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Validation of a Computationally Efficient Computational Fluid Dynamics (CFD) Model for Industrial Bubble Column Bioreactors Dale D. McClure, Hannah Norris, John M. Kavanagh, David F. Fletcher,* and Geoffrey W. Barton School of Chemical and Biomolecular Engineering, Building J01, The University of Sydney, Sydney, New South Wales 2006, Australia ABSTRACT: In this work we investigated the fluid dynamics in a pilot-scale bubble column equipped with an asymmetric “tree” type sparger at superficial velocities between 0.01 and 0.37 m s−1. We present an extensive experimental data set consisting of overall holdup measurements, liquid velocity, gas velocity, and local gas volume fraction profiles as well as bubble size distributions. The second part of this work examines the modeling of the column using computational fluid dynamics (CFD). It is found that the computationally efficient single bubble size model used in this work offered satisfactory predictions of the complex flow patterns found inside bubble columns operated in the industrially relevant heterogeneous flow regime.

1. INTRODUCTION Bubble columns are widely used as gas−liquid contactors due to their mechanical simplicity and good heat and mass transfer properties.1 It is for these reasons that bubble columns are widely used in the bioprocessing industry to produce products such as baker’s yeast and amino acids.2,3 Typical bubble columns used in the bioprocessing industry have height to diameter ratios of 2−5 and are operated in the heterogeneous flow regime, corresponding to superficial velocities >0.05−0.1 m s−1.1 Despite their mechanical simplicity, the hydrodynamics of such columns is very complex.4 To deal with this complexity, authors have increasingly turned to computational fluid dynamics (CFD) as a tool to model these systems.4,5 Being able to successfully model the complex and transient flow patterns inside a bubble column operating in the heterogeneous regime is a key first step toward modeling mixing in such columns, a topic of considerable interest at the industrial scale as it is thought that the yield of such processes may be improved by achieving a more homogeneous distribution of substrate.6 The Euler−Euler framework is typically used to model bubble columns operating in the heterogeneous regime; hence, choice of appropriate interphase momentum and turbulence transfer terms is a key issue in the development of any model.4,7 Of the four proposed mechanisms of interphase momentum transfer (i.e., drag, added mass, turbulent dispersion, and lift), it is generally acknowledged that the drag force is the most significant.4,8 At high superficial velocities, a volume fraction correction term that accounts for the reduction in drag experienced by a bubble due to the presence of other bubbles is typically added to the expression used to calculate the drag coefficient.4,8−10 Indeed, omission of such a term has been shown to lead to unphysical results for simulations performed at a superficial velocity of 0.12 m s−1.8 Similarly, it was also shown that inclusion of the terms developed by Pfleger and Becker11 for bubble-induced turbulence to the transport equations for turbulence kinetic energy (k) and turbulence eddy dissipation (ε) led to an improved agreement with experimental results.8 Published hydrodynamic data for bubble columns operating in the homogeneous regime have generally been generated using a column with a symmetrical sparger (typically a perforated plate).4,5,12−16 Hence, one of the key aims of this work was to generate a comprehensive experimental data set (i.e., one that © 2014 American Chemical Society

consists of measurements of the bubble size distribution (BSD) and the overall holdup, as well as profiles of the local holdup, liquid velocity, and gas velocity) for a column equipped with an asymmetric “tree” type sparger of the sort commonly used in the bioprocessing industry. Such knowledge is of interest because bubble columns used in bioprocessing typically have aspect ratios of 2−5, meaning that the volume of the column where the sparger design has an impact can be a substantial proportion of the total.1 Thus, the aim of the second part of this work was to validate a CFD model developed previously8 against the comprehensive experimental data set generated in the first. Such a validated model has obvious potential uses as a tool in modeling aerobic bioprocesses.

