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Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid

  • KAK NAMKOONG (a1), JUNG YUL YOO (a2) and HYOUNG G. CHOI (a3)
Abstract

The two-dimensional motion of a circular cylinder freely falling or rising in an infinite fluid is investigated numerically for the range of Reynolds number Re, < 188 (Galileo number G < 163), where the wake behind the cylinder remains two-dimensional, using a combined formulation of the governing equations for the fluid and the dynamic equations for the cylinder. The effect of vortex shedding on the motion of the freely falling or rising cylinder is clearly shown. As the streamwise velocity of the cylinder increases due to gravity, the periodic vortex shedding induces a periodic motion of the cylinder, which is manifested by the generation of the angular velocity vector of the cylinder parallel to the cross-product of the gravitational acceleration vector and the transverse velocity vector of the cylinder. Correlations of the Strouhal–Reynolds-number and Strouhal–Galileo-number relationship are deduced from the results. The Strouhal number is found to be smaller than that for the corresponding fixed circular cylinder when the two Reynolds numbers based on the streamwise terminal velocity of the freely falling or rising circular cylinder and the free-stream velocity of the fixed one are the same. From numerical experiments, it is shown that the transverse motion of the cylinder plays a crucial role in reducing the Strouhal number. The effect of the transverse motion is similar to that of suction flow on the low-pressure side, where a vortex is generated and then separates, so that the pressure on this side recovers with the vortex separation retarded. The effects of the transverse motion on the lift, drag and moment coefficients are also discussed. Finally, the effect of the solid/fluid density ratio on Strouhal–Reynolds-number relationship is investigated and a plausible correlation is proposed.

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Author to whom correspondence should be addressed: hgchoi@snut.ac.kr
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K. Y. Billah & R. H. Scanlan 1991 Resonance, Tacoma narrows bridge failure, and undergraduate physics textbooks. Am. J. Phys. 59, 118124.

H. G. Choi 2000 Splitting method for the combined formulation of the fluid-particle problem. Comput. Meth. Appl. Mech. Engng 190, 13671378.

U. Fey , M. König & H. Eckelmann 1998 A new Strouhal-Reynolds-number relationship for the circular cylinder in the range 47 < √ Re < 2 × 105. Phys. Fluids 10, 15471549.

M. Horowitz & C. H. K. Williamson 2006 Dynamics of a rising and falling cylinder. J. Fluids Struct. 22, 837843.

H. H. Hu , D. D. Joseph & M. J. Crochet 1992 Direct simulation of fluid particle motions. Theor. Comput. Fluid Dyn. 3, 285306.

H. H. Hu , N. A. Patankar & M. Y. Zhu 2001 Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169, 427462.

M. Jenny , G. Bouchet & J. Dušek 2003 Nonvertical ascension or fall of a free sphere in a Newtonian fluid. Phys. Fluids 15, L9L12.

M. Jenny & J. Dušek 2004 Efficient numerical method for the direct numerical simulation of the flow past a single light moving spherical body in transitional regimes. J. Comput. Phys. 194, 215232.

D. Karamanev , C. Chavarie & R. Mayer 1996 Dynamics of the free rise of a light solid sphere in liquid. AIChE J. 42, 17891792.

D. Karamanev & L. Nikolov 1992 Free rising spheres do not obey Newton's law for free settling. AIChE J. 38, 18431846.

Y. S. Nam , H. G. Choi & J. Y. Yoo 2002 AILU preconditioning for the finite element formulation of the incompressible Navier–Stokes equations. Comput. Meth. Appl. Mech. Engng 191, 43234339.

P. Nithiarasu & O. C. Zienkiewicz 2000 Adaptive mesh generation for fluid mechanics problems. Intl J. Numer. Meth. Engng 47, 629662.

H. A. Van Der Vorst 1992 Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 13, 631644.

C. H. J. Veldhuis , A. Biesheuvel 2007 An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid. Intl J. Multiphase Flow 33, 10741087.

C. Veldhuis , A. Biesheuvel , L. van Wijngaarden & D. Lohse 2005 Motion and wake structure of spherical particles, Nonlinearity 18, C1C8.

C. H. K. Williamson 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.

C. H. K. Williamson & G. L. Brown 1998 A series in 1/√ Re to represent the Strouhal-Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 10731085.

O. C. Zienkiewicz & J. Z. Zhu 1987 A simple error estimator and adaptive procedure for practical engineering analysis. Intl J. Numer. Meth. Engng 24, 337357.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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