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1.
This paper presents a comparison between two theoretical methods for computing the second-order diffraction loads on arrays of bottom-mounted, surface-piercing vertical circular cylinders in regular waves. One method presents a complete solution for the second-order hydrodynamic loads on the cylinder array via a numerical integration over the mean fluid free-surface. The other method is based on a large spacing approximation between the array members and involves the solution of a set of equivalent isolated body problems to obtain estimates for the second-order hydrodynamic loads. Numerical results for a pair of cylinders indicate very good agreement between the two methods at center-to-center spacing of both three and five radii, indicating that the approximate method may be sufficient to compute hydrodynamic interference effects to the second-order in many practical engineering situations. 相似文献
2.
The wave diffraction around an array of fixed vertical circular cylinders is simulated in a numerical wave tank by using a fully nonlinear model in the time domain. The emphasis of the paper lies in the insightful investigation of the nonlinear properties of the near-trapping phenomenon associated with the multiple cylinders. The numerical model is validated by analytical solutions as well as experimental data for waves propagating past two and four vertical cylinders in certain arrangements. An array of four identical circular cylinders at the corners of a square with an incident wave along the diagonal of the square is the main focus here for investigating the near-trapping phenomenon. When near-trapping occurs, the present study shows that an extremely high wave elevation near the cylinders can be observed. At the same time, the hydrodynamic forces on different cylinders are found to be either in phase or out of phase, leading to some characteristic force patterns acting on the whole structure. Due to the nature of the numerical model adopted, nonlinearity at different orders can be captured using a harmonic analysis. In addition to first- and second-order near-trapping, the third-order (triple-frequency) nonlinear component is presented for the first time. For the configuration selected, it is found that at one specific incident wave frequency and direction one trapped mode is excited by second-order effects, while a different trapped mode (having similar symmetries) is excited by the third harmonic of the incident wave frequency. 相似文献
3.
A time-domain method is employed to analyse the resonant oscillations of the liquid confined within the two floating bodies. The velocity potentials at each time step are obtained through a finite-element method (FEM) with quadratic shape functions. The matrix equation of the FEM is solved through an iteration. The radiation condition is satisfied through a combination of the damping zone method and the Sommerfeld–Orlanski equation. A detailed analysis is made for two rectangular floating cylinders undergoing forced oscillation. The first-order potential reveals the resonant behaviour of the wave motion at certain frequencies ωi, which is similar to sloshing in a tank. More interestingly, the second-order theory further reveals that when the oscillation frequency is at ωi/2 or half of the resonant frequency, no first-order resonance is observed as expected, but the second-order resonant motion becomes evident, which does not seem to have been extensively investigated so far. Detailed results for two rectangular cylinders are provided to show some insights into the resonant effect due to the interaction between the bodies. The first- and second-order resonant phenomena have been observed and the result has shown that the second-order components have significant influence on the wave and force in some cases, especially at the second-order resonance. 相似文献
4.
Second-order springing on an elastic body with forward speed is analyzed by numerical simulations. The boundary-value problem for the velocity potential is solved by means of the direct time-domain higher-order boundary element method (HOBEM). The free-surface boundary condition in the boundary-value problem is approximated on the mean surface up to second order by use of perturbation and Taylor-series expansion methods. The body boundary condition for an elastic body is derived with various quantities which are redefined in the generalized mode. These variables such as mode shape, normal vector, etc. are obtained by using directional derivative and continuum mechanics, and the same mathematical expressions are used to obtain several second-order generalized forces. To validate the numerical results, the second-order hydrodynamic force on the bottom-mounted rigid/elastic cylinders without forward speed is compared with other semi-analytic results. The property of second-order forces on an elastic ship is studied by changing the flexural rigidity and forward speed with elastic response. It is confirmed that the second-order velocity potential is important for a body with forward speed and investigation should be made more on numerical methods for accurate computation of the second-order velocity-potential force with forward speed. 相似文献
5.