2. EXPERIMENTAL METHOD A pilot-scale bubble column with an internal diameter of 390 mm and a height of 2000 mm constructed from clear acrylic was used, as shown schematically in Figure 1. The coordinate system for both experimental and modeling aspects was defined such that the origin is on the column centerline at the bottom of the cylindrical section. Air was introduced via a “tree” type sparger, located such that the midpoint of the sparger was at a height of 135 mm above the base of the cylindrical section of the column (shown dashed in Figure 1). The sparger had a free area of 2.2%; the orifices were 0.5 mm in diameter, with the drilled area being shaded in Figure 1. The air flow rate was measured using a vortex flow-meter (Foxboro I/A series) to an accuracy within ±2%; the superficial velocities reported are for air at standard conditions (298 K, 1 atm). Superficial velocities between 0.01 and 0.37 m s−1 were investigated. Tap water (κ = 133 μS cm−1) was used as the liquid phase, with the unaerated liquid height being 1000 mm. Received: Revised: Accepted: Published: 14526

March 15, 2014 August 10, 2014 August 22, 2014 August 22, 2014 dx.doi.org/10.1021/ie501105m | Ind. Eng. Chem. Res. 2014, 53, 14526−14543

Industrial & Engineering Chemistry Research

Article

From this, the overall volume fraction can be found on the basis of the differential pressure: α=

ΔP (ρL − ρG )g Δh

(3)

Values of 998 and 1.2 kg m−3 were used for the liquid density (ρL) and gas density (ρG), respectively. The differential pressure was measured for a duration of 60 s, at a frequency of 1 kHz, with the data being recorded using a USB-1208FS DAQ (Measurement Computing). The holdup was calculated using the arithmetic average of the pressure difference over the measurement period; the reported errors are the standard deviation of this mean value. This approach gives an estimate of the variation due to transient behavior (primarily “sloshing” of the liquid), which was observed to be of greater magnitude than the error in the measurement (±0.125%). Bubble size distributions, local gas holdup, and liquid velocity profiles were measured in the XZ plane at heights of 550, 1050, and 1350 mm, corresponding to approximately 1, 2, and 3 column diameters above the sparger. Measurements of the liquid velocity and local holdup profiles were made at 13 points, 30 mm apart, with the extremes being ±180 mm from the column centerline. Bubble size distributions and local gas holdup and velocity profiles were measured using an approach developed by others17−19 with the method used in this study being described in detail elsewhere.12 The liquid velocity was measured using a pitot tube; similar methods having been used by other authors.20,21 A series 160 F pitot tube (Dwyer Instruments) was used in this work. To ensure an accurate measurement, it is necessary to prevent any air from entering the pitot tube.20 This was done by purging the system with a pulse of liquid prior to the measurements. The differential pressure was measured using the previously mentioned IDP-10 transducer. The pitot tube was used to measure the upward (z) component of the liquid velocity:

UL =

2ΔP ρmix

(4)

Figure 1. Schematic diagram of the pilot-scale bubble column.

Holdup in the column was measured using the differential pressure method, as shown schematically in Figure 1. An IDP-10 transducer (Foxboro) was used to measure the pressure difference to an accuracy of ±0.125%. Knowing the difference in height between the two pressure tappings (Δh = 570 mm) allows the mixture density to be found: ρmix =

ΔP g Δh

(1)

The mixture density is related to the gas volume fraction: ρmix = (1 − α)ρL + αρG

(2)

Figure 2. Comparison between experimental holdup measurements. 14527

dx.doi.org/10.1021/ie501105m | Ind. Eng. Chem. Res. 2014, 53, 14526−14543


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The differential pressure was measured for a duration of 60 s, at a frequency of 1 kHz, with the data being recorded using a USB-1208FS DAQ (Measurement Computing). The liquid velocity was calculated at each time point, with the values being averaged arithmetically, to give the time-averaged local velocity at a given point. The measurement process was repeated at least three times for each point, with reported values being the arithmetic average, whereas error bars indicate one standard deviation about the mean or the estimated systematic error in the liquid velocity measurement (10%), whichever is greater.

