Submarine debris flow impact on pipelines — Part II: Numerical analysis

Computational Fluid Dynamics (CFD) numerical analysis was employed to analyze the situations tested experimentally, as described in Part I. The methodology and results of the CFD analyses are discussed and compared with the observations made from the experiments. The numerical model performed satisfactorily with regard to obtaining the impact forces exerted on the model pipe as well as simulating the hydroplaning phenomenon and estimating slurry flow heights. The experimental results were combined with the results of the CFD analyses to develop a practical method to compute the drag force caused by a submarine debris flow impact on a pipeline. The CFD analyses provided some insight to the separated region characterization, but the attempt to analyze the vortex shedding phenomenon as observed in the experiments was unsuccessful. Additional studies are required for better understanding of both the separated region characteristics and vortex shedding.     

海底滑坡对置于海床表面管线作用力的CFD模拟

海底管线是海洋工程中用于传输原油和天然气等的重要通道,通常放置在海床表面或处于悬跨状态。本文采用计算流体动力学CFD法模拟了不同冲击角度下海底滑坡对置于海床表面的海底管线的作用,得到了管线所受的轴向荷载和法向荷载与滑坡冲击角度之间的关系。同时分析了沿冲击方向管线截面形状与管线所受阻力之间的关系。对已有研究进行拓展延伸,丰富了不同工况下轴向阻力系数和法向阻力系数的计算成果,得出了海底滑坡对置于海床表面管线冲击力的计算公式。     

Numerical analysis of the impact forces exerted by submarine landslides on pipelines

Submarine pipelines that transport crude oil and natural gas are often in a complex marine geological environment and may become unstable and fail upon impact by submarine landslides. Previous research has mostly focused on the impact forces exerted by submarine landslides on suspended pipelines, but the impact of submarine landslides on pipelines laid on the seafloor at various impact angles, θ, have been relatively infrequently discussed, and the effects of suspended height, H, on the impact forces exerted by submarine landslides on pipelines have not been thoroughly investigated. In this study, based on the Herschel–Bulkley model, the impact forces exerted by a submarine landslide on laid-on or suspended pipelines at various impact angles θ were simulated using the computational fluid dynamics (CFD) approach. Equations for calculating the axial and normal drag coefficients of a submarine pipeline were proposed. The CFD numerical simulation results were rearranged based on the soil mechanics approach. By comparing the parameters, an essentially corresponding relationship was found between the soil mechanics and CFD approaches when the equations were used to calculate the impact forces exerted by a submarine landslide on a pipeline. In addition, a semi-analytical expression for the failure envelope was provided. Furthermore, the effects of H on the forces on a pipeline were discussed, and an equation for calculating the acting forces on a pipeline along the flow direction of a submarine landslide that comprehensively accounts for the effects of θ and H was proposed. The lift force was discussed preliminarily and the results provide a basis for further investigation. The achievement of this study is applicable for selecting locations of submarine pipeline routes and for designing submarine pipelines.     

Submarine debris flow impact on suspended (free-span) pipelines: Normal and longitudinal drag forces

Computational fluid dynamics (CFD) analysis was employed to numerically simulate impact of clay-rich submarine debris flows on a suspended (free-span) pipeline at various angles of attack. The resultant horizontal drag force can be decomposed into two components: normal and parallel to the pipe axis. A method is presented for estimating the normal and longitudinal drag forces on a suspended pipeline and is applicable to a wide of impact situations. The work presented here complements the results of an earlier investigation into the drag forces on suspended and laid-on-seafloor pipelines. The previous investigation consisted of both physical laboratory experiments and CFD numerical analyses, for an impact situation normal to the pipe axis. The impact Reynolds numbers presented in this paper range between about 2 and 320. This range is considered appropriate for practical design purposes.     

海底滑坡对海洋单桩冲击力试验研究

为了研究海底滑坡对海洋单桩的冲击力大小,首先通过调整高岭土、粉砂的不同含量,得到不同流变特性、不同密度的碎屑流,采用Herschel-Bulkley模型和幂率模型对流体流变性质进行描述;随后利用自制海底滑坡模型槽,模拟碎屑流在不同流速和黏度下对模型桩的冲击;并结合流体力学理论,建立阻力系数与非牛顿流体雷诺数之间关系表达式。试验数据表明:碎屑流黏度和流速是影响海底滑坡冲击力的主要因素,海底滑坡冲击力随着泥浆黏度和流速的增加而增大。同时,考虑碎屑流剪切稀释特性,得到管桩阻力系数随雷诺数变化的拟合公式,为海洋桩基础设计提供参考。     

