DOI QR코드

DOI QR Code

Using a Lagrangian-Lagrangian approach for studying flow behavior inside a bubble column

  • YoungWoo Son (Department of Mechanical Engineering, Hanyang University) ;
  • Cheol-O Ahn (Metariver Technology Co. Ltd.) ;
  • SangHwan Lee (Department of Mechanical Engineering, Hanyang University)
  • Received : 2023.03.02
  • Accepted : 2023.08.10
  • Published : 2023.12.25

Abstract

Bubble columns are widely encountered in several industries, especially in the field of nuclear safety. The Eulerian-Eulerian and the Eulerian-Lagrangian methods are commonly used to investigate bubble columns. Eulerian approaches require additional tasks such as strict volume conservation at the interface and a predefined well-structured grid. In contrast, the Lagrangian approach can be easily implemented. Hence, we introduce a fully Lagrangian approach for the simulation of bubble columns using the discrete bubble model (DBM) and moving particle semi-implicit (MPS) methods. Additionally, we propose a rigorous method to estimate the volume fraction accurately, and verified it through experimental data and analytical results. The MPS method was compared with the experimental data of Dambreak. The DBM was verified by analyzing the terminal velocity of a single bubble for each bubble size. It agreed with the analytical results for each of the four drag correlations. Additionally, the improved method for calculating the volume fraction showed agreement with the Ergun equation for the pressure drop in a packed bed. The implemented MPS-DBM was used to simulate the bubble column, and the results were compared with the experimental results. We demonstrated that the MPS-DBM was in quantitative agreement with the experimental data.

