(380g) Quantifying Mixing in Multiphase Flows Via Lagrangian-Recurrence Tracking

Mixing is a physical process which aims at reducing non-uniformities in a single-phase or a multiphase system through dissipation of mechanical energy to achieve a desired process result. This is an important industrial operation which is often conducted in mechanically agitated vessels on a wide range of scales, and is critical to the successful manufacturing of numerous products including fine chemicals, pharmaceuticals, personal/home care products, paper and pulp, polymers, food, and the formulation of products for these sectors. The design of mechanically agitated vessels, however, is still often as much an art as a science and for many applications a global black-box approach is often adopted as it is hard to obtain detailed accurate information to describe the internal flow. Therefore, theoretical methodologies for unravelling information about such complex flows to help evaluate mixing performance are of crucial importance.

Traditional mixing performance indicators are generally based on Eulerian data which are often unable to capture the detailed hidden features of what is intrinsically a Lagrangian process. Abundant information resides in the Lagrangian trajectories of fluid elements or particles, which can provide better and more detailed distributed description of the relevant mixing phenomena which determine the degree of mixedness. Over a long period of time, the trajectory of a particular phase in mixing system tends to recur repeatedly in a form close to that of its initial state. On the basis of this principle, we exploit Lagrangian experimental data obtained by a unique technique of positron emission particle tracking (PEPT) to develop a new methodology for characterizing mixedness in mechanically agitated vessels. In PEPT, radio-labelled particles are used as flow followers and tracked in 3D space and time through positron detectors. Thus, each component in a multiphase particle-liquid flow can be labelled and its behaviour observed.

Compared with leading optical laser techniques (e.g. LDV, PIV), PEPT has the enormous and unique advantage that it can image opaque fluids, and fluids inside opaque apparatus with comparable accuracy. Thus, PEPT provides the long-term 3D trajectories of all the components in a multiphase particle-liquid flow. By considering the recurring states of the PEPT trajectories and the positions at which these recurrences occur, a new data-driven approach is developed for the description of global and local mixing. For this purpose, a windowing recurrence quantification analysis of the phase trajectories is performed based on the Shannon entropy of the probability distribution of diagonal lines of recurrence structures, which leads to a detailed ‘pointwise’ description of mixedness in the multiphase flow (Figures 1-2). The implementation and potential of this new method are demonstrated by analysing long-term PEPT trajectories tracked in single-phase liquid as well as particle-liquid suspensions inside a 30 cm diameter vessel agitated by a six pitched-blade turbine operating in both up- and down-pumping configurations over a wide range of experimental conditions. Detailed information is obtained on global as well as local mixedness, allowing the identification of well-mixed and poorly-mixed cells. Such detailed information is invaluable for unravelling the complexities of multiphase flows inside stirred vessels including the ability to identify optimal cells for injection or withdrawal of suspension.