3. EXPERIMENTAL RESULTS 3.1. Overall Holdup Measurements. Measurements of the overall holdup are shown in Figure 2, along with a comparison with published data.4,5,16 Results from this current work are in good agreement with published data in the heterogeneous regime (UG > 0.1 m s−1), with differences being observed in the homogeneous and transition regimes. It is conjectured that the observed discrepancy is due to the different sparger configurations used, with columns equipped with a sparger with small orifices (do = 0.5 mm) and relatively high free areas (i.e., the column used by Chaumat et al.16 and the column used in this work) having a “peak” in the overall holdup. No such peak was observed for columns equipped with spargers with large (do ≥ 1 mm) orifices (i.e., those used by Krishna et al.5 and Rampure et al.4). Chaumat et al.16 also used a sparger with 1 mm diameter orifices in their work, with no peak in overall holdup being observed. Collectively, these results indicate that relatively small changes in sparger design can have a significant impact on column hydrodynamics, particularly at low superficial velocities. 3.2. BSD Measurements. Measurements of the BSD were made at heights of z = 475, 975, and 1275 mm (approximately 1, 2, and 3 column diameters above the sparger), with the probe

Figure 3. Effect of height on BSD as measured at the column centerline, with the probe pointing downward. Measurements were performed at superficial velocities of 0.08 m s−1 (a), 0.16 m s−1 (b), and 0.25 m s−1 (c) and heights of 1275 mm (H/D = 3), 975 mm (H/D = 2), and 475 mm (H/D = 1) above the base of the column. Figure 4. Impact of superficial velocity on mean bubble size measured at a height of 975 mm above the base of the column (approximately 2 column diameters above the sparger).

The mixture density (ρmix) was calculated using eq 2 using the experimentally measured local volume fraction values. 14528



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Figure 5. Effect of radial position on the BSD. Measurements were made at approximately 2 column diameters above the sparger (z = 975 mm). The mean bubble size is shown in panel a, along with more detailed distributions at superficial velocities of 0.08 m s−1 (b), 0.16 m s−1 (c), and 0.25 m s−1 (d). All measurements were made with the probe pointing down. For the sake of clarity, measurements at −100 and −190 mm have not been shown in panels b−d.

Two possible reasons for the observed change in BSD with superficial velocity are that the sparger produces different sized bubbles at different superficial velocities or that changing the superficial velocity affects coalescence and breakup processes (most likely by changing the level of turbulence in the liquid phase). Akita and Yoshida22 and Davidson and Schuler23 have both proposed correlations that relate the initial bubble diameter to the orifice size and orifice velocity, with larger bubbles being produced at higher orifice flow rates (i.e., superficial velocities).

pointing downward. Results are shown in Figure 3. It can be seen that at all superficial velocities examined (0.08, 0.16, and 0.25 m s−1) the bubbles produced by the sparger undergo some degree of breakup, with the distribution becoming narrower. Once the bubbles reach a height of some 2 column diameters above the sparger, however, there is very little change in the BSD with height, suggesting that bubbles have reached their “equilibrium” size. Such results are in line with previous measurements12 made at a smaller scale. 14529



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Figure 6. Effect of radial position on the BSD, with the probe pointing upward. The mean bubble size is shown in panel a, along with more detailed distributions at superficial velocities of 0.08 m s−1 (b), 0.16 m s−1 (c), and 0.25 m s−1 (d). For the sake of clarity, measurements at −100 and −190 mm have not been shown in panels b−d. Measurements were made at a height of approximately 2 column diameters above the sparger.

At a superficial velocity of 0.08 m s−1 these correlations predict an initial bubble size of the order 5−6 mm, which is in excellent agreement with our measured mean bubble size. At the higher superficial velocities measured (0.16 and 0.25 m s−1), the correlations predict initial bubble sizes of 7−8 mm, again in good agreement with our experimental data. Hence, it is reasonable to think that the observed increase in mean bubble size with

superficial velocity can be attributed to an increase in the size of bubbles produced at the sparger. It is proposed that the increased rate of bubble breakup observed at the higher (0.16 and 0.25 m s−1) superficial velocities examined is due to the higher volumetric power input. For example, at a superficial velocity of 0.25 m s−1, the power input is 1.7 kW m−3, which is 3.3 times greater than the volumetric power input at 0.08 m s−1 (0.5 kW m−3). 14530



