Experimental study and simulation of a three-phase flow stirred bioreactor
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摘要
In order to obtain the reasonable operating conditions and minimize the power consumption in the stirred bioreactor, the hydrodynamic experiments in the stirred bioreactor have been taken to obtain the basic data. Subsequently, an Eulerian model for the gas–liquid–solid three phase flow in the stirred bioreactor has been proposed and the CFD simulation has been conducted. By comparing the results of experiment and simulation, it can be concluded that the simulation results were consistent with the experimental data. The inner relationship between operating variables and indicators could be obtained by comparing the results of just suspension speed, gas holdup, power consumption and operational maps, further the reasonable operating conditions could be also determined under the minimum power consumption. The operational maps could provide the theoretical foundation for industrial application of the gas–liquid–solid stirred bioreactors under the low solid concentration(no more than 20 wt%).
In order to obtain the reasonable operating conditions and minimize the power consumption in the stirred bioreactor, the hydrodynamic experiments in the stirred bioreactor have been taken to obtain the basic data. Subsequently, an Eulerian model for the gas–liquid–solid three phase flow in the stirred bioreactor has been proposed and the CFD simulation has been conducted. By comparing the results of experiment and simulation, it can be concluded that the simulation results were consistent with the experimental data. The inner relationship between operating variables and indicators could be obtained by comparing the results of just suspension speed, gas holdup, power consumption and operational maps, further the reasonable operating conditions could be also determined under the minimum power consumption. The operational maps could provide the theoretical foundation for industrial application of the gas–liquid–solid stirred bioreactors under the low solid concentration(no more than 20 wt%).
In order to obtain the reasonable operating conditions and minimize the power consumption in the stirred bioreactor, the hydrodynamic experiments in the stirred bioreactor have been taken to obtain the basic data. Subsequently, an Eulerian model for the gas–liquid–solid three phase flow in the stirred bioreactor has been proposed and the CFD simulation has been conducted. By comparing the results of experiment and simulation, it can be concluded that the simulation results were consistent with the experimental data. The inner relationship between operating variables and indicators could be obtained by comparing the results of just suspension speed, gas holdup, power consumption and operational maps, further the reasonable operating conditions could be also determined under the minimum power consumption. The operational maps could provide the theoretical foundation for industrial application of the gas–liquid–solid stirred bioreactors under the low solid concentration(no more than 20 wt%).
引文
[1] M. Davoody, A.A.B. Abdul Raman, R. Parthasarathy, Maximizing gas–liquid interfacial area in a three-phase stirred vessel operating at high solids concentrations,Chem. Eng. Process. Process Intensif. 104(6)(2016)133–147.
[2] G.H. Sedahmed, Y.A. El-Taweel, M.H. Abdel-Aziz, et al., Mass and heat transfer enhancement at the wall of cylindrical agitated vessel by turbulence promoters,Chem. Eng. Process. Process Intensif. 80(4)(2014)43–50.
[3] M.Y. Chisti, M. Moo-Young, Hydrodynamics and oxygen transfer in pneumatic bioreactor devices, Biotechnol. Bioeng. 31(5)(1988)487–494.
[4] F. Scargiali, A. Busciglio, F. Grisa?, et al., Mass transfer and hydrodynamic characteristics of unbaf?ed stirred bio-reactors:In?uence of impeller design, Biochem. Eng. J.82(15)(2014)41–47.
[5] J.B. Joshi, C.B. Elias, M.S. Patole, Role of hydrodynamic shear in the cultivation of animal, plant and microbial cells, Chem. Eng. J. Biochem. Eng. J. 62(2)(1996)121–141.
[6] J.P. Arnaud, C. Lacroix, L. Choplin, Effect of agitation rate on cell release rate and metabolism during continuous fermentation with entrapped growing, Biotechnol.Tech. 6(3)(1992)265–270.
[7] J.P. Arnaud, C. Lacroix, C. Foussereau, et al., Shear stress effects on growth and activity of Lactobacillus delbrueckii subsp. bulgaricus, J. Biotechnol. 29(1)(1993)157–175.
[8] N. Edwards, S. Beeton, A.T. Bull, et al., A novel device for the assessment of shear effects on suspended microbial cultures, Appl. Microbiol. Biotechnol. 30(2)(1989)190–195.
