Low Frequency Second Order Roll of a Semi-Submersible Crane Vessel

Abstract

Heerema Marine Contractors is constructing a new semi-submersible crane vessel, the Sleipnir. Due to low initial stability, semi-submersibles may present significant wave induced resonant motions in heave, roll and pitch. For practical reasons, especially the roll motion could play a limiting factor for future lift operations of the Sleipnir. In order to study the hydrodynamic behaviour of the Sleipnir, model tests in waves have been performed atMaritime Research Institute Netherlands. In the tested sea states low frequent second order roll has been observed. In order to evaluate the impact of the low frequent motions of the Sleipnir it is important to create an accurate (low frequent) simulation model. The aim of this thesis is to investigate if a low frequency roll motion simulation model, in the frequency and time domain, can be created. It is challenging to predict the low frequent second order roll motions in good agreement with the measurements due to two main non-linear phenomenons. In the first place, the (viscous) roll damping is considered to be non-linear. In the second place, the second order wave forces in the vertical plane, which have not been investigated extensively in the past, are non-linear phenomena. A calculation method in order to simulate the low frequency roll motions is created. This simulation method makes use of a first and second order hydrodynamic date base, first and second order moment spectra and a moment transfer function in order to define the roll motion spectrum. In order to implement viscous roll damping in the frequency domain method, a linearization of the roll damping is necessary. First empirical linear viscous damping values have been obtained for the three tested sea states. The frequency domain method predicts the roll motion energy in good agreement with the measurements, using the empirical linear viscous roll damping values, for the three tested sea states. In order to predict the low frequent roll motions for any sea state, a calculation scheme is proposed. In this calculation scheme, a linear roll damping prediction method based on linearization techniques, is incorporated. However, the investigated linearization techniques do not predict the linear viscous damping in agreement with the measurements. The energy in the rollmotion response spectrumis highly dependent on the amount of added viscous damping in the calculation. Therefore, it will be hard, due to inaccurate linear viscous damping predictions assigned to the linearization techniques, to estimate the low frequency second order roll motions in good agreement with the measurements. In the time domain simulations non-linear viscous damping terms are incorporated by means of a linear and quadratic damping coefficient. Still water decay test simulations show a very good agreement with the measurements when using damping coefficients obtained from decay tests. However, the statistics of the simulated model tests are not in exact agreement with statistics of the model tests. Possible causes for this mismatch are discussed. It must be noted that the time domain simulations have been validated with only one sea state. It is recommended to validate the time domain model for more sea states. Although the model tests and simulation methods show significant second order roll motions, which are undesirable for performing a heavy lift, it must be realized that a combination of the tested conditions (very low initial stability, long crested beam waves) will be very rare during a future heavy lift of the Sleipnir. Additionally it is noted, that the tested sea states exceed the typical heavy lift operability limit, used by Heerema.