Hydrodynamic behavior of an airlift reactor with net draft tube with different configurations: Numerical evaluation using CFD technique

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Hydrodynamic behavior of an airlift reactor with net draft tube with different configurations: Numerical evaluation using CFD technique Reza Salehpour, Elham Jalilnejad ∗ , Mehran Nalband, Kamran Ghasemzadeh Faculty of Chemical Engineering, Urmia University of Technology, Urmia, Iran

a r t i c l e

i n f o

Article history: Received 26 May 2019 Received in revised form 22 September 2019 Accepted 23 September 2019 Available online xxx Keywords: Airlift reactor Net draft tube Hydrodynamic behavior Computational fluid dynamics (CFD) Gas holdup Mass transfer coefficient

a b s t r a c t In terms of gas holdup, liquid velocity, and volumetric mass transfer coefficient for oxygen (KL a), the hydrodynamic behavior of four configurations of an airlift reactor (ALR) with a net draft tube (NDT) of different net mesh sizes (ALR-NDT-3, 6, 12, and ALR) have been numerically simulated for a range of inlet air flow rates. The effect of various levels of ratio of height (H) to inner tube diameter (D) of the net draft tube (H/D: 9.3, 10.7, 17.5, and 20) and ratio of inner cross-sectional area of the riser (Ar ) to the inner cross sectional area of the downcomer (Ad ) (Ad /Ar : 1.3 and 7) for different air flow rates is also evaluated for each reactor configuration operating with an air–water system. The two-fluid formulation coupled with the k–ε turbulence model is used for computational fluid dynamics (CFD) analysis of flow with Eulerian descriptions for the gas and liquid phases. Interactions between air bubbles and liquid are taken into account using momentum exchange and drag coefficient based on two different correlations. Trends in the predicted dynamical behavior are similar to those found experimentally. A good agreement was achieved suggesting that geometric effects are properly accounted for by the CFD model. After a comparison with experimental data, numerical simulations show significant enhanced gas holdup, liquid velocity, and KL a for the ALR-NDTs compared with the conventional ALR. Higher gas holdup values are achieved for ALR-NDT-3 than that for the other ALRs because it acts like a bubble column reactor as the holes present in the NDT are large. Maximum liquid velocities are seen in ALR-NDT-12, which operates like a conventional ALR. Moreover, the interaction between the NDT and upward gas flow leads to cross flow through the net, small bubbles, and high interfacial area as well as good mass transfer. This was significant in ALR-NDT-6 with maximum KL a value of 0.031 s−1 . The applied methodology provides an insightful understanding of the complex dynamic behavior of ALR-NDTs and may be helpful in optimizing the design and scale-up of reactors. © 2019 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Introduction Airlift reactors (ALRs) have received much attention as promising reactors for various applications in chemical, petrochemical, and biochemical industries. They are mostly used in aerobic fermentation, wastewater treatment, and chemical reactions. The ALR is a pneumatically agitated reactor that is designed to address the shortcomings present in the bubble column. This device is attractive for its lower likelihood for mechanical failure, relatively lower shear rate in the absence of mechanical agitation, and minimal loss of sterility. In biological applications, the mild and constant-shear environment in ALRs, in contrast to mixing tanks, is preferable

∗ Corresponding author. E-mail address: [email protected] (E. Jalilnejad).

for bioprocesses involving fragile particles (Jiang, Yang, & Yang, 2016; Mavaddat, Mousavi, Amini, Azargoshasb, & Shojaosadati, 2014). To improve its liquid mixing behavior and to increase its oxygen-transfer capability, the solid wall draft tube was replaced by a wire-mesh draft tube, known as a net draft tube (NDT). The resultant ALR-NDT produces a better local liquid circulation and larger gas–liquid interfacial areas, and therefore, produces a much higher mixing efficiency and an oxygen transport capability between rising and falling liquid streams in the ALR-NDT compared with the conventional ALR. The intensity of this type of interaction between the streams is optimized by balancing the pattern of flow distribution in both axial and radial directions (Jalilnejad & Vahabzadeh, 2014; Ranjbar, Aghtaei, Jalilnejad, & Vahabzadeh, 2016; Sanjari, Vahabzadeh, Naderifar, & Pesaran, 2014). A modified networks-of-zones model was developed (Fu et al., 2004) that revealed and distinguished the fundamental difference between

https://doi.org/10.1016/j.partic.2019.09.005 1674-2001/© 2019 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Salehpour, R., et al. Hydrodynamic behavior of an airlift reactor with net draft tube with different configurations: Numerical evaluation using CFD technique. Particuology (2019), https://doi.org/10.1016/j.partic.2019.09.005

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Nomenclature a Cd Ck C␮ C␧ db D Eö F g k mgl M P Qg KL a R Reb Sk T u uslip

Specific interfacial area, m2 /m3 Viscous drag coefficient, dimensionless Constant in k–ε model, dimensionless Constant in k–ε model, dimensionless Model parameter in turbulent dissipation energy equation, dimensionless Bubble diameter, m Diffusivity coefficient, m2 /s Eötvös number, dimensionless Volume force, N/m2 Gravitational constant, m/s2 Turbulent kinetic energy per unit mass, m2 /s2 Mass transfer rate from gas to liquid, kg/(m3 s) Molecular weight, kg/mol Pressure, Pa Inlet gas flow rate Volumetric mass transfer coefficient, s−1 Ideal gas constant, J/(mol K) Reynolds number, dimensionless Turbulent kinetic energy added term, kg/(m s3 ) Temperature, K Velocity, m/s Relative velocity between two phases (gas and liquid), m/s

