Wave Elevation for an Array of Columns Under Wave-Current Interactions

2021 ◽  
pp. 1-15
Author(s):  
Song Gao ◽  
Bin Teng
Keyword(s):  
Free Surface ◽  
Singular Integrals ◽  
Spatial Location ◽  
Current Speed ◽  
Wave Direction ◽  
Wave Elevation ◽  
Diffraction Model ◽  
Nearly Singular Integrals ◽  
Free Surface Wave ◽  
A Current

Abstract A wave and current diffraction model is developed based on the potential flow theory and a high-order boundary element method with the successful treatment of singular and nearly singular integrals. The wave-current diffraction from four mounted cylindrical columns are computed, and the free surface wave elevations among the columns are investigated. The influences of the current speed, wave direction, and column spacing on the wave elevation are examined. Ultimately, the presence of a current has a significant influence on the magnitude, spatial location and occurrence frequency of the maximum wave elevation.

Response of Liquid in Cylindrical Tank with Rigid Annual Baffle Considering Damping Effect

2011 ◽  
Vol 255-260 ◽  
pp. 3687-3691 ◽  
Author(s):  
Jia Dong Wang ◽  
Ding Zhou ◽  
Wei Qing Liu
Keyword(s):  
Free Surface ◽  
Dynamic Response ◽  
Potential Function ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Cylindrical Tank ◽  
Generalized Coordinates ◽  
Damping Effect ◽  
Total Potential ◽  
Free Surface Wave

Sloshing response of liquid in a rigid cylindrical tank with a rigid annual baffle under horizontal sinusoidal loads was studied. The effect of the damping was considered in the analysis. Natural frequencies and modes of the system have been calculated by using the Sub-domain method. The total potential function under horizontal loads is assumed to be the sum of the tank potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. Substituting potential functions into the free surface wave conditions, the dynamic response equations including the damping effect are established. The damping ratio is calculated by Maleki method. The liquid potential are obtained by solving the dynamic response equations of the system.

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

scholarly journals A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Guizhong Xie ◽  
Fenglin Zhou
Keyword(s):  
Boundary Element ◽  
Crack Front ◽  
Singular Integrals ◽  
Triangular Element ◽  
Crack Problems ◽  
Nearly Singular Integrals ◽  
Triangular Elements ◽  
Displacement Extrapolation Method ◽  
Element Shape ◽  
Displacement Extrapolation

This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

Mitigation of liquid sloshing in a rectangular tank due to slotted porous screen

2020 ◽  
Vol 234 (3) ◽  
pp. 686-698
Author(s):  
Sunny Kumar Poguluri ◽  
Il-Hyoung Cho
Keyword(s):  
Free Surface ◽  
Numerical Technique ◽  
Liquid Sloshing ◽  
Tank Wall ◽  
Air Entrapment ◽  
Jet Formation ◽  
Induced Motion ◽  
Free Surface Wave ◽  
Nonlinear Free Surface ◽  
Porous Screen

Liquid sloshing inside a tank with a slotted porous screen at the center is studied based on numerical and experimental methods. Slotted screens with three different porosities (0.0964, 0.1968 and 0.3022) for two submergence depths of 1 and 2 cm have been considered. One of the main advantages of the slotted screens is that the resonance frequency of the sloshing tank can be altered and the sloshing-induced motion/load can be suppressed by energy dissipation across the porous screen. The complexities of slotted screens equipped in a sloshing tank are accompanied by wave breaking, jet formation and liquid fragmentations which are commonly seen phenomena across the porous screen. These violent free surface behaviors in a tank are studied based on numerical simulations using the incompressible turbulent model and compared with the experiments. For the numerical sloshing tank with porous screen, free surface elevation and pressure at the tank wall are in good agreement with the experimental results. The adopted numerical technique will be able to capture the nonlinear free surface wave profile, air entrapment and jet formation across the screen in agreement with the experiments. For the fully submerged screen, the lowest resonance period shifted slightly to higher values. The sloshing tank equipped with porous screen of 0.1968 for the fully submerged screen predicted lower values of the amplification factor and pressure at the tank wall compared to other cases.

scholarly journals Comparison of a Floating Cylinder with Solid and Water Ballast

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2487 ◽  
Author(s):  
Roman Gabl ◽  
Thomas Davey ◽  
Edd Nixon ◽  
Jeffrey Steynor ◽  
David M. Ingram
Keyword(s):  
Free Surface ◽  
Wave Direction ◽  
Floating Structure ◽  
Parametric Rolling ◽  
Rotation Direction ◽  
Wide Range ◽  
Heave Motion ◽  
Floating Platforms ◽  
Floating Objects ◽  
Validation Experiments

Modelling and understanding the motion of water filled floating objects is important for a wide range of applications including the behaviour of ships and floating platforms. Previous studies either investigated only small movements or applied a very specific (ship) geometry. The presented experiments are conducted using the simplified geometry of an open topped hollow cylinder ballasted to different displacements. Regular waves are used to excite the floating structure, which exhibits rotation angles of over 20 degrees and a heave motion double that of the wave amplitude. Four different drafts are investigated, each with two different ballast options: with (water) and without (solid) a free surface. The comparison shows a small difference in the body’s three translational motions as well as the rotation around the normal axis to the water surface. Significant differences are observed in the rotation about the wave direction comparable to parametric rolling as seen in ships. The three bigger drafts with free surface switch the dominant global rotation direction from pitch to roll, which can clearly be attributed to the sloshing of the internal water. The presented study provides a new dataset and comparison of varying ballast types on device motions, which may be used for future validation experiments.

Tow Forces for Emergency Towing of Containerships

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Vladimir Shigunov ◽  
Thomas E. Schellin
Keyword(s):  
Wave Height ◽  
Current Speed ◽  
Sea Waves ◽  
Wave Direction ◽  
Equilibrium Equations ◽  
Significant Wave ◽  
Wind Speeds ◽  
Time Average ◽  
Wave Drift Forces ◽  
Drift Forces

For a series of five containerships of differing capacities (707, 3400, 5300, 14,000, and 18,000 TEU), systematic computations were performed to estimate the tow force required in an emergency. Time-average ship positions with respect to the given waves, wind, and current directions and the corresponding time-average forces were considered. Current speed was considered to include also towing speed. Directionally aligned as well as not aligned wind and waves were investigated. Wave height, wind speed, and wave and wind direction relative to current direction were systematically varied. Wind speeds based on the Beaufort wind force scale corresponded to significant wave heights for a fully arisen sea. Waves were assumed to be irregular short-crested seaways described by a Joint North Sea Wave Observation Project (JONSWAP) spectrum with peak parameter 3.3 and cosine squared directional spreading. For each combination of current speed, wave direction, significant wave height, and peak wave period, the required tow force and the associated drift angle were calculated. Tow force calculations were based on the solution of equilibrium equations in the horizontal plane. A Reynolds-Averaged Navier–Stokes (RANS) solver obtained current and wind forces and moments; and a Rankine source-patch method, drift forces and moments in waves. Tow forces accounted for steady (calm-water) hydrodynamic forces and moments, constant wind forces and moments, and time-average wave drift forces and moments. Rudder and propeller forces and towline forces were neglected.

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