On the Motion of a Slender Body Submerged Beneath Surface Waves

1988 ◽  
Vol 32 (03) ◽  
pp. 208-219 ◽  
Author(s):  
P. Wilmott
Keyword(s):  
Velocity Potential ◽  
Axisymmetric Body ◽  
The Body ◽  
Body Motion ◽  
Vertical Force ◽  
Forward Speed ◽  
Body Velocity ◽  
Exciting Forces ◽  
Deep Fluid ◽  
The Mean

A slender axisymmetric body is submerged beneath a regular train of waves on an inviscid, incompressible, infinitely deep fluid. Using the method of matched asymptotic expansions, the velocity potential in the neighborhood of the body is calculated, thus determining the mean second-order vertical force when the body is permitted to respond to the exciting forces and moment but is otherwise moving with constant forward speed and depth beneath a head sea. To stablilize the body motion, the effects of a hydrofoil placed on the body axis are included. Several examples are computed showing the dependence of mean vertical force on body velocity.

scholarly journals Wave forces on three-dimensional floating bodies with small forward speed

1991 ◽  
Vol 227 ◽  
pp. 135-160 ◽  
Author(s):  
Jan Nossen ◽  
John Grue ◽  
Enok Palm
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Wave Forces ◽  
Forward Speed ◽  
Floating Bodies ◽  
Wave Drift ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Wave Drift Damping ◽  
The Mean

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.

Radiation and diffraction of water waves by a submerged sphere at forward speed

1988 ◽  
Vol 417 (1853) ◽  
pp. 433-461 ◽  
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Surface Condition ◽  
Wave Resistance ◽  
The Body ◽  
Legendre Functions ◽  
Forward Speed ◽  
Submerged Sphere ◽  
Exciting Forces ◽  
Similar Equation

A submerged sphere advancing in regular deep-water waves at constant forward speed is analysed by linearized potential theory. A distribution of sources over the surface of the sphere is expanded into a series of Legendre functions, by extension of the method used by Farell ( J . Ship Res . 17, 1 (1973)) in analysing the wave resistance on a submerged spheroid. The equations governing the velocity potential are satisfied by use of the appropriate Green function and by choosing the coefficients in the series of Legendre functions such that the body surface condition is satisfied. Numerical results are obtained for the wave resistance, hydrodynamic coefficients and exciting forces on the sphere. Some theoretical aspects of a body advancing in waves are also discussed. The far-field equation of Newman ( J . Ship Res . 5, 44 (1961)) for calculation of the damping coefficients is extended, and a similar equation for the exciting forces is derived.

The Vertical Mean Force and Moment of Submerged Bodies Under Waves

1971 ◽  
Vol 15 (03) ◽  
pp. 231-245 ◽  
Author(s):  
C. M. Lee ◽  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Added Mass ◽  
Cross Sectional Area ◽  
The Body ◽  
Slender Body ◽  
Longitudinal Distribution ◽  
Vertical Force ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Mean

A neutrally buoyant slender body of arbitrary sectional form, submerged beneath a free surface, is free to respond to an incident plane progressive wave system. The fluid is assumed inviscid, incompressible, homogeneous and infinitely deep. The first-order oscillatory motion of the body and the second-order time-average vertical force and pitching moment acting on the body are obtained in terms of Kochin's function. By use of slender-body theory for a deeply submerged body, the final expressions for the mean force and the moment are shown to depend on the longitudinal distribution of sectional area and added mass and on the amplitude and the frequency of the ambient surface waves. The magnitude of the mean force for various simple geometric cylinders is compared with that of a circular cylinder of equal cross-sectional area. The mean force on a nonaxisymmetric body is often approximated by replacing the section with circular profiles of equivalent cross-sectional area. A better scheme of approximation is presented, based on a simple way of estimating the two-dimensional added mass. It is expected that the effect of the cross-sectional geometry on mean vertical force and moment will be more significant when the body is very close to the free surface.

