A finite volume solution of wave forces on submarine pipelines

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.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.     

Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k– turbulence modeling

A two-equation k– turbulence model is used in this paper to simulate the propagation of cnoidal waves over a submerged bar, where the free surface is handled by the volume-of-fluid (VOF) method. Using a VOF partial-cell variable and a donor–acceptor method, the model is capable of treating irregular boundaries, including arbitrary bottom topography and internal obstacles, where the no-slip condition is satisfied. The model also allows the viscous sublayer to be modeled by a wall function approximation implemented in the grid nodes that are immediately adjacent to a wall boundary. The numerical model applied to the propagation of cnoidal waves over a submerged bar can produce results that are in general agreement with some laboratory measurements. Some remarks arising from the comparison between the computational and experimental results are presented.     

A numerical study of three-dimensional wave interaction with a square cylinder

In this study, a three-dimensional numerical model is used to study the wave interaction with a vertical rectangular pile. The model employs the large eddy simulation (LES) method to model the effect of small-scale turbulence. The velocity and vorticity fields around the pile are presented and discussed. The drag and inertial coefficients are calculated based on the numerical computation. The calculated coefficients are found to be in a reasonable range compared with the experimental data. Additional analyses are performed to assess the relative importance of drag and initial effects, which could be quantified by the force-related Keulegan and Carpenter (KC) number: KC_f=UT/(4πL). Here U is the maximum fluid particle velocity, T the wave period and L the length of structure aligned with the wave propagation direction. For small KC_f, the effective drag coefficient is proportional to 1/KC_f, provided the wavelength is much longer than the structural length. When wavelength is comparable to the structure dimension, the effective drag coefficient would be reduced significantly due the cancellation of forces, which has been demonstrated by numerical results.     

Hydrodynamic forces on a partly buried cylinder exposed to combined waves and current

The present study extends the investigations of the hydrodynamic forces on a cylinder, laid on, or partly buried in the bed. They were determined by measuring the pressure distribution on the cylinder surface in the case of steady current, waves and coexisting flow. The pressure distribution around the cylinder was measured by using pressure transducers, which were replaced in the cylinder. Force coefficients were obtained for the ranges of Re=0.8×10⁴–1.5×10⁴, for steady current, low KC numbers (KC<5) for wave alone case and, for current-to-wave velocity RATIO=0, 3, 6 and infinity (current) for coexisting flow. The forces were also determined for the various burial-depth-to-diameter ratios between 0 and 0.7 values of the cylinder.     

On the modeling of wave propagation on non-uniform currents and depth

By transforming two different time-dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into wave-action conservation equation and eikonal equation, respectively, shown are the different effects of dissipation term on the eikonal equation in the two different mild slope equations. The performances of intrinsic frequency and wave number are also discussed. Thus the suitable mathematical model is chosen in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, an extended evolution equation, which is of time-dependent parabolic type, is developed from the time-dependent hyperbolic mild slope equation which exists in the suitable mathematical model, and solved by using the alternating direction implicit (ADI) method. Presented is the numerical model for wave propagation and transformation on non-uniform currents in water of slowly varying topography. From the comparisons of the numerical solutions with the theoretical solutions of two examples of wave propagation, respectively, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach [Arthur, R.S., 1950. Refraction of shallow water waves. The combined effects of currents and underwater topography. EOS Transactions, August 31, 549–552], the differences of wave number vector between refraction and combined refraction–diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown.     

Numerical simulation of fluid–structure interaction using a combined volume of fluid and immersed boundary method

In this work, a combined immersed boundary (IB) and volume of fluid (VOF) methodology is developed to simulate the interactions of free-surface waves and submerged solid bodies. The IB method is used to account for the no-slip boundary condition at solid interfaces and the VOF method, utilizing a piecewise linear interface calculation, is employed to track free surfaces. The combined model is applied in several case studies, including the propagation of small-amplitude progressive waves over a submerged trapezoidal dike, a solitary wave traveling over a submerged rectangular object, and wave generation induced by a moving bed. Numerical results depicting the free-surface evolutions and velocity fields are in good agreement with either experimental data or numerical results obtained by other researchers. In addition, the simplification of the initial free-surface deformation used in most tsunami earthquake source study is justified by the present model application. The methodology presented in the paper serves as a good tool for solving many practical problems involving free surfaces and complex boundaries.     

浪流作用下系泊船舶撞击力和系缆力试验研究

以某25万吨矿石码头工程为例,分别进行了单流、单浪和浪流共同作用下,系泊船舶撞击力和系缆力试验。研究了不同水位、不同船舶载度、不同浪流夹角,单流、单浪和浪流共同作用时对船舶撞击力和系缆力的影响。分析了该码头工程护舷和缆绳的布置情况,为工程设计提供了依据。