Visualization study and quantitative velocity measurements in turbulent taylor-couette flow by phantomm flow tagging: a description of the transition to turbulence

Abstract

A visualization study and Quantitative velocity measurements have been performed in Taylor-Couette flow with a medium-gap (c= 0.356), over a large range of Taylor numbers (2.1x104 < Ta < 1.1x1011), with the outer cylinder fixed and the inner cylinder rotating about its axis. Quantitative velocity measurements were carried out using the PHANTOMM flow tagging technique. Two techniques were used for visualization study: the PHANTOMM technique that allowed flow structure visualization from small to moderate Taylor numbers, and the Particle Streak Imaging, PSI (the flow was seeded with neutrally buoyant polystyrene micro spheres) that permitted the flow structure visualization from moderate to high Taylor numbers. The results illustrate the expected three-dimensional features of flow and presence of Taylor cells at low Taylor numbers. Our study examined the interplay between small and large scales present in the flow as well as showed the gradual transition to turbulence with increasing Taylor numbers. Taylor cells were found for Taylor numbers less than 1.13 x 1010. At low Taylor numbers, the flow in the cells appeared to be a rotational laminar flow with a high degree of coherence. At higher Taylor numbers, the cells aspect became more irregular, and the flow inside them became turbulent. The Gortler instability developed inside Taylor cells and close to the inner cylinder wall. At the highest Taylor numbers, turbulence increased up to the point where no Taylor cells could be detected. For the flow in our study, at Ta = 1.13 x 1010, the homogenization by turbulence spread across the gap, and the flow structure sharply changed its pattern as a toroidal vortex in helical motion developed in a thin layer on the inner cylinder wall. Instantaneous velocities, average velocities, angular-momentum ratio and spectral density function were computed for all ranges of Taylor numbers in the range studied. These quantitative results show the same conclusions as the ones presented by the visualization study