**1. Introduction**

394 Computational Simulations and Applications

Velocity Analysis of Fly Ash Solid Particles Conveyed by Dense-phase Pneumatic Force. (YI

Effects of an electrostatic field in pneumatic conveying of granular materials through

Evaluation of models and correlations for pressure drop estimation in dense phase

Dilute gas–solid two-phase flows in a curved 90◦ duct bend: CFD simulation with

Analytical prediction of pressure loss through a sudden-expansion in two-phase pneumatic

Numerical simulation on dense phase pneumatic conveying of pulverized coal in horizontal

experimental validation( B. Kuan, W.Yang, M.P. Schwarz., 2007).

inclined and vertical pipes. ( EldinWee Chuan Lim, Yan Zhang, Chi-HwaWang,

pneumatic conveying and an experimental analysis. ( Luis Sancheza, Nestor A.

conveying lines. (Mehmet Yasar Gundogdu, Ahmet Ihsan Kutlar, Hasan Duz, 2009)

pipe at high pressure. (Wenhao Pu,Changsui Zhao,Yuanquan Xiong,et al.,

Hua ,LIU Zong-ming ,DU Bin, et al., 2007).

Vasqueza, George E. Klinzinga, et al, 2005).

2006).

2010).

Offshore oil and gas production is advancing fast towards water depth deeper and deeper. In the last couple of years, offshore oil production depth world records have been successively superseded. Oil industry is about to achieve production in fields approaching 2000m water depth while keeping on exploring new oil reservoirs in ocean depths close to 3000m. As water depth increases, the distance from oil field to mainland depots increases at similar rates and more hostile the ocean environment becomes. In such operational conditions the use of VLCC ship tanker, as a production unit, has been proved to be technically and economically appealing.

Good hydrodynamic characteristics in severe sea environments, adequate storage capability and possibly the low prices of used tanker hulls in the ship market are the main reasons to justify the increasing popularity of tanker hull as production units (Floating Storage and Offloading – FSO and Floating Production Storage and Offloading – FPSO) among offshore oil producer companies. The complete assessment of the dynamic behavior of moored tankers depends very much on the accuracy of the hydrodynamic loading and response evaluation that need to be performed. Potential and viscous effects on the FSO/FPSO come into play equally important role on the acting flow around the ship hull. Furthermore, translational and rotational motions of the hull have to be incorporated all together into the analysis to produce a realistic picture of the physical problem.

Recently, Computational Fluid Dynamics (CFD) has been experiencing rapid advances due to both computer technology progress and efficient algorithms that have been developed to solve the Navier-Stokes (N-S) equations used in the flow analysis around ship hulls. The present work is a contribution to the numerical solution of the viscous flow around ship-like bodies.

In the present work, the slightly compressible Navier-Stokes equations (Wanderley et al. [1]) are solved through the conservative upwind TVD scheme of Roe [2] and Sweby [3]. This finite difference method is second order accurate in space and time. The physical domain is discretized using a Cartesian mesh and the no-slip boundary condition on the body surface is imposed through the Immersed Boundary Method (IBM), Marcelo et al. [4]. The Cartesian mesh is not conformed to the body contour and the IBM is used to inform the fluid flow the presence of a body through a force field added to the momentum equations. The code was implemented using the message passing interface (MPI) and can be run in a cluster with an arbitrary number of computers. Numerical results were obtained for the flows around a

A Three-Dimensional Numerical Simulation of the Free Surface Flow Around a Ship Hull 397

1

*p u M v w c* 

 

0 0

1

*p u M v w c* 

 

0 0

Equation (9) shows the conservative scheme used to solve the governing equations. The second order Lax-Wendroff method is used for the time integration, and the spatial

*vv v*

1/2, 1/2, 1, , 2 *n n E A QQ RS i j i j ij i j*

*EFG*

 

 

The Roe – Sweby fluxes are responsible for the upwinding and TVD of the scheme, see Eq. (10). For more details about the application of the upwind TVD scheme of Roe –Sweby to

 

 

*RS RS RS*

*E F GH*

*ij ij ee e*

 

*Q Q tE F G*

the slightly compressible Navier-Stokes equations, refer to Wanderley et al. (2008).

derivatives are approximated using second order finite differences.

<sup>1</sup>

1 , , *n n* *p n u v w c n*

 

(6)

(7)

(8)

*n*

<sup>1</sup> *A T T* (11)

(9)

(10)

Initial conditions:

Boundary conditions on the body surface:

Free stream boundary conditions:

**3. Numerical formulation** 

where

sphere without free surface and around a series-60 ship hull in order to verify the implemented code. The agreement between the numerical results and the experimental and numerical data from the literature indicates that the implemented code is able to reproduce correctly the drag coefficient, pressure field, velocity field, and the free-surface elevation around a ship hull.