[9] M. Cai, X. Zhou, J. Lu, et al., Enhancing aspergiolide A production from a shearsensitive and easy-foaming marine-derived?lamentous fungus Aspergillus glaucus by oxygen carrier addition and impeller combination in a bioreactor, Bioresour.Technol. 102(3)(2011)3584–3586.
[10] Y. Chisti, U.J. Jauregui-Haza, Oxygen transfer and mixing in mechanically agitated airlift bioreactors, Biochem. Eng. J. 10(2)(2002)143–153.
[11] A. Karimi, F. Golbabaei, M.R. Mehrnia, et al., Oxygen mass transfer in a stirred tank bioreactor using different impeller con?gurations for environmental purposes,Iran. J. Environ. Health Sci. Eng. 10(6)(2013)1–9.
[12] F. Scargiali, A. Busciglio, F. Grisa?, et al., Oxygen transfer performance of unbaf?ed stirred vessels in view of their use as biochemical reactors for animal cell growth,Chem. Eng. Trans. 27(1)(2012)205–210.
[13] N.M. Atef, M.H. Abdel-Aziz, Y.O. Fouad, et al., Mass and heat transfer at an array of horizontal cylinders placed at the bottom of a square agitated vessel, Chem. Eng.Res. Des. 94(9)(2015)449–455.
[14] G. Baldi, R. Conti, E. Alaria, Complete suspension of particles in mechanically agitated vessels, Chem. Eng. Sci. 33(1)(1978)21–25.
[15] R. Angst, M. Kraume, Experimental investigations of stirred solid/liquid systems in three different scales:Particle distribution and power consumption, Chem. Eng. Sci.61(9)(2006)2864–2870.
[16] T.Y. See, A.A. Abdul Raman, R.S.S. Raja Ehsan Shah, et al., Study of sparger location on solid suspension in a triple-impeller stirred vessel, Asia Pac. J. Chem. Eng. 11(2)(2016)229–236.
[17] M.M. Buffo, L.J. Corrêa, M.N. Esperan?a, et al., In?uence of dual-impeller type and con?guration on oxygen transfer, power consumption, and shear rate in a stirred tank bioreactor, Biochem. Eng. J. 114(10)(2016)130–139.
[18] C.H. Zheng, Y.J. Huang, J.S. Guo, et al., Investigation of cleaner sul?de mineral oxidation technology:Simulation and evaluation of stirred bioreactors for goldbioleaching process, J. Clean. Prod. 192(8)(2018)364–375.
[19] Y. Sano, N. Yamaguchi, T. Adachi, Mass transfer coef?cients for suspended particles in agitated vessels and bubble columns, J. Chem. Eng. Jpn. 7(4)(1974)255–261.
[20] N. Dohi, T. Takahashi, K. Minekawa, et al., Power consumption and solid suspension performance of large-scale impellers in gas–liquid–solid three-phase stirred tank reactors, Chem. Eng. J. 97(2–3)(2004)103–114.
[21] A. Satio, M. Kamiwano, Power consumption, gas dispersion and solid suspension in three phase mixing vessels, Proceedings of the Proc 6th European Conference on Mixing Pavia, Italy F, 1998, Springer, Pavia, Italy, 1998.
[22] H. Ameur, M. Bouzit, Power consumption for stirring shear thinning?uids by two-blade impeller, Energy 50(2)(2013)326–332.
[23] Y. Chisti, Animal-cell damage in sparged bioreactors, Trends Biotechnol. 18(10)(2000)420–432.
[24] T.N. Zwietering, Suspending of solid particles in liquid by agitators, Chem. Eng. Sci. 8(3)(1958)244–253.
[25] L.-j. Zhang, T. Li, W.-y. Ying, et al., Rising and descending bubble size distributions in gas–liquid and gas–liquid–solid slurry bubble column reactor, Chem. Eng. Res. Des.86(10)(2008)1143–1154.
[26] L.j. Zhang, T. Li, W.y. Ying, et al., Experimental study on bubble rising and descending velocity distribution in a slurry bubble column reactor, Chem. Eng. Technol. 31(9)(2008)1362–1368.
