The absorption of wave energy by a three-dimensional submerged duct

1981 ◽  
Vol 104 ◽  
pp. 189-215 ◽  
Author(s):  
J. R. Thomas
Keyword(s):  
Three Dimensional ◽  
Added Mass ◽  
Axisymmetric Body ◽  
The Body ◽  
Forced Oscillations ◽  
Radiation Problem ◽  
Absorption Length ◽  
Damping Coefficients ◽  
Sea Bed ◽  
Linear Spring

It has been shown (Evans 1976) that the power absorbed by a general, axisymmetric body depends solely upon the added-mass and damping coefficients. These coefficients are fundamental properties of the body, representing the component of the force on the body proportional to the acceleration and velocity of the body respectively in the radiation problem, where the body is forced to oscillate in the absence of incoming waves.In the present paper these coefficients are determined by solution of the radiation problem, for a mouth-upward cylindrical duct situated on the sea bed and fitted with a piston undergoing forced oscillations. The added-mass and damping coefficients are then used to study the power absorption properties of the duct when the power take-off is modelled by a linear-spring–dashpot system attached to the piston. Curves of the added mass, damping coefficients and absorption length (a measure of the power absorbed) as functions of wavenumber are presented, for different duct diameters and different depths of submergence.

On the Radiation and Diffraction of Surface Waves by Submerged Spheroids

1989 ◽  
Vol 33 (02) ◽  
pp. 84-92
Author(s):  
G. X. Wu ◽  
R. Eatock Taylor
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Added Mass ◽  
Wave Radiation ◽  
Legendre Functions ◽  
Incoming Wave ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients ◽  
Exciting Forces

The problem of wave radiation and diffraction by submerged spheroids is analyzed using linearized three-dimensional potential-flow theory. The solution is obtained by expanding the velocity potential into a series of Legendre functions in a spheroidal coordinate system. Tabulated and graphical results are provided for added mass and damping coefficients of various spheroids undergoing motions in six degrees of freedom. Graphs are also provided for exciting forces and moments corresponding to a range of incoming wave angles.

Radiation of waves by a cylinder submerged in water with ice floe or polynya

2015 ◽  
Vol 784 ◽  
pp. 373-395 ◽  
Author(s):  
Izolda V. Sturova
Keyword(s):  
Elastic Plate ◽  
Diffraction Problem ◽  
Open Water ◽  
Finite Depth ◽  
The Body ◽  
Elastic Plates ◽  
Radiation Problem ◽  
Radiation Load ◽  
Body Contour ◽  
Damping Coefficients

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

On the harmonic oscillations of a rigid body on a free surface

1965 ◽  
Vol 21 (3) ◽  
pp. 427-451 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Rigid Body ◽  
Potential Problem ◽  
Harmonic Oscillation ◽  
Added Mass ◽  
The Body ◽  
Rigorous Solution ◽  
Damping Coefficients

The present paper deals with the practical and rigorous solution of the potential problem associated with the harmonic oscillation of a rigid body on a free surface. The body is assumed to have the form of either an elliptical cylinder or an ellipsoid. The use of Green's function reduces the determination of the potential to the solution of an integral equation. The integral equation is solved numerically and the dependency of the hydrodynamic quantities such as added mass, added moment of inertia and damping coefficients of the rigid body on the frequency of the oscillation is established.

Computation of Added Mass and Damping Coefficients of a Horizontal Circular Cylinder in OpenFOAM

2016 ◽  
Author(s):  
Hao Chen ◽  
Erik Damgaard Christensen
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Numerical Computation ◽  
Added Mass ◽  
Forced Oscillations ◽  
Surface Zone ◽  
Computational Domain ◽  
Frequency Range ◽  
Two Phase ◽  
Damping Coefficients

This paper presents numerical computation of added mass and damping coefficients of a slender horizontal cylinder in the free surface zone, which typically serves as a fish cage floater. A fully viscous two phase flow solver in OpenFOAM was employed in the numerical computation. The purpose was to validate the capability of this solver and dynamic mesh functionality. A two dimensional numerical wave tank was set up, and two wave relaxation zones were used to reduce the size of the computational domain. Harmonic forced oscillations of the cylinder were performed at different frequencies and amplitudes. The mesh at free surface zone was refined based on the radiated wave heights at different oscillation frequencies in order to properly resolve the radiated waves. The result shows that in most frequency ranges, the numerical computation agreed well with the experimental data and analytical solution. However at low frequency range for added mass coefficient in heave motion, deviations were observed, and it was due to the effect of finite water depth. In addition for sway motion at high frequency range, the damping coefficient was underestimated comparing with analytical solution. This was believed to be as a result of high steepness of the radiated waves.

