Application of the CIP Method to Strongly Nonlinear Wave-Body Interaction Problems
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- Institutt for marin teknikk 
Water entry and exit, green water on deck, sloshing in tanks and capsizing in intact and damaged conditions are examples on violent fluid motion. The combination of model tests, theoretical analysis and Computational Fluid Dynamics (CFD) methods is emphasized in treating these problems. Because mixing of air and liquid may occur, the interaction between the flow in the air and in the liquid ought to be considered in numerical simulations. Further, the mixing of air and liquid represents a scaling problem of model tests. In order to make a rational step in improving the analysis of nonlinear wave-induced ship motions and loads, it is necessary to base a solution on the Navier-Stokes equations, i.e. a CFD method has to be used. The Constrained Interpolation Profile (CIP) method described in this thesis is used as a CFD method for exterior water-body interaction studies. Because it is a rather new method, careful validation and verification are needed. This includes linear flow cases and sub-problems associated with large amplitude water entry and exit. In this method, the solid body and free surface interaction is treated as a multiphase problem, which includes liquid (water), gas (air) and solid (rectangular cylinder, circular cylinder, bow flare section, V-shaped section, etc.) phases. The flow is represented by one set of governing equations, which are solved numerically on a non-uniform, staggered Cartesian grid by a finite difference method. The free surface as well as the body boundary is immersed in the computational domain. First of all, linear and weakly nonlinear wave-body interaction problems are investigated by using a CIP-based finite difference method. The numerical wave tank (NWT) encounters difficulties in handling the long time simulation of large amplitude motions. Therefore, the wave-body interaction problem is isolated into water entry and water exit sub-problems. This thesis describes the fully nonlinear free-surface deformations of initially calm water caused by water-entry and water-exit of a horizontal circular cylinder with both forced and free vertical motions. This has relevance for marine operations as well as for the ability to predict large amplitude motions of floating sea structures. The numerical results of the water entry and exit force, the free surface deformation and the vertical motion of the cylinder are compared with experimental results, and favorable agreement is obtained. The CIP method is also applied to 2D water entry of vertical and heeled bow flare and Vshaped sections. The results for the bow flare section have relevance for slamming loads on a ship in bow sea with large roll oscillations and relative vertical motions. The results for the heeled V-shaped section can be combined with a 2D+t numerical method to study how the steady heel moment on a prismatic planing hull on a straight course in calm water depends on the Froude number (Faltinsen, 2005). A generally satisfactory agreement with experimental drop test results of vertical water entry velocity, vertical and horizontal hydrodynamic forces as a function of time is demonstrated. This includes the effect of flow separation from the knuckles. The experimental results have bias errors due to eigenfrequency oscillations of the test rig and the use of elastic ropes to stop the models. The occurrence of ventilation of the leeward hull side is examined. An example on 3D calculations by means of the CIP method is presented. Green water on the deck of a Wigley hull at Froude number 0.25 in head sea is studied. Our studies are a step towards developing rational CFD methods for predicting strongly nonlinear wave-induced motions and loads on a ship.