Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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On the Numerical Solution of the Total Ship Resistance Problem under a Predetermined Free Surface
On the Numerical Solution of the Total Ship Resistance Problem under a Predetermined Free Surface
Pages 789-800
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From page 789... ...
convection term of Cp pressure coefficient Cf skin friction coefficient G generation term of k g gravitational acceleration hi metrics h vertical distance kij curvature tensor k turbulence kinetic energy deformation tensor - 1J P pressure PI pressure (P+ggh) RF frictional resistance Rp pressure resistance RT total resistance velocity components collinear co-ordinates ui xi S.`:, source terms Greek symbols dissipation of k ~ fluid viscosity lit eddy viscosity he effective viscosity Q fluid density oil stress tensor variable Dept.
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From page 790... ...
In this manner, and looking at the ship from below, the actual solid and liquid boundaries for the flow were determined. It was thed straightforward to run the NTUA viscous flow computer code for this prescribed fluid region, applying appropriate conditions at the boundaries and obtain the total ship resistance, as the sum of the pressure and the wall shear stress forces.
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From page 791... ...
Measurements of the Steady Wave Pattern The wavy free surface necessary for the numerical calculations was obtained in a mixed manner. Different methods were used for the intersection of the free surface and the hull surface, for the wave region near the hull surface and for the wave region away from the hull surface.
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From page 792... ...
After the element source or eddy distributions are computed, the grid nodes can be specified as intersections of equi-potential and equi-stream function lines, following the iterative procedure described in (9~. The velocity components and the other flow variables refer to local orthogonal curvilinear co-ordinate systems coinciding in two dimensions with the grid lines x1 = const and x2 = const, while their third direction X3 is always parallel to the ship longitudinal axis.
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From page 794... ...
art g re 2 (conffnued)
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From page 795... ...
1 where dip stands for the velocity components, the turbulence kinetic energy and its discipation rate and Hi are the values at the neighbouring nodes of P Central differences are used to model Al along x1 and x2 directions while the corresponding coefficients on upstream ala downstream planes are calculated by the hybrid scheme (12)
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From page 796... ...
It should be noticed here that the external boundary N for the viscous flow calculations is almost five times closer to the ship hull than NP and, therefore, it is expected that the calculation of the velocity components at N will not be practically affected by the aforementioned effects. A total of 1400 panels has been used to model the ship hull and 2000 panels to model the free surface.
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From page 797... ...
That is whereas the static for the potential flow hour for 3500 elements on equilibrium wetted surface of the model was 1.694 me, the wetted surface underway was 1.738 ma, that is increased by 2,6%, and the wetted surface of the double model was 1.734 ma, very close to the actual wetted surface. In addition, the pressure resistance of the potential flow for the actual wetted surface and the measured wave pattern was computed.
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From page 798... ...
The first such area is connected with an artificial blockage effect, which is inserted to the procedure by imposing the potential flow velocities as boundary conditions relatively close to the surface of the body. Obviously, this is done to reduce the time of computations and our experience a, shows that if this effect is eliminated, the predicted value of the resistance will be reduced by 2-3%.
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From page 799... ...
Chen, H.C. and Patel, V.C., "Practical Near-Wall Turbulence Models for Complex Flows Including Separation", Proceedings of AIAA 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference Honolulu, 1987.
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