Abstract
In this paper, we performed a comparison of four turbulence models using for numerical simulation of the hydrodynamic structure generated by a Rushton turbine in a cylindrical tank. The finite volume method was employed to solve the Navier-Stokes equations governing the transport of momentum. In this study four closure models tested were: k-ɛ standard, k-ɛ RNG, k-ɛ Realizable and RSM (Reynolds Stress Model). MRF (Multi Reference Frame) technique was used with FLUENT software package. The present work aimed to provide improved predictions of turbulent flow in a stirred vessel and in particular to assess the ability to predict the dissipation rate of turbulent kinetic energy (e) that constitutes a most stringent test of prediction capability due to the small scales at which dissipation takes place. The amplitude of local and overall dissipation rate is shown to be strongly dependent on the choice of turbulence model. The numerical predictions were compared with literature results for comparable configurations and with experimental data obtained using Particle Image Velocimetry (PIV). A very good agreement was found with regards to turbulence.
[1] Brucato A., Ciofalo M., Grisafi F., Micale G., Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modelling approaches, Chemical Engineering Science 1998, 53,21, 3653–3684 http://dx.doi.org/10.1016/S0009-2509(98)00149-310.1016/S0009-2509(98)00149-3Search in Google Scholar
[2] Jaworski Z., Zakrazewska B., Modeling of the turbulent wall jet generated by a pitched blade turbine impeller. The effect of turbulence model, Trans Ichem. E 2002, 80 10.1205/026387602321143381Search in Google Scholar
[3] Kumaresan T., Joshi J.B., Effect of impeller design on the flow pattern and mixing in stirred tanks, Chemical Engineering Science 2006, 115, 173–193 http://dx.doi.org/10.1016/j.cej.2005.10.00210.1016/j.cej.2005.10.002Search in Google Scholar
[4] Murthy N.B., Joshi J.B., Assessment of standard k-ɛ RSM and LES turbulent models in a baffled stirred agitated by various impeller designs, Chemical Engineering Science 2008, 63, 5468–5495 http://dx.doi.org/10.1016/j.ces.2008.06.01910.1016/j.ces.2008.06.019Search in Google Scholar
[5] Yakhot V., Orsgaz S.A., Renormalization group and local order in strong turbulence, Nuclear Physics B. Proceedings Supplements 1987, 2, 417–440 http://dx.doi.org/10.1016/0920-5632(87)90031-410.1016/0920-5632(87)90031-4Search in Google Scholar
[6] Orsgaz A., Yakhot V., Recent ideas on turbulence transport modeling, in 2nd world conference in Applied CFD 1994, 8.1–8.7 Search in Google Scholar
[7] Kelly W., Gigas B., Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime, Chemical Engineering Science 2003, 58, 2141–2152 http://dx.doi.org/10.1016/S0009-2509(03)00060-510.1016/S0009-2509(03)00060-5Search in Google Scholar
[8] Shih T.H., Liou W.W., Shabbir A., Zhu J., A New k-ɛ Eddy-Viscosity Model for High Reynolds Number Turbulent Flows Model Development and Validation, Computers Fluids, 1995, 24(3), 227–238 http://dx.doi.org/10.1016/0045-7930(94)00032-T10.1016/0045-7930(94)00032-TSearch in Google Scholar
[9] Launder B.E., Spalding D.B., Progress in the Development of a Reynolds Stress turbulence closure, J.Fluid. Mech 1974, 68(3), 537–566 http://dx.doi.org/10.1017/S002211207500181410.1017/S0022112075001814Search in Google Scholar
[10] Eggels J.G.M., Direct and large-eddy simulation of turbulent fluid flow using the lattice-Boltzmann scheme. International Journal of Heat and Fluid Flow 1996, 17, 307–323 http://dx.doi.org/10.1016/0142-727X(96)00044-610.1016/0142-727X(96)00044-6Search in Google Scholar
