Large-Amplitude Transient Motion of Two-Dimensional Floating Bodies

1979 ◽  
Vol 23 (01) ◽  
pp. 20-31
Author(s):  
R. B. Chapman
Keyword(s):  
Boundary Condition ◽  
Wave Field ◽  
Large Amplitude ◽  
The Body ◽  
Body Motion ◽  
Source Distribution ◽  
Floating Body ◽  
Two Dimensional ◽  
Body Boundary ◽  
Free Mode

A numerical method is presented for solving the transient two-dimensional flow induced by the motion of a floating body. The free-surface equations are linearized, but an exact body boundary condition permits large-amplitude motion of the body. The flow is divided into two parts: the wave field and the impulsive flow required to satisfy the instantaneous body boundary condition. The wave field is represented by a finite sum of harmonics. A nonuniform spacing of the harmonic components gives an efficient representation over specified time and space intervals. The body is represented by a source distribution over the portion of its surface under the static waterline. Two modes of body motion are discussed—a captive mode and a free mode. In the former case, the body motion is specified, and in the latter, it is calculated from the initial conditions and the inertial properties of the body. Two examples are given—water entry of a wedge in the captive mode and motion of a perturbed floating body in the free mode.

The energy distribution resulting from an impact on a floating body

2000 ◽  
Vol 417 ◽  
pp. 157-181 ◽  
Author(s):  
A. A. KOROBKIN ◽  
D. H. PEREGRINE
Keyword(s):  
Kinetic Energy ◽  
Energy Distribution ◽  
Water Flow ◽  
Compression Wave ◽  
The Body ◽  
The Other ◽  
Body Motion ◽  
Floating Body ◽  
Pressure Impulse ◽  
Work Done

The initial stage of the water flow caused by an impact on a floating body is considered. The vertical velocity of the body is prescribed and kept constant after a short acceleration stage. The present study demonstrates that impact on a floating and non-flared body gives acoustic effects that are localized in time behind the front of the compression wave generated at the moment of impact and are of major significance for explaining the energy distribution throughout the water, but their contribution to the flow pattern near the body decays with time. We analyse the dependence on the body acceleration of both the water flow and the energy distribution – temporal and spatial. Calculations are performed for a half-submerged sphere within the framework of the acoustic approximation. It is shown that the pressure impulse and the total impulse of the flow are independent of the history of the body motion and are readily found from pressure-impulse theory. On the other hand, the work done to oppose the pressure force, the internal energy of the water and its kinetic energy are essentially dependent on details of the body motion during the acceleration stage. The main parameter is the ratio of the time scale for the acoustic effects and the duration of the acceleration stage. When this parameter is small the work done to accelerate the body is minimal and is spent mostly on the kinetic energy of the flow. When the sphere is impulsively started to a constant velocity (the parameter is infinitely large), the work takes its maximum value: Longhorn (1952) discovered that half of this work goes to the kinetic energy of the flow near the body and the other half is taken away with the compression wave. However, the work required to accelerate the body decreases rapidly as the duration of the acceleration stage increases. The optimal acceleration of the sphere, which minimizes the acoustic energy, is determined for a given duration of the acceleration stage. Roughly speaking, the optimal acceleration is a combination of both sudden changes of the sphere velocity and uniform acceleration.If only the initial velocity of the body is prescribed and it then moves freely under the influence of the pressure, the fraction of the energy lost in acoustic waves depends only on the ratio of the body's mass to the mass of water displaced by the hemisphere.

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.

A multimodal method for liquid sloshing in a two-dimensional circular tank

2010 ◽  
Vol 665 ◽  
pp. 457-479 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Form ◽  
The Body ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Natural Modes ◽  
Body Boundary ◽  
Multimodal Method

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

Second-Order Diffraction and Radiation of a Floating Body With Small Forward Speed

2010 ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Boundary Condition ◽  
Coordinate System ◽  
Traditional Method ◽  
Higher Order ◽  
Second Order ◽  
The Body ◽  
New Method ◽  
Forward Speed ◽  
Inertial Coordinate System ◽  
Body Boundary

The formulation of the second-order wave-current-body problem in the inertial coordinate system involves higher-order derivatives in the body boundary condition. A new method taking advantage of the body-fixed coordinate system in the near field is presented to avoid the calculation of higher-order derivatives in the body boundary condition. The new method has advantage over the traditional method when the body surface is with sharp corner or high curvature. The nonlinear wave diffraction and forced oscillation of floating bodies are studied up to second order in wave slope. A small forward speed is taken into account. The results of the new method are compared with that of the traditional method based on a formulation in the inertial coordinate system. When the traditional method applies, good agreement has been obtained.

scholarly journals Numerical Simulation of Fully Nonlinear Interaction Between Regular and Irregular Waves and a 2D Floating Body

2019 ◽  
Author(s):  
Haoran Li ◽  
Erin E. Bachynski
Keyword(s):  
Numerical Results ◽  
The Body ◽  
Body Motion ◽  
Irregular Waves ◽  
Floating Body ◽  
Computational Time ◽  
Wave Loads ◽  
Nonlinear Loads ◽  
Fully Nonlinear ◽  
Irregular Wave

Abstract A fully nonlinear Navier-Stokes/VOF numerical wave tank, developed within the open-source CFD toolbox OpenFOAM, is used to investigate the response of a moored 2D floating body to nonlinear wave loads. The waveDyMFoam solver, developed by extending the interDyMFoam solver of the OpenFOAM library with the waves2Foam package, is applied. Furthermore, a simple linear spring is implemented to constrain the body motion. An efficient domain decomposition strategy is applied to reduce the computational time of irregular wave cases. The numerical results are compared against the results from potential flow theory. Numerical results highlight the coupling between surge and pitch motion and the presence of nonlinear loads and responses. Some minor numerical disturbance occurs when the maximum body motion response is achieved.

