Added Mass and Damping of Rectangular Bodies Close to the Free Surface

1984 ◽  
Vol 28 (04) ◽  
pp. 219-225
Author(s):  
John Nicholas Newman ◽  
Bjørn Sortland ◽  
Tor Vinje
Keyword(s):  
Hydrodynamic Force ◽  
Standing Waves ◽  
Present Theory ◽  
Added Mass ◽  
The Body ◽  
Simple Explanation ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Calm Water ◽  
Heave Motion

A submerged two-dimensional rectangle in calm water with infinite depth is studied. The rectangle is oscillating in a heave motion. Negative added mass and sharp peaks in the damping and added-mass coefficients have been found when the submergence is small and the width of the shallow region on top of the rectangle is large. Resonant standing waves will occur in this area. A linear theory is developed to provide a relatively simple explanation of the occurrence of negative added mass for submerged bodies. The vertical hydrodynamic force is associated only with the flow in the shallow region, and the resulting pressure which acts on the top face of the rectangle. The results from this theory are compared with numerical results from the Frank method. The importance of the interaction effect between the top and the bottom of the body, which is neglected in the present theory, is discussed.

scholarly journals The Exciting Forces on Fixed Bodies in Waves

1962 ◽  
Vol 6 (04) ◽  
pp. 10-17 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Wave Amplitude ◽  
Amplitude Ratio ◽  
Exciting Force ◽  
The Body ◽  
Forced Oscillations ◽  
Wave Number ◽  
Far Field ◽  
Two Dimensional ◽  
Calm Water ◽  
Exciting Forces

General expressions, originally given by Haskind, are derived for the exciting forces on an arbitrary fixed body in waves. These give the exciting forces and moments in terms of the far-field velocity potentials for forced oscillations in calm water and do not depend on the diffraction potential, or the disturbance of the incident wave by the body. These expressions are then used to compute the exciting forces on a submerged ellipsoid, and on floating two-dimensional ellipses. For the ellipsoid, the problem is solved using the far-field potentials, and detailed results and calculations are given for the roll moment. The other forces agree, for the special case of a spheroid, with earlier results obtained by Havelock. In the case of two-dimensional motion the exciting forces are related to the wave amplitude ratio A for forced oscillations in calm water, and this relation is used to compute the heave exciting force for several elliptic cylinders. Expressions are also given relating the damping coefficients and the exciting forces. A = wave amplitude A = wave-height ratio for forced oscillations(a1 a2 a3) = semi-axis of ellipsoidBij = damping coefficientsC4 = nondimensional roll exciting-force coefficientDj = virtual-mass coefficients, defined by equations (18) and (19)g = gravitational accelerationh = depth of submergencei = √ — 1j = index referring to direction of force or motionn(z) = spherical Bessel function, K = wave number, K = ω2/gPj = functions defined following equation (17)R = polar coordinateV, = velocity components (x, y, z) = Cartesian coordinatesαi = Green's integrals, defined by equation (20)β = angle of incidence of wave systemθ = polar coordinateρ= fluid densityφj = velocity potentialsω = circular frequency of encounter

scholarly journals Generalized two-dimensional Lagally theorem with free vortices and its application to fluid–body interaction problems

2012 ◽  
Vol 698 ◽  
pp. 73-92 ◽  
Author(s):  
C. T. Wu ◽  
F.-L. Yang ◽  
D. L. Young
Keyword(s):  
Hydrodynamic Force ◽  
Density Ratio ◽  
Vortex Pair ◽  
The Body ◽  
Body Motion ◽  
Liquid Density ◽  
Two Dimensional ◽  
Fixed Target ◽  
Two Dimensional Flow ◽  
Neutrally Buoyant

