Simulating Gas-Liquid Flows in an External Loop Airlift Reactor

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1 Mechanical Engineering Conference Presentations, Papers, and Proceedings Mechanical Engineering Simulating Gas-Liquid Flows in an External Loop Airlift Reactor Deify Law Virginia Polytechnic Institute and State University Francine Battaglia Virginia Polytechnic Institute and State University Theodore J. Heindel Iowa State University, Follow this and additional works at: Part of the Complex Fluids Commons, Energy Systems Commons, and the Fluid Dynamics Commons Recommended Citation Law, Deify; Battaglia, Francine; and Heindel, Theodore J., "Simulating Gas-Liquid Flows in an External Loop Airlift Reactor" (2008). Mechanical Engineering Conference Presentations, Papers, and Proceedings This Conference Proceeding is brought to you for free and open access by the Mechanical Engineering at Iowa State University Digital Repository. It has been accepted for inclusion in Mechanical Engineering Conference Presentations, Papers, and Proceedings by an authorized administrator of Iowa State University Digital Repository. For more information, please contact

2 Simulating Gas-Liquid Flows in an External Loop Airlift Reactor Abstract The external loop airlift reactor (ELALR) is a modified bubble column reactor that is composed of two vertical columns that are connected with two horizontal connectors. Airlift reactors are utilized in fermentation processes and are preferred over traditional bubble column reactors because they can operate over a wider range of conditions. Computational fluid dynamics (CFD) simulations can be used to enhance our understanding of the hydrodynamics within these reactors. In the present work, the gas-liquid flow dynamics in an external loop airlift reactor are simulated using CFDLib with an Eulerian-Eulerian ensembleaveraging method in two-dimensional (2D) and three-dimensional (3D) coordinate systems. In addition, models are employed for the interphase momentum transfer drag coefficient and turbulence behavior. The CFD simulations for temporal and spatial averaged gas holdup are compared to the experimental measurements of Jones and Heindel [1] who used a 10.2 cm diameter ELALR over a range of superficial gas velocities from 0.5 to 20 cm/s. The effect of specifying a mean bubble diameter size for the CFD modeling is examined. The objectives are to validate 2D and 3D CFD simulations with experimental data in order to predict the hydrodynamics in an airlift reactor for future studies on scale-up and design. Disciplines Complex Fluids Energy Systems Fluid Dynamics Comments This is a conference proceeding from ASME 2008 International Mechanical Engineering Congress and Exposition 10 (2008): 395, doi: /imece Posted with permission. This conference proceeding is available at Iowa State University Digital Repository:

3 Proceedings of IMECE ASME International Mechanical Engineering Congress and Exposition October 31-November 6, 2008, Boston, Massachusetts, USA IMECE Simulating Gas-Liquid Flows in an External Loop Airlift Reactor Deify Law and Francine Battaglia Department of Mechanical Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Theodore J. Heindel Department of Mechanical Engineering Iowa State University Ames, Iowa ABSTRACT The external loop airlift reactor (ELALR) is a modified bubble column reactor that is composed of two vertical columns that are connected with two horizontal connectors. Airlift reactors are utilized in fermentation processes and are preferred over traditional bubble column reactors because they can operate over a wider range of conditions. Computational fluid dynamics (CFD) simulations can be used to enhance our understanding of the hydrodynamics within these reactors. In the present work, the gas-liquid flow dynamics in an external loop airlift reactor are simulated using CFDLib with an Eulerian-Eulerian ensemble-averaging method in twodimensional (2D) and three-dimensional (3D) coordinate systems. In addition, models are employed for the interphase momentum transfer drag coefficient and turbulence behavior. The CFD simulations for temporal and spatial averaged gas holdup are compared to the experimental measurements of Jones and