Mass and Moment of Inertia Govern the Transition in the Dynamics and Wakes of Freely Rising and Falling Cylinders

Varghese Mathai, Xiaojue Zhu, Chao Sun, Detlef Lohse
2017 Physical Review Letters  
In this Letter, we study the motion and wake-patterns of freely rising and falling cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid m^* ≡ρ_p/ρ_f and its relative moment-of-inertia I^* ≡I_p/I_f. This supersedes the current understanding that a critical mass density (m^*≈ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144
more » ... nations of m^* and I^*, we comprehensively map out the parameter space covering very heavy (m^* > 10) to very buoyant (m^* < 0.1) particles. The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, St_t ≈ 0.17. St_t separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical 2S (2-Single) vortex mode to a 2P (2-Pairs) vortex mode. Thus, auto-rotation can have a significant influence on the trajectories and wakes of freely rising isotropic bodies.
doi:10.1103/physrevlett.119.054501 pmid:28949731 fatcat:kif5aweotbhuzjmzlpwn7wvsmm