Turbulent mixing in a precessing sphere

By numerically simulating turbulent flows at high Reynolds numbers in a precessing sphere, we propose a method to enhance the mixing of a fluid confined within a smooth cavity by its rotational motion alone. To precisely evaluate the mixing efficiency, we extend the quantification method proposed by Danckwerts ["The definition and measurement of some characteristics of mixtures," Appl. Sci. Res. A 3, 279-296 (1952)] to the case in which only a finite number of fluid particle trajectories can be known. Our accurate numerical tracking of fluid particles in the flow, which is controlled by the Reynolds number (an indicator of the spin rate) and the Poincare number (the precession rate), shows the following results. First, the mixing process on the time scale normalized by the spin period is independent of the Reynolds number as long as it is high enough for the flow to be developed turbulence. Second, fastest mixing is achieved under weak precession (Poincare number approximate to 0.1); in such cases, perfect mixing requires only 10-15 spins of the container. Third, the power to sustain turbulence is a weakly increasing function of the Poincare number, and the energy efficiency of the mixing is also maximized when the Poincare number is about 0.1. Fourth, efficient mixing driven by the weak precession arises from the effective cooperation of complex large-scale flow and small-scale turbulence, which itself is sustained by the large-scale flow. (C) 2014 AIP Publishing LLC.