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above the sparger. It was observed that increases in the superficial velocity led to an increase in the mean bubble size, up to a value of approximately 0.15 m s−1. This trend has been observed by others.4,13 At velocities above 0.15 m s−1, it was found that further increases had a minimal impact on the mean bubble size. Interestingly, it appears as though the increase in mean bubble size (as well as the broadening of the BSD; see Figure 3) corresponds to the transition from the homogeneous to the heterogeneous flow regime. Figure 5 shows measurements of the BSD made at distances of ±100 and ±190 mm from the column centerline. It was observed that the BSD was essentially symmetrical about the column centerline, with little variation with radial position, a result in agreement with the work of others.4 The data shown in Figure 5 were measured at approximately 2 column diameters above the sparger (z = 975 mm); similar results were observed at the other axial positions examined (i.e., z = 475 and 1275 mm). Measurements were repeated with the probe facing upward to obtain the size distribution of bubbles moving downward. Figure 6 shows the BSD as measured at a height of 1125 mm above the base of the sparger with the probe pointing upward. As with the case for a downward-pointing probe, results were symmetrical about the column centerline. At a superficial velocity of 0.08 m s−1, very little variation of bubble size with radial position was observed. However, at higher superficial velocities, it was found that the BSD did vary with radial position, with the distribution becoming narrower with a smaller mean size near the walls. This size segregation for downward flowing bubbles may be explained by the fact that smaller bubbles are more likely to be entrained by downward flowing liquid due to the fact that they have a smaller rise velocity than larger bubbles.

Figure 7. Bubble terminal velocity calculated as a function of bubble diameter calculated using the correlation developed by Clift et al.26 Data are for air bubbles in water.

Such an increase in volumetric power input will lead to an increase in liquid-phase turbulence, thereby increasing the rate of bubble breakup. Figure 4 shows the impact of superficial velocity on the mean bubble size at a height of approximately 2 column diameters

Figure 8. Schematic showing setup used to model the “slot” boundary condition. 14531



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Figure 9. Schematic diagram showing setup used to model the “complex” boundary condition.

3.3. Implications of BSD Measurements for CFD Modeling. From a practical perspective the use of a single bubble sized CFD model is strongly favored, as such an approach has the benefits of minimizing computational demand while avoiding the need to incorporate closures for bubble coalescence and bubble breakup (an area of some considerable uncertainty in the literature).24,25 For such a single bubble size model to be valid, the BSD should be relatively narrow and not change throughout the column. As demonstrated in Figure 3, however, it was found that for velocities of interest (UG > 0.1 m s−1) the BSD did change with distance above the sparger. Such a change in the bubble size will undoubtedly affect the magnitude of the drag force (FD), which is given by FD =

3C D ρ αG(UG − UL)|UG − UL| 4db L

of bubbles missing the probe tips. It was found that the area-averaged holdup as measured was consistently 10− 20% lower than the overall value at superficial velocities of 0.16 and 0.25 m s−1 (in line with our previous work at a smaller scale).12 Hence, the experimental results were corrected by a factor of 1.1 to account for the observed difference. Measured profiles were essentially symmetric about the column centerline, with the exception of measurements made at x = −180 mm. It is thought that the small (15 mm) distance between the probe tip and column wall led to bubbles striking the probe at a much lower frequency. Hence, measurements made at this position were excluded from any further analysis; when necessary (e.g., calculation of the liquid velocity), the value at x = 180 mm was used in place of this excluded measurement.

(5)

4. CFD MODELING 4.1. Model Setup. A commercial code (ANSYS CFX 14.5) was used to model the column using the Euler−Euler approach. Interphase momentum transfer due to turbulent dispersion was modeled using the Favre-averaged drag model proposed by Burns et al.,27 with drag being modeled using the Grace et al.26 term for isolated bubbles in combination with a modified form of the Simonnet et al.28 volume fraction correction term as outlined elsewhere.8 In this work the lift-force was not included as it has been shown that inclusion of this interphase momentum transfer term has a relatively small effect on the CFD predictions.8 Liquid phase turbulence was modeled using the k−ε model, with additional source terms accounting for bubble-induced turbulence using the model developed by Pfleger and Becker.11 Gas phase turbulence was modeled using the dispersed-phase zero equation model. Bubbles were introduced as a single size, using the experimentally measured mean value (8 mm), with a velocity of 0.25 m s−1 in the upward (z) direction.

