A coupled CFD-DEM simulation of upward seepage flow in coarse sands

Abstract

The suction anchor becomes more popular for offshore oil and gas industry in deeper water. For suction anchor–soil interaction, the prediction of hydraulic conductivity of porous materials is a long-standing problem in offshore engineering. To investigate the hydraulic characteristics, an upward seepage flow through saturated sands is considered in this study. A numerical approach, which is able to describe the fluid–particle interaction at particle scale, has been employed to analyse fluid flow in sands. This approach is constructed by adopting a coupled discrete element method and computational fluid dynamic approach (CFD-DEM numerical model). The coupled CFD-DEM approach is first benchmarked by a classic geomechanics problem where analytical solutions are available, and then employed to investigate the characteristics of upward seepage flow in coarse sand columns. Through numerical modelling, the predicted relation between hydraulic gradient and flow velocity is obtained and it is compared with the classical analytical correlation. The effect of several bulk and micromechanical parameters including packing porosity, particle size combination and inter-particle rolling resistance on the flow characteristics is numerically examined. The results show that the particle polydispersity and packing porosity have significant effect on the hydraulic conductivity in the seepage flow. The introduction of inter-particle rolling resistance can change initial packing structure of particle assembly in some extent rather than the hydraulic conductivity from the particle shape effect perspective. A further development of numerical model, in which the effect of non-spherical particles on the seepage flow, will be carried out later.     

Effects of mass and damping ratios on VIV of a circular cylinder

In this study the basic characteristics of the dynamic response and vortex shedding from an elastically mounted circular cylinder in laminar flow is numerically investigated. The Reynolds number ranges from 80 to 160, a regime that is fully laminar. The governing equations of fluid flow are cast in terms of vorticity. The two-dimensional vorticity transport equation is solved using a vortex method. Effects of important parameters on the system response and vortex shedding are investigated; these include: mass ratio, damping ratio, Reynolds number and reduced velocity. The numerical results show that a decrease in either the mass ratio or damping ratio of the system can lead to an increase in both the oscillation amplitude and the reduced velocity range over which lock-in occurs. The results also suggest that the mass-damping parameter may characterize the system response adequately, although the effect of changing mass ratio appears to be a little more profound compared to damping ratio. Vorticity contour plots suggest that the vortex shedding occurs in the 2S mode, although a wake structure similar to the C(2S) mode appears at distances 15–20 diameters downstream in the lock-in region. The simulation results are in good agreement with previously published data.     

Nonplanar multi-modal vibrations of fluid-conveying risers under shear cross flows

Risers/pipes conveying fluid are a typical kind of slender structures commonly used in marine engineering. It is of great academic significance and application value for us to evaluate and understand the vibration characteristics and nonlinear responses of these risers under the combined action of internal and external fluid flows. In this paper, the nonplanar vibrations and multi-modal responses of pinned-pinned risers in shear cross flow are numerically studied. With this objective in mind, the van der Pol wake oscillators are used to simulate the dynamical behavior of the vortex shedding in the wake. Two nonlinear equations of motion of the riser are proposed to govern the lateral responses of the riser structure. The nonplanar nonlinear equations for the riser and wake are then discretized by employing Galerkin's method and solved by using a fourth-order Runge–Kutta integration algorithm. Theoretical results show that the coupled frequencies for cross-flow (CF) and in-line (IL) motions and the corresponding coupled damping ratio could be influenced by the external and/or internal fluid velocities. Based on extensive calculations, the dynamical behavior of the riser with various internal and external flow velocities are presented in the form of bifurcation diagrams, time traces, phase portraits, oscillation trajectories and response spectrum curves. It is shown that some interesting dynamical phenomena, such as ‘lock-in’ state, ‘figure-of-eight’ trajectory and quasi-periodic oscillation, could occur in such a fluid-structure interaction system. Our results also demonstrate that the shear parameter can significantly affect the dynamic responses of the riser. When the shear parameter of the cross flow is large, multi-modal quasi-periodic responses of the riser can be excited, showing some new features undetected in the system of fluid-conveying risers in uniform cross flow.     