Numerical analysis of a cylinder moving through rate-dependent undrained soil

Geo-hazard assessment of the potential damage to a pipeline caused by a submarine landslide requires a quantitative model to evaluate the impact forces on the pipeline. In contrast with typical geotechnical problems, the strain rate within the fast moving, flow-like submarine landslide is typically far higher, which will lead to enhancement of the soil strength and therefore result in larger impact forces. Generally, there are two possible predictive frameworks for strain-rate dependence: a fluid dynamics framework and a geotechnical framework. By comparison of common rheological models adopted in these two different approaches, a unified additive power-law model, a normalised form of the Herschel-Bulkley model from fluid mechanics, is explored in this paper. This model has been used in conjunction with a large deformation finite element approach to investigate the undrained limiting loads on a cylinder moving steadily through inertia-less soft rate-dependent material, in order to quantify the strain-rate effects.The flow mechanism and the effects of the shear-thinning index and Oldroyd number on the shear zones are explored. The calculated resistance factors are compared with the drag coefficients obtained from computational fluid dynamics analysis. The average rate of strain experienced by the soil flowing past the cylinder is estimated for a given flow velocity and an expression in the form of a conventional bearing capacity equation, but with shear strength linked directly to the normalised flow velocity, is proposed to predict the magnitude of the viscous force exerted by the debris flow.     

海底滑坡作用下滩海管道结构安全分析

海底滑坡作为常见的海洋地质灾害,对海洋油气工程安全产生巨大威胁。海床土体失稳引起滑坡体滑动,会对海底管道产生拖曳作用。基于计算流体动力学方法(CFD)建立海底滑坡体对管道作用的评估模型,采用H-B模型描述块状滑坡体并与试验比较验证,分析不同海床倾斜度滑坡对管道的作用并拟合表达式;研究了海底管道在滑坡作用下的力学响应,并采用极限状态方法开展海底滑坡作用下管道结构极限安全分析,探讨了管道埋地状态时的极限安全界限,建立滑坡作用下管道结构安全分析方法。研究表明:滑坡对管道作用力与海床倾角呈现正相关,而覆土层厚度对作用力影响较小;随着不排水抗剪强度的减小,允许的滑坡宽度和速度均增加,表明土体不排水抗剪强度与引起的拖曳力呈正相关;滑坡土体宽度对极限安全速度影响较大。     

Interaction between submarine landslides and suspended pipelines with a streamlined contour

Recently, the security and stability of submarine pipelines have attracted much attention in ocean engineering. In this paper, pipelines with a streamlined contour (wedge, airfoil, double-ellipse, and arc-angle hexagon) are designed in hopes of defending against the impact of submarine landslides, and the computational fluid dynamics (CFD) approach is used to investigate the interaction between submarine landslides and streamlined pipelines. The results show that the peak interactional force is more representative of the hazard level of pipelines imposed by submarine landslides. It is also found that the streamlined pipelines possess a significant advantage in reducing the drag force and lift force of landslide–pipeline interaction with a maximum lessening percentage of 66.32 and 40.17%, compared with a conventional circular pipeline. In addition, the influence of applying streamlined pipelines to engineering is briefly discussed, and the empirical equation for estimating the drag force and lift force of streamlined pipelines induced by landslides is recommended based on the numerical test results.     

高雷诺数下近壁圆柱绕流数值模拟与分析

近壁圆柱绕流问题在海底悬跨管道的研究中具有重要的意义。在绕流阻力、升力以及海底土壤的耦合作用下,海底管道所发生的移位、悬跨等现象对于海底管道的安全运行构成了很大的威胁。正确预测各种绕流条件下管流之间的作用力是保证油气管道安全的首要任务。海底管道在极端海洋环境条件下的管、流相互作用为高雷诺数绕流问题,处于高雷诺数下的绕流模拟比处于低雷诺数下的绕流模拟要复杂很多,它需要更精细的网格以及合适的湍流模型。此文对处于悬跨状态下的海底管道进行数值研究,给出不同间隙比下海流绕流海底管道的流场结构形态,分析了间隙比对绕流阻力和绕流升力的影响,为进一步研究海底悬跨管道的受力和变形提供载荷边界数据。     

An improved analytical approach for simulating the lateral kinematic distress of deepwater offshore pipelines

Offshore pipelines are critical infrastructures and any possible damage may have devastating financial and environmental consequences. Earthquake-related geohazards (such as strong ground motion, active seismic faults, submarine landslides and debris flows) consist crucial threats that an offshore pipeline has to overcome. The main aim of the current study is to examine analytically a seabed-laid offshore pipeline subjected to a lateral kinematic distress due to a submarine landslide or a debris flow. Extra emphasis is given on the impact of pipe-soil interaction on the pipe response, by the realistic representation of the soil resistance via a tri-linear model. Firstly, the proposed analytical model is validated with a numerical model utilizing the finite-element method. Subsequently, various combinations of soil parameters and loading conditions that affect the examined problem are investigated with realistic input data taken from the offshore section of the high-pressure natural-gas pipeline TAP (Trans Adriatic Pipeline) in the Adriatic Sea. Finally, useful conclusions are drawn regarding the applicability and the efficiency of the proposed approach.     