Forward-Speed Vertical Wave Exciting Forces on Ships

1985 ◽  
Vol 29 (02) ◽  
pp. 105-111
Author(s):  
P. D. Sclavounos
Keyword(s):  
Velocity Potential ◽  
Reverse Flow ◽  
Diffraction Problem ◽  
Three Dimensional ◽  
Forward Speed ◽  
Direct Solution ◽  
Radiation Problem ◽  
Strip Theory ◽  
Exciting Forces ◽  
Wave Exciting Forces

Expressions are derived for the heave and pitch exciting force and moment on a ship advancing in waves. They are obtained in the form of an integral over the ship axis of the outer source strength of the reverse-flow radiation problem multiplied by the value of the incident-wave velocity potential. Their performance is tested for two slender spheroids. Comparisons are made with predictions obtained from a three-dimensional numerical solution at zero speed—the expression common to strip-theory programs which uses the ship hull as the integration surface—and the direct solution of the diffraction problem.

scholarly journals On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number

2017 ◽  
Vol 828 ◽  
pp. 395-423 ◽  
Author(s):  
M. Moriche ◽  
O. Flores ◽  
M. García-Villalba
Keyword(s):  
Aerodynamic Force ◽  
The Body ◽  
Body Motion ◽  
Fluid Inertia ◽  
Aerodynamic Forces ◽  
Noticeable Improvement ◽  
Large Amplitude Motions ◽  
Flow Circulation ◽  
The Mean ◽  
Force Decomposition

The influence that the kinematics of pitching and heaving 2D airfoils has on the aerodynamic forces is investigated using direct numerical simulations and a force decomposition algorithm. Large-amplitude motions are considered (of the order of one chord), with moderate Reynolds numbers and reduced frequencies of order $O(1)$, varying the mean pitch angle and the phase shift between the pitching and heaving motions. Our results show that the surface vorticity contribution (viscous effect) to the aerodynamic force is negligible compared with the contributions from the body motion (fluid inertia) and the vorticity within the flow (circulation). For the range of parameters considered here, the latter tends to be instantaneously oriented in the direction normal to the chord of the airfoil. Based on the results discussed in this paper, a reduced-order model for the instantaneous aerodynamic force is proposed, taking advantage of the force decomposition and the chord-normal orientation of the contribution from vorticity within the flow to the total aerodynamic force. The predictions of the proposed model are compared with those of a similar model from the literature, showing a noticeable improvement in the prediction of the mean thrust, and a smaller improvement in the prediction of the mean lift and the instantaneous force coefficients.

A Velocity Metric for Rigid-Body Planar Motion

2010 ◽  
Author(s):  
Joseph M. Schimmels ◽  
Luis E. Criales
Keyword(s):  
Rigid Body ◽  
Average Distance ◽  
The Body ◽  
Body Motion ◽  
Length Scale ◽  
Translational Velocity ◽  
Body Velocity ◽  
Assembly Problem ◽  
Instantaneous Center ◽  
Selection Of

A planar rigid-body velocity metric based on the instantaneous velocity of all particles that constitute a rigid body is developed. A measure based on the discrepancy in the translational velocity at each particle for two different planar twists is introduced. The calculation of the measure is simplified to the calculation of the product of: 1) the discrepancy in angular velocity, and 2) the average distance of the body from the instantaneous center associated with the twist discrepancy. It is shown that this measure satisfies the mathematical requirements of a metric and is physically consistent. It does not depend on either the selection of length scale or the frames used to describe the body motion. Although the metric does depend on body geometry, it can be calculated efficiently using body decomposition. An example demonstrating the application of the metric to an assembly problem is presented.

