave potential model are discussed and the importance of the study and its prototype applications are highlighted.     

近岸沿岸流及污染物运动的数值模拟

基于双曲型缓坡方程和近岸浅水方程对近岸波浪斜向入射破碎所生成的沿岸流及污染物在沿岸波流作用下的运动进行了数值模拟,并对数值模拟结果进行了验证分析。数值模拟结果表明,在相近工况参数下,随着入射波高的增大,沿岸流流速和平均水面升高值均明显增大;随着岸坡坡度的增加,沿岸流流速和平均水面升高值明显增大;随着入射波浪周期的增大,平均水面升高值明显增大。在沿岸缓坡区域,由斜向入射波浪破碎所产生的沿岸流对污染物的运动起着不可忽略的影响。     

Numerical study of the Reynolds-number dependence of two-dimensional scour beneath offshore pipelines in steady currents

A numerical model for local scour below pipelines is employed to investigate the Reynolds-number dependence of the two-dimensional scour beneath offshore pipelines in steady currents. A novel wall function is proposed in calculating the suspended sediment transport rate in the model. Scour developments beneath a model pipeline and the corresponding prototype pipeline are simulated under the same undisturbed Shields parameter but different values of Reynolds number. The effects of the Reynolds number difference on the scour profile development are investigated. It is found that scour depths for prototype pipelines are about 10–15% smaller than those for model pipelines. The flow phenomena that causes this difference are discussed by means of flow visualization. The normalized time scales are found to be approximately the same. The simulated scour profiles for the model pipelines agree well with the experimental results from an independent study.     

A numerical experiment on the variations of western boundary currents: Part I. Formation of western boundary currents

A numerical experiment is made using a barotropic model for the western boundary currents. The time-dependent, non-linear vorticity equation is integrated with and without the variable of bottom topography. The inertial and frictional boundary flow is resolved with a fine grid size of 10 km. Connection of the western boundary currents with the general circulation is facilitated by giving the fixed Sverdrup transport at the eastern boundary of the model (400 km offshore).For the flat bottom topography, steady flow forRe=35 shows dynamical balance essentially of a frictional model. The transient response leading to the formation of the western boundary currents in the model seems to support theLighthill's theory (1969). ForRe=350, unsteady features revealed byBryan (1963) is re-established. A phenomenon of barotropic instability is also observed with sufficient resolution. For the model with a continental slope the steady flow is also obtained forRe=35. The boundary currents flow over the continental slope, deviating offshore as they flow northward.     

Numerical simulation of currents in a basin of variable depth with two straits

Within the framework of the linear theory of long waves, with regard for the turbulent viscosity, we study the development of tidal currents in a basin of variable depth with two straits. The problem is solved numerically. The velocity field on the strait-basin boundary is regarded as known. The numerical analysis is performed for different depths of the straits. We study the influence of the geometric characteristics of the basin on the amplitudes of the profile of free surface and wave velocity and establish the dependences of the wave characteristics on the period of current velocities in the strait and the parameters of the basin. In particular, it is shown that the increase in the period of current velocities in the strait leads to significant changes in the level and structure of currents. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–12, July–August, 2007.     

利用被动示踪物模拟对黑潮入侵南海的数值研究

由于缺少观测数据和对黑潮水准确定义,很难识别出从太平洋入侵到南海的黑潮水团。本文基于一个经过观测验证的三维模式MITgcm,利用被动示踪物标记黑潮水,研究了入侵南海的黑潮水的时空变化。研究表明,在冬季,黑潮水入侵的范围最广,几乎占据了18°N-23°N和114°E-121°E的区域;并有一个分支进入台湾海峡;黑潮入侵的范围随深度增加逐渐减小。在夏季,黑潮水被限制在118°E以东,且没有分支进入台湾海峡;入侵的范围从海面到约205米是增大的,之后随深度增加逐渐减小。通过分析从2003年到2012年黑潮入侵的年际变化,与厄尔尼诺年和正常年相比,冬季黑潮入侵后向台湾海峡的分支在拉尼娜年是最弱的,这可能与中国大陆东南方向的风应力旋度有关。通过吕宋海峡的黑潮入侵通量（KIT）是西向的,其年平均值约为-3.86×10⁶ m³/s,大于吕宋海峡通量（LST,约-3.15×10⁶ m³/s）。250米以上的KIT约占了全深度通量的60-80%。此外,从2003年到2012年KIT与Niño 3.4指数的相关系数到达0.41,小于LST与Niño 3.4指数的相关系数0.78。     

