On the Drift Forces of a Vertical Cylinder in Water of Finite Depth

2004 ◽  
Author(s):  
Matiur Rahman ◽  
S. Hossein Mousavizadegan
Keyword(s):  
Analytical Solutions ◽  
Gaussian Quadrature ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Interior Region ◽  
Exterior Region ◽  
Gaussian Quadrature Formula ◽  
Analytical Technique ◽  
Wave Induced ◽  
Drift Forces

Analytical solutions for the wave-induced second-order time independent drift forces and moments due to the dynamic and the waterline pressures on a fixed vertical circular cylinder are derived. The results are displayed graphically for a number of depth to radius ratios. An analytical technique is used to determine the first-order velocity potential by considering two regions, namely, interior region and exterior region. We have also demonstrated a numerical solution by a higher order panel method in which the kernel of the integral equation is modified to make it non-singular and amenable to solutions by the Gaussian quadrature formula. The numerical results are found to comply with the analytical solutions.

scholarly journals Surge motion on a floating cylinder in water of finite depth

2003 ◽  
Vol 2003 (57) ◽  
pp. 3643-3656 ◽  
Author(s):  
Dambaru D. Bhatta
Keyword(s):  
Velocity Potential ◽  
Separation Of Variables ◽  
Finite Depth ◽  
Added Mass ◽  
Computational Results ◽  
Complex Matrix ◽  
Interior Region ◽  
Exterior Region ◽  
Damping Coefficients ◽  
Calm Water

We derived added mass and damping coefficients of a vertical floating circular cylinder due to surge motion in calm water of finite depth. This is done by deriving the velocity potential for the cylinder by considering two regions, namely, interior region and exterior region. The velocity potentials for these two regions are obtained by the method of separation of variables. The continuity of the solutions has been maintained at the imaginary interface of these regions by matching the functions and gradients of each solution. The complex matrix equation is numerically solved to determine the unknown coefficients. Some computational results are presented for different depth-to-radius and draft-to-radius ratios.

scholarly journals Wave loadings on a vertical cylinder due to heave motion

1995 ◽  
Vol 18 (1) ◽  
pp. 151-170 ◽  
Author(s):  
D. D. Bhatta ◽  
M. Rahman
Keyword(s):  
Velocity Potential ◽  
Diffraction Problem ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Wave Forces ◽  
Wave Loads ◽  
Exterior Region ◽  
Calm Water ◽  
Heave Motion ◽  
Fixed Structure

Wave forces and moments due to scattering and radiation for a vertical circular cylinder heaving in water of finite depth are derived analytically. These are derived from the total velocity potential which can be decomposed as two velocity potentials; one due to scattering in the presence of an incident wave on fixed structure (diffraction problem), and the other due to radiation by the heave motion on calm water (radiation problem). For each part, the velocity potential is derived by considering two regions, namely, interior region and exterior region. The complex matrix equations are solved numerically to determine the unknown coefficients to compute the wave loads. Some numerical results are presented for different depth to radius and draft to radius ratios.

scholarly journals WAVE-INDUCED SEEPAGE EFFECTS ON A VERTICAL CYLINDER

1980 ◽  
Vol 1 (17) ◽  
pp. 108
Author(s):  
Thomas J.P. Durand ◽  
Peter L. Monkmeyer
Keyword(s):  
Circular Cylinder ◽  
Water Waves ◽  
Theoretical Calculations ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Pressure Amplitude ◽  
Uplift Force ◽  
Overturning Moment ◽  
Wave Induced ◽  
Circular Base

