Rankine Source Method Research Articles

Numerical Analysis of Rankine Source Collocation Method for the Steady Wave Making Resistance Problem

The so called previous collocation technic, which was applied to satisfy the wave radiation condition in the Rankine source method, has often induced some unstable conditions to solve the steady wave making problems for commercial ships. These troubles prevented us from practical uses of the above collocation method to apply to the practical hull form design.The present author, trying to overcome these troubles, discusses the following instability problems caused by Rankine source collocation method.(a) Steep inclination of oblique grid causes unstable conditions to solve the free surface problems.(b) Very low speed condition generates singular state.(c) Very high speed condition also makes unnatural wave deformation in near flow field around a ship.In order to avoid above problems, some practical ideas including technics are considered as following manners;(a) In case of steeply inclined grid and low speed condition, improvement of free surface matrix of Rankine source is needed to avoid the unstable condition.(b) In high speed condition the inverse image flow system is helpful as a basic flow of Rankine source method.To validate that these ideas are efficient, the author programmed several Rankine source programs and applied them to some practical problems. Through these analyses, the author shows that the present improved collocation technic, if carefully applied, leads to a good result and becomes a useful tool for preliminary hull form design. In addition, the author proves that the Conjugate Gradient method, that is a kind of iterative and memory saving algorithm, is recommendable to solve a fragile linear simultaneous equation generated by Rankine source method.

Numerical Investigation on Wave Reduction by Wings Attached to Hull

Wave phenomena of a ship to which a pair of wings are attached are simulated and investigated by Rankine source method. In the simulation, the wing is approximately replaced by a lifting line. The comparison with the measured wave profile shows good agreements. Through the investigation of the wave resistances due to the strength or location of the line vortex, it is found that the wave resistance of the ship can be reduced by a proper selection of the location and lifting force of the wing. This finding is confirmed through the comparison of wave profiles.

Interaction of Incoming Waves With a Steady Intake-Pipe Flow

A linear ray theory is developed to study the interaction of water waves with a steady intake-pipe flow in deep water. The wave-current interaction model is based on the assumption that the current field is slowly varying in comparison with the wave field. With the use of the dispersion relation, an equation is derived for the wave number that also depends on the current velocity field. Imposing the condition of irrotationality of wave number, a nonlinear set of characteristic equations of oblique waves is obtained and solved numerically to determine the rays. The current field is generated by solving the 3-D potential problem of specified intake normal-velocity at the entrance of a horizontal, circular pipe of semi-infinite length, situated on the still-water level, by using the axisymmetric Rankine source method. It appears that the velocity-potential solution of the intake-pipe flow problem presented here does not exist in the literature. Finally, the local wave amplitudes are calculated through the conservation of wave-action equation to predict the focusing of wave energy.

Numerical Analysis of 3-D WIG Advancing over the Still Water Surface

The craft by Wing In Ground effect (WIG) is considered as one of the future high speed vessel on seaway. As well known, the lift of the wing advancing over the rigid surface becomes larger than the case of the wing in infinite air field by the ground effect. In the present investigation, the free surface effect on aerodynamic characteristics of WIG is computed by means of boundary element techniques. The air flow field around WIG is analyzed by the panel method, and interactions between WIG and the free surface are represented as pressure distributions acting on the free surface by this method. In order to analyze the wave making phenomena caused by the pressure distributions on the water surface, Rankine source method is employed, in which the linearized free surface condition is imposed on the still water surface. The interaction problem between WIG and the free surface can be solved by the interative procedure based on the panel method for the air flow field and Rankine source method for water flow field. From results of these computations, the free surface effect on aerodynamic characteristics of WIG can be clarified.

An application of the rankine source method to the estimation of wave-current interaction effects

The Rankine Source Method is applied to the calculation of wave current interaction effects. Introducting the small numerical damping which is equivalent to the artifice due to Rayleigh, a new radiation condition for unsteady flows is developed. The error due to the numerical damping is estimated. The most suitable value for the numerical damping is determined so as to minimize the error. Numerical results are verified with analytical solutions including wave diffraction and radiation by a vertical circular cylinder and a hemisphere. Wave-current interaction effects on wave diffraction and radiation are calculated by means of the above mentioned scheme. Effects on radiation force are small but effects on diffractiion force are significant.

Numerical Solutions of Interaction Problem between Hull and Propeller of a Ship Considering the Effect of Free Surface

The present paper deals with the interaction problem between the hull and the propeller of a ship advancing at a constant speed on the still water surface. The Rankine source method has been employed in order to take into consideration the effect of the free surface on the hull and the propeller. The vortex lattice lifting surface method has been applied to the propeller. The interaction problem between the hull and the propeller has been solved numerically by an iterative procedure, starting from the Hess & Smith solution for the source distribution on the hull surface of the double model approximated ship as the basic flow. The effect of the interaction of the propeller has appeared on the closest hull surface as the pressure reduction and on the upper free surface as the increase of the wave just above the propeller. The calculated thrust deduction factor has showed a fairly good agreement with measured ones for 4 m and 6 m model ships.

On Interaction Problem between Boundary Layer and Wave around Ship

In this paper an iterative method is proposed, combining an integral method based on 3-D boundary layer theory with Rankine-source method and considering the head loss due to viscosity in the equation of boundary condition on the free surface. The numerical calculation is carried out by using the Wigley models. The results of pressure distributions on the hull surface, wave profiles along the hull side, velocity distributions in the boundary layer and resistance components have been shown in comparison with measurements. They display good results to some extent. And the method has also been applied to the practical ship model Series 60 (Cd =0.6).

Influence of Boundary Layer and Wake on Free Surface Flow around a Ship Model

The Rankine-source method has been combined with an integral method for boundary layer and wake so as to investigate the influence of boundary layer and wake on the free surface flow around a ship model. The head loss due to viscosity has been taken into account in the equation of the boundary condition on the free surface. The numerical solution of the free surface flow with the boundary layer and wake around 6 m long Wigley model has been obtained with aid of the technique of matrix calculation for source densities on the panel array on the hull surface along with center plane in wake and on the free surface. The computed results as for pressure distributions on the hull surface, wave profiles along the hull side and pressure, frictional and total resistances have been shown in comparison with measurements. They display good results by considering the existence of boundary layer and wake around the hull of the model.

Prediction of Flow Fields around Ships by Modified Rankine Source Method

Prediction of Flow Fields around Ships by Modified Rankine Source Method