Vertical Surface-piercing Cylinder Research Articles

SPH Simulation of Solitary Wave Interaction with Cylinder

The wave impact on marine structures is concerning in ocean and coastal engineering. Cylinders are important components of various marine structures such as piers of sea-crossing bridge, columns of oil and gas platforms and subsea pipelines. In this study, the interaction of solitary wave with a submerged horizontal cylinder and a surface-piercing vertical cylinder are numerically studied by the Smoothed Particle Hydrodynamics (SPH) code SPHinXsys. SPHinXsys is an open-source multi-physics library based on the weakly compressible SPH and invokes the low-dissipation Riemann solver for alleviating numerical noises in the simulation of fluid dynamics. The capability of SPHinXsys in reproducing the fluid fields of solitary wave propagating through cylinders is demonstrated by comparing with the experimental data. With the validation in hand, the features of the wave–structure process are examined.

Probabilistic analysis of irregular wave runup on a fixed and truncated surface-piercing vertical cylinder

This paper presents a numerical and experimental study on irregular wave runup on a fixed and truncated surface-piercing vertical cylinder. The numerical model was set up based on the incompressible two-phase flow solver in the open-source toolbox OpenFOAM. The model was successfully validated against the experimental data on both regular and irregular incident wave and wave runup. We analyse the characteristics of the runup spectrum against different kpHs and kpD, where kp is the wave number at peak frequency, Hs is the significant wave height and D is the diameter of the cylinder. A new method is proposed to predict the distribution of runup height. In this method, the average height of the highest one-third of all wave runup R1/3 is calculated based on the expansion of an empirical formula proposed in Cao et al., (2017). Then the non-dimensional runup height R/R1/3 is fitted into a two-parameter Weibull distribution, where the shape parameter and scale parameter are provided as a function of kpHs and kpD based on the interpolation of the experimental and numerical data. Based on the fitted Weibull distribution, the runup height at any cumulative probability can be determined. This newly proposed method is validated against the numerical and experimental data on the 2% excess wave runup height R2%, and the deviations are found to be within ±15% for most of the cases. Finally, a sensitivity analysis is conducted to demonstrate that the model uncertainty is within 15%.

Numerical modelling of interactions of waves and sheared currents with a surface piercing vertical cylinder

Vertical surface piercing cylinders, such as typical coastal wind turbine foundations and basic elements of many coastal structures, are often exposed to combined loading from waves and currents. Accurate prediction of hydrodynamic loads on a vertical cylinder in a combined wave-current flow is a challenging task. This work describes and compares two different approaches for numerical modelling of the interaction between focussed wave groups and a sheared current, and then their interactions with a vertical piercing cylinder. Both approaches employ an empirical methodology to generate a wave focussed at the location of the structure in the presence of sheared currents and use OpenFOAM, an open source Computational Fluid Dynamics (CFD) package. In the first approach, the empirical wave-on-current focussing methodology is applied directly in the OpenFOAM domain, replicating the physical wave-current flume. This approach is referred to as the Direct Method. In the second approach, a novel Lagrangian model is used to calculate the free surface elevation and flow kinematics, which are then used as boundary conditions for a smaller 3-D OpenFOAM domain with shorter simulation time. This approach is referred to as the Coupling Method. The capabilities of the two numerical methods have been validated by comparing with the experimental measurements collected in a wave-current flume at UCL. The performance of both approaches is evaluated in terms of accuracy and computational effort required. It is shown that both approaches provide satisfactory predictions in terms of local free surface elevation and nonlinear wave loading on the vertical cylinders with an acceptable level of computational cost. The Coupling Method is more efficient because of the use of a smaller computational domain and the application of the iterative wave-current generation in the faster Lagrangian model. Additionally, it is shown that a Stokes-type perturbation expansion can be generalized to approximate cylinder loads arising from wave groups on following and adverse sheared currents, allowing estimation of the higher-order harmonic shapes and time histories from knowledge of the linear components alone.

