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.     

Three-dimensional scour below offshore pipelines in steady currents

This paper presents the results of an experimental investigation on three-dimensional scour below offshore pipelines subject to steady currents. The major emphasis of the investigation is on the scour propagation velocity along the pipeline after the scour initiation. Physical experiments were conducted to quantify the effects of various parameters on scour propagation velocity along the pipeline in a water flume of 4 m wide, 2.5 m deep and 50 m long. Local scour depths directly below the model pipeline were measured using specifically developed conductivity scour probes. Effects of various parameters such as pipeline embedment depth, incoming flow Shields parameter and flow incident angle (relative to the pipeline) on scour propagation velocity along the pipeline were investigated. It was found that scour propagation velocity generally increases with the increase of Shields parameter but decreases with the increase of the pipeline embedment depth. A general predictive formula for scour propagation velocity is proposed and validated against the experimental results.     

Equilibrium scour depths around piles in noncohesive sediments under currents and waves

A universal formula for the estimation of equilibrium scour depth around a single cylindrical pile under the action of steady currents, tidal and short waves is presented.     

Onset of scour below pipelines and self-burial

This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.     

A numerical model for onset of scour below offshore pipelines

A numerical model is developed to predict the onset of local scour below offshore pipelines in steady currents and waves. The scour is assumed to start when the pressure gradient underneath the pipeline exceeds the floatation gradient of the sediments. In this model, the water flow field above the bed is determined by solving the two-dimensional (2-D) Reynolds-averaged Navier–Stokes equations with a k-ω turbulence closure. The seepage flow below the seabed is calculated by solving the Darcy's law (Laplace's equation) with known pressure distribution along the common boundaries of the flow domains-seabed. The numerical method used for both the turbulent flow around the pipeline and Darcy's flow in the seabed is a fractional finite element method. The average pressure gradient along the buried pipe surface is employed in the evaluation of onset condition with a calibration coefficient. The numerical model is validated against experimental data available in literature. A unified onset condition for steady currents and waves is proposed. Influences of flow parameters, including water depth, embedment depth, boundary layer thickness, Reynolds number (Re) and Keuleagan–Carpenter (KC) number, on the pressure drop coefficient over the pipeline are studied systematically.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Estimation of scour around submarine pipelines with Artificial Neural Network

The process of scour around submarine pipelines laid on mobile beds is complicated due to physical processes arising from the triple interaction of waves/currents, beds and pipelines. This paper presents Artificial Neural Network (ANN) models for predicting the scour depth beneath submarine pipelines for different storm conditions. The storm conditions are considered for both regular and irregular wave attacks. The developed models use the Feed Forward Back Propagation (FFBP) Artificial Neural Network (ANN) technique. The training, validation and testing data are selected from appropriate experimental data collected in this study. Various estimation models were developed using both deep water wave parameters and local wave parameters. Alternative ANN models with different inputs and neuron numbers were evaluated by determining the best models using a trial and error approach. The estimation results show good agreement with measurements.     

Investigation of the effects of offshore breakwater parameters on sediment accumulation

Littoral sediment transport is the main reason for coastal erosion and accretion. Therefore, various types of structures are used in shore protection and littoral sediment trapping studies. Offshore breakwaters are one of these structures. Construction of offshore breakwaters is one of the main countermeasures against beach erosion. In this paper, offshore protection process is studied on the effect of offshore breakwater parameters (length, distance and gap), wave parameters (height, period and angle) and on sediment accumulation ratio, one researched in a physical model. In addition to the experimental studies, numerical model in which the formulae of the sediment discharge (i.e. the formulae of CERC and Kamphuis), was used was developed and employed. The results of the experimental and numerical studies were compared with each other.     

Prediction of wave-induced scour depth under submarine pipelines using machine learning approach

The scour around submarine pipelines may influence their stability; therefore scour prediction is a very important issue in submarine pipeline design. Several investigations have been conducted to develop a relationship between wave-induced scour depth under pipelines and the governing parameters. However, existing formulas do not always yield accurate results due to the complexity of the scour phenomenon. Recently, machine learning approaches such as Artificial Neural Networks (ANNs) have been used to increase the accuracy of the scour depth prediction. Nevertheless, they are not as transparent and easy to use as conventional formulas. In this study, the wave-induced scour was studied in both clear water and live bed conditions using the M5’ model tree as a novel soft computing method. The M5’ model is more transparent and can provide understandable formulas. To develop the models, several dimensionless parameter, such as gap to diameter ratio, Keulegan-Carpenter number and Shields number were used. The results show that the M5’ models increase the accuracy of the scour prediction and that the Shields number is very important in the clear water condition. Overall, the results illustrate that the developed formulas could serve as a valuable tool for the prediction of wave-induced scour depth under both live bed and clear water conditions.     

