Motion Characteristics of Floating Bodies

1976 ◽  
Vol 20 (04) ◽  
pp. 181-189
Author(s):  
Choung M. Lee
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Linear Theory ◽  
Cross Sections ◽  
Wave Length ◽  
Added Mass ◽  
Exciting Force ◽  
Hydrodynamic Coefficients ◽  
Floating Bodies ◽  
Motion Characteristics

The motion characteristics of floating bodies, in and below a free surface, that are subject to surface waves are examined. The effects of various degrees of approximation of hydrodynamic coefficients on the results of the motion computations are investigated on the basis of linear theory. The behavior of hydrodynamic coefficients such as added mass, damping, and wave-exciting force with respect to frequency of oscillation (or wave length) and depth of submergence is also investigated. Numerical results are obtained for three cylindrical bodies of circular, rectangular, and rhombic cross sections. The results reveal that fairly crude approximations can be applied to compute the oscillatory motion of submerged bodies.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

2019 ◽  
Vol 869 ◽  
pp. 610-633 ◽  
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
D. Petrolo ◽  
V. Di Federico ◽  
S. Longo
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Density Ratio ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Numerical Code ◽  
Long Distance ◽  
Front Speed

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

Hydrodynamic Analysis of Two Side-by-Side Moored Floating Bodies

2010 ◽  
Author(s):  
D. C. Hong ◽  
Y. Y. Kim ◽  
S. H. Han
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Hydrodynamic Coefficients ◽  
Potential Solution ◽  
Floating Bodies ◽  
Matching Method ◽  
Free Surface Condition ◽  
Wave Elevation ◽  
Resonance Frequencies ◽  
Boundary Matching

The hydrodynamic interaction of two bodies floating in waves is studied. The two-body hydrodynamic coefficients of added mass, wave damping and exciting forces and moments are calculated using the irregular frequency free radiation-diffraction potential solution of the improved Green integral equation associated with the free surface Green function (Hong 1987) according to the conventional two-body analysis. It is well known that the conventional two-body potential solution with usual grid fineness largely overestimates the hydrodynamic coefficients at and near the resonance frequency of the free surface in the gap between two floating bodies moored side-by-side in close proximity (Huijsmans et al. 2001, Hong et al. 2005). The two-body diffraction problem has been solved by both the conventional two-body analysis without damped free surface condition and a boundary matching method with and without damped free surface condition. Numerical results of the wave exciting force coefficients of two identical caissons floating side by side obtained by the two methods have been presented and the discrepancies between them have been discussed. Particular attention is paid to the wave elevation in the gap at the resonance frequencies. Amplitudes and phases of the scattering wave elevations in the gap at the first three free surface resonance frequencies computed by the boundary matching method without damped free surface condition have been presented. It has also been shown that the unrealistic wave elevation due to the resonance of the free surface in the gap can be reduced by imposing the damped free surface condition upon the flow in the gap as used in the oscillating water column hydrodynamics (Hong et al. 2004).

Importance of Added Mass for the Interaction Between IL and CF Vibrations of Free Spanning Pipelines

2011 ◽  
Author(s):  
Ida M. Aglen ◽  
Carl M. Larsen
Keyword(s):  
Cross Sections ◽  
Amplitude Ratio ◽  
Large Diameter ◽  
Cross Flow ◽  
Added Mass ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Cross Sectional ◽  
Mass Coefficient ◽  
The Stability

The importance of cross-flow (CF) response generated by vortex induced vibrations (VIV) of free spanning pipelines has long been recognised. The significance of in-line (IL) vibrations has recently been understood and hence also been subjected to research. The combined effect of CF and IL vibrations is, however, still not fully described. This paper highlights the CF-IL interaction with focus on the transition zone from pure IL to CF dominated response, giving special attention to how the added mass influences the interaction. Results from extensive flexible beam tests connected to the Ormen Lange (OL) development have been used as a basis for this study. Trajectories for cross sectional motions from the flexible beam test were identified, and then used as forced motions of a large diameter rigid cylinder exposed to uniform flow. Non-dimensional parameters like Reynolds number (Re), amplitude ratio and reduced frequency were identical for the two tests. Hence, forces found from the forced motion test could be used to find hydrodynamic coefficients valid for the flexible beam case. This paper discusses the results from the flexible beam tests with a relatively short length to diameter ratio (L/D) of 145. Modal analyses by Nielsen et al. (2002) show that the first mode dominates in both directions for these particular tests, even though the IL response frequency is twice the CF frequency. In this paper the added mass variations along the OL flexible beam is studied. Forces acting on 4 different cross sections along the beam are measured for 7 different prototype velocities. For each test the hydrodynamic coefficients are calculated, and the results show how the added mass changes along the beam for increasing velocities, and thereby creates resonance for both IL and CF response. The stability of the added mass coefficient throughout the time series is also evaluated.