Heindel [I] who used a 10.2 em diameter ELALR over a range of superficial gas velocities from 0.5 to 20 cm/s. The effect of specifying a mean bubble diameter size for the CFD modeling is examined. The objectives are to validate 2D and 3D CFD simulations with experimental data in order to predict the hydrodynamics in an airlift reactor for future studies on scale-up and design. INTRODUCTION Airlift reactors are widely used in many bioprocessing applications due to their excellent heat and mass transfer characteristics, simple construction, and ease of operation [2]. The airlift reactor is made of two sections interconnected at top and bottom with horizontal connectors. One section (the riser) is gased, while the other (the downcomer) is not. As a consequence of the density difference between the bubbly mixture in the riser and liquid in the downcomer, the liquid starts to circulate [3]. Two basic classifications of airlift reactors are the internal loop and external loop reactors. An internal loop reactor is a modified bubble column that has been subdivided into a riser and downcomer by the addition of a bafile or a draught tube [1]. The external loop airlift reactor (ELALR) is composed of a riser and downcomer that are joined together with two horizontal connectors. A schematic of an ELALR is shown in Figure 1. The airlift reactors are preferred over traditional bubble column reactors due to well directed liquid circulation, thus facilitating the cultivation of shear sensitive organisms; as a result these reactors are widely used in the biochemical industry and for waste water treatment [ 4]. Airlift reactor hydrodynamics are studied experimentally and computationally for scale-up and design considerations. Fullscale experimentation in airlift reactors is expensive and therefore, a more cost-effective approach is by using validated computational fluid dynamics (CFD) models. In the past, numerous research projects have been performed experimentally [I,5-18] and computationally [3-4, 18-19] to develop a better understanding of airlift reactor hydrodynamics. Numerical simulations of airlift reactors employing an Eulerian-Eulerian two-fluid model [3-4,18-19] were surveyed and literature on Eulerian-Lagrangian simulations of airlift reactor hydrodynamics were not found. The Eulerian-Eulerian model treats dispersed (gas bubbles) and continuous (liquid) phases as interpenetrating continua, and describes the motion for gas and liquid phases in an Eulerian frame of reference. Mudde and van Den Akker [3] and van Baten et al. [19] performed two-dimensional (2D) and three-dimensional (3D) simulations of gas-liquid flows for an internal airlift reactor using an Eulerian-Eulerian approach. Mudde and van Den Akker [3] investigated a rectangular reactor whereas van Baten et al. [ 19] studied a cylindrical reactor. Other investigators, such as Wang et al. [ 18] who Corresponding author; fbattaglia@vt.edu 395

4 conducted two-dimensional steady state simulations of a cylindrical external loop airlift reactor and Roy et al. [4] who conducted three-dimensional steady state simulations of a cylindrical external loop airlift reactor, used the Eulerian Eulerian method as well. It should be noted that Wang et al. [18] conducted experiments in addition to numerical simulations. In the present work, the gas-liquid flow dynamics in an external loop airlift reactor are simulated using CFDLib in twoand three-dimensions. The Schiller-Naumann drag coefficient model is used and the turbulence model employed is either the bubble-pressure with bubble induced turbulence (BP+BIT) or the multiphase k-e model. An appropriate effective bubble diameter size is determined based on the superficial gas velocity in a parametric study for both 2D and 3D simulations. Simulations of the airlift reactor operated with different downcomer configuration modes are investigated. Temporal and spatial averaged gas holdup over a region in the riser and downcomer are computed using an averaged pressure difference method and compared to the experimental measurements for a cylindrical external loop airlift reactor. The objectives are to validate the CFD simulations with experimental data in order to determine an appropriate set of model parameters