Numerical analysis of hydrodynamics in a mechanically agitated gas–liquid pseudophase system
 139 Downloads
Abstract
The paper presents the results of numerical simulations of hydrodynamics in a gas–liquid pseudophase system (sucrose solution with yeast suspension). The simulations were performed in a bioreactor with a working volume of 0.02 m^{3}, equipped with a Rushton turbine or Smith turbine stirrers. The results of the study were developed in the form of vectors of liquid velocity and the contours of the analyzed magnitudes. Also, the local values of the gas holdup φ in the gas–liquid pseudophase system were presented. The results of numerical simulations of the gas holdup were compared to the results of my own experimental study.
Keywords
Bioreactor Mixing Gas holdup Numerical modeling Gas–liquid pseudophase systemList of symbols
 B
Width of the baffle (outer diameter of the tubular baffle), m
 D
Diameter of the impeller, m
 d_{d}
Sparger diameter, m
 H
Liquid height in the vessel, m
 h
Distance between impeller and bottom of the vessel, m
 k_{c}
Consistency index, Pa s^{m1}
 m
Flow index
 n
Impeller speed, s^{−1}
 T
Inner diameter of the agitated vessel, m
 V_{g}
Gas flow rate, m^{3} s^{−1}
 z
Axial coordinate, m
Greek letters
 φ
Gas holdup
 η
Dynamic viscosity of the liquid, Pa s
 ρ
Density of the liquid, kg m^{−3}
 k
Interfacial tension, N m^{−1}
Introduction
Multiphase systems in a mixer are widely used in chemical and biochemical engineering processes. Their hydrodynamics is very complicated due to the interactions occurring between the rotating stirrer and the baffles. The application of the computational fluid dynamics (CFD) method allows to reduce the costs and time needed to perform experimental research (Wang et al. 2014; Sommerfeld and Decker 2004).
Due to the fact that the processes in bioreactors run in multiphase systems (biophase–gas–liquid), the following should be defined in numerical calculations: due to the presence of more than one phase (multiphase model), due to turbulent flow (turbulence model) and due to different sizes and properties of the dispersed phase (models that take into account division and connection (birth and death), for example, gas bubbles or microbial cells) (Ranade 2002; Jaworski 2005).
In the case of modeling the hydrodynamics of the gas–liquid system, characterized by a relatively high proportion of the dispersed phase (gas phase), the twophase model is often used as a model in which both phases are treated as two interpenetrating continuums (Euler–Euler approach) (Kerdouss et al. 2008; Jaworski 2005; Joshi et al. 2011; Kaiser et al. 2011; Knopkar and Ranade 2006). To obtain better agreement between the data obtained as a result of simulations and experimental data, the computational fluid dynamics (CFD) method is combined with the population balance method (PBM) (Gimbun et al. 2009; Ranganathan and Sivaraman 2011; Musiał et al. 2014, 2017). Based on the results of numerical simulations of hydrodynamics of multiphase systems, a number of information on the distribution of liquid and gas velocities, local values of gas holdup and distributions of kinetic energy of turbulence and its dissipation in a stirred tank can be obtained (Oniscu et al. 2002; Vrábel et al. 2000; Delafosse et al. 2014; Gelves et al. 2014).
Gimbun et al. (2009) used a twofluid model and an Euler–Euler approach to perform a simulation in gas–liquid system in a tank with a Rushton turbine or Smith turbine stirrer. Local bubble size distributions were obtained using a quadrature method of moments (QMOM), whereas local k_{L}a values were estimated using the Higbie permeation theory and the model of the renewed surface. Obtained results regarding hydrodynamics of the gas–liquid system (power number, local bubble sizes, dissolved oxygen concentration, average twophase flow velocities) were quite consistent with the literature data, which proves that the simulations were performed correctly.
