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Fully three-dimensional ship seakeeping computations with a surge-corrected Rankine panel method

 

VOLKER BERTRAM* and GERHARD THIART

 

Department of Mechanical Engineering, University of Stellenbosch, 7600 stellenbosch, south Africa

 

Abstract: A 3-d seakeeping code uses first-order Rankine panels with special numerical integration on the ship's hull and Rankine point source clusters above the free surface. The code computes the motions of the ship in regular waves of small height (linearized). The steady flow is captured without simplification by solving the fully nonlinear wave-resistance problem first. A special treatment of the surge motion considers the influence of periodic quantities on thrust and resistance, and improves surge motion predictions. Radiation and open-boundary conditions are enforced by staggered grids. Results for the ITTC standard test case S-175 containership agree well with experiments except for very long waves. The importance of capturing the three-dimensional steady flow contributions is also demonstrated.

 

Key words: seakeeping, panel method, containership, surge correctron

 

Address correspondence to: V. Bertram, TUHH, Lammersieth 90, 22305 Hamburg, Germany

Received for publication on Oct. 6, 1997; accepted on Jan. 28, 1998

*visiting scientist

 

Introduction

 

In their 1950 milestone paper,1 Weinblum and St. Denis said:“The present hydrodynamic methods used in studying problems of seaworthiness are based largely on the powerful concept of sources and sinks.”Almost half a century later, this statement still describes the state of the art. Of course, today's methods are far more powerful, with the main advances being in capturing nonlinearities and the three dimensionality of the flow. We present here a“fully”three-dimensional Rankine panel method, capturing both the steady and the time-harmonic potentials three-dimensionally. For a recent survey of Rankine panel methods for forward-speed seakeeping, we refer to Bertram and Yasukawa. 2 Our method captures all forward-speed effects, so in addition to the change in encounter frequency, we capture:

 

dynamic trim and sinkage;

steady wave profile (average wetted surface) and generally the steady wave elevation on the free surface; local steady flow field.

 

Physical model

 

We consider a ship with average speed U in a regular wave of small amplitude h. The boundary conditions will be linearized with respect to h (and all other related time-harmonic quantities). We refer to Bertram3 for an extensive derivation of the boundary conditions.

The fundamental differential equation for the assumed ideal flow is Laplace's equation, which can be interpreted as describing conservation of mass. In addition, we formulate the following boundary conditions:

 

1. water does not penetrate the ship hull;

2. water does not penetrate the free water surface;

3. there is atmospheric pressure on the free surface;

4. there is undisturbed flow far away from the ship;

5. waves created by the ship propagate away from the ship; for τ > 0.25 these waves are limited to a sector downstream;

6. waves created by the ship must leave an artificial boundary of the computational domain without reflection;

7. the forces on the ship result in periodic motions. (We assume that the time-averaged added resistance is compensated by increased propulsion forces, i.e., the average speed remains constant.)

 

The radiation condition (5) deserves a more detailed discussion. To date, our method is limited to cases

 

 

 

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