# Modeling of Two-Phase Flow Parameters of a Multi-Channel Cylindrical Cyclone

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## Abstract

**:**

## 1. Introduction

## 2. Methods Introduction

^{3}/h, 1200 m

^{3}/h, and 1900 m

^{3}/h. The main structural parameters are: diffuser, width × height—0.008–0.025 × 0.3 (m); radius of semi-rings—0.2, 0.17, 0.14, 0.11, and 0.08 (m); air flow outlet—0.16 m; and height of the conical hopper—0.25 m. These velocities are 9.3 m/s, corresponding to the maximum flow, 8.3 m/s, corresponding to the average flow, and 6.3 m/s, corresponding to the minimum flow.

#### 2.1. Determination of the Biphasic Flow Rate Distribution in a Six-Channel Cyclone

#### 2.2. Determination of the Pressure Distribution of a Two-Phase Flow in a Six-Channel Cyclone

^{3}particulate matter due to the extremely negligible effect of the second-phase concentration on the gas (air) pressure distribution in the cyclone. When the mathematical model was created, it was observed that the pressure distribution remained the same for the single- and two-phase flows, i.e., the uncontaminated flow and the two-phase flow contaminated with median-diameter particulate matter (8.995 μm). Therefore, it is limited to determining the dynamic pressure distribution in the model in the case of a two-phase flow by varying the inlet velocity parameter, which is included in the list of input data in the mathematical model.

#### 2.3. Determination of the Two-Phase Flow Separation Efficiency in a Six-Channel Cyclone

^{3}. In all cases, the efficiency of the separation of glass particulate matter from the air stream with a median diameter (8.995 μm) was considered. After performing the modeling task, in the case of different parameter variants, the average values of the volumes of the second phase in the outflow of the cyclone separation chamber were presented in two-dimensional space. The obtained results were comparable with those of experimental studies performed on the physical model [34].

_{k}is the variation in the turbulent kinetic energy (TKE) due to the internal rate gradient, which, according to Businesko’s hypothesis, is equal to ${G}_{k}={\mu}_{t}{S}^{2}$; µ

_{t}is the turbulent dynamic viscosity; S is the deformation tensor; G

_{b}is the variation in TKE due to the average flow rate gradient, which is equal to ${G}_{b}=\beta {g}_{i}\frac{{\mu}_{t}}{P{r}_{t}}\frac{\partial T}{\partial {x}_{i}}$; β is the temperature expansion coefficient; Pr

_{t}is the Prandtl number of energy turbulence; g

_{i}is the gravitation vector in direction I; Y

_{M}is the fluid rate distribution due to the space movement under turbulent compression, which is equal to ${Y}_{M}=2\rho \epsilon {M}_{t}^{2}$; M

_{t}is the turbulence Mach number, a coefficient; C

_{1ε}, C

_{2ε}, and C

_{3ε}are the constants; σ

_{ε}and σ

_{k}denote the Prandtl number for ε and k variables; and S

_{ε}and S

_{k}are the users chosen.

_{i}—i-phase volume; ρ

_{i}—i-phase density; Φ

_{i}—i-phase dependent variable, such as movement per unit mass, turbulence energy, or phase volume;

**v**

_{i}—i-phase velocity vector; Γ

_{i}—exchange coefficient of variable Φ

_{i}; and S

_{Φi}—flow (source) member for the variable Φ

_{i}.

^{3}was introduced (bulk density of 1650 kg/m

^{3}was not estimated).

_{dal.1}—volume fraction of particulate matter before treatment and concentration of particulate matter before treatment; and V

_{dal.2}—volume fraction of particulate matter at the outlet of the cyclone and minimum concentration of particulate matter after treatment.

#### 2.4. Initial and Boundary Conditions

## 3. Results and Analysis

^{3}and an inlet velocity of 9.3 m/s, the maximum value of the particulate matter in the two-phase flow in the cyclone (R2) was 0.37 and the minimum cleaning efficiency was 63%. When the inlet velocity decreased to 8.3 m/s, the maximum value of the particulate volume in the two-phase flow in the cyclone (R2) was 0.42 and the minimum cleaning efficiency was 58%.