非线性波浪时域计算的三维耦合模型

将计算区域Ω划分为内域Ω₁和外域Ω₂(Ω₂=Ω-Ω₁),外域控制方程采用改进线性频散特性的二维Boussinesq方程,用预报一校正法数值求解;结构物附近的内域控制方程为三维Navier-Stokes方程,由VOF方法数值求解。通过在外域和内域相匹配的交界面上设置合适的速度和波面边界条件,建立了三维非线性波浪时域计算的耦合模型。模拟试验表明:(1)耦合模型数值波浪水池可以产生稳定的、重复性较好的波动过程;(2)用耦合模型数值波浪水池求解较大浅水区域上的非线性波浪数值计算问题可以取得较高的计算效率,同时又能得出结构物附近的复杂流场。     

Fluid flow equations governing primary oil migration as a separate phase

A mathematical model of primary oil migration as a separate phase out of compacting shales is presented. During burial and oil generation, source rock porosity decreases and oil saturation increases until residual oil saturation is reached. At this stage oil is expelled out by capillary and excess fluid pressure gradients. The model is a system of differential equations which relate changes in oil and water saturation in time to water and oil flow out of the source rock during burial. An additional set of equations for periods of erosion of overburden are also provided. The equations can be numerically solved by finite difference method. If oil and water flow is to be simulated during oil generation, then at each time step, changes by oil generation in oil and water saturations and porosity must be calculated. The solution procedure is briefly outlined.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

万米级深海陶瓷耐压结构水下内爆流场数值模拟

耐压结构是深海潜器的重要组成部分,但在深海的高压环境中却存在内爆的风险。为研究陶瓷耐压结构水下内爆的流场特性,使用针对可压缩多相流问题开发的开源代码,采用直接数值模拟,应用自适应直角网格,对两种压力条件下的耐压结构水下内爆进行了数值模拟。通过低压模拟结果与理论解和试验值比较,验证了模拟方法的有效性,进而开展万米级深海陶瓷耐压结构水下内爆模拟。分析发现：陶瓷耐压结构发生内爆后,其内部气腔存在多次压缩—反弹现象,深海环境压力越大则反弹越不明显;气腔反弹阶段,在结构外部将产生数倍于深海环境压力的冲击波,且传播速度接近声速;冲击波压力峰值与到球心距离呈负指数幂函数关系;在相同深海环境压力下,耐压结构外部监测点的冲击波压力与球体半径呈正比例关系。     

Hydrodynamic coefficients of a submerged pulsating sphere in finite depth

By extending the work of Linton (Linton, C.M., 1991. Radiation and diffraction of waver waves by a submerged sphere in finite depth. Ocean Engineering 18 (1/2), 61–74), the problem of radiation of water waves by a submerged pulsating sphere in finite depth is formulated using the multipole method. As in Linton (1991), this leads to an infinite system of linear equations, which are easily solved numerically. Simple expressions are derived for the hydrodynamic characteristics of such a body. Results showing the effect of varying both the immersion depth and the water depth on the hydrodynamic coefficients of the pulsating sphere are given. The paper resumes the work presented in Lopes (Lopes, D.B.S., 1999. On the study of the Archimedes wave swing device for wave energy utilization (in Portuguese). MSc on the Management and Modelling of the Marine Environment, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa.).     

Finite element analysis of flow control using porous media

A finite element model is established for simulating flow in and out a porous media. The extended Darcy equation inside the porous media and the Navier–Stokes equations in the fluid are coupled via the continuity condition at the interface between the two media. The model is firstly validated against the analytical and the numerical results available in literature. Then it is applied to simulate flow past a circular cylinder covered by a porous layer. The effect of the porous layer on the reduction of lift coefficient is investigated numerically. It is found that the lift reduction can be achieved by properly choosing the porous material. However, the amount of reduction greatly depends on the Reynolds number, the permeability and the Forchheimer coefficient.     