[11] Derksen J.J., Van den Akker H.E.A., Large-eddy simulations on the flow driven by a Rushton turbine. A.I.Ch.E, Journal 1999, 45, 209–219 10.1002/aic.690450202Search in Google Scholar
[12] Bakker A., Oshinowo L.M., Marshall E. M., The Use of Large Eddy Simulation to Eddy Simulation to Study Stirred Vessel Hydrodynamics, Proceeding of the 10th European Conference on Mixing, Delft, The Netherlands 2000, July 2–5, 247–254 10.1016/B978-044450476-0/50032-7Search in Google Scholar
[13] Roussinova C., Kresta S.M., Weetman R., Low frequency macroinstabilities in stirred tank: scale-up and prediction based on large eddy simulations, Chemical Engineering 2003, 58, 2297–2311 http://dx.doi.org/10.1016/S0009-2509(03)00097-610.1016/S0009-2509(03)00097-6Search in Google Scholar
[14] Hartmann H., Derksen J.J., Montavon C., Pearson J., et al., Assessment of large eddy and RANS stirred tank simulations by means of LDA, Chemical Engineering Science 2004, 52, 2419–2432 http://dx.doi.org/10.1016/j.ces.2004.01.06510.1016/j.ces.2004.01.065Search in Google Scholar
[15] Yeoch M., Papadakis G., Yianneskis G., Numerical simulation of turbulent flow characteristics in a stirred vessel using the LES and RANS approaches with the sliding deforming mesh methodology, Chemical Eng. Research and Design 2004, 82, 834–848 http://dx.doi.org/10.1205/026387604159675110.1205/0263876041596751Search in Google Scholar
[16] Alcamo R., Micalea G., Grisafia F., Brucatoa A., et al., Large-eddy simulation of turbulent flowing an unbaffled stirred tank driven by a Rushton turbine, Chemical Engineering Science 2005, 60, 2303–2316. http://dx.doi.org/10.1016/j.ces.2004.11.01710.1016/j.ces.2004.11.017Search in Google Scholar
[17] Derksen J.J., Assessment of large eddy simulations for agitated flows. Chemical Engineering Research & Design 2001, 79, 824–830 http://dx.doi.org/10.1205/0263876015272133410.1205/02638760152721334Search in Google Scholar
[18] Derksen J.J., Kontomaris K., McLaughlin J.B., Van den Akker H.E.A., Largeeddy simulation of single-phase flow dynamics and mixing in an industrial crystallizer, Chemical Engineering Research & Design 2007, 85, 169–179 10.1205/cherd06025Search in Google Scholar
[19] Aubin J., Fletcher D., Xuereb C., Modelling turbulent flow in stirred tanks with CFD: the influence of the modelling approach, turbulence model and numerical schema, Experimental Thermal and Fluid Science 2004, 28, 431–445 http://dx.doi.org/10.1016/j.expthermflusci.2003.04.00110.1016/j.expthermflusci.2003.04.001Search in Google Scholar
[20] Abujelala M.T., Lilley D.G., Limitations and empirical extensions of the k-ɛ model as applied to turbulent confined swirling flows, Chemical Engineering Communications 1984, 31, 223–236 http://dx.doi.org/10.1080/0098644840891115210.1080/00986448408911152Search in Google Scholar
[21] Armenante P.M., Chou C.C., Velocity profiles in a baffled vessel with single or double pitchedblade turbines, AIChE Journal 1997, 42, 42–54 http://dx.doi.org/10.1002/aic.69042010610.1002/aic.690420106Search in Google Scholar
[22] Jenne M., Reuss M., A critical assessment on the use of k-ɛ turbulent models for simulation of the turbulent liquid flow induced by a Rushtonturbine in a baffled stirredtank reactor, Chemical Engineering Science 1999, 54, 3921–3942 http://dx.doi.org/10.1016/S0009-2509(99)00093-710.1016/S0009-2509(99)00093-7Search in Google Scholar
[23] Patankar S.V., Numerical heat transfer and fluid flow 1980, Mc Graw Hill Search in Google Scholar
© 2011 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.