## 4. Conclusions

- Examining the two-phase flow in the cyclone channels, the maximum velocity was determined to be 12.8 m/s at the inflow velocity to the cyclone of 9.3 m/s. The maximum velocities of both phases were the same, but their distribution within the cyclone structure was slightly different;
- The pressure distribution was only affected by the inlet velocity parameter at the highest selected speed of 9.3 m/s, the maximum pressure set in channels II, III, and IV was 282 Pa, and the average pressure value varied between 37 Pa and 233 Pa. At the inlet velocities of 8.3 m/s and 6.3 m/s, the maximum pressures were 234 Pa and 151 Pa, respectively;
- Analyzing the cleaning efficiency of a multi-channel cyclone, the maximum separation efficiency calculated from the mathematical model was 63%. This value was obtained at the inlet velocity of 9.3 m/s using glass particulate matter with a median diameter (8.995 μm) (density 2600 kg/m
^{3}) to provide a concentration flow of 5 g/m^{3}; - In this research, new-generation multi-channel cyclone physics were simulated and the effects of the variation in the two-phase flow parameters in a cylindrical body were determined. The principal trends of gas flow in the numerical model were determined, which were verified with the physical model, and a good coincidence was obtained. Work on modified viscosity models is planned for further investigation of this research object in the future. The vertical distribution of the aerodynamic parameters in the cyclone was determined in this work. To optimize the purification process, it would be useful to examine the peculiarities of the two-phase flow at the flow-distribution zones, which occurs only in the construction of a multi-channel cyclone. The particulate matter removal efficiency of individual fractions would be relevant in the application of this equipment for gas flow purification by the precipitation of finely divided solid particles. These future studies would broaden the scope of our theoretical knowledge and provide more knowledge for design work and experimental research.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

G_{k} | Variation in turbulent kinetic energy (TKE) due to the internal rate gradient |

μ_{t} | Turbulent or Eddy dynamic viscosity |

S | Deformation tensor |

G_{b} | Variation in TKE due to the average flow rate gradient |

β | Temperature expansion coefficient |

Pr_{t} | Prandtl number of energy turbulence |

g_{i} | Gravitational vector in direction I |

Y_{M} | Fluid rate distribution due to space movement under turbulent compression |

M_{t} | Turbulence Mach number |

C_{1ε}, C_{2ε}, and C_{3ε} | Constants |

σ_{ε} and σ_{k} | Prandtl number for ε and k variables |

S_{ε} and S_{k} | User-chosen coefficients |

t | Time |

r_{i} | i-phase volume |

ρ_{i} | i-phase density |

Φ_{i} | i-phase dependent variable as moment per unit mass, turbulence energy, or phase volume |

v_{i} | i-phase velocity vector |

Γ_{i} | Exchange coefficient of variable Φ_{i} |

S_{Φi} | Flow (source) member for the variable Φ_{i} |

η | Cyclone cleaning efficiency |

V_{dal}_{.1} | Volume fraction of particulate matter before treatment, concentration of particulate matter before treatment |

V_{dal}_{.2} | Volume fraction of particulate matter at the outlet of the cyclone, minimum concentration of particulate matter after treatment |

