Numerical analysis on free surface waves and stern viscous flow of a ship model
SHIGEAKI SHIOTANI1 and YOSHIAKI KODAMA2
1 Department ot Fishery, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 852-8521, Japan
2Ship Perftormance Division, Ship Research Institute, 6-38-1 Shinkawa Mitaka, Tokyo 181-0004, Japan
Abstract： This paper deals with numerical techniques for computing the viscous flow past a ship hull with and without a free surface using a Reynolds-averaged Navier-Stokes solver with global conservation. In the first technique, a coarse grid is used to find an approximate solution to the free surface problem. Interpolation of a fine grid is subsequently carried out, and a more exact solution, particularly in the boundary layer and wake, is obtained. In the second technique, a modified
Baldwin-Lomax model is introduced to compute the viscous flow with and without a free surface. These numerical techniques are applied to simulations of the flow around a Series 60 and an SR196C ship model. The results are compared with measurement data, and the usefulness of the numerical techniques is demonstrated.
Key words： ship hydrodynamics, ship waves, ship wake, finite volume method, modified Baldwin-Lomax turbulence model
Address correspondence to： S. Shiotani
Received for publication on June 19, 1997; accepted on June 22, 1998
Introduction
There have been many efforts to simulate the viscous flow around an advancing ship with a free surface using Reynolds-averaged Navier-Stokes (NS) equations.1-12 The main objective of these studies has been to contribute to hull design or to an estimation of ship propulsion, taking into account the effects of a free surface. These simulations, however, have been very difficult to carry out, and the results have been unsatisfactory. The problems with the simulations are due to remaining difficulties in dealing with free-surface problems, such as the boundary condition of a free surface adjacent to a hull surface or the effects of turbulence. Therefore, the computation of viscous flow around a ship with a free surface is still a challenging task.
In general, in calculating this kind of flow, it is assumed that the viscous flow around the stern of a ship is influenced by the turbulent viscosity term of a high Reynolds number. On the other hand, calculations for free surface waves around a passing ship are concerned with the Froude number, and the effects of viscosity are not as important. Regarding the viscous flow around a ship hull, the predictions of stern flow and wake flow are very important in accurately estimating the resistances acting on an advancing ship hull and the flow near the propeller plane. One of the authors has developed an NS solver for successfully computing the turbulent flows around a double-body model without a free surface.13 The governing equations are the law of the conservation of momentum and continuity with pseudocompressibility. The characteristics of this scheme are the finite volume method, MUSCL-type third-order upwind differencing, the flux-difference splitting method, Roe's approximate Riemann solver, the cell-centered layout, the IAF method, and Euler implicit time-integration. The Baldwin-Lomax (BL) turbulence model of a kind of zero-equation model is used for simplicity. As this turbulence model is derived from a two-layer algebraic eddy viscosity model with the assumption of two-dimensional turbulent shear flow, the calculated flow in the thin boundary layer around a slender ship hull such as a thin ship model is in good agreement with the experimental values. However, this model shows poor agreement in calculating the viscous flow around the stern of a full ship such as a tanker, which results in a thick boundary layer and a bilge vortex at the stern producing complex flow fields. Therefore, a partial modification of the Baldwin-Lomax model is required for simulating the flow around the stern for a full ship model.