Greek letters ϕ Phase volume fraction, m3 /m3  Density, kg/m3 ∼ Effective viscosity, Pa s T Turbulent viscosity, Pa s Turbulent energy dissipation rate per unit mass, ε m2 /s3  Surface tension, N/m k Prandtl number for turbulent kinetic energy, dimensionless Prandtl number for turbulent energy dissipation ␧ rate, dimensionless

three bubble-agitated tower-type bioreactors, using a key parameter ˇ representing the interaction intensity between neighboring rising and falling streams. A superior mixing performance of the net column reactors (ALR-NDT) over the conventional airlift and bubble column reactors (BCRs) was demonstrated and was attributed to an optimum local circulation achieved by the partial stream interactions available when using the NDT (Fu et al., 2004). The hydrodynamic characteristics such as gas holdup, liquid velocity, and mass transfer are of vital importance for evaluating the performance of all types of ALRs. Scaling up an ALR is still currently challenging because there is a complex relationship between the hydrodynamic behavior and the geometry of the reactor. Therefore, to design a good ALR, a method to predict accurately its behavior is needed and requires a comprehensive consideration of geometric designs and operating conditions influencing the hydrodynamic behavior and efficiency of various mass transfer processes. Several researchers have focused on these aspects (Ebadi Amooghin, Jafari, Sanaeepur, & Kargari, 2014; Moraveji & Davarnejad, 2011; Wadaugsorn, Limtrakul, Vatanatham, & Ramachandran, 2016; Zheng, Chen, Zhan, Gao, & Wang, 2018; Ziegenhein, Zalucky, Rzehak, & Lucas, 2016). Many empirical correlations have been proposed to evaluate the effect of riser-to-downcomer ratio, gas holdup, and superficial gas velocity in the reactors that are used to aid in current

industrial scale-up procedures. These correlations were however derived based on global hydrodynamics measurements that may not reflect the local intrinsic information. In addition, both global and local hydrodynamics measurements used to derive empirical correlations for scale-up purposes are accurate only for similar geometrical designs, operating conditions, and liquid properties (Luo & Al-Dahhan, 2011). Numerical methods have become appealing alternative procedures that allow flexible design solutions in a virtual experimentation environment where potential designs and configurations can be screened and also associated costs can be reduced. Computational fluid dynamic (CFD) modeling using the COMSOL Multiphysics software has been widely applied as one of the standard industrial simulation tools for the design, analysis, performance determination, and investigation of engineering systems involving fluid flows. CFD provides an alternative way to understand the gas–liquid behavior by providing the transient flow information that most experiments are unable to offer. As a result, it has motivated researchers to use CFD techniques to predict multiphase flow dynamics accurately for design and scale-up of reactor systems. Most studies are chiefly based on the two-fluid model, which assumes a gas phase and a liquid phase as an interpenetrating media; it is equivalent to the Euler–Euler approach, which describes the motion for the gas and liquid in an Eulerian frame of reference (Amani & Jalilnejad, 2017; Amani, Jalilnejad, & Mousavi, 2018; Ghasemzadeh, Zeynali, Basile, & Iulianelli, 2017; Ghasemzadeh, Ghahremani, Amiri, & Basile, 2019; Habibi, Nalband, & Jalilnejad, 2019). In recent years, to simulate gas–liquid twophase flow systems, a wide range of CFD studies on ALRs were performed, all of which were based on the Euler–Euler method (AL-Mashhadani, Wilkinson, & Zimmerman, 2015; Jiang et al., 2016; Lestinsky, Vecer, Vayrynen, & Wichterle, 2015; Nalband & Jalilnejad, 2018). Oey, Mudde, and van den Akker (2003) presented three-dimensional (3D) CFD simulations in a rectangular internal loop ALR with a two-fluid approach using a k–ε turbulence model. The effective stress and interfacial momentum transfer of the twophase flow was modeled using extra source terms and a drag force at different superficial gas velocities. An increase in superficial gas velocity had an inverse effect on the oscillation period of the liquid velocity in the downcomers (Oey et al., 2003). Mudde and van den Akker (2001) performed 2D and 3D CFD simulations of the gas–liquid flow in a rectangular internal loop ALR at low superficial gas velocities using a two-fluid model. The simulation took into consideration the effects of the drifting velocity, drag force, and virtual mass force on the overall liquid velocity and gas holdup at various superficial gas velocities. Better agreement with experimental data was achieved for the 3D simulations than for the 2D simulations for both hydrodynamic parameters (Mudde & van den Akker, 2001). In another work (Van Baten, Ellenberger, & Krishna, 2003), the Eulerian–Eulerian model was used to simulate the hydrodynamics of internal loop ALRs for various superficial gas velocities. Closure terms for the drag force and the standard k–ε turbulence model were applied and a reliable agreement was observed between the simulation results and the experimental data for gas holdup and liquid velocity in the downcomer and riser (Van Baten et al., 2003). Ebrahimifakhar, Mohsenzadeh, Moradi, Moraveji, and Salimi (2011) used CFD to investigate the hydrodynamic parameters of two internal airlift bioreactors with different configurations. A two-phase flow model provided by the application model for bubbly flow was employed to predict the effect of reactor geometry on the reactor hydrodynamics. The k–ε model was used to describe turbulence in the liquid phase and good agreement was found between simulation and experimental data for gas holdup and liquid circulation velocity. In work described in Jiang et al. (2016), the CFD method was used to evaluate the local hydrodynamics in the riser of an external loop ALR (EL-ALR) and the performances of three drag models were evaluated. The dual-bubble-size local drag

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Table 1 Structural parameters of the simulated ALR-NDT. Riser diameter, D (cm) Reactor diameter, DR (cm) Height of the NDT, H (cm) Height of the reactor, HR (cm) Mesh size of NDT

3

track the volume fraction of the bubbles. The governing equations used in this study are as follows: 1.6, 3 4.5 28, 32 37 3, 6, 12