Numerical analysis of water exit for a sphere with constant velocity using the lattice Boltzmann method

In this paper, the three-dimensional water exit of a sphere with different vertical velocities is investigated numerically using the lattice Boltzmann method (LBM). In this method, the liquid-gas two-phase flow is simplified as a single-phase free surface flow. To capture the free surface, a mass tracking algorithm is incorporated into the LBM. The gravity as a body force is introduced in the form of calculating the equilibrium distribution with an altered velocity, while the surface tension is neglected. Besides, the employed bounce-back boundary conditions are used for a moving sphere. What’s more, the Wall-Adapting Local Eddy (WALE) viscosity model is employed to capture the turbulent structures of the flow and stabilize the simulation. The accuracy of the numerical results is demonstrated through comparisons with the previous numerical and experimental results in the literature. The results show that the spike height is significantly influenced under the Froude number (Fr) below 4.12 and slightly affected under the Fr varying from 4.12 to 8.24. After the sphere exits water totally, the evolution of the free surface waterfall can be described as two phases and becomes more intense with the Froude number increasing. The non-uniform distribution of velocity results in the breaking of the free surface after the sphere completely exits the water. Moreover, the Reynolds number greatly affects the wake dynamics and hydrodynamics acting on the sphere when it moves beneath the water surface.     

Simulation for the propulsion of a micro-hydro robot with an unstructured grid

The flow mechanism of contractive and dilative motion was numerically investigated to obtain a propulsive force in a highly viscous fluid. The computing program for the analysis of complicated motions was numerically developed with a cell-centered, unstructured grid scheme. The developed program was validated by the well-known equation of an oscillating plane below viscous fluid for an unsteady problem, which is known as Stokes’ second problem. Validation has continued through comparison with the experimental results.In this case, sinusoidal motion was applied to the validation, instead of trochoidal motion, because it was very difficult to actually simulate trochoidal motion in this experiment. Finally, the validation and comparison with the nodal-point scheme was accomplished by Stokes’ problem, which is the famous problem at a low Reynolds number. The validated code was applied to contractive and dilative motion in a narrow tube, whose motion was embodied by trochoidal movement. In a highly viscous fluid, such as a very sticky honey or a swamp, the computed results show that a viscous force can be used for propulsion instead of a dynamic force.From the present results, it was found that a propulsive force can be obtained by contractive and dilative motion at a low Reynolds number, which can be applied to the propulsion of micro-robots in a highly viscous fluid such as a blood vessel or a swamp. This research could also be considered fundamental research for the propulsion of micro-hydro robots, which are expected to be actively studied in the future in accord with further development of nanotechnology.     

Motion Law of a Sphere in Bingham Fluid with Thixotropy

-The thixotropy properties and the motion law of a sphere in the Bingham fluid have been stu-died.Through observation of the settling motion of a single sphere in the Bingham fluid on the X-rayscreen,it has been discovered that the mud in estuaries and along sea bay,and the hyperconcentrated flowall behave as the Bingham fluid with thixotropy properties as the large sediment concentration.Throughderivation,the theoretical relationship between the yield stress and non-settling maximum sphere sup-ported by the stress for the Bingham fluid has been developed,the equations for calculating the increasingyield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have beenobtained.In consideration of the effect of thixotropy on fluid motion,the Navier-Stokes equation groupfor the Bingham thixotropy fluid has been developed.Through further study of the flow boundary condi-tion of settling motion of a single sphere in the Bingham thixotropy fluid,and the solving of theNavier     

Physical controls on mixing and transport within rising submarine hydrothermal plumes: A numerical simulation study

A computational fluid dynamics (CFD) model was developed to simulate the turbulent flow and species transport of deep-sea high temperature hydrothermal plumes. The model solves numerically the density weighted unsteady Reynolds-averaged Navier–Stokes equations and energy equation and the species transport equation. Turbulent entrainment and mixing is modeled by a k–ε turbulence closure model. The CFD model explicitly considers realistic vent chimney geometry, vent exit fluid temperature and velocity, and background stratification. The model uses field measurements as model inputs and has been validated by field data. These measurements and data, including vent temperature and plume physical structure, were made in the ABE hydrothermal field of the Eastern Lau Spreading Center. A parametric sensitivity study based on this CFD model was conducted to determine the relative importance of vent exit velocity, background stratification, and chimney height on the mixing of vent fluid and seawater. The CFD model was also used to derive several important scalings that are relevant to understanding plume impact on the ocean. These scalings include maximum plume rise height, neutrally buoyant plume height, maximum plume induced turbulent diffusivity, and total plume vertically transported water mass flux. These scaling relationships can be used for constructing simplified 1-dimensional models of geochemistry and microbial activity in hydrothermal plumes. Simulation results show that the classical entrainment assumptions, typically invoked to describe hydrothermal plume transport, only apply up to the vertical level of ~0.6 times the maximum plume rise height. Below that level, the entrainment coefficient remains relatively constant (~0.15). Above that level, the plume flow consists of a pronounced lateral spreading flow, two branches of inward flow immediately above and below the lateral spreading, and recirculation flanking the plume cap region. Both turbulent kinetic energy and turbulence dissipation rate reach their maximum near the vent; however, turbulent viscosity attains its maximum near the plume top, indicating strong turbulent mixing in that region. The parametric study shows that near vent physical conditions, including chimney height and fluid exit velocity, influence plume mixing from the vent orifice to a distance of ~10 times the vent orifice diameter. Thus, physical parameters place a strong kinetic constraint on the chemical reactions occurring in the initial particle-forming zone of hydrothermal plumes.     

