(671b) A Multiscale Lagrangian Analysis of Turbulence in Agitated Tanks

Mixing aims to enhance the homogeneity of a single-phase or multiphase system through input of mechanical energy to achieve a desired process result. 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. 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. Therefore, theoretical methodologies for evaluation of mixing performance are crucial.

The process of mixing occurs at two different levels: micromixing and macromixing. Quantitative analysis at both levels is important for studying fluid mixing problems. Micromixing is achieved through molecular diffusion of individual species and eddy motion. Improper mixing on this level leads to segregation. Macromixing, on the other hand, relies on bulk or convective motion to distribute the materials to be mixed and reduce their local concentration gradients. These levels of mixing can be quantitatively assessed using 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. In PEPT, radio-labelled particles are used as flow followers and tracked in 3D space and time through positron detectors. 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 can provide the long-term 3D trajectories of all the components in a multiphase particle-liquid flow.

The new technique herein proposed is based on wavelet decomposition of Lagrangian trajectories provided by PEPT and is used to separate the mean (deterministic) and oscillatory (stochastic) parts of Lagrangian trajectories. The mean part includes low-frequency (non-diffusive; i.e., background motion) component while the 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 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 turbulent kinetic energies as well as turbulent diffusion coefficients, allowing the assessment of mixing on both the micro and macro levels (Fig. 1). 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 or other additives such as reactants.