Journal of Pharmaceutical Innovation

, Volume 7, Issue 3–4, pp 181–194 | Cite as

DOE-Based CFD Optimization of Pharmaceutical Mixing Processes

  • Thomas Hörmann
  • Daniele Suzzi
  • Siegfried Adam
  • Johannes G. KhinastEmail author
Research Article


Fluid mixing and homogenization are key manufacturing processes in the pharmaceutical industry that in an industrial setting are typically optimized and adapted using empirical techniques rather than numerical methods. In the recent years, in silico techniques have increasingly attracted interest due to the many advantages and the increased information content. Computational fluid dynamics, for example, have often been applied to mixing problems. Although numerical flow simulations are nowadays common for simple applications, more complex cases (e.g., industrial mixing) still require much work to achieve reliable results with reasonable resources. In our work, we present an efficient procedure for optimizing the mixing performance of an unbaffled tank for pharmaceutical applications. The optimization objectives were the position of an impeller in the tank defined by the bottom clearance, the eccentricity of the impeller, the angle of the impeller shaft, and the impeller rotational speed. In order to generate a regression model for prediction of the optimal performance, design of experiments was used. Our optimization study showed that the impeller eccentricity had significantly more impact on mixing performance than the shaft angle, that the impeller speed was the main driver for the power input and the average shear forces, and that the bottom clearance may have strongly impacted the flow in the bottom tank area.


Mixing CFD simulation DOE Optimization 



Bottom clearance, in meters


Bottom clearance in base position, in meters


Impeller diameter, in meters


Off-center distance, in meters


Off-center distance in base position, in meters


Elliptic relaxation function


Gravitational acceleration, in meters per square second


Filling level, in meters


Turnover rate, per second


Turbulence kinetic energy per unit mass, in square meters per square second


Torque, in newton meters


Impeller rotational speed, in revolutions per minute


Power input by an impeller, in watts


Volumetric flow rate, in cubic meters per second


Goodness of prediction


Distance between center points, in meters


Goodness of fit


Reynolds number


Tank diameter, in meters


Mean tank diameter (cone-shaped tank), in meters


Cell volume of the computational cell i, in cubic meters


Total volume of the domain, in cubic meters


x-coordinate, in meters


y-coordinate, in meters


Impeller shaft angle, in degrees


Cone angle, in degrees


Volumetric mean shear rate, per second


Shear rate of a mesh cell i, per second


Normalized velocity scale


Kinematic viscosity, in square meters per second


Density of the liquid, in kilograms per cubic meter


Rotating angle concerning the z-axis, in radians


Rotating angle concerning the y-axis, in radians


Angular impeller velocity, per second



This work was performed as part of the K1 Competence Center program of the Federal Ministry of Transport, Innovation and Technology (BMVIT) and the Federal Ministry of Economy, Family and Youth (BMWFJ) and was funded by the Austrian Research Promotion Agency (FFG), the State of Styria, and Styrian Business Promotion Agency (SFG).


