Three-Dimensional Modeling of Wave-Induced Seabed Response Around a Semi-Buried Pipeline: A Small-Scale Case

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Jianfeng Zhu ◽  
Hongyi Zhao
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Small Scale ◽  
Buried Pipeline ◽  
Consolidation Process ◽  
Soil Response ◽  
Wave Flume ◽  
Wave Induced

Abstract In this paper, a three-dimensional integrated numerical model for a small-scale case of wave-induced oscillatory soil response around a semi-buried pipeline (PORO-WSSI-PIPE 3D) is proposed. In this model, we combine the Reynolds-averaged Navier–Stokes (RANS) equations for the 3D wave motions and the Biot’s consolidation equations for a porous elastic seabed foundation through pressure continuity at common boundaries, with pipeline being an elastic and impermeable medium. The computational results are validated through comparison with previous analytical solutions and laboratory wave flume tests, obtaining good agreement. Following validation, the numerical model is applied to simulate wave-seabed-pipeline interaction with different obliquities between pipeline and incident wave, varying from 30 deg to 90 deg. Snapshots of wave-seabed-pipeline interaction, as well as dynamic pore pressure distributions at typical locations in the vicinity of a semi-buried pipeline, are obtained and analyzed. The three-dimensional consolidation process of seabed under gravitational forces including the body forces of a pipeline is also discussed.

scholarly journals A Three-Dimensional Model for the Seabed Response Induced by Waves in Conjunction with Currents in the Vicinity of an Offshore Pipeline Using OpenFOAM

2018 ◽  
Vol 01 (03) ◽  
pp. 1850004 ◽  
Author(s):  
Zuodong Liang ◽  
Dong-Sheng Jeng
Keyword(s):  
Three Dimensional ◽  
Ocean Current ◽  
Navier Stokes ◽  
Key Factors ◽  
Three Dimensional Model ◽  
Soil Response ◽  
Fluid Field ◽  
Offshore Pipeline ◽  
Waves And Currents ◽  
Wave Induced

To better understand the physical processes involved in the wave–seabed–pipeline interactions (WSPI), a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. Seabed instability around an offshore pipeline is one of the key factors that need to be considered by coastal engineers in the design of offshore infrastructures. Most previous investigations into the problem of WSPI have only considered wave conditions and have not included currents, despite the co-existence of waves and currents in natural ocean environments. Unlike previous studies, currents are included in the present study for the numerical modeling of WSPI, using an integrated FVM model, in which the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equation is used to solve the mean fluid field, while Biot’s consolidation equation is used to describe the solid–pore fluid interaction in the porous medium. Numerical examples demonstrate a significant influence of ocean current direction and angle on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in two-dimensional (2D) numerical simulation.

scholarly journals Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading

2019 ◽  
Vol 7 (3) ◽  
pp. 66 ◽  
Author(s):  
Cynthia Foo ◽  
Chencong Liao ◽  
Jinjian Chen
Keyword(s):  
Numerical Model ◽  
Pore Pressure ◽  
Numerical Study ◽  
Current Model ◽  
Navier Stokes ◽  
Buried Pipeline ◽  
Soil Permeability ◽  
Biot’S Equation ◽  
Current Loading ◽  
Wave Induced

The evaluation of the wave-induced seabed response around a buried pipeline has been widely studied. However, the analysis of seabed response around marine structures under the wave and current loadings are still limited. In this paper, an integrated numerical model is proposed to examine the wave and current-induced pore pressure generation, for instance, oscillatory and residual pore pressure, around a buried pipeline. The present wave–current model is based on the Reynolds-Averaged Navier–Stokes (RANS) equation with k - ε turbulence while Biot’s equation is adopted to govern the seabed model. Based on this numerical model, it is found that wave characteristics (i.e., wave period), current velocity and seabed characteristics such as soil permeability, relative density, and shear modulus have a significant effect on the generation of pore pressure around the buried pipeline.

Three-Dimensional Effects on Slamming Loads

2021 ◽  
Author(s):  
Shan Wang ◽  
C. Guedes Soares
Keyword(s):  
3D Model ◽  
Numerical Solutions ◽  
Pressure Coefficient ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Courant Number ◽  
Dimensional Effects ◽  
Coefficient Distribution ◽  
Experimental Values

Abstract Three-dimensional effects on slamming loads predictions of a ship section are investigated numerically using the unsteady incompressible Reynolds-Average Navier-Stokes (RANS) equations and volume of fluid (VOF) method, which are implemented in interDyMFoam solver in open-source library OpenFoam. A convergence and uncertainty study is performed considering different resolutions and constant Courant number (CFL) following the ITTC guidelines. The numerical solutions are validated through comparisons of slamming loads and motions between the CFD simulations and the available experimental values. The total slamming force and slamming pressures on a 2D ship section and the 3D model are compared and discussed. Three-dimensional effects on the sectional force and the pressures are quantified both in transverse and longitudinal directions of the body considering various entry velocities. The non-dimensional pressure coefficient distribution on the 3D model is presented.