A New Slender-Ship Theory Valid for all Oscillatory Frequencies and Forward Speeds

2013 ◽  
Author(s):  
Masashi Kashiwagi ◽  
Xin Wang
Keyword(s):  
Green Function ◽  
Present Theory ◽  
Added Mass ◽  
Source Distribution ◽  
Unified Theory ◽  
Forward Speed ◽  
Radiation Problem ◽  
Damping Coefficients ◽  
Radiation Wave ◽  
The Green Function

A new theory is presented for the radiation problem of heave and pitch of a slender ship advancing at arbitrary forward speed. The theory has no restriction on the order of forward speed and oscillation frequency. The general inner solution is constructed by the source distribution with Green function over the ship’s hull surface plus a line distribution along the ship’s centerline on the free surface with the radiation-wave related residue part of the Green function. By matching the inner solution with the outer solution, the source strengths on both hull surface and line distribution can be obtained. Numerical results of the added-mass and damping coefficients based on the present theory are shown for two modified Wigley models and compared with the unified theory and experiment results.

scholarly journals Impulsive Motion Inside a Cylindrical Cavity

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 192
Author(s):  
Yuriy Savchenko ◽  
Georgiy Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Cylindrical Cavity ◽  
Experimental Studies ◽  
Added Mass ◽  
Axisymmetric Body ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Main Concern ◽  
Free Boundaries ◽  
Hodograph Method

Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface.

scholarly journals ON THE HYDRODYNAMIC FORCES OF TWIN-HULL VESSELS

1970 ◽  
Vol 1 (12) ◽  
pp. 103
Author(s):  
Shen Wang
Keyword(s):  
Oscillation Frequency ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Added Mass ◽  
Hydrodynamic Forces ◽  
Theory Approach ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Spacing Ratio ◽  
Strip Theory

The added mass and damping coefficients for semi- and fully submerged twin cylinders in vertical motion are determined as functions of the oscillation frequency, the cylinder spacing ratio, and the cylinder submergence ratio It has been found that resonance may occur in particular combinations of cylinder spacing and oscillation frequency at which the hydrodynamic mertial and damping characteristics deviate from the trend curves for the case of a single cylinder Justification of using the two-dimensional results to calculate motions of three dimensional twin-hull vessels is discussed It is suggested that, by means of strip theory approach, these results can be used to estimate the hydrodynamic forces for catamaran type vessels in pitch and heave motions.

A relation between the radiation and scattering of surface waves by axisymmetric bodies

1976 ◽  
Vol 76 (1) ◽  
pp. 85-88 ◽  
Author(s):  
A. M. J. Davis
Keyword(s):  
Plane Wave ◽  
Surface Waves ◽  
Axisymmetric Body ◽  
The Body ◽  
Forced Oscillations ◽  
Scattering Effect ◽  
Phase Angles ◽  
Axisymmetric Bodies

Results corresponding to those of Newman (1975) for wholly or partially immersed cylinders are obtained, namely relations between the phase angles of the cylindrical outgoing surface waves generated either by the forced oscillations of an immersed axisymmetric body or by the scattering effect of the body on a plane wave.

scholarly journals Low-dimensional dynamics of a turbulent axisymmetric wake

2014 ◽  
Vol 755 ◽  
Author(s):  
G. Rigas ◽  
A. R. Oxlade ◽  
A. S. Morgans ◽  
J. F. Morrison
Keyword(s):  
Vortex Shedding ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Turbulent Wake ◽  
Axisymmetric Body ◽  
The Body ◽  
Slow Rotation ◽  
Mean Pressure ◽  
Low Dimensional

AbstractThe coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$. Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$. In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

scholarly journals Extensions of d'Alembert's paradox for elongated bodies

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150106
Author(s):  
Philippe R. Spalart
Keyword(s):  
Cross Section ◽  
Unit Length ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Added Mass ◽  
The Body ◽  
Pitching Moment ◽  
Constant Cross Section ◽  
Slender Body Theory ◽  
The Cross

The steady incompressible irrotational flow past a three-dimensional body of any shape generates no forces. The historic paradox refers only to drag, but lift is also zero, which has been known but not emphasized. The new material concerns a body with a long constant cross section, such as a train. The final results for forces and moments are very simple. With zero angle of attack, we show that the force vectors on the front and rear parts of the body are each (asymptotically) equal to zero, if the pressure is referred to the freestream pressure. The lift and drag coefficients, based on frontal area, vanish proportionally to d / l and ( d / l ) 2 , respectively, where d / l is the diameter-to-length ratio. This applies to any shape of the cross section, and of the ends. With an angle of attack, the nose and tail forces are non-zero but depend only on the angle of attack and the cross section's added mass per unit length. The pitching moment is proportional to the total added mass and the sine of twice the angle of attack. The present results clarify slender-body theory results. The practical consequence is that, for a long body with constant cross section, the shape of the nose or the tail is irrelevant to its own ‘partial’ drag and lift, and to the pitching moment.

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