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. 相似文献
6.
With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume. 相似文献
7.
Non-linear loads on a fixed body due to waves and a current are investigated. Potential theory is used to describe the flow, and a three-dimensional (3D) boundary element method (BEM), combined with a time-stepping procedure, is used to solve the problem. The exact free-surface boundary conditions are expanded about the still-water level by Taylor series so that the solution is evaluated on a time-invariant geometry. A formulation correct to second order in the wave steepness and to first order in the current speed is used. Numerical results are obtained for the first-order and the second-order oscillatory forces and for the second-order mean force on a fixed vertical circular cylinder in waves and a current. The second-order oscillatory forces on the body in waves and current are new results, while the remaining force components are verified by comparison with established numerical and analytical models. It is shown that the current can have a significant influence on the forces, and especially on the amplitude of the second-order oscillatory component. 相似文献
8.
Local and far-field surface elevation around a vertical cylinder in unidirectional steep wave groups
The problem of diffraction of a unidirectional incident wave group by a bottom-seated cylinder is considered. We assume the amplitude of the incoming wave to be small in comparison with other linear scales of the problem, and develop the corresponding second-order perturbation theory. We use the Fourier transform to treat time variation and separate spatial variables when solving the non-homogeneous second-order problem. The resulting set of non-homogeneous Bessel equations is solved numerically.Solutions for various types of incoming wave spectrum are obtained including the Gaussian spectrum and the Pierson–Moskowitz spectrum. To validate the method, problems with gradually decreasing bandwidth of Gaussian spectrum are solved and it is shown that the corresponding solution approaches that for the monochromatic case. The Pierson–Moskowitz spectrum with a set of realistic physical parameters is used as an example of extreme wave interaction with an offshore structure. The corresponding first- and second-order solutions are obtained and the effect of non-linearity on the solution is discussed with the emphasis on the growth of maximum free-surface elevation on the cylinder’s surface and generation of high frequency free radiated waves. 相似文献
9.
Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders. 相似文献
10.
The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified. 相似文献
11.
《Coastal Engineering》2005,52(5):391-407
A numerical solver is presented of the modified time-independent mild-slope equation, which incorporates energy dissipation. Using a second-order parabolic approximation, the following external boundary conditions are modelled: open and fully transmitting to both incoming and outgoing waves; partially reflecting, and; fully absorbing. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The numerical predictions are in excellent agreement with the analytical solution for the interaction of non-breaking waves with an array of vertical surface-piercing circular cylinders on a horizontal bed. Results are compared with those for the same array on various seabed topographies. The model is robust and can be used for wave propagation in complex geometries. It has fewer restrictions associated with wave obliqueness at boundaries than traditional models based on the mild-slope equation. 相似文献
12.
1.Introduction Owingtoitssignificanteffectofreductionofwaveloadsandwaverun up,theperforatedwallon anarrayofcylindricalstructureshasreceivedconsiderableattentioninrecentyears.Manyresearches havebeencarriedoutinthisfield.Anexactsolutionforthediffractionoflinearwaterwaveswithan arrayofimpermeablecylinderswasfirstgivenbySpringandMonkmeyer(1974)usinganeigenfunction expansionapproach.Subsequently,LintonandEvans(1990)madeamajorsimplificationtothetheo ry,whichallowedthenear fieldquantitiessuchasload… 相似文献
13.
