Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method

Hydrodynamic interactions between two ships advancing in waves

A numerical model for simulation of the hydrodynamic interactions between a marine floater and fragmented sea ice

The irrotational flow past two slender bodies of revolution at angles of yaw, translating in parallel paths in very close proximity, is analysed by extending the classical slender body theory. The flow far away from the two bodies is shown to be a direct problem, which is represented in terms of two line sources along their longitudinal axes, at the strengths of the variation rates of their cross-section areas. The inner flow near the two bodies is reduced to the plane flow problem of the expanding (contracting) and lateral translations of two parallel circular cylinders with different radii, which is then solved analytically using conformal mapping. Consequently, an analytical flow solution has been obtained for two arbitrary slender bodies of revolution at angles of yaw translating in close proximity. The lateral forces and yaw moments acting on the two bodies are obtained in terms of integrals along the body lengths. A comparison is made among the present model for two slender bodies in close proximity, Tuck & Newman's (1974) model for two slender bodies far apart, and VSAERO (AMI)–commercial software based on potential flow theory and the boundary element method (BEM). The attraction force of the present model agrees well with the BEM result, when the clearance, h 0 , is within 20% of the body length, whereas the attraction force of Tuck & Newman is much smaller than the BEM result when h 0 is within 30% of the body length, but approaches the latter when h 0 is about half the body length. Numerical simulations are performed for the three typical manoeuvres of two bodies: (i) a body passing a stationary body, (ii) two bodies in a meeting manoeuvre (translating in opposite directions), and (iii) two bodies in a passing manoeuvre (translating in the same direction). The analysis reveals the orders of the lateral forces and yaw moments, as well as their variation trends in terms of the manoeuvre type, velocities, sizes, angles of yaw of the two bodies, and their proximity, etc. These irrotational dynamic features are expected to provide a basic understanding of this problem and will be beneficial to further numerical and experimental studies involving additional physical effects.

An analytical solution for two slender bodies of revolution translating in very close proximity

Study of the hydrodynamic derivatives of vertical-axis tidal current turbines in surge motion

The equations of motion of two bodies in translation motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation, which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

Interaction between two bodies translating in an inviscid fluid

The oblique motion of a circular cylinder through an inviscid and incompressible fluid, conveyed by a uniform flow at infinity, in the vicinity of another cylinder fixed in space is considered. In a relative polar co-ordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centres of the cylinder pair. The Lagrange equations of motion are then integrated for the trajectories of the moving cylinder. In order to evaluate the added masses and their derivatives with respect to the separation distance between the cylinders in terms of the hydrodynamic singularities, the method of successive images, initiated by Hicks, and the Taylor added-mass formula are applied, and analytic solutions in closed form are obtained thereafter. The dynamic behaviour of a drifting body in close proximity of a fixed one is investigated by considering the limiting values of the fluid kinetic energy and the interaction forces on each body. The reliability of the numerical approximation of added masses and their derivatives is also discussed in the present study. The integral equations, in terms of surface source distributions and also discussed in the present study. The integral equations, in terms of surface source distributions and their derivatives on both circles, are carefully modified for obtaining accurate numerical solutions.

Oblique Impact of Two Cylinders in a Uniform Flow

The general planar translation of two bodies of revolution through an inviscid and incompressible fluid is considered. The moving trajectories and the hydrodynamic interactions are computed based on the generalised Lagrange equations of motion, including the effects of solid constraints, external forces in the plane of motion, and a uniform stream in any direction parallel to the plane of motion. In a relative co-ordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centres of two bodies. Analytical solutions of added masses in series form are obtained for the motion of two spheres. A new iterative formula based on the analysis of velocity potentials around each body is developed for added masses and their derivatives with respect to the separation distance due to the transverse motion. The method of successive images and Taylor's added-mass formula are applied to determine the added masses and their derivatives due to the centroidal motion. These results are compared with the numerical solution of added masses computed by the boundary0integral method and the generalised Taylor added-mass formula. The integral equations, in terms of surface-source distributions on both surfaces, are modified for obtaining accurate numerical solutions. Numerical results are given for several practical engineering problems.

On the planar translation of two bodies in a uniform flow

Oblique impact of two cylinders in a uniform flow

Hydrodynamic interactions between a three-dimensional body of revolution and an infinitely long circular cylinder in an inviscid fluid are studies numerically by the boundary-integral method. The added-mass coefficients and their derivatives are computed in terms of the solutions of four integral equations of the second kind. A numerical technique based on variable transformations is developed to evaluate integrations over steep peaks. Integrations over the cylindrical surface are properly computed by mapping the infinite region onto a finite region and regularizing the ill-behaved kernels with sharp peaks. The discrete added masses and their derivatives are fitted by the least-squares approximation on the basis of Legendre polynomials. As a practical example, the moving trajectories of a sphere conveyed by a uniform flow around a fixed circular cylinder are computed and presented.

Zhi Guo

Papers

Interaction between two bodies translating in an inviscid fluid

Oblique Impact of Two Cylinders in a Uniform Flow

On the planar translation of two bodies in a uniform flow

Oblique impact of two cylinders in a uniform flow

Boundary-integral computation of hydrodynamic interactions between a three-dimensional body and an infinitely long cylinder