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Rankine Source Method for Seakeeping Analysis in Shallow Water

[+] Author Affiliations
Alexander von Graefe

DNV GL, Hamburg, Germany

Paper No. OMAE2014-23211, pp. V08AT06A017; 8 pages
  • ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 8A: Ocean Engineering
  • San Francisco, California, USA, June 8–13, 2014
  • Conference Sponsors: Ocean, Offshore and Arctic Engineering Division
  • ISBN: 978-0-7918-4550-9
  • Copyright © 2014 by ASME


Following Hachmann approach, Söding’s Rankine source method describes the steady perturbation potential in the body-fixed reference frame. This is beneficial for seakeeping predictions at forward speed, because error-prone m-terms do not occur in the boundary condition on the ship hull. Although similar terms arise in the boundary condition on the free surface, numerical inaccuracies in these terms have much less influence on the behaviour of the ship than in the traditional approach, where m-terms are evaluated on the hull. The periodic flow is linearised with respect to the amplitude of the incident wave, taking into account the steady ship wave.

A problem arises for shallow water problems if the Hachmann approach is used. For the shallow water problem, the boundary condition ‘no flow through the bottom’ must be fulfilled. Usually, this is done using image sources. If the steady perturbation potential is described in the body-fixed reference frame, this is not possible directly. This paper extends the Hachmann approach to treat this issue. Following the usual procedure for steady flow calculation, the boundary condition at the flat bottom of the steady problem is realised using image sources. For seakeeping computations, the steady perturbation potential is split into two parts, modelled respectively by steady sources above and below the flat bottom. The first part is assumed to be constant in the body-fixed reference frame, whereas the second part is assumed to be constant in the reference frame of the mirror image of the ship. This extended Hachmann approach fulfils the boundary condition at the flat bottom analytically.

Computed ship motions with and without forward speed in shallow water are validated by model test results from Flanders Hydraulics Research, Antwerp, and from TU Berlin.

Copyright © 2014 by ASME
Topics: Water



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