Governing equations The momentum equation for the air–water mixture is given by

ϕq q model gave reasonable radial and axial distributions of gas holdup because correct values of the lumped parameter (i.e., the ratio of the coefficient of drag to the bubble diameter) could be achieved by this model for various operating conditions and radial positions. The radial profiles of the axial velocity of the liquid and gas predicted by this local model also agreed well with experimental data (Jiang et al., 2016). Although there are a number of experimental and modeling studies on conventional ALRs, only a few experimental studies have been conducted on applications of ALR-NDTs. However, none have conducted CFD simulations of this type of reactor as a novel and efficient type of ALR. In this study, a 3D model using CFD tools is developed for the first time based on a two-fluid system to simulate unsteady state flows in three ALR-NDTs configurations with different net mesh sizes (ALR-NDT-12, ALR-NDT-6, ALR-NDT-3) and in a conventional ALR as reference. The objective of this modeling was to evaluate the effect of the geometrical parameters, specifically, net tube mesh size (3, 6, 12), ratio of height (H) to inner tube diameter (D) of the NDT (H/D), ratio of inner cross-sectional area of the riser (Ar ) to the inner cross sectional area of the downcomer (Ad ) on hydrodynamic behavior of the reactors in terms of gas holdup (εg ), liquid velocity (VL ), and volumetric mass transfer coefficient (KL a). The predicted values of the hydrodynamic parameters for the four simulated reactors operating with different inlet air flow rates are validated using the experimental data presented in Sanjari et al. (2014) to confirm the two-fluid CFD model precision. Successful results would confirm the accuracy and efficiency in using CFD techniques in predicting dynamic flow behavior in different configurations of ALR-NDTs, which is necessary to achieve optimum design and successful scaling-up.

Computational fluid dynamics modeling The 3D transient simulations were performed using COMSOL Multiphysics 5.2 software to study the multiphase flow dynamics in an ALR with a NDT within the bubbly flow regime reported in Sanjari et al. (2014). The experimental set-up of the ALR (Fig. 1) used in the simulation includes a reactor, a cylindrical glass column with a diameter of 4.5 cm and a height of 37 cm. A conventional ALR is a reactor in which a solid draft tube is used instead of a NDT. The geometric specifications of the two reactors are listed in Table 1. The liquid phase is the primary phase and the gas phase is the dispersed phase. As a suitable model to set up a two-phase flow model for gas bubbles rising through a liquid, a turbulent bubbly flow model interface was used. This model is restricted to two parameters: the bubble equivalent diameter and the drag coefficient. This choice is related to the kind of bubbly flow that is of interest in this study, in which the dispersed phase controls the hydrodynamics. The bubbly flow model is a simplification of the two-fluid Euler–Euler model based on these assumptions: (a) gas density is negligible compared with liquid density; (b) the balance between viscous drag and pressure forces is responsible for the motion of the gas bubbles relative to the liquid; and (c) the two phases share the same pressure field. Accordingly, the momentum and continuity equations for the two phases combine although a gas phase transport equation is kept to



∂uq + ϕq q uq · ∇ uq = −∇ P + ∇ · ∂t



ϕq q + T



∇ uq + ∇ uq T −

2 (∇ uq )I 3



+ ϕq q g + F

(1)

where P denotes pressure, g the gravity vector, F any additional volume force, ϕ the phase volume fraction, and ␮ viscosity. Subscript q refers to the phase type (q=l for liquid phase and q=g for gas phase). The continuity equation for the liquid and gas phase system is

   ∂  l ϕl + g ϕg + ∇ · l ϕl ul + g ϕg ug = 0 ∂t

(2)

where u represents the velocity vector,  the density, and ϕ is the phase volume fraction. Subscripts “l” and “g” signify liquid and gas phase, respectively (Davarnejad, Bagheripoor, & Sahraei, 2012). The gas phase transport equation is

  ∂g ϕg + ∇ · g ϕg ug = −mgl ∂t

(3)

where mgl denotes the mass transfer rate from the gas to the liquid phase. Because the experimental data were not sufficient for the calculation of mgl , it was for this work assumed zero as a first approximation (AL-Mashhadani et al., 2015; Ebrahimifakhar et al., 2011). However, an empirical time model based on Higbie’s penetration theory was used for predicting volumetric mass transfer coefficient which is introduced in Section “Mass transfer modeling”. The gas velocity is determined from (Lestinsky, Vayrynen, Vecer, & Wichterle, 2012) ug = ul + uslip + udrift

(4)

where uslip is the relative velocity between the gas and the liquid. The drift velocity, udrift , is the additional condition for the chosen turbulent model arising from the correlation between the instantaneous distribution of bubbles and the motion of the liquid. The role of the drift velocity in the momentum balance equation is significant and necessary to explain the dispersion of the bubbles. It is calculated using udrift = −

∼ ∇ ϕg l ϕ

(5)

where ∼ represents an effective viscosity causing the drift (Lestinsky et al., 2015). The liquid volume fraction (ϕl ) is calculated from ϕl = 1 − ϕg

(6)

The equations of state for the liquid and gas phases are l = const

(7)

PM g = RT

(8)

where M denotes the molecular weight of the gas, Rthe ideal gas constant (8.314 J/(mol K)), and T the temperature (AL-Mashhadani et al., 2015). The choice of closure model for turbulence is of great importance for multiphase flow simulations. Although there are sophisticated models in use, the turbulence of the two-phase flow is more often modeled using the standard k–ε model as it offers reasonable accuracy at low computational cost as well as a robust convergence. In the majority of publications on numerical simulations of turbulent

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Fig. 1. Schematic of the ALR-NDT experimental set-up (Sanjari et al., 2014).

bubbly flows, the standard k–ε model developed for two-phase flow has been employed (Sokolichin, Eigenberger, & Lapin, 2004; Zhang, Wu, Feng, & Wei, 2018). A k–ε multiphase flow model in an ALR was validated in Dhanasekharan, Sanyal, Jain, and Haidari (2005) and hence used in this work to simulate turbulence. Turbulence modeling of a continuous phase is based on a two-equation turbulence model derived from the two-phase flow, including interfacial transfer of turbulent kinetic energy (k) and its dissipation rate (ε) (Luo & Al-Dahhan, 2011). According to the k–ε model, the turbulent viscosity is given by T = l C

k2 ε

∂k + l ul · ∇ k = ∇ · ∂t







Pk = T ∇ ul : ∇ ul + (∇ ul )T −

l

∂ε + l ul · ∇ ε = ∇ · ∂t



l +

T ε

2 (∇ · ul )2 3



ε ε2 ε + Cε1 Cε1 Pk − l Cε2 + Cε Sk k k k



−

2 k∇ · ul 3

(11)



∇ε

(12)

(9)

where C is a model constant. The values of k and ε are calculated using the closure equations (Ebrahimifakhar et al., 2011; Lestinsky et al., 2012) l

where the production term is calculated using



l +

T k





∇ k + Pk − l ε + Sk

(10)

The constants used in the standard k–ε turbulence model are (Lestinsky et al., 2012; Luo & Al-Dahhan, 2011) C = 0.09, Cε1 = 1.44, Cε2 = 1.92, k = 1, and ε = 1.3. The term Sk accounts for the bubble-induced turbulence and is given by Sk = −Ck ϕg ∇ P · uslip

(13)

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where Ck is a constant considered to be within the range of 0.01 < Ck < 1 as suggested in the literature (Ebrahimifakhar et al., 2011; Lestinsky et al., 2012; Nalband & Jalilnejad, 2018).

