32. Haringa C, Tang W, Deshmukh AT, Xia J, Reuss M, Heijnen JJ, Mudde RF, Noorman HJ
(2016) Euler-Lagrange computational fluid dynamics for (bio)reactor scale down: an analysis of
organism lifelines. Eng Life Sci 16(7):652–663. https://doi.org/10.1002/elsc.201600061
33. Liu Y, Wang ZJ, Xia JY, Haringa C, Liu YP, Chu J, Zhuang YP, Zhang SL (2016) Application
of Euler–Lagrange CFD for quantitative evaluating the effect of shear force on Carthamus
tinctorius L. cell in a stirred tank bioreactor. Biochem Eng J 114:209–217. https://doi.org/10.
1016/j.bej.2016.07.006
34. Gunyol O, Mudde RF (2009) Computational study of hydrodynamics of a standard stirred tank
reactor and a large-scale multi-impeller fermenter. Int J Multiscale Comput Eng:559–576.
https://doi.org/10.1615/IntJMultCompEng.v7.i6.60
35. Coroneo M, Montante G, Paglianti A, Magelli F (2011) CFD prediction of fluid flow and
mixing in stirred tanks: numerical issues about the RANS simulations. Comput Chem Eng 35
(10):1959–1968. https://doi.org/10.1016/j.compchemeng.2010.12.007
36. Lapin A, Müller D, Reuss M (2004) Dynamic behavior of microbial populations in stirred
bioreactors simulated with Euler-Lagrange methods: traveling along the lifelines of single cells.
Ind Eng Chem Res 43(16):4647–4656. https://doi.org/10.1021/ie030786k
37. Ducci A, Yianneskis M (2005) Direct determination of energy dissipation in stirred vessels with
two-point LDA. AICHE J 51(8):2133–2149. https://doi.org/10.1002/aic.10468
38. Chaouat B (2017) The state of the art of hybrid RANS/LES modeling for the simulation of
turbulent flows. Flow Turbul Combust 99(2):279–327. https://doi.org/10.1007/s10494-0179828-8
39. Fröhlich J, von Terzi D (2008) Hybrid LES/RANS methods for the simulation of turbulent
flows. Prog Aerosp Sci 44(5):349–377. https://doi.org/10.1016/j.paerosci.2008.05.001
40. Sweere APJ, Janse L, Luyben KCAM, Kossen NWF (1988a) Experimental simulation of
oxygen profiles and their influence on Baker’s yeast production: II. Two-fermentor system.
Biotechnol Bioeng 31(6):579–586. https://doi.org/10.1002/bit.260310610
41. Sweere APJ, Giesselbach J, Barendse R, de Krieger R, Honderd G, Luyben KCAM (1988c)
Modelling the dynamic behaviour of Saccharomyces cerevisiae and its application in control
experiments. Appl Microbiol Biotechnol 28(2):116–127. https://doi.org/10.1007/BF00694298
42. Sweere APJ, Matla YA, Zandvliet J, Ch K, Luyben AM, Kossen NWF (1988d) Experimental
simulation of glucose fluctuations - the influence of continually changing glucose concentrations on the fed-batch Baker’s yeast production. Appl Microbiol Biotechnol 28(2):109–115.
https://doi.org/10.1007/BF00694297
43. Pham HTB, Larsson G, Enfors SO (1998) Growth and energy metabolism in aerobic fed-batch
cultures of Saccharomyces cerevisiae: simulation and model verification. Biotechnol Bioeng 60
(4):474–482. https://doi.org/10.1002/(SICI)1097-0290(19981120)60:4<474::AID-BIT9>3.0.
CO;2-J
44. Serio M, Di RT, Santacesaria E (2001) A kinetic and mass transfer model to simulate the growth
of Baker’s yeast in industrial bioreactors. Chem Eng J 82(1–3):347–354. https://doi.org/10.
1016/S1385-8947(00)00353-3
45. Wright MR, Bach C, Gernaey KV, Krühne U (2018) Investigation of the effect of uncertain
growth kinetics on a CFD based model for the growth of S. cerevisiae in an industrial bioreactor.
Chem Eng Res Des 140:12–22. https://doi.org/10.1016/j.cherd.2018.09.040
46. Sokolichin A, Eigenberger G, Lapin A, Lübbert A (1997) Dynamic numerical simulation of
gas-liquid two-phase flows: Euler/Euler versus Euler/Lagrange. Chem Eng Sci 52(4):611–626.
https://doi.org/10.1016/S0009-2509(96)00425-3
47. Ireland PJ, Desjardins O (2017) Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling. J Comput Phys 338:405–430. https://doi.org/10.1016/j.jcp.