for future design analyses. NUMERICAL FORMULATION Governing equations The code, CFDLib, a multiphase simulation library developed at Los Alamos National Laboratory, is used to solve the governing equations for the two-phase flow of this study. The two-fluid Eulerian-Eulerian model is employed to represent each phase as interpenetrating continua and the conservation equations for mass and momentum for each phase are ensemble-averaged. Subscript c refers to the continuous (liquid water) phase and subscript d refers to the dispersed (air bubble) phase. The continuity equations for each phase, neglecting mass transfer, are: a -(acpc)+v (a pii )=0 8, c c c (1) The momentum equations for each phase are: :, (acpciij+ V (acpciiciij (3) = -acvp+ V Tc + Kdc(Ud -iij+ Fvm + PPcg (2) :, (adpdiid) + V (adpdii)id) =-a/vp+v.;. +Kcd(iic -ii.)-fvm + p.a.g The terms on the right hand side of Equations (3) and (4) represent, from left to right, the pressure gradient, effective stress, interfacial momentum exchange (drag and virtual mass forces), and the gravitational force. The closures for turbulence modeling and interfacial momentum exchange in Equations (3) and ( 4) are discussed next. Turbulence modeling Turbulence contributions for the continuous and the dispersed phases are modeled through a set of modified standard k-& equations that calculate the turbulence generated at the gas-liquid interface in the form of a slip-production energy term [20,21]. The modified k-& equations are used only for high superficial gas velocity flows and the equations are:! (a 1 p 1 k 1 )+ V (a 1 p 1 ka) =V (a 1 11 ' 1 Vk 1 J+a 1G 1 -a 1p 1& 1 + LPkiKkllii 1 -iil +2LEkl(k,-k 1 ) where u" I-* I** It should be noted that the subscripts k and I represent two different phases. The first three terms on the right hand side of Eq. (5) account for turbulent diffusion, mean flow shear production, and decay of turbulence kinetic energy of phase k, respectively. The fourth term on the right hand side of Eq. (5) accounts for production of turbulence energy from slip between phases. The coefficient pkl is given by: (4) (5) (6) (7) (8) (9) (10) 396

5 where a 1/ 3 at=_t_ Pt +pc (11) and Pc is the continuous phase density. The last term in Eq. (5) accounts for the exchange of turbulence energy among phases. The ftrst three terms on the right hand side of Eq. (6) account for the diffusion of turbulence dissipation, the mean flow velocity gradient production term, and the homogeneous dissipation term, respectively. The last group of terms in Eq. (6) describes the effect of interfacial momentum transfer on the production of turbulence dissipation. The form of Eq. (9) models a return-to-isotropy effect due to fluctuating interfacial momentum coupling and reduces the turbulent viscosity from that predicted by the single-phase model. The turbulence energy exchange rate coefficient Ekl is given by: (12) and Re is the bubble Reynolds number to be discussed later. The time constant T 11 is given by the following empirical correlation: (13) This correlation was obtained by fttting predictions of turbulence kinetic energy to data from experiments on homogeneous sedimenting and bubbly systems [22-25]. The term K 11 is the momentum exchange coefficient and the model will be discussed next. Equations (7) and (8) are closure models for the turbulent viscosity J.L,,t and the production of turbulent kinetic energy Gk of phase k. The turbulent parameters are set using standard empirical values for k-c turbulence modeling where C 1 = 1.44, C 2 c = 1.92, C"' = 0.09, O'k = 1.0, and O'c = 1.3. Interfacial momentum exchange The interfacial momentum exchange terms in the momentum conservation equations for each phase consist of drag and virtual mass force terms. The drag force for the gas and liquid is modeled, respectively, as: where Cn is the drag coefficient. The virtual mass force F..., is modeled as: F = 0 Sa p ( diic _ diid)... d c dt dt and the coefficient of0.5 is used for a spherical bubble. (15) Drag coefficient model The drag coefficient model proposed by Schiller and Naumann [26] is used in the present work: C ={24(1+0.15Re 0687 )/Re D 0.44 Re~1000 Re > 1000 (16) where Re = Pc iud -ucidb/.uc is the bubble Reynolds number based on a characteristic (effective) bubble diameter, relative velocity between the two phases, and the liquid density and dynamic viscosity. Bubble Pressure Model The bubble pressure (BP) model represents the transport of momentum ansmg from bubble-velocity fluctuations, collisions, and hydrodynamic interactions. The BP model is reported in the literature to play an important role in bubblephase stability [27]. Biesheuvel and Gorissen [28] proposed a bubble pressure model of the form: (17) The gradient of Eq. (17) is added to the right hand side of the gas momentum Eq. (4). A positive value of dp,/da.:t acts as a driving force for bubbles to move from areas of higher a.:t to areas of lower a.:t and facilitates stabilization of the bubblyflow regime. The virtual mass coefficient C 8 p of an isolated spherical bubble is 0.5. The bubble pressure is proportional to the slip velocity and gas holdup. The gas holdup at close packing adcp is set equal to 1.0 in this study. The BP model must be employed with a bubble induced turbulence (BIT) model to obtain numerical stability and they are only used for low superficial gas velocity flows (typically homogeneous flow) [29-30]. Sato et al. [31] proposed a BIT model proportional to the bubble diameter and slip velocity of the rising bubbles: (18) (14) where the value of the proportionality constant C 8 r is 0.6. Eq. (18) replaces Eq. (7) when the BIT model is applied. The BIT model yields an effective viscosity in the liquid (continuous) phase that is the sum of the molecular viscosity of the 397

6 continuous phase and the turbulent viscosity calculated from the BIT model, whereas the effective viscosity for the dispersed phase is assumed to equal the molecular viscosity of the dispersed phase. SIMULATION CONDITIONS CFDLib uses a finite-volume technique to integrate the time-dependent equations of motion that govern multiphase flows. The code is based on an Arbitrary Lagrangian-Eulerian (ALE) scheme as described by Hirt et al. [32]. The name refers to the flexibility of the scheme, which allows for the mesh either to be moved along with the fluid (Lagrangian), to remain in a fixed position (Eulerian), or to be moved in another fashion as selected by the user. The ALE scheme is designed to handle flows at any speed, including the incompressible flow and hypersonic flow, and it allows for multifluid and multiphase calculations for an arbitrary number of fluid fields. The Marker and Cell (MAC) method has been selected in CFDLib to simulate the incompressible gas-liquid two phase flow. Simulations are performed using a fixed grid to match the experimental conditions of Jones and Heindel [I]; the cylindrical external loop airlift reactor is H 1 = 2.4 m high for a d 1 = m riser diameter and a d 2 = downcomer diameter, as shown in Figure 1. The static water height in the column is H 2 = 1.42 m. The horizontal connectors are located at H 4 = 0.05 m and H 3 = 1.27 m. The length of the horizontal connector is W = 13.3 em. In the experiments [1], air was aerated through the bottom of the riser column using a 2.22% open area ratio distributor plate, which creates a relatively uniform inlet flow. Therefore, the computational inlet condition assumes a uniform inlet velocity Ug to approximate the experimental condition for a large number of uniformly distributed holes. The three downcomer configurations are: both valve A and vent B closed (BC mode for bubble column), valve A open and vent B closed (CV mode for closed vent), and both valve A and vent B open (OV mode for open vent). No-slip and outflow conditions are applied at the walls and top of the column, respectively. If the vent is closed, the noslip condition is applied; otherwise the outflow condition is used for the open vent. An effective bubble size db depending on the superficial gas velocity is used to represent the dispersed gas phase. The convergence criteria are set to 1 x 1 o 8 for a change in the residuals of the dependent variables. All the simulations used an adaptive time step to march the solution forward; the flow achieves a pseudo-steady state after 20 s. The time-averaging process includes results from 20 s to 90 s for a total of 7000 realizations. The simulations are performed at 1, 5, 10, 15, and 20 crnls