Offshore & Dredging Engineering Technische Universiteit Delft

Second Order Roll of Semi-Submersible Crane Vessel 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 test its hydrodynamic properties. In the model test, an obvious 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 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 2

nd 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 2

nd 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 low within the natural frequency range because of the ship’s shape features. For the nonlinear excitations, Quadratic transfer functions (QTF’s) are first calculated based on Pinkster’s theory. The second order forces and moments are further simulated by three methods both in the 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. The second order roll motion is further simulated both in the frequency domain and time domain. All simulations are validated by comparing 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 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 2

nd order roll should be predicted as a

probability distribution instead of a certain value because it has a much larger variance when compared to 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 physical reasons supported by simulations. In the third part, the discussion is moved on to the reality. The second order roll is identified both in the free floating and free hanging stage from offshore measurements for the existing semi-submersible ‘Thialf’. It is further checked whether the simulation methodology and the discussed characteristics for 2

nd order roll works in the real situation.

Finally the operability of the Sleipnir is checked, and it is concluded the 2

nd order roll actually has a dominant

contribution to the overall roll motion. However, even if 2nd

order roll is added to the overall roll motion, Sleipnir’s roll motion is still acceptable.. The overall roll motion stays below a maximum amplitude of 0.5 degree in normal operational sea states (HsTp

2 < 75). In the end bilge keels,

Tugger dampers and DP systems are proposed for mitigation of the 2

nd order roll phenomenon.

____________________________________________________________________________________ Student Sponsor Thesis committee Wen Gao Heerema Marine Contractors Prof.dr. A. Metrikine July 10

th, 2017 Dr. E. Lourens

Dr. F. Pisanó