In this work, we have used the correlation developed by Clift et al.26 to determine the terminal velocity (and hence drag coefficient) of an isolated bubble. It can be appreciated by examining the plot of terminal velocity as a function of bubble diameter shown in Figure 7 that there is a range of bubble sizes (3−13 mm) for which the bubble terminal velocity is approximately constant (0.24 ± 0.01 m s−1). For this reason, it is reasonable to think that if the majority of bubbles fall within this size range, the use of a single bubble size would be a reasonable approximation. It was found that depending on measurement location and superficial velocity (as shown in Figure 3) between 40 and 80% of the measured BSD was within this size range; hence, it was felt that a single bubble size would be a reasonable assumption given the very considerable reduction in modeling complexity that would result. 3.4. Gas Volume Fraction Measurements. When the local gas volume fraction is measured using an intrusive probe, there will always be some systematic error caused by the possibility 14532



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Figure 10. Effect of grid size on CFD predictions at a superficial velocity of 0.16 m s−1. Results in the first row are predictions of the local holdup at heights of 1050 mm (a) and 800 mm (b) above the base of the column. Results shown in the second row are predictions of the average upward liquid velocity profile at heights of 1050 mm (c) and 800 mm (d) above the base of the sparger.

face of this cylinder being modeled as an inlet boundary condition. Air was introduced at the semicircular areas corresponding to the “stems” of the tree sparger (shown shaded in Figure 8), with all other faces being modeled as walls. The second approach to modeling the column is shown schematically in Figure 9. In this, the so-called “complex” boundary condition, the mesh used was a more faithful description of the column geometry, whereby the individual “stems” of the tree sparger were meshed, with air being

In any CFD model, it is necessary to strike an appropriate balance between accurately representing the system and minimizing computational demand. As it was not known to what extent the complex, industrial sparger configuration used in this current work could be simplified, two different approaches to meshing the column were examined. In the first approach (the so-called “slot” boundary condition), shown schematically in Figure 8, a cylindrical volume with the same diameter (360 mm) and height (19 mm) as the sparger was removed, with the upper 14533



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Figure 11. Effect of simulation duration on predicted holdup profiles at heights of 1050 mm (a) and 550 mm (b) above the base of the column. Also shown are predicted liquid velocity profiles at heights of 1050 mm (c) and 550 mm (d) above the base of the column. Simulations were performed at a superficial velocity of 0.16 m s−1.

sedimentation of solids) it would be necessary to include this volume; however, in this case it was felt that the reduction in computational demand justified the omission of the conical section. Walls were modeled using free-slip boundary conditions for the gas phase and no-slip for the liquid, with the outlet of the column being modeled as an opening, at atmospheric pressure. A grid refinement study was performed using the “slot” boundary condition, using meshes with 20,000, 36,000 and 67,000 elements (as shown in Figure 8). Simulations were

introduced at the top faces of the stems (shown shaded in Figure 9). In both instances, the conical section was omitted, as this considerably simplifies matters by making it possible to mesh the column using only hexahedral cells. This was deemed acceptable as the conical section is only a small fraction (4%) of the total volume and is below the sparger, so its omission is unlikely to have a major impact on the predicted flow patterns within the column proper. In some circumstances (e.g., modeling the 14534



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Figure 12. Plot showing the instantaneous values of the gas volume fraction and liquid velocity at a superficial velocity of 0.25 m s−1, at 5 s intervals commencing at t = 100 s. Plots are for the XZ plane.

duration becomes an important consideration. Thus, simulations were performed for durations of 30, 90, 120, and 180 s using the “slot” boundary condition, the medium mesh and a superficial velocity of 0.16 m s−1. For reasons of numerical stability the first 500 iterations were performed with a time step of 5 × 10−4 s using the segregated solver; all subsequent iterations used the coupled solver and a time step of 1 × 10−3 s. Figure 11 shows the effect of simulation duration on the CFD predictions, with a simulation duration of 120 s being sufficient to achieve a pseudo-steady state. Performing such simulations took approximately 10 days using a four-core 3.33 GHz Intel Xeon X5680 system. Repeating

performed for a duration of 120 s. On the basis of the results shown in Figure 10, it was decided to use the medium mesh, as although strict mesh independence had not been achieved, the difference between the medium and fine meshes was judged to be too small to justify the (very considerable) extra computational time. 4.2. Solution Method. The bubble column was modeled as a transient system, with the second-order backward Euler transient scheme being used in conjunction with the high-resolution advection scheme for the convective terms. As the bubble column is modeled as a transient system, the choice of simulation 14535



