Cylinder In Regular Waves Research Articles

An adaptive harmonic polynomial cell method for three-dimensional fully nonlinear wave-structure interaction with immersed boundaries

To accurately simulate wave-structure interaction based on fully nonlinear potential flow theory, a three-dimensional (3 D) high-order immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method is proposed. Both the free surface and body surface are immersed in background octree cells that are adaptively refined near the boundaries of interest, thereby dramatically reducing computational costs without loss of accuracy. We also propose an easy-to-implement IB strategy to deal with possible instabilities in the time-domain solution arising from the intersection of Dirichlet–Neumann boundaries. For a linearized problem of wave-wall interaction, a matrix-based stability analysis is performed, providing mathematical support for the robustness of the proposed IB strategy. In contrast to the two-dimensional HPC method, compressed cells are found to offer superior stability compared to stretched cells in the vertical direction, while equal mesh aspect ratio in the horizontal plane is superior. Cubic octree cells are, however, still preferred in practice. The free surface is primarily described by a set of massless background wave markers; however, to address the challenges of IB methods in tracking the free surface evolution near the structure, additional body-fitted wave markers are introduced close to the waterline. The information exchange between these two sets of wave markers is realized by radial basis function (RBF) interpolation. While standard RBF schemes have grid-size-dependent filtering performance, we propose a normalized RBF scheme, which is then optimized in terms of the number of neighboring nodes, a smoothing coefficient and the basis functions. Excellent accuracy properties of the proposed 3 D IB-AHPC method are demonstrated by studying fully nonlinear wave propagation. The method is further applied to study relevant fully nonlinear wave-structure interaction problems, including sloshing in 3 D rectangular tanks and wave diffraction of a bottom-mounted cylinder in regular waves. Satisfactory agreement is demonstrated with existing experimental and numerical results, suggesting that the proposed 3 D IB-AHPC method is a promising potential-flow method in marine hydrodynamics.

A viscous investigation on the hydrodynamic coefficients and wave loads under the interaction of side-by-side cylinders in regular waves

The paper introduces a two-dimensional Reynolds-Averaged Navier-Stokes Computational Fluid Dynamics (RANS CFD) model to investigate the effects of adjacently floating bodies on the hydrodynamic coefficients and wave loads acting on these bodies. The analysis considers two square cylinders with a narrow gap in way of the free water surface. The physical significance of subsections of the hydrodynamic coefficient matrix becomes evident when comparing coefficients obtained from oscillating-oscillating versus oscillating-fixed models. This understanding is significant, particularly in applications where only specific portions of the hydrodynamic coefficient matrix are utilized, such as in ship-ice collision scenarios (Jiang et al., 2023a). The correlation between wave loads and wave elevations reveals that the sway force and roll moment are associated with the disparity in wave elevation at both sides of each cylinder, while heave forces correlate with the averaged wave elevation on both sides of each cylinder. It is concluded that hydrodynamic interactions are sensitive to the displacement of a floater and accordingly can dominate added mass and damping effects.

CFD Study for Wave Run-up Characteristics Around a Truncated Cylinder with Damper

In this study, numerical simulations for a single fixed truncated circular cylinder in regular waves were conducted to investigate the nonlinear wave run-up under various dampers and wave period conditions. The present study used the volume of fluid (VOF) technique to capture the air-water interface. The unsteady Reynolds-averaged Navier–Stokes (URANS) equation with the k– ϵ turbulence model was solved using the commercial computational fluid dynamics (CFD) software STAR-CCM+. First, a systematic spatial convergence study was conducted to assess the performance and precision of the present numerical wave tank. The numerical scheme was validated by comparing the numerical results of wave run-up on a bare truncated cylinder with the experimental results, and a good agreement was achieved. Then, a series of parametric studies were carried out to examine the wave run-up time series around the truncated cylinder with single and dual dampers in terms of the first- and second-order harmonic and mean set-up components. Additionally, the local wave field and the flow velocity vectors adjacent to the cylinder were evaluated. It was confirmed that under short wave conditions, the high position of the damper led to a noticeable increase in the wave run-ups with significant changes in the first- and second-order harmonic components.