5

balance between viscous drag and pressure forces of the gas bubble (Ebrahimifakhar et al., 2011; Lestinsky et al., 2012): −∇ P = Cd

 3 l  uslip  uslip , 4 db

(14)

Drag force The interfacial forces include drag, lift, virtual mass force, and turbulent dispersion force. It is generally believed that drag is the predominant force in modeling the gas–liquid flows of bubble columns as well as ALRs (Chen, Sanyal, & Dudukovic, 2004). The magnitude of the drag force was found to be more than 100 times that of the other forces (Jiang et al., 2016; Laborde-Boutet, Larachi, Dromard, Delsart, & Schweich, 2009; Lucas & Tomiyama, 2011). The negligible effect of virtual mass force has also been pointed out in several works (Deen, Solberg, & Hjertager, 2001; Sokolichin & Eigenberger, 1994; Tabib, Roy, & Joshi, 2008; Thakre & Joshi, 1999). As suggested by Sokolichin and Eigenberger (1994), neglecting the lift force leads to satisfactory results if no clear experimental evidence for its direction and magnitude are available. Because the circulation in the ALR is controlled by the gas flow and primarily by buoyancy effects, drag is the only force taken into account in this work; in capturing the dynamics, the other forces are discarded to keep the number of interfacial forces to a minimum. This fact makes the selection of a proper drag model more important in simulations. The pressure–drag balance obtained from the slip model was used to calculate uslip . Based on the assumptions of this model, there is a

where db (m) denotes the bubble diameter, and Cd (dimensionless) the coefficient of viscous drag. The inlet bubble diameter in our numerical simulations is calculated using the equation reported in Johansen and Boysan (1988),

db = 0.35

Qg 2 g

0.2 (15)

where Qg is the inlet gas flow rate. From this bubble diameter, bubbles with diameters larger than 2 mm obey the large bubble drag law introduced in Sokolichin et al. (2004) and used to define Cd , Cd =

E o¨ =

0.622 1 E o¨

+ 0.235

gl db 

(16)

2

(17)

where E o¨ denotes the Eötvös number and the surface tension. Bubbles with diameter smaller than 2 mm obey the

Fig. 2. Generated meshes of the simulated reactors: (a) ALR-NDT-12, (b) ALR-NDT-6, (c) ALR-NDT-3, (d) conventional ALR, (e) symmetric and boundary conditions applied on computational domain (upper view of the reactor), (f) magnified view of the generated mesh.

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Hadamard–Rybczynski model, which is used to define Cd (Crowe, Sommerfeld, & Tsuji, 1997), Cd =

16 Reb

Reb =

(18)

  db l uslip  l

(19)

Mass transfer modeling The oxygen absorption capability in an ALR is often expressed by the volumetric mass transfer coefficient (KL a). Several theories have proposed formulas for gas-liquid mass transfer coefficient. However, a time model based on Higbie’s penetration theory has been widely used and accepted for determination of this coefficient. According to this theory, the liquid phase mass transfer coefficient for a bubble with a mobile surface has the form (Higbie, 1935; Huang, Yang, Yu, & Mao, 2010): 12ϕg KL a = db



Duslip db

(20)

where D denotes the diffusivity coefficient for gas in a liquid and is defined as T D= (21) l Mass transfer modeling is therefore applied based on an analytic function Eq. (20) dependent on ϕg , uslip , db , and D, which in turn are obtained from Eqs. (3), (14), (15), and (21). Initial and boundary conditions For this work, the entire volume of the ALR and ALR-NDTs and the NDT formed the computational domain and symmetrical conditions were applied along the centerline for all variables (Fig. 2). The boundary conditions for all reactor walls and the NDT were set as “no-slip” for the liquid phase and “no gas flux” for the gas phase. On the upper surface of the sparger, the wall function boundary condition was used for the liquid phase and the gas flux boundary condition was applied at six levels of 0.25, 0.5, 1, 1.5, 2, and 2.5 vvm for the gas phase. Because the outlet is a free surface (xy-plane, z = 37 cm), the outlet was considered to be at atmospheric pressure so that the gas leaving of the reactor moves freely. Considering the complex computations required and the symmetry of the reactor, only a quarter of the reactor was simulated to reduce run times. The temperature and pressure were 300 K and 1 atm, respectively. All gas bubbles were assumed to be the spheres with various diameters given by Eq. (15). Fig. 2 shows the geometry, the grid, and the axial symmetry used in the present 3D simulation of all the reactors tested. A time-dependent segregated solver was used for the calculation and the threshold for convergence is set to 10−3 . The time step was initially 0.0001 s and increased gradually. The final time step was not greater than 0.001 s. Initial simulation runs were conducted up to 30 s but, as shown in Fig. 3(a), a quasi-steady state was achieved in 15 s of simulation runtime and no difference was seen between the results of gas holdup value after 15 and 30 s. Thus, 15 s was chosen as the proper runtime for this simulation. The Courant–Friedrichs–Lewy (CFL) condition is the maximum allowable Courant number that a time-integrator can use and represents the quality of the solution. CFL constraint imposes severe restrictions on the size of the time-step relative to the spatial step in conventional explicit finite difference schemes. Explicit methods have the CFL condition near 1, whereas implicit solvers are usually less sensitive to numerical instability and so larger values from the CFL condition may be tolerated. COMSOL uses by default implicit timeintegration schemes for solving the transport equation instead