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Figure 13. Effect of inlet boundary condition on CFD predictions at a superficial velocity of 0.16 m s−1. Results are given at a height of 1050 mm above the base of the column for the local volume fraction profile (a) and liquid velocity (b), as well as at a height of 550 mm above the base of the column for the local volume fraction profile (c) and liquid velocity (d).

representation of the flow field is likely to be of more interest than the instantaneous value at any given time. However, it is important to note the model developed in the current work does capture the instantaneous behavior. This is demonstrated in Figure 12, where considerable variation in both the instantaneous gas volume fraction and liquid velocity can be observed, such results being in line with the work of other authors.4 4.3. Impact of Sparger Representation. Simulations were performed at a superficial velocity of 0.16 m s−1, using both the

the same simulation using the “complex” boundary condition resulted in an approximately 5-fold increase in computational demand, with the simulation duration increasing to 47 days. All subsequent simulations were performed for a duration of 120 s, with results reported being transient averages unless stated otherwise, with the first 5 s of simulation time being discarded (to avoid averaging over the startup period). In this work we have generally chosen to report transient averages as such results are likely to be of the most relevance in the simulation of industrial bioreactors, as an average 14536



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Figure 14. Contour plots of the predicted average gas volume fraction for the “slot” (a, b) and “complex” (c, d) inlet boundary conditions. Reported values are for the XZ plane, plots b and d, as well as the YZ plane, plots a and c. Results are for a superficial velocity of 0.16 m s−1.

“slot” and “complex” boundary conditions, with a comparison between the two CFD predictions and experimental data being given in Figure 13. It was found that the choice of boundary condition did not affect predictions of the overall holdup; simulations performed using the “slot” and “complex” boundary condition both predicted an overall holdup of 0.27 (compared with an experimentally measured value of 0.23 ± 0.01). As shown in Figure 13, however, use of the “complex” boundary condition led to an improved prediction of the shape of the holdup profile, particularly for measurements made near the sparger (i.e., z = 550 mm). Similar results were observed for the liquid velocity profile, with these results also being shown in Figure 13. However, this modest improvement necessitates an approximately 5-fold increase in computational demand, with simulation times increasing from the order of 10 days (using the “slot” boundary condition) to around 47 days for the “complex” boundary condition. To further investigate the impact of the inlet boundary condition, contour plots of the average local volume fraction in both the XZ and XY planes were produced for both boundary conditions examined, with the results being shown in Figure 14. It can be clearly seen that the asymmetric sparger design results

Figure 15. Comparison between experimentally measured overall holdup values and those predicted by the CFD model. 14537



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Figure 16. Comparison between experimental results and CFD predictions at a superficial velocity of 0.25 m s−1. Results are given at a height of 1050 mm above the base of the column for the local volume fraction profile (a) and liquid velocity (b), as well as at a height of 550 mm above the base of the column for the local volume fraction profile (c) and liquid velocity (d).

involved in the setup of any CFD model and suggest that the improvement in predictive ability derived through the use of the “complex” boundary condition may not justify the resultant increase in computational demand. Hence, all subsequent simulations were performed using the simpler “slot” boundary condition. 4.4. Comparison with Experimental Results. A comparison between the experimentally measured and predicted values for the overall gas volume fraction is presented in Figure 15. It can be seen that, as previously noted, the model as it currently

in the generation of two plumes of gas in the vicinity of the sparger, this behavior being more pronounced for the “complex” boundary condition. The results shown in Figure 13 illustrate that while the use of the (more computationally expensive) “complex” boundary condition leads to an improved prediction of the shape of the local holdup profile in the vicinity of the sparger, it does not offer an improved prediction of the magnitude of the holdup, nor does it offer a large improvement in the prediction of the liquid velocity profiles. Such results clearly demonstrate the compromise 14538



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Figure 17. Plot showing average liquid velocity streamlines predicted by the CFD model projected onto the XZ plane (a, c) as well as 3D plots (b, d). Predictions are for a superficial velocity of 0.16 m s−1 (a, b) as well as a superficial velocity of 0.25 m s−1 (c, d).

