Numerical Analysis of Parametric Roll Resonance of a Containership Sailing in Nonlinear, Longitudinal Seas - Ντούσια, Γεωργία (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ναυπηγών Μηχανολόγων Μηχανικών. Τομέας Μελέτης Πλοίου και Θαλάσσιων Μεταφορών, 2015)
Parametric roll or “autoparametrically excited roll” is one of the major stability issues on large containerships. It is the phenomenon of substantial roll amplitude development, when the vessel is sailing in following or head seas. Even though hazard for capsizing exists mainly to smaller ships, such as fishing vessels, the economic consequences of cargo loss and damage of large containerships are extremely harmful to ship owners and the market in general. As a parametric resonance phenomenon, parametric roll is characterized by a periodical alteration of one of its characteristics, in our case the restoring. As containerships have tended in the last twenty years to become larger, the need for maintaining low fuel consumption has led to the design of thinner hulls, with bow and stern flare sections. However, new containerships are optimized for a lower speed and their beam has become larger. In general, containerships are characterized by wide waterplane when the wave though is amidships, and respectively narrower when the ship is located in the wave crest. Since the waterplane area is directly connected to the transverse stability of the ship, a phenomenon of stability gain when the ship is in the wave trough and stability loss when it is positioned in the wave crest occurs. The purpose of the present thesis is the construction of stability charts for parametric roll resonance of a containership sailing in longitudinal (head or following), regular and irregular seas. The investigation is focused on three layers: the nonlinearity of the waves, the influence of ship’s forward speed and the effect of the loading condition. A single-degree of freedom in roll with linear damping, characterized by an exact variation of the restoring has been used for the calculations. The stability charts are similar to Mathieu’s Ince-Strutt diagrams. Therefore, the horizontal axis is a function of the ship’s forward speed and the vertical axis is related to the wave steepness. At first, numerical calculations were performed, which can provide the local value of metacentric height while the ship passes through each position on the wave. After the calculations of the variation of the metacentric height have been completed, numerical simulation is performed, by solving the differential equation of roll motion, for several values of ship’s forward speed and wave steepness. Finally, stability charts are produced, where the instability regions correspond to the roll amplitudes exceeding a given threshold value, within a given number of wave cycles. In particular, stability charts for four different loading conditions are created. The selected conditions correspond to the design as well as the scantling draft. In addition, the values of the initial metacentric height cover the whole range of all loading cases. For the three out of four conditions, comparison of ship tendency for parametric rolling inharmonic and in nonlinear waves is realized. Furthermore, charts with the instability regions separated into regions of ship’s forward speed are constructed, for all loading cases and for both regular and irregular seas. These charts can provide valuable information on the proper speed regions for the prevention of parametric roll resonance, according to the selected loading case and whether regular or irregular seas are considered .Given the fact that nowadays containership are designed with a Slow Steaming service speed, these charts can indicate in which cases Slow Steaming speeds should be preferred to higher speeds, and in converse. Consequently, these charts can be also used as a guide for speed on board, apart from tools of early detection of parametric roll resonance.