superficial gas velocity. For the following section, the averaged gas holdup for a region within the height a and b in the column is defined as (20) where P 1, p 1, hab and g are the liquid hydrostatic pressure, liquid density, height difference between a and b, and gravitational acceleration. The over bar represents the temporal and spatial average of the studied variable. The heights a and bare 10.2 and em, respectively, in the riser column, and 5 and 67.1 em, respectively, in the downcomer column. RESULTS AND DISCUSSION Bubble Column (BC) Study The 2D and 3D computational domains were simulated using a Cartesian coordinate system. The 2D simulation used single-block structured cells with /);x = em and Ay = 0.45 em, whereas the 3D grid used multi-block structured cells with /);x = em, Ay = em, and!lz = 1 em. The Ay and!lz represent vertical increments in 2D and 3D, respectively. The BC mode simulations were conducted for the riser column only; as mentioned, the external loop airlift reactor approximates a semi-batch bubble column when both the valve A and vent B are closed [1]. For the BC study, the computational models are tested to determine the effects of selecting an effective bubble diameter, turbulence modeling, and 2D versus 3D simulations. d2 w d2 air dl water Figure 1. Geometrical model of air-water external loop airlift reactor. Figure 2 compares the averaged gas holdup for the 2D and 3D simulations with the experiments [1]. The absolute gas holdup uncertainty for the experiments presented in Figure 2 is ± The effective bubble diameter size used was guided by experimental observations [35], which were reported to be within 0.4 and 0.5 em, depending on the superficial gas ug H3 H2 HI 398

7 ~ A "1::! ~:r Experiments db= 0.4 em (20, BP+BIT) db= 0.4 em (20) db= 0.5 em (20) db= 0.6 em (20) db= 0.4 em (30, BP+BIT) db= 0.4 em (30) db= 0.5 em (30) I" l... t. I 0 -g I 10 Ug (cm/s) I 15 I 20 Figure 2. Comparison of averaged gas holdup simulations with experiments [ 1] for the BC mode at different superficial gas velocities. velocity. As a starting point, the effective bubble diameter used in the 2D simulations was 0.4 em for Ug = 1, 5, and 10 crn!s. For U 8 = 15 crnls, db= 0.5 em was used and for U 8 = 20 crnls, db= 0.6 em was specified. The reason for using larger effective bubble diameters with increasing gas velocity is that the averaged gas holdup magnitude is found to be inversely proportional to the bubble diameter size with 2D simulations. The 2D predictions agree well with the experiments except at U 8 = 5 crnls, which is considered a transitional flow regime [33]. Two turbulent models, the BIT and the multiphase k-c models were tested at 5 crnls superficial gas velocity. The BP+BIT model predicts a slightly larger gas holdup as compared to the multiphase k-c model but neither 2D case compares well with the experiments. The simulation predicts the experiment well at 1 crnls superficial gas velocity that employs the BP+BIT model, which is expected for a homogeneous flow [30,34]. A parametric study of the effective bubble diameter was also performed for 3D simulations. At 15 crn!s superficial gas velocity, the 3D simulation underpredicts the experiment using db = 0.5 em whereas the predicted gas holdup has a closer agreement with the experiment when db = 0.4 em. This finding further substantiates that the bubble diameter size is within the experimental observations of Jones [33]. It should be noted that the 3D simulation using BP+BIT model with 0.4 em bubble diameter size resolves the failed prediction by the 2D simulation at 5 crnls and the 3D simulation compares very well with the experiment. Figure 3 shows the comparison of averaged gas holdup at 15 crnls superficial gas velocity for the 2D and 3D simulations. Averaged gas holdup in the BC mode predicted by the 2D and (a) 2D (b) 3D Figure 3. Comparison of averaged gas holdup of mode BC at 15 crnls superficial gas velocity in (a) 2D and (b) 3D simulations. 