predicts that the liquid velocity will increase with distance above the sparger, reaching a maximum in the vicinity of the free surface; such behavior is in line with experimental measurements at a superficial velocity of 0.25 m s−1. The results shown in Figure 17 (particularly the 3D plots) clearly illustrate the highly complex flow behavior occurring within the column. Overall, though, agreement between the experimental results and CFD predictions is satisfactory at both superficial velocities examined. However, it must be stated that there are areas in which the model predictions could be improved. As previously discussed, the CFD model overpredicts the magnitude of the local holdup by approximately 20%. Additionally, it was observed that the model underpredicted the liquid velocity near the column walls and at a height of 1050 mm above the sparger at a superficial velocity of 0.25 m s−1. The agreement with experimental data might be improved by introducing additional empirical terms into the interphase transfer terms. However, it is a task of considerable complexity to determine if such parameters are dependent on the column design or indeed if they are a reasonable representation of the physics involved. Given that the aim of this work was to develop a model for industrial

stands generally overestimates the global holdup (typically by a factor of 20%). Comparison between the CFD predictions of local holdup and liquid velocity and experimental measurements is presented in Figure 13 for a superficial velocity of 0.16 m s−1 and in Figure 16 for a superficial velocity of 0.25 m s−1. It was observed that the magnitude of the variation in the liquid velocity measurement changed with location, with the largest variation being observed at distances of 90−150 mm from the column centerline. This is unsurprising given that in this region the average direction of the liquid flow transitions from being upward (in the center of the column) to being downward (in the vicinity of the walls). The effect of the asymmetric sparger design on measurements of the local hold up and liquid velocities profiles made at z = 550 mm was also apparent at a superficial velocity of 0.25 m s−1. Figure 17 shows CFD predictions of streamlines for the average liquid velocity in the XZ plane at superficial velocities of 0.16 and 0.25 m s−1. It can be seen that the liquid velocity is greatest in the central portion of the column and that there are clear zones of liquid recirculation. Additionally, the model 14539



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Figure 18. Comparison between experimentally measured upward gas velocities and the results predicted by the CFD model. Measurements were made at heights of 1050 mm (a, b) and 550 mm (c, d) above the base of the column in the XZ plane. Results in the first column (a, c) are for a superficial velocity of 0.16 m s−1, and those in the second column (b, d) are for a superficial velocity of 0.25 m s−1.

the error reported is the physical error in the chord length measurement, which is outlined elsewhere12 as being of the order of ±8%. For the purposes of comparison, the standard deviation of the mean of five repeat measurements made at the column centerline was found to be of the order of 3−15%. As a check on the experimental measurements the product of the area-averaged gas velocity and the overall volume fraction was compared with the superficial velocity. It was found that calculation of the superficial velocity using the experimental measurements led to the value being underpredicted by a factor of 10−40%, with the greatest discrepancy occurring at higher superficial velocities, a

applications (i.e., a model that can be applied to a range of column designs) and that the current model offers satisfactory predictions for a range of parameters (overall holdup, local holdup, liquid velocity, and gas velocity) across a range of industrially relevant superficial velocities, it was felt that it was not necessary to introduce additional empirical terms into the model. A comparison between the experimentally measured upward gas velocity and the CFD predictions is given in Figure 18. The experimental measurements are the number-weighted averages of both the upward and downward gas velocities. In Figure 18, 14540



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result in line with that of other authors.4 The needle probe used in this work can measure only bubbles that strike the tips in the correct order. This may introduce a bias against bubbles moving at high speed, offering a potential explanation for the previously discussed discrepancy. Agreement between the CFD predictions and experimental results is thus once again satisfactory, although the CFD model overestimates the gas velocity in the central portion of the column. However, as previously noted, this disagreement could also be due to the experimental measurements underestimating the local gas velocity. 4.5. Effect of the Volume Fraction Correction Term Applied to the Drag Coefficient. As previously noted, the CFD model slightly overpredicts the holdup, both locally and globally for both meshes examined. This suggests the model as it currently stands overestimates the magnitude of the drag experienced by the bubbles. As discussed previously, the drag coefficient used in the model is the product of two terms: the drag coefficient of an isolated bubble and a volume fraction correction term that takes into account the reduction in drag due to the presence of other bubbles. Hence, it is reasonable to think that modifying the volume fraction correction (f(α)) term such that the magnitude of the drag force is reduced may lead to improved agreement with experimental results, particularly given that it was shown elsewhere8 that the model was sensitive to this correction term. To investigate the effect of the volume fraction term, simulations were performed at a superficial velocity of 0.16 m s−1, using a further modified form of the term developed by Simonnet et al.,28 where f(α) has been reduced for local volume fractions >0.15 as shown in Figure 19.