Experimental investigations of secondary load cycle formation in wave force on a circular cylinder under steep regular waves

When a large wave interacts with a marine structure, it would lead to a high-frequency structure response, and impose great threats to marine structures. In this paper, wave forces on a vertical cylinder in regular waves with moderate to extreme steepness were measured experimentally. The secondary load cycle phenomenon in wave force time history was observed and its generation mechanism was analyzed. It is found that secondary load cycle strongly depends on wave steepness. When the wave steepness exceeds critical values, the secondary load cycle phenomenon appears in the time history of wave force, and a high frequency response accompanied this phenomenon. Further, a new critical wave steepness kA = 0.3tanh(kh) (A is wave crest height, k is wavenumber and h is water depth) is found to distinguish the secondary load cycle occurrence. Here the wave steepness threshold value is no more a constant value that was proposed before, it varies with water depth and becomes smaller with the decrease of water depth. Moreover, the secondary load cycle and the subsequent high-frequency response are divided from the wave force signal based on the empirical mode decomposition (EMD) method. The results show that the high-frequency response locates in the natural frequency region of cylinders, which is much higher than the high-order wave components. Finally, the generation mechanism of this phenomenon is explained. As a steep wave passes a cylinder, a large wave run-up would be generated on the front side of the cylinder. One part of water body of the run-up swashes down and impacts the wave surface heavily. The other part of wave run-up fills into the cavity on the lee side of the cylinder, and generates violent turbulence. Both processes are found to lead to an instant impact on the structure, and then excite structural high-frequency vibration. This instant impact expresses as secondary load cycle in wave force history. These new findings from experimental studies have provided new insights into the generation mechanism and the associated changes in wave properties during the formation of secondary load cycle.

Numerical Study of Non-Linear Wave Run-Up Around a Circular Cylinder in Regular Waves

Lee, J.-H. and Koo, B., 2021. Numerical study of non-linear wave run-up around a circular cylinder in regular waves. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 554–558. Coconut Creek (Florida), ISSN 0749-0208. In this study, numerical simulations have been carried out to investigate the non-linear wave run-up phenomena of a single cylinder according to wave period and slope. In order to perform numerical analysis on a three-dimensional incompressible viscous turbulent two phase flow, this study used a Volume Of Fluid (VOF) technique and a realizable turbulence model based on the Computational Fluid Dynamics (CFD) commercial code, “STAR-CCM+”. Various incoming wave conditions have been applied to see how the wave steepness and wave periods affect the wave run-up height on the circular cylinder. Finally, the wave run-up estimation results for wave slopes and periods were compared with the related experimental results and they had good agreement. It was confirmed that as the wave steepness increased, the run-up phenomenon appeared largely at the part where the cylinder hit the incident wave.

Spectral Wave Explicit Navier-Stokes Equations for wave-structure interactions using two-phase Computational Fluid Dynamics solvers

This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential part - represents the incident waves - is solved with spectral wave models; the viscous part - represents the complementary perturbation on the incident waves - is solved with the CFD solver. The decomposition strategy is called Spectral Wave Explicit Navier-Stokes Equations (SWENSE), originally proposed for single-phase CFD solvers ( Ferrant et al., 2003). Firstly, this paper presents a new two-phase SWENS Equations with interface capturing technique. To achieve this single-phase and two-phase decomposition, the incident fields are extended in the air with a density-weighted pressure. Secondly, an accurate and efficient interpolation method is proposed to transfer High Order Spectral (HOS) wave model's result on CFD mesh, which reduces drastically the divergence error of the interpolated velocity. Implemented within OpenFOAM, these methods are tested by three verification, validation, and application cases, considering incident wave propagation, high-order loads on a vertical cylinder in regular waves, and a Catenary Anchor Leg Mooring buoy in both regular and irregular waves. Speed-ups between 1.7 and 4.2 are achieved. The wave models and the interpolation method are released open-source to the public.