Numerical study of wave run-up on a fixed and vertical surface-piercing cylinder subjected to regular, non-breaking waves using OpenFOAM

In wave-structure interaction, wave run-up is an important phenomenon that needs to be considered in the design of offshore structures. A thorough understanding of the physics of the nonlinear flow phenomena is necessary for the better insight into the run-up phenomenon. The present work, primarily, is focused on the hydrodynamic simulation of wave run-up and mainly seeks to evaluate the importance of wave scattering types identified by Swanet al. (2005) and lateral progressive edge waves on nonlinear wave amplification around a single fixed cylinder. The analysis is performed numerically using Navier-Stokes solver based on OpenFOAM over a range of wave steepnesses and wavelengths. In order to study wave-cylinder interaction, a numerical wave tank is utilized which includes IHFOAM toolbox for wave generation. For the simulations, the cylinder is assumed vertical and surface piercing with a circular cross-section and the incident wave is considered fifth-order Stokes, regular and non-breaking in deep water. The obtained numerical results that are mainly analyzed in this study include local surface elevation, the scattered wave field around the cylinder and the wave forces. A grid-space and time step refinement study are carried out to evaluate the performance and accuracy of numerical wave tank. The numerical results are compared with experimental data provided by ITTC (OEC), (2013) and a good agreement was obtained which indicates that OpenFOAM is very capable of accurate modeling of nonlinear wave interaction with offshore structures. The harmonic analysis for both short and long wave cases indicates that the scattered wave field around the cylinder involves high harmonics wave run-up. It is confirmed that even the wave-structure interaction caused by the linear incident wave, can lead to weakly nonlinear wave amplification around the cylinder. In the case of long waves cases, the harmonic loading involves at-least third harmonics due to the occurrence of the second wave run-up at the front part of the cylinder.

Bichromatic synthetic schlieren applied to surface wave measurements

The present paper provides an introduction to bichromatic synthetic schlieren (BiCSS) for surface measurements, a novel extension of the free surface synthetic schlieren (FS-SS) by Moisy et al. (Exp Fluids 46:1021–1036, 2009). The new technique is based on the fact that light diffraction through a medium varies with wavelength. Therefore, one may apply light at two different wavelengths to measure the change in density gradient in a medium. This paper explores the use of the difference between blue visual and near-infrared light, but the choice of wavelengths will typically depend on the application. Calibration was performed using stationary targets of plexiglass and the results show that the new BiCSS technique improves accuracy for large surface gradients, compared to the traditional FS-SS technique. In order to test the applicability of the technique in the laboratory, two sets of experiments were performed. Firstly, an experiment using phase-locked regular waves was conducted for comparing BiCSS with FS-SS, analyze the properties and give an estimation of the error. Secondly, to investigate the applicability for more complex surface patterns, a study on a vertical surface-piercing cylinder exposed to a focused wave was conducted, obtaining the complex surface characteristics. The new technique clearly reveals nonlinear wave diffraction, in addition to cross waves and parasitic capillary waves.

Mach-like capillary-gravity wakes.

We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers Bo(D)=D/λ(c) ranging between 0.1 and 4.2, where D is the cylinder diameter and λ(c) the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α∼U(-1), but with different prefactors depending on the value of Bo(D). For small Bo(D) (large capillary effects), the wake angle approximately follows the law α≃c(g,min)/U, where c(g,min) is the minimum group velocity of capillary-gravity waves. For larger Bo(D) (weak capillary effects), we recover a law α∼√[gD]/U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α≃c(g,min)/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.

Numerical study of multidirectional focusing wave run-up on a vertical surface-piercing cylinder

In this article, a numerical model based on improved Boussinesq equations and the Finite Element Method (FEM) with unstructured triangular elements is proposed and verified by experimental results for the focusing wave group interaction with a vertical surface-piercing cylinder. The multidirectional focusing waves with different directional spreading parameters and their interaction with a vertical surface-piercing cylinder are numerically simulated. The directional spreading parameter influences the wave form, that is, a wider directional spreading would induce a narrower wave form in space. The wave run-up on the cylinder increases with the increase of the wave directional spreading parameter, but when the parameter is greater than 30–40, the wave run-up changes only slightly and the influence of the directional spreading can be neglected. A larger diameter cylinder may have a larger wave run-up at the front face. But at the back side, it is other way round.

Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

A numerical model for three-dimensional fully nonlinear free-surface waves is developed by applying a boundary-type meshless approach with a leap-frog time-marching scheme. Adopting Gaussian Radial Basis Functions to fit the free surface, a non-iterative approach to discretize the nonlinear free-surface boundary is formulated. Using the fundamental solutions of the Laplace equation as the solution form of the velocity potential, free-surface wave problems can be solved by collocations at only a few boundary points since the governing equation is automatically satisfied. The accuracy of the present method is verified by comparing the simulated propagation of a solitary wave with an exact solution. The applicability of the present model is illustrated by applying it to the problem of a solitary wave running up on a vertical surface-piercing cylinder and the problem of wave generation in infinite water depth by a submerged moving object.

Second-order Wave Loads On Offshore StructuresUsing TheWeber’s Transform Method

The second-order wave loads are computed for the diffraction of monochromatic waves by a surface-piercing vertical cylinder in the finite and infinite fluid depths. The Weber transform method which is essentially a Hankel transform method with a more general kernel, is applied to compute the second-order force due to the second-order velocity potential. Suitable closed contours in the complex plane are used to derive the analytical solution of the improper integrals involved in this study. This makes the present solution distinct from the other available solution of the second-order forces.

Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body

The mixed-Eulerian–Lagrangian method using high-order boundary elements, described in Xue et al. (2001) for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions, is here extended and applied to the study of two nonlinear three-dimensional wave–body problems: (a) the development of bow waves on an advancing ship; and (b) the steep wave diffraction and nonlinear high-harmonic loads on a surface-piercing vertical cylinder. For (a), we obtain convergent steady-state bow wave profiles for a flared wedge, and the Wigley and Series 60 hulls. We compare our predictions with experimental measurements and find good agreement. It is shown that upstream influence, typically not accounted for in quasi-two-dimensional theory, plays an important role in bow wave prediction even for fine bows. For (b), the primary interest is in the higher-harmonic ‘ringing’ excitations observed and quantified in experiments. From simulations, we obtain fully nonlinear steady-state force histories on the cylinder in incident Stokes waves. Fourier analysis of such histories provides accurate predictions of harmonic loads for which excellent comparisons to experiments are obtained even at third order. This confirms that ‘ringing’ excitations are directly a result of nonlinear wave diffraction.

Godunov-Type Solution of Curvilinear Shallow-Water Equations

This paper presents details of a second-order accurate Godunov-type numerical model of the two-dimensional conservative hyperbolic shallow-water equations written in a nonorthogonal curvilinear matrix form and discretized using finite volumes. Roe's flux function is used for the convection terms, and a nonlinear limiter is applied to prevent spurious oscillations. Validation tests include frictionless rectangular and circular dam-breaks, an oblique hydraulic jump, jet-forced flow in a circular basin, and vortex shedding from a vertical surface-piercing cylinder. The results indicate that the model accurately simulates sharp fronts, a flow discontinuity between subcritical and supercritical conditions, recirculation in a basin, and unsteady wake flows.

Radiation Hydrodynamics of Floating Vertical Cylinder in Viscous Fluid

Fully nonlinear axisymmetric viscous flow due to heave oscillation of a surface-piercing vertical cylinder is analyzed using a finite-difference method based on curvilinear coordinates. Of significance to numerical modeling is the present finding that the free-slip condition used to model the movement of the contact line affects neither the overall flow nor the hydrodynamic pressure force acting on vertical cylinder. The viscous-flow results are compared with fully nonlinear inviscid-flow results, which are obtained using a mixed Eulerian-Lagrangian formulation, to contrast the effects of viscosity on the flow field, hydrodynamic force, and radiating surface waves. New results are presented for a range of parameters to illustrate physical mechanisms of the inception and evolution of vertical structures due to body motion in a free surface and their effects on the hydrodynamic force.

