Lagrangian tools for the analysis of mixing in single‐phase and multiphase flow systems

Abstract

Mixing is intrinsically a Lagrangian process and, while Eulerian data are very important, Lagrangian information is necessary for its complete description. Lagrangian data can, in principle, be generated by using numerical simulations or experimental techniques based on Lagrangian tracking to provide the trajectories of fluid elements or particles. We present a set of theoretical and computational tools specifically developed for the analysis and validation of single-phase and multiphase Lagrangian flow data obtained from tracer trajectories in mechanically agitated vessels. The implementation and power of these tools are demonstrated by analyzing a wide range of measurements acquired using the technique of positron emission particle tracking during mixing of Newtonian and non-Newtonian fluids as well as mixing of concentrated solid-liquid suspensions. Finally, the accuracy of the raw Lagrangian data treatment developed here is illustrated by comparing with an Eulerian technique and showing very precise mass continuity for an agitated solid-liquid system.

Positron emission particle tracking: A powerful technique for flow studies

“…Velocities and accelerations are determined from measured position-time coordinates (x, y, z; t) via an interpolation and differentiation algorithm. 4,7,8 Other parameters, such as occupancy, residence time, mixing indices, diffusion constants, vorticity and porosity, are also routinely determined from the measured coordinates.…”

Lagrangian particle tracking in mechanically agitated polydisperse suspensions: Multi-component hydrodynamics and spatial distribution

“…PEPT uses a single positron-emitting particle as a flow tracer which is then tracked in 3-D space and time to reveal its full Lagrangian trajectory. The measurements can be analysed in two different ways: a Lagrangian-statistical analysis exploiting concepts such as residence time, circulation time and trajectory length distribution; or, a (Guida et al, 2012). PEPT has been validated by comparing its measurements with PIV in water, and has been shown to be an accurate and reliable technique (Pianko-Oprych et al, 2009).…”

“…PEPT has been validated by comparing its measurements with PIV in water, and has been shown to be an accurate and reliable technique (Pianko-Oprych et al, 2009). More details about the technique can be found in our earlier papers (Barigou, 2004;Guida et al, 2009;Barigou et al, 2009;Guida et al, 2010aGuida et al, , 2011Guida et al, , 2012.…”

Lagrangian Recurrence Tracking: A Novel Approach for Description of Mixing in Liquid and Particle–Liquid Flows

“…Thus, each component in a multiphase particle–liquid flow can be labeled and its behavior 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 inside opaque apparatus with comparable accuracy. − …”

“…In addition to powerful experimental techniques such as PEPT, suitable theoretical methodologies are also crucial for interpreting experimental data in complex mixing flows. The vast majority of studies have focused on attempts to visualize flow patterns to obtain a qualitative description of mixing phenomena and measurements of global mixing time. ,− However, a more detailed localized and quantitative description in terms of dispersion, diversification, microscale and macroscale mixing, and flow structures is necessary to provide a better understanding of these complicated phenomena. Guida et al defined entropy mixing indices for quantifying local and global mixing based on the Shannon entropy of substance probability distribution and found that macromixing characteristic times calculated from 3D PEPT data agree very well with correlations of mixing time in the literature.…”