Nonlinear wave loads on a slender vertical cylinder

1995 ◽  
Vol 289 ◽  
pp. 179-198 ◽  
Author(s):  
O. M. Faltinsen ◽  
J. N. Newman ◽  
T. Vinje
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Vertical Cylinder ◽  
Nonlinear Effects ◽  
Total Force ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Outer Domain ◽  
Wave Slope

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.

Accuracy Effects of Low Frequency Wave Loads on Ships Offshore to LNG Marine Terminal Design

2004 ◽  
Author(s):  
Monica J. Holboke ◽  
Robert G. Grant
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Frequency Wave ◽  
First Order ◽  
Terminal Design

This paper presents the results of a two-body analysis for a moored ship sheltered by a breakwater in shallow water with and without free surface forcing in the low frequency wave load calculation. The low frequency wave loads are determined by second order interactions from the first order. The free surface forcing term arises from the free surface boundary condition, which is trivial to first order but is not at second order. We demonstrate in the frequency domain the importance of this term in a two-body analysis. Additionally, we show how inaccurate calculations of the off-diagonal terms of the Quadratic Transfer Function can translate to over or under prediction of low frequency wave loads on moored ships sheltered by breakwaters in shallow water. Low frequency wave load accuracy has direct consequence for LNG marine terminal design. Generally, LNG marine terminals are sited in sheltered harbors, however increasingly they are being proposed in offshore locations where they will require protection from persistent waves and swells. Since breakwaters typically cost twice as much as the rest of the marine facilities, it is important to optimize their size, orientation and location. In a previous paper we described this optimization process [1], which identified a key step to be the transforming of waves just offshore the breakwater into wave loads on the moored ships. The ability to do this step accurately is of critical importance because if the loads are too large, the breakwater will be larger and more expensive than necessary and if the loads are too small, the terminal will experience excessive downtime and loss of revenue.

Nonlinear water waves generated by an accelerated circular cylinder

1979 ◽  
Vol 92 (4) ◽  
pp. 767-781 ◽  
Author(s):  
H. J. Haussling ◽  
R. M. Coleman
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Numerical Solutions ◽  
Nonlinear Effects ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Pressure Distributions ◽  
Surface Boundary Conditions ◽  
Surface Profiles

Numerical solutions for the irrotational flow of an incompressible fluid about a circular cylinder accelerated from rest below a free surface are presented. The usual restriction to linearized free-surface boundary conditions has been avoided. The transient period from the start to a local steady state or to the development of a very steep wave slope is investigated in terms of free-surface profiles and body-surface pressure distributions. Linear and nonlinear results are used to illustrate the transition from deep submergence when nonlinear effects are small to shallow submergence when linearized analysis is inaccurate.

Effective Power and Speed Loss of Underwater Vehicles in Close Proximity to Regular Waves

2017 ◽  
Author(s):  
Stefan Daum ◽  
Martin Greve ◽  
Renato Skejic
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Water Waves ◽  
Underwater Vehicles ◽  
Total Resistance ◽  
Wave Load ◽  
Regular Waves ◽  
Effective Power ◽  
Close Proximity ◽  
Deep Water Waves