An Improved Prediction for Wave Runup on a Circular Cylinder

Previous studies have applied various methods to analyze the wave runup on fixed columns, including linear and higher order diffraction theories and semi-empirical correlations. However, none of them seems to be adequate to accurately predict the wave runup over a full range of wave steepness and cylinder sizes when further compared with experimental data from the literature. The focus of this study is on a better semi-empirical formula for wave runup on a circular cylinder. We: (i) report on a set of experimental results obtained for a circular cylinder with various diameters in regular waves; (ii) evaluate the performance of existing theories or empirical equations using a full data set comprising new experimental results and results reported in the literature; and (iii) propose a new equation for predicting the wave runup on a fixed circular cylinder in regular waves. The proposed semi-empirical equation considers both the effects of wave scattering and wave nonlinearity and is able to estimate the runup of regular waves on a circular cylinder with significantly improved accuracy when tested with the full experimental data set.

Numerical Simulation of the Oscillating Water Column inside a Vertical Cylinder in Regular Waves Using IHFOAM

The motion of the free-surface inside a surface-piercing vertical cylindrical tube can be seen as a simplified approximation of an oscillating-water-column ocean-wave energy-converter (OWC-OWEC). In the present work the IHFOAM code, which solves the Reynolds-averaged Navier-Stokes (RANS) equations by a finite-volume method using the volume-of-fluid (VoF) technique, was used to simulate the action of a regular wave on the free-surface inside a vertical cylinder open to the atmosphere. In this paper the results obtained by IHFOAM are compared with other numerical results and with experimental data, showing a good correspondence between these results. In this way the IHFOAM code was verified (by comparison with other numerical results) and validated (by comparison with experimental data).

Wave runup on a surging vertical cylinder in regular waves

The wave runup caused by a vertical cylinder surging in regular waves is studied both experimentally and numerically. The so-called DualSPHysics Smoothed Particle Hydrodynamics (SPH) code is used for the 3-D numerical modelling. A wide range of cylinder sizes and wave conditions is investigated with results comparing favourably between the experimental and SPH model under both fixed and forced-surge conditions. The experimental and SPH results are further used to predict the maximum runup amplification, in particular the ratio of the runup caused by the surging cylinder to that of the fixed, over the phase difference between the incident wave and surge motion. This maximum runup ratio has been analysed for its dependence on factors such as wave steepness, wave scattering and surge amplitude. An empirical equation is proposed for predicting the maximum runup ratio from known incident wave and surge conditions. Comparison with results from linear solvers suggests that the linear solvers under-predict the full nonlinear runup by a factor of 1.3–1.5.

Numerical analysis of the wave force acting on a cylinder in regular waves using the MPS method

We simulated the interactions between a second-order Stokes wave and vertical circular cylinder in a three-dimensional numerical wave tank using the moving particle semi-implicit method. The numerical wave tank was modified to generate a series of Stokes waves. Fluid–structure interactions were simulated under the same wave conditions as the model experiments. We compared the hydrodynamic coefficients obtained by the simulations with those of the experiment to validate this method. We also simulated the wave force around a free surface using the developed method in different wave conditions.

High-fidelity CFD simulation of wave run-up for single/multiple surface-piercing cylinders in regular head waves