  1. 1.
    Armenante PM, Chang GM. Power consumption in agitated vessels provided with multiple-disk turbines. Ind Eng Chem Res. 1998;37:284–91.CrossRefGoogle Scholar
  2. 2.
    Armenante PM, Mazzarotta B, Chang GM. Power consumption in stirred tanks provided with multiple pitched-blade turbines. Ind Eng Chem Res. 1999;38:2809–16.CrossRefGoogle Scholar
  3. 3.
    Hörmann T, Suzzi D, Khinast JG. Mixing and dissolution processes of pharmaceutical bulk materials in stirred tanks: experimental and numerical investigations. Ind Eng Chem Res. 2011;50:12011–25.CrossRefGoogle Scholar
  4. 4.
    Armenante PM, Chou CC. Velocity profiles in a baffled vessel with single or double pitched-blade turbines. Aiche J. 1996;42:42–54.CrossRefGoogle Scholar
  5. 5.
    Hartmann H, Derksen JJ, Montavon C, Pearson J, Hamill IS, van den Akker HEA. Assessment of large eddy and RANS stirred tank simulations by means of LDA. Chem Eng Sci. 2004;59:2419–32.CrossRefGoogle Scholar
  6. 6.
    Lia M, White G, Wilkinson D, Roberts KJ. Scale up study of retreat curve impeller stirred tanks using LDA measurements and CFD simulation. Chem Eng J. 2005;108:81–90.CrossRefGoogle Scholar
  7. 7.
    Karcz J, Mackiewicz B. Effects of vessel baffling on the drowdown of floating solids. Chem Paper. 2009;63(2):164–71.CrossRefGoogle Scholar
  8. 8.
    Assirellia M, Bujalskia W, Eagleshamb A, Nienow AW. Macro- and micromixing studies in an unbaffled vessel agitated by a Rushton turbine. Chem Eng Sci. 2008;63(1):35–46.CrossRefGoogle Scholar
  9. 9.
    Zlokarnik M. Stirring—theory and practice. Weinheim: Wiley; 2001. ISBN 3-527-29996-3.Google Scholar
  10. 10.
    Paul EL, Atiemo-Obeng VA, Kresta SM, editors. Handbook of industrial mixing: science and practice. Hoboken: Wiley-IEEE; 2004.Google Scholar
  11. 11.
    Ochieng A, Onyango MS. CFD simulation of the hydrodynamics and mixing time in a stirred tank. Chem Ind Chem Eng Q. 2010;16:379.CrossRefGoogle Scholar
  12. 12.
    Song X, Zhang M, Wang J, Li P, Yu J. Optimization design for DTB industrial crystallizer of potassium chloride. Ind Eng Chem Res. 2010;49:10297–302.CrossRefGoogle Scholar
  13. 13.
    Hai S, Wenli G, Hui Z, Hongbo L, Jian L, Zheng L. Optimization of stirring parameters through numerical simulation for the preparation of aluminum matrix composite by stir casting process. J Manuf Sci Eng. 2010;132:7.Google Scholar
  14. 14.
    Murthy BN, Joshi JB. Assessment of standard k-e, RSM and LES turbulence models in a baffled stirred vessel agitated by various impeller designs. Chem Eng Sci. 2008;63:5468–95.CrossRefGoogle Scholar
  15. 15.
    Montante G, Lee KC, Yianneskis ABM. Numerical simulation of the dependency of flow pattern on impeller clearance in stirred vessels. Chem Eng Sci. 2001;56:3751–70.CrossRefGoogle Scholar
  16. 16.
    Derksen J. Assessment of large eddy simulations for agitated flows. Trans IChemE. 2001;79:824–30.CrossRefGoogle Scholar
  17. 17.
    Wang Y, Rao Q, Fan J and Fei W. PIV measurements and CFD simulation of viscous fluid flow in a stirred tank agitated by a Rushton turbine. In: 5th International Conference on CFD in the Process Industries.Google Scholar
  18. 18.
    Bakker A, LaRoche RD, Wang M and Calabrese RV. Sliding mesh simulation of laminar flow in stirred reactors. Online CFM Book. 2000; 1–8Google Scholar
  19. 19.
    Lamberto DJ, Alvarez MM, Muzzio FJ. Experimental and computational investigation of the laminar flow structure in a stirred tank. Chem Eng Sci. 1999;54(7):919–42.CrossRefGoogle Scholar
  20. 20.
    Aubin J, Fletcher DF, Xuereb C. Modeling turbulent flow in stirred tanks with CFD: the influence of the modeling approach, turbulence model and numerical scheme. Exp Thermal Fluid Sci. 2004;28:431–45.CrossRefGoogle Scholar
  21. 21.
    Deglon DA, Meyer CJ. CFD modelling of stirred tanks: numerical considerations. Miner Eng. 2006;19:1059–68.CrossRefGoogle Scholar
  22. 22.
    Kumaresan T, Joshi JB. Effect of impeller design on the flow pattern and mixing in stirred tanks. Chem Eng J. 2006;115(Issue 3):173–93.CrossRefGoogle Scholar
  23. 23.
    Hosseini S, Patel D, Ein-Mozaffari F, Mehrvar M. Study of solid–liquid mixing in agitated tanks through computational fluid dynamics modeling. Ind Eng Chem Res. 2010;49:4426–35.CrossRefGoogle Scholar
  24. 24.
    Ding J, Wang X, Zhou XF, Ren NQ, Guo WQ. CFD optimization of continuous stirred-tank (CSTR) reactor for biohydrogen production. Bioresour Technol. 2010;101:1005–13.Google Scholar
  25. 25.
    Korakianiti E, Rekkas D. Statistical thinking and knowledge management for quality-driven design and manufacturing in pharmaceuticals. Pharm Res. 2011;28:1465–79.PubMedCrossRefGoogle Scholar
  26. 26.
    Eriksson L, Johansson E, Kettaneh-Wold N, Wikström C, Wold S. Design of experiments—principles and applications. Umea: Umetrics Academy; 2008.Google Scholar
  27. 27.
    Ackoff R. Towards a system of systems concepts. Manage Sci. 1971;17:661–71.CrossRefGoogle Scholar
  28. 28.
    Lewis GA, Matieu D, Tan-Luu RP. Pharmaceutical experimental design. New York: Marcel Dekker; 1999.Google Scholar
  29. 29.
    Lepore J, Spavins J. Product quality lifecycle implementation (PQLI) innovations. PQLI design space. J Pharm Innov. 2008;3:79–87.CrossRefGoogle Scholar
  30. 30.
    AVL. AVL user manual, FIRE v2009, CFD solver manual; 2009.Google Scholar
  31. 31.
    Hanjalic K, Popovac M, Hadziabdic M. A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD. Int J Heat Fluid Flow. 2004;25:1047–51.CrossRefGoogle Scholar
  32. 32.
    Durbin PA. Near-wall turbulence closure modeling without ‘damping functions’. Theor Comput Fluid Dyn. 1991;3:1–13.Google Scholar
  33. 33.
    Holland FA, Bragg R. Fluid flow for chemical engineers. 2nd ed. Oxford: Butterworth-Heinemann; 1999.Google Scholar
  34. 34.
    Lundstedt T, Seifert E, Abramo L, Thelin B, Nyström A, Pettersen J, et al. Experimental design and optimization. Chemom Intell Lab Syst. 1998;42:3–40.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Thomas Hörmann
    • 1
  • Daniele Suzzi
    • 1
  • Siegfried Adam
    • 1
  • Johannes G. Khinast
    • 2
    Email author
  1. 1.Research Center Pharmaceutical Engineering GmbHGrazAustria
  2. 2.Institute for Process and Particle EngineeringGraz University of TechnologyGrazAustria

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