The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Computation of a Free Surface Flow around an Advancing Ship by the Navier-Stokes Equations
Computation of a Free Surface Flow around an Advancing Ship by the Navier-Stokes Equations
Pages 103-118
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From page 103... ...
There are much more difficulties to be overcome in the development of free surface flow solvers, such as the treatment of free surface boundary condition, grid generation strategy and turbulence model. In the present paper, the finite-diRerence method for the Navier-Stokes equations with nonlinear free surface condition developed in Reference t13 is extended to high Reynolds number flow simulation around an advancing ship.
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From page 104... ...
The spatial differences are the third-order upstream difference by Kawamura and Kuwahara t6] for the convection terms, the second-order central difference for the pressure gradient terms and for the diffusion terms and the fourth-order central difference for the grid metrics terms.
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From page 105... ...
2.4 Body Surface Conditions For the body surface condition, the wall function approach is used to reduce the computation time. With the no-slip condition, the minimum grid spacing in the direction normal to the body surface should be small enough to resolve the viscous sublayer of the boundary layer on the body.
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From page 106... ...
The dimensionless time increment is 0.0005 for the coarse grid computation. In the fine grid case, the dimensionless time increment is 0.0005 from 1 to 2000-th time step and 0.0003 from 2001-th time step for stabilization of computation.
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From page 107... ...
J Fig. 2b Time evolution of computed wave pattern around Wigley's hull with the fine grid.
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From page 108... ...
Fig.3a and 3b show the pressure distribution on body surface, center plane and free surface in the coarse and fine grid cases, respectively. Pressure value on the free surface is identical to the wave elevation, because hydrostatic component is extracted from static pressure.
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From page 109... ...
Computed pressure distribution on body surface is shown in Fig.6 together with the measured one [103. Pressure patterns are in good accordance with each other, except for the region of wiggles described above.
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From page 110... ...
Fig. 7 Computed wake contours and cross flow vectors at various stations of Wigley's hull.
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From page 111... ...
9 Computational Grid for Series 60, Cb=0.60 The second result is for the practical ship hull form, Series 60, Cb=0.6. The computational domain is -1 < x < 1, 0 < y < 0.5, -0.5 < z < 0.0384 and the number of grid points is 100 x 20 x 38 which is same as the fine grid case for Wigley's hull.
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From page 112... ...
The wave field has not reached the steady state at 35000-th time step (the dimensionless time is 7.89~. It takes very large time to get converged solution for free surface problems by the time marching procedure, though the use of the wall function approach contributes to time saving to some extent.
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From page 113... ...
13 Comparison of computed and measured wave profiles on ship surface of Series 60. En = 0.22, Re = 106 in computation and Re = 1.39 x 107 in measurement.
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From page 114... ...
Measured Computed / 0.9 /0.9 (go\ 1 ~ ·,.-lU Measured Computed O .9 1 /: / —f ' Fig. 15 Computed and measured wake contours and cross flow vectors at various stations of Series 60.
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From page 115... ...
The numerical results for Wigley's hull and Series 60, Cb=0.6 show good agreement with the experimental data in wave profiles and pressure distributions on the hull surface. The further efforts are required in the turbulence modeling under the free surface effect to obtain quantitative agreement for the wake distribution.
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From page 116... ...
Fujisawa, "ITTC Cooperative Experiments on a Series 60 Model at Ship Research Institute", PapeTs of Ship Research Institute, Supplement No.9, (1987~.
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From page 117... ...
1) Because you are solving a symmetric problem, and therefore, using the symmetry condition on the center plane, the normal vector at the point where the center plane meets the bow or stern is double valued or it has discontinuous first derivatives.
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