Impact of impeller modelling approaches on SBES simulations of flow and residence time in a draft tube reactor
Graphical abstract
Introduction
A significant body of literature describes the modelling of baffled stirred tanks. Many turbulence and impeller modelling approaches have been used, but the use of Reynolds Averaged Navier Stokes (RANS) models with a Multiple Reference Frame (MRF) approach for the impeller is prevalent due to the high computational cost associated with large-eddy simulation (LES) and full sliding mesh approaches (see, for example the discussions in Yeoh et al. (2005), Fletcher and Brown (2009), Rave et al. (2021) and Tamburini et al. (2021).
Draft tube reactors with large height to diameter ratios have been far less frequently studied and modelling approaches have varied. Lane (2006) studied flow in an alumina precipitator using the turbulence model with a momentum source representing the impeller. He then applied an LES model but, due to the limited computational resources at the time, was only able to model one quarter of the vessel and used prescribed boundary conditions at the draft tube exit. Kumaresan and Thakre (2014) simulated an alumina precipitator using a Reynolds Stress turbulence model and both momentum source and MRF approaches for the impeller. The flow in a mechanically-agitated evaporative crystalliser with a draft tube was modelled using LES and a full sliding mesh approach by Derksen et al. (2007).
The current authors have modelled the flow and residence time in a draft tube reactor geometry extensively, using both RANS and scale-resolving turbulence models and a momentum source approach for the impeller (Brown et al., 2018, 2020, 2021). There was poor agreement with experimental data with RANS models, particularly for the exit residence time distribution. However, using scale-resolving approaches, good agreement with experimental data was achieved for both mean and fluctuating velocities in the annulus, and for tracer response curves at the vessel floor and exit, which was cited as validating the impeller modelling approach. The hypothesis advanced was that the large-scale turbulence dominating the flow in the annulus is generated at the separating shear layer at the draft tube exit, and that this would not be impacted by the fine-scale turbulence generated by the impeller, but further modelling was needed to confirm this.
This study directly addresses this point by comparing predictions for mean and fluctuating velocities, and exit residence time distribution (RTD) curves, obtained using a momentum source, with those obtained using MRF and sliding mesh approaches that fully resolve the impeller geometry in conjunction with the Stress Blended Eddy Simulation (SBES) turbulence model. The accuracy of the predictions will also be quantified through comparison with experimental data. The focus is to establish the best approach for industrial simulation, considering both accuracy and computational cost. There are few published studies applying the SBES model in complex internal flows, and a secondary objective is therefore to demonstrate this model works well in a complex internal flow featuring an impeller.
Section snippets
Validation data
Experimental data were obtained by CSIRO Minerals in a 1 m diameter laboratory-scale draft tube reactor in two studies commissioned by Alcoa (Nguyen et al., private communication, 2007, 2015). Water was used as the working fluid and the vessel was agitated by an axial-flow impeller with a Reynolds number based on impeller tip speed of ∼350,000. The experimental rig included straightening vanes immediately downstream of the impeller and re-suspension slots in the draft tube wall, consistent with
Mean and fluctuating velocities
Simulations were conducted for the closed vessel using momentum source, MRF and sliding mesh approaches. When using the MRF approach stage averaging was applied, which results in circumferential averaging of the velocity and all scalar fields at the exit of the impeller subdomain.
The momentum source and MRF simulations were run with a 0.01 s time step to meet a Courant number target of ∼1 in the bulk of the vessel (Brown et al., 2020; 2021). The sliding mesh simulations used a time step of
Conclusions
For the draft tube reactor geometry studied, good agreement can be obtained with experimental data for mean and fluctuating velocities in the annulus, and for the exit residence time distribution, using the scale-resolving SBES turbulence model in conjunction with a momentum source, MRF or full sliding mesh approach for the impeller. This confirms that the small-scale turbulence generated by the impeller has limited impact on the flow or mixing in the annulus, which is dominated by the
Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research has been supported by an Australian Government Research Training Program Scholarship and by Alcoa of Australia Limited. The authors acknowledge the contribution made by Dr Jie Wu, Dr Lachlan Graham and Mr Bon Nguyen of CSIRO who conducted the experimental study under contract to Alcoa.
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