The capabilities of CFDShip-Iowa V4.5 and V6.2 simulations for wave run-up for single/multiple surface-piercing cylinders in regular waves are assessed in conjunction with the ITTC OEC Workshop on VIV and Wave Run-up held in Nantes, France October 17⿿18, 2013. Statistical convergence and grid/domain/turbulence model sensitivity studies show uncertainty UI values are less than 1% for both the experiment/simulation data and grid/domain/turbulence model sensitivities are less than the facility bias UFB. Simulations are qualitatively validated using UFB and error E between experiment and simulation. Errors for single/four cylinder(s) are comparable with UFB and average error E¯ for the other CFD data of the workshop participants. Results from both V4.5 and V6.2 agree well with experiment and also show capabilities to apply for complex/large-scale problem and to describe detailed wave breaking/spraying for V4.5 and V6.2, respectively. Study on run-up profile shows mean wave elevations are similar to free surface elevations for a cylinder in a steady current. For wave steepness/wave length effect, 2nd to 1st harmonic ratio on the cylinder weather face decreases with steepness for short wave, but increases for long wave. Wave diffraction analysis shows that 2nd/3rd to 1st harmonic ratio in diffracted wave contour reach up to 18⿿41%/9⿿16% respectively. Due to interaction between cylinders, crest/trough heights increase 5⿿17%/4⿿10% for 4C, respectively. Study on vortex shedding shows short wave has insufficient time to develop periodic vortex shedding compared to long wave.

Comparison of flow fields induced by fixed and oscillatory vertical cylinders in regular waves using 3D numerical model

The influences of a flexibly mounted cylinder and a fixed cylinder on the flow field in regular waves are studied numerically. Performances of the flexibly mounted cylinder oscillating freely in still water and in regular waves are first simulated. Then the in-line forces on the two cylinders in regular waves are compared to the theoretical results. All results indicate the present model is valid. Then the entire flow fields induced by the two cylinders are analyzed in detail. The windward and leeward regions of the cylinder are each divided into eight sections. Results of the windward side are complex because of the superposition of incoming and reflected waves. Results of the leeward side show that the sectional average wave height decreases as the wave frequency increases. In general, the flexibly mounted cylinder attenuates wave energy more effectively. Moreover, the wave frequency is a major factor influencing the flow field. When the incident wave frequency approaches the natural frequency of the cylinder, differences of the two data sets become significant. Distance between the section and the cylinder is another influential factor. The two sets of results become more similar as the distance increases, especially in cases of low incident wave frequencies.

Numerical Simulation of In-Line Response of a Vertical Cylinder in Regular Waves

ABSTRACT Han, Y.; Zhan, J-M.; Su, W.; Li, Y.S., and Zhou, Q. 2015. Numerical simulation of in-line response of a vertical cylinder in regular waves. In-line response of a flexibly mounted, vertical cylinder in a series of regular waves was studied with numerical simulation. A dynamic mesh scheme and a laminar flow model were adopted. The experimental and simulated time histories of five wave gages and the response of the cylinder were compared. At low-incident wave frequencies, although the ratios of the diameters of the cylinders to the wavelength were small, the oscillating cylinder had little influence on the flow field. The numerical responses of the cylinder were in very good agreement with the experimental data. As the frequency of the incoming wave increased, the diffraction effect caused by the cylinder became significant, and the simulated responses of the cylinder were slightly weaker than those of experiment. When the incident wave frequency approached the natural frequency of the cylinder, the...

Wave Forces on Linear Arrays of Rigid Vertical Circular Cylinders in Regular Waves

The present investigation aims to experimentally determine the variation of forces and force coefficients acting on circular cylinders, which are arranged in a linear array along the direction of the waves. Most commonly used structural and non-structural elements in the construction of offshore platforms are circular cylindrical members. In many cases, these members are found in very close neighbourhood of each other, thus modifying the surrounding flow and wave forces acting on them. Model tests were conducted in the wave tank on a maximum of four cylinders of the same diameter. A reasonable scale factor was chosen considering the pertinent factors such as water depth, wave generating capability and accuracy of measurements. The cylinders were installed inside the wave tank as vertical cantilevers fixed at the top. Wave forces acting on the cylinders were measured using special wave force sensors exclusively designed and fabricated for the present project, while the wave profiles were recorded using wave probes installed in the wave basin. The results confirmed the presence of a force shielding effect on the trailing cylinders by the leading cylinders with few exceptions. The findings also substantiated the significant modification of the forces on cylinders when they are present in a linear array. A common practice adopted for the design of offshore platforms was identified with a possibility of underestimating the wave forces acting on the cylindrical elements. In many cases, the experimentally computed hydrodynamic force coefficients were found to be lower than the standard values adopted by various design codes. These findings portray the significance of the present work in achieving economy in the design of jacket platforms and risers.