## References

- Przystupa, K.; Ambrożkiewicz, B.; Litak, G. Diagnostics of Transient States in Hydraulic Pump System with Short Time Fourier Transform. Adv. Sci. Technol. Res. J.
**2020**, 14, 178–183. [Google Scholar] [CrossRef] - Aydın, N.; Ozalp, A.; Karagoz, I. Numerical Investigation of Heat and Flow Characteristics in a Laminar Flow Past Two Tandem Cylinders. Therm. Sci.
**2021**, 25, 2807–2818. [Google Scholar] [CrossRef] - Ma, L.; Ingham, D.B.; Wen, X. Numerical Modelling of the Fluid and Particle Penetration through Small Sampling Cyclones. J. Aerosol Sci.
**2000**, 31, 1097–1119. [Google Scholar] [CrossRef] - Tan, F.; Karagoz, I.; Avci, A. The Effects of Vortex Finder Dimensions on the Natural Vortex Length in a New Cyclone Separator. Chem. Eng. Commun.
**2016**, 203, 1216–1221. [Google Scholar] [CrossRef] - Altmeyer, S.; Mathieu, V.; Jullemier, S.; Contal, P.; Midoux, N.; Rode, S.; Leclerc, J.-P. Comparison of Different Models of Cyclone Prediction Performance for Various Operating Conditions Using a General Software. Chem. Eng. Process. Process Intensif.
**2004**, 43, 511–522. [Google Scholar] [CrossRef] - Banerjee, C.; Cepeda, E.; Joshi, N.; Muralidhara, A. Cyclonic Separator. Patent No. GB2586623, 3 March 2021. [Google Scholar]
- Chu, Q.; Chang, X.; Chen, D. A Physiochemical Model for the Combustion of Aluminum Nano-Agglomerates in High-Speed Flows. Combust. Flame
**2021**, 237, 111739. [Google Scholar] [CrossRef] - Seenivasan, V.; Sivapirakasam, S.P.; Swaminathan, G.; Sakthivel, M. The Gas Cyclone Separator A Review; LAP LAMBERT Academic Publishing: Sunnyvale, CA, USA, 2020; ISBN 978-620-3-04028-9. [Google Scholar]
- Xing, X.; Pu, W.; Zhang, Q.; Yang, Y.; Han, D. The Multi-objective Optimization of an Axial Cyclone Separator in the Gas Turbine. Int. J. Energy Res.
**2021**, 46, 3428–3442. [Google Scholar] [CrossRef] - Baltrėnas, P.; Chlebnikovas, A. The Investigation of the Structure and Operation of a Multi-Channel Cyclone, Separating Fine Solid Particles from an Aggressive Dispersed Gas and Vapour Flow. Powder Technol.
**2018**, 333, 327–338. [Google Scholar] [CrossRef] - Fu, S.; Zhou, F.; Sun, G.; Yuan, H.; Zhu, J. Performance Evaluation of Industrial Large-Scale Cyclone Separator with Novel Vortex Finder. Adv. Powder Technol.
**2021**, 32, 931–939. [Google Scholar] [CrossRef] - Ghodrat, M.; Qi, Z.; Kuang, S.B.; Ji, L.; Yu, A.B. Computational Investigation of the Effect of Particle Density on the Multiphase Flows and Performance of Hydrocyclone. Miner. Eng.
**2016**, 90, 55–69. [Google Scholar] [CrossRef] - Kaya, F.; Karagoz, I. Performance Analysis of Numerical Schemes in Highly Swirling Turbulent Flows in Cyclones. Curr. Sci.
**2008**, 94, 1273–1278. [Google Scholar] - Katare, P.; Krupan, A.; Dewasthale, A.; Datar, A.; Dalkilic, A.S. CFD Analysis of Cyclone Separator Used for Fine Filtration in Separation Industry. Case Stud. Therm. Eng.
**2021**, 28, 101384. [Google Scholar] [CrossRef] - Kadeejathul Kubra, P.; Poulose, S. 3D-Simulation of Cyclone Separator. In Proceedings of the International Conference on Systems, Energy & Environment (ICSEE) 2019, Kannur, India, 12–13 July 2019. [Google Scholar] [CrossRef]
- Sakin, A.; Karagoz, I.; Avci, A. A Computational Comparison of Flow and Pressure Fields in Axial and Reverse Flow Cyclone Separators. Int. J. Comput. Exp. Sci. Eng.
**2017**, 3, 20–25. [Google Scholar] - Gong, G.; Yang, Z.; Zhu, S. Numerical Investigation of the Effect of Helix Angle and Leaf Margin on the Flow Pattern and the Performance of the Axial Flow Cyclone Separator. Appl. Math. Model.
**2012**, 36, 3916–3930. [Google Scholar] [CrossRef] - Li, Y.; Qin, G.; Xiong, Z.; Fan, L. Gas-Liquid Separation Performance of a Micro Axial Flow Cyclone Separator. Chem. Eng. Sci.
**2021**, 249, 117234. [Google Scholar] [CrossRef] - Lim, J.-H.; Oh, S.-H.; Kang, S.; Lee, K.-J.; Yook, S.-J. Development of Cutoff Size Adjustable Omnidirectional Inlet Cyclone Separator. Sep. Purif. Technol.
**2021**, 276, 119397. [Google Scholar] [CrossRef] - Boysan, F.; Ayers, W.H. A Fundamental Mathematical Modeling Approach to Cyclone Design. Trans. Inst. Chem. Eng.
**1982**, 60, 222–230. [Google Scholar] - Hoffmann, A.C.; Stein, L.E. Gas Cyclones and Swirl Tubes Principles, Design and Operation, 2nd ed.; Springer: Berlin, Germany, 2007; ISBN 3-540-74694-3. [Google Scholar]
- Meier, H.F.; Mori, M. Anisotropic Behavior of the Reynolds Stress in Gas and Gas-Solid Flows in Cyclones. Powder Technol.