An Analytical Solution for the Run-Out of Submarine Debris Flows

Submarine debris flows have a significant impact on offshore and coastal facilities. The unique characteristics of submarine debris flows involve large mass movements and long travel distances over very gentle slopes. To improve our insight and knowledge of the basic mechanism behind submarine debris flows, an analytical model was derived for the mobility of submarine debris flows. This model takes into account the mass change of debris flows induced by deposition, stagnation pressure, and the topography of the depositional area. One case study on the Palos Verdes debris flow proves its ability to predict the run-out distance of a submarine debris flow to a reasonable level of accuracy. On the gentle slopes, the submarine debris flow progressively loses mass due to deposition, which in turn influences the flow velocity. In addition, the results show that the slope angle and spreading angle of the debris depositional zone play important roles in the sliding process.     

Numerical simulation of micro-bubble drag reduction using population balance model

The phenomenon of drag reduction by the injection of micro-bubbles into turbulent boundary layer has been investigated using an Eulerian-Eulerian two-fluid model. Multiple-size group (MUSIG) based on population balance models, which resolve a wide range of bubble sizes taking into account the bubble break-up and coalescence have been used for this purpose. The simulated results are compared against the experimental findings of Madavan et al. [1984. Reduction of turbulent skin friction by micro-bubbles. Physics of Fluids 27, 356-363] and also other numerical studies explaining the sophisticated phenomena of drag reduction. For the two Reynolds number cases considered, the buoyancy with the plate on the bottom configuration is investigated, as from the experiments it is seen that buoyancy seem to play a role in the drag reduction. Numerical model employed in the investigation comprises of a micro-bubble laden flow wherein two independent sets of Reynolds averaged Navier-Stokes (RANS) transport equations were used to describe both the phases of the flow. The shear stress transport (SST) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. Change in the mean streamwise velocity profiles, void fraction, turbulence modification and other results are presented and discussed with corresponding change in the gas injection rates. The complex mechanism of drag reduction are scrutinised and explained in context to our numerical findings. Special attentions have been also devoted to divulge the effect of bubble coalescence and break-up caused by random collision and turbulent impact. Numerical results showed good agreement for the skin-friction coefficients against experimental data throughout various air injection rates. The MUSIG model was found to be one of the best candidates to resolve the bubble dynamics in micro-bubble-induced drag reduction problems.     

复杂荷载作用下海底腐蚀管线破坏机理研究进展

腐蚀是引起海底管线破坏的一种重要原因。综述在内部工作压力和外部环境荷载作用下海底腐蚀管线破坏机理的研究,论述海底腐蚀管线在单一荷载和多种荷载联合作用下的破坏状态,并说明了当前研究的热点问题。最后,对该领域进一步的研究工作进行了展望。     

Exchange flow of oil and sea-water in a ruptured submarine pipeline

The rupture of a submarine oil pipeline starts various mechanisms leading to an oil spill. Among these mechanisms the leakage of oil driven by the difference in specific gravities of oil and sea-water is difficult to estimate. A simple mathematical model has been developed and laboratory experiments have been carried out to obtain an insight into the density-driven exchange flow and to determine the leak rate. The mathematical model is predictive and takes account of the effects of friction, inclination of the pipeline, and inertia of the fluid. The experiments were done in a horizontal model pipeline. Theoretical and experimental results are in satisfactory agreement.     

Wave-induced uplift force on a submarine pipeline buried in a compressible seabed

A two-dimensional finite-element simulation of the wave-induced hydrodynamic uplift force acting on a submarine pipeline buried in sandy seabed sediments subject to continuous loading of sinusoidal surface waves is presented. Neglecting inertia forces, a linear-elastic stress-strain relationship for the soil and Darcy's law for the flow of pore fluid are assumed. The model takes into account the compressibility of both components (i.e., pore fluid and soil skeleton) of the two-phase medium.The results of numerical analysis are presented and discussed with respect to soil and pore fluid parameters where special attention is paid to the question of soil saturation conditions. The meaning of the results is also related to surface wave conditions. As a general conclusion, the practical, engineering recommendation is given in order to make a realistic, safe and economic estimation of the wave-induced uplift force acting on a buried submarine pipeline.     