An inverse modeling study in Fram Strait. Part I: dynamics and circulation

In order to reconstruct the circulation in the northern Greenland Sea, between 77°N and 81°N, and the exchanges with the Arctic Ocean through Fram Strait, a variational inverse model is applied to the density field observed in summer 1984 during the MIZEX 84 experiment. An estimate of the three-dimensional large-scale pressure field is obtained in which the solution is decomposed into a limited number of vertical modes and the mode amplitudes are described by piece-wise polynomials on a finite-element grid. The solution should be consistent with a frictional depth-integrated vorticity balance and with the density data. The global model parameters are tuned to ensure agreement between the retrieved geostrophic velocity and independent currentmeter data. In a companion paper (Schlichtholz and Houssais, 1999b), the same method, but without dynamical constraint, is applied to the same hydrographic dataset to perform a detailed water mass analysis and to estimate individual water mass transports.A comprehensive picture of the summer geostrophic circulation in Fram Strait is obtained in which northward recirculations in the East Greenland Current (EGC) and various recirculations from the West Spitsbergen Current (WSC) to the EGC are identified. It is suggested that the branch of the WSC following the upper western slope of the Yermak Plateau turns westward beyond 81°N and recirculates southward along the lower slope, then merging with a westward recirculating branch south of 79°N. At 79°N, a southward net transport of 6.5 Sv is found in the EGC which, combined with a northward net transport of only 1.5 Sv in the WSC, results in a fairly large outflow of 5 Sv from the Arctic Ocean to the Greenland Sea.The inverse solutions show that, in summer, the local induction of vorticity by the wind stress curl or by meridional advection of planetary vorticity should be small, so that, in the EGC and in the WSC, the vorticity balance is mainly achieved between the bottom pressure torque and dissipation of vorticity through bottom friction. A substantial barotropic flow associated with along-slope potential energy gradients is indeed identified on both sides of the strait.     

张力腿平台绕流数值模拟分析

在一定来流条件下,张力腿平台(tension leg platform,简称TLP)的立柱后缘出现周期性的交替旋涡脱落,致使立柱受到垂直于来流方向的升力和平行于来流方向的阻力作用,导致TLP产生大幅度往复运动,显著增加平台结构和系泊系统的负载。目前,关于单柱、多柱结构绕流问题的研究较多,但对于TLP绕流特性的研究较少,机理尚存不明确的地方。为研究TLP的绕流力变化情况和流场特征,开展了数值模拟分析。利用计算流体动力学数值模拟软件,基于雷诺平均(RANS)法和分离涡模拟(DES)法对TLP绕流场进行仿真分析,揭示了TLP的绕流特性。结果表明,在3种来流角度和多个折合速度V_r下,TLP绕流的流体力系数存在明显差异,升力系数时域曲线呈现脉动性。TLP的上、下游立柱间存在明显的相互作用,影响了旋涡的形成与发展。TLP的旋涡脱落大多集中在平台固有频率附近,且在V_r=7,来流角度为0°时,升力系数频谱峰值最大,旋涡脱落集中。     

Numerical modeling of perforated plates in oscillating flow

Perforated plates, relevant for several marine applications, are experimentally and numerically investigated. The numerical investigations are performed using a presently developed Navier–Stokes solver. Several comparison and sensitivity studies are presented, in order to validate and verify the solver. Forced heave experiments are performed on two perforated plates with perforation ratios 19% and 28%. Amplitude-dependent added mass and damping coefficients are presented. Good agreement is obtained between the solver and the present experiments. Consistent with existing data, the results show that the hydrodynamic coefficients of perforated plates are highly amplitude dependent. The damping force is found to dominate over added mass force. The damping force dominance increases with increasing perforation ratio. It is highlighted that plate-end flow separation has an important effect on the damping coefficient. The developed numerical solver is two-dimensional, but is found to yield reasonable estimates of hydrodynamic force coefficients when compared with a previous three-dimensional experimental investigation. This could indicate that three-dimensional effects are not dominant for the hydrodynamic forces of perforated plates, and that a two-dimensional viscous flow solver could have relevance as a tool for estimating hydrodynamic forces on three-dimensional perforated structures.