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1.
In this paper, a numerical model is established for simulating the wave forces on a submarine pipeline. A set of two-dimensional Navier–Stokes equations is discretized numerically with a finite volume method in a moving mesh system. After each time step, the mesh is modified according to the changed wave surface boundary. The deffered correction second-order upwind scheme (SUDC) is adopted here to discretize the convective fluxes. The effects of the clearance between the pipeline and the seabed, water depth and wave height on wave forces are studied, respectively. The results by the numerical simulation agree well with the experimental data and theory value. 相似文献
2.
Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described. 相似文献
3.
A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed. 相似文献
4.
Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping. 相似文献
5.
Sloshing in a three-dimensional rectangular tank: Numerical simulation and experimental validation 总被引：1，自引：0，他引：1
Pressure variations and three-dimensional effects on liquid sloshing loads in a moving partially filled rectangular tank have been carried out numerically and experimentally. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the non-linear behavior and damping characteristics of liquid sloshing. A moving coordinate system is used to include the non-linearity and avoid the complex boundary conditions of moving walls. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of the finite difference approximations. In order to mitigate a series of discrete impacts, the signal computed is averaged over several time steps. In order to assess the accuracy of the method used, computations are compared with the experimental results. Several configurations of both baffled and unbaffled tanks are studied. Comparisons show good agreement for both impact and non- impact type slosh loads in the cases investigated. 相似文献
6.
A Navier–Stokes solver is used to examine steep waves as they run up a steep beach (10.54°). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results shows reasonable overall agreement in the prediction of the free-surface, velocities and accelerations within the flow. A spurious feature at the free-surface was found which does reduce the quality of the results. For a steep wave we see the transition from a steep wave front to a smooth run-up tongue at the beach that is in qualitative agreement with experiment. 相似文献
7.
A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results. 相似文献
8.
The unsteady, two-dimensional Navier–Stokes equations and the exact free surface boundary conditions were solved to study the interaction of a solitary wave and a submerged dike. A piston-type wavemaker was set up in the computational domain to produce the incident solitary waves. The incident wave and the associated boundary layer flow in a wave tank with a flat bed were compared with the analytical solutions to verify the accuracy of this numerical scheme. Effects of the incident wave height and the size of the dike on the wave transformation, the flow fields, and the drag forces on the dike were discussed. Our numerical results showed that even though the induced local shear stress on the top surface of the dike is large at some particular locations, the resultant pressure drag is much larger than the friction drag. The primary vortex generated at the lee side of the dike and the secondary vortex at the right toe of the dike may scour the bottom and cause a severe problem for the dike. 相似文献
9.
The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications. 相似文献
10.
Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (CB=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow
, and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when
, the frequency dispersion can be neglected in supercritical flows. 相似文献
11.
The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate. 相似文献
12.
This paper presents a numerical model for simulating wave interaction with porous structures. Incompressible smoothed particle hydrodynamics in porous media (ISPHP) method is introduced in this study as a mesh free particle approach that is capable of efficiently tracking the large deformation of free surfaces in a Lagrangian coordinate system. The developed model solves two porous and pure fluid flows simultaneously by means of one equation that is equivalent to the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the extended Forchheimer equation for the flows inside the porous media. Interface boundary between pure fluid and porous media is effectively modeled by the SPH integration technique. A two-step semi-implicit scheme is also used to solve the fluid pressure satisfying the fluid incompressibility criterion.The developed ISPHP model is then validated via different experimental and numerical data. Fluid flow pattern through porous dam with different porosities is studied and regular wave attenuation over porous seabed is investigated. As a practical case, wave running up and overtopping on a caisson breakwater protected by a porous armor layer are modeled. The results show good agreements between numerical and laboratory data in terms of free surface displacement, overtopping rate and pressure distribution. Based on this study, ISPHP model is an efficient method for simulating the coastal applications with porous structures. 相似文献
13.
In this paper we use an industrial Navier–Stokes (NS) solver to model high amplitude internal waves. The model simulates a fluid with a shallow upper layer with linear stratification and a deep lower layer with constant density, relevant to conditions in the ocean at several locations. Waves are generated by trapping a volume of light water behind a gate in one end of the numerical wave tank. The velocity and vorticity fields predicted by the model agree well with experiment. The high amplitude waves produced by the NS solver experience an upper bound on the velocity and a broadening in agreement with experiment. These effects have not previously been captured by theoretical models. 相似文献
14.
The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress. 相似文献
15.
In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated. 相似文献
16.
The flow characteristics of tidal jets induced by a Tidal-Jet Generator (TJG) are investigated using a finite-difference numerical scheme, named Navier–Stokes (NS)–Marker and Cell (MAC)-TIDE, based on the fully 3D NS equations. The TJG is an enclosed rectangular breakwater, which has vertical opening and a large enclosed volume inside. During both phases of tide, strong and uni-directional jets can be obtained locally from the inlet of the TJG, due to the water level difference between the inner and outer sides of TJG.The computed results are extensively compared with three other independently developed numerical models; 3D-ADI, DVM, and CIP-CSF. These models are based on quasi-3D, 2D depth-averaged, and fully 3D NS equations, respectively. It is seen that the present fully 3D numerical model NS–MAC-TIDE can predict the maximum intensity of inlet velocity with higher accuracy than the other numerical models when compared with the empirical function proposed from the experiments. The numerical simulations based on NS–MAC-TIDE can reproduce successfully the processes of generation, development, and dissipation of tidal jets. The effects of gap opening on the main characteristics of the tidal jet flow are assessed. Through numerical assessment, it is also clearly demonstrated that the residual time of a pollutant distributed around the front of the TJG can be decreased by significant amount due to the locally induced tidal jet. The TJG can thus utilize tidal energy for water purification in local marine environment by providing a flushing mechanism. 相似文献
17.
