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Transient torque in stirred tanks

Published online by Cambridge University Press:  13 October 2017

K. Steiros Open the ORCID record for K. Steiros [Opens in a new window]
K. Steiros*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: ksteiros@princeton.edu
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Abstract

The transient dynamics of stirred tanks whose impeller speed undergoes smooth or step changes is investigated. First, a low-order model is developed, linking the impeller torque with the ‘extent’ of the solid-body rotation in the tank, derived from an angular momentum balance in a control volume around the impeller. Utilisation of this model enables the prediction of the torque ‘spike’ appearing after an impulsive change of the shaft speed, and of the torque evolution during a quasi-steady transition. For the case of a small impulsive change in the shaft speed, a characteristic spin-up time is also proposed. Torque measurements performed in an unbaffled stirred tank show considerable agreement with the theoretical predictions.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Rotating turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 831 , 25 November 2017 , pp. 554 - 578
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Copyright
© 2017 Cambridge University Press 

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References

Başbuğ, S., Papadakis, G. & Vassilicos, J. C.2017 Reduced energy consumption in stirred vessels by means of fractal impellers. arXiv:1707.01730.Google Scholar
Benton, E. R. 1973 Nonlinear hydrodynamic and hydromagnetic spin-up driven by Ekman-Hartmann boundary layers. J. Fluid Mech. 57 (2), 337–360.Google Scholar
Benton, E. R. & Clark, A. 1974 Spin-up. Annu. Rev. Fluid Mech. 6, 257–280.Google Scholar
Busciglio, A., Caputo, G. & Scargiali, F. 2013 Free-surface shape in unbaffled stirred vessels: experimental study via digital image analysis. Chem. Engng Sci. 104, 868–880.Google Scholar
Furukawa, H., Kato, Y., Inoue, Y., Kato, T., Tada, Y. & Hashimoto, S. 2012 Correlation of power consumption for several kinds of mixing impellers. Intl J. Chem. Engng 2012, 1–6.Google Scholar
Gao, D., Acharya, S., Wang, Y. & Uhm, J. 2004 Flow field around Rushton turbine in stirred tank by particle image velocimetry measurement. Chin. J. Chem. Engng 12 (6), 843–850.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Laity, D. S. & Treybal, R. E. 1957 Dynamics of liquid agitation in the absence of an air-liquid interface. AIChE J. 3 (2), 176–180.CrossRefGoogle Scholar
Maynes, D. & Butcher, M. 2002 Steady-state and decay dynamics for impellers of varying aspect ratio in unbaffled tanks. AIChE J. 48 (1), 38–49.Google Scholar
Maynes, D., Klewicki, J. & Mcmurtry, P. 1999 Spin-up in a tank induced by a rotating bluff body. J. Fluid Mech. 388, 49–68.Google Scholar
Myers, K. J., Reeder, M. F. & Fasano, J. B. 2002 Optimize mixing by using the proper baffles. Chem. Engng Prog. 98, 42–47.Google Scholar
Nagata, S. 1975 Mixing: Principles and Applications. Wiley.Google Scholar
Roy, S. & Acharya, S. 2011 Scalar mixing in a turbulent stirred tank with pitched blade turbine : role of impeller speed perturbation. Chem. Engng Res. Des. 90 (7), 884–898.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 1979 Boundary Layer Theory. McGraw-Hill.Google Scholar
Steiros, K., Bruce, P. J. K., Buxton, O. R. H. & Vassilicos, J. C. 2017a Effect of blade modifications on the torque and flow field of radial impellers in stirred tanks. Phys. Rev. Fluids 2, 094802.Google Scholar
Steiros, K., Bruce, P. J. K., Buxton, O. R. H. & Vassilicos, J. C. 2017b Power consumption and form drag of regular and fractal- shaped turbines in a stirred tank. AIChE J. 63 (2), 843–854.Google Scholar
Winardi, S. & Nagase, Y. 1994 Characteristics of trailing vortex (discharged wake vortex) produced by a flat blade turbine. Chem. Engng Commun. 129 (1), 277–289.Google Scholar
Woziwodzki, S. 2011 Unsteady mixing characteristics in a vessel with forward-reverse rotating impeller. Chem. Engng Technol. 34 (5), 767–774.CrossRefGoogle Scholar
Yoon, H. S., Hill, D. F., Balachandar, S., Adrian, R. J. & Ha, M. Y. 2005 Reynolds number scaling of flow in a Rushton turbine stirred tank. Part I - mean flow, circular jet and tip vortex scaling. Chem. Engng Sci. 60 (12), 3169–3183.Google Scholar
Yoshida, M., Ito, A., Yamagiwa, K., Ohkawa, A., Abe, M., Tezura, S. & Shimazaki, M. 2001 Power characteristics of unsteadily forward - reverse rotating impellers in an unbaffled aerated agitated vessel. J. Chem. Technol. Biot. 76, 383–392.Google Scholar