Study On Hydrodynamic Characteristics Of Moonpool With Bottom Open

The moonpool is widely used in the application of equipment for offshore oil-gas exploration. The moonpool acts as the domain of fluid through which both riser and casing pass, its shape and structure type have important influence on the motion characteristics of the platform. Therefore, the research on dynamic characteristics of fluid in the moonpool is greatly meaningful for the design of moonpool and the control of the platform both theoretically and practically.This paper focuses on the rectangular moonpool with full open bottom. The motion of fluid in the moonpool is established on the basis of potential flow theory. The new boundary condition that the bottom is full open is adopted; the natural vibration characteristics and the hydrodynamic characteristics are investigated. According to Lagrangian analysis, the equation is established by coupling the heave-roll of the structure and motion of the fluid in the moonpool and the effect of the fluid in the moonpool on the motion stability of the structure is investigated. The main contents and conclusions are as follows:The natural vibration characteristics of the 2-D fluid in the moonpool are investigated. The fluid is simplified as 2-D flow, using Galerkin method to expand the velocity potential function; each orders of natural frequencies and corresponding modal function are solved. The convergence of the solution is analyzed and the effect of parameters of the moonpool on the natural frequency and mode of vibration are investigated. The results show that the fluid in the moonpool has two types of motion, i.e. piston-like vertical vibration and horizontal sloshing of free surface. The natural frequencies of the vertical motion mode are mainly determined by the water depth in the moonpool, while the natural frequencies of the sloshing modes are mainly determined by the distance between the two side walls. As the free surface approaches the bottom, the frequencies will increase by the influence of the velocity of the bottom flow.The natural vibration characteristics of the 3-D fluid in the moonpool are investigated. Expanding the velocity potential function by means of Galerkin method, the equations of 3-D natural vibration characteristics are transformed to a 2-D eigenvalue equation. Each order of natural frequencies and corresponding modes of vibration are solved. The effect of geometric parameters of the moonpool on natural frequencies of the fluid is investigated. With comparison with results from the 2-D case, the application condition for the 2-D model is discussed. It is showed that the natural frequency of the fluid in the moon pool is mainly determined by the orders in width when the ratio of the length and width of the moon pool is greater than 3. As a consequence, the 2-D model can be used. However, when the length is close to the width, frequencies of each orders show big difference with 2-D results.Hydrodynamic characteristics of the fluid in response to the motion of the moonpool are investigated. Considering the swaying simple harmonic motion of the moonpool, a semi-analytical solution of velocity potential is derived in light of Galerkin method. The swaying added mass, pressure distribution on the side wall and the distribution of flow velocity on the bottom is calculated and the changing way of the added mass along with the excitation frequency. It is showed that the added mass reaches a peak when the swaying frequency of the moonpool is close to its natural frequency. The added mass in the range of the natural frequency of the fluid can be as much as several times of the moon pool displacement itself. The pressure on the bottom of the moonpool is distributed symmetrically taking the center of the bottom for the center, which shows significant dominance on the side wall within the region of influence of the free surface.The equivalent pendulum model of the fluid in the moonpool is established and the law that the parameters of the pendulum model vary with the parameters of the moonpool is given. The water depth is taken as heaving of the moonpool, and a parametric database is set up for the equivalent model of the moon pool with different water depths. It is showed that the 2nd order equivalent mass is far smaller than the 1st order, and correspondingly the 2nd order can be neglected in general computation.The motion characteristics of the fluid in the moonpool coupling with the heave-roll of floating body are investigated. The influence of the fluid on the motion stability of the floating body in analyzed. The equations are established for the coupling motion of the moon pool and the floating body by means of Lagrangian equations. Taking the fluid in the moonpool into consideration, the Mathieu equation of the roll parametric excitations is derived. The Floquet theory is used to study the stability of the periodic solution and to determine the stable region of the rolling motion. It is showed that the unstable region decreases dramatically due to the damp of the fluid in the moonpool. However, it has no obvious effect on the unstable region of the 1/2 subharmonic wave. And the stable region of the roll for the floating body decreases significantly by increasing the length of the moon pool.The nonlinear dynamical behaviors including bifurcation and chaos of a truss Spar platform is studied by numerical method. Considering mutual influences between the heave mode and the pitch mode, the coupling heave and pitch motion equations of the platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, the three dimensions maximum Lyapunov exponents graph and the bifurcation graph were constructed, the Poincare′ maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to the wave frequency, with changing of wave frequency the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion.