# Experimental Study and Numerical Simulation of Gas–Liquid Two-Phase Flow in Aeration Tank Based on CFD-PBM Coupled Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}SO

_{3}(deoxidizer) and CoCl

_{2}·6(H

_{2}O) (catalyst). The high-speed camera is used to capture the characteristic distribution of bubbles in the aeration tank, and the specific parameters of the camera are shown in Table 2. The flow on both sides of the aerator has the same law and shows approximately symmetrical distribution. Therefore, the left area is selected to study gas–liquid two-phase flow distribution in the tank.

## 3. Test Results and Discussion

#### 3.1. Results and Discussion of Dissolved Oxygen Concentration Test

_{L}a, of the inverted-umbrella aerator is calculated through dissolved oxygen concentration. The oxygen mass transfer coefficient, k

_{L}a, is the mass of oxygen transferred from gas phase to liquid phase in unit volume in unit time. The mass transfer of oxygen plays a decisive role in the biochemical reaction in the aeration tank. Therefore, the oxygen mass transfer coefficient, k

_{L}a, is often used to indicate the aeration performance of the aerator.

_{L}a is the oxygen mass transfer coefficient, min

^{−1}. Cs is the oxygen saturation concentration under the experimental conditions, mg/L. C is the dissolved oxygen concentration at time T, mg/L.

_{t1}is the dissolved oxygen concentration at time T

_{1}, mg/L. C

_{t2}is the dissolved oxygen concentration at time T

_{2}, mg/L.

_{L}a, is linearly related to the logarithmic concentration ln (C

_{s}− C

_{t}), k

_{L}a is the opposite of the slope of the time history plot of logarithmic concentration ln (C

_{s}− C

_{t}). The dissolved oxygen concentration is converted into logarithmic concentration, and the scatter plot is made. Scattered points are fitted linearly. The curve fitting has high accuracy, and the coefficient of determination R

^{2}reaches more than 0.98. The curve of dissolved oxygen concentration and the fitting results are shown in Figure 3 (the blue line in the figure is the saturated dissolved oxygen concentration, and the magenta line is the slope of ln (C

_{s}− C

_{t})).

_{L}a

_{(T)}is oxygen mass transfer coefficient at test liquid temperature T, min

^{−1}. 1.024 is the correction coefficient.

_{L}a

_{(20)}is 0.1237 min

^{−1}when the rotational speed of the impeller is 250 r/min.

#### 3.2. Results and Discussion of High-Speed Photography

#### 3.2.1. Image Processing

#### 3.2.2. Feature Extraction

- a.
- Bubble position

- b.
- Bubble size

_{b}, is introduced. The diameter of a circle with the same area as the elliptical projection is defined as the equivalent diameter of a bubble, as shown in Equation (6):

^{2}.

#### 3.2.3. Gas Holdup

_{bubbles}is the total area of bubbles, m

^{2}, and S

_{L}is the total area of gas–liquid two-phase, m

^{2}.

## 4. Numerical Calculation Method

#### 4.1. Model and Meshing

^{6}. Therefore, the third grid is selected for numerical simulations. Namely, the grid number of the static domain is 8.68 × 10

^{5}, and the grid number of the rotation domain is 2.26 × 10

^{5}. The simulation results are less than the experiment results, and the error is about 9.1%. The bubbles with different sections cannot be distinguished in the image processing, which results in the high gas holdup in the experiment.

#### 4.2. Boundary Conditions

^{5}Pa, and the gravity acceleration is 9.81 m/s

^{2}.

#### 4.3. Numerical Calculation Model

^{3}, ${u}_{l}$ is velocity of liquid phase, m/s, ${u}_{g}$ is velocity of gas phase, m/s, ${d}_{g}$ is the diameter of bubbles, m, and ${\mu}_{g}$ is the dynamic viscosity of gas phase, Pa·s.

^{3}, ${u}_{g}$ is velocity of gas phase, m/s, and ${u}_{l}$ is velocity of liquid phase, m/s.

_{k}is turbulent kinetic energy generated by average velocity gradient, m

^{2}/s

^{2}, G

_{b}is turbulent kinetic energy generated by buoyancy, m

^{2}/s

^{2}, σ

_{k}and σ

_{ε}are prandtl number of k and ε, μ is viscosity coefficient, Pa·s, $\rho $ is arithmetic mean of two-phase density, kg/m

^{3}, C

_{1ε}, C

_{2ε}, C

_{3ε}and C

_{μ}are constant, and μ

_{l}is turbulent viscosity, Pa·s.

#### 4.3.1. Two-Fluid Model

- (1)
- Volume fraction equation:$${\mathrm{V}}_{\mathrm{q}}={\displaystyle \sum}_{\mathrm{V}}{\mathsf{\alpha}}_{\mathrm{q}}\mathrm{dV}$$
_{q}is the volume fraction of q-phase.

- (2)
- Mass-conservation equation:

_{q}is the volume fraction of q-phase, ${\mathsf{\rho}}_{\mathrm{q}}$ is the density of q-phase, kg/m

^{3}, ${\overrightarrow{\mathrm{v}}}_{\mathrm{q}}$ is current velocity of q-phase, m/s, ${\dot{\mathrm{m}}}_{\mathrm{pq}}$ is mass transfer from p-phase to q-phase, kg, ${\dot{\mathrm{m}}}_{\mathrm{qp}}$ is mass transfer from q-phase to p-phase, kg, generally, ${\mathrm{S}}_{\mathrm{q}}$ = 0.

- (3)
- Momentum conservation equation:

_{q}is the volume fraction of q-phase, ${\mathsf{\rho}}_{\mathrm{q}}$ is the density of q-phase, kg/m

^{3}, ${\overrightarrow{\mathrm{v}}}_{\mathrm{q}}$ is current velocity of q-phase, m/s, $\overline{\overline{\mathsf{\tau}}}$ is stress-strain tensor of q-phase, ${\overrightarrow{\mathrm{F}}}_{\mathrm{q}}$ is external volume force, N, ${\overrightarrow{\mathrm{F}}}_{\mathrm{lift},\mathrm{q}}$ is lift, N, ${\overrightarrow{\mathrm{F}}}_{\mathrm{wl},\mathrm{q}}$ is wall slip force, N, ${\overrightarrow{\mathrm{F}}}_{\mathrm{vm},\mathrm{q}}$ is virtual mass force, N, ${\overrightarrow{\mathrm{F}}}_{\mathrm{td},\mathrm{q}}$ is turbulent diffusion force, N, ${\overrightarrow{\mathrm{R}}}_{\mathrm{pq}}$ is interphase force, N, and ${\overrightarrow{\mathrm{v}}}_{\mathrm{pq}}$ is interphase velocity, m/s, which is defined as follows: if ${\dot{\mathrm{m}}}_{\mathrm{pq}}$ > 0, ${\overrightarrow{\mathrm{v}}}_{\mathrm{pq}}$ = ${\overrightarrow{\mathrm{v}}}_{\mathrm{p}}$, if ${\dot{\mathrm{m}}}_{\mathrm{pq}}$ < 0, ${\overrightarrow{\mathrm{v}}}_{\mathrm{pq}}$ = ${\overrightarrow{\mathrm{v}}}_{\mathrm{q}}$, if ${\dot{\mathrm{m}}}_{\mathrm{pq}}$ > 0, ${\overrightarrow{\mathrm{v}}}_{\mathrm{qp}}$ = ${\overrightarrow{\mathrm{v}}}_{\mathrm{q}}$, and if ${\dot{\mathrm{m}}}_{\mathrm{pq}}$ < 0, ${\overrightarrow{\mathrm{v}}}_{\mathrm{qp}}$ = ${\overrightarrow{\mathrm{v}}}_{\mathrm{p}}$.

#### 4.3.2. CFD-PBM Coupled Model

_{RC}is coalescence model constant, C

_{RC1}= 2.86, C

_{RC2}= 1.017, C

_{RC3}= 1.922. C

_{TI}is rupture model constant, C

_{TI1}= 1.6, C

_{TI2}= 0.42. We

_{cr}is critical Weber for bubble fragmentation, W

_{ecr}= 1.42, and α

_{max}is critical gas holdup, α

_{max}= 0.52.

## 5. Results and Discussion of Gas–liquid Two-Phase Flow Considering Bubble Size

#### 5.1. Results and Discussion of the Gas–Liquid Two-Phase Flow Field

#### 5.2. Results and Discussion of Mass Transfer Coefficient

_{L}a, includes two parameters: the liquid-phase mass transfer coefficient, k

_{L}, and the interfacial area, a (the total area of interface between bubbles and liquid). The gas–liquid two-phase flow in the aeration tank is explained from the above two parameters.

- a.
- Liquid-phase mass transfer coefficient

_{L}is calculated as follows [31]:

_{L}is diffusivity on the liquid, m

^{2}/s, ε is turbulent dissipation rate, w/kg, ρ is liquid density, kg/m

^{3}, μ is dynamic viscosity, Pa·s, and C is correction coefficient, taken as 1.13.

_{L}, the turbulent dissipation rate, ε, needs to be estimated, and ε is calculated as follows [31]:

_{ave}is average value of turbulent dissipation rate, w/kg, P is power input under gassed conditions, W, $\rho $ is liquid density, kg/m

^{3}, T is impeller diameter, m, and H is blade height of impeller, m.

_{L}varies with the change of turbulent dissipation rate, which is different at different positions. Therefore, the turbulent dissipation rate is solved by the volume average method in post-processing, and the liquid-phase mass transfer coefficient, k

_{L}, is calculated.

- b.
- Interfacial area

_{g}is gas holdup, %, and d

_{b}is bubble equivalent diameter, m.

#### 5.2.1. Results and Discussion of Liquid-Phase Mass Transfer Coefficient

_{L}. So, it is necessary to analyze the turbulence dissipation rate. The turbulent dissipation rate is the rate at which mechanical energy is converted into heat energy, and most of them occur in the fluid–solid contact area. Therefore, the impeller of the inverted-umbrella aerator is selected to analyze the turbulent dissipation rate.

_{L}, is shown in Figure 12. The liquid-phase mass transfer coefficient, k

_{L}, decreases rapidly during 0~6 s, and it is stable at 6 s. The variation of k

_{L}tends to be smooth and keeps at about 4 × 10

^{−4}m·s

^{−1}. The concentration gradient on both sides of the gas–liquid two-film is the largest at the beginning, the resistance when the gas enters liquid through the liquid membrane is the smallest, and liquid-phase mass transfer coefficient is more substantial. Bubble transfer and mass transfer appear in liquid with the increase of calculation time due to hydraulic jump and entrainment. The concentration difference between the two sides of the gas–liquid two-film decreases, and liquid-phase mass transfer coefficient decreases. Liquid-phase mass transfer coefficient of the PBM scheme is higher than the average diameter scheme. Bubble coalescence occurs in the PBM scheme, which leads to the increase of bubble size, and the retention time of bubbles in liquid is shortened. The total mass transfer is reduced at the same time, resulting in a higher concentration difference.

_{L}. However, the order of the liquid-phase mass transfer coefficient is small, and it needs to be 1/4 square root through the turbulent dissipation rate. Therefore, the variation of liquid-phase mass transfer coefficient with different bubble sizes is not apparent. It is necessary to study the interfacial area.

#### 5.2.2. Results and Discussion of Interfacial Area

^{−1}.