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrodynamic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equations of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.

Suppression of flow-induced vibrations using ribbon fairings

An experimental study was conducted to investigate the ability of ribbon fairings to suppress fl ow-induced vibrations on a long fl exible horizontal cylinder. The test matrix included towing the cylinder at various speeds, towing the cylinder in regular waves, and investigating the infl uence of partial coverage on the response behavior. The test cylinder was 29 m long with a length to diameter (L/D) ratio of ~760. Interior to the tensioned cylinder model were six sets of unequally spaced biaxial accelerometers in a lightly pressurized environment keeping the interior dry. A string potentiometer was externally attached at the center of the model to provide a reference for later displacement estimates based on integration of the acceleration data. The time domain decomposition method (TDD) was used to recover mode shapes, damping characteristics, and modal contribution factors. For the uniform current cases, the fi ndings illustrate that ribbon fairings are effective and provide increased damping when compared with bare cylinders. Partial coverage demonstrates that localized suppression becomes increasingly less effective as the percentage coverage is reduced. The introduction of regular waves to the towed cylinder cases illustrates the ineffectiveness of ribbon fairing to suppress the orbital motions induced by the waves, which is preferable to the amplifi cation typically observed for airfoil fairings.

내부가 빈 원기둥의 수직운동 특성

In the present investigation, the hydrodynamic characteristics of a vertically floating hollow cylinder in regular waves have been studied. The potential theory for solving the diffraction and radiation problem was employed by assuming that the heave response motion was linear. By using the matched eigenfunction expansion method, the characteristics of the exciting forces, hydrodynamic coefficients, and heave motion responses were investigated with various system parameters such as the radius and draft of a hollow cylinder. In the present analytical model, two resonances are identified: the system resonance of a hollow cylinder and the piston-mode resonance in the confined inner fluid region. The piston resonance mode is especially important in the motion response of a hollow circular cylinder. In many cases, the heave response at the piston resonance mode is large, and its resonant frequency can be predicted using the empirical formula of Fukuda (1977). The present design tool can be applied to analyze the motion response of a spar offshore structure with a moon pool.

The effect of sloshing on the sway motions of 2D rectangular cylinders in regular waves

In this paper, we investigated the effect of sloshing on the sway motions of two-dimensional rectangular cylinders in regular waves, bearing in mind possible applications for LNG-FPSO and LNG-FSRU. First, we carried out experiments for two models with different drafts, or the same draft but different filling ratios, in which the models were firmly connected to each other. The sway motion was measured with a noncontact video camera. This is an extension of Rognebakke and Faltinsen’s work for a single model (J Ship Res 47(3):208–221, 2003). It was found that the sway motion became small when the incident wave frequency was close to the lowest natural frequency of each model. The sway motion greatly increased when the wave frequency was higher than this frequency. The measured data were compared with numerical results obtained by a single-dominant multi-modal method; relatively good agreement was noted. However, the numerical results deviated from the experimental results near the lowest natural frequency of the smaller model, which was believed to be due to overturning waves, as observed during the experiment. Since this is out of the valid range for the single-dominant multi-modal method, other, more appropriate, methods such as the multi-dominant modal method must be applied instead.

An experimental study of inertia and drag coefficients for a truncated circular cylinder in regular waves

It is of academic and practical importance to predict accurate wave loads on cylindrical members of finite length. In this study, the in-line force on a small segment of a vertical circular cylinder of various truncated lengths was experimentally investigated in regular waves. Based on Morison equation, the inertia and drag coefficients (CD and CM) were evaluated and presented as a function of KC number for various values of relative truncated length in order to understand 3-D end wake effects on the truncated cylinder. The factors that may affect the determination of CD and CM were also discussed. A weighted least square method was employed to improve the predictive accuracy of maximum measured forces.