Laboratory study of plunging wave impacts on vertical cylinders

The characteristics of pressures associated with plunging wave impacts on a vertical cylinder are presented. Despite a high variability in the peak pressures, spatial distributions of the impact pressure time histories, both in the vertical direction and around the seaward front of the cylindrical surface, are found to vary systematically for a range of cylinder locations in the wave plunging region. Through correlations between the incident wave kinematics and the impact pressures, the mechanics of the impact process have been identified and elucidated. These results serve as a useful reference for future numerical and theoretical modelling of extreme wave loads on surface-piercing vertical cylinders.

Mean Drift Loads on Array of Vertical Cylinders in Narrow Tank

The influence of tank walls on the mean drift loads on an array of bottom-mounted surface-piercing vertical cylinders of arbitrary uniform cross section in a narrow wave tank is investigated theoretically. The problem is rendered two-dimensional by specifying analytically the z-dependency of the linearised velocity potential. Application of Green's second identity, utilising an appropriate two-dimensional Green's function, yields an integral equation of the velocity potential on the cylinder surfaces. Discretising this equation leads to a matrix system for the potential at the nodal points on the cylinders. The mean drift forces and moments on the array members are obtained via a direct pressure integration. A forward difference approximation is used to calculate the fluid velocity components on the cylinders from the corresponding potentials. Numerical results are presented that illustrate the effect of the tank walls on the mean drift loads for various array configurations. It is found that the mean drift loads experienced by the array members in a narrow tank are quite different from those experienced by the same array members in the open sea.

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.

Wave impact pressures on vertical cylinders

Laboratory measurements of the pressure distributions on surface-piercing vertical cylinders due to breaking waves are presented. Breaking waves are generated in a repeatable fashion under program control, and both vertical and azimuthal distributions of pressures were measured over many repeats of the experiments. Despite the repeatability of the controllable experimental conditions, it is found that the highest impact pressures are subject to considerable variability, including pressure oscillations, from run to run. This high impact region is found to be localized in space and time, and the variability is attributed to the random dynamics of the breaking wave front and the entrapped air. Thus, despite the repeatability of the upstream incident wave hydrodynamics, it appears that the prediction of the largest pressures is essentially a stochastic problem. For those aspects of flow-structure interaction which do not depend on the higher-frequency impact pressures, these experimental results may be extrapolated to full scale through the use of the pressure impulse.

Hydrodynamic Coefficients of Vertical Cylinders of Arbitrary Section

The calculation of added masses and damping coefficients of a large surface-piercing vertical cylinder of arbitrary section extending to the seabed and undergoing harmonic oscillations is described. The linear radiation problem in three dimensions is reduced to a series of two-dimensional problems in the horizontal plane by the use of appropriate eigenfunctions that represent the variation of the velocity potential in the vertical direction. Each of these is solved by a numerical approach based on the method of integral equations. Comparisons are made with an analytic solution available for the case of a circular cylinder. Results are also provided for square cylinders, and the application to typical offshore structures subject to base motions is discussed.

Nonlinear Free-Surface Flow Around an Impulsively Moving Cylinder

Nonlinear free-surface flow around an impulsively accelerating, vertical surface-piercing cylinder is investigated analytically. The exact solutions for the velocity potential and free-surface elevation are derived up to the third order by the small-time-expansion method. The hydrodynamic pressure acting on the cylinder wall is also obtained. A constant horizontal acceleration is considered to illustrate our theoretical results. It is found that, during the initial stage of this impulsive motion, no travelling free-surface waves are present. A surge of water appears on the upwind face and a depression forms on the down-wind face. The second-order free-surface elevation is singular along the contact line between the fluid surface and the cylinder surface. The nonlinear pressure distribution on the cylinder surface has been determined.

Wave Forces on Large Objects in the Sea

Three methods of finding wave forces on large, rigid axisymmetric stationary objects in the sea are examined. The problem is formulated in terms of an integral equation and the three methods are successive approximations, direct calculations by means of simultaneous algebraic equations, and use of Haskind's relations. The latter method is included as it offers a large saving of computational efforts for axisymmetric bodies. The applicability of the methods is studied from both the theoretical and applied points of view. Numerical results are given for submerged and floating spheres and for shapes comprising a vertical surface-piercing cylinder atop a sphere.