Euler-Euler two-phase flow simulation of tunnel erosion beneath marine pipelines

In this study an Euler-Euler two-phase model was developed to investigate the tunnel erosion beneath a submarine pipeline exposed to unidirectional flow. Both of the fluid and sediment phases were described via the Navier-Stokes equations, i.e. the model was implemented using time-averaged continuity and momentum equations for the fluid and sediment phases and a modified k−ε turbulence closure for the fluid phase. The fluid and sediment phases were coupled by considering the drag and lift interaction forces. The model was employed to simulate the tunnel erosion around the pipeline laid on an erodible bed. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully predicts the bed profile and velocity field during the tunnel erosion. It is evident that the sediments are transported as the sheet-flow mode in the tunnel erosion stage. Also the transport rate under the pipe increases rapidly at the early stage and then reduces gradually at the end of the tunnel erosion beneath pipelines.     

A wave-flume study of scour at a pile breakwater: Solitary waves

Understanding the sediment transport and the resulting scour around coastal structures such as pile breakwaters under local extreme wave conditions is important for the foundation safety of various coastal structures. This study reports a wave-flume experiment investigating the scour induced by solitary waves at a pile breakwater, which consists of a row of closely spaced large piles. A wave blacking gate with a simple operation procedure in the experiment was designed to eliminate possible multiple reflections of the solitary wave inside the flume. An underwater laser scanner and a point probe were used in combination to provide high-resolution data of the bed profile around the pile breakwater. Effects of incident wave height and local water depth on the maximum scour depth, the maximum deposition height and the total scour and deposition volumes were examined. An existing empirical formula describing the evolution of the scour at a single pile in current or waves was extended to describe the scour at the pile breakwater under the action of multiple solitary waves, and new empirical coefficients were obtained by fitting the formula to the new experimental data to estimate the equilibrium scour depth. It appears that the maximum scour depth and the total scour volume are two reliable quantities for validation of numerical models developed for the scour around pile breakwaters under highly nonlinear wave conditions.     

Two-dimensional,two-phase granular sediment transport model with applications to scouring downstream of an apron

We present a two-dimensional, two-phase model for non-cohesive sediment transport. This model solves concentration-weighted averaged equations of motion for both fluid and sediment phases. The model accounts for the interphase momentum transfer by considering drag forces. A collisional theory is used to compute the sediment stresses, while a two-equation (k–ε) fluid turbulence closure is implemented. A benchmark sediment transport problem concerning the scouring downstream of an apron is carried out as an example and numerical results agree with existing experimental data.     

海底输油管道底砂床冲刷机理研究

设计了海底输油管道水槽冲刷试验模型,研究了海底输油管道与砂床处于不同相对位置情况下床砂起动流速的变化,采用理想流体映射定理对其进行了理论分析,探讨起动流速变化规律。结合有限元数值模拟对试验进行细化分析,研究了海底管道底砂床砂粒起动的产生机理,根据研究结果将冲刷过程划分为五个阶段。阐明了海底管道暴露冲刷的危害性和实时监测的重要性。     

Experimental observations and evaluations of formulae for local scour at pile groups in steady currents

Bridge scour is recognized as one of the key factors that causes structure failures, which in turn leads to economic and life loss. In this study, flume tests of four typical arrangements of pier groups embedded in sand under steady clear water conditions were carried out to observe the process and maximum depth around piles of scour. The investigation included single pile, tandem piles, side-by-side piles, and 3 × 3 pile groups. Different conditions including different pile spacing, flow velocity, and water depth are considered. Moreover, the evaluation of design methods from the United States, New Zealand, and China was analyzed and compared through experimental and mathematical methods. The experimental results show that shielding and jetting effects are obvious in pile groups, which become less obvious with the increase of pile spacing. The dynamic process of scour around single pile and pile groups are quite different. Meanwhile, most of the predicted scour depths by these equations tend to be much larger than those from field data, which may lead to overdesign and consequently high construction cost. In addition, data from this study and some laboratory experiment data from previous work were used to derive the correction factors of a new scour prediction equation, which can be used to estimate the scour in a sand bed and agree well with the observations.     