The results of numerical simulations showing the influence of baffles and the curvature shape of stirrer blades (concave or convex blades) on hydrodynamics in liquid or gas–liquid systems mixed in a tank equipped with a turbine stirrer with curved blades were obtained by Musiał et al. (2014). They used the k–ε or SST turbulence model and Euler–Euler approach to predict turbulent flow. Based on the obtained simulations, they found that hydrodynamic interactions between the curved stirrer blades and mixing tank baffles are responsible for disturbing the symmetry of the fluid flow in the axial and radial planes of the stirrer tank. Numerical analysis of the impact of sucrose concentration on the distribution of continuous phase velocity, share of gas holdup and size of gas bubbles was the subject of research by Musiał et al. (2017). Based on the conducted simulations, they found that the local liquid velocity values decrease with the increase in sucrose concentration in the system, while the distributions of gas holdup and the size of gas bubbles to a small extent depend on sucrose concentration.
The modeling of the impact of apparent gas velocity w_{og} on the hydrodynamics of flow and the processes of mass exchange in the gas–liquid system in bioreactor was examined by Devi and Kumar (2014). They performed numerical simulations in a bioreactor with two Rushton turbine or CD 6 stirrers. They found that dissipation rate ε increases with the increase in apparent linear gas velocity w_{og}. Significantly higher values of relative mixing power P_{g}/P_{o} were obtained for a CD 6 stirrer than for Rushton turbine stirrer. However, Devi and Kumar (2014) did not find a significant influence of the stirrer type on the value of the average coefficient of mass transfer k_{L}a. Xia et al. (2009) modeled the flow dynamics in the bioreactor with various stirrer combinations. Simulation results were compared with experimental results obtained in analogously equipped bioreactors. The Streptomyces avermitilis yeast suspension was a biophase in all cases. Measurements and numerical simulations were carried out in bioreactors in which three highspeed stirrers were mounted on a common shaft. Comparing the results of experimental tests and numerical simulations, it was found that the most favorable conditions are provided by a system of three stirrers: two pumping down modified propeller stirrers and a turbine stirrer with six curved blades (bottom).
The study presented in this paper aimed to determine the influence of stirrer speed and volumetric gas flow rate on the gas holdup in a bioreactor with a Rushton turbine or Smith turbine stirrer. The results of numerical simulations of the gas holdup were compared to the results of my own experimental study.
The range of simulations

in the vicinity of the stirrer,

in the rest of the tank.
In the area of the stirrer and in the vicinity of the tank walls, the grid was characterized by a much denser structure than in the remaining volume of the tank. The MRF zone is much larger than the stirrer volume. It was designated as a disk with a diameter of 0.164 m. In the MRF zone, the unstructured mesh consisted of about 150,000 tetrahedral elements.
The mathematical model of the process and the corresponding initial and boundary conditions were defined using ANSYS CFXPre. The continuous phase was modeled using the Shear Stress Transport model (SST). The assumptions of the k–ε model regarding the volume of the stream and the assumption of the k–ω model taking into account mixing functions in the boundary areas are taken into account in the SST model (ANSYS 2015). Due to the nonuniform size of gas bubbles in the gas–liquid system, numerical modeling also included coalescence and bubbles disruption models as well as a model determining the bubbles size distribution (Podgórska 2006). To describe the gas bubble disruption, Luo Svendsen’s model was used, taking into account the theory of isotropic turbulence and the theory of probability (Wang et al. 2014: ANSYS 2015). The phenomenon of gas bubbles coalescence was described using the Prince Blanch model (ANSYS 2015). In this model, the authors assumed that the connection of two bubbles into one occurs in three stages: in the first—the bubbles collide with a small amount of fluid between them, in the second—the liquid film reaches a critical thickness, in the third—the film breaks and the bubbles connect. Thus, the process of bubbles connection depends on the speed of collision between the two bubbles and on the effectiveness of the collision determined on the basis of the time needed for the connection. This model is often simplified taking into account only the frequency of collisions (Wang et al. 2014).
The dispersion of gas bubbles was determined using the Particle model (ANSYS 2015). In addition, the forces of interphase resistance were taken into account, as defined by the Schiller–Naumann equation, as well as the uplift force according to the Tomiyama model (ANSYS 2015). The transfer of turbulence between the phases was modeled on the basis of the extended Sato correlation (ANSYS 2015). Gas bubble sizes, divided into ten classes, were modeled using the Multiple Size Group (MUSIG) model that combines flow simulations with the population balance method (Wang et al. 2014; Ahmed et al. 2010; Frank et al. 2005).