R.D. Firouz-Abadi 《Ocean Engineering》2011,38(1):11-21
This paper aims at developing a modal approach for the non-linear analysis of sloshing in an arbitrary-shape tank under both horizontal and vertical excitations. For this purpose, the perturbation technique is employed and the potential flow is adopted as the liquid sloshing model. The first- and second-order kinematic and dynamic boundary conditions of the liquid-free surface are used along with a boundary element model which is formulated in terms of the velocity potential of the liquid-free surface. The boundary element model is used to determine the natural mode shapes of sloshing and their corresponding frequencies. Using the modal analysis technique, a non-linear model is presented for the calculation of the first- and second-order potential which can be used to obtain a reduced-order model for the sloshing dynamics. The results of the presented model are verified with the analytical solution for the second-order analysis of sloshing in a rectangular tank and very good results were obtained. Also, the second-order sloshing in some other example tanks with complex bed shapes is studied. The second-order resonance conditions of liquid sloshing in the example tanks are investigated and some conclusions are drawn. 相似文献
14.
An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129–139). The isolated cylinder diffraction potential is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129–139).Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement. 相似文献
15.
Sloshing in a two-dimensional rectangular tank in horizontal motion is analysed based on the velocity potential theory. It is found that even when the first-order excitation is away from all the natural frequencies of the tank, second-order resonance can still occur when the sum-frequency or the difference-frequency is equal to one of the natural frequencies corresponding to the even mode. However, such resonance is not excited when the sum or difference frequency is equal to the natural frequency of an odd mode. 相似文献
16.
The paper provides a detailed analysis for the second-order diffraction of monochromatic waves. For the second-order potential on the free surface, the paper proposed a forward prediction method for computing the integration on the free surface. By this method we only need to run the infinity integration on the free surface directly for a few points; a one-step quadrature can then be applied successively outward from the body for potentials at other points. For wave diffraction from a body of revolution with a vertical axis, the paper derives a new integral equation, which can cancel the leading singularity in the derivative of ring Green's functions automatically. To obtain accurate results, different approaches are also used to deal with singularities in the ring Green's functions in the integration on both the body surface and free surface. The method has been implemented for bodies of revolution with vertical axes, but the theory is also available for arbitrary bodies.A numerical examination is made to validate the numerical code by comparing the second-order forces and moments on uniform and truncated cylinders and second-order diffraction potentials on the free surface with some published results. The comparison shows that the present results are in good agreement with those published. The method is also used to compute the second-order wave elevation around uniform and truncated cylinders. 相似文献
17.
可渗透结构具有使波浪作用减弱的效应,而海水的层化及水波的非线性使结构的波绕射产生多层复杂机制。将可渗透结构应用于复杂海况条件中,海水的层化性、波浪的非线性及结构的透空性构成了波绕射的一个十分复杂的数学问题。该问题存在理论研究的必要性,而文章则着重探讨其数学分析的可能性。通过引入二层海的层化海模式及Stokes二阶波的非线性波模式,给出了二阶多色波对透空结构的波绕射的定解问题提法,提出了复合形式的二阶多色波辐射条件式及可渗透结构的二阶物面条件式,应用特征函数解法与积分法推导了多色波对结构绕射的一阶势解与二阶作用的耦合积分解式,并讨论了解式所涉及无穷积分的算法。 相似文献
18.
《Ocean Engineering》2004,31(11-12):1437-1446
Diffraction of water waves by an array of vertical cylinders of circular cross section is studied. In order to account for first order interaction among the cylinders, the body boundary condition is satisfied for each cylinder considering the scattered wave field from other cylinders in an iterative way. After each iteration, coefficients in the partial wave decomposition of the wave potential are modified. Convergence is fast for the whole range of frequencies and for a large number of bodies, compared with exact algebraic methods of Linton and Evans [J. Fluid Mech. 46 (1990) 549] and Kagemoto and Yue [J. Fluid Mech. 166 (1) (1986) 189]. 相似文献
19.
The membrane forces are included in the hydroelastic analysis of a floating plate undergoing large vertical deflections in regular monochromatic multidirectional waves. The first-order vertical displacements induced by the linear wave exciting forces are calculated by the mode expansion method in the frequency domain. The second-order vertical displacements induced by the membrane forces are calculated by the von Karman plate theory. The results show that the membrane contribution both in terms of the axial stresses and the effect on the bending stresses can be important. 相似文献