The present study is focused on performance issues of underwater vehicles near the free surface and gives insight into the analysis of a speed loss in regular deep water waves. Predictions of the speed loss are based on the evaluation of the total resistance and effective power in calm water and preselected regular wave fields w.r.t. the non-dimensional wave to body length ratio. It has been assumed that the water is sufficiently deep and that the vehicle is operating in a range of small to moderate Froude numbers by moving forward on a straight-line course with a defined encounter angle of incident regular waves. A modified version of the Doctors & Days [1] method as presented in Skejic and Jullumstrø [2] is used for the determination of the total resistance and consequently the effective power. In particular, the wave-making resistance is estimated by using different approaches covering simplified methods, i.e. Michell’s thin ship theory with the inclusion of viscosity effects Tuck [3] and Lazauskas [4] as well as boundary element methods, i.e. 3D Rankine source calculations according to Hess and Smith [5]. These methods are based on the linear potential fluid flow and are compared to fully viscous finite volume methods for selected geometries. The wave resistance models are verified and validated by published data of a prolate spheroid and one appropriate axisymmetric submarine model. Added resistance in regular deep water waves is obtained through evaluation of the surge mean second-order wave load. For this purpose, two different theoretical models based on potential flow theory are used: Loukakis and Sclavounos [6] and Salvesen et. al. [7]. The considered theories cover the whole range of important wavelengths for an underwater vehicle advancing in close proximity to the free surface. Comparisons between the outlined wave load theories and available theoretical and experimental data were carried out for a submerged submarine and a horizontal cylinder. Finally, the effective power and speed loss are discussed from a submarine operational point of view where the mentioned parameters directly influence mission requirements in a seaway. All presented results are carried out from the perspective of accuracy and efficiency within common engineering practice. By concluding current investigations in regular waves an outlook will be drawn to the application of advancing underwater vehicles in more realistic sea conditions.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

Wave Load and Structural Analysis for a Jack-Up Platform in Freak Waves

2007 ◽  
Author(s):  
Ould el Moctar ◽  
Thomas E. Schellin ◽  
Milovan Peric
Keyword(s):  
Structural Model ◽  
Stokes Equations ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Wave Loads ◽  
Wave Load ◽  
Two Phase ◽  
Freak Waves ◽  
Highly Nonlinear ◽  
Jack Up

The paper analyzed effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced CFD techniques. The code used here solves the Reynolds-averaged Navier-Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the FEM was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.

Ringing Analysis of a Vertical Cylinder by Euler Overlay Method

2012 ◽  
Author(s):  
Jang Kim ◽  
Jim O’Sullivan ◽  
Alex Read
Keyword(s):  
Fluid Dynamic ◽  
Damping Ratio ◽  
Vertical Cylinder ◽  
Breaking Wave ◽  
Computational Domain ◽  
Wave Load ◽  
Offshore Structure ◽  
Outer Domain ◽  
Overlay Method ◽  
Dynamic Amplification

A Computation Fluid Dynamic (CFD) analysis procedure is demonstrated for estimating the ringing loads on an offshore structure modeled as a simple vertical cylinder. The procedure is based on the Euler Overlay Method, where the computational domain of CFD solution is minimized to the immediate vicinity of the structure by overlaying Euler solution defined in the outer domain. The simulated ringing load shows good agreement with experimental data. Dynamic amplification factor due to the simulated ringing load is investigated for different damping ratio and natural frequency of the structure. Ringing response due to breaking wave shows significance of ringing load when evaluating dynamic amplification of wave load.

scholarly journals Second Order Diffraction of Water Waves by a Bottom Mounted Vertical Circular Cylinder and Some Related Numerical Problems

2006 ◽  
Vol 129 (1) ◽  
pp. 68-70
Author(s):  
Oguz Yilmaz
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Circular Cross Section ◽  
Vertical Cylinder ◽  
Second Order ◽  
Published Data ◽  
Hankel Transformation ◽  
Third Order ◽  
Improper Integral ◽  
Order Diffraction

A Hankel transformation is used to obtain the second order diffraction solution of vertical cylinder of circular cross section. The improper integral over the free surface is tackled carefully. The singularity at the free surface is overcome effectively using a third order nonlinear transformation. Numerical results for free surface elevations compare well with the published data.

