Abstract：The aim of this work is to investigate the effect of the shaft eccentricity on the hydrodynamics of unbaffled stirred vessels. The difference between coaxial and eccentric agitation is studied using a combination of experiments carried out by particle image velocimetry, that provide an accurate representation of the time-averaged velocity, and computational fluid dynamics simulations, that offer a complete, transient volumetric representation of the three-dimensional flow field, once a proper modelling strategy is devised. The comparison of the experimental and simulated mean flow fields has demonstrated that calculations based on Reynolds-averaged Navier–Stokes equations are suitable for obtaining accurate results. Depending on the position of the shaft, steady-state or transient calculations have to be chosen for predicting the correct flow patterns. Care must be exerted in the choice of turbulence models, as for the unbaffled configurations the results obtained with the Reynolds stress model are superior to that of the k–n  model.

Keywords: Fluid mechanics; Hydrodynamics; Mixing; Simulation; Eccentric agitation; Unbaffled vessel; PIV

1. Introduction

Nowadays, computational fluid dynamics (CFD) simulations based on the solution of Reynolds-averaged Navier–Stokes equations (RANS) are feasible tools for design and optimisa- tion of several apparatuses of chemical and process industry (Joshi and Ranade, 2003, Bakker et al., 1994a,b). In the past decade, many efforts have been devoted to the development of mathematical models for CFD and the capabilities of the models in predicting equipment fluid dynamics have often been assessed through the comparison with experimental data. After many years of investigations, the potential of RANS calculations to simulate the flow field in stirred vessels have been widely inspected: satisfactory predictions of the mean flow field of single-phase, baffled stirred tanks have been obtained (Brucato et al., 1998), while poor results are often achieved for the turbulent characteristics of the flow (Ng   and Yianneskis, 2000). In the earlier studies, the simulations of baffled stirred vessels were performed using “black box” meth- ods, that require experimental data as boundary conditions (e.g. Ranade et al., 1989). The successful development of ap- propriate fully predictive strategies, as reviewed by Brucato et al. (1998), has allowed to overcome the need of preliminary experimentation and has opened the way for the adoption of CFD for the selection and the design of stirred vessels. For the simulation of single-phase baffled stirred vessels, the more appropriate mathematical models and computational strategy to adopt when using RANS-based CFD codes is presently fairly well known. From a geometrical point of view, the un- baffled vessels are simpler than the baffled ones. Therefore, it could be presumed that reliable forecasts of the fluid dy- namics of such apparatuses are obtainable just by solving the same mathematical models that were proved to be suitable for baffled vessels, but without the need of resorting to particular simulation strategies, thus reducing the computational cost and complexity. However, previous works have already assessed that the simulation of unbaffled stirred tanks is not an easy task (Armenante et al., 1997; Ciofalo et al., 1996). Nevertheless, the unbaffled stirred tank configuration has been adopted as a test case for two-equation turbulence models instead of the baffled case due to the geometrical simplicity (Jones et al., 2001) and treated in the same way as baffled tanks (Murthy and Jayanti, 2002). A review on the modelling of unbaffled stirred vessels can be found in Alcamo et al. (2005), who performed large eddy simulations (LES) of an unbaffled stirred vessel pro- vided with a coaxial impeller and obtained satisfactory results in terms of both mean and turbulent characteristics of the flow. Generally, scarce information concerning unbaffled stirred ves- sels provided with coaxial mixers is available, although unbaf- fled vessels are sometimes used in industrial practice, e.g. when fouling on the vessel internals is to be limited or for mixing of very viscous materials (Novak and Rieger, 1994). Eccentric configurations have been even less studied, but probably they have a wider practical interest, as the off-centre impeller posi- tioning improves the mixing performance with respect to that of centred impellers (Hall et al., 2004) while being featured by smaller surface vortexing. The effect of impeller eccentricity on mixing has been experimentally investigated in a few works (e.g. Nishikawa et al., 1979; Medek and Fort, 1985; Karcz et al., 2005; Hall et al., 2005), but knowledge on these systems is still rather incomplete. For the laminar regime, the effect of the shaft position on the flow field has been experimentally investi- gated by Alvarez et al. (2002), who found important changes in the flow structure and major enhancement in mixing behaviour even for low eccentricity conditions. On the computational side, Rivera et al. (2004) have already pointed out that off-centred im- pellers pose particular simulation difficulties. They performed the simulations of eccentric mixer configurations in laminar regime, while to the best of our knowledge validated simula- tions of eccentric stirred vessels in the turbulent flow regime have not been published in the open literature to  date.