On the main flow features and instabilities in an unbaffled vessel agitated with an eccentrically located impeller
Introduction
Mixing is one of the most common unit operations in the process industry and it is typically achieved in stirred tanks. These are usually equipped with baffles in order to promote small scale mixing by breaking the primary vortex. Indeed most of the research on stirred vessels focuses on baffled configuration (Tatterson, 1991; Harnby et al., 1997; Paul et al., 2004).
However, there are applications where unbaffled vessels are preferred, as for instance in food and pharmaceutical industry where cleaning is a major issue (Assirelli et al., 2008) or as in crystallisation because baffles can damage growing particles or as in laminar regime where baffles can cause the formation of dead regions. Most of the available literature on unbaffled vessels concerns this latter application. Among others, Lamberto et al. (1996) and Alvarez et al. (2002) pointed out that the unbaffled stirred vessels were not optimised with large waste of power, because of the presence of large poor mixing regions with a typical toroidal shape, located both above and below the impeller plane. Therefore, two different strategies have been suggested in order to improve mixing in unbaffled vessel in the laminar regime: the use of variable speed protocols (Lamberto et al., 1996) and the eccentric position of the shaft (Alvarez et al., 2002). The second strategy performs better as it enhances the axial circulation in the tank destroying the toroidal segregated regions and the separation plane between the upper and lower part of the vessel. This was noted even for impellers without blades (see the disc impeller of Alvarez et al., 2002) and this finding was exploited lately by Sánchez Cervantes et al. (2006) who suggested a disc impeller in eccentric position for the culture of suspended mammalian cells; in this manner mixing conditions are ensured with low mechanical stresses, so that damage to the cells is limited (Aloi and Cherry, 1996). Recently a combination of two eccentric impellers was studied for single-phase (Ascanio and Tanguy, 2005) and gas–liquid (Cabaret et al., 2008) systems with both Newtonian and non-Newtonian fluids.
Only a few works regard eccentric agitation for turbulent flows, even though this operation mode is also suggested in the industrial practice (e.g. paint and food processes, Karcz et al., 2005) in alternative to baffles to break the primary vortex. Eccentric agitation for turbulent flows was pioneered by Kramers et al. (1953), Nishikawa et al. (1979) and Medek and Fort (1985). Kramers et al. carried out a comparative study on the rate of mixing and power consumption of three kinds of agitators, a three-blade marine impeller and two-impeller type agitators. Nishikawa et al. evaluated the effect of eccentricity on mixing time of a paddle impeller, whereas Medek and Fort determined energetic efficiencies for different eccentricity values and number of baffles.
More recently Karcz et al. (2005) investigated an unbaffled tank stirred by a propeller placed at different eccentric positions from to 0.285. The authors carried out comprehensive computer-aided mixing time measurements, showing the strong decrease of mixing time with increasing the impeller eccentricity. They also provide shear rate, friction and heat transfer coefficients at the vessel walls. Recently, their investigation was extended to different types of eccentrically located impellers (e.g. radial, axial and mixed flow) (Karcz and Cudak, 2006; Cudak and Karcz, 2006, Cudak and Karcz, 2008).
Hall et al. (2005a) investigated with particle image velocimetry (PIV) the best configuration of small tanks (high throughput experimentation reactors, HTE) stirred by an up-pumping pitched blade turbine with blades inclined by . In particular the authors considered both baffled and unbaffled configurations with centric agitation, as well as unbaffled eccentric agitation. Mean flow field, rms and turbulent kinetic energy distribution were provided. The authors showed that eccentricity improves the axial motion which becomes comparable to baffled configuration. In addition the eddy dissipation rate was evaluated across the vessel through the Smagorinsky sub-grid scale (SGS) model. Planar induced fluorescence (PLIF) was also used in the same work to evaluate mixing times which indicated eccentric agitation to perform better than baffled agitation. In a later work of the same group the eccentric agitation was discussed also for gas–liquid application of HTE reactors (Hall et al., 2005b).
