Second Order Roll of Semi Submersible Crane Vessel

Abstract

Heerema Marine Contractors is building the world’s largest semi-submersible crane vessel ‘Sleipnir’. During the design phase of this vessel, model tests were performed to evaluate the hydrodynamic properties. In the model test, a significant roll motion at a period of 40s was found. Because this response is not within the range of first order wave excitation, it received great attention. Later, the 40s is proved to be the natural roll period of the vessel which can be excited by the difference frequency of the two first order wave components, thus it is called a 2nd order roll in this thesis. The aim of this thesis is to explain this phenomenon in a better way and to investigate whether this 2nd order roll identified in the model test will be a true problem in reality.

In the first part of the thesis, the physical reasons for the existence of 2nd order roll as well as the methodology to quantify 2nd order roll are discussed. Besides the resonance effect, the nonlinear excitation is proved to be quite considerable and the damping ratio is low within the natural frequency range because of the ship’s shape features. For the nonlinear excitations, Quadratic Transfer Functions (QTF’s) are firstly calculated based on the Pinkster’s theory. The second order forces and moments are further simulated by three methods in both frequency domain and time domain, where the advantages and limitations of each method are discussed. For the damping, special attention is paid to the linearization method in the frequency domain and the application of Cummins’ equation in the time domain. The use of a cubic damping term is proposed to fix the inaccuracies of the current methods. Furthermore, the second order roll motion is simulated both in the frequency domain and time domain. All simulations are validated by comparing the results with the measured data from the model test. Multi-directional wave conditions are also simulated to make the methodology applicable in the real world.

The second part of the thesis discusses an important phenomenon in the second order roll, i.e. the variance of the standard deviation of each simulation is quite large. The reasons for this phenomenon are the non-uniqueness in the excitation and the low damping ratio. Thus 2nd order roll should be predicted as a probability distribution instead of a specific value because it has a much larger variance compared to the first order motions. The sensitivity of the factors makes the model test and the real situation different, and the factors causing a difference in the real situation are discussed by an explanation of the physical reasons supported by simulations.

In the third part, the discussion is moved on to the reality. The second order roll is identified from offshore measurements of the existing semi-submersible ‘Thialf’, in both the free floating and free hanging stage. It is further used to validate the simulation methodology and the discussed characteristics for 2nd order roll.

In the end the operability of the Sleipnir is evaluated, and it is concluded that the 2nd order roll actually has a dominant contribution to the overall roll motion. However, with the 2nd order roll included, Sleipnir’s roll motion is still acceptable. The overall roll motion stays below a maximum amplitude of 0.5 degree in the normal operational sea states (HsTp2 < 75). As mitigations, bilge keels, tuggers and DP systems are proposed for the 2nd order roll phenomenon.