Numerical investigation of bore hole filling volume in a coastal area

Tidal energy is a promising way to reduce the carbon fossil energy. Installing tidal converters remains difficult particularly due to the bore hole filling by drill residuals and ambient sediments. To fix this issue, we perform a coupling between a coastal circulation model and a discrete element model, with an application to Alderney Race, and considering spherical particles. The coupled model is firstly described, validated and then used to investigate the parameters controlling the filling volume of monopile and tripod technologies. The results are analysed for different disposition of residuals and initial current direction and intensity. We show that: the distance between the bore hole centre and the residuals is the key parameter controlling the filling by drill residuals; the current direction plays a negligible role in monopile while this distance remains smaller than 20 m; the filling of tripod is strongly influenced by current effects and seabed morphology. Impacts of bed roughness (modelled by steady spherical particles inlaying in the seabed) and ambient sediments are quantified and discussed. Interactions between moving particles and bottom roughness lead to a slight increase of the filling while the impact of ambient sediments strongly depends on seabed morphology and current effects.     

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。     

清水沟北汊流路入海泥沙对东营港影响的数值分析

本文用平面二维潮流泥沙数学模型,模拟了清水沟流路北汊入海口海域的潮流泥沙扩散和河口淤积延伸方向等问题。在此基础上从流速场分布,泥沙扩散浓度分布及淤积厚度零米线的范围及河口淤积延伸方向等方面探讨了入海泥沙对东营港的影响。结论认为如果按此口门入海,入海泥沙不会对黄河海港产生直接淤积影响。     

Numerical study on scale effect of form factor

The scale effect of form factor is investigated via a numerical approach in this paper, where the turbulent ship flow is computed by solving the steady and incompressible Reynolds-averaged Navier-Stokes and continuity equations. A wall function approach is employed to bridge the near-wall and outer turbulent flow region. The numerical scheme based on a finite-volume formulation is applied to discretize the coupled governing equation. For the sake of numerical stability, accuracy and economy, an identical grid is employed to compute ship flow at different Reynolds number, where the grid is optimized for the medium Reynolds number of the investigated range. Four surface ships and two sub-bodies with notably different geometrical characteristics are chosen as the investigated cases, where double-model flow without appendages is computed. The calculated total resistance coefficient shows a decreasing tendency against Reynolds number among all studied hulls. Similar to the calculated total resistance coefficient, the calculated friction resistance coefficient decreases with the Reynolds number and varies relatively little for a given Reynolds number among different hulls. The viscous pressure resistance coefficient is less insensitive to the Reynolds number but apparently depends on hull form. Compared with the form factor calculation based on empirical friction lines, the flat-plate friction prediction based on CFD approach clearly gives smaller Re-dependent form factor, which should more realistically reflect the scale effect of form factor. The form factor exhibits a near linear and increasing dependence on Reynolds number. The numerical results show that the dependence of r_P on Reynolds number mainly governs the scale effect of form factor.     

Numerical study of baroclinic tides in Luzon Strait

The spatial and temporal variations of baroclinic tides in the Luzon Strait (LS) are investigated using a three-dimensional tide model driven by four principal constituents, O₁, K₁, M₂ and S₂, individually or together with seasonal mean summer or winter stratifications as the initial field. Barotropic tides propagate predominantly westward from the Pacific Ocean, impinge on two prominent north-south running submarine ridges in LS, and generate strong baroclinic tides propagating into both the South China Sea (SCS) and the Pacific Ocean. Strong baroclinic tides, ∼19 GW for diurnal tides and ∼11 GW for semidiurnal tides, are excited on both the east ridge (70%) and the west ridge (30%). The barotropic to baroclinic energy conversion rate reaches 30% for diurnal tides and ∼20% for semidiurnal tides. Diurnal (O₁ and K₁) and semidiurnal (M₂) baroclinic tides have a comparable depth-integrated energy flux 10–20 kW m⁻¹ emanating from the LS into the SCS and the Pacific basin. The spring-neap averaged, meridionally integrated baroclinic tidal energy flux is ∼7 GW into the SCS and ∼6 GW into the Pacific Ocean, representing one of the strongest baroclinic tidal energy flux regimes in the World Ocean. About 18 GW of baroclinic tidal energy, ∼50% of that generated in the LS, is lost locally, which is more than five times that estimated in the vicinity of the Hawaiian ridge. The strong westward-propagating semidiurnal baroclinic tidal energy flux is likely the energy source for the large-amplitude nonlinear internal waves found in the SCS. The baroclinic tidal energy generation, energy fluxes, and energy dissipation rates in the spring tide are about five times those in the neap tide; while there is no significant seasonal variation of energetics, but the propagation speed of baroclinic tide is about 10% faster in summer than in winter. Within the LS, the average turbulence kinetic energy dissipation rate is O(10⁻⁷) W kg^{− 1} and the turbulence diffusivity is O(10⁻³) m²s⁻¹, a factor of 100 greater than those in the typical open ocean. This strong turbulence mixing induced by the baroclinic tidal energy dissipation exists in the main path of the Kuroshio and is important in mixing the Pacific Ocean, Kuroshio, and the SCS waters.