[27] B. Wang, T. Li, Q.W. Sun, et al., Experimental study on?ow behavior in a gas–solid?uidized bed for the methanol-to-ole?ns process, Chem. Eng. Technol. 33(10)(2010)1591–1600.
[28] S. Kim, X.Y. Fu, X. Wang, et al., Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, Int. J. Heat Mass Transf. 43(22)(2000)4101–4118.
[29] P. Riedlberger, D. Weuster-Botz, New miniature stirred-tank bioreactors for parallel study of enzymatic biomass hydrolysis, Bioresour. Technol. 106(Supplement C)(2012)138–146.
[30] J. Ding, X. Wang, X.-F. Zhou, et al., CFD optimization of continuous stirred-tank(CSTR)reactor for biohydrogen production, Bioresour. Technol. 101(18)(2010)7005–7013.
[31] A.R. Khopkar, J. Aubin, C. Xuereb, et al., Gas-liquid?ow generated by a pitchedblade turbine:Particle image velocimetry measurements and computational?uid dynamics simulations, Ind. Eng. Chem. Res. 42(21)(2003)5318–5332.
[32] C. Gentric, D. Mignon, J. Bousquet, et al., Comparison of mixing in two industrial gas–liquid reactors using CFD simulations, Chem. Eng. Sci. 60(8–9)(2005)2253–2272.
[33] X. Wang, J. Ding, W.-Q. Guo, et al., A hydrodynamics-reaction kinetics coupled model for evaluating bioreactors derived from CFD simulation, Bioresour. Technol. 101(24)(2010)9749–9757.
[34] R. Panneerselvam, S. Savithri, G.D. Surender, CFD modeling of gas–liquid–solid mechanically agitated contactor, Chem. Eng. Res. Des. 86(12)(2008)1331–1344.
[35] B.N. Murthy, R.S. Ghadge, J.B. Joshi, CFD simulations of gas–liquid–solid stirred reactor:Prediction of critical impeller speed for solid suspension, Chem. Eng. Sci. 62(24)(2007)7184–7195.
[36] J.X. Xu, H. Wang, J.J. Wang, et al., CFD Simulation of Mixing Effects in Gas–Liquid–Solid Stirred Reactor, Proceedings of the Adv Mat Res, F, 2012.
[37] F. Wang, Z. Mao, Y. Wang, et al., Measurement of phase holdups in liquid–liquid–solid three-phase stirred tanks and CFD simulation, Chem. Eng. Sci. 61(22)(2006)7535–7550.
[38] A. Inc., Ansys Fluent Theory Guide, ANSYS, Inc., Canonsburg, 2013.
[39] A.R. Khopkar, A.R. Rammohan, V.V. Ranade, et al., Gas–liquid?ow generated by a Rushton turbine in stirred vessel:CARPT/CT measurements and CFD simulations,Chem. Eng. Sci. 60(8–9)(2005)2215–2229.
[40] M. Ljungqvist, A. Rasmuson, Numerical simulation of the two-phase?ow in an axially stirred vessel, Chem. Eng. Res. Des. 79(5)(2001)533–546.
[41] R. Zadghaffari, J.S. Moghaddas, Evaluation of drag force effect on hold-up in a gas–liquid stirred tank reactor, J. Chem. Eng. Jpn. 43(10)(2010)833–840.
[42] A.R. Khopkar, G.R. Kasat, A.B. Pandit, et al., CFD simulation of mixing in tall gas–liquid stirred vessel:Role of local?ow patterns, Chem. Eng. Sci. 61(9)(2006)2921–2929.
[43] G.L. Lane, M.P. Schwarz, G.M. Evans, Modelling of the interaction between gas and liquid in stirred vessels, 10th European Conference on Mixing, Elsevier Science,Amsterdam 2000, pp. 197–204.
[44] A. Brucato, F. Grisa?, G. Montante, Particle drag coef?cients in turbulent?uids, Chem.Eng. Sci. 53(18)(1998)3295–3314.
[45] A. Tomiyama, Struggle with computational bubble dynamics, Proceedings of the Third International Conference on Multiphase Flow, Lyon, France, F, 1998, Elsevier Science Ltd., Lyon, France, 1998.
[46] L. Schiller, Z. Naumann, A drag coef?cient correlation, VDI Ztg. 77(1935)318–320.
