**PO059**

**Numerical study of hydrodynamic coefficients of multiple hulls by large eddy simulations with volume of fluid method**

__Shining Zhang__, Takeshi Ishihara

*The University of Tokyo, The University of Tokyo, Japan*

**Abstract**

Hydrodynamic coefficients of multiple hulls are studied for offshore structures to reduce heave responses in oscillating flows. Large eddy simulations with volume of fluid method are performed to predict the hydrodynamic force on a forced vibrated model with multiple hulls. Predicted added mass coefficient and nonlinear hydrodynamic damping parameter are validated by a water tank test. Then, flow pattern around the multiple hulls is investigated to clarify the mechanism of hydrodynamic forces on each hull, and a systematic study on the effects of geometric parameters, such as spacing ratio, diameter ratio and aspect ratio on the hydrodynamics of octagonal hull are conducted. Finally, formulas of added mass coefficient and nonlinear hydrodynamic damping parameter for a single and double hulls with circular, octagonal and square cross-sections are proposed to cover a wide range of application of the hull.

**Method**

Numerical models of a floater with multiple hulls, which is a down-scaled model of a substation employed in Fukushima FORWARD project are introduced. The floater contains three hulls, which are octagonal cross-sectional plate.

Forced oscillation test in vertical direction is carried out in both water tank test and numerical simulations. The predicted and measured hydrodynamic force is written in the form of Morison's equation, then the added mass coefficient (Ca) and nonlinear hydrodynamic damping parameter (Cd) are estimated by Fourier averaged method. The numerical simulations are also used to study the effect of geometric parameters, and to validate the performance of proposed formulas for both Ca and Cd.

**Results**

Firstly, the hydrodynamic coefficients are almost independent of frequency parameter. The application of multiple hulls increases both added mass and nonlinear hydrodynamic damping compared with that of single one.

Secondly, the change of aspect ratio only influences the Cd. Change of the spacing ratio between multiple hulls affects both Ca and Cd, while the variation of diameter ratio only affects Ca.

Thirdly, formulas of hydrodynamic coefficient for single and double hulls are proposed and validated against the water tank test and numerical simulations. The new parameters, namely shape correction factor and KC number correction factor are introduced in the proposed formulas. Shape factor mainly accounts for the application for square, circular or octagonal hulls.

**Conclusions**

1). Hydrodynamic coefficients of multiple hulls predicted by large eddy simulations with volume of fluid method show a good agreement with the experimental data by the water tank test.

2). Effects of spacing ratio and diameter ratio of the multiple hulls are systematically studied. The added mass coefficient,Ca, increases as the spacing ratio and the diameter ratio increase, while the nonlinear hydrodynamic damping parameter,Cd, increases as the spacing ratio increases and is independent of the diameter ratio.

3). Shape correction factor and KC number factor are proposed in the formulas of Ca and Cd for a single hull and double hulls. The proposed formulas are beneficial for the design of the structures with multiple hulls.

**Objectives**

A numerical method to predict hydrodynamic coefficients can be learnt, and hydrodynamic characteristics of multiple hulls will be gained from this research. The new proposed formulas of hydrodynamic coefficients could be used in the design of offshore structures with multiple hulls or heave plates.