Twenty-Second Symposium on Naval Hydrodynamics (1999) / Chapter Skim
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11 Water Entry and Wake Dynamics
11 Water Entry and Wake Dynamics
Pages 638-664
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From page 638... ...
An additional transport equation for the void fraction of one of the fluids is solved to determine the spatial distribution of the two fluids, and a special discretization scheme for the convective fluxes in the void fraction transport equation is used to achieve a sharp interface between the two fluids and to ensure void fractions bounded between zero and unity. Investigating water entry of flared ships sections, Arai et al.
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From page 639... ...
They found that the motion history of water entry significantly affected predicted pressures. We computed water entry processes for a flared ship section and a wedge and compared numerical results with measurements.
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From page 640... ...
Ideally, its discretization should neither produce numerical diffusion nor unbounded values of the volume fraction, i.e. the value of the volume fraction in each cell should lie between the minimum and maximum value of the neighbor cells.
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3 Results ant} discussion We systematically applied the new computational method to simulate water entry phenomena. Twodimensional simulations of water entry of a flared ship section and two- as well as three-dimensional simulations of water entry of a wedge were compared with experimental data of Zhao et al.
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Figure 7 shows time series of predicted vertical force Fz during water entry including measurements. Numerical results showed that the 775 CVs grid was not sufficiently fine to capture the maximum vertical force.
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| ~ 60 Second set of computations to find an optimum grid density. 0.06 0.08 Table 2: CPU times for water entry simulation of the flared ship section.
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Schumann's computations of this flared section also showed an overprediction of pressure coefficients around mid girth (12~. a Cp 2 1 1200 CVs 3100 CVs ~ Exp., t=0.06 s 0 ,p - Exp., t=0.07 s o ~ Exp.,t=0.08s ~ ~5~~ 'I,\ /, 0 0 0.2 0.4 0.6 0.8 Nondimensional depth 1 1.2 Figure 11: Pressure coefficients Cp along section girth for three time instants during water entry.
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From page 645... ...
3.2 Water entry of a wedge 3.2.1 Two-dimensional simulations We employed three two-dimensional grids to investigate effects of grid and time step refinement. Table 4 summarizes particulars of the three grids.
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From page 646... ...
rat 3000 1500 750 CVs 17408 4352 1280 CPU time [h] 15.15 1.56 0.21 3.2.2 Three-dimensional results We studied effects of three-dimensional water entry by extending the two-dimensional grid in the longitudinal direction of the wedge.
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From page 647... ...
Table 7 lists the CPU times for three-dimensional computations described above. To save CPU time, we performed the simulation on the 206848 CVs grid until water entry of the keel with fewer time steps.
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From page 648... ...
The finite volume discretization technique dealt with complex geometries based on control volumes with an arbitrary number of cell faces. Our method was systematically applied to simulate two problems of water entry.
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From page 649... ...
11. Zhao, R., Faltinsen, O.M., and Aarsens, J., " Water entry of arbitrary two-dimensional sections with and without flow separation", Proceedings of the Twenty-First Symposium on Naval Hydrodynamics, Trondheim, June 24-28, 1996.
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Figure 22: Free surface deformation at two time instants for the 206848 CVs grid. Graphs a)
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From page 651... ...
, the spatial discretization scheme selected is dependent on the time step used. It means ~at, when the method is applied to steady-state problems, the final solution is dependent on the time step size.
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This is a first step towards developing a rational method for three-dimensional slamming load on ships. Water entry of axisymmetric bodies with small local deadrise angles are studied analytically by for instance Shiffman and Spencer(1951)
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From page 653... ...
This makes it unneces sary to find the intersection line between the body and free surface. The intersection angle is very small for bodies with small deadrise angles and will cause numerical problems(Greenhow(1987~.
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SF and SC. Here SB is the instantaneous wetted body surface below A, SF is the instantaneous free surface, SO is a control surface infinitely far away from the body.
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From page 655... ...
the body surface is about 1.8° during water entry with constant velocity of a wedge(2-D) with deadrise angle 30°.
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4 SIMPLIFIED SOLUTION Wagnerf l 932) developed an asymptotic solution for water entry of two-dimensional bodies with small local deadrise angles.
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with small deadrise angles. Satisfactory predictions of the pressure distribution and the slamming forces were obtained.
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Good agreement is obtained. The comparison between the fully nonlinear and simplified solution have been carried out for cones with different deadrise angles and an axisymmetric body with the geometry based on a two-dimensional bow flare section of a ship.
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From page 659... ...
^x x x ~.2 0 0.2 zl(Vt) aymptotic solut on nonlinear solution simplified solution x ~' ~: ~ : Jx, lX ' 04 0.6 Pressure distribution of a cone with deadrise angb 20 deg.
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From page 660... ...
ayrnptotic solution simplified solution ~ fully nonlinear sexton x Figure 8: Numerical results of total slamming force F3 of cones with different deadrise angles ,0. The fully nonlinear, simplified and asymptotic solution are used.
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From page 661... ...
Figure 12: Total slamming force F3 of an axisymmetric body with the geometry based on a two-dimensional bow flare section of a ship. The flow separated at the knuckle.
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X, X Y ~ X+ ant AN ~_. X+ ' 4~X~XXXxxx X Xi ~X4CY - , I I I I ~I 0.4 0.6 0.8 1 1.2 1.4 VVH Figure 14: Numerical results of total slamming force of cones with deadrise angle 30°.
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From page 663... ...
27 . simplified solution fully nonlinear solution x _ ~x ~ x 2.0r/B - x I, Figure 16: Numerical results of total slamming pressure on an axisymmetric body with the geometry based on a two-dimensional bow flare section of a ship.
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From page 664... ...
Or is it maybe the same? AU'1~HORS' REPLY We have done the comparison of slamming pressure between a 2D wedge and a cone for different deadrise angles.
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