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.     

VORTEX SHEDDING FROM A CIRCULAR CYLINDER IN OSCILLATORY FAR FLOW

By using a process of successive approximations, the Boundary-Layer equations are solved to determine the separation points of a circular cylinder in oscillatory flow under the conditions of vortex existing. Combining with the discrete vortex model, the separation points and the fluid force coefficients are calculated at different KC numbers and Re numbers, A modified Morison equation is used in calculating the inline forces, and good agreements are obtained between the calculated results and those from other's experiments.     

三维顶板斜向驱动方腔流有限元并行计算

基于PETSc FEM开源代码,采用分步有限元算法和区域分解法,并行计算了不同雷诺数下的三维顶板斜向驱动方腔流问题。计算结果表明,当顶板沿其对角线方向运动时,流体与下游侧壁发生斜向碰撞后在下游对角处汇聚并形成射流,该射流在与底面、上游侧壁碰撞后形成较为复杂的涡流结构。雷诺数大小对三维顶板斜向驱动方腔流的涡流场结构形态具有重要影响。并行性能分析表明区域分解法能有效地提高三维粘性方腔流的计算速度。     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.     

波浪作用下液化粉土流动特性拖球试验研究

粉质土大量存在于黄河水下三角洲地区,粉土液化过程中具有类似流体的性质,可以把液化过程中的粉土视为黏性流体进行研究。基于流体力学中Stokes黏滞阻力原理,在波浪水槽试验基础上,设计了一套测量液化过程中粉土流变特性的拖球装置,并对其实用性进行验证。在铺设有粉土底床的波浪水槽中埋入可以水平滑动的小球,通过拖动小球在粉土中水平运动,测量小球所受阻力值的大小,用以计算液化粉土表观动力黏度。充分考虑试验中波浪要素、超孔压比等因素的影响。结果表明,该装置能够满足试验要求;波浪循环荷载作用下,观察到了孔压的累积至液化的过程;波浪参数对结果有较大影响,其中波高越大,表观黏度值越小;同一波高情况下,表观黏度随时间缓慢增加;随着超孔压比的升高,波浪作用下粉土表观黏度值逐渐减小。     

Invertebrate recolonisation of previously dry channels in the Rakaia River

Recolonisation of previously dry channels by stream invertebrates was studied in the Rakaia River during winter 1981 and summer 1982. The winter experiment continued for 42 days, with stable low flows, whereas the summer experiment was characterised by fluctuating large flows which caused it to be abandoned after 27 days. The fauna was dominated numerically by Chironomidae, a leptophlebiid mayfly (Deleatidium), and oligochaetes during the winter, and by Deleatidium alone during the summer. Recolonisation was considered complete after 33 days in winter and 15 days in summer. Flow fluctuations were the main factor affecting colonisation rates, and it was assumed that drift was the main source of colonising animals. Small freshes during low‐flow periods in winter resulted in a rapid increase in total density of invertebrates and number of taxa present and also affected the population structure of Deleatidium larvae in colonisation baskets. Before these freshes numbers had increased steadily over a 27 day period. In summer large floods during high flow periods initially decreased benthic invertebrate numbers in samples but numbers increased rapidly once the flood had passed. This appears to be the first study of its kind on a large unstable river system.