A Linear Algebra Approach to the Analysis of Rigid Body Velocity From Position and Velocity Data

1983 ◽  
Vol 105 (2) ◽  
pp. 92-95 ◽  
Author(s):  
A. J. Laub ◽  
G. R. Shiflett
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Matrix Theory ◽  
The Body ◽  
Instantaneous Velocity ◽  
Body Motion ◽  
Translational Velocity ◽  
Velocity Data ◽  
Algebra Approach ◽  
Body Velocity

The instantaneous velocity of a rigid body in space is characterized by an angular and translational velocity. By representing the angular velocity as a matrix and the translational component as a vector the velocity of any point in the rigid body may be found if the position of the point and the parameters of the angular and translational velocities are known. Alternatively, the parameters of the rigid body velocity may be determined if the velocity and position of three points fixed in the body are known. In this paper, a new matrix-theory-based method is derived for determining the instantaneous velocity parameters of rigid body motion in terms of the velocity and position of three noncollinear points fixed in the body. The method is shown to possess certain advantages over traditional vectoral solutions to the same problem.

scholarly journals Theoretical modeling of hydrodynamic characteristics of a compound column-plate structure based on a novel derivation of mean drift force formulation

2018 ◽  
Vol 233 (4) ◽  
pp. 1022-1036 ◽  
Author(s):  
Peiwen Cong ◽  
Yingyi Liu ◽  
Ying Gou ◽  
Bin Teng
Keyword(s):  
Theoretical Model ◽  
Velocity Potential ◽  
Wave Force ◽  
The Body ◽  
Hydrodynamic Characteristics ◽  
Linear Potential ◽  
Wave Runup ◽  
Plate Structure ◽  
The Mean ◽  
Drift Force

To improve the seakeeping capability, some devices, such as submerged plates, are often installed on floating structures. The attached plate can not only suppress the motion response but also provide an additional immersed body surface that receives fluid action, aggravating the wave loads. In this study, a theoretical model is developed within the context of linear potential theory to study the hydrodynamic characteristics of a floating column with a submerged plate attached at the bottom. The eigenfunction expansion matching method is applied to obtain the velocity potential, based on which the linear wave force and wave runup can be found immediately. A novel derivation of the mean drift force formulation is developed via the application of Green’s second identity to the velocity potential and its derivative in finite fluid volume surrounding the body. Mean drift force formulation that involves control surfaces is then obtained. With the availability of the velocity potential, semi-analytical solution of the mean drift force on the compound column-plate structure is developed based on, respectively, the derived and the classic far-field formulations. After conducting convergence tests and validating the theoretical model, detailed numerical analysis is performed thereafter based on the theoretical model. The influence of the plate size, such as the radius and height, on the wave force and the associated wave runup is assessed.

The Coupled Damping Coefficients of a Symmetric Ship

1963 ◽  
Vol 6 (01) ◽  
pp. 1-7
Author(s):  
R. Timman ◽  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
Surface Condition ◽  
The Body ◽  
Forward Speed ◽  
Small Oscillations ◽  
Damping Coefficients ◽  
Submerged Body ◽  
Symmetry Properties ◽  
Transverse Symmetry ◽  
Oscillatory Velocity

A study is made of a floating or submerged body with longitudinal and transverse symmetry, which is moving with constant forward speed and performing small oscillations. The analysis is quite general in the sense that the shape of the body and the nature of the oscillations are unspecified, but it is assumed that the linearized free-surface condition holds. With this assumption the oscillatory velocity potential is found in terms of an unknown Green's function, the existence of which is also assumed. This potential is then used to show the symmetry properties of the cross-coupling damping coefficients.

Simulation of water entry of a wedge through free fall in three degrees of freedom

2010 ◽  
Vol 466 (2120) ◽  
pp. 2219-2239 ◽  
Author(s):  
G. D. Xu ◽  
W. Y. Duan ◽  
G. X. Wu
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Free Fall ◽  
Water Entry ◽  
Auxiliary Function ◽  
The Body ◽  
Body Motion ◽  
Time Stepping ◽  
The Impact ◽  
Three Degrees Of Freedom

The water entry problem of a wedge through free fall in three degrees of freedom is studied through the velocity potential theory for the incompressible liquid. In particular, the effect of the body rotation is taken into account, which seems to have been neglected so far. The problem is solved in a stretched coordinate system through a boundary element method for the complex potential. The impact process is simulated based on the time stepping method. Auxiliary function method has been used to decouple the mutual dependence between the body motion and the fluid flow. The developed method is verified through results from other simulation and experimental data for some simplified cases. The method is then used to undertake extensive investigation for the free fall problems in three degrees of freedom.

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