Numerical calculations were carried out for three stirrer speeds n = 8, 10, 12 1/s, and two gas flow rates V_{g} = \(1.67 \times 10^{  4}\) m^{3}/s and V_{g} = \(3.33 \times 10^{  4}\).
Results and discussion
Radial contours of the gas holdup φ obtained for the bioreactor with Rushton turbine stirrer, for three axial coordinates z/H = 0.25; 0.33 and 0.42, are compared in Figs. 8, 9, 10 and 11. Distinct differences in the values of the proportion of gas holdup φ are visible for the coordinate z/H = 0.25 (zone under the stirrer). For this coordinate, a rosetteshaped area is visible between the gas distributor and the stirrer, with a minimal gas holdup φ. The highest values of the gas holdup φ, for z/H = 0.25 are located near the baffles (Fig. 8a) and near the walls of the tank (Figs. 9a, 10, 11a). With an increase of the speed of the stirrer n (V_{g} = const), the area with the lowest gas holdup φ is reduced (Figs. 8a, 9a).
In all the analyzed cases, characteristic gas caverns were found behind the stirrer blades (Figs. 8b, 9, 10, 11b). The size of these caverns decreases with the increase in the speed of the stirrer n (assuming V_{g} = const; Figs. 8b, 9, 10b) and increases with the increase in V_{g} (assuming n = const; Figs. 9b, 11b).
Conclusions
 1.
The most intense mixing takes place in the area of the stirrer, and the influence of the shape of stirrer blades on the liquid circulation is revealed. In the case of bioreactor with Rushton turbine stirrer, the area characterized by the most intense mixing is placed symmetrically around the stirrer. In the bioreactor with Smith turbine stirrer, the areas with the highest liquid phase velocities are behind the stirrer blades. In both cases, the liquid velocities in the bioreactor decrease toward the free liquid surface.
 2.
A better dispersion of the gas bubbles in the system is obtained increasing the speed of the stirrer n, assuming a constant value of the gas flow V_{g}. The areas with the largest gas holdup φ are placed symmetrically to the vertical axis of the bioreactor and coincide with the central points of the circulation loops. These areas increase, assuming V_{g} = const, with an increase in the stirrer speed.
 3.
In all the analyzed cases, characteristic gas caverns were found behind the stirrer blades. The size of these caverns decreases with an increase in the speed of the stirrer n (assuming V_{g} = const) and increases with an increase in V_{g} (assuming n = const).
References
 Ahmed SU, Ranganathan P, Pandey A, Sivaraman S (2010) Computational fluid dynamics modelling of gas dispersion in multi impeller bioreactor. J Biosci Bioeng 109:588–597. https://doi.org/10.1007/j.jbiosc.2009.11.014 CrossRefGoogle Scholar
 ANSYS (2015) ANSYS CFXSolver Theory Guide, Release 15.0. ANSYS, IncGoogle Scholar
 Delafosse A, Collignon ML, Calvo S, Delvigne F, Crini M, Thonart P, Toye D (2014) CFDbased compartment model for description of mixing in bioreactors. Chem Eng Sci 106:76–85. https://doi.org/10.1016/j.ces.2013.11.033 CrossRefGoogle Scholar
 Devi TT, Kumar B (2014) Effects of superficial gas velocity on process dynamics in bioreactors. Thermophys Aeromech 21:365–382. https://doi.org/10.1134/S0869869431403010X CrossRefGoogle Scholar
 Frank T, Zwart PJ, Shi JM, Krepper E, Lucas D, Rohde U (2005) Inhomogeneous MUSIG model—a population balance approach for polydispersed bubbly flows. In: International conference “nuclear energy for new Europe 2005”, BledGoogle Scholar
 Gelves R, Dietrich A, Takors R (2014) Modeling of gasliquid mass transfer in a stirred tank bioreactor agitated by Rushton turbine or a new pitched blade impeller. Bioprocess Biosyst Eng 37:365–375. https://doi.org/10.1007/s0044901310018 CrossRefGoogle Scholar