of explicit schemes. Although explicit schemes have an important CFL-type stability restriction on the time step, COMSOL uses implicit schemes within a sequential iterative approach that are stable for any t and remove stability limits (Dutykh, 2016; Giraldo, 2005; Heredia, 2017; O’Sullivan & O’Sullivan, 2011). Thus, the effect of applying different CFL values was not significant in this work. CFD simulations were used to predict the hydrodynamic parameters such as gas holdup, liquid velocity, and volumetric mass transfer coefficient for the different ALR-NDTs and the conventional ALR. Results and discussion The hydrodynamic behavior of ALRs are dependent on the column, the NDT dimensions, and gas/liquid flow rates. To understand their flow characteristics, we followed a systematic approach involving: (1) a preliminarily investigation of the grid independence of our model; (2) a verification of the reliability of simulations by comparing them with experimental measurements (model validation); (3) a study of the effect of different H/D and Ad /Ar values and NDT mesh size on gas holdup, liquid velocity, and volumetric mass transfer coefficient through simulations to understand the hydrodynamic behavior and flow distribution in ALRs; and (4) the evaluation and comparison of the accuracy of results of the CFD simulation model with the generated experimental correlation and their compatibility with experimental data. Investigation of grid independency The mesh generation method used in this study for different configurations of ALRs is shown in Fig. 2. Details of the computational grids for the different ALR configurations are summarized in Table 2. An unstructured mesh is used to manage the lower section and around the internal NDT to accommodate the complicated geometrical configuration of the gas distributor and net (Grid size 2), whereas a structured mesh is used for the rest (Grid size 1). The absolute value of the mesh element quality is always between 0 and 1, where 0 represents a degenerate element and 1 represents the best possible element. To avoid the impact of an inadequate mesh on the numerical simulation results, a mesh-independence study was performed using a gas flux of 0.5 vvm. Fig. 3(b) shows the CFD simulation results of gas holdup at different grid numbers for ALR-NDT-6. Clearly, increasing the number of grid cells leads to small variations in gas holdup; when the number of grid cells were 312,119 and 409,000, the difference in the simulation result for gas holdup was within 2% for ALR-NDT-6. Indeed, for the five different grid numbers used in this study, increasing the number of grid cells above 312,119 cells did not increase the accuracy of the simulation results significantly, although the computation expense was increased. Therefore, 288,905 cells was considered sufficient to ensure valid simulation results and was used in subsequent simulations. The same procedure was also applied to the rest of the columns used for simulations yielding optimum grid numbers of 358,997, 276,244, and 104,148 for ALR-NDT-12, ALR-NDT-3, and ALR, respectively. No finer meshes were used because of the limited calculation resources. Model validation To verify the reliability of the CFD model and accuracy of the numerical method for the laboratory-scale ALRs simulations, the CFD simulation results for gas holdup were validated against the experimental data acquired for four different configurations of ALRs at fixed geometrical conditions (Fig. 4). The hydrodynamic experiments were performed at five gas flow rates of 0.25, 0.5, 1, 1.5, 2, and 2.5 vvm (Sanjari et al., 2014). Based on these results,

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Fig. 3. (a) Gas holdup trend in time (convergence analysis), (b) CFD grid independence study based on gas holdup values for ALR-NDT-6. Table 2 Details of computational grids for the different ALR configurations. Reactor configuration

ALR-NDT-12 ALR-NDT-6 ALR-NDT-3 ALR

Sieve opening of NDT (mm)

1.41 3.36 6.73 –

Grid size 1 (mm)

Grid size 2 (mm)

Max

Min

Max

Min

3.7 3.7 4.1 4.1

1.14 1.14 1.2 1.2

1.59 1.91 2.1 2.84

0.28 0.59 0.63 0.85

Mesh number

Average grid quality

358,997 312,119 276,244 104,148

0.6774 0.6915 0.6749 0.7001

Fig. 4. Comparison of CFD predictions with experimental data based on gas holdup for four different configurations of ALRs at fixed geometrical conditions (H/D = 10.7, Ad /Ar = 1.3): (a) ALR-NDT-12, (b) ALR-NDT-6, (c) ALR-NDT-3, and (d) conventional ALR.

CFD simulation results agreed well with the experimental values. For the majority of tested reactors, the maximum difference between the experimental values and the CFD simulation results does not exceed 15% and an excellent compatibility was seen. Therefore, all the numerical solutions applied for modeling of the ALR-NDTs are acceptable and thus, the CFD simulation results are trustworthy.

Effect of net tube mesh size, H/D, and Ad /Ar on gas holdup in ALR–NDTs and ALR The influence of height-to-diameter ratio (H/D) and area ratios Ad /Ar on gas holdup parameter for ALR-NDT-12, ALR-NDT-6, ALRNDT-3, and the conventional ALR was obtained at various air flow rates (Figs. 5–8, respectively). The plots are drawn taking into

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Fig. 5. Gas holdup as a function of inlet air flow rate for ALR-NDT-12 with different geometry settings.

Fig. 6. Gas holdup as a function of inlet air flow rate for ALR-NDT-6 with different geometry settings.

account the different values of H/D (9.3, 10.7, 17.5, and 20) and Ad /Ar (1.3, 7). An air–water mixture circulation arises in the ALRs because of the differences in density between the gas and liquid phases. By increasing the inlet air flow rate, a larger number of

bubbles are generated in the riser resulting in an increase in the average gas holdup. The 3D gas holdup contours (Fig. 9) show similar trends in the distribution of local gas holdup along the column for all tested reactors. From an overall comparison among the

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Fig. 7. Gas holdup as a function of inlet air flow rate for ALR-NDT-3 with different geometry settings.

Fig. 8. Gas holdup as a function of inlet air flow rate for ALR with different geometry settings.

