The Effect of Liquid Viscosity on the Polygonal Instabilities Observed within Hollow Vortex Core.

摘要

The dynamics of liquid vortices generated by rotating a flat disc near the bottom of a cylindrical tank is investigated experimentally. Several former investigations have found that the main parameters affecting the flow behaviour are incorporated in two non-dimensional numbers: Reynold's number and the aspect ratio. Despite some evidence of the important role of fluid viscosity on the polygonal pattern instability behaviour observed within the hollow vortex core, a systematic study has not yet been carried out. This thesis examines the role of viscosity in the development, evolution, wave speed propagation and the overall transition of vortex core instabilities. The data analysis was performed using the digital image processing technique. Increasing the viscosity of the fluid by mixing glycerol with tap water at room temperature, was found to significantly decrease the polygonal patterns' limits of endurance and distort their geometry until all mode shapes were eventually destroyed and never recognized, beginning with high mode shapes progressively until the lower polygonal patterns are reached. Increasing the fluid viscosity to 22 times that of water resulted into an up to 25% augmentation of the maximum polygonal pattern speed. In all cases, the pattern speed (fp ) was found to be almost 1/3 the disc speed (fd), which confirms the pure water results obtained by Vatistas et al. (2008). The effect of varying the viscosity on the transitional processes between subsequent polygonal patterns is also addressed in this thesis. Alike to the case of pure water, the transition between polygonal patterns is found to occur in two stages: a quasi-periodic phase followed by frequency locking.