#### 5.2.3. Results and Discussion of Standard Oxygen Mass Transfer Coefficient

## 6. Conclusions

- (1)
- The size of bubbles in the aeration tank was different at an immersion depth of 0 mm and a rotational speed of 250 r/min, ranging from 0.4 to 1.6 mm.
- (2)
- The CFD-PBM coupled model can be considered as the effect of real bubble breakup and coalescence. Compared with the Euler-Euler two-fluid model with a single particle size, it can better simulate the gas–liquid two-phase flow field in the aeration tank.
- (3)
- The calculation precision of the liquid-phase mass transfer coefficient, k
_{L}, interfacial area, a, and standard oxygen mass transfer coefficient, k_{L}a, of the PBM scheme was higher than the average diameter scheme. The CFD-PBM coupled model can improve the accuracy of calculation, resulting in the simulation of gas–liquid two-phase flow.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Dong, L.; Wang, Y.; Dai, C.; Liu, H.; Ming, J. Prediction of aeration performance for inverted umbrella aerator based on dimensional analysis. J. Chem. Eng. Jpn.
**2019**, 52, 369–376. [Google Scholar] [CrossRef] - Fayolle, Y.; Cockx, A.; Gillot, S.; Roustan, M.; Heduit, A. Oxygen transfer prediction in aeration tanks using CFD. Chem. Eng. Sci.
**2007**, 62, 7163–7171. [Google Scholar] [CrossRef] - Burgess, J.M.; Calderbank, P.H. The measurement of bubble parameters in Two-Phase dispersions—I: The development of an improved probe technique. Chem. Eng. Sci.
**1975**, 30, 743–750. [Google Scholar] [CrossRef] - Burgess, J.M.; Calderbank, P.H. The measurement of bubble properties in two-phase dispersions—III: Bubble properties in a freely bubbling Fluidised-Bed. Chem. Eng. Sci.
**1975**, 30, 1511–1518. [Google Scholar] [CrossRef] - Liu, J.W. Gas-Liquid Flow Mechanism and Optimization Design Research for Inverted Umbrella Aerator. Master’s Thesis, Jiangsu University, Zhenjiang, China, 2019. [Google Scholar]
- Lee, W.H.; Lee, J.-H.; Bishop, P.L.; Papautsky, I. Biological application of Micro-Electro mechanical systems microelectrode array sensors for direct measurement of phosphate in the enhanced biological phosphorous removal process. Water Environ. Res.
**2009**, 81, 748–754. [Google Scholar] [CrossRef] [PubMed] - Xing, C.; Wang, T.; Wang, J. Experimental study and numerical simulation with a coupled CFD–PBM model of the effect of liquid viscosity in a bubble column. Chem. Eng. Sci.
**2013**, 95, 313–322. [Google Scholar] [CrossRef] - Dhotre, M.; Niceno, B.; Smith, B. Large eddy simulation of a bubble column using dynamic Sub-Grid scale model. Chem. Eng. J.
**2008**, 136, 337–348. [Google Scholar] [CrossRef] - Milelli, M.; Smith, B.L.; Lakehal, D. Large-Eddy Simulation of Turbulent Shear Flows Laden with Bubbles. Mech. Eng. Cong. Exp.
**2001**, 8, 461–470. [Google Scholar] - Deen, N.G.; Solberg, T.; Hjertager, B. Large eddy simulation of the Gas–Liquid flow in a square cross-sectioned bubble column. Chem. Eng. Sci.
**2001**, 56, 6341–6349. [Google Scholar] [CrossRef] - Dong, L.; Liu, J.; Liu, H.; Dai, C.; Gradov, D.V. Study on the internal Two-Phase flow of the Inverted-Umbrella aerator. Adv. Mech. Eng.
**2019**, 11, 1–13. [Google Scholar] [CrossRef] - Karpinska, A.M.; Bridgeman, J. CFD-Aided modelling of activated sludge Systems—A critical review. Water Res.
**2016**, 88, 861–879. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, X.K.; Yao, T. CFD analysis seawater treatment plant for Flue Gas Desulphurization (FGD). Power Eng.
