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

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.