Characterization of stirred vessel hydrodynamics by three dimensional trajectography

Abstract

A simple method has been developed to track the three-dimensional motion of a small particle convected in a stirred tank for about 1 h. Different flow patterns induced by a Rushton or a pitched blade turbine have been studied. The results have been compared with known results obtained by conventional techniques. Several tools which have been proposed for this purpose give rise to new insights and interpretation of transport and mixing processes in stirred tanks for engineering applications.On a mis au point une mCthode simple pour suivre le dtplacement tridimensionnel d'une petite particule dans un rCservoir agitC pendant environ 1 heure. DiffCrents profils d'tcoulement induits par une turbine Rushton ou h pales inclinkes sont CtudiCs. Les rksultats sont comparCs avec des rtsultats connus obtenus par des techniques traditionnelles. Plusieurs outils proposCs h cette fin permettent de mieux comprendre et interprtter les procCdts de transport et de mClange dans les rCservoirs agitCs pour des applications d'ingenierie. The RTD approach is easy to handle in open systems and allows to detect hydrodynamic problems such as short-cut flows or dead flow zones. The information provided by the RTD is however not sufficient because the technique considers the vessel as a black-box system and does not provide a description of the internal flows. It is not adapted to provide understanding and characterization of the interactions of multi-feed and multi-outlet flows and this is a strong limitation of the method. Furthermore, RTD may suggest different flow-models which can represent the same RTD but whose structures can be very different. 'Author to whom correspondence may be addressed. E-mail address: falh@en~ic.u-nancy.frThe first of these two approaches supplies a great amount of data which is, however, not easily applied and the second approach provides information which is condensed in a tractable -but not always adequate -way. The idea of trajectography, which consists of following the long-trajectory of a fluid particle tracer, is to provide an intermediate technique which can describe internal flows in a vessel together with giving condensed and tractable information on macromixing processes for engineers who have to make the link between hydrodynamics and mixing or chemical reactor performance. The concept is not totally new as several authors have characterized internal flow performance by trajectography. Rubinovitch and Mann (1983) studied the flow in inter-connected volumes, representing the movement of particles by a Markow chain. Information on the probability of visiting a volume and total residence time in the specific volumes could be given. The approach developed by Rubinovitch and Mann was, however very conceptual and has not been applied to real systems such as stirred vessels.Several tracking techniques, often 2 dimensional, have been developed to characterize hydrodynamics (Pervez and Solomon, 1994). PIV is a widely used technique for the measurement of velocity and vorticity fields in fine scale resolution,...

Mixing of dense binary suspensions: Multi‐component hydrodynamics and spatial phase distribution by PEPT

“…However, it can be mathematically shown that, if the probability of tracer visit is sufficiently high everywhere, ergodicity can be safely assumed when the trajectory of the tracer is recorded over a sufficiently long time so that adequate data resolution is achieved in every region. 13 In the flow system examined here, the probability of visit is well-distributed by virtue of the open geometry of the vessel where all regions are more or less equally accessible by the tracer, and the highly turbulent state of the sus- 10 5 ). Confirmation of the ergodicity assumption through experimental verifications has been reported in a previous article.…”

“…It has been argued for some time that Lagrangian data obtained from a single particle trajectory, where such data can be accurately determined, may unravel valuable mixing information which is not provided by Eulerian observations. [12][13][14][15][16][17] The technique of positron emission particle tracking (PEPT) allows noninvasive probing of opaque fluids and within opaque apparatus by using a single small sub-millimeter positron-emitting particle as flow tracer. 14,18 Being able to examine flow phenomena in three dimensions in dense opaque systems that could not be observed as effectively by using other techniques, PEPT is particularly useful for the study of nontransparent multiphase or multi-component flows, where one component can be selectively labeled and its behavior observed.…”

Using CFD to understand chaotic mixing in laminar stirred tanks

“…mensional 3-D laminar flows. One group Wittmer, 1998 has developed a method to track the 3-D position of a particle in a stirred vessel for about 1 h. However, a particle large enough to be detected is unlikely to follow the flow closely.…”

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

“…Other examples of quantities and maps that can be obtained by virtue of Lagrangian particle tracking are local and global entropy mixing indices 22 by using the Shannon entropy concept, the decorrelation time 8,22 by autocorrelating the particle tracer trajectory, and Poincaré maps 28 via a computational process based on the mathematical concept of Poincaré section and the solution of numerous systems of equations similar to the systems in Eqs. 11-13.…”

“…7 Experimental techniques which are effective in providing Lagrangian data in flow systems, however, are very limited. 8,9 A number of authors have shown that the analysis of Lagrangian data obtained from a single particle trajectory allows important mixing information to be obtained which is not measurable by Eulerian observations. Positron emission particle tracking (PEPT) represents a recent and improved addition to the experimental techniques available for Lagrangian studies, particularly useful for the very complex three-dimensional (3-D) flow fields found in agitated vessels.…”