**2004**, 24, 276–279. [Google Scholar] - Lehr, F.; Millies, M.; Mewes, D. Bubble-Size distributions and flow fields in bubble columns. AIChE J.
**2002**, 48, 2426–2443. [Google Scholar] [CrossRef] - Buwa, V.V.; Ranade, V.V. Characterization of dynamics of Gas-Liquid flows in rectangular bubble columns. AIChE J.
**2004**, 50, 2394–2407. [Google Scholar] [CrossRef] - Gupta, A.; Roy, S. Euler–Euler simulation of bubbly flow in a rectangular bubble column: Experimental validation with Radioactive Particle Tracking. Chem. Eng. J.
**2013**, 225, 818–836. [Google Scholar] [CrossRef] - Xu, Y.; Dong, H.F.; Tian, X.; Zhang, X.P.; Zhang, S.J. CFD-PBM coupled simulation of ionic Liquid-Air Two-Phase flow in bubble column. J. Chem. Ind. Eng.
**2011**, 62, 2699–2706. [Google Scholar] - Wang, L.; Su, J.W.; Zhang, X.P.; Yang, S. Numerical simulation of Gas-Liquid Two-Phase flow at variousinlet positions in bubble column at low gas velocity. J. Southwest Jiaotong Univ.
**2018**, 53, 164–172. [Google Scholar] - Wang, T.; Wang, J. Numerical simulations of Gas–Liquid mass transfer in bubble columns with a CFD–PBM coupled model. Chem. Eng. Sci.
**2007**, 62, 7107–7118. [Google Scholar] [CrossRef] - Wang, T. Simulation of bubble column reactors using CFD coupled with a population balance model. Front. Chem. Sci. Eng.
**2010**, 5, 162–172. [Google Scholar] [CrossRef] - Inverted-Umbrella Type Surface Aerator; Standards Press of China: Beijing, China, 2014; pp. 10–11.
- De Jesus, S.S.; Neto, J.M.; Santana, A.; Filho, R. Influence of impeller type on hydrodynamics and Gas-Liquid Mass-Transfer in stirred airlift bioreactor. AIChE J.
**2015**, 61, 3159–3171. [Google Scholar] [CrossRef] - De Jesus, S.S.; Neto, J.M.; Filho, R. Hydrodynamics and mass transfer in bubble column, conventional airlift, stirred airlift and stirred tank bioreactors, using viscous fluid: A comparative study. Biochem. Eng. J.
**2017**, 118, 70–81. [Google Scholar] [CrossRef] - Liu, L.G. Flow Simulation and Optimization Research of Oxidation Ditch with Fine Bubble Based on CFD-PBM Coupled Model. Master’s Thesis, Shanxi Agricultural University, Ya’an, China, 2017. [Google Scholar]
- Guo, Y.Y. Numerical Simulation of the Effect of Radius of Impeller and Its Installation Deptht on the Gas-Liquid Two-Phase Flow in a Stirred Tank. Master’s Thesis, Xi’an University of Technology, Xi’an, China, 2018. [Google Scholar]
- Karpinska, A.M.; Bridgeman, J. Towards a robust CFD model for aeration tanks for sewage Treatment—A Lab-Scale study. Eng. Appl. Comput. Fluid Mech.
**2017**, 11, 371–395. [Google Scholar] [CrossRef] - Xiao, H.F. CFD Numerical Simulation of Gas-Liquid Flow in Aeration Tank. Master′s Thesis, Dong Hua University, Shanghai, China, 2010. [Google Scholar]
- Zhang, X.; Peng, J.M.; Cong, J.L.; Li, X.J.; Chen, Y.Y. Uncertainty analysis on boundary condition in subcooled boiling flow by deterministic sampling. Atom. Energy Sci.
**2019**, in press. [Google Scholar] - Zhang, B. Numercial Simulation of Gas-Liquid Flow in a Pressurized Bubble Column Using the CFD-PBM Coupled Model. Master’s Thesis, Beijing Institute of Petrochemical Technology, Beijing, China, 2018. [Google Scholar]
- Duan, X.Y.; Zhang, Z.B.; Li, Y.Z.; Tu, J.Y. Simulation of Flowing Characteristics in Complex Bubbly Flow with Population Balance Model. J. Chem. Ind. Eng.
**2011**, 62, 928–933. [Google Scholar] - Garcia-Ochoa, F.; Gomez, E. Theoretical prediction of Gas–Liquid mass transfer coefficient, specific area and Hold-Up in sparged stirred tanks. Chem. Eng. Sci.
**2004**, 59, 2489–2501. [Google Scholar] [CrossRef]