scholarly journals The method of images in some problems of surface waves

1927 ◽  
Vol 115 (771) ◽  
pp. 268-280 ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Unit Length ◽  
Wave Length ◽  
Fluid Motion ◽  
Degree Of Approximation ◽  
Image Point ◽  
Horizontal Line ◽  
Image System

1. When a circular cylinder is submerged in a uniform stream, the surface elevation may be calculated, to a first approximation, by a method due originally to Lamb for this case, and later extended to bodies of more general form: the method consists in replacing the cylinder by the equivalent doublet at its centre and then finding the fluid motion due to this doublet. In discussing the problem some years ago, I remarked that if the solution so obtained were interpreted in terms of an image system of sources, we should then be able to proceed to further approximations by the method of successive images, taking images alternately in the surface of the submerged body and in the free surface of the stream. This is effected in the following paper for two-dimensional fluid motion, and the method is applied to the circular cylinder. It provides, theoretically at least, a process for obtaining any required degree of approximation but, of course, the expressions soon become very complicated. It is, however, of interest to examine some cases numerically so as to obtain some idea of the degree of approximation of the first stage. An expression is first obtained for the velocity potential of the fluid motion due to a doublet at a given depth below the surface of a stream, the doublet being of given magnitude with its axis in any direction. A transformation of this expression then gives a simple interpretation in terms of an image system. This system consists of a certain isolated doublet at the image point above the free surface, together with a line distribution of doublets on a horizontal line to the rear of this point; the moment per unit length of the line distribution is constant, but the direction of the axis rotates as we pass along the line, the period of a revolution being equal to the wave-length of surface waves for the velocity of the stream. The contribution of each part of the image system to the surface disturbance is indicated.

scholarly journals The Diffraction of Free-Surface Waves by a Slender Ship

1984 ◽  
Vol 28 (01) ◽  
pp. 29-47
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Three Dimensional ◽  
Practical Interest ◽  
Prolate Spheroid ◽  
Exciting Force ◽  
Dimensional Solution ◽  
Free Surface Waves ◽  
Dimensional Approximation ◽  
Inner Region

A linear theory is presented for the scattering of small-amplitude monochromatic and unidirectional free-surface waves by a ship fixed at its mean advancing position. In an inner region close to the ship the hull geometrical slenderness is used to justify a quasi-two-dimensional approximation of the flow. The method of matched asymptotic expansions is then introduced to enforce the compatibility of the inner solution with the three-dimensional solution in the far field. The theory is shown to be uniformly valid for all wavelengths of practical interest and all angles of wave incidence. In the short-wavelength limit, existing theories are recovered and the singularity that is present in the limit from oblique to head incidence is removed. Computations are included for the pressure and the sectional exciting force distributions, the wave elevation, and the vertical exciting force and moment in head and bow waves on a prolate spheroid.

Influence of Draft Variation on Heave Added-Mass and Hydrodynamic Damping Coefficients of Floating Bodies

1990 ◽  
Vol 34 (03) ◽  
pp. 172-178
Author(s):  
Marc Vantorre
Keyword(s):  
Numerical Data ◽  
Integral Equation Method ◽  
Added Mass ◽  
Boundary Integral ◽  
Hydrodynamic Coefficients ◽  
Floating Bodies ◽  
Damping Coefficients ◽  
Hydrodynamic Damping ◽  
Harmonic Components ◽  
Heave Motion

A general nonlinear theory for solving the radiation problem for floating or immersed bodies in a periodic heave motion, composed of a number of harmonic components, is applied for calculating the influence of draft variations on the linear hydrodynamic coefficients for heave. It is shown that a calculation method for added-mass and damping coefficients of axisymmetric bodies based on a boundary integral equation method can easily be modified to obtain numerical values of the first and second derivatives with respect to draft of the hydrodynamic coefficients as well. The method is illustrated by experimental and numerical data for a floating cone.

scholarly journals The resistance of a ship among waves

1937 ◽  
Vol 161 (906) ◽  
pp. 299-308 ◽  
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Fluid Velocity ◽  
Wave Length ◽  
Steady Motion ◽  
Degree Of Approximation ◽  
Point Of View ◽  
Similar Degree ◽  
Horizontal Line ◽  
Free Surface Waves

1—The wave resistance of a ship advancing in still water may be calculated under certain assumptions, which amount to supposing the forced wave motion to be small so that squares of the fluid velocity may be neglected; moreover, the ship is supposed to advance with constant velocity in a horizontal line. It does not appear to have been noticed that we may super­ pose on the solution so obtained free surface waves of small amplitude, and that the addition to the resistance may be calculated, to a similar degree of approximation, as the horizontal resultant of the additional fluid pressures due to the free surface waves; this additional resistance, which may be negative, depends upon the position of the ship among the free waves. Various calculations are now made from this point of view. We consider first transverse following waves moving at the same speed as the ship, and then a ship moving in the waves left by another ship in advance moving at the same speed; finally, we examine the more general case of a ship moving through free transverse waves of any wave-length. All the cases are discussed with reference to such experimental results as are available. 2—We treat the problem first as one of steady motion with the ship at rest in a uniform stream of velocity c in the negative direction of Ox ; we take the origin O in the undisturbed water surface, and Oz vertically upwards. The velocity potential is given by ϕ = cx + ϕ 1 , (1)