compared with a value of 0.27 with the original volume fraction correction term. Such indicative results strongly suggest that further experimental work to more reliably determine the magnitude of the volume fraction correction term particularly at high superficial velocities would be invaluable in improving CFD models of bubble columns.

5. CONCLUSIONS In this work, we have investigated the behavior of a pilot-scale bubble column with a “tree” type sparger, generating a comprehensive experimental data set, consisting of measurements of the BSD and overall holdup, as well as profiles of the local holdup, liquid velocity, and gas velocity for superficial velocities between 0.01 and 0.37 m s−1. The second half of this study compared these data with predictions based on a CFD model previously developed for a smaller scale column,8 with the aim of evaluating the applicability of a computationally efficient single bubble size model in the modeling of industrial bubble column bioreactors. It was found that the model offered satisfactory predictions over a range of experimental measurements made over a range of superficial velocities. For example, for the superficial velocities examined (0.11−0.35 m s−1) the model was able to predict the overall holdup within engineering accuracy (±20%). Predictions of the local gas volume fraction, liquid velocity, and gas velocity were also acceptable, although the model tended to slightly overpredict the magnitude of the local holdup. To provide even better agreement between model predictions and experimental data, a modified form of the volume fraction correction term applied to the bubble drag law was evaluated, implementation of which resulted in improved agreement with experimental data. Such results suggest that future efforts to more accurately measure both the magnitude and form of this correction term, especially for bubble columns operating at high superficial velocities (and hence local volume fractions), are warranted for the successful development of even more reliable CFD models. Notwithstanding the above qualifications, our current, computationally efficient model makes predictions within engineering accuracy that describe the complex and time-varying behavior within a pilot-scale bubble column operating at industrially relevant superficial velocities. Plans are currently underway to extend the experimental and modeling aspects of this work to examining mixing in both the pilot- and industrialscale columns.

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AUTHOR INFORMATION

Corresponding Author

*(D.F.F.) E-mail: david.fl[email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge that this work was partially funded by ARC Linkage Grant LP120100608. Computational resources were provided by Intersect Australia Ltd.; we thank Dr. Joachim Mai and Simon Yin for their assistance in this regard.

Figure 19. Plot showing the modified Simonnet et al.28 term used in this work along with the reduced version of the term.

It was found that reducing the magnitude of the volume fraction correction term led to an improved agreement with experimental results, particularly for the local gas volume fraction profiles, as shown in Figure 20. Modification of the volume fraction correction term also resulted in improved agreement between the experimentally measured overall volume fraction (0.23 ± 0.01) and the result predicted by the CFD model (0.24),

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CD db do 14541

NOMENCLATURE bubble drag coefficient bubble diameter, m diameter of sparger orifice. m dx.doi.org/10.1021/ie501105m | Ind. Eng. Chem. Res. 2014, 53, 14526−14543


Article

Figure 20. Effect of the volume fraction correction term f(α) at a superficial velocity of 0.16 m s−1. Results for the local volume fraction profiles at heights of 1050 mm above the base of the column (a) and 550 mm above the base of the column (c) are shown, along with liquid velocity profile measurements at heights of 1050 mm (b) and 550 mm (d) above the base of the column.

D f(α) FD g h H P UG UL x y

z α κ ρG ρL ρmix

column diameter, m volume fraction correction term drag force, kg m−2 s−2 acceleration due to gravity, m s−2 height, m column height, m pressure, Pa gas velocity, m s−1 liquid velocity, m s−1 distance, m distance, m

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distance, m volume fraction conductivity, μS cm−1 gas density, kg m−3 liquid density, kg m−3 mixture density, kg m−3

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