**1999**, 101, 108–119. [Google Scholar] [CrossRef] - Bernardo, S.; Mori, M.; Peres, A.; Dionísio, R.P. 3-D Computational Fluid Dynamics for Gas and Gas-Particle Flows in a Cyclone with Different Inlet Section Angles. Powder Technol.
**2006**, 162, 190–200. [Google Scholar] [CrossRef] - Dong, Y.; Wang, D.; Wang, G.; Deng, X. Preliminary Application of Reynolds Stress Model. J. Natl. Univ. Def. Technol.
**2016**, 38, 46–53. [Google Scholar] [CrossRef] - Eisfeld, B. Turbulent Equilibrium Conditions for Reynolds-Stress Models. Phys. Fluids
**2021**, 34, 1–15. [Google Scholar] - Troshin, A.; Matyash, I.; Mikhaylov, S. Reynolds Stress Model Adjustments for Separated Flows. In Proceedings of the 14th World Congress in Computational Mechanics (WCCM), Virtual, 11–15 January 2021. [Google Scholar]
- Chok, C. Reynolds Stress Model for Recirculating Flows. Ph.D. Thesis, Texas Tech University, Lubbock, TX, USA, 1993. [Google Scholar]
- Janicka, J. Model Functions of Reynolds Stress Models. Phys. Fluids
**1988**, 31, 49–55. [Google Scholar] [CrossRef] - Chen, L.; Ma, H.; Sun, Z.; Ma, G.; Li, P.; Li, C.; Cong, X. Effect of Inlet Periodic Velocity on the Performance of Standard Cyclone Separators. Powder Technol.
**2022**, 402, 117347. [Google Scholar] [CrossRef] - Babaoğlu, N.U.; Parvaz, F.; Hosseini, S.H.; Elsayed, K.; Ahmadi, G. Influence of the Inlet Cross-Sectional Shape on the Performance of a Multi-Inlet Gas Cyclone. Powder Technol.
**2021**, 384, 82–99. [Google Scholar] [CrossRef] - Chen, J.; Jiang, Z.; Yang, B.; Wang, Y.; Zeng, F. Effect of Inlet Area on the Performance of a Two-Stage Cyclone Separator. Chin. J. Chem. Eng.
**2022**, 44, 8–19. [Google Scholar] [CrossRef] - Baltrėnas, P.; Chlebnikovas, A. Removal of Fine Solid Particles in Aggressive Gas Flows in a Newly Designed Multi-Channel Cyclone. Powder Technol.
**2019**, 356, 480–492. [Google Scholar] [CrossRef] - Gimbun, J.; Luqman Chuah, A.; Fakhru’l-Razi, A.; Choong, T. The Influence of Temperature and Inlet Velocity on Cyclone Pressure Drop: A CFD Study. Chem. Eng. Process.
**2005**, 44, 7–12. [Google Scholar] [CrossRef] - Baltrėnas, P.; Chlebnikovas, A. Investigation into the Aerodynamic Parameters of the Recently Designed Two-Level Cylindrical Multi-Channel Cyclone-Separator. Sep. Sci. Technol.
**2015**, 50, 1257–1269. [Google Scholar] [CrossRef] - Concentration, Heat and Momentum Limited. Phoenics Overview. Available online: http://www.cham.co.uk/phoenics/d_polis/d_docs/tr001/tr001.htm (accessed on 5 May 2022).
- Qiaorui, S.; Ali, A.; Biaobiao, W.; Wang, P.; Bois, G.; Jianping, Y.; Kubar, A. Numerical Study on Gas-Liquid Two Phase Flow Characteristic of Multistage Electrical Submersible Pump by Using a Novel Multiple-Size Group (MUSIG) Model. Phys. Fluids
**2022**, 34, 063311. [Google Scholar] [CrossRef] - Ali, A.; Si, Q.; Yuan, J.; Shen, C.; Cao, R.; AlGarni, T.; Awais, M.; Aslam, B. Investigation of Energy Performance, Internal Flow and Noise Characteristics of Miniature Drainage Pump under Water–Air Multiphase Flow: Design and Part Load Conditions. Int. J. Environ. Sci. Technol.
**2021**, 18, 1–18. [Google Scholar] [CrossRef] - Ali, A.; Si, Q.; Wang, B.; Yuan, J.; Wang, P.; Rasool, G.; Shokrian, A.; Ali, A.; Zaman, M.A. Comparison of Empirical Models Using Experimental Results of Electrical Submersible Pump under Two-Phase Flow: Numerical and Empirical Model Validation. Phys. Scr.
**2022**, 97, 65209. [Google Scholar] [CrossRef]

