Bottom-mounted Vertical Cylinders Research Articles

CFD Investigations of Interaction Between Freak Wave and Bottom-Mounted Vertical Cylinder

CFD Investigations of Interaction Between Freak Wave and Bottom-Mounted Vertical Cylinder

Time-Domain Simulation of Second-Order Diffracted Forces on Marine Structures in Multidirectional Irregular Seas

Abstract A new method for the accurate discrete technique of directional spectra is proposed for the simulation of the second-order incident potential of directional seas, and a second-order time-domain analysis program is developed for nonlinear wave forces on marine structures in multidirectional irregular seas. The boundary-value problems for the diffracted potential are solved by a higher-order boundary element method (HOBEM). The fourth-order Adams–Bashforth–Moulton method combined with the Newton–Raphson iteration is implemented for time integration. The present method is validated by comparison with the published frequency-domain results for a bottom-mounted vertical cylinder in bichromatic bidirectional waves. The second-order diffracted forces on a truncated cylinder are examined for different combinations of storms and swell seas, and major efforts are focused on investigating the effects of wave directionality, directional spreading, and the spectral peak frequency of mixed seas.

An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$th-harmonic force scales with the $n$th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

On the dispersion equation for linear waves traveling through or over dense arrays of vertical cylinders

Sloshing tests are performed on a rectangular tank filled with bottom-mounted vertical cylinders. The cylinders, in regular staggered arrangements, are first emergent then shortened to be fully submerged. Different porosities are achieved by varying the number of cylinders. The tank undergoes forced horizontal motion at frequencies around the natural frequency of the first sloshing mode. The free surface elevation and the hydrodynamic loads are measured. When resonance is attained, it means that the wavelength is exactly twice the length of the tank and that this wavelength and the sloshing frequency are related by a specific dispersion equation. From literature several theoretical dispersion equations are proposed in the emergent and submerged cases. New dispersion equations are offered based on the cylinder cluster being considered as an anisotropic porous medium. The latter ones provide the best agreement with the experimental results.

Numerical investigation of multidirectional random wave interaction with a large cylinder

To investigate the multidirectional wave run-up and forces on a large cylinder, a numerical model of multidirectional random wave loads on a large-scale cylinder is established based on the linear theory of wave interaction with a large-scale bottom-mounted vertical cylinder. The incident directional wave is specified using a discrete form of the Mitsuyasu-type spreading function. A wave basin experiment was carried out, and the numerical calculation results were verified by the results of the physical experiment. The results indicate that the wave directionality has significant effects on the distribution of the wave run-up around the cylinder. The transverse wave force occurs due to which the multidirectional waves at the two sides of the cylinder are totally different from each other at any time because of the wave directionality. Specially, for the multidirectional random wave with small directional spreading parameter ( s = 5), the transverse force Fy is about 57% of the normal force Fx and cannot be neglected any more. Results can provide reference for the real engineering design.

Multi-directional random wave interaction with an array of cylinders

Based on the linear theory of wave interaction with an array of circular bottom-mounted vertical cylinders, systematic calculations are made to investigate the effects of the wave directionality on wave loads in short-crested seas. The multi-directional waves are specified using a discrete form of the Mitsuyasu-type spreading function. The time series of multi-directional wave loads, including both the wave run-up and wave force, can be simulated. The effect of wave directionality on the wave run-up and wave loading on the cylinders is investigated. For multi-directional waves, as the distribution of wave spreading becomes wider, the wave run-up at some points around the cylinders is found to increase. This suggests that multi-directional wave run-up tends to be larger than unidirectional wave run-up. In addition, the wave directionality has a significant influence on the transverse force. The biggest transverse force is found to occur on the rear cylinder rather than the front one. This is quite different from the results in unidirectional waves and should be paid much more attention in the design of offshore structures. At last, the possibility of the near-trapping under the multi-directional random waves is investigated. It is found that the near-trapping also occurs for multi-directional wave conditions.

Focusing of liquid surface waves by gradient index lens

In the long-wavelength limit, a periodic array of bottom-mounted vertical cylinders may be used as a homogeneous medium for liquid surface waves and their effective parameters, such as their refractive index, depending on the filling fraction of the cylinders. Based on this effective medium theory, a gradient index (GRIN) lens for the focusing of liquid surface waves has been designed and fabricated here through the gradual modification of the cylinder filling fraction along a direction perpendicular to the lens axis. Their focusing performance and the transmission properties for liquid surface waves are then studied both experimentally and numerically. Both the wave patterns and spatial intensities obtained by experiment and numerical calculation demonstrate that the GRIN lens is able to focus planar liquid surface waves within a certain frequency region.