 Gimbun J, Rielly CD, Nagy ZK (2009) Modelling of mass transfer in gasliquid stirred tanks agitated by Rushton turbine and CD6 impeller: a scaleup study. Chem Eng Res Des 87:437–451. https://doi.org/10.1016/j.cherd.2008.12.017 CrossRefGoogle Scholar
 Jaworski Z (2005) Numeryczna mechanika płynów w inżynierii chemicznej i procesowej. Akademicka Oficyna Wydawnicza, Warszawa, p 2005Google Scholar
 Joshi JB, Nere NK, Rane ChV, Murthy BN, Mathpati ChS, Patwardhan AP, Ranade VV (2011) CFD simulation of stirred tanks: comparison of turbulence models. Part I: radial flow impellers. Can J Chem Eng 89:23–82. https://doi.org/10.1002/cjce.20446 CrossRefGoogle Scholar
 Kaiser SC, Eibl R, Eibl D (2011) Engineering characteristics of a singleuse stirred bioreactor at benchscale: the Mobius Cell Ready 3L bioreactor as a case study. Eng Life Sci 11:359–368. https://doi.org/10.1002/elsc.201000171 CrossRefGoogle Scholar
 Kerdouss F, Bannari A, Proulx P, Bannari R, Skrga M, Labrecque Y (2008) Twophase mass transfer coefficient prediction in stirred vessel with a CFD model. Comput Chem Eng 32:1943–1955. https://doi.org/10.1016/j.compchemeng.2007.10.010 CrossRefGoogle Scholar
 Knopkar AR, Ranade VV (2006) CFD simulation of gasliquid stirred vessel: VC, S33, and L33 flow regimes. AIChE J 52:1654–1672. https://doi.org/10.1002/aic.10762 CrossRefGoogle Scholar
 Musiał M, Karcz J, Cudak M (2014) Zastosowanie metody CFD do analizy hydrodynamiki w mieszalniku z przegrodami i mieszadłem CD 6. Przemysł Chemiczny 93:1599–1603. https://doi.org/10.12916/przemchem.2014.1599 Google Scholar
 Musiał M, Cudak M, Karcz J (2017) Numerical analysis of momentum transfer processes in a mechanically agitated airbiophaseliquid system. Chem Process Eng 38(3):465–475. https://doi.org/10.1515/cpe20170036 CrossRefGoogle Scholar
 Oniscu C, Galaction AI, Cascaval D, Ungureanu F (2002) Modeling of mixing in stirred bioreactors 2. Mixing time for nonaerated broths. Biochem Eng J 12:61–69 (pii:S1369703X(02)000426) CrossRefGoogle Scholar
 Podgórska W (2006) Rozpad i koalescencja kropel w intermitentnym polu burzliwym. Oficyna Wydawnicza Politechniki Warszawskiej, WarszawaGoogle Scholar
 Ranade VV (2002) Computation flow modeling for chemical reactor engineering. Academic, San DiegoGoogle Scholar
 Ranganathan P, Sivaraman S (2011) Investigations on hydrodynamics and mass transfer in gasliquid stirred reactor using computational fluid dynamics. Chem Eng Sci 66:3108–3124. https://doi.org/10.1016/j.ces.2011.03.007 CrossRefGoogle Scholar
 Sommerfeld M, Decker S (2004) State of the art and future trends in CFD simulation of stirred vessel hydrodynamics. Chem Eng Technol 27(3):215–224. https://doi.org/10.1002/ceat.200402007 CrossRefGoogle Scholar
 Vrábel P, van der Lans RGJM, Luyben KChAM, Boon L, Nienow AW (2000) Mixing in largescale vessels stirred with multiple radial or radial and axial uppumping impellers: modeling and measurements. Chem Eng Sci 55:5881–5896CrossRefGoogle Scholar
 Wang H, Jia X, Wang X, Zhou Z, Wen J, Zhang J (2014) CFD modeling of hydrodynamic characteristics of gasliquid twophase stirred tank. Appl Math Model 38:63–92. https://doi.org/10.1016/j.apm.2013.05.032 CrossRefGoogle Scholar
 Xia JY, Wang YH, Zhang SL, Chen N, Yin P, Zhung YP, Chu J (2009) Fluid dynamics investigation of variant impeller combinations by simulation and fermentation experiment. Biochem Eng J 43:252–260. https://doi.org/10.1016/j.bej.2008.10.010 CrossRefGoogle Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.