3D simulations are generally comparable with each other. The 2D simulation predicts a higher bed height as compared to the 3D simulation, which corresponds to the higher gas holdup as shown in Figure 2. Open Vent {OV) Study The 2D computational domain was simulated to compare with experiments of the OV mode [1]. The 2D simulation used 7574 block structured cells with,ix = em and ~y = em. Figure 4 compares averaged gas holdup for the 2D simulations with the experiments [ 1] at various superficial gas velocities for the riser and downcomer. The absolute gas holdup uncertainty for the experiments presented in Figure is ± Predictions generally agree well with the experiments except at 5 crnls superficial gas velocity and this finding is similar to BC mode study. Both turbulent models were tested. Likewise, the BP+BIT model has a closer agreement with experiment as compared to the multiphase k-e model. It should be noted that the downcomer simulation predicted by the BP+BIT model compares well with the experiment for 5 crnls superficial gas velocity. The simulation predicts both the riser and downcomer experiments quantitatively well for U 8 = 1 crn!s when the BP+BIT model is employed and at higher superficial gas velocities that employ the multiphase k-t: model. The effective bubble diameter size used in the simulations is 399

8 "l:s ~ 0.25 Riser Experiments Downcomer Experiments db= 0.4 em (Riser, BP+BIT) db= 0.4 em (Downeomer, BP+BIT) db= 0.4 em (Riser) db= 0.4 em (Downeomer) db= 0.5 em (Riser) db= 0.5 em (Downcomer) db= 0.6 em (Riser) db= 0.6 em (Downcomer) I I:..I...:. I I... <I! I I Ug (cmls) Figure 4. Comparison of averaged gas holdup simulations and experiments [ 1] for the OV mode at different superficial gas velocities. also found to increase as the superficial gas velocity increases and Jones and Heindel [l] observed similar trends. The 3D simulations for the OV mode that will be performed as future work have the potential of delivering closer bubble diameter size to the experimental findings based on the previous discussion of the BC mode study. Comparison of Different Configuration Modes A comparison of different configuration modes is investigated. The simulations are conducted at 10 crnls superficial gas velocity in a 2D Cartesian coordinate system. The intention is to understand the flow dynamics within the reactor operated with different downcomer configurations. Figures 5 and 6 present the instantaneous and time-averaged gas holdup results, respectively, for the BC, CV, and OV configuration modes. The instantaneous gas holdup exhibits a vortex street structure in the liquid bed for all modes. The OV mode gas holdup distribution becomes smeared near the upper connection of the downcomer as compared to the CV mode. The CV mode predictions indicate a higher expansion of the bubbling bed to approximately 190 em. For both the CV and OV modes, a large gas bubble region is observed in the downcomer in the vicinity of the horizontal connector at 127 em height. Jones and Heindel [1] obtained similar gas bubble profiles at the mentioned location and qualitatively compares well with the CFD predictions. Furthermore, zero gas holdup is predicted in the lower liquid bed region of the downcomer in the CV mode simulation and it agrees well with the experimental findings [1]. For the time-averaged gas holdups shown in Figure 6, both BC and CV modes predict a gas-rich central region in the riser, whereas the OV mode predicts nonuniform gas holdup. CONCLUSIONS The gas-liquid flow dynamics in an external loop airlift reactor were simulated using CFDLib in two- and threedimensional Cartesian coordinates using the Schiller-Naumann drag coefficient model. The turbulence modeling choices of BP+BIT or multiphase k-e model, and a parametric study on the appropriate effective bubble diameter size was performed. Simulations of the airlift reactor operating with different downcomer configurations were also investigated. Temporal and spatial averaged gas holdup was computed using an averaged pressure difference method and compared to the experimental measurements for a cylindrical external loop airlift reactor. For the BC mode, the numerical predictions agree well with the experiments except at 5 crnls superficial gas velocity, which is considered a transitional flow regime. The effective bubble diameter size used in the simulations was found to be close to experimental observation that is within 0.4 and 0.5 em and this notion was further substantiated when the simulation was performed for a 3D domain. The BP+BIT model predicted a closer gas holdup magnitude to the experiment at 5 crnls superficial gas velocity as compared to the multiphase k-e model Similar findings in terms of bubble diameter size and turbulence models were found for the OV mode study. The bubble diameter size for the simulations increased as superficial gas velocity increased for both BC and OV modes. Jones and Heindel [ 1] reported similar bubble I 0.9 (a) BC (b) cv (c) OV Figure 5. Instantaneous gas holdups with (a) BC, (b) CV, and (c) OV modes of operation at Ug = 10 cm/s. 400