ALRs, higher gas holdup values were achieved for ALR-NDT-3 for which a maximum gas holdup value of 0.07 is attained at H/D = 9.3, Ad /Ar = 1.3, and air flow rate of 2.5 vvm (Fig. 7(b)) as verified by

experimental data. In Figs. 5–8, the H/D value has a reverse effect on gas holdup. By decreasing H/D at constant Ad /Ar , a slight increase is seen in gas holdup in the majority of the plots (the comparison

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Fig. 9. Gas holdup distribution profile in the reactors at fixed geometrical conditions (H/D = 10.7, Ad /Ar = 1.3): (a) ALR-NDT-12, (b) ALR-NDT-6, (c) ALR-NDT-3, and (d) conventional ALR.

was done for each figure between plots (a) with (b) and plots (c) with (d)). The simulated gas holdup values in all tested reactors are in qualitative agreement with the experimental data suggesting that the geometric effects are properly accounted for by the CFD model. In the majority of plots, absolute errors of less than 20% are seen for ALR-NDT-12, ALR-NDT-6, and ALR-NDT-3 (Figs. 5–7) which is acceptable in CFD simulations (Dhanasekharan et al., 2005; Ghasemi & Hosseini, 2012; Lopes, Almeida, & QuintaFerreira, 2011). Experimental and simulation errors are the main origin of this discrepancy, which is discussed comprehensively below and subsequent sections. The applied CFD method lead to underestimations of gas holdup in the majority of plots, most likely the consequence of the deviation in the average diameter of bubbles estimated in the reactor. Similar results were also reported by Huang et al. (2010) and lower bubble diameters were recommended to reduce the discrepancy between simulation and experiment. However, the gas holdup in gas–liquid systems changes widely with variations in bubble diameter and bubble number density as a result of coalescence and dissociation. Therefore, an accurate prediction of bubble size and number using better models such as the population balance model is critical. Nevertheless, because there is no experimental evidence of bubble diameter in the work of Sanjari et al. (2014), the bubble-size distribution is not considered in the present study and therefore may be the

source of discrepancies between CFD and experimental results. In addition, forces such as the Magnus force and virtual mass force were neglected as the gas bubble rotation is assumed negligible and the difference in density between liquid and air phase is great. However, drag force is very important and cannot be neglected. Thus, the source of the errors seen in plots may be due to these reasons and also experimental errors. From the results reported in Chisti (1998), the experimental methods used for measurements of hydrodynamic parameters in Sanjari et al. (2014) may lead to inaccurate results in small column reactors. Experimental errors are certain to be present and may be another source of large errors in the plots of this work. As the present work is the first simulation study on ALR-NDTs, clearly more experimental and modeling studies are needed in light of the above-mentioned aspects to produce more accurate results. The overall findings of gas holdup are in accordance with the results reported in Jalilnejad and Vahabzadeh (2014) in which the maximum and minimum gas holdup values were achieved in a BCR and conventional ALR. The performance of the latter was a little below that of the former. Obviously, the liquid-mixing capability of ALRs is significantly different from that in BCRs (Merchuk & Gluz, 2002). The pattern of fluid flow is more defined in the ALRs than in BCR because of the physical separation of upflowing and downflowing streams. As ALR-NDT-3 has the largest NDT mesh size, this reactor configuration acts similarly to BCR. By pumping the air

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Fig. 10. Liquid velocity as a function of inlet air flow rate for ALR-NDT-12 with different geometry settings.

through the riser section, the bubbles pass through the NDT easily, and the circulatory effect induced by NDT is not as significant in this reactor (Fig. 9). Therefore, higher gas holdup values are achieved in ALR-NDT-3 (Fig. 7) compared with other ALR-NDTs (Figs. 5 and 6) with the same H/D and Ad /Ar values. The minimum gas holdup value in the tested air flow rate range is seen in conventional ALR with H/D = 20 and Ad /Ar = 7 (Fig. 8(c)). In this reactor, the concentric solid tube used in the center blocks the radial movement of bubbles and causes bubbles to move upward in the riser in a uniform direction at a relatively uniform velocity. This may lead to a high coalescence rate of bubbles especially near the wall, and slug flow in high flow rates. After passing the riser section, the sudden widening at the top of the reactor leads to a lowering in bubble velocity, a dissociation of bubbles into smaller ones, and thus a disengagement of bubbles from the liquid surface. Therefore, very few bubbles are recirculated by the downward fluid as large bubbles escape from the gas–liquid separation region. However, in ALR-NDTs, the concentric NDT allows the bubbles in the riser to pass easily through the net. More bubbles then enter the downcomer section and remain in the main stream of the reactor leading to an enhancement of gas holdup in the system. Altogether, these facts lead to low gas holdup values for the ALR than for ALR-NDTs for the same H/D and Ad /Ar (Figs. 8 and 9). It is complicated to discuss the net effect of different H/D and Ad /Ar values on gas holdup of the tested reactor because H/D varies in all plots and no similar trend is seen in them. However, considering the results of Figs. 5–8, the (b) series of plots corresponding to H/D = 9.3 and Ad /Ar = 1.3 are representative of the highest gas holdup values among the reactors. The other main point to consider is the results of the empirical correlation developed in Sanjari et al. (2014) to model the experimental data that is also demonstrated in all figures. A significant difference is seen between the experimental data and the predicted values by Sanjari’s correlation model for gas holdup. These dif-

ferences confirm that the proposed correlation is inadequate in modeling and predicting the effect of different configurations on hydrodynamic behavior of the reactors. In regard to quantitative comparisons between simulations results and measurements, and also considering the inadequate empirical correlation proposed by Sanjari et al., the CFD model developed above is sufficient and gives a reasonably good agreement. Effect of net tube mesh size, H/D, and Ad /Ar on the liquid velocity in ALR–NDTs and ALR Liquid velocity is a very important design parameter that governs several key hydrodynamic parameters in rector design. Rates of heat and mass transfer, gas–liquid effective interfacial area, and mixing time are some parameters that exhibit a dependence on liquid velocity. Thus, it is very important to predict the liquidvelocity profile accurately. The CFD simulation results of liquid velocity along with experimental data are presented for ALR-NDT12, ALR-NDT-6, ALR-NDT-3, and conventional ALR (Figs. 10–13, respectively). Different geometrical ratios of the central NDT (different H/D and Ad /Ar values) are considered for each reactor in each figure. The overall liquid velocity increased in all reactor configurations by increasing the inlet air flow rate from 0.5 to 2.5vvm. This is as expected because, by increasing the inlet gas velocity, a well-directed intense liquid circulation improves and facilitates mixing and leads to higher liquid velocities. The liquid velocity in the conventional ALR for all H/D and Ad /Ar values is higher than that obtained for ALR-NDTs. This result is attributed to the presence of the solid tube in the ALR and leads to the appearance of a regular vertical flow in the riser, thereby obtaining higher liquid velocities. The central solid tube acts as a pumping device forcing the liquid through the riser without loss of energy by lateral flows through the NDT as for example in ALR-NDTs. In ALR-NDTs, the fluid velocity crashes through the NDT increasing turbulence by

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Fig. 11. Liquid velocity as a function of inlet air flow rate for ALR-NDT-6 with different geometry settings.

