Experimental and Numerical Investigation on the Effect of Varying Hull Shape Near the Water Plane on the Mathieu-Type Instability of Spar

Abstract

Spar platforms have been used for oil and gas exploration in deep water for the past two decades. Spar experience low heave and pitch motions in operating conditions with its deep draft and large inertia. The heave motions can be large when encountered by long period swells. These resonant response leads to unstable motions due to heave-pitch coupling in spar platforms when the heave/pitch natural period ratio is 0.5, 1.0, 1.5 and 2.0, referred to as Mathieu-type instability. This instability can be avoided by changing heave or pitch natural periods, so that the heave-pitch coupling can be avoided. The buoy form Spar proposed in this study is a cylindrical hull with curved surface near the water plane. A classic Spar of 31 m diameter and deep draft buoy form Spars with 25 m and 20 m diameter at the water plane area have been considered. The moon pool diameter of 12.5 m and the displacement of 63000 tonnes are maintained for all Spars. The experimental investigations are conducted using 1:100 scale models in the wave flume. Numerical simulations have been carried out using panel method. The classic Spar experiences Mathieu-type instability, since the heave/pitch natural period ratio is 0.5. The heave natural period of the buoy form Spar is higher than the classic Spar by 24% and 72%. The heave/pitch natural period ratio of the first buoy form Spar with 25 m diameter at the water plane area is 0.667; hence the heave-pitch coupling is avoided. The second buoy form Spar with 20 m diameter at the water plane area does not experience Mathieu-type instability, even though the heave/pitch natural period ratio is 1.0. Also the heave natural period of the second buoy form Spar is 36s (3.6 s in scale model) which is much above the design wave period. The possibility of Mathieu-type instability is avoided in the Spar by varying the hull shape near the water plane.