[47] N.T. Padial, W.B. VanderHeyden, R.M. Rauenzahn, et al., Three-dimensional simulation of a three-phase draft-tube bubble column, Chem. Eng. Sci. 55(16)(2000)3261–3273.
[48] Y. Sato, M. Sadatomi, K. Sekoguchi, Momentum and heat transfer in two-phase bubble?ow—I. Theory, Int. J. Multiphase Flow 7(2)(1981)167–177.
[49] J.O. Hinze, Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChE J. 1(3)(1955)289–295.
[50] R.S. Cherry, E.T. Papoutsakis, Hydrodynamic effects on cells in agitated tissue culture reactors, Bioprocess Eng. 1(1)(1986)29–41.
[51] K.M. Dhanasekharan, J. Sanyal, A. Jain, et al., A generalized approach to model oxygen transfer in bioreactors using population balances and computational?uid dynamics, Chem. Eng. Sci. 60(1)(2005)213–218.
[52] F. Kerdouss, A. Bannari, P. Proulx, et al., Two-phase mass transfer coef?cient prediction in stirred vessel with a CFD model, Comput. Chem. Eng. 32(8)(2008)1943–1955.
[53] S. Nedeltchev, Correction of the penetration theory applied for prediction of mass transfer coef?cients in a high-pressure bubble column operated with gasoline and toluene, J. Chem. Eng. Jpn. 36(5)(2003)630–633.
[54] R. Higbie, The rate of absorption of a pure gas into a still liquid during short period of exposure, Trans. AIChE 31(16)(1935)365–389.
[55] Y. Zhang, Y. Bai, H. Wang, CFD analysis of inter-phase forces in a bubble stirred vessel, Chem. Eng. Res. Des. 91(1)(2013)29–35.
[56] G. Montante, D. Horn, A. Paglianti, Gas–liquid?ow and bubble size distribution in stirred tanks, Chem. Eng. Sci. 63(8)(2008)2107–2118.
[57] S. Yang, X. Li, C. Yang, et al., Computational?uid dynamics simulation and experimental measurement of gas and solid holdup distributions in a gas–liquid–solid stirred reactor, Ind. Eng. Chem. Res. 55(12)(2016)3276–3286.
[58] X. Geng, Z. Gao, Y. Bao, PIV study of?ow in an aerated tank with a hollow blade turbine, Int. J. Chem. React. Eng. 10(1)(2012)850–868.
[59] G. Montante, A. Paglianti, F. Magelli, Analysis of dilute solid–liquid suspensions in turbulent stirred tanks, Chem. Eng. Res. Des. 90(10)(2012)1448–1456.
[60] V.B. Rewatkar, K.S.M.S.R. Rao, J.B. Joshi, Critical impeller speed for solid suspension in mechanically agitated three-phase reactors. 1. Experimental part, Ind. Eng.Chem. Res. 30(8)(1991)1770–1784.
[61] N.N. Dutta, V.G. Pangarkar, Critical impeller speed for solid suspension in multiimpeller agitated contactors:Solid–liquid system, Chem. Eng. Commun. 137(1)(1995)135–146.
[62] K. Saravanan, A.W. Patwardban, J.B. Joshi, Critical impeller speed for solid suspension in gas inducing type mechanically agitated contactors, Can. J. Chem. Eng. 75(8)(1997)664–676.
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[65] S. Hosseini, D. Patel, F. Ein-Mozaffari, et al., Study of solid-liquid mixing in agitated tanks through computational?uid dynamics modeling, Ind. Eng. Chem. Res. 49(9)(2010)4426–4435.
[66] M. Bohnet, G. Niesmak, Distribution of solids in stirred suspension, Ger. Chem. Eng.51(4)(1979)314–315.
[67] L.M. Oshinowo, A. Bakker, CFD modeling of solids suspension in stirred tanks,Proceedings of the TMS Annual Meeting, Seattle, WA, F, 2002. Minerals and Materials:Seattle, WA, 2002.
[68] A. Tamburini, A. Cipollina, G. Micale, et al., CFD simulations of dense solid–liquid suspensions in baf?ed stirred tanks:Prediction of solid particle distribution, Chem.Eng. J. 223(2013)875–890.
[2] G.H. Sedahmed, Y.A. El-Taweel, M.H. Abdel-Aziz, et al., Mass and heat transfer enhancement at the wall of cylindrical agitated vessel by turbulence promoters,Chem. Eng. Process. Process Intensif. 80(4)(2014)43–50.
[3] M.Y. Chisti, M. Moo-Young, Hydrodynamics and oxygen transfer in pneumatic bioreactor devices, Biotechnol. Bioeng. 31(5)(1988)487–494.
[4] F. Scargiali, A. Busciglio, F. Grisa?, et al., Mass transfer and hydrodynamic characteristics of unbaf?ed stirred bio-reactors:In?uence of impeller design, Biochem. Eng. J.82(15)(2014)41–47.
[5] J.B. Joshi, C.B. Elias, M.S. Patole, Role of hydrodynamic shear in the cultivation of animal, plant and microbial cells, Chem. Eng. J. Biochem. Eng. J. 62(2)(1996)121–141.
[6] J.P. Arnaud, C. Lacroix, L. Choplin, Effect of agitation rate on cell release rate and metabolism during continuous fermentation with entrapped growing, Biotechnol.Tech. 6(3)(1992)265–270.
[7] J.P. Arnaud, C. Lacroix, C. Foussereau, et al., Shear stress effects on growth and activity of Lactobacillus delbrueckii subsp. bulgaricus, J. Biotechnol. 29(1)(1993)157–175.
[8] N. Edwards, S. Beeton, A.T. Bull, et al., A novel device for the assessment of shear effects on suspended microbial cultures, Appl. Microbiol. Biotechnol. 30(2)(1989)190–195.
[9] M. Cai, X. Zhou, J. Lu, et al., Enhancing aspergiolide A production from a shearsensitive and easy-foaming marine-derived?lamentous fungus Aspergillus glaucus by oxygen carrier addition and impeller combination in a bioreactor, Bioresour.Technol. 102(3)(2011)3584–3586.
[10] Y. Chisti, U.J. Jauregui-Haza, Oxygen transfer and mixing in mechanically agitated airlift bioreactors, Biochem. Eng. J. 10(2)(2002)143–153.
[11] A. Karimi, F. Golbabaei, M.R. Mehrnia, et al., Oxygen mass transfer in a stirred tank bioreactor using different impeller con?gurations for environmental purposes,Iran. J. Environ. Health Sci. Eng. 10(6)(2013)1–9.
[12] F. Scargiali, A. Busciglio, F. Grisa?, et al., Oxygen transfer performance of unbaf?ed stirred vessels in view of their use as biochemical reactors for animal cell growth,Chem. Eng. Trans. 27(1)(2012)205–210.
[13] N.M. Atef, M.H. Abdel-Aziz, Y.O. Fouad, et al., Mass and heat transfer at an array of horizontal cylinders placed at the bottom of a square agitated vessel, Chem. Eng.Res. Des. 94(9)(2015)449–455.
[14] G. Baldi, R. Conti, E. Alaria, Complete suspension of particles in mechanically agitated vessels, Chem. Eng. Sci. 33(1)(1978)21–25.
[15] R. Angst, M. Kraume, Experimental investigations of stirred solid/liquid systems in three different scales:Particle distribution and power consumption, Chem. Eng. Sci.61(9)(2006)2864–2870.
[16] T.Y. See, A.A. Abdul Raman, R.S.S. Raja Ehsan Shah, et al., Study of sparger location on solid suspension in a triple-impeller stirred vessel, Asia Pac. J. Chem. Eng. 11(2)(2016)229–236.
[17] M.M. Buffo, L.J. Corrêa, M.N. Esperan?a, et al., In?uence of dual-impeller type and con?guration on oxygen transfer, power consumption, and shear rate in a stirred tank bioreactor, Biochem. Eng. J. 114(10)(2016)130–139.
[18] C.H. Zheng, Y.J. Huang, J.S. Guo, et al., Investigation of cleaner sul?de mineral oxidation technology:Simulation and evaluation of stirred bioreactors for goldbioleaching process, J. Clean. Prod. 192(8)(2018)364–375.
