Neumann Kelvin Research Articles

Seakeeping computations using double-body basis flows

Three-dimensional, time-domain, ship–wave interactions are studied in this paper for problems with forward speed. Free surface boundary conditions are derived based on a double-body linearization and the mixed Euler–Lagrange time stepping technique. The boundary integral equations are solved at each time step by distributing desingularized sources above the calm water surface and employing constant-strength panels on the body surface. Radiation, diffraction, and free motion results for a Wigley hull and a Series 60 hull are presented and systematically compared with the experiments and other numerical solutions using the Neumann–Kelvin approach with simplified m -terms, linearized free surface boundary conditions with double-body m -terms, and the time-domain body-exact strip theory. By comparing the present results to experiments and other numerical solutions, it is found that the present computational model using double-body linearization gives improved results. It is also demonstrated that the m -terms are very important to obtain accurate hydrodynamic coefficients, while the leading-order terms included in the free surface boundary conditions of the present model can also improve the computational accuracy of the cross-coupling radiation damping.

ON SOME THEORETICAL AND NUMERICAL ASPECTS OF THE NEUMANN–KELVIN MODEL WITH CAPILLARITY IN HYDRODYNAMICS

A discussion and an improvement of the Neumann–Kelvin's model are suggested in this paper. This model is used in the simulation of progressive wave phenomenon. As mentioned by several authors ([7, 19, 23, 29]), this model is ill posed unless a capillary energy is introduced. The mathematical explanation is that a compactness inversions' property occurs if the capillary forces are omitted. Theoretical arguments and numerical simulations are used in the following which aims at giving an explanation of what happens from a mechanical point of view.

On the forward motion of an interface-crossing body in a two-layer fluid: the role of asymptotics in the problem’s statement

A two-dimensional body moves forward with a constant velocity in an inviscid, incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body is totally submerged so that it intersects the interface between the fluids. The resulting fluid motion is assumed to be steady-state in a coordinate system attached to the body. A well-posed statement of the problem for the velocity potentials is proposed in the framework of linearized water-wave theory. This statement consists of the so-called Neumann–Kelvin problem augmented by supplementary conditions, formulated in terms of the interface’s elevation at the points, where the body intersects the interface. The analysis which leads to these two conditions involves the derivation of asymptotics near the intersection points and Green’s representation for solutions to the Neumann–Kelvin problem. The uniqueness theorem for the suggested statement is proved under the assumption that the kinetic energy is finite. The asymptotics of a solution at infinity is found and an explicit formula for the resistance to forward motion is derived. The relationship of the formulae with the supplementary conditions is discussed.

Time domain prediction of power absorption from ocean waves with latching control

A three-dimensional panel method using Neumann–Kelvin method is presented for the transient wave-body interaction problems in order to absorb maximum power from the sea. The exact initial boundary value problem is linearized about a uniform flow, and recast as an integral equation using the transient free-surface Green function. The hydrodynamics part of the solution including radiation and diffraction problem is solved as impulsive velocity problem. A discrete control of latching is used to increase the bandwidth of the efficiency of the wave energy converters (WEC). When latching control is applied to WEC in the case of off-resonance condition it increases the amplitude of the motion as well as absorbed power. It is assumed that the exciting force is known in the close future and that body is hold in position during the latching time. A heaving hemisphere as a point-absorber WEC is used for the numerical prediction of the different parameters. The calculated hydrodynamics coefficients, response amplitude operator, absorbed power, relative capture width of this device compared with analytical and other published results.

Hydroelastic analysis of cantilever plate in time domain

Numerical solutions for the hydroelastic problems of bodies are studied directly in the time domain using Neumann–Kelvin formulation. In the hydrodynamic part of problem, the exact initial boundary value problem is linearized using the free stream as a basis flow, replaced by the boundary integral equation applying Green theorem over the transient free surface Green function. The resultant boundary integral equation is discretized using quadrilateral elements over which the value of the potential is assumed to be constant and solved using the trapezoidal rule to integrate the memory or convolution part in time. In the structure part of the problem, the finite element method is used to solve the hydroelastic problem. The Mindlin plate as a bending element, which includes transverse shear effect and rotary inertia effect are used. The present numerical results show acceptable agreement with experimental, analytical, and other published numerical results.

The Neumann–Kelvin problem revisited

The plane Neumann–Kelvin problem for a semisubmerged body in a fluid of finite depth is considered in the subcritical regime. We prove the existence of a unique solution for any subcritical velocity under the assumption that the body is symmetric about its midsection and is confined within a vertical strip bounded by straight lines going through the end-points of the body's contour.

Solvability of a Plane Elliptic Problem for the Flow in a Channel with a Surface-Piercing Obstacle

Let us consider the three-dimensional problem of steady flow of a heavy ideal fluid past a surface-piercing obstacle in a rectangular channel of constant depth. The flow is parallel at infinity upstream with constant velocity c . We discuss an approximate linear problem obtained in the limit of a “flat obstacle”. This is a boundary value problem for the Laplace equation in a three-dimensional unbounded domain, with a second order condition on part of the boundary – the Neumann–Kelvin condition. By a Fourier expansion of the potential function we reduce the three-dimensional problem to a sequence of plane problems for the Fourier coefficients. For every value of the velocity c these problems can be described in terms of a two parameter elliptic problem in a strip. We discuss a well-posed formulation of such problem by a special variational approach, relying on some a priori properties of finite energy solutions. As a result, we prove unique solvability for c\ne c_{m,k} , where c_{m,k} is a known sequence of values depending on the dimensions of the channel and on the limit length of the obstacle. Accordingly, we can prove the existence of a solution of the three-dimensional problem; the related flow has in general a non-trivial wave pattern at infinity downstream. We also investigate the regularity of the solution in a neighborhood of the obstacle. The meaning of the singular values c_{m,k} is discussed from the point of view of the nonlinear theory.

The Neumann–Kelvin Problem for a Beam

We discuss existence, uniqueness and regularity of the solution of the plane Neumann–Kelvin problem in a strip, in the case of a beam. The problem is obtained by linearization of the equations of the wave-resistance problem for a “slender” cylinder semisubmerged in a heavy fluid and moving at uniform, supercritical speed in the direction orthogonal to its generators. The results obtained may be relevant for the resolution of the nonlinear wave-resistance problem.