A Localized Finite-Element Method for Two-Dimensional Steady Potential Flows with a Free Surface

1978 ◽  
Vol 22 (04) ◽  
pp. 216-230
Author(s):  
Kwang June Bai
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Complex Geometry ◽  
The Body ◽  
Finite Domain ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Test Functions ◽  
Infinite Domain

A numerical method is presented for solving two-dimensional uniform flow problems with a linearized free-surface boundary condition. The boundary-value problem governed by Laplace's equation is replaced by a weak formulation (also known as Galerkin's method) with certain essential boundary conditions. The infinite domain of the fluid is reduced to a finite domain by utilizing known solution spaces in certain subdomains. The bases for the trial and test functions are chosen from the same subspace of the polynomial function space in the reduced subdomain. The essential boundary conditions are properly taken into account by an unconventional choice of the basis for the trial functions, which is different from that for the test functions in other subdomains. This method is applied to two-dimensional steady flow past a submerged elliptic section, a hydrofoil at an arbitrary angle of attack, and a bump on the bottom. In each example the body boundary condition is satisfied exactly. Both subcritical and supercritical flows are treated. We present the numerical results of wave resistance, lift force, moment, circulation strength, and flow blockage parameter. The computed pressure distributions on the hydrofoil and wave profiles are shown. The test results obtained by the present method agree very well with existing results. The main advantage of this method is that any complex geometry of the boundary can be easily accommodated.

Hydrodynamic Forces on a Submerged Sphere Undergoing Large Amplitude Motion

1994 ◽  
Vol 38 (04) ◽  
pp. 272-277
Author(s):  
G. X. Wu
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Large Amplitude ◽  
Multipole Expansion ◽  
The Body ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Submerged Sphere ◽  
Instantaneous Position ◽  
Surface Boundary Condition

The hydrodynamic problem of a sphere submerged below a free surface and undergoing large amplitude oscillation is investigated based on the velocity potential theory. The body surface boundary condition is satisfied on its instantaneous position while the free-surface boundary condition is linearized. The solution is obtained by writing the potential in terms of the multipole expansion.

Instantaneous Center of Rotation in Pitch Response of a FPSO Submitted to Head Waves

2018 ◽  
Author(s):  
Daniel de Oliveira Costa ◽  
Antonio Carlos Fernandes ◽  
Joel Sena Sales Junior ◽  
Peyman Asgari
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Tracking System ◽  
The Body ◽  
Body Motion ◽  
Floating Body ◽  
Wave System ◽  
Center Of Rotation ◽  
Head Waves ◽  
Instantaneous Center

When under influence of an incident wave system, any floating body presents a general motion with all six degrees of freedom, unless it presents some kind of restrains on it. For a free moving body, the center of rotation will depend on the force distribution and might not coincide with its center of gravity. For long and slender floating structures, such as FPSO platforms, a small change in the center of Pitch rotation would result in significant change in the overall motions in its fore and aft regions. Therefore, it is of high importance to obtain a better understating of the instantaneous position of the body center of rotation in Heave and Pitch response. This paper investigates the position of the Instantaneous Center of Rotation in Pitch Response of a scaled down model of a FPSO platform under different regular wave conditions. The investigation uses basic kinematics equations for rigid body, defining the 6 degrees of freedom of the rigid body motion from a finite number of markers installed in the model. A high quality tracking system captures the markers positions in order to define the rigid body at each instant of time. For an initial approach, the study considers the response due to head waves seas with experimental validation.

Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body

1987 ◽  
Vol 31 (04) ◽  
pp. 227-234
Author(s):  
Lawrence J. Doctors ◽  
Robert F. Beck
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Body Condition ◽  
Numerical Experiments ◽  
Surface Condition ◽  
The Body ◽  
Convergence Properties ◽  
Submerged Body ◽  
Body Boundary ◽  
The Galerkin Method

The Neumann-Kelvin method for solving the flow past a body moving at a steady speed requires that the body boundary condition be satisfied exactly, while the free-surface condition is satisfied in a linearized sense. The solution is generally obtained by discretizing the body surface into panels, each of which has an unknown singularity strength. In the present work, two types of numerical experiments have been carried out. In the first approach, the body condition is satisfied at one point on each panel (the collocation method). In the second approach, the body condition is satisfied in an integrated sense on each panel (the Galerkin method). Improved convergence properties are demonstrated by the second approach.

On the Wave Resistance of a Submerged Spheroid

1973 ◽  
Vol 17 (01) ◽  
pp. 1-11
Author(s):  
César Farell
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Wave Resistance ◽  
The Body ◽  
Spheroidal Harmonics ◽  
Survey Technique ◽  
Body Boundary ◽  
Significant Comparison ◽  
The Difference ◽  
Infinite Set

A solution to the problem of potential flow about a submerged prelate spheroid in axial horizontal motion beneath a free surface has been derived within the theory of infinitesimal waves, satisfying exactly the body boundary condition, and the wave resistance of the spheroid has been evaluated. The solution is in the form of a distribution of sources on the surface of the spheroid; the analysis yields an infinite set of equations for determining the coefficients of the expansion of the potential of the distribution in spheroidal harmonics. The difference between the present results for the wave resistance and those given by Havelock's approximation is found to be rather significant. Comparison with experimental wave resistance measurements obtained using the wake-survey technique shows agreement for Froude numbers between 0.35 and 0.40.

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