[19] Y. Sano, N. Yamaguchi, T. Adachi, Mass transfer coef?cients for suspended particles in agitated vessels and bubble columns, J. Chem. Eng. Jpn. 7(4)(1974)255–261.
[20] N. Dohi, T. Takahashi, K. Minekawa, et al., Power consumption and solid suspension performance of large-scale impellers in gas–liquid–solid three-phase stirred tank reactors, Chem. Eng. J. 97(2–3)(2004)103–114.
[21] A. Satio, M. Kamiwano, Power consumption, gas dispersion and solid suspension in three phase mixing vessels, Proceedings of the Proc 6th European Conference on Mixing Pavia, Italy F, 1998, Springer, Pavia, Italy, 1998.
[22] H. Ameur, M. Bouzit, Power consumption for stirring shear thinning?uids by two-blade impeller, Energy 50(2)(2013)326–332.
[23] Y. Chisti, Animal-cell damage in sparged bioreactors, Trends Biotechnol. 18(10)(2000)420–432.
[24] T.N. Zwietering, Suspending of solid particles in liquid by agitators, Chem. Eng. Sci. 8(3)(1958)244–253.
[25] L.-j. Zhang, T. Li, W.-y. Ying, et al., Rising and descending bubble size distributions in gas–liquid and gas–liquid–solid slurry bubble column reactor, Chem. Eng. Res. Des.86(10)(2008)1143–1154.
[26] L.j. Zhang, T. Li, W.y. Ying, et al., Experimental study on bubble rising and descending velocity distribution in a slurry bubble column reactor, Chem. Eng. Technol. 31(9)(2008)1362–1368.
[27] B. Wang, T. Li, Q.W. Sun, et al., Experimental study on?ow behavior in a gas–solid?uidized bed for the methanol-to-ole?ns process, Chem. Eng. Technol. 33(10)(2010)1591–1600.
[28] S. Kim, X.Y. Fu, X. Wang, et al., Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, Int. J. Heat Mass Transf. 43(22)(2000)4101–4118.
[29] P. Riedlberger, D. Weuster-Botz, New miniature stirred-tank bioreactors for parallel study of enzymatic biomass hydrolysis, Bioresour. Technol. 106(Supplement C)(2012)138–146.
[30] J. Ding, X. Wang, X.-F. Zhou, et al., CFD optimization of continuous stirred-tank(CSTR)reactor for biohydrogen production, Bioresour. Technol. 101(18)(2010)7005–7013.
[31] A.R. Khopkar, J. Aubin, C. Xuereb, et al., Gas-liquid?ow generated by a pitchedblade turbine:Particle image velocimetry measurements and computational?uid dynamics simulations, Ind. Eng. Chem. Res. 42(21)(2003)5318–5332.
[32] C. Gentric, D. Mignon, J. Bousquet, et al., Comparison of mixing in two industrial gas–liquid reactors using CFD simulations, Chem. Eng. Sci. 60(8–9)(2005)2253–2272.
[33] X. Wang, J. Ding, W.-Q. Guo, et al., A hydrodynamics-reaction kinetics coupled model for evaluating bioreactors derived from CFD simulation, Bioresour. Technol. 101(24)(2010)9749–9757.
[34] R. Panneerselvam, S. Savithri, G.D. Surender, CFD modeling of gas–liquid–solid mechanically agitated contactor, Chem. Eng. Res. Des. 86(12)(2008)1331–1344.
[35] B.N. Murthy, R.S. Ghadge, J.B. Joshi, CFD simulations of gas–liquid–solid stirred reactor:Prediction of critical impeller speed for solid suspension, Chem. Eng. Sci. 62(24)(2007)7184–7195.
[36] J.X. Xu, H. Wang, J.J. Wang, et al., CFD Simulation of Mixing Effects in Gas–Liquid–Solid Stirred Reactor, Proceedings of the Adv Mat Res, F, 2012.
[37] F. Wang, Z. Mao, Y. Wang, et al., Measurement of phase holdups in liquid–liquid–solid three-phase stirred tanks and CFD simulation, Chem. Eng. Sci. 61(22)(2006)7535–7550.
[38] A. Inc., Ansys Fluent Theory Guide, ANSYS, Inc., Canonsburg, 2013.
