Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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An Interactive Approach for Calculating Ship Boundary Layers and Wakes for Nonzero Froude Number
An Interactive Approach for Calculating Ship Boundary Layers and Wakes for Nonzero Froude Number
Pages 699-720
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From page 699... ...
ABSTRACT An interactive approach is set form for calculating ship boundary layers and wakes for nonzero Froude number. The Reynolds-averaged Navier-Stokes equations are solved using a small domain with edge conditions matched with those from a source-doublet-Dawson method solved using the displacement body.
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From page 700... ...
In the following, an overview is given of both the viscous- and inviscid-flow methods, with particular emphasis on their treatments of the free-surface boundary conditions and the interaction procedures. Results are presented for the Wigley hull, including comparisons for zero and nonzero Fr and with available experimental data and inviscid-flow results, which validate the overall approach and enable an evaluation of the wave-boundary layer and wake interaction.
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From page 701... ...
for a thick boundary layer and wake can be defined unambiguously by the two requirements that it be a stream surface of the inviscid flow continued from outside the boundary layer and wake and that the inviscid-flow discharge between this surface and any stream surface exterior to the boundary layer and wake be equal to the actual discharge between the body and wake centerplane and the latter stream surface. A method for implementing this definition for practical geometries is presently under development [171; however, in lieu of this, an approximate definition is used in which two-dimensional definitions for a*
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From page 702... ...
3 k (7) Vt is defined in terms of the turbulent kinetic energy k and its rate of dissipation £ by k2 Vt = Cot £ where Cp is a model constant and k and £ are governed by the modeled transport equations Dk_ a (1 ak fit ax Rkax)
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From page 703... ...
On the exit plane Se, axial diffusion is negligible so that the exit conditions used are a2~/aX2 = 0, and a zero-gradient condition is used for 19. On the outer boundary SO, the edge conditions are specified according to (2)
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From page 704... ...
is (i = Hi, Aij ale + Hi, Bij Hi = 0 (26) Sb + Sw Sb + Sw The free-surface shape is determined by representing the undisturbed free surface by panels, whereupon free-surface boundary conditions linearized with respect to zero Fr are imposed [261.
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From page 705... ...
The free-surface perspective view and contours, wave profile, and surface-pressure profiles and contours are shown in figures 6 through 10, respectively. The axial-velocity contours, crossplane-velocity vectors, and pressure, axial vorticity, and turbulent kinetic energy contours for several representative stations are shown in figures 11 through 13.
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From page 706... ...
Reference [14] provides detailed discussion of the zero Fr solution, including comparisons with the available experimental data.
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From page 707... ...
On the waterplane, the surface and wake centerplane pressure displays very dramatic differences, the wall-shear velocity shows similar trends, but with reduced magnitude, and the wake centerplane velocity indicates faster recovery in the intermediate and far wake. As will be shown later, the first closely follows the wave profile, the second is due to an increase in boundary-layer thickness near the waterplane for the nonzero Fr case, and the third can be explained by the wave-induced pressure gradients.
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From page 708... ...
Most of the differences were explicable in terms of the differences between the zero and nonzero Fr surfacepressure distributions and, in the latter case, the additional pressure gradients at the free surface associated with the wave pattern. The viscous-inviscid interaction appears to be greater for nonzero as compared to zero Fr.
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From page 709... ...
domain approach to the present problem is also of Interest and will enable such an evaluation. Finally, some of the issues that need to be addressed while further developing and validating the present approach are as follows: further assessment of the most appropriate free-surface boundary conditions; improved definition and construction of displacement bodies; the inclusion and resolution of the bow-flow region; extensions for lifting flow; and the ever present problem of grid generation and turbulence modeling.
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From page 710... ...
28. Toda, Y., Stern, F., and Longo, J., "Mean-Flow Measurements in the Boundary Layer and Walce and Wave Field of a Series 60 CB = .6 Ship Model for Froude Numbers .16 and .316," Iowa Institute of Hydraulic Research, The University of Iowa, IIHR Report No.
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From page 711... ...
~tINTERACTtoN, THICK BOUNDARY LAYER ~ WAKE REGION 1.
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From page 712... ...
~ =~__= =~; I ~ 1 ~ 0.0 0.2 0.4 0.6 O.B 1.0 X Figure 8. Wave profile.
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From page 713... ...
axial-vorticity contours; and (e) turbulent kinetic energy contours.
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From page 714... ...
opulent anemic entry congas.
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From page 715... ...
axial-vorticity contours; and (e) turbulent kinetic energy contours.
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From page 716... ...
Velocity, pressure, and turbulent kinetic energy proD~les at x = .5.
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From page 717... ...
Velocity, pressure, and turbulent kinetic energy proD~les at x = .9.
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From page 718... ...
Velocity, pressure, and turbulent kinetic energy profiles at x = 1.1.
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From page 719... ...
DISCUSSION Hoyle Raven Maritime Research Institute Netherlands, The Netherlands This valuable paper addresses the difficult problem of prescribing free-surface boundary conditions inside the viscous domain. The authors solve the wave elevation from integration of the kinematic condition, and thus from the velocities at the undisturbed free surface.
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