The Karman Vortex Street generated by a circular cylinder is investigated by the numerical solution of the compressible Navier–Stokes equations in the incompressible Mach number range (Mach<0.3) using the Beam and Warming implicit scheme. The agreement with the fully incompressible projection method (Chorin, 1968) is fairly good while convergence time is very much better. The investigation suggests that the compressible Navier–Stokes equations may be used as an efficient alternative to study incompressible flows as well. Mach numbers just below 0.3 are enough to simulate incompressible flow behavior and at the same time do not cause numerical ill-conditioning in the solution. In addition, some relevant features of the vortices generated and carried by the wake of the cylinder could be fairly well captured. 相似文献
18.
The paper studies longitudinal vibrations of an ultra-deepwater drilling riser whose bottom end is disconnected from the sea floor and covered by a plug (a blind one or the one with a hole). An elastic shell is used as a model of a riser pipe. The fluid column motion in the riser is described by the Navier–Stokes equation for a compressible fluid. Losses of fluid pressure during its flowing through a hole in the plug are taken into account. Solution of the riser equations is carried out in the frequency domain. Analysis of the effect which the riser length, wave period and height, and the plug-hole diameter on the amplitude of the riser's tension vibrations is conducted. A riser manufactured of strong aluminium alloys, some of prospective materials for ultra deepwater drilling, was considered as a prototype. It has been shown that risers 2000–4000 m long, plug-hole, and a riser 6000 m long with plug-hole of 0.087 m in diameter can withstand wave height of >15 m throughout the frequency range. 相似文献
19.
Wave-induced liquefaction in a porous seabed around submarine pipeline may cause catastrophic consequences such as large horizontal displacements of pipelines on the seabed, sinking or floatation of buried pipelines. Most previous studies in relation to the wave and seabed interactions with embedded pipeline dealt with the wave-induced instaneous seabed response and possible resulting momentary liquefaction (where the soil is liquefied instantaneously during the passage of a wave trough), using theory of poro-elasticity. Studies for the interactions between a buried pipeline and a soil undergoing build-up of pore pressure and residual liquefaction have been comparatively rare. In this paper, this complicated process was investigated by using a new developed integrated numerical model with RANS (Reynolds averaged Navier–Stokes) equations used for governing the incompressible flow in the wave field and Biot consolidation equations used for linking the solid–pore fluid interactions in a porous seabed with embedded pipeline. Regarding the wave-induced residual soil response, a two-dimensional poro-elastoplastic solution with the new definition of the source term was developed, where the pre-consolidation analysis of seabed foundation under gravitational forces including the body forces of a pipeline was incorporated. The proposed numerical model was verified with laboratory experiment to demonstrate its accuracy and effectiveness. The numerical results indicate that residual liquefaction is more likely to occur in the vicinity of the pipeline compared to that in the far-field. The inclusion of body forces of a pipeline in the pre-consolidation analysis of seabed foundation significantly affects the potential for residual liquefaction in the vicinity of the pipeline, especially for a shallow-embedded case. Parametric studies reveal that the gradients of maximum liquefaction depth with various wave and soil characteristics become steeper as pipeline burial depth decreases. 相似文献
20.
Internal inlet for wave generation and absorption treatment 总被引：1，自引：0，他引：1
A new method of implementing, in two-dimensional (2-D) Navier–Stokes equations, a numerical internal wave generation in the finite volume formulation is developed. To our knowledge, the originality of this model is on the specification of an internal inlet velocity defined as a source line for the generation of linear and non-linear waves. The use of a single cell to represent the source line and its transformation to an internal boundary condition proved to be an interesting alternative to the common procedure of adding a mass source term to the continuity equation within a multi-cell rectangular region. Given the reduction of the source domain to a one-dimensional region, this simple new type of source introduced less perturbation than the 2-D source type. This model was successfully implemented in the PHOENICS code (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). In addition, the volume of fluid (VOF) fraction was used to describe the free surface displacements. A friction force term was added to the momentum transport equation in the vertical direction, in order to enhance wave damping, within relatively limited number of cells representing the sponge layers at the open boundaries. For monochromatic wave, propagating on constant water depth, numerical and analytical results showed good agreements for free surface profiles and vertical distribution of velocity components. For solitary wave simulation, the wave shape and velocity were preserved; while, small discrepancy in the tailing edge of the free surface profiles was observed. The suitability of this new numerical wave generation model for a two source lines extension was investigated and proven to be innovative. The comparisons between numerical, analytical and experimental results showed that the height of the merging waves was correctly reproduced and that the reflected waves do not interact with the source lines. 相似文献