[39] A.R. Khopkar, A.R. Rammohan, V.V. Ranade, et al., Gas–liquid?ow generated by a Rushton turbine in stirred vessel:CARPT/CT measurements and CFD simulations,Chem. Eng. Sci. 60(8–9)(2005)2215–2229.
[40] M. Ljungqvist, A. Rasmuson, Numerical simulation of the two-phase?ow in an axially stirred vessel, Chem. Eng. Res. Des. 79(5)(2001)533–546.
[41] R. Zadghaffari, J.S. Moghaddas, Evaluation of drag force effect on hold-up in a gas–liquid stirred tank reactor, J. Chem. Eng. Jpn. 43(10)(2010)833–840.
[42] A.R. Khopkar, G.R. Kasat, A.B. Pandit, et al., CFD simulation of mixing in tall gas–liquid stirred vessel:Role of local?ow patterns, Chem. Eng. Sci. 61(9)(2006)2921–2929.
[43] G.L. Lane, M.P. Schwarz, G.M. Evans, Modelling of the interaction between gas and liquid in stirred vessels, 10th European Conference on Mixing, Elsevier Science,Amsterdam 2000, pp. 197–204.
[44] A. Brucato, F. Grisa?, G. Montante, Particle drag coef?cients in turbulent?uids, Chem.Eng. Sci. 53(18)(1998)3295–3314.
[45] A. Tomiyama, Struggle with computational bubble dynamics, Proceedings of the Third International Conference on Multiphase Flow, Lyon, France, F, 1998, Elsevier Science Ltd., Lyon, France, 1998.
[46] L. Schiller, Z. Naumann, A drag coef?cient correlation, VDI Ztg. 77(1935)318–320.
[47] N.T. Padial, W.B. VanderHeyden, R.M. Rauenzahn, et al., Three-dimensional simulation of a three-phase draft-tube bubble column, Chem. Eng. Sci. 55(16)(2000)3261–3273.
[48] Y. Sato, M. Sadatomi, K. Sekoguchi, Momentum and heat transfer in two-phase bubble?ow—I. Theory, Int. J. Multiphase Flow 7(2)(1981)167–177.
[49] J.O. Hinze, Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChE J. 1(3)(1955)289–295.
[50] R.S. Cherry, E.T. Papoutsakis, Hydrodynamic effects on cells in agitated tissue culture reactors, Bioprocess Eng. 1(1)(1986)29–41.
[51] K.M. Dhanasekharan, J. Sanyal, A. Jain, et al., A generalized approach to model oxygen transfer in bioreactors using population balances and computational?uid dynamics, Chem. Eng. Sci. 60(1)(2005)213–218.
[52] F. Kerdouss, A. Bannari, P. Proulx, et al., Two-phase mass transfer coef?cient prediction in stirred vessel with a CFD model, Comput. Chem. Eng. 32(8)(2008)1943–1955.
[53] S. Nedeltchev, Correction of the penetration theory applied for prediction of mass transfer coef?cients in a high-pressure bubble column operated with gasoline and toluene, J. Chem. Eng. Jpn. 36(5)(2003)630–633.
[54] R. Higbie, The rate of absorption of a pure gas into a still liquid during short period of exposure, Trans. AIChE 31(16)(1935)365–389.
[55] Y. Zhang, Y. Bai, H. Wang, CFD analysis of inter-phase forces in a bubble stirred vessel, Chem. Eng. Res. Des. 91(1)(2013)29–35.
[56] G. Montante, D. Horn, A. Paglianti, Gas–liquid?ow and bubble size distribution in stirred tanks, Chem. Eng. Sci. 63(8)(2008)2107–2118.
[57] S. Yang, X. Li, C. Yang, et al., Computational?uid dynamics simulation and experimental measurement of gas and solid holdup distributions in a gas–liquid–solid stirred reactor, Ind. Eng. Chem. Res. 55(12)(2016)3276–3286.
[58] X. Geng, Z. Gao, Y. Bao, PIV study of?ow in an aerated tank with a hollow blade turbine, Int. J. Chem. React. Eng. 10(1)(2012)850–868.
[59] G. Montante, A. Paglianti, F. Magelli, Analysis of dilute solid–liquid suspensions in turbulent stirred tanks, Chem. Eng. Res. Des. 90(10)(2012)1448–1456.
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