In this work the hydrodynamics of an unbaffled vessel, stirred with a Rushton turbine located either coaxially or eccentrically are investigated by particle image velocimetry (PIV). The par- ticular flow features of the eccentric configuration are further investigated by RANS-based CFD simulations. The comparison of the results with the experiments has confirmed that unsteady RANS (URANS) simulations predict correctly the mean flow field in off-centre stirred vessels. In this case, the proper simu- lation strategy differs from that commonly adopted for baffled stirred vessels as well as from that devised for unbaffled vessels stirred coaxially.

2. Experimental

The investigation was carried out in a cylindrical tank (tank diameter, T = 23.6 cm, tank height, H = T ), made of Perspex, provided with a flat base and a lid on the top. Agitation was provided with a standard six bladed Rushton turbine (RT) of diameter D = T /3 placed at the distance C = T /2 from the vessel base (Fig. 1a). For the eccentric configuration, the shaft was located at 58 mm (E = T /4) from the vessel axis (Fig. 1b). The shaft and impeller were painted matt black to min-imise light reflection. The vessel was contained inside a trough filled with the working liquid, that was water at room temper- ature, in order to reduce the laser light refractive effects at the curved tank surface. The impeller rotational speed was  fixed at 400 rpm, corresponding to a velocity of the blade tip, Vtip, equal to 1.65 m/s, and producing an impeller Reynolds number,Re, equal to 4.1 × 104.

The  measurements  were  performed  using  a  Dantec  Dy-namics PIV system. The laser sheet source adopted was a pulsed Nd:YAG laser, emitting light at 532 nm with a maxi- mum frequency of 15 Hz. The image capturing was performed by a Dantec PCO Camera with a 1280×1024 pixel CCD, cooled by a Peltier module to improve the signal-to-noise ratio. The laser control, the laser/camera synchronisation and the data ac-

quisition and processing were handled by a hardware module (FlowMap System Hub) and FlowManager software installed on a PC. The liquid was seeded with silver-coated hollow glass particles of mean diameter equal to 10 µm. The seeding parti- cles concentration was carefully chosen in order to obtain from 5 to 10 particles for each interrogation area. The measurements were performed in several horizontal and vertical planes  and in each case 300 images were found to be sufficient for ob- taining the time averaged flow field. The cross-correlation of the image pairs was performed on a rectangular grid with 50% overlap between adjacent cells; the interrogation area was   set at 32 × 32 pixel and each image contained the whole horizontal or vertical vessel section. Particular care was used to eliminate

measuring error sources. For instance, the average pixel inten- sity was subtracted from each single image pair for reducing noise and the velocity vectors of magnitude bigger than Vtip were discarded. The vessel was closed with a lid on the top, in order to avoid uncertainties in the velocity measurements due to air bubbles entrainment.

Preliminary measurements were performed in order to assess the PIV set-up and data processing procedure. To this end the vessel described above was provided with removable baffles and coaxial stirrer and the measured mean velocities were com- pared with the corresponding LDA data collected by Brunazzi et al. (2003) in the same vessel and with the same turbine. The accuracy of the PIV data was found to be sufficiently high, as can be observed in Fig. 2, where the two mean radial velocity profiles normalised with Vtip  are shown.

3. CFD simulations

The simulations were performed running the finite volume general purpose CFD code FLUENT 6.2. The computational grid, that was refined in the region containing the impeller blades, where the biggest velocity gradients were expected, consisted of a total of about 314,000 hexahedral cells over a domain of 2n. A specific grid independency study was not per- formed on the basis of previous experience on stirred vessel simulations, suggesting that the present grid was fine enough for obtaining accurate result (e.g. Oshinowo et al., 2000; Mon- tante et al., 2001; Aubin et al., 2004). Wall boundary condi- tions with conventional “wall-functions” were adopted on the vessel bottom, the lateral wall and the top. A special treat- ment of the  water  surface,  such  as  that  devised  in Ciofalo et al. (1996) was not required, as the vessel was provided with a lid. This choice was made in order to avoid measurement er- rors and allowed us to separate experimental uncertainties from modelling problems. The RANS equations coupled with the standard k–n turbulence model or the Reynolds stress model (RSM), as implemented in the code, were numerically solved in a Cartesian coordinate system. The rotating reference frame where the agitator is steady was chosen for the inner part of the domain, containing the impeller, while a steady reference frame was used for the rest of the vessel. The steady-state mul- tiple reference frame (MRF) approach or the unsteady slid- ing mesh (SM) approach were adopted. For the MRF and the SM simulations, the extension of the internal and the exter- nal domains was identical. The vertical extension of the rotat- ing region was limited to the impeller vicinity—to about 2.5 times the blade height—for avoiding problems of artificial swirl (Oshinowo et al., 2000), while the diameter, imposed by the narrow space between the impeller and vessel wall, was taken equal to 1.25D. For the transient SM simulation, 329 impeller revolutions with 120 time steps per revolution have been run that correspond to about 50 s of real time. The solution con- vergence was carefully checked by monitoring the residuals of all variables as well as physical values of the swirl velocity. Residuals were dropped to the order of 10−4 or less, which is at least one order of magnitude tighter than Fluent’s default crite- ria. About 120 revolutions were necessary in order to obtain a fully developed flow field and further 80 revolutions were run to obtain a refined solution based on time monitoring of the volume-averaged tangential velocity as well as on the resid- uals value. After obtaining a fully developed flow field, 129 more impeller revolutions were calculated and the results were time averaged for performing a consistent comparison with the PIV data.