On physical and numerical resonances for water wave problems using the dual boundary element method

Abstract Scattering problems of water waves impinging on bottom-mounted vertical cylinders are solved by using the dual boundary element method (DBEM). Both resonances due to near-trapped mode (physics) and fictitious frequency (mathematics) are examined. It is found that the near-trapped mode is a physical phenomenon and the fictitious frequency stems from the numerical instability. A trapped mode is associated with a singularity that lies on the real axis of complex wave number. A near-trapped mode means a localized behavior that energy is trapped in a truncated periodical structure. Critical wave number for the near-trapped mode and fictitious frequency of numerical instability are detected in this work. Numerical oscillation of the resultant force near the fictitious frequency is also observed by using the DBEM. Fictitious frequencies depend on the formulation instead of the specified boundary condition. Both the Burton and Miller approach and the CHIEF method are employed to alleviate the problem of irregular frequencies. Highly rank-deficiency matrices for four identical cylinders are numerically examined and the rank is promoted by adding valid CHIEF constraints. Parameter study of spacing and radius of cylinders on the near-trapped mode and fictitious frequency is also addressed. Several examples of water wave interaction by circular and square cylinders are demonstrated to see the validity of the present formulation.

Using a time-domain higher-order boundary element method to simulate wave and current diffraction from a 3-D body

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method (HOBEM). By assuming small flow velocities, the velocity potential could be expressed for linear and higher order components by perturbation expansion. A 4th-order Runge-Kutta method was applied for time marching. An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves. Validation of the numerical method was carried out on run-up, wave exciting forces, and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder. The results were in close agreement with the results of a frequency-domain method and a published time-domain method. The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.

Refraction of Water Waves by Periodic Cylinder Arrays

We show that in the long wavelength limit, water waves propagate through an array of bottom-mounted vertical cylinders as if the water has an effective depth and effective gravitational constant that depends on the filling ratio of the cylinders, leading to refraction phenomena that can be described by analytic formulas. The results are obtained with rigorous homogenization techniques, as well as the multiple scattering formalism that gives full dispersion relationships. This phenomenon provides a mechanism to control the flow of ocean wave energy, as exemplified by a water-wave focusing lens.

Hydrodynamic Interaction Effects on Wave Exciting Force in Large Scale Floating Structures

On analysis of wave exciting forces of large scale floating structure consisted of multiple elements, a part of authors proposed a computation method taking hydrodymamic interaction between elements into account, and proved effectiveness of the method by model testes in previous papers.In this method, such an assumption is laid down, which gives a restriction in application of the method, that a fictitious, bottom-mounted vertical cylinder circumscribing one element does not contain any part of the other element itself. Although existence of lower-hull connecting column elements violates the above assumption, it can be proved that the effect of violation is small in case of lower-hull. This fact is confirmed by model tests. The computer program for this method is leveled up for the sake of making large scale computation possible, and the upper limit of computation is discussed.

Difference-frequency wave loads on a large body in multi-directional waves

The second-order difference-frequency wave forces on a large three-dimensional body in multi-directional waves are computed by the boundary integral equation method and the so-called FML formulation (assisting radiation potential method). Semi-analytic solutions for a bottom-mounted vertical circular cylinder are also developed to validate the numerical method. Difference-frequency wave loads on a bottom-mounted vertical cylinder and stationary four legs of the ISSC tension-leg platform (TLP) are presented for various combinations of incident wave frequencies and headings. These force quadratic transfer functions (QTF) can directly be used in studying slowly varying wave loads in irregular short-crested seas described by a particular directional spectrum. From our numerical results, it is seen that the slowly varying wave loads are in general very sensitive to the directional spreading function of the sea, and therefore wave directionality needs to be taken into account in relevant ocean engineering applications. It is also pointed out that the uni-directionality of the sea is not necessarily a conservative assumption when the second-order effects are concerned.

Nonlinear wave loads on a vertical cylinder

Nonlinear contributions due to elevation of the free surface, the dynamic head, and the second-order velocity potential on the wave loads are presented in closed-form expressions. Such nonlinearities resulting from large-amplitude ocean waves are associated with the irrotational flow interacting with a fixed bottom-mounted vertical cylinder piercing the surface. These are expressed in the form of dynamic, waterline and quadratic forces all of which depend on the square of the wave amplitude. The appropriate modifications are made to both the classical Morison equation and the well-known linear diffraction theory of MacCamy and Fuchs for accounting the second-order effects. A limited comparative study is performed to verify the present theoretical derivations. In general, satisfactory agreements have been obtained with the test results from various laboratory studies by different researchers. However, under certain environmental conditions, some discrepancies still exist with the measured results.