Fig. 12. Liquid velocity as a function of inlet air flow rate for ALR-NDT-3 with different geometry settings.

adding radial flow. The turbulent eddies then break up the bubbles into many smaller ones leading to a loss of some energy through bubble dissociation and the change in direction of the flow veloc-

ity. Therefore, lower liquid velocities are achieved in ALR-NDTs in comparison with the conventional ALR. These results are also seen in Fig. 14, which clearly shows the motion of fluid and the velocity

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Fig. 13. Liquid velocity as a function of inlet air flow rate for ALR with different geometry settings.

Fig. 14. Velocity stream lines along the simulated reactors at t = 15 s: (a) ALR-NDT-12, (b) ALR-NDT-6, (c) ALR-NDT-3, and (d) conventional ALR.

streamlines in the reactors after reaching a steady state (t = 15 s). Among the ALR-NDTs, the highest liquid velocities are seen in ALRNDT-12 similar to those in the conventional ALR, in consequence of the small mesh size of the net, which prevents easy passage of flow and acts like a solid draft tube. The lowest liquid velocities are found

in ALR-NDT-3 as this reactor operates like a bubble column because of the large mesh size of the net and a low resistance against cross flows. As noted in Sanjari et al. (2014), large liquid throughputs in the BCR were only possible with significant recycle rates, whereas

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Fig. 15. Coefficient of volumetric mass transfer for oxygen as a function of inlet air flow rate for ALR-NDT-12 with different geometry settings.

high liquid velocities are generated in the ALR without an external recirculation mechanism. At constant ratio Ad /Ar = 7, liquid velocity values are very close to each other for different H/D values (Figs. 10–13), whereas liquid velocities increase considerably with increasing H/D values from 9.3–10.7 at constant ratio Ad /Ar = 1.3. For all ALR-NDTs (Figs. 10–12), the maximum liquid velocity is obtained for the (a)-series of plots with H/D = 10.7 and Ad /Ar = 1.3. According to this result, a longer NDT (H = 32 cm) with larger diameter (D = 3 cm) is preferable in reaching larger liquid velocities in ALR-NDTs. Overall, a reasonable match was found between the two-fluid CFD model and the experimental data except for Fig. 11(c), in which the absolute error exceeds 20%. We remark that the values from the empirical correlation proposed by Sanjari et al. are acceptable only in a few plots and therefore not adequate in predicting liquid velocities for all conditions. The omission of the flow pattern and local intrinsic information may be the main shortcoming of the empirical correlation. In comparison, the CFD model is completely acceptable for simulating liquid velocities in reactors despite absolute errors of less than 20%; its performance moreover is significantly better. Effect of net tube mesh size, H/D, and Ad /Ar on the volumetric mass transfer coefficient in ALR–NDTs and ALR At this stage, a comparative analysis of the volumetric mass transfer coefficient is of interest for the different ALR-NDTs with different net mesh sizes. The coefficient KL a is the main characteristic of the reactors and determines the capability of the reactor to sustain a completely mixed condition. The average volumetric mass transfer coefficient as a function of inlet air flow rate for all reactors ALR-NDT-12, ALR-NDT-6, ALR-NDT-3, and conventional ALR, is presented respectively in Figs. 15–18. By increasing the inlet air flow rate, a significant increase is seen in KL a values of all reactors. When the air flow rate was low, relatively large bubbles are produced by the sparger because of the

hydrostatic pressure of the fluid inside the rector. Therefore, large bubbles were rising in the central region. With an increase in inlet gas flow rate, the air sparger performed more effectively and the bubble size decreased. With a further increase in the air flow rate, the bubble size was dependent on the equilibrium between bubble dissociation and coalescence, and the bubble size increased slightly with increasing air flow rate because coalescence dominates and larger bubbles are generated especially near the wall region of the riser. Therefore, a slight increase is seen in the KL a values of all reactors at higher inlet air flow rates because the specific surface area of large bubbles decreases. In ALRs, some bubbles are carried downward by the liquid circulation and are dragged downward with the circumfluent liquid and may enter the riser again during this recirculation. For all ALR-NDTs, the bubbles present in the riser also pass through the NDT under axial movements and enter the downcomer. Thus, higher values of the volumetric mass transfer coefficient are achieved for ALR-NDTs in comparison to conventional ALR because of the vertical and axial movements of bubbles in these reactors, leading to longer residence times for bubbles in the medium. The more bubbles retained in the medium, the higher the KL a value becomes. The 3D contours of the KL a distribution in the different types of the reactors (Fig. 19) clearly demonstrate the above-mentioned phenomena. This unsteady flow is in accordance with experimental observations (Sanjari et al., 2014). Similar results have been reported (Hsiun & Wu, 1995; Oey et al., 2003). By evaluating the effect of H/D and Ad /Ar values on the KL a value of each reactor, we concluded that this dimensional variation has no considerable effect on its value and a slight increase is seen in KL a by increasing the H/D value at constant Ad /Ar in a majority of plots. By comparing the different ALR-NDTs, we found high KL a values for ALR-NDT-6 (Fig. 16(c), H/D = 20 and Ad /Ar = 7) and ALR-NDT3 (Fig. 17(c), H/D = 20 and Ad /Ar = 7) with simulated KL a values of 0.031 and 0.028, respectively, at the air flow rate of 2.5 vvm. These results are supported by the experimental data.

