Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Free-Surface Effects on a Yawed Surface-Piercing Plate
Free-Surface Effects on a Yawed Surface-Piercing Plate
Pages 273-284
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From page 273... ...
A Kutta condition is imposed at the trailing edge. The linear free-surface boundary condition and far-field condition are satisfied by using for the dipole potential the transverse derivative of the classical ship-wave Green function for steady forward motion.
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From page 274... ...
This jump cannot be reconciled with the potential-flow boundary conditions since, if the pressure is constant on the free surface and continuous across the wake, the free-surface elevation must be continuous. The theoretical results described below are derived on this basis, but a pronounced nonuniformity exists in the solution near the intersection of the free surface and trailing edge.
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From page 275... ...
In accordance with the Kutta condition the velocity ~s assumed to be finite and continuous at the trailing edge. Finally, for large depths beneath the free surface, the velocity is assumed to vanish.
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From page 276... ...
Except for the Rankine singularity 1/r, which must be treated separately to account correctly for its limiting contribution on the boundary SB, the kernel of the integral equation (10) can be evaluated from the second normal derivative of G on the centerplane x = 0.
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From page 277... ...
Here the pressure coefficient is derived from L'Hospital's rule in terms of the second derivative of m with respect to the angular coordinate ~ defined by the relation sing = 2//c. From the Kutta condition the pressure coefficient should vanish at the trailing edge, whereas the actual values computed in this manner are not precisely zero and the error appears to increase without limit as the free surface is approached from below.
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From page 278... ...
u ~ -~Figure 6. Normalized pressure distributions on the plate, at the indicated Froude numbers.
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From page 279... ...
Figure 9 shows the corresponding view from below. Most of the threads at the trailing edge are oriented in the expected manner to accord with the Kutta condition of smooth tangential flow past the trailing edge, but the uppermost two threads are sharply deflected indicating a pronounced cross-flow near the free surface.
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From page 280... ...
Note the sharp deflection of the two uppermost threads at the trailing edge.
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From page 281... ...
Extending this argument, the kinematic boundary condition on the free surface implies continuity of the vertical velocity component across the wale, and hence vanishing of the trailing vorticity on the free surface. On this basis the slope of the spanwise lift distribution should vanish at the free surface, as in the simpler limiting case of zero Froude number where a simple image solution applies.
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From page 282... ...
Further progress with the numerical analysis may also lead to a more robust algorithm for calculating the pressure coefficient and free-surface elevation near the trailing edge.
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From page 283... ...
In the case of SWATH ships, we see that there is a jump at the trailing edge for IF ~ 0.3 - 0.35, where the SWATH strut aspect ratio is 0.10 - 0.15 and the Angle of attack" of the strut is due to the flow induced by the opposite strut and the two hulls. Please comment on the effect of aspect ratio on critical IF and critical IF for SWATH ships.
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