Instabilities and hydrodynamic origins of a freely moving spherical particle in Newtonian fluid by direct numerical simulation

Investigations of instabilities of a dynamical system consisting of a single spherical particle freely moving under the action of gravity in a Newtonian quiescent fluid are carried out by a direct numerical simulation method. To do this, the direct numerical simulation code, developed by Diaz-Goano et al. (2003), Veeramani et al. (2007) and Reddy et al. (2010) for Reynolds number (Re) under 210, has been modified to enable simulation Reynolds numbers up to 1800 and solid particle fluid density ratio in the range 0.08-4. Following its successful modification, the code was applied to identify successive transitions in particle trajectory and surrounding fluid vortex pattern. The simulation results were then used to explore the hydrodynamic origin of vortex-induced vibration (VIV) of the particle which were then related to the relevant vortex dynamics theory. With increase of Reynolds number, regimes of particle trajectory are identified as, (I) straight vertical, (II) straight oblique, (III) wavy oblique, (IV) zigzagging, (V) helical, (VI) early stage of chaotic, (VII) chaotic. The corresponding flow features are axisymmetric wake, counter-rotating streamwise vortex pairs in the wake, vortex rings, and eventual breakdown of symmetry (axisymmetric and planar) leading to the chaotic regime. A map of frequency spectrum is developed in terms of Re for both light and heavy particle, which indicates the heavy particle oscillations in a way of two-frequency modes since Re>250 and the light particle since Re>320. The low branch corresponds to the large-scale vortex shedding, and the high branch is associated with the presence of the small-scale vortex structure emanating from the free shear layer. The hydrodynamic origin of the zigzagging motion of the particle is investigated based on insights gained from the numerical simulation. The flow field represented by the pressure distribution, streamline pattern, vorticity distribution and vortical structure are carefully inspected at the Reynolds number of 294 and density ratio of 0.5, where the particle presents a planar zigzagging motion. The vortex system is decomposed into bound vortex and streamwise vortex. The bound vortex leads to a positive transverse force, while the streamwise vortex leads to a reduction of the transverse force. The contributions of the present Ph.D. study can be highlighted by the following points: (1) improvement of the previous DNS in-house code to make it adapted to simulations with high Reynolds number; (2) systematic identification of the scenario of transition to chaos; (3) establishment of the corresponding relationship between the particle oscillating trajection and the vortex pattern; (4) quantitatively discovery of the hydrodynamic origin of the vortex induced vibration (VIV).