AbstractThe Lagally theorem describes the unsteady hydrodynamic force on a rigid body exhibiting arbitrary motion in an inviscid and incompressible fluid by the properties of the singularities employed to generate the flow and the body motion and to meet the boundary condition. So far, only sources and dipoles have been considered, and the present work extends the theorem to include free vortices in a two-dimensional flow. The present extension is validated by reproducing the system dynamics or the force evolution of three literature problems: (i) a free cylinder interacting with a free vortex; (ii) the moving Föppl problem; and (iii) a cylinder in constant normal approach to a fixed identical cylinder. This work further extends the bifurcation analysis on the moving Föppl problem by including the solid-to-liquid density ratio as a new parameter, in addition to the system total impulse and the vortex strength. We then apply the theorem to the problem where a moving Föppl system is made to approach a fixed or a free neutrally buoyant target cylinder of identical size from far away. The force developed on each cylinder is examined with respect to the vortex pair configuration and the target mobility. When approaching a fixed target, a greater force is developed if the vortex pair has stronger circulation and larger structure. The mobility of the target cylinder, however, can modify the hydrodynamic force by reducing its magnitude and reversing the force ordering with respect to the vortex pair configuration found for the case with fixed target. Possible mechanisms for such a change of force nature are given based on the currently derived equation of motion.

scholarly journals A Semi-Analytical Method for Calculating the Hydrodynamic Force on Perforated Plates in Oscillating Flow

2019 ◽  
Author(s):  
Fredrik Mentzoni ◽  
Trygve Kristiansen
Keyword(s):  
Analytical Method ◽  
Hydrodynamic Force ◽  
Added Mass ◽  
Navier Stokes ◽  
Oscillating Flow ◽  
Force Model ◽  
Hydrodynamic Coefficients ◽  
Two Dimensional ◽  
Force Coefficient ◽  
Perforated Plates

Abstract A two-dimensional numerical analysis on the hydrodynamic force of perforated plates in oscillating flow is presented, and a new semi-analytical force model is proposed. Plates with ten different perforation ratios, τ, from 0.05 to 0.50 are simulated. The Keulegan–Carpenter numbers in the simulations cover a range from 0.002 to 2.2 when made nondimensional with the width of the plates. Resulting hydrodynamic added mass and damping coefficients are presented. All perforated plates with perforation ratios greater than or equal to 10% are found to be damping dominant. The numerical results are obtained using a two-dimensional Navier–Stokes solver (CFD), previously validated against dedicated 2D experiments on perforated plates. Furthermore, we present verification of the code against the analytical solid flat plate results by Graham. The presently obtained hydrodynamic coefficients are compared with the state-of-the-art semi-analytical method for force coefficient calculation of perforated plates by Molin, as well as the recommended practice for estimating hydrodynamic coefficients of perforated structures by DNV GL. Based on the CFD results, a new method for calculating the hydrodynamic force on perforated plates in oscillating flow is presented. The method is based on curve fitting the present CFD results for perforated plates, to the analytical expressions obtained for solid plates by Graham. In addition to its simplicity, a strength of the method is that coefficients for both the added mass and damping are obtained.

Sway Added-Mass Coefficients for Rectangular Profiles in Shallow Water

1971 ◽  
Vol 15 (04) ◽  
pp. 257-265 ◽  
Author(s):  
C. N. Flagg ◽  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Added Mass ◽  
Two Dimensional ◽  
Low Frequency Oscillations ◽  
Calm Water ◽  
Low Froude Number ◽  
Finite Water Depth ◽  
Rectangular Cylinders

This paper presents analytic and numerical results for the added-mass coefficients of two-dimensional rectangular cylinders, accelerating laterally in shallow water. The free surface is assumed rigid, corresponding to low-frequency oscillations in waves or low Froude number maneuvers in calm water. The effects of finite water depth are most significant for rectangles of large beam-draft ratio.

