The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Numerical Calculations of the Viscous Flow over the Ship Stern by Fully Elliptic and Partially Parabolic Navier-Stokes Equations
Numerical Calculations of the Viscous Flow over the Ship Stern by Fully Elliptic and Partially Parabolic Navier-Stokes Equations
Pages 175-184
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From page 175... ...
Kobayashi University of Tokyo Tokyo, Japan Abstract Two computer codes have been developed to solve the Reynolds averaged Navier-Stokes equations; namely the fully elliptic method and the partially parabolic method. These are applied to simulate flows over the stern of the SSPA model as a bench mark as well as a multi-purpose ship with a barge type stern.
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From page 176... ...
eddy viscosity is given by turbulence kinetic energy k and dissipation rate ~ which are obtained from their transport equations. In the cylindrical coordinate, above governing equations can be written in the general form as follows; a 1 d 1 ~ d df - (U¢)
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From page 177... ...
The turbulent kinetic energy k and the dissipation rate ~ are also given by the flat plate correlations with the boundary layer thickness and skinfriction coefficient.
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From page 178... ...
.~% 08 0.9 ·~ 0.4 _ STREAK LINE 3 0.34 ~ do_— on o.S 1 o · ,~ 0.5 __ · - ~ Q4 :: ~ · ·~, STREAK LINE I Ql _ 0.0 _ 0.5 O.2 ~ O.' .0 0.6 0'7 0'8 o'g 1. l X/L Fig.6 Skin friction coefficients over several streamlines on the SSPA model.
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From page 179... ...
It is seen that coefficients of skin friction reduces over the stern, where the shear layer grows thick according to the strong adverse pressure gradient and the stream line convergence except along the keel line. Girthwise
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From page 180... ...
distribution of pressure coefficients and skin friction coefficients calculated in the present study are compared with measured values in Fig.7 and Fig.8. Secondary flow is directed away from the keel and the water plane according to the girth-wise pressure gradient, and the shear layer rapidly grows thick at the mid-girth.
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From page 181... ...
Although the physical propeller plane is not divided into fine enough grids to expect reasonable results, estimations of the nominal wakes are tried. It is not found how to allocate grids effectively not only for the whole flow domain but also for the local region near the propeller by adjusting grid control functions.
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From page 182... ...
(4) The streamlines over the stern of the barge type ship form show uniform distributions, consequently the gradual girth-wise variations of the boundary layer thickness and the pressure distribution are noted.
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From page 183... ...
A coefficients of the viscous resistance predicted by the present method are shown to be under-estimated by 10 percent. If further developments on the turbulence model and numerics are accomplished, the numerical simulation of the viscous flow over the stern will be promising for the hull form design.
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