Shape optimization of axisymmetric cavitators in supercavitating flows, using the NSGA II algorithm

The reduction of energy consumption for high speed submersible bodies is an important challenge in hydrodynamic researches. Supercavitation is a hydrodynamic process in which a submerged body gets enveloped in a layer of gas. As the density and viscosity of the gas is much lower than that of seawater, skin friction drag can be reduced considerably. If the nose of the body (cavitator) has a proper shape, the attendant pressure drag remains at a very low value, so the overall body drag reduces significantly. Total drag force acting on the supercavitating self-propelled projectiles dictates the amount of fuel consumption and thrust requirements for the propulsion system to maintain a required cavity at the operating speed. Therefore, any reduction in the drag coefficient, by modifying the shape of the cavitator to achieve optimal shape, will lead to a decrease of this force. The main objective of this study is to optimize the axisymmetric cavitator shape in order to decrease the drag coefficient of a specified after-body length and body velocity in the axisymmetric supercavitating potential flow. To achieve this goal, a multi-objective optimization problem is defined. NSGA II, which stands for Non-dominated Sorting Genetic Algorithm, is used as the optimization method in this study. Design parameters and constraints are obtained according to the supercavitating flow characteristics and cavitator modeling. Then objective functions will be generated using the Linear Regression Method. The results of the NSGA II algorithm are compared with those generated by the weighted sum method as a classic optimization method. The predictions of the NSGA II algorithm seem to be excellent. As a result, the optimal cavitator’s shapes are similar to a cone.     

Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model

The impact of parameterized topographic internal lee wave drag on the input and output terms in the total mechanical energy budget of a hybrid coordinate high-resolution global ocean general circulation model forced by winds and air-sea buoyancy fluxes is examined here. Wave drag, which parameterizes the generation of internal lee waves arising from geostrophic flow impinging upon rough topography, is included in the prognostic model, ensuring that abyssal currents and stratification in the model are affected by the wave drag.An inline mechanical (kinetic plus gravitational potential) energy budget including four dissipative terms (parameterized topographic internal lee wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity) demonstrates that wave drag dissipates less energy in the model than a diagnostic (offline) estimate would suggest, due to reductions in both the abyssal currents and stratification. The equator experiences the largest reduction in energy dissipation associated with wave drag in inline versus offline estimates. Quadratic bottom drag is the energy sink most affected globally by the presence of wave drag in the model; other energy sinks are substantially affected locally, but not in their global integrals. It is suggested that wave drag cannot be mimicked by artificially increasing the quadratic bottom drag because the energy dissipation rates associated with bottom drag are not spatially correlated with those associated with wave drag where the latter are small. Additionally, in contrast to bottom drag, wave drag is a non-local energy sink.All four aforementioned dissipative terms contribute substantially to the total energy dissipation rate of about one terawatt. The partial time derivative of potential energy (non-zero since the isopycnal depths have a long adjustment time), the surface advective fluxes of potential energy, the rate of change of potential energy due to diffusive mass fluxes, and the conversion between internal energy and potential energy also play a non-negligible role in the total mechanical energy budget. Reasons for the <10% total mechanical energy budget imbalance are discussed.     

Drag force on a circular cylinder in unseparated laminar high Reynolds number nonlinear random oscillatory flow

The stochastic properties of the drag force maxima on a circular cylinder subjected to nonlinear random waves are investigated. Unseparated laminar high Reynolds number flow is considered. A simplified approach based on second order Stokes waves is presented, including the sum-frequency effect only. It is demonstrated how a drag force formula valid for regular linear waves can be used to find the cumulative distribution function of individual drag force maxima for nonlinear irregular waves. Here the [Wang, 1968] drag force coefficient is used.     

泥沙突变理论在海底管线冲刷中应用

基于泥沙突变理论,针对海底管线冲刷下泥沙的运动特征,建立恒定流作用下的泥沙起动模式,确定希尔兹数、无量纲参数、冲刷坑深度之间相互作用的非线性方程,推导了恒定流作用下海底管线冲刷坑深度的预测公式。将相同条件下该公式的计算结果与前人的试验资料进行了对比,可发现尽管计算结果存在一定的误差,但也基本能满足对冲刷坑深度的预测和判断,从而证明了泥沙突变模型在预测海底管线冲刷坑深度中的适用性。     

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.