Two-dimensional subsonic and sonic flow past thin bodies

1957 ◽  
Vol 3 (1) ◽  
pp. 93-109 ◽  
Author(s):  
J. B. Helliwell ◽  
A. G. Mackie
Keyword(s):  
Complex Analysis ◽  
Free Stream ◽  
Present Theory ◽  
The Body ◽  
Sonic Velocity ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past ◽  
Sonic Flow

Hodograph methods are applied to determine the flow at high subsonic and sonic velocities past two-dimensional, thin, symmetrical bodies. The boundary value problem for the determination of the stream function Ψ, which in the present theory is a solution of Tricomi's equation, is simplified by the assumption of a free stream breakaway at sonic velocity from the shoulder of the body. A solution is obtained in terms of Bessel functions.In § 2 and 3 the flow past a wedge of small angle is discussed and expressions are obtained for the pressure on the nose, the drag coefficient and the width of the wake. A comparison with the corresponding results in the case of sonic velocity derived by the more complex analysis of Guderley & Yoshihara (1950) shows that the present simpler theory yields very similar values for the pressure over the nose.In § 4 the flow at sonic velocity past a profile which is a first-order perturbation upon a wedge profile is analysed on the basis of the same free streamline theory. The flow pattern is obtained past an arbitrarily specified body by an application of the Hankel inversion theorem and an expression is deduced for the drag.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

scholarly journals Spinning rough disc moving in a rarefied medium

2010 ◽  
Vol 466 (2119) ◽  
pp. 2033-2055 ◽  
Author(s):  
Alexander Plakhov ◽  
Tatiana Tchemisova ◽  
Paulo Gouveia
Keyword(s):  
The Body ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Optimal Mass Transport ◽  
Dense Gases ◽  
Magnus Effect ◽  
Inverse Effect ◽  
Transversal Force ◽  
The Moment ◽  
Complementary Mechanism

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

On the short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

A Hybrid Numerical Framework for Simulation of Ships Maneuvering in Waves

2021 ◽  
pp. 1-13
Author(s):  
Paul F. White ◽  
Dominic J. Piro ◽  
Bradford G. Knight ◽  
Kevin J. Maki
Keyword(s):  
Hydrodynamic Force ◽  
Linear Time ◽  
Domain Boundary ◽  
Critical Role ◽  
Force Model ◽  
Efficient Computation ◽  
Fast Running ◽  
Surface Ship ◽  
Calm Water ◽  
Maneuvering In Waves

The maneuvering characteristics of a surface ship play a critical role in the safety of navigation both in port and in an open seaway, and are vital to the overall operational ability of the ship. The vast majority of maneuvering analyses for ships have been performed under the assumption of calm water, yet ships mostly operate in waves. Understanding of maneuvering in waves is limited by the complexity of the problem and the challenges of performing physical experiments and numerical simulations. In this work, a new fast-running method that allows for the study of maneuvering in waves is formulated. The newly formulated approach is categorized as a “hybrid method,” taking its name from the multiple numerical methods and force models used to predict the total hydrodynamic force acting on the vessel maneuvering in waves. The framework presented here uses a combination of Computational Fluid Dynamics, a linear time-domain boundary element method, and a propeller-force model for efficient computation of the total hydrodynamic force.

FUNDAMENTAL ANALYSIS OF THREE-DIMENSIONAL ‘NEAR FLING’

1993 ◽  
Vol 183 (1) ◽  
pp. 217-248 ◽  
Author(s):  
S. Sunada ◽  
K. Kawachi ◽  
I. Watanabe ◽  
A. Azuma
Keyword(s):  
Numerical Calculation ◽  
Hydrodynamic Force ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Added Mass ◽  
Opening Angle ◽  
Rotation Axes ◽  
Adequate Accuracy ◽  
Series Of Experiments ◽  
The Moment

A series of experiments on three-dimensional ‘near fling’ was carried out. Two pairs of plates, rectangular and triangular, were selected, and the distance between the rotation axes of the two plates of each pair was varied. The motion of the plates as well as the forces and the moment were measured, and the interference between the two plates of a pair was studied. In addition, a method of numerical calculation was developed to aid in the understanding of the experimental results. The interference between the two plates of a pair, which acted to increase both the added mass of each plate and the hydrodynamic force due to dynamic pressure, was noted only when the opening angle between the plates was small. The hydrodynamic forces were strongly influenced by separated vortices that occurred during the rotation. A method of numerical calculation, which took into account the effect both of interference between the plates and of separated vortices, was developed to give adequate accuracy in analyzing beating wings in ‘near fling’.

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