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Fig. 16. Coefficient of volumetric mass transfer for oxygen as a function of inlet air flow rate for ALR-NDT-6 with different geometry settings.

Fig. 17. Coefficient of volumetric mass transfer for oxygen as a function of inlet air flow rate for ALR-NDT-3 with different geometry settings.

Lower values of KL a were achieved in the conventional ALR than in the ALR-NDTs (Fig. 18). From this result, we concluded that the presence of the NDT considerably increases gas holdup and consequently, the mass transfer coefficient by establishing cross flow

conditions, the dissociation of large bubbles when passing through the central net, and the reduction in bubble coalescence. Therefore, both simulation and experimental results corroborate the increase seen in KL a value in ALR-NDTs by 30%–55% relative to that for ALR

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Fig. 18. Coefficient of volumetric mass transfer for oxygen as a function of inlet air flow rate for ALR with different geometry settings.

under the same conditions for the various configurations. Both the volumetric mass transfer coefficient and gas holdup have similar trends with inlet air flow rate, and therefore similar trends are seen in the plots for both of these hydrodynamic parameters. According to the results of gas holdup and KL a presented for different H/D values, the lowest gas holdup and KL a value is obtained when H/D = 10.7 and Ad /Ar = 1.3 for all ALR-NDTs ((a)-series of plots in Figs. 5–7 and 15–17). Thus, these dimensions are not preferable for these reactors. The predicted values of the oxygen mass transfer coefficient in the test reactors are indeed significantly closer to the experimental values. Even if some discrepancies are still apparent, the overall agreement is considered satisfactory and the proposed two-fluid Eulerian model showed satisfactory accuracy over a wide range of inlet air flow rates for different configurations of ALR-NDTs. Ignoring bubble coalescence and dissociation is considered the main reason for the slight disparity in KL a values from the k–ε model used. Given the results of Figs. 15–18, we remark that the predicted results of the experimental correlation proposed in Sanjari et al. (2014) show better accuracy for KL a values in comparison to gas holdup predictions but still significant differences are seen in some plots (Figs. 16(c)–(d) and 17 (c)–(d)), which confirms the uncertainty and ineffectiveness of this correlation in predicting the hydrodynamic behavior of the ALR-NDTs. Ignoring the flow pattern, existing flow transition, dynamic behavior and also the bubble distribution are the main sources of inadequacy of the correlation, which is only based on output measurements of the experiments.

Conclusions The effect of different mesh sizes of the central NDT on the hydrodynamic parameters of ALR-NDTs and conventional ALR were investigated theoretically in different air flow rates using CFD techniques. The reactor geometry specified by various H/D and Ad /Ar

values has an influence on the hydrodynamic behavior of the reactor. A k–ε two-fluid turbulence model was employed to investigate the hydrodynamics in ALR-NDTs taking into account drag and equivalent bubble size correlations. As inlet air flow rate increase, the gas holdup, liquid velocity, and KL a increase. The CFD predicted data for gas holdup, liquid velocity, and coefficient of volumetric mass transfer for all tested reactors were in good agreement with the experimental data published in the literature, suggesting that the geometric effects are properly accounted for by the CFD model. Comparison between the simulated results and the experimental data shows that the mesh size of NDT and reactor geometry (H/D and Ad /Ar ratios) have different effects on the hydrodynamic performance of the reactor. By comparing the performance of the ALR-NDTs with conventional ALR, the hydrodynamic parameter values were shown to be improved with the introduction of the central NDT. The larger the net mesh size is, the more the reactor acts as an ALR. The smaller the net mesh size is, the more the reactor acts as a BCR. Choosing a configuration with an optimum geometry that improved gas-holdup, liquid velocity, and coefficient of mass transfer, simultaneously, was complicated because all parameters exhibited mutual dependences and therefore have a correlated effect on the hydrodynamic behavior of the reactors. Statistical analysis seems necessary to evaluate all the interactions and to optimize the ALR-NDT configuration, a task which remains for future studies. A poor agreement was seen between the CFD model and the results predicted by the empirical correlation of Sanjari and collaborators. This failing indicates that the experimental data were considerably affected by the fluid flow inside the reactor, which was unaccounted for in the correlation equation. Therefore, for an accurate modeling, additional details are required on the physics of the flows, for example, flow pattern, local intrinsic information, interaction between bubbles and with the continuous phase in particular, lateral forces and interphase turbulence. They were not taken into account in deriving the empirical correlation but are

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Fig. 19. Contour plots of the coefficient of volumetric mass transfer for the simulated reactors at fixed geometry settings (H/D = 20, Ad /Ar = 7) and t = 15 s: (a) ALR-NDT-12, (b) ALR-NDT-6, (c) ALR-NDT-3, and (d) conventional ALR.

thoroughly considered in the framework of the two-fluid formulation coupled with a k–␧ turbulence model using the CFD method. The simulation results showed that additional details have a noticeable influence on modeling results and should be included in the CFD model. The lack of information on these features may lead to the development of inadequate empirical correlations that limit the applicability of the models. These significant constraints may be overcome using more accurate general modeling methods such as the CFD technique. Funding No funding was received for this work. Conflict of interest None. References AL-Mashhadani, M. K. H., Wilkinson, S. J., & Zimmerman, W. B. (2015). Airlift bioreactor for biological applications with micro-bubble mediated transport processes. Chemical Engineering Science, 137, 243–253. Amani, A., & Jalilnejad, E. (2017). CFD modeling of formaldehyde biodegradation in an immobilized cell bioreactor with disc-shaped Kissiris support. Biochemical Engineering Journal, 122, 47–59. Amani, A., Jalilnejad, E., & Mousavi, S. M. (2018). Simulation of phenol biodegradation by Ralstonia eutropha in a packed-bed bioreactor with batch recycle mode using CFD technique. Journal of Industrial and Engineering Chemistry, 59, 310–319.

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Please cite this article in press as: Salehpour, R., et al. Hydrodynamic behavior of an airlift reactor with net draft tube with different configurations: Numerical evaluation using CFD technique. Particuology (2019), https://doi.org/10.1016/j.partic.2019.09.005