**Figure 4.**Image processing process. (

**a**) Original image, (

**b**) nonlinear smoothing filtering, (

**c**) watershed image after segmentation, (

**d**) binarization image.

**Figure 5.**Bubble size distribution. (

**a**) Bubble diameter distribution, (

**b**) percentage of bubble size of each group.

**Figure 7.**Computational domain and mesh. (

**a**) Computational domain, (

**b**) mesh generation, (

**c**) mesh of the impeller.

**Figure 8.**The diagram of the computational fluid dynamics-population balance model (CFD-PBM) coupled model.

Name | Type | Range | Precision | Manufacturer |
---|---|---|---|---|

Portable dissolved oxygen meter | JPB-607A | 0~20 mg/L | ±0.3 mg/L | Lei Ci in Shanghai |

Projects | Technical Index |
---|---|

Maximum resolution | 1024 × 1024 |

Pixel size/μm | 14 × 14 |

Memory/G | 16 |

Continuous shooting time/s | 45 |

Whole resolution shooting speed/Frames Per Second (fps) | 4000 |

Reduced resolution shooting speed/fps | 256,000 |

Time (s) | Concentration (mg/L) | Time (s) | Concentration (mg/L) | Time (s) | Concentration (mg/L) | Time (s) | Concentration (mg/L) |
---|---|---|---|---|---|---|---|

0.5 | 0.1 | 5 | 3.3 | 9.5 | 5.4 | 14 | 6.8 |

1 | 0.4 | 5.5 | 3.5 | 10 | 5.6 | 14.5 | 7.0 |

1.5 | 0.8 | 6 | 3.8 | 10.5 | 5.7 | 15 | 7.1 |

2 | 1.2 | 6.5 | 4.0 | 11 | 5.9 | 15.5 | 7.2 |

2.5 | 1.6 | 7 | 4.3 | 11.5 | 6.1 | 16 | 7.3 |

3 | 1.9 | 7.5 | 4.5 | 12 | 6.2 | 16.5 | 7.4 |

3.5 | 2.3 | 8 | 4.7 | 12.5 | 6.4 | 17 | 7.5 |

4 | 2.6 | 8.5 | 5.0 | 13 | 6.5 | 17.5 | 7.6 |

4.5 | 3.0 | 9 | 5.2 | 13.5 | 6.7 | 18 | 7.6 |

Grid Number | Gas Holdup/% | Relative Error/% | |||
---|---|---|---|---|---|

Static Domain | Rotation Domain | Experiment | Simulation | ||

1 | 579,000 | 136,000 | 0.0769 | 0.0646 | 16.0 |

2 | 726,000 | 181,000 | 0.0692 | 10.0 | |

3 | 868,000 | 226,000 | 0.0696 | 9.1 | |

4 | 1,113,000 | 272,000 | 0.07 | 8.9 | |

5 | 1,412,000 | 316,000 | 0.0695 | 8.7 | |

6 | 1,856,000 | 362,000 | 0.0703 | 8.6 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dong, L.; Guo, J.; Liu, J.; Liu, H.; Dai, C.
Experimental Study and Numerical Simulation of Gas–Liquid Two-Phase Flow in Aeration Tank Based on CFD-PBM Coupled Model. *Water* **2020**, *12*, 1569.
https://doi.org/10.3390/w12061569

**AMA Style**

Dong L, Guo J, Liu J, Liu H, Dai C.
Experimental Study and Numerical Simulation of Gas–Liquid Two-Phase Flow in Aeration Tank Based on CFD-PBM Coupled Model. *Water*. 2020; 12(6):1569.
https://doi.org/10.3390/w12061569

**Chicago/Turabian Style**

Dong, Liang, Jinnan Guo, Jiawei Liu, Houlin Liu, and Cui Dai.
2020. "Experimental Study and Numerical Simulation of Gas–Liquid Two-Phase Flow in Aeration Tank Based on CFD-PBM Coupled Model" *Water* 12, no. 6: 1569.
https://doi.org/10.3390/w12061569