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.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

Finite-difference simulation of nonlinear ship waves

1985 ◽  
Vol 157 ◽  
pp. 327-357 ◽  
Author(s):  
Hideaki Miyata ◽  
Shinichi Nishimura
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Surface Condition ◽  
Vertical Direction ◽  
Cell System ◽  
The Body ◽  
Rectangular Cell ◽  
Ship Waves ◽  
Body Boundary ◽  
Hull Forms

A finite-difference solution method for nonlinear wave generation in the near field of ships of arbitrary three-dimensional configuration is developed. Momentum equations of finite-difference form in a fixed rectangular cell system are solved by a time-marching scheme. The exact inviscid free-surface condition is approximately satisfied at the actual location of the free surface, and the free-slip body boundary condition is implemented by use of approximation of the body configuration and a special pressure computation in body boundary cells. The degree of accuracy is raised by employing a variable-mesh system in the vertical direction. Computed results are presented for three hull forms: a mathematical and two practical hull forms. Agreement with experiment seems to be fairly good. In particular, the computed wave profiles and contour maps of bow waves show excellent resemblance to the measured ones, having some typical characteristics of nonlinear ship waves.

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.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

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.

Towards Fully Non-Linear Floating Body Simulations by a Potential Method

2012 ◽  
Author(s):  
Heinrich Söding
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Computing Time ◽  
Potential Method ◽  
The Body ◽  
Floating Body ◽  
Rankine Source ◽  
Exact Boundary ◽  
Approximate Wave ◽  
Steep Waves

A 3-dimensional Rankine source panel method for simulating a rigid floating body in steep waves is being developed. The aim is to obtain the same quality as free-surface RANSE methods, which are well suited for this application, but to require only a small fraction of the computing time needed by RANSE methods. The body may have forward speed or perform maneuvering motions. The exact boundary conditions are satisfied at the actual location of the fluid boundaries. The waves are generated not by a material wave maker, but by an approximate wave potential which needs not satisfy the exact free-surface condition. No wave damping regions are required. Whereas for steep waves without a body the method appears satisfactory, it needs further improvements if a body is present.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

On the solution near the critical frequency for an oscillating and translating body in or near a free surface

1993 ◽  
Vol 254 ◽  
pp. 251-266 ◽  
Author(s):  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Free Surface ◽  
Closed Form Solution ◽  
Geometric Interpretation ◽  
Form Solution ◽  
The Body ◽  
Geometric Condition ◽  
Sufficient Condition ◽  
Gravitational Acceleration ◽  
Submerged Body ◽  
Necessary And Sufficient

We consider a floating or submerged body in deep water translating parallel to the undisturbed free surface with a steady velocity U while undergoing small oscillations at frequency ω. It is known that for a single source, the solution becomes singular at the resonant frequency given by τ ≡ Uω/g=¼, where g is the gravitational acceleration. In this paper, we show that for a general body, a finite solution exists as τ → ¼ if and only if a certain geometric condition (which depends only on the frequency ω but not on U) is satisfied. For a submerged body, a necessary and sufficient condition is that the body must have non-zero volume. For a surface-piercing body, a sufficient condition is derived which has a geometric interpretation similar to that of John (1950). As an illustration, we provide an analytic (closed-form) solution for the case of a submerged circular cylinder oscillating near τ = ¼. Finally, we identify the underlying difficulties of existing approximate theories and numerical computations near τ = ¼, and offer a simple remedy for the latter.

scholarly journals The Prediction of Hull Gesture and Flow Around Ship Based on Taylor Expansion Boundary Element Method

2019 ◽  
Vol 26 (2) ◽  
pp. 198-211
Author(s):  
Jiaye Gong ◽  
Yunbo Li
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Element Method ◽  
Flow Field ◽  
Boundary Element ◽  
Taylor Expansion ◽  
Surface Condition ◽  
Control Point ◽  
Surface Boundary ◽  
Element Method

Abstract Based on the potential flow theory and traditional boundary element method (BEM), Taylor expansion boundary element method (TEBEM) is introduced in this paper for the prediction of the flow field around ship, as a result, hull gesture and pressure distribution on hull surface are obtained. By this method, dipole strength of every field point is expanded in Taylor expansion, so that approximately continuous hull and free surface boundary condition could be achieved. To close the new equation system, the boundary condition of tangent velocity in every control point is introduced. With the simultaneous solving of hull boundary condition and free surface condition, the disturbance velocity potential could be obtained. The present method is used to predict the flow field and hull gesture of Wigley parabolic hull, Series 60 and KVLCC2 models. To validate the numerical model for full form ship, the wave profile, the computed hull gesture and hull surface pressure of KVLCC2 model are compared with experimental results.

On the Experimental Determination of the Resistance Components of a Submerged Spheroid

1973 ◽  
Vol 17 (02) ◽  
pp. 72-79
Author(s):  
César Farell ◽  
Oktay Güven
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Surface Wind ◽  
Rigid Wall ◽  
The Body ◽  
Viscous Drag ◽  
Viscous Resistance ◽  
Surface Boundary ◽  
Total Resistance ◽  
Viscous Effects

Towing-tank measurements of the viscous resistance of a spheroid model by means of wake surveys together with total resistance measurements show that the proximity of the free surface greatly influences the viscous resistance, which becomes much larger than the deep-submergence resistance as the spheroid approaches the free surface. Wind tunnel measurements reveal a similar effect of a rigid wall on the viscous drag of a body. The values of the wave resistance obtained as the difference between the measured values of total resistance and viscous resistance are found to be in agreement, for the range of Froude numbers investigated, with the analytical results obtained neglecting viscous effects and linearizing the free-surface boundary condition, but satisfying exactly the boundary condition on the surface of the body.

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