Keywords

References

  1. E. Kim, W.H. Jung, J.H. Park, H.S. Park, K. Moriyama, Experiments on sedimentation of particles in a water pool with gas inflow, Nucl. Eng. Technol. 48 (2016), https://doi.org/10.1016/j.net.2015.12.007.
  2. Y.B. Jo, S. Park, E.S. Kim, Numerical simulation of 3-phase debris bed hydrodynamic leveling behavior using multi-phase SPH-DEM coupling, in: Transactions Of the Korean Nuclear Society Virtual Spring Meeting, Online, 2020. July 9-10.
  3. S. Yakush, P. Kudinov, Simulation of ex-vessel debris bed formation and coolability in a LWR severe accident, in: Proceedings of ISAMM-2009, Bottstein, Switzerland, 2009. Oct 25-28.
  4. E.S. Kim, S.H. Park, Y.B. Jo, Status of particle-based multi-physics simulation for nuclear severe accident: review, in: Transactions Of the Korean Nuclear Society Virtual Spring Meeting, Online, May 13-14, 2021.
  5. S.H. Park, Y.B. Jo, Y. Ahn, H.Y. Choi, T.S. Choi, S.S. Park, H.S. Yoo, J.W. Kim, E. S. Kim, Development of multi-GPU-based smoothed particle hydrodynamics code for nuclear thermal hydraulics and safety: potential and challenges, Front. Energy Res. (2020) 8, https://doi.org/10.3389/fenrg.2020.00086.
  6. Y.B. Jo, S.H. Park, H.S. Yoo, E.S. Kim, GPU-based SPH-DEM method to examine the three-phase hydrodynamic interactions between multiphase flow and solid particles, Int. J. Multiphas. Flow (2022) 153, https://doi.org/10.1016/j.ijmultiphaseflow.2022.104125.
  7. E. Kim, M. Lee, H.S. Park, K. Moriyama, J.H. Park, Development of an ex-vessel corium debris bed with two-phase natural convection in a flooded cavity, Nucl. Eng. Des. 298 (2016), https://doi.org/10.1016/j.nucengdes.2015.12.028.
  8. A. Konovalenko, S. Basso, P. Kudinov, S.E. Yakush, Experimental investigation of particulate debris spreading in a pool, Nucl. Eng. Des. 297 (2016), https://doi.org/10.1016/j.nucengdes.2015.11.039.
  9. D. Jain, J.A.M. Kuipers, N.G. Deen, Numerical study of coalescence and breakup in a bubble column using a hybrid volume of fluid and discrete bubble model approach, Chem. Eng. Sci. 119 (2014), https://doi.org/10.1016/j.ces.2014.08.026.
  10. M. Van Sint Annaland, N.G. Deen, J.A.M. Kuipers, Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method, Chem. Eng. Sci. 60 (2005), https://doi.org/10.1016/j.ces.2005.01.031.
  11. R.F.L. Cerqueira, E.E. Paladino, F. Evrard, F. Denner, B. Wachem, van Multiscale modeling and validation of the flow around taylor bubbles surrounded with small dispersed bubbles using a coupled VOF-DBM approach, Int. J. Multiphas. Flow (2021) 141, https://doi.org/10.1016/j.ijmultiphaseflow.2021.103673.
  12. D. Darmana, N.G. Deen, J.A.M. Kuipers, Detailed modeling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model, Chem. Eng. Sci. 60 (2005) 3383-3404, https://doi.org/10.1016/J.CES.2005.01.025.
  13. D. Darmana, R.L.B. Henket, N.G. Deen, J.A.M. Kuipers, Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model: chemisorption of CO2 into NaOH solution, numerical and experimental study, Chem. Eng. Sci. 62 (2007), https://doi.org/10.1016/j.ces.2007.01.065.
  14. D. Jain, Y.M. Lau, J.A.M. Kuipers, N.G. Deen, Discrete bubble modeling for a micro-structured bubble column, Chem. Eng. Sci. 100 (2013), https://doi.org/10.1016/j.ces.2013.02.060.
  15. J.B. Joshi, Computational flow modelling and design of bubble column reactors, Chem. Eng. Sci. 56 (2001).
  16. G.R. Guedon, G. Besagni, F. Inzoli, Prediction of gas-liquid flow in an annular gap bubble column using a Bi-dispersed eulerian model, Chem. Eng. Sci. 161 (2017), https://doi.org/10.1016/j.ces.2016.12.015.
  17. A. Asad, C. Kratzsch, R. Schwarze, Influence of drag closures and inlet conditions on bubble dynamics and flow behavior inside a bubble column, Eng. Appl. Comput. Fluid Mech. 11 (2017), https://doi.org/10.1080/19942060.2016.1249410.
  18. X. Sun, M. Sakai, Y. Yamada, Three-dimensional simulation of a solid-liquid flow by the DEM-SPH method, J. Comput. Phys. 248 (2013), https://doi.org/10.1016/j.jcp.2013.04.019.
  19. M. Robinson, M. Ramaioli, S. Luding, Fluid-particle flow simulations using twoway-coupled mesoscale SPH-DEM and validation, Int. J. Multiphas. Flow 59 (2014), https://doi.org/10.1016/j.ijmultiphaseflow.2013.11.003.
  20. S.J. Neethling, D.J. Barker, Using smooth particle hydrodynamics (SPH) to model multiphase mineral processing systems, Miner. Eng. 90 (2016), https://doi.org/10.1016/j.mineng.2015.09.022.
  21. E. Harada, H. Gotoh, H. Ikari, A. Khayyer, Numerical simulation for sediment transport using MPS-DEM coupling model, Adv. Water Resour. 129 (2019), https://doi.org/10.1016/j.advwatres.2017.08.007.
  22. E. Harada, T. Tazaki, H. Gotoh, Numerical investigation of ripple in oscillating water tank by DEM-MPS coupled solid-liquid two-phase flow model, J.HydroEnviron. Res. (2020) 32, https://doi.org/10.1016/j.jher.2020.07.001.
  23. E. Harada, H. Ikari, T. Tazaki, H. Gotoh, Numerical simulation for coastal morphodynamics using DEM-MPS method, Appl. Ocean Res. 117 (2021), https://doi.org/10.1016/j.apor.2021.102905.
  24. T. Tazaki, E. Harada, H. Gotoh, Vertical sorting process in oscillating water tank using DEM-MPS coupling model, Coast Eng. (2021) 165, https://doi.org/10.1016/j.coastaleng.2020.103765.
  25. S. Koshizuka, Y. Oka, Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nucl. Sci. Eng. 123 (1996), https://doi.org/10.13182/NSE96-A24205.
