Computational calculations of ship hydrodynamics


In November 2010, the BAW’s Hamburg office began efforts to enhance its experimental fluid dynamics (EFD) work by adding the computational fluid dynamics (CFD) method to its investigations of how seagoing ships and approach channels interact. Since 1996 external research institutions have been tasked with developing this method and provided with support as part of research projects.

There were several reasons for introducing the CFD method at the BAW: the institute needed to build up expertise in analysing third-party numerical data, while there was also a requirement to strengthen hydraulic engineering modelling in the long term. Computational simulations are enjoying rapidly rising popularity in all specialist fields and, as far as the reliability of these simulations is concerned, it is becoming increasingly important to understand and evaluate their background, boundary conditions and approaches.

Computational fluid dynamics offers some key benefits. For instance, the model dimension of a simulation enables calculations to be carried out at any point, such as the flow directly beneath a ship’s hull. Comparable measurements in the BAW’s ship wave basin could only be done with a great deal of time and effort. Another major advantage is the fact that the model setup can be changed quickly: it takes less time and effort to switch a model setup from a flat to a steeper embankment on the computer than it does in the hydraulic model.

Validating squat and trim

The actual introduction of the CFD method formed part of the research and development (R&D) project entitled “Computational calculations of ship hydrodynamics and manoeuvrability in shallow water”. It used commercial software that is employed in the shipbuilding and aerospace industries as well as in other technology sectors and that is continuously being further developed. One of the main aims of the R&D project was to calculate two parameters in ship dynamics – the squat (the way a moving ship is lowered in the wave that it generates itself) and trim (the way a ship rotates around its transverse (or pitch) axis) of large seagoing vessels in shallow and confined water. The model setup for the computational model mirrored the setup for the various series of tests run in the BAW’s ship wave basin in 2001 (Uliczka et al. 2004). The data produced by the hydraulic engineering tests enable the applicability of the computational method to be assessed and, ultimately, validated by comparing calculations with measurements. Of particular interest are the sensitivities of the simulation’s numerical parameters in terms of the result and indications of where there still might be major deviations in and problems with the computational simulation.

The unique setup of the hydraulic engineering test series – i.e. minimal keel clearance, lateral restrictions and movement of the ship right up until it nearly runs aground – placed considerable demands on the computational engine and on implementation in the computational model. Ship dynamics is modelled using a flexible (deformable) mesh, although this only permits minimal deflections of movement (morphing technique). The ship’s path through the still water is achieved by switching the reference system: in the computational model, the ship is stationary while water flows against it. In order to calculate squat and trim values at high speeds, the speed of the water flowing against the ship has to be increased slowly and gradually. This is done to prevent the ship from running aground during the tuning phase required for computational reasons since the CFD-code will abort its calculation in such a case.

The model validation (Figure 1) illustrates that the computational calculations are in fact close to the measurements from the hydraulic model. The stern squat – the critical parameter in the case of this ship – is accurate. The angle of trim is slightly less than the value measured in the ship wave basin. Any further analysis must bear in mind that, in the model test the ship was self-propelled while the computational model only simulated water flow against the ship’s hull, excluding the rudder and propulsion system. In particular, the acceleration of the water at the back of the ship caused by a propeller results in a further drawdown of the water level at the stern and thus a larger aft squat, which in turn causes the ship to pitch more (larger angle of trim). If the computational model is to be fine-tuned in future, therefore, it will have to simulate travel through still water while also taking account of the propeller.

Validating load factors

As part of a Master’s degree dissertation (Ahrens 2017), the two load factors of drawdown (minimum water level deflection over time) and the maximum flow speed (backflow) of flow simulations were validated together with ship dynamic parameters of squat and trim. The prototype of the model ship (PPM52) had a length lpp of 347.2 m, a beam b of 52 m and a draught t of 14.5 m with a water depth h of 19.2 m. Its schematic profile including its dimensions in model scale is shown in Figure 2.

Although the model setups for the physical (EFD) and numerical (CFD) model were the same in principle, there were differences in terms of the ship’s propulsion and the length of the channel. In the hydraulic model, the ship was self-propelled, while in the computational model the propeller was represented by a model of mean values over time (actuator disc). This uses given characteristics of the chosen propeller to model the momentum and surge force acting on the ship. In the simulation, the ship was made to carry on moving at a constant speed following a sigmoidal acceleration phase.

A large number of simulations including optimisation were carried out in order to calculate key values such as squat, drawdown and maximum flow speed (Ahrens 2017). A direct comparison with the measurements from the hydraulic model revealed the following deviations:

  • Maximum flow speed ~20% (the deviations amounted to between 1.3 and 5.5 cm/s with a flow probe resolution of 0.5 cm/s)
  • Maximum drawdown ~10%
  • Bow squat ~7%
  • Stern squat ~15%

Figure 3 below illustrates one example of a validation result for the drawdown parameter depending on the ship speed vs.


The CFD method has been and continues to be used in various projects, including some relating to issues raised by the German government’s Federal Waterways and Shipping Administration (WSV).
The areas studied cover both ship dynamics (focus on the ship) and load factors such as ship waves and flows (focus on the waterway).
As well as the two parameters of ship dynamics – squat and trim – already mentioned, the forces and yaw moments acting on ships that encounter one another, for example, are also calculated. In addition, the CFD method is used in expansion projects to predict project-related changes in loads generated by ships by looking at different design ships in various cross-sections.
Some projects use only the CFD method, while others use it alongside hydraulic model tests, in which case these latter form the basis for validating the CFD model in order to provide validation for its results.


Ahrens, E. C. (2017): Validierung von CFD-Simulationen mit Overset-Technik anhand von Messungen aus Modellversuchen. Masterarbeit. Hochschule Bremen, Bremen. Schiffbau und Meerestechnik.

Uliczka, K. et al. (2004): Dynamisches Fahrverhalten sehr großer Containerschiffe in seitlich begrenztem extremen Flachwasser. In: Hansa 141 (1), S. 59–65.

Mathematical Methods