This study deals with the seepage effects experienced by a large, vertical, circular cylinder resting on a submerged bed of sand when planar water waves interact with it. Potential theory is used to describe the seepage flow field. The sea bottom pressure condition is determined from the water field velocity potential derived by MacCamy and Fuchs (1954) in the case of planar waves diffracted by a large impervious cylinder. Consideration is also given to cylinders with a thin circular base whose diameter exceeds that of the cylinder itself. The problem formulation as well as the initiation of the analysis apply to the general case of a bed of sand with finite depth. For the case of infinite depth of the porous medium, theoretical solutions for the seepage pressure are obtained in the form of infinite integrals. Theoretical solutions for the pressure along the cylinder circular base are then derived, leading by integration to closed form expressions for the wave-induced seepage uplift force and overturning moment exerted on the cylinder. These expressions for the force and moment, which are presented in non-dimensional form are shown to be universal functions of a unique variable. Graphs are provided so that very few computations are required to determine the uplift force and overturning moment exerted on a cylinder. A comparison with various approximate theories reveals the present theory to be the only one which gives reliable results in general. The amplitude and phase angle of the oscillating wave-induced pressure along the cylinder base are determined numerically. Results for the pressure amplitude are presented as non-dimensional ratios to the amplitude of the pressure that would prevail if no cylinder were disturbing the wave field. Expressions for the exit gradient around the cylinder base are also determined. Contours of the ratio of the exit gradient to the one that would prevail in the absence of a cylinder are presented. Laboratory measurements of uplift pressure amplitudes on a circular cylinder show good agreement with theoretical calculations.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

scholarly journals WAVE LOADS ON HORIZONTAL CYLINDERS

1978 ◽  
Vol 1 (16) ◽  
pp. 147
Author(s):  
P. Holmes ◽  
J.R. Chaplin
Keyword(s):  
Oscillatory Flow ◽  
Vertical Plane ◽  
Vertical Cylinder ◽  
Irregular Waves ◽  
Wave Loads ◽  
Incident Flow ◽  
Cylinder Axis ◽  
Straight Line ◽  
Horizontal Cylinders ◽  
Wave Induced

The problem of predicting wave induced loads on cylinders is an enormously complex one. It is clear from the scatter present in most experimental determinations of force coefficients that there are many individual factors which influence the mechanisms of flow induced loading. Among these are some, for instance Reynolds number, separation and periodic vortex shedding, which are inter-related and whose influences cannot be studied in isolation. Others, such as shear flow, irregular waves and free surface effects, can at least be eliminated in the laboratory, in order to approach an understanding of the more fundamental characteristics of the flow. A vertical cylinder in uniform waves experiences an incident flow field which can be described in terms of rotating velocity and acceleration vectors, always in the same vertical plane, containing also the cylinder axis, whose magnitudes are functions of time and of position along the length of the cylinder. Some of the essential features of this flow can be studied under two-dimensional oscillatory conditions, in which either the cylinder or the fluid is oscillated relative to the other along a straight line (planar oscillatory flow). The incident velocity and acceleration vectors are then always concurrent, normal to the cylinder axis, and oscillating in magnitude with time.

Numerical Computation of Circumferential Waves in Cylindrical Curved Waveguides

2020 ◽  
Vol 17 (10) ◽  
pp. 2050001
Author(s):  
Zhirong Lin ◽  
Peng Yu ◽  
Haokun Xu
Keyword(s):  
Numerical Computation ◽  
Cross Section ◽  
Analytical Solutions ◽  
Present Method ◽  
Complex Field ◽  
Analytical Technique ◽  
Trial Wavefunction ◽  
The Waves ◽  
Variational Statement ◽  
Circumferential Waves

We present a complex field general variational statement to study the waves propagating in the circumferential directions of cylindrical curved waveguides. A semi-analytical technique that has been applied on straight waveguides in the literature is reformulated to adapt to the circumferential directions and used for constructing the trial wavefunction in complex field. The method requires the waveguide to be analyzed to be geometrically and physically uniform along its circumferential axis; however, its circumferential cross-section can be arbitrarily complex. The formulation is verified using various examples, which were examined previously by other numerical or analytical solutions. Different cases were studied and comparisons with those published are also performed show the utility and advantages of present method.