  26. S. Koshizuka, A. Nobe, Y. Oka, Numerical analysis of breaking waves using the moving particle semi-implicit method, Int. J. Numer. Methods Fluid. 26 (1998), https://doi.org/10.1002/(sici)1097-0363(19980415)26:7<751::aid-fld671>3.0.co;2-c.
  27. S. Koshizuka, H. Ikeda, Y. Oka, Numerical analysis of fragmentation mechanisms in vapor explosions, Nucl. Eng. Des. 189 (1999) 423-433, https://doi.org/10.1016/S0029-5493(98)00270-2.
  28. Y. Yamada, M. Sakai, Lagrangian-Lagrangian simulations of solid-liquid flows in a bead mill, Powder Technol. 239 (2013), https://doi.org/10.1016/j.powtec.2013.01.030.
  29. G. Duan, S. Koshizuka, A. Yamaji, B. Chen, X. Li, T. Tamai, An accurate and stable multiphase moving particle semi-implicit method based on a corrective matrix for all particle interaction models, Int. J. Numer. Methods Eng. 115 (2018) 1287-1314, https://doi.org/10.1002/nme.5844.
  30. T. Zhang, S. Koshizuka, P. Xuan, J. Li, C. Gong, Enhancement of stabilization of MPS to arbitrary geometries with a generic wall boundary condition, Comput. Fluids 178 (2019) 88-112, https://doi.org/10.1016/J.COMPFLUID.2018.09.008.
  31. M.A. Basit, W. Tian, R. Chen, R. Basit, S. Qiu, G. Su, Investigation of single bubble behavior under rolling motions using multiphase MPS method on GPU, Nucl. Eng. Technol. (2021) 53, https://doi.org/10.1016/j.net.2020.12.013.
  32. J. Ma, G.L. Chahine, C.T. Hsiao, Spherical bubble dynamics in a bubbly medium using an euler-Lagrange model, Chem. Eng. Sci. 128 (2015), https://doi.org/10.1016/j.ces.2015.01.056.
  33. T. Ziegenhein, R. Rzehak, E. Krepper, D. Lucas, Numerical simulation of polydispersed flow in bubble columns with the inhomogeneous multi-size-group model, Chem. Ing. Tech. 85 (2013), https://doi.org/10.1002/cite.201200223.
  34. D. Lucas, R. Rzehak, E. Krepper, T. Ziegenhein, Y. Liao, S. Kriebitzsch, P. Apanasevich, A strategy for the qualification of multi-fluid approaches for nuclear reactor safety, in: Proceedings of the Nuclear Engineering and Design vol. 299, 2016.
  35. R. Rzehak, M. Krauss, P. Kovats, K. Zahringer, Fluid dynamics in a bubble column: new experiments and simulations, Int. J. Multiphas. Flow 89 (2017), https://doi.org/10.1016/j.ijmultiphaseflow.2016.09.024.
  36. E.I.V. Van Den Hengel, N.G. Deen, J.A.M. Kuipers, Application of coalescence and breakup models in a discrete bubble model for bubble columns, Ind. Eng. Chem. Res. 44 (2005), https://doi.org/10.1021/ie0492449.
  37. S.H. Park, Y.B. Jo, Y. Ahn, H.Y. Choi, T.S. Choi, S.S. Park, H.S. Yoo, J.W. Kim, E. S. Kim, Development of multi-GPU-based smoothed particle hydrodynamics code for nuclear thermal hydraulics and safety: potential and challenges, Front. Energy Res. (2020) 8, https://doi.org/10.3389/fenrg.2020.00086.
  38. H. Gotoh, T. Sakai, T. Shibahara, Lagrangian flow simulation with SUB-PARTICLESCALE turbulence model, Proc. Hydraul. Eng. 44 (2000), https://doi.org/10.2208/prohe.44.575.
  39. J. Arai, S. Koshizuka, K. Murozono, Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method, Int. J. Numer. Methods Fluid. 71 (2013), https://doi.org/10.1002/fld.3685.
  40. E. Delnoij, J.A.M. Kuipers, W.P.M. van Swaaij, A three-dimensional CFD model for gas-liquid bubble columns, Chem. Eng. Sci. 54 (1999) 2217-2226, https://doi.org/10.1016/S0009-2509(98)00362-5.
  41. H. Rusche, Computational Fluid Dynamics of Dispersed Two-phase Flows at High Phase Fractions, PhD Thesis, Imperial College London (University of London), 2002.
  42. A. Tomiyama, H. Tamai, I. Zun, S. Hosokawa, Transverse migration of single bubbles in simple shear flows, Chem. Eng. Sci. 57 (2002) 1849-1858, https://doi.org/10.1016/S0009-2509(02)00085-4.
  43. S. Hosokawa, A. Tomiyama, S. Misaki, T. Hamada, Lateral migration of single bubbles due to the presence of wall, in: Proceedings of the American Society of Mechanical Engineers vol. 257, Fluids Engineering Division (Publication) FED, 2002.
  44. R. Rzehak, E. Krepper, C. Lifante, Comparative study of wall-force models for the simulation of bubbly flows, Nucl. Eng. Des. 253 (2012), https://doi.org/10.1016/j.nucengdes.2012.07.009.
  45. A.D. Burns, T. Frank, I. Hamill, J.M. Shi, The Favre Averaged Drag Model for Turbulent Dispersion in Eulerian Multi-phase Flows, 5th International Conference on Multiphase Flow, Yokohama, Japan, 2004. May 30 - June 4.
  46. Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technol. 71 (1992), https://doi.org/10.1016/0032-5910(92)88030-L.
  47. T.B. Anderson, R.O.Y. Jackson, A fluid mechanical description of fluidized beds, Ind. Eng. Chem. Fundam. 6 (1967).
  48. Z.Y. Zhou, S.B. Kuang, K.W. Chu, A.B. Yu, Discrete particle simulation of particlefluid flow: model formulations and their applicability, J. Fluid Mech. 661 (2010), https://doi.org/10.1017/S002211201000306X.
  49. K.M.T. Kleefsman, G. Fekken, A.E.P. Veldman, B. Iwanowski, B. Buchner, A volume-of-fluid based simulation method for wave impact problems, J. Comput. Phys. (2005) 206, https://doi.org/10.1016/j.jcp.2004.12.007.
  50. S. Ergun, Fluid flow through packed columns, Chem. Eng. Prog. 48 (1952) citeulike-article-id:7797897.
  51. R. di Felice, The voidage function for fluid-particle interaction systems, Int. J. Multiphas. Flow 20 (1994), https://doi.org/10.1016/0301-9322(94)90011-6.
  52. N.G. Deen, T. Solberg, B.H. Hjertager, Large eddy simulation of the gas-liquid flow in a square cross-sectioned bubble column, Chem. Eng. Sci. 56 (2001), https://doi.org/10.1016/S0009-2509(01)00249-4.