9 I Fvm virtual mass force Gk production of turbulent kinetic energy for phase k (m 2 /s 3 ) g acceleration due to gravity (m/s 2 ) H height from gas distributor Kkl interfacial momentum exchange term between phase k and I (kg/m 3 ) k turbulent kinetic energy per unit mass (m 2 /s 2 ) p pressure (Pa) u velocity (m/s) Re Reynolds number (a) BC (b) cv (c) OV Figure 6. Time-averaged gas holdups with (a) BC, <?) CV, and (c) OV modes of operation at 10 cm/s superficial gas velocity. diameter size observations. Simulations of different configuration modes predicted instantaneous gas holdup~ of both CV and OV modes, especially at the downcomer regwn, which agreed well with the experiments. In general, both BC and CV modes predicted a central gas rich region whereas the OV mode predicted a nonuniform gas holdup distribution in the external loop airlift reactor column. ACKNOWLEDGMENTS The authors would like to thank the generous financial support from the U.S. Department of Agriculture, Grant no Additional appreciation is extended to the High Performance Computing Center at Iowa State University for their computer and technical support. NOMENCLATURE a coefficient in turbulence model equation c,.. C 1.. CP turbulence model parameters C 8 p Csr C 0 d db E virtual mass coefficient bubble induced turbulence constant drag coefficient column diameter (m) effective bubble diameter (m) turbulence energy exchange rate coefficient (kg/m 3 s) Greek Symbols adcp gas holdup at close packing a holdup p coefficient in turbulence model equation turbulent energy dissipation rate for continuous phase (m 2 /s 3 ) molecular dynamic viscosity for continuous phase (Pa s) turbulent dynamic viscosity for continuous phase (Pa s) p density (kg/m 3 ) turbulent Schmidt number for k and &, respectively effective stress (N/m 2 ) time constant Subscripts c d k continuous phase dispersed phase represents either continuous or dispersed phase if k is continuous phase, then I is dispersed phase and vice versa REFERENCES [1] Jones, S.T., Heindel, T.J., 2006, "The effect of a mod~fi~d downcomer on the hydrodynamics in an external loop arrhft reactor", Proceedings of the ASME Joint U.S.-European F~uid.s Engineering Summer Meeting, FEDSM , Miami, FL. [2] Chisti, M. Y., 1989, "Airlift bioreactors", Elsevier Applied Biotechnology Series, Elsevier Applied Science, London. [3] Mudde, R.F., Van Den Akker, H.E.A., 2001, "2D a?d 3D simulations of an internal airlift loop reactor on the basis of a two-fluid model", Chemical Engineering Science, 56, pp

10 [4] Roy, S., Dhotre, M.T., Joshi, J.B., 2006, "CFD Simulation of flow and axial dispersion in external loop airlift reactor", Chemical Engineering Research and Design, 84(A8), pp [5] Bentifraouine, C., Xuereb, C., and Riba, J.-P., 1997, "Effect of gas liquid separator and liquid height on the global hydrodynamic parameters of an external loop airlift contactor", Chemical Engineering Journal, 66, pp [6) Choi, K.H., 2001, "Hydrodynamic and mass transfer characteristics of external- loop airlift reactors without an extension tube above the downcomer", Korean Journal of Chemical Engineering, 18(2), pp [7] Gavrilescu, M., and Tudose, R.Z., 1997, "Mixing studies in external- loop airlift reactors", Chemical Engineering Journal, 66, pp [8] Merchuk, J.C., and Siegal, M.H., 1988, "Air-lift reactors in chemical and biological technology", Journal of Chemical Technology and Biotechnology, 41, pp [9] Snape, J.B., Zahradnik, J., Fialova, M., and Thomas, N.M., 1995, "Liquid-phase properties and sparger design effects in an external-loop airlift reactor", Chemical Engineering Science, 50(20), pp [10] Bello, R., Ade, Robinson, C.W., and Moo-Young, M., 1984, "Liquid circulation and mixing characteristics of airlift contactors", The Canadian Journal of Chemical Engineering, 62, pp [ 11] Bentifraouine, C., Xuereb, C., and Riba, J.