On the Occurrence of Strong Higher Harmonic Wave Forces and Induced Ringing Loads on Vertical Cylinders

2002 ◽  
Author(s):  
John Grue ◽  
Morten Huseby
Keyword(s):  
Harmonic Wave ◽  
Vertical Cylinder ◽  
Offshore Structures ◽  
Load Cycle ◽  
Wave Forces ◽  
Wave Elevation ◽  
Secondary Load ◽  
Steep Waves ◽  
Acceleration Of Gravity ◽  
Vertical Cylinders

Experimental observations of a secondary load cycle in the force acting on a vertical cylinder exposed to long and steep waves are discussed. A complementary discussion of the occurrence of ringing of models of offshore structures is given. The height of the secondary load cycle is typically up to about 0.1–0.15 times the peak to peak force on the cylinder. The load cycle is observed for a nondimensional wavenumber kR in the range 0.1–0.33 and for a Froude number Fr = ωζm/gD exceeding about 0.4. Pronounced ringing occurs for the same parameter range. (k the wavenumber, R the cylinder radius, ω the wave frequency, ζm the maximal wave elevation, g the acceleration of gravity, D = 2R.)

Hydrodynamic Coefficients of Vertical Cylinders of Arbitrary Section

1991 ◽  
Vol 113 (2) ◽  
pp. 109-116 ◽  
Author(s):  
M. Isaacson ◽  
T. Mathai
Keyword(s):  
Vertical Cylinder ◽  
Vertical Direction ◽  
Numerical Approach ◽  
Offshore Structures ◽  
Three Dimensions ◽  
Method Of Integral Equations ◽  
Square Cylinders ◽  
Added Masses ◽  
Arbitrary Section ◽  
Vertical Cylinders

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 Wave Forces on a Pair of Vertical Cylinders

1991 ◽  
Vol 113 (1) ◽  
pp. 1-8
Author(s):  
K. Masuda ◽  
T. Nagai
Keyword(s):  
Numerical Calculation ◽  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Cross Sections ◽  
Present Method ◽  
Integration Method ◽  
Vertical Cylinder ◽  
Experimental Results ◽  
Wave Forces ◽  
Vertical Cylinders

The present paper is concerned with development of a powerful scheme for calculating nonlinear wave forces on a pair of vertical cylinders with arbitrary cross sections. The Laguerre integration method is applied and its convergence is confirmed in the cases of a single vertical cylinder and a twin circular cylinder. Further, the present method is compared with the method given by Eatock-Taylor and Hung [9], and then the computational times and those properties for a numerical calculation are investigated. The numerical results for maximum wave forces on the vertical cylinders obtained by the present method are compared with the experimental results, so that the usefulness is clarified.

Wave Forcing and Wave Scattering From a Vertical Surface-Piercing Cylinder

2005 ◽  
Author(s):  
Chris Swan ◽  
Stephen Masterton ◽  
Rizwan Sheikh ◽  
Alessandra Cavalletti
Keyword(s):  
High Frequency ◽  
Harmonic Wave ◽  
Laboratory Data ◽  
Perturbation Expansion ◽  
Vertical Cylinder ◽  
Scattered Wave ◽  
Vertical Surface ◽  
The Body ◽  
Wave Forces ◽  
High Frequency Waves

This paper concerns the nonlinear, higher-harmonic, wave-forces acting on a vertical surface-piercing cylinder. New laboratory data is presented which confirms that in the case a vertical cylinder, the diameter of which is large but not sufficiently large that the body lies within the linear diffraction regime, the second- and third-harmonic forces are not well described by existing models. This is particularly apparent when the incident waves are steep and have a relatively small wave period. Indeed, under these conditions the second-, third- and fourth-harmonic forces are shown to be comparable in size. This is clearly at odds with the results of a traditional perturbation expansion. An explanation for this lies in the nature of the scattered wave field, particularly the high-frequency waves identified by Sheikh & Swan [1]. The phasing of these scattered waves are, at least in part, dependent upon the motion of the fluid around the circumference of the cylinder and will not therefore be captured by a series solution based solely on the harmonics of the incident wave motion. The paper considers several test cases, fully exploring the correlation between the nonlinear forcing and the high-frequency scattering. The practical implications of these results are also addressed.

Numerical investigation of secondary load cycle and ringing response of a vertical cylinder

2019 ◽  
Vol 91 ◽  
pp. 101872 ◽  
Author(s):  
Shuang Chang ◽  
Weiping Huang ◽  
Hongyuan Sun ◽  
Lei Li
Keyword(s):  
Numerical Investigation ◽  
Vertical Cylinder ◽  
Load Cycle ◽  
Secondary Load

Numerical Simulations of Breaking Waves and Steep Waves Past a Vertical Cylinder at Different Keulegan–Carpenter Numbers

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Shengnan Liu ◽  
Muk Chen Ong ◽  
Charlotte Obhrai
Keyword(s):  
Dynamic Pressure ◽  
Vertical Cylinder ◽  
Breaking Waves ◽  
Numerical Results ◽  
Wave Forces ◽  
Breaking Wave ◽  
Wave Loads ◽  
Time Step ◽  
Two Phase ◽  
Steep Waves

