The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Simulations of Forces Acting on a Cylinder in Oscillatory Flow by Direct Calculation of the Navier-Stokes Equations
Simulations of Forces Acting on a Cylinder in Oscillatory Flow by Direct Calculation of the Navier-Stokes Equations
Pages 313-328
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From page 313... ...
Hinatsu Ship Research Institute, Tokyo, Japan S Murashige University of Tokyo, Tokyo, Japan Abstract Flow around floating vessels sometimes accompanies separations, and is unsteady in ocean waves.
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From page 314... ...
carried out an analysis of a flow around a circular cylinder in an oscillatory flow at R-=1000 and K==5 and 7 using the finite difference method and showed qualitative agreement with observations. Objective of this paper is to accurately simulate instantaneous unsteady flow field around an oscillating circular cylinder and to estimate hydrodynamic forces acting on the circular cylinder quantitatively at R-=10000 and Kc=sm10 .
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From page 315... ...
In order to use the present computational scheme as a practical tool, we must determine the validity of it. We compare the computed results with the analytical solutions and examine effects of total number of grid points, minimum grid size, time increment, and the Reynolds number on the computed results.
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From page 316... ...
using the Euler explicit time differencing scheme. The flow chart of computation is shown in Fig.3.
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From page 317... ...
4.1 Hydrodynamic Forces Acting on a Circular Cylinder (l) In-Line Force Published experimental data of hydrodynamic forces are arranged by the drag coefficient, Cat, and the inertia coefficient, Cm, or the added mass coefficient, C^, where Cm=l+C~ ( see Appendix)
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From page 318... ...
The computed results of Cat and Can are shown in Figs.4.1 and 2 with experimental data of Sarpkaya[6] and Tanaka et al.[13]
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From page 319... ...
Here it should be noted that the Morison equation assumes an odd-harmonic in-line force, neglects higher frequency components and cannot express the experimental data in the range of K==8m 25. The first assumption means that the flow field repeats every half period of the oscillation.
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From page 320... ...
The peak value in the first half period is lower than that in the last half period. It means that the Morison equation can not express the experimental data well in this range of Kc as pointed out by Sarpkaya, who says that the range is 8 |
From page 321... ...
t=7.} (6) t=7.6 Fig.8.1 Vorticity contour, pitch=2.0, K==5 solid line: counterclockwise, broken line: clockwise 321
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From page 322... ...
. "N Fig.8.2 Vorticity contour, pitch=2.0, Kc=lO ·.
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From page 323... ...
Table 1 Effect of total number of grid points on Cat and C" (K==5, R.=104) r loo x 30 120 X50 140 X60 Cd 1.031 0.480 0.664 Ca 0.649 0.795 0.809 Figure 11 shows that the computed results by the grid 120 x50 and 140 x60 qualitatively agree with experimental data very well, but that those by the grid lOOx 30 do not agree with them.
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From page 324... ...
t=1.8 ~11~ Cal (c) 140x 60 Grid near the cylinder surface Vorticity contour Fig.11 Effect of total number of grid points on flow field (K==5, R.=10^, t=7.8)
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From page 325... ...
Table 3 shows that Cat and Can using ~t=O.OOO1 are not in the range of scatters of experimental data. Table 3 Effect of time increment on Cat and Can (K==5, R-=104)
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From page 326... ...
Solutions for the flow around an oscillating circular cylinder at R-=10000 and K==5,7 and 10 are obtained by the direct calculation of the Navier-Stokes equations using bodyfitted coordinates system, moving mesh technique, and the MAC method. The results are in excellent agreement with published experimental data quantitatively.
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From page 327... ...
(b) Flow around a Circular Cylinder Fixed in an Oscillatory Flow Assuming that the ambient flow oscillates in the x-direction, the governing equations are written as follows: ant + U0U + viny eat + UbV+ any _ _ asp + v( ~ 2 + a 2)
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From page 328... ...
, is related to the added mass coefficient, Can, which is defined in flow(a) as follows: (35)
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