-P., 1997, "An experimental study of the hydrodynamic characteristics of external loop airlift contactors", Journal of Chemical Technology and Biotechnology, 69, pp [12] Gavrilescu, M., and Tudose, R.Z., 1996, "Effects of downcomer-to-riser cross sectional area ratio on operation behavior of external loop airlift bioreactors", Bioprocess Engineering, 15, pp [13] Gavrilescu, M., and Tudose, R.Z., 1995, "Study of the liquid circulation velocity in external-loop airlift bioreactors", Bioprocess Engineering, 14, pp [14] Merchuk, J.C., and Stein, Y., 1981, "Local holdup and liquid velocity in air-lift reactors", AIChE Journal, 27(3), pp [15] Choi, K.H., and Lee, W.K., 1993, "Circulation liquid velocity, gas holdup and volumetric oxygen transfer coefficient in external-loop airlift reactors", Journal of Chemical Technology and Biotechnology, 56, pp [16) Su, X., and Heindel, T.J., 2005, "Effect of perforated plate open area on gas holdup in rayon fiber suspensions", Journal of Fluids Engineering, 127(4), pp [17] Chisti, M.Y., Halard, B., and Moo-Young, M., 1988, "Liquid circulation in airlift reactors", Chemical Engineering Science, 43(3), pp [18] Wang, T., Wang, J., Jin, Y., 2004, "Experimental study and CFD simulation of hydrodynamics behaviours in an external loop airlift slurry reactor", The Canadian Journal of Chemical Engineering, 82, pp [19] van Baten, J.M., Ellenberger, J., and Krishna, R., 2003, "Using CFD to describe the hydrodynamics of internal air-lift reactors", The Canadian Journal of Chemical Engineering, 81, pp [20] Kashiwa, B.A., VanderHeyden, W.B., 2000, "Toward a General Theory for Multiphase Turbulence", LA MS Report. [21] Launder, B.E., Spalding, D.B., 1974, "The numerical computation of turbulent flows", Computer Methods in Applied Mechanical Engineering, 3, pp [22] Lance, M., Bataille, J., 1991, "Turbulence in the liquid phase of a uniform bubbly air-water flow", Journal of Fluid Mechanics, 222, pp [23] Mizukami, M., Parthasarathy, R.N., Faeth, GM., 1992, "Particle-generated turbulence in homogeneous dilute dispersed flows", International Journal of Multiphase Flow, 18, pp [24] Parthasarathy, R.N., Faeth, G.M., 1990a, "Turbulence modulation in homogeneous dilute particle-lade flows", Journal of Fluid Mechanics, 220, pp [25] Parthasarathy, R.N., Faeth, GM., 1990b, "Turbulent dispersion of particles in self-generated homogenous turbulence", Journal of Fluid Mechanics, 220, pp [26] Schiller, L., Naumann, A., 1933, "Uber die grundlegenden berechnungen bei der schwerkraftaufbereitung. Zeitung des vereins deutscher ingenieure", pp [27) Spelt PDM, Sangani A, 1998, "Properties and averaged equations for flows of bubbly liquids", Applied Science Reserve, 58, pp [28] Biesheuvel A, Gorissen WCM, 1990, "Void fraction disturbances in a uniform bubbly fluid", International Journal ofmultiphase Flow, 16, pp

11 (29) Monahan, S.M., Vitankar, V.S., Fox, R.O., "CFD predictions for flow-regime transitions in bubble columns", AIChE Journal, 51, pp (30] Law, D., Battaglia, F., Heindel, T.J., 2008, "Model Validation for Low and High Superficial Gas Velocity Bubble Column Flows", Chemical Engineering Science, doi /j.ces (31] Sato, Y., Sadatomi, M., Sekoguchi, K., 1981, "Momentum and heat transfer in two-phase bubble flow 1", International Journal ofmultiphase Flow, 7, pp (32] Hirt CW, Amsden AA, Cook JL., 1974, "An arbitrary Lagrangian-Eulerian computing method for all flow speeds", Journal of Computational Physics, 14, pp [33] Shah, Y.T., Deckwer, W-D, 1983, "Hydrodynamics of bubble columns", Handbook of Fluids in Motion, Ann Arbor, MI: Ann Arbor Science, pp [34) Law, D., Battaglia, F., Heindel, T.J., 2007, "Stability issues for gas-liquid flows in bubble columns", Proceedings of the ASME Fluids Engineering Division, IMECE , Seattle, WA. [35] Jones, S.T., 2007, "Gas-liquid mass transfer in an external airlift loop reactor for syngas fermentation", Ph.D. Thesis, Dept. of Mechanical Engineering, Iowa State University, Ames, la. 403

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