A three-dimensional (3D) numerical two-phase flow model based on solving unsteady Reynolds-averaged Navier–Stokes (URANS) equations has been used to simulate breaking waves and steep waves past a vertical cylinder on a 1:10 slope. The volume of fluid (VOF) method is employed to capture the free surface and the k–ω shear–stress transport (k–ω SST) turbulence model is used to simulate the turbulence effects. Mesh and time-step refinement studies have been conducted. The numerical results of wave forces on the structure are compared with the experimental data (Irschik et al., 2004, “Breaking Wave Loads on a Slender Pile in Shallow Water,” Coastal Engineering, Vol. 4, World Scientific, Singapore, pp. 568–581) to validate the numerical model, and the numerical results are in good agreement with the measured data. The wave forces on the structure at different Keulegan–Carpenter (KC) numbers are discussed in terms of the slamming force. The secondary load cycles are observed after the wave front past the structure. The dynamic pressure and velocity distribution, as well as the characteristics of the vortices around the structure at four important time instants, are studied.

scholarly journals A theory of nonlinear wave loading on offshore structures

1981 ◽  
Vol 4 (3) ◽  
pp. 589-613 ◽  
Author(s):  
Lokenath Debnath ◽  
Matiur Rahman
Keyword(s):  
Nonlinear Wave ◽  
Vertical Cylinder ◽  
Nonlinear Effects ◽  
Diffraction Theory ◽  
Offshore Structures ◽  
The Body ◽  
Wave Number ◽  
Wave Forces ◽  
Wave Loading ◽  
Nonlinear Contribution

A theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation,D≡Fℓ+FDfor estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the formD≡Fℓ+Fnℓ+FDwhereFnℓ≡Fd+Fw+Fqis the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational-flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body's responses to the oncoming wave's fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison's equation increases with increasingkbwherebis the characteristic dimension of the body andkis the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasingkb. Several interesting results and limiting cases are discussed in some detail.

Third-Order Hydrodynamic Loads on an Oscillating Vertical Cylinder in Water

1999 ◽  
Vol 121 (1) ◽  
pp. 16-21 ◽  
Author(s):  
M. Markiewicz ◽  
P. Łe¸tkowski ◽  
O. Mahrenholtz
Keyword(s):  
Harmonic Component ◽  
Vertical Cylinder ◽  
Offshore Structures ◽  
Third Order ◽  
Earthquake Excitation ◽  
Hydrodynamic Loads ◽  
Third Harmonic ◽  
The Third ◽  
Steep Waves ◽  
Order Components

The third-harmonic component of the third-order hydrodynamic loads on a vertical circular cylinder oscillating in water is calculated by a conventional perturbation method within the framework of a potential theory. Although the third-order forces are expressed in terms of the first, second, and third-order components of the velocity potential, the latter is not directly required for the calculation. It is replaced by a properly defined linearized radiation potential via Haskind-like theorem. The results of the study are applicable to the analysis of high-frequency resonances of deepwater offshore structures under earthquake excitation or under steep waves (ringing problem).

RANS Simulation on Hydrodynamic Forces of a Horizontal Cylinder in Focused Steep Waves and Current

2014 ◽  
Author(s):  
Junli Bai ◽  
Ning Ma ◽  
Xiechong Gu
Keyword(s):  
Nonlinear Interaction ◽  
Offshore Structures ◽  
Horizontal Cylinder ◽  
Hydrodynamic Forces ◽  
Wave Forces ◽  
Offshore Structure ◽  
Wave Deformation ◽  
Current Interaction ◽  
Focused Wave ◽  
Steep Waves

The wave and current loads are the primary loads acting on the offshore structures. Rogue wave, a typical steep wave, is considered to occur due to wave focusing and wave-current interaction in the ocean and becomes one of the major causes of offshore structure damage. In this study, the hydrodynamic forces on horizontal cylinders exerted by the focused steep waves has been investigated considering wave-current interaction. The RANS equations solving by finite volume method are applied to evaluate the strongly nonlinear interaction between waves and current, in which the VOF method is adopted to capture the free surface. The velocity and water depth are given at the inlet boundary of the computation domain to generate deep water focused wave. In this paper, the wave forces acting on the cylinder in focused waves without current are investigated firstly. The wave forces are simulated for different horizontal distances between the cylinder and the pre-designed wave concentration point, and the maximal wave forces are analyzed. Meanwhile, the effects of the cylinder on wave deformation are also discussed. To validate the numerical model, the simulation results of wave forces on a cylinder by regular wave and the water surface elevation of a focused wave are compared with published experiment and simulated results. Then, the nonlinear interaction between the focused wave and current are investigated, the hydrodynamic forces acting on cylinder are simulated for different current velocities. Accordingly, the nonlinear effects of wave-current interaction on the hydrodynamic forces are discussed with respect to the results of wave deformation at concentration point, forces under actions of focused wave and combined wave-current conditions.

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