Kinetics and Mechanism of Cationic Micelle/Flexible Nanoparticle Catalysis: A Review

2018 ◽  
Vol 43 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Mohammad Niyaz Khan ◽  
Ibrahim Isah Fagge
Keyword(s):  
Rate Increase ◽  
Molecular Level ◽  
Binding Constants ◽  
Exchange Constant ◽  
Interior Region ◽  
Bimolecular Reactions ◽  
Exterior Region ◽  
Different Shapes ◽  
Molecular Origin ◽  
Kinetics Of

The aqueous surfactant (Surf) solution at [Surf] > cmc (critical micelle concentration) contains flexible micelles/nanoparticles. These particles form a pseudophase of different shapes and sizes where the medium polarity decreases as the distance increases from the exterior region of the interface of the Surf/H2O particle towards its furthest interior region. Flexible nanoparticles (FNs) catalyse a variety of chemical and biochemical reactions. FN catalysis involves both positive catalysis ( i.e. rate increase) and negative catalysis ( i.e. rate decrease). This article describes the mechanistic details of these catalyses at the molecular level, which reveals the molecular origin of these catalyses. Effects of inert counterionic salts (MX) on the rates of bimolecular reactions (with one of the reactants as reactive counterion) in the presence of ionic FNs/micelles may result in either positive or negative catalysis. The kinetics of cationic FN (Surf/MX/H2O)-catalysed bimolecular reactions (with nonionic and anionic reactants) provide kinetic parameters which can be used to determine an ion exchange constant or the ratio of the binding constants of counterions.

Wave-Current Loading on a Vertical Slender Cylinder by Two Different Numerical Models

2006 ◽  
Author(s):  
M. H. Zaman ◽  
R. E. Baddour
Keyword(s):  
Numerical Models ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Offshore Structure ◽  
Current Field ◽  
Oblique Wave ◽  
Waves And Currents ◽  
Current Loading

The study of the effects resulting from the interaction of a combined wave-current field with any ocean structure is important for the design and performance evaluation of that structure. The prudent computation of forces exerted by waves and currents is an essential task in the study of the stability of an offshore structure. A study on the loading of an oblique wave and a current field on a fixed vertical slender cylinder in a 3D flow frame is illustrated in Zaman and Baddour (2004). The three dimensional expressions describing the characteristics of the combined wave-current field in terms of mass, momentum and energy flux conservation equations are formulated. The parameters before the interaction of the oblique wave-free uniform current and current-free wave are used to formulate the kinematics of the flow field. These expressions are also employed to formulate and calculate the loads imparted by the wave-current fluid flow on a bottom mounted slender vertical cylinder. In this work a 2D version of the above 3D model called here Model-I has been used for the numerical computations presented in this paper. The second model denoted model-II in the present paper is based on Euler equations. This model is formulated through the vertical integration of the continuity equation and the equations of motions, Zaman et al (1997). A semi-implicit numerical technique is employed for the numerical solution. In the present paper comparisons are made between the results obtained from the 2D version of the above models in finite depth. Both models are then compared with some relevant experimental data. Morison et al equation (1950) is deployed for the load computations in all cases.

scholarly journals Erratum: “Wave-induced vortex generation around a slender vertical cylinder” [Phys. Fluids 32, 042105 (2020)]

2020 ◽  
Vol 32 (10) ◽  
pp. 109902
Author(s):  
Giulia Antolloni ◽  
Atle Jensen ◽  
John Grue ◽  
Bjørn H. Riise ◽  
Maurizio Brocchini
Keyword(s):  
Vertical Cylinder ◽  
Vortex Generation ◽  
Wave Induced

Hydrodynamic Analysis of a Vertical Axisymmetric Oscillating Water Column Device Floating in Finite Depth Waters

2012 ◽  
Author(s):  
Spyros A. Mavrakos ◽  
Dimitrios N. Konispoliatis
Keyword(s):  
Water Column ◽  
Wall Thickness ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Wave Forces ◽  
Oscillating Water Column ◽  
Wells Turbine ◽  
Present Contribution ◽  
Outer Atmosphere ◽  
Incident Waves

A floating oscillating water column device (OWC) consists of a vertical cylinder, with a finite wall thickness, partly submerged as an open-bottom chamber in which air is trapped above the inner water free surface. The chamber is connected with the outer atmosphere by a duct housing an air turbine. Forced by incident waves from any direction, the water surface inside pushes the dry air above through a Wells turbine system to generate power. In the present contribution the volume flows, the wave forces, the added mass and damping coefficients and the mean second-order loads for various configurations of OWC devices are being presented. Finally, it is tested how differentiations in the device’s geometry (wall thickness, draught, shape of the chamber, turbine characterises) affect the inner pressure and as a result the absorbed power by the device.

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