Experimental Assessment of Hydrodynamic Coefficients of Disks Oscillating Near a Free Surface

2009 ◽  
Author(s):  
Hemlata Wadhwa ◽  
Krish P. Thiagarajan
Keyword(s):  
Free Surface ◽  
Circular Disk ◽  
Added Mass ◽  
Rate Of Change ◽  
Forced Oscillations ◽  
Base Case ◽  
Published Data ◽  
Hydrodynamic Coefficients ◽  
Widespread Application ◽  
Field Development

The use of different types of subsea equipment is continuously increasing in offshore field development. Installation operations such as lifting and lowering of these equipments require knowledge of the hydrodynamic coefficients of the object. An accurate prediction of these coefficients on typical subsea structures is a challenging task. The main coefficients in this context relate to added mass, damping and slamming effects. Formulations have been presented by various authors in literature for evaluating these coefficients for simple shapes. Some of them have found widespread application in the industry. The authors have considered a solid circular disk as a base case for initiating study on subsea module hydrodynamics. Experiments were conducted on an oscillating solid disk of diameter 200 mm and thickness 2 mm near the free surface. Forced oscillations were conducted at amplitudes varying from 3mm–36mm and frequencies 0.9–1.5 Hz respectively. The forces on the disk were measured using a submersible high-sensitivity load cell. The motions of the disk were restricted to axial (heave) direction, and were measured with a displacement transducer. The measured forces and displacement were analyzed using a Fast Fourier Transform algorithm to separate the added mass and damping effects. From the rate of change of added mass with depth of submergence, slamming forces were identified. The measured coefficients were compared with similar published data by Vu et al [1] and Tao & Dray [2]. The paper presents various formulations for added mass, damping and slamming obtained from literature and currently in use in the industry. These formulations are compared with measured values of the coefficients and suggestions are made on the importance of these formulations for flat subsea structures.

scholarly journals Wave Induced Effects on the Hydrodynamic Coefficients of an Oscillating Heave Plate in Offshore Wind Turbines

2020 ◽  
Vol 8 (8) ◽  
pp. 622
Author(s):  
Krish Thiagarajan ◽  
Javier Moreno
Keyword(s):  
Free Surface ◽  
Vertical Plane ◽  
Research Problem ◽  
Added Mass ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Hydrodynamic Coefficients ◽  
Offshore Wind Turbines ◽  
Turbine Design ◽  
Wave Induced

The research problem discussed in this paper is of relevance to floating offshore wind turbine design, where heave plates are attached to the columns of a semi-submersible in order to improve vertical plane stability and the power output. Because of the shallow draft of these structures, the heave plates are proximal to the water surface. When subject to vertical plane motions the flow around a plate is altered by the presence of the free surface, resulting in changes in added mass and damping forces. In this paper, we present the experimental results for the added mass and damping coefficients for circular heave plates attached to a column, when oscillating in heave in the presence of oncoming waves. The results tend to indicate that applying the hydrodynamic coefficients obtained from still water experiments for a structure moving in waves may only be an approximation. For different relative phases of the wave and the motion, large variations could occur. We define a modified Keulegan—Carpenter (KC) number that depends on the relative amplitude of motion with respect to the wave. With this definition, the added mass and damping values are seen to be closer to the still water trends. However, at lower KC values, the added mass coefficients could differ by 30%, which can affect natural frequency estimates. Thus, caution needs to be exerted in the selection of hydrodynamic coefficients for heave plates oscillating in proximity to the free surface.

Influence of Viscous Effects on the Hydrodynamics of Ship-Like Sections Undergoing Symmetric and Anti-Symmetric Motions, Using RANS

2008 ◽  
Author(s):  
A. Que´rard ◽  
P. Temarel ◽  
S. R. Turnock
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Systematic Approach ◽  
Added Mass ◽  
Experimental Measurements ◽  
Hydrodynamic Coefficients ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Numerical Predictions ◽  
Fluid Damping

The aim of this investigation is to assess the influence of viscous effects on the predicted hydrodynamic coefficients for a range of ship-like sections, such as rectangular, triangular, chine and bulbous. Hydrodynamic coefficients, of added mass or inertia and fluid damping, for two-dimensional sections harmonically heaving, swaying and rolling at the undisturbed free surface are obtained using the ANSYS-CFX11.0 RANS solver, for a range of frequencies of oscillation. All predictions are compared with available experimental measurements and other numerical predictions (potential flow and RANS). It is concluded from these comparisons that the proposed RANS approach can offer a better prediction for the hydrodynamic coefficients when viscous effects become significant, in particular for sway and roll motions. It is important that a reliable and systematic approach is adopted for the application of the unsteady free surface RANS methodology.

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