Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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The Calculations of Fluid Actions on Arbitrary Shaped Submerged Bodies Using Viscous Boundary Elements
The Calculations of Fluid Actions on Arbitrary Shaped Submerged Bodies Using Viscous Boundary Elements
Pages 801-814
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From page 801... ...
To illustrate the method, preliminary results are presented of the unsteady and steady state fluid actions and flow fields associated with arbitrary shaped, submerged bodies moving through prescribed manoeuvres. INTRODUCTION When a rigid body departs from steady motion in a straight line the surrounding fluid exerts a resultant force and a resultant moment about the centre of gravity of the body as a consequence of the disturbance.
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From page 802... ...
derived by the non-linear model are relatively insensitive to panel distribution, idealization etc., allowing simplifications in the numerical procedures; however, the evaluation of a detailed flow velocity field is more sensitive to idealization and the wake fluid domain must be modelled to allow for the complete formation of the vortex wake pattern. Building on these previous studies, here we present a viscous boundary element panel distribution method to evaluate the unsteady fluid actions experienced by two and three-dimensional arbitrary shaped bodies moving in a stationary, unbounded, incompressible viscous fluid.
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From page 803... ...
f = 0. FUNDAMENTAL SOLUTIONS OR OSEENLETS TIME DEPENDENT SOLUTIONS Analogous to the steady state solutions (v = 0)
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From page 804... ...
It can be shown that both approaches produce the same steady state fundamental solutions. Three Dimensional Solution (s = 1,2,3 = j = k)
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From page 805... ...
MODIFIED INTEGRAL EQUATIONS Using the fundamental solutions derived in the previous section, the integral equation described in equation (16) can be written in alternative forms.
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From page 806... ...
steady state drag coefficient data Cd for a circular cylinder in uniform flows. In the linear model, the cylinder's surface was idealised by a distribution of 100 equally spaced viscous boundary elements though it was shown that a 10 element distribution produced similar convergent solutions and both sets of numerical results compared very well with Oseen's theoretical prediction as given by LambE23, Re 13.
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From page 807... ...
V / \ / \ to \ / \ ,, ~\ \ / \ \ ~ \ 720 1! \ to \ / \ / \ / \ , Figure 3 The time histories of the prescribed manoeuvre of the circular cylinder and the associated calculated Oseen drag coefficient CdX and sway transverse force coefficient Cdy for different Reynolds number flows.
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From page 808... ...
The cylinder's surface was again idealised by a distribution of 40 equally spaced viscous boundary elements, each containing a time dependent oseenlet and in a similar procedure to the equivalent steady state calculations, 400 panels were distributed into the fluid domain contained within an imposed surrounding outer boundary at R = 6D (say)
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From page 809... ...
, ~ ~ ,, " `-~ ~ , ' , this figure shows the associated drag ' ~ ~ "a -- ,, coefficient CdX and sway transverse force ' ~ ~" ~ _ - , coefficient Cdy for different Reynolds number ~ ~ _ ~ flows calculated from the non-linear convective ' \ model. The abscissa denotes the number of ' time interval increments passed into the simulation.
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From page 810... ...
~ ~ - ~ t~ Air it's Ott / l l ~- ~" ~- - ~- ' ~- ~ 40 70 t _ 1 _ t ~_ ' t ~/ ~_ _ ~ i~ ' I it ~ ,'- ~ ~ _ - - ; ~1.
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From page 811... ...
. CONCLUSIONS The hybrid analytical and numerical viscous boundary element approach using time dependent oseenlets described herein, allows the predictions of the fluid actions and flow fields associated with arbitrary shaped bodies moving in a prescribed manoeuvre in an incompressible, viscous fluid.
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From page 812... ...
and Tan, M., "The Evaluation of Steady Fluid Forces on Single and Multiple Bodies in Low Speed Flows Using Viscous Boundary Elements," International Union of Theoretical and Applied Mechanics Symposium on The Dynamics of Marine Vehicles and Structures in Waves, June 1990, Brunei University, (Also Elsevier Press, 1991~.
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From page 813... ...
] then the surface integral involving the two-dimensional, time dependent oseenlet is given by the analytical expression 2 2~ | vSj d~ = | { t (6 -- )
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From page 814... ...
In fact, from the values of the steady state forces at the appropriate Reynolds numbers for a model and full scale submarine a simple correction factor could be deduced and incorporated into maneuvering prediction mathematical models. The calculated fluid flow field around a body appendage configuration Elm)
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