Shallow Water Breaking Wave Loads on Vertical Cylinders

2013 ◽  
Vol 694-697 ◽  
pp. 659-664
Author(s):  
Li Xu ◽  
Song Gao ◽  
Da Zheng Wang ◽  
N. Barltrop
Keyword(s):  
Water Surface ◽  
Vertical Cylinder ◽  
Breaking Wave ◽  
Total Force ◽  
Outer Diameter ◽  
Wave Loads ◽  
Cylinder Model ◽  
Vertical Cylinders ◽  
Special Case ◽  
Wave Shapes

Many offshore and harbor structures are composed of cylindrical members. In this paper, the special case of shoaling breaking wave loads on a vertical cylinder is investigated in a tank. A segmented cylinder model with outer diameter of 0.204m and total height of 1m was built and tested. Also a 1:20 slope ramp was constructed in the tank to provide the shoaling effect. During the experiments the total force on each segment of the cylinder was measured and the water surface elevations at the cylinder and in deep water were also recorded. Studies on wave shapes and wave loads are presented here.

Cloaking a vertical cylinder via homogenization in the mild-slope equation

2016 ◽  
Vol 796 ◽  
Author(s):  
G. Dupont ◽  
S. Guenneau ◽  
O. Kimmoun ◽  
B. Molin ◽  
S. Enoch
Keyword(s):  
Free Surface ◽  
Conformal Mapping ◽  
Water Waves ◽  
Vertical Cylinder ◽  
Far Field ◽  
Physical Constraints ◽  
Mild Slope Equation ◽  
The Mean ◽  
Drift Force ◽  
Linear Water Waves

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.

High frequency resonant response of a monopile in irregular deep water waves

2018 ◽  
Vol 853 ◽  
pp. 564-586 ◽  
Author(s):  
Bjørn Hervold Riise ◽  
John Grue ◽  
Atle Jensen ◽  
Thomas B. Johannessen
Keyword(s):  
Resonance Frequency ◽  
Deep Water ◽  
Water Waves ◽  
Irregular Waves ◽  
Breaking Wave ◽  
Wave Load ◽  
Irregular Wave ◽  
The Third ◽  
Extreme Response ◽  
Wave Slope

Experiments with a weakly damped monopile, either fixed or free to oscillate, exposed to irregular waves in deep water, obtain the wave-exciting moment and motion response. The nonlinearity and peak wavenumber cover the ranges: $\unicode[STIX]{x1D716}_{P}\sim 0.10{-}0.14$ and $k_{P}r\sim 0.09{-}0.14$ where $\unicode[STIX]{x1D716}_{P}=0.5H_{S}k_{P}$ is an estimate of the spectral wave slope, $H_{S}$ the significant wave height, $k_{P}$ the peak wavenumber and $r$ the cylinder radius. The response and its statistics, expressed in terms of the exceedance probability, are discussed as a function of the resonance frequency, $\unicode[STIX]{x1D714}_{0}$ in the range $\unicode[STIX]{x1D714}_{0}\sim 3{-}5$ times the spectral peak frequency, $\unicode[STIX]{x1D714}_{P}$. For small wave slope, long waves and $\unicode[STIX]{x1D714}_{0}/\unicode[STIX]{x1D714}_{P}=3$, the nonlinear response deviates only very little from its linear counterpart. However, the nonlinearity becomes important for increasing wave slope, wavenumber and resonance frequency ratio. The extreme response events are found in a region where the Keulegan–Carpenter number exceeds $KC>5$, indicating the importance of possible flow separation effects. A similar region is also covered by a Froude number exceeding $Fr>0.4$, pointing to surface gravity wave effects at the scale of the cylinder diameter. Regarding contributions to the higher harmonic forces, different wave load mechanisms are identified, including: (i) wave-exciting inertia forces, a function of the fluid acceleration; (ii) wave slamming due to both non-breaking and breaking wave events; (iii) a secondary load cycle; and (iv) possible drag forces, a function of the fluid velocity. Also, history effects due to the inertia of the moving pile, contribute to the large response events. The ensemble means of the third, fourth and fifth harmonic wave-exciting force components extracted from the irregular wave results are compared to the third harmonic FNV (Faltinsen, Newman and Vinje) theory as well as other available experiments and calculations. The present irregular wave measurements generalize results obtained in deep water regular waves.

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