Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Vorticity Fields due to Rolling Bodies in a Free Surface-Experiment and Theory
Vorticity Fields due to Rolling Bodies in a Free Surface-Experiment and Theory
Pages 359-376
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From page 359... ...
When a marine vehicle undergoes extreme roll motion, separation from the bilge corners, or from bilge keels are the dominant contribution to damping, whose magnitude critically determines the severity of motion, especially in cond tions close to resonance. Thus any theoretical or computational model should be properly validated.
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From page 360... ...
In the last section of the paper, we present predictions of added inertia and "equivalent" linear damping for a rectangular hull section and compare them with some existing data. 2 THE ROLLING-PLATE EXPERIMENT 2.1 Design of experiment A special model was designed and fabricated to study the vertical structures generated by a plate undergoing rolling motion in a free surface.
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From page 361... ...
The desired hydrodynamic forces and moment can be obtained by deducting contributions of the hydrostatic component (computed from the plate roll angle) and of the inertia components from the measured values.
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From page 362... ...
Only a "reasonable" estimate of the velocity field is required since "fine tuning" is carried out in the third step. A graphic interface showing simultaneously the digitized images and corresponding velocity field was helpful in speeding up this "manual" process.
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From page 363... ...
Figure 4 shows a digitized image of a typical data frame. 3 VORTICITY STRUCTURESEXPERIMENTAL RESULTS For the specific seu-up described in Section 2, the "Rolling Plate Experiment" can be characterized by the three dimensionless parameters.
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From page 364... ...
Left: vorticity contours, 7~ght: veloc~ty field; (a)
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From page 365... ...
Vorticity-contour plots of the transient state have shown that a vorticity imbalance originating during the first few strokes of the plate is responsible for determining the direction toward which the vortex pairs move after establishment of a steady state. In some cases, this can take as many as ten periods of motion.
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From page 366... ...
left: vGrricity contours, right: velocity field; (a)
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From page 367... ...
The experimental results of the last section provide an excellent opportunity to validate and calibrate the theoretical model. Towards this goal, the FSRVM code was improved and adapted to solve the rolling plate problem.
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From page 368... ...
(22) t=1 At any given time t, the location of the body boundary is prescribed while the location of the free surface boundary is determined from its previous location by using the kinematic boundary condition (Eqn.
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From page 369... ...
is solved, and then the fluid velocity is computed along the body surface B The tangential component of this velocity will not satisfy the no-slip boundary condition (Eqn.
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From page 370... ...
This peculiar behavior was first observed in some earlier computations by FSRVM and was later confirmed by experiment. The behavior is attributable to the nonlinear body boundary conditions, i.e., Eqn.
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From page 371... ...
400 _ 300 _ 200 _ 100 _ :....................................................................... 300 400 500 600 I I I I I 1 0 100 200 300 400 500 600 Figure 8: Vorticity contours, comparison between results of FSRVM (left)
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From page 372... ...
If one adopts an equivalent linearized characterization of the roll moment as Vugts, M3 -—p66(i—366CY (35) where ,u66 is the added moment of inertia, A66 is the total damping, a Fourier analysis of the moment signature will yield the JLl66 and 266.
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From page 373... ...
~ l soo 400 Ann on 1 soot 400 300 200 100 500 400 300 200 Ago Hi., J:..,3 v ~ it' hi ~ ,~ 0 100 200 300 400 Soo 600 A,.:, I. .
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From page 374... ...
A "rolling plate in a free surface" is taken as the canonical problem. A Digital Particle Image Velocimetry (DPIV)
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From page 375... ...
The method is not particularly effective in predicting features observed in the symmetrical flow regime. For the asymmetrical flow regime, i.e., large K~number cow, the FSRVM provides accurate predictions.
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From page 376... ...
(1991~. "Digital particle image velocimetry", Experiments in Fluids, 10, pp.
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