Theoretical Solution for Concentrated Force on the Free Surface of a Coating Material. 2nd Report. Three Dimensional Solution for a Normal Force.

In this work, the spatial theoretical solutions of concentrated normal forces acting in the substrate and at the interface of semi-infinite coating materials have been deduced based on the image point method. The explicit solution is given in the series of the displacement functions corresponding to each image point. It is found that all displacement functions can be deduced by the order of the image point. Numerical analysis has been carried out to verify the theoretical deductions. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account. The fundamental solutions for a concentrated force acting at interface of two bonded semi-infinite bodies is also deduced, which is necessary in the analysis of coating materials by using these theoretical solution as the fundamental solution.

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The Diffraction of Free-Surface Waves by a Slender Ship

Journal of Ship Research ◽

10.5957/jsr.1984.28.1.29 ◽

1984 ◽

Vol 28 (01) ◽

pp. 29-47

Author(s):

P. D. Sclavounos

Keyword(s):

Free Surface ◽

Surface Waves ◽

Three Dimensional ◽

Practical Interest ◽

Prolate Spheroid ◽

Exciting Force ◽

Dimensional Solution ◽

Free Surface Waves ◽

Dimensional Approximation ◽

Inner Region

A linear theory is presented for the scattering of small-amplitude monochromatic and unidirectional free-surface waves by a ship fixed at its mean advancing position. In an inner region close to the ship the hull geometrical slenderness is used to justify a quasi-two-dimensional approximation of the flow. The method of matched asymptotic expansions is then introduced to enforce the compatibility of the inner solution with the three-dimensional solution in the far field. The theory is shown to be uniformly valid for all wavelengths of practical interest and all angles of wave incidence. In the short-wavelength limit, existing theories are recovered and the singularity that is present in the limit from oblique to head incidence is removed. Computations are included for the pressure and the sectional exciting force distributions, the wave elevation, and the vertical exciting force and moment in head and bow waves on a prolate spheroid.

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An Approximate Three-Dimensional Solution for Melting or Freezing Around a Buried Pipe Beneath a Free Surface

Journal of Heat Transfer ◽

10.1115/1.3247031 ◽

1986 ◽

Vol 108 (4) ◽

pp. 900-906 ◽

Cited By ~ 2

Author(s):

G.-P. Zhang ◽

S. Weinbaum ◽

L. M. Jiji

Keyword(s):

Approximate Solution ◽

Free Surface ◽

Phase Change ◽

Initial Conditions ◽

Three Dimensional ◽

Three Dimensions ◽

Computational Time ◽

Buried Pipe ◽

Dimensional Solution ◽

Pipe Surface

This paper presents a quasi-steady-state approximate solution for small Stefan number for the three-dimensional melting or freezing around a fluid-carrying pipe buried in a semi-infinite phase change medium (PCM). The two-dimensional quasi-steady approximate solution method, the virtual free surface technique [18], has been extended to three dimensions where axial thermal interaction between the moving fluid and the PCM is considered. Of particular interest in the motion of the phase change interface and the time variation of the axial temperature distribution in the fluid. Due to the singularities of the differential equations along the pipe surface, an axisymmetric analytic solution is provided for the region near the pipe wall. Solutions are presented for several representative dimensionless pipe burial depths and initial conditions. The computational time to predict the three-dimensional interface location up to 10 years is several minutes on an IBM 4341 computer.

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The Influence of a Free Surface on the Hydroelastic Stability of a Flat Panel

Journal of Applied Mechanics ◽

10.1115/1.3422668 ◽

1972 ◽

Vol 39 (1) ◽

pp. 53-58 ◽

Cited By ~ 4

Author(s):

D. S. Weaver ◽

T. E. Unny

Keyword(s):

Free Surface ◽

Three Dimensional ◽

Surface Displacement ◽

Two Dimensional ◽

Flat Panel ◽

Dimensional Solution ◽

Dimensional Approximation ◽

Free Surface Displacement

This paper examines the influence of a parallel free surface on the hydroelastic stability of a flat panel. A quasi-two-dimensional approximation is made for the free surface displacement and the results compared with the more general but cumbersome three-dimensional solution. This comparison shows that the former approach is quite reasonable as well as being considerably simpler and more instructive. It is found that the free surface has no effect for depth ratios greater than about one half and is stabilizing for smaller depth ratios.

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Three-dimensional theory on supercavitating hydrofoils near a free surface

Journal of Fluid Mechanics ◽

10.1017/s0022112075002613 ◽

1975 ◽

Vol 71 (2) ◽

pp. 339-359 ◽

Cited By ~ 12

Author(s):

Okitsugu Furuya

Keyword(s):

Free Surface ◽

Aspect Ratio ◽

Three Dimensional ◽

Leading Edge ◽

Reference Level ◽

Two Dimensional ◽

Large Aspect Ratio ◽

Dimensional Solution ◽

Aspect Ratios ◽

Lifting Line

Supercavitating hydrofoils of large aspect ratio operating near a free surface are investigated, assuming an inviscid and irrotational flow with the effects of gravity and surface tension neglected. The flow near the foil, treated as two-dimensional, is solved by a nonlinear free-streamline theory, then a three-dimensional ‘downwash’ correction is made using Prandtl's lifting-line theory. The strength of the lifting-line vortex is determined by information from the two-dimensional solution through a matching procedure, in which the inverse of aspect ratio is used as a small parameter for asymptotic expansions. The analysis incorporates a free-surface reference level to determine the submergence depth of the foil. The present method can be applied to any type of foil having an arbitrary planform or profile shape, including a rounded leading edge, a twist and even a small dihedral angle, within the assumption of large aspect ratio. Numerical computations made on rectangular flat-plate hydrofoils show excellent agreement of results with existing experimental data, even for large angles of attack and relatively low aspect ratios. The pressure distributions, shapes of the cavity and free surface are also calculated as a function of spanwise position.

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Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

Polish Maritime Research ◽

10.2478/pomr-2020-0003 ◽

2020 ◽

Vol 27 (1) ◽

pp. 29-38

Author(s):

Teng Zhang ◽

Junsheng Ren ◽

Lu Liu

Keyword(s):

Free Surface ◽

Incident Wave ◽

Time Domain ◽

Three Dimensional ◽

Adaptive Mesh ◽

Wave Profile ◽

Time Domain Method ◽

Ship Motions ◽

Quad Tree ◽

Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

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