2017.02.070
48. Linkès M, Fede P, Morchain JÔ, Schmitz P (2014) Numerical investigation of subgrid mixing
effects on the calculation of biological reaction rates. Chem Eng Sci 116:473–485. https://doi.
org/10.1016/j.ces.2014.05.005
252
C. S. S. Hajian et al.
(2016) Euler-Lagrange computational fluid dynamics for (bio)reactor scale down: an analysis of
organism lifelines. Eng Life Sci 16(7):652–663. https://doi.org/10.1002/elsc.201600061
33. Liu Y, Wang ZJ, Xia JY, Haringa C, Liu YP, Chu J, Zhuang YP, Zhang SL (2016) Application
of Euler–Lagrange CFD for quantitative evaluating the effect of shear force on Carthamus
tinctorius L. cell in a stirred tank bioreactor. Biochem Eng J 114:209–217. https://doi.org/10.
1016/j.bej.2016.07.006
34. Gunyol O, Mudde RF (2009) Computational study of hydrodynamics of a standard stirred tank
reactor and a large-scale multi-impeller fermenter. Int J Multiscale Comput Eng:559–576.
https://doi.org/10.1615/IntJMultCompEng.v7.i6.60
35. Coroneo M, Montante G, Paglianti A, Magelli F (2011) CFD prediction of fluid flow and
mixing in stirred tanks: numerical issues about the RANS simulations. Comput Chem Eng 35
(10):1959–1968. https://doi.org/10.1016/j.compchemeng.2010.12.007
36. Lapin A, Müller D, Reuss M (2004) Dynamic behavior of microbial populations in stirred
bioreactors simulated with Euler-Lagrange methods: traveling along the lifelines of single cells.
Ind Eng Chem Res 43(16):4647–4656. https://doi.org/10.1021/ie030786k
37. Ducci A, Yianneskis M (2005) Direct determination of energy dissipation in stirred vessels with
two-point LDA. AICHE J 51(8):2133–2149. https://doi.org/10.1002/aic.10468
38. Chaouat B (2017) The state of the art of hybrid RANS/LES modeling for the simulation of
turbulent flows. Flow Turbul Combust 99(2):279–327. https://doi.org/10.1007/s10494-0179828-8
39. Fröhlich J, von Terzi D (2008) Hybrid LES/RANS methods for the simulation of turbulent
flows. Prog Aerosp Sci 44(5):349–377. https://doi.org/10.1016/j.paerosci.2008.05.001
40. Sweere APJ, Janse L, Luyben KCAM, Kossen NWF (1988a) Experimental simulation of
oxygen profiles and their influence on Baker’s yeast production: II. Two-fermentor system.
Biotechnol Bioeng 31(6):579–586. https://doi.org/10.1002/bit.260310610
41. Sweere APJ, Giesselbach J, Barendse R, de Krieger R, Honderd G, Luyben KCAM (1988c)
Modelling the dynamic behaviour of Saccharomyces cerevisiae and its application in control
experiments. Appl Microbiol Biotechnol 28(2):116–127. https://doi.org/10.1007/BF00694298
42. Sweere APJ, Matla YA, Zandvliet J, Ch K, Luyben AM, Kossen NWF (1988d) Experimental
simulation of glucose fluctuations - the influence of continually changing glucose concentrations on the fed-batch Baker’s yeast production. Appl Microbiol Biotechnol 28(2):109–115.
https://doi.org/10.1007/BF00694297
43. Pham HTB, Larsson G, Enfors SO (1998) Growth and energy metabolism in aerobic fed-batch
cultures of Saccharomyces cerevisiae: simulation and model verification. Biotechnol Bioeng 60
(4):474–482. https://doi.org/10.1002/(SICI)1097-0290(19981120)60:4<474::AID-BIT9>3.0.
CO;2-J
44. Serio M, Di RT, Santacesaria E (2001) A kinetic and mass transfer model to simulate the growth
of Baker’s yeast in industrial bioreactors. Chem Eng J 82(1–3):347–354. https://doi.org/10.
1016/S1385-8947(00)00353-3
45. Wright MR, Bach C, Gernaey KV, Krühne U (2018) Investigation of the effect of uncertain
growth kinetics on a CFD based model for the growth of S. cerevisiae in an industrial bioreactor.
Chem Eng Res Des 140:12–22. https://doi.org/10.1016/j.cherd.2018.09.040
46. Sokolichin A, Eigenberger G, Lapin A, Lübbert A (1997) Dynamic numerical simulation of
gas-liquid two-phase flows: Euler/Euler versus Euler/Lagrange. Chem Eng Sci 52(4):611–626.
https://doi.org/10.1016/S0009-2509(96)00425-3
47. Ireland PJ, Desjardins O (2017) Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling. J Comput Phys 338:405–430. https://doi.org/10.1016/j.jcp.
2017.02.070
48. Linkès M, Fede P, Morchain JÔ, Schmitz P (2014) Numerical investigation of subgrid mixing
effects on the calculation of biological reaction rates. Chem Eng Sci 116:473–485. https://doi.
org/10.1016/j.ces.2014.05.005
252
C. S. S. Hajian et al.