Numerical Study on Mathieu Instability of DDMS Platform

Deep draft multi-spar (DDMS) is an innovative platform which is specially designed for deepwater drilling and production in 2009 by Center for Deepwater Engineering, Dalian University of Technology. The hard tank of DDMS is composed of four columns at corners and a novel moonpool protecting the top tension risers at center. In addition, the top tension and self-weight of rigid risers are provided by air-cans in the moonpool. At the foot of hard tank, the pontoons and horizontal bracing are used to connect the separated columns and moonpool. It is noted that two heave plates are directly integrated with the hard tank in order to reduce the heave response. The middle section consists of 4 columns of smaller diameter which connect the hard tank and ballast tank. The early investigation indicates that the global hydrodynamic and motion behavior of DDMS are similar with Spar platform, and furthermore the heave natural period is close to the half pitch natural period. Therefore the DDMS platform may have possibility to trigger the Mathieu instability which has been validated on Spar platform through the numerical and experimental method. In this paper, a coupled heave and pitch motion equations of DDMS platform are established with accounting the time-varying restoring heave and pitch restoring stiffness. A damping case matrix is generated considering the heave plate damping, mooring line damping and hull drag damping. The damping ratios are identified by free-decay tests. The nonlinear motions under the action of regular waves of different periods and heights are numerically solved by the 4th order Runge-kutta method. The calculational results reveal that the heave damping significantly influences the occurrence of pitch instability, meanwhile the damping contribution of heave plates and mooring lines also play an important role in suppressing the instability. The phenomenon of Mathieu instability is owing to the energy exchange in this paper, and the mechanism of this phenomenon is amply studied as well as 3 different ways of instability are summarized.