**Figure 1.**The basic diagram of the six-channel cyclone’s structure: 1—air flow inlet, 2—diffuser, 3–7—curvilinear semi-rings of different radii, 8—air flow outlet, 9—six-channel cyclone’s bottom with segmented circular spaces, 10—six-channel cyclone’s conical hopper.

**Figure 3.**The gas (air) flow (first phase (

**a**) and second phase (

**b**)) velocity components’ distribution in the six-channel cyclone structure using median-diameter (8.995 μm) glass particulate matter at a 9.3 m/s inlet velocity in the cyclone.

**Figure 4.**The gas (air) flow (first phase (

**a**) and second phase (

**b**)) velocity components’ distribution in the six-channel cyclone structure using the median-diameter (8.995 μm) glass particulate matter at 8.3 m/s inlet velocity in the cyclone.

**Figure 5.**The gas (air) flow (first phase (

**a**) and second phase (

**b**)) flow velocity components’ distribution in the six-channel cyclone structure using median-diameter (8.995 μm) glass particulate matter at a 6.3 m/s inlet velocity in the cyclone.

**Figure 6.**Air flow pressure distribution in the six-channel cyclone structure using the median-diameter (8.995 μm) glass particulate matter at 9.3 m/s (

**a**), 8.3 m/s (

**b**), and 6.3 m/s (

**c**) cyclone inlet velocities.

**Figure 7.**Particle distribution and volume in the two-phase flow in the cyclone at 9.3 m/s (

**a**), 8.3 m/s (

**b**), and 6.3 m/s (

**c**) inlet velocities using the median-diameter (8.995 μm) glass particulate matter at a 5 g/m

^{3}inlet concentration.

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**MDPI and ACS Style**

Chlebnikovas, A.; Selech, J.; Kilikevičius, A.; Przystupa, K.; Matijošius, J.; Vaišis, V.
Modeling of Two-Phase Flow Parameters of a Multi-Channel Cylindrical Cyclone. *Energies* **2022**, *15*, 4690.
https://doi.org/10.3390/en15134690

**AMA Style**

Chlebnikovas A, Selech J, Kilikevičius A, Przystupa K, Matijošius J, Vaišis V.
Modeling of Two-Phase Flow Parameters of a Multi-Channel Cylindrical Cyclone. *Energies*. 2022; 15(13):4690.
https://doi.org/10.3390/en15134690

**Chicago/Turabian Style**

Chlebnikovas, Aleksandras, Jarosław Selech, Artūras Kilikevičius, Krzysztof Przystupa, Jonas Matijošius, and Vaidotas Vaišis.
2022. "Modeling of Two-Phase Flow Parameters of a Multi-Channel Cylindrical Cyclone" *Energies* 15, no. 13: 4690.
https://doi.org/10.3390/en15134690