Recently, Montante et al. (2006) used both PIV and computational fluid dynamics (CFD) to analyse the flow field in a vessel stirred by a Rushton turbine placed eccentrically and for . The authors showed that the flow field was characterised by two vortices, departing from the impeller towards the top and the bottom of the vessel, and inclined with respect to the vertical plane. The authors addressed also numerical issues and suggested the use of transient calculations (unsteady RANS) for the CFD prediction of eccentric agitation operation. Actually steady RANS approaches can give satisfactory results for unbaffled vessel with centric agitation if coupled with direct turbulence model (Reynolds stress model), but steady RANS predictions for eccentric agitation are always poor. As far as eccentric agitation is concerned, modelling difficulties were also pointed out by Rivera et al. (2004).
Laser Doppler Anemometry (LDA) was used by Wang et al. (2006) to determine mean flow and turbulent characteristics (turbulent kinetic energy and Reynolds stresses) induced by a semi-ellipse impeller placed in eccentric position in a rectangular vessel.
In the present work two experimental techniques, LDA and flow visualisation, are combined in order to determine the main flow features in an unbaffled vessel agitated by a Rushton turbine in eccentric position and in turbulent regime. An analysis is also performed on the various instabilities which were found to characterise the flow. Indeed flow instabilities in stirred vessels have received much attention in the last decade and their implication on meso- and macro-mixing have been investigated (see among others Roussinova et al., 2003; Galletti et al., 2003; Ducci and Yianneskis, 2007; Paglianti et al., 2006). However, to our knowledge no indication of instabilities in unbaffled vessel with eccentric agitation is reported in the literature.
Section snippets
Experimental apparatus
Measurements were performed in a cylindrical vessel made of Perspex with inner diameter . The vessel was filled with distilled water up to a height of and was covered with a lid (equipped with plugs of different sizes) in order to avoid air entrainment. The agitation was provided by a standard Rushton turbine with . The impeller blade thickness to diameter ratio was . The impeller was positioned in an off-axis location, at a distance of , i.e., , from the
Measuring system
Measurements were performed with a single-component LDA operating in back scatter mode. A pair of blue beams () was separated from a 3 W Argon-ion Spectra Physics laser through a Bragg cell which provided also frequency shifting. The scattered light is transmitted by means of optical fibres to photo-multipliers and then processed by a Dantec Burst Spectrum Analyser. The measurement volume was an ellipsoid with a diameter of 0.141 mm and a length of 3.7 mm. The working fluid was seeded with
Flow visualisation results
Fig. 2 shows a typical flow visualisation image taken from view A (Fig. 1b). Two main vortices occur, one above and one below the impeller plane. These vortices will be denoted as upper vortex (UV) and lower vortex (LV), respectively. The former vortex shows an axis deviating from the -axis, whereas the second vortex axis is almost coincident with the -axis if seen from above. This is confirmed by Fig. 3a which shows the stirred vessel from view B (Fig. 1b). The vortex above the impeller,
Discussion and conclusions
An experimental investigation of an unbaffled stirred vessel with eccentric impeller configuration is presented. LDA is combined to flow visualisation in order to determine the main flow features. Two main vortical structures, one above and one below the impeller have been observed. The former vortex departs the impeller towards the top of the vessel and it is inclined at with respect to the vertical plane near the impeller and far away. Such vortex leads to a strong circumferential flow
Notation
impeller off-bottom clearance, defined as the distance between the vessel base and the middle of the impeller blades, m impeller diameter, m shaft diameter, m eccentricity, i.e., distance of the shaft from the vessel axis, m energy, energy associated with cyclic variation due to the blade passage, energy associated with the lower vortex, energy associated with the vortex shedding, energy associated with the upper vortex, total kinetic energy along
Acknowledgements
This work was financially supported by the Italian Ministry of University and Education (FIRB 2001, PRIN 2005). The collaboration of Ms. Diana Di Marco in carrying out the experimental programme and of Messrs. Sandro Pintus and Cesare Merello for the technical support on the LDA and experimental set ups are gratefully acknowledged. We thank also Prof. Michael Yianneskis for the useful discussion on macro-instabilities.
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