Mixing aims to enhance the homogeneity of a single phase or multiphase system through input of mechanical energy to achieve a desired process result.&nbsp; This is an important industrial operation which is often conducted in a mechanically agitated vessel 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.&nbsp; The design of mechanically agitated vessels, however, is still often as much an art as a science and for many applications it cannot be carried out from first principles.&nbsp; Therefore, theoretical methodologies for evaluation of mixing performance are vital.The process of mixing occurs at two different levels: micromixing and macromixing. Estimation of these two levels are crucial for studying problems associated with mixing of fluids. Micromixing level includes molecular diffusion of individual species and eddy motion. Improper mixing on this level leads to segregation. On the other hand, macromixing comprises bulk motion or convective motion and has a property of providing spread of materials needed for mixing. These levels of mixing can be estimated from decomposed Lagrangian trajectories of fluid elements or particles. 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 mixing levels in mechanically agitated vessels.&nbsp; In PEPT, radio-labelled particles are used as flow followers and tracked in 3D space and time through positron detectors.&nbsp; 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.&nbsp; Thus, PEPT provides the long-term 3D trajectories of all the components in a multiphase particle-liquid flow.For this purpose, a new technique is proposed for estimating micro and macromixing levels based on wavelet decomposition of Lagrangian trajectories provided by PEPT. This technique separates the mean (deterministic) and oscillatory (stochastic) parts of Lagrangian trajectories. The mean part includes low-frequency (non-diffusive; i.e., background motion) component while oscillatory part represents high-frequency (diffusive; i.e., eddies) component of the trajectory. 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.&nbsp; Detailed information is obtained on turbulent kinetic energies as well as turbulent diffusion coefficients, allowing the identification of mixing levels.&nbsp; Such detailed information is invaluable for unravelling the complexities of single and multiphase flows inside stirred vessels including the ability to identify optimal cells for injection or withdrawal of suspension.

Multiresolution Analysis of Lagrangian Trajectories in Multiphase Flow Mixing

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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