scholarly journals A numerical geotechnical model for computing soil slides at banks of water reservoirs

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Nils Reidar B. Olsen ◽  
Stefan Haun
Keyword(s):  
Numerical Model ◽  
Water Level ◽  
Stokes Equations ◽  
Limit Equilibrium ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Adaptive Grids ◽  
Groundwater Levels ◽  
Before And After

AbstractSoil slides can occur when the water level in a lake or a reservoir is lowered. This may take place in situations when a reservoir is flushed to remove sediments. The current study describes a three-dimensional numerical model used for the simulation of reservoir flushing that includes the slide movements. The geotechnical failure algorithms start with modelling the groundwater levels at the banks of the reservoir. A limit equilibrium approach is further used to find the location of the slides. The actual movement of the sediments is computed by assuming the soil to be a viscous liquid and by solving the Navier–Stokes equations. The resulting bed elevation changes from the slides are computed in adaptive grids that change as a function of water level, bed erosion and slide movements. The numerical model is tested on the Bodendorf reservoir in Austria, where field measurements are available of the bank elevations before and after a flushing operation. The results from the numerical simulations are compared with these observations. A parameter test shows that the results are very sensitive to the cohesion and less sensitive to the E and G modules of the soil.

Numerical Modelling of Circulation in Lake Sperillen, Norway

2000 ◽  
Vol 31 (1) ◽  
pp. 57-72 ◽  
Author(s):  
N. R. B. Olsen ◽  
D. K. Lysne
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Water Current ◽  
Simple Method ◽  
Vertical Temperature Profile ◽  
Navier Stokes Equations ◽  
Good Agreement

A three-dimensional numerical model was used to model water circulation and spatial variation of temperature in Lake Sperillen in Norway. A winter situation was simulated, with thermal stratification and ice cover. The numerical model solved the Navier-Stokes equations on a 3D unstructured non-orthogonal grid with hexahedral cells. The SIMPLE method was used for the pressure coupling and the k-ε model was used to model turbulence, with a modification for density stratification due to the vertical temperature profile. The results were compared with field measurements of the temperature in the lake, indicating the location of the water current. Reasonably good agreement was found.

Studies on natural convection-induced flow and thermal behaviour inside electronic equipment cabinet model

2003 ◽  
Vol 217 (3) ◽  
pp. 323-328 ◽  
Author(s):  
M Ishizuka ◽  
Y Kitamura
Keyword(s):  
Natural Convection ◽  
Thermal Behaviour ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Electronic Equipment ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Surface Boundary Layer ◽  
Induced Flow

In the present work, an important basic flow phenomenon, natural convection-induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the energy equation are solved based on the finite difference method. A generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behaviour inside an electronic equipment cabinet model, which is very difficult, if not impossible, to gather by experiment.

scholarly journals Physical and numerical analysis of the front of a gravity current on a horizontal bottom

1998 ◽  
Vol 26 ◽  
pp. 289-295
Author(s):  
Mohamed Naaim ◽  
Thierry Pellarin
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Gravity Current ◽  
Processing System ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Experimental Approaches ◽  
Two Parameters ◽  
Two Stages

In this paper, numerical and experimental approaches are applied to analyse the dynamics of the front of a gravity current. This study focused on two parameters: internal density and velocity fields. The salt concentration was determined by a potentiometric process. The internal velocities were determined using an optical device and an image-processing system. The structure of the head of the gravity current was analysed. Its density was measured and two stages of evolution were observed. This analysis allows us to coufirm the existence of two important stages. Forxf<xs, where the dynamics depend on the initial condition, the flow consists of a head and body and the front density is constant. Forxf>xs, we show that the density of the front decreases and evolves towards the Hallworth and others (1993) law. From a comparison between the experiments and the numerical model, we show that the numerical model, which is based on Navier–Stokes equations and on thek−Lturbulence model (whereLis the height of the gravity current), can predict well flow in the slump regime and in the inertia–buoyancy regime with smoothed results in the transition from the head to the body of the gravity current.

On the Weis-Fogh mechanism of lift generation

1973 ◽  
Vol 60 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Body ◽  
Navier Stokes ◽  
Encarsia Formosa ◽  
Concentrated Force ◽  
Stagnation Points ◽  
Wing Tips

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.

Secondary instability of a temporally growing mixing layer

1987 ◽  
Vol 184 ◽  
pp. 207-243 ◽  
Author(s):  
Ralph W. Metcalfe ◽  
Steven A. Orszag ◽  
Marc E. Brachet ◽  
Suresh Menon ◽  
James J. Riley
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Mixing Layers ◽  
Navier Stokes ◽  
Small Scale ◽  
Two Dimensional ◽  
Mean Flow ◽  
Direct Numerical Integration

The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.

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