DOI: https://doi.org/10.14710/ijred.2023.46696

Study of Two Layered Immiscible Fluids Flow in a Channel with Obstacle by Using Lattice Boltzmann RK Color Gradient Model

Laboratory of Mechanics and Energy, First Mohammed University, 60000 Oujda, Morocco

Received: 8 Jun 2022; Revised: 16 Aug 2022; Accepted: 5 Sep 2022; Available online: 24 Sep 2022; Published: 1 Jan 2023.
Editor(s): H. Hadiyanto
Open Access Copyright (c) 2023 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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Abstract

Lattice Boltzmann method (LBM) is employed in the current work to simulate two-phase flows of immiscible fluids over a square obstacle in a 2D computational domain using the Rothman-Keller color gradient model. This model is based on the multiphase Rothman-Keller description, it is used to separate two fluids in flow and to assess its efficacy when treating two fluids in flow over a square obstacle with the objective of reducing turbulence by adjusting the viscosities of the two fluids. This turbulence can cause major problems such as interface tracking techniques in gas-liquid flow and upward or downward co-current flows in pipes. So, the purpose of the study is to replace a single fluid with two fluids of different viscosities by varying these viscosities in order to reduce or completely eliminate the turbulence. The results show that to have stable, parallel and non-overlapping flows behind the obstacle, it is necessary that the difference between the viscosities of the fluids be significant. Also, showing that the increase in the viscosity ratio decreases the time corresponding to the disappearance of the vortices behind the obstacle. The results presented in this work have some general conclusions: For M≥2, the increase in the viscosity difference leads to an increasing of friction between fluids, reducing of average velocity of flow and decreasing the time corresponding to the disappearance of the vortices behind the obstacle. However, for M≤1/2, the opposite occurs.

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Keywords: Lattice Boltzmann method; Viscous fluid; RK color-gradient; Immiscible layered two-phase flows; Flow through obstacle

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Section: Original Research Article
Language : EN
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  1. Admi, Y., Channouf, S., Lahmer, E. B., Moussaoui, M. A., Jami, M., & Mezrhab, A. (2022). Effect of a Detached Bi-Partition on the Drag Reduction for Flow Past a Square Cylinder. International Journal of Renewable Energy Development, 11(4), 902-915, doi: https://doi.org/10.14710/ijred.2022.43619
  2. Admi, Y., Moussaoui, M. A., and Mezrhab, A. (2022). Numerical Investigation of Convective Heat Transfer and Fluid Flow Past a Three-Square Cylinders Controlled by a Partition in Channel. International Journal of Renewable Energy Development, 11(3), 766-781, doi: https://doi.org/10.14710/ijred.2022.43790
  3. Behrend O., Harris R. and Warren P. B. (1994). Hydrodynamic behavior of lattice Boltzmann and lattice Bhatnagar-Gross-Krook models, Physical Review E, 50(6), 4586, doi: https://doi.org/10.1103/PhysRevE.50.4586
  4. Benamour M., Liberge E., Ghein C. B. and Hamdouni A. (1994). Numerical simulation of flow around obstacles using lattice Boltzmann method, In AIP Conference Proceedings, 1648(1), 850039, AIP Publishing LLC, doi: https://doi.org/10.1063/1.4913094
  5. Bitsch B., Dittmann J., Schmitt M., Scharfer P., Schabel W. and Willenbacher N. (2014). A novel slurry concept for the fabrication of lithiumion battery electrodes with beneficial properties, J. Power Sources, 265, 81–90, doi: https://doi.org/10.1016/j.jpowsour.2014.04.115
  6. Bitsch B., Gallasch T., Schroeder M., Borner M., Winter M. and Willenbacher N. (2016). Capillary suspensions as beneficial formulation concept for high energy density Li-ion battery electrodes, J. Power Sources, 328, 114–123, doi: https://doi.org/10.1016/j.jpowsour.2016.07.102
  7. Breuer M., Bernsdorf J., Zeiser T. and Durst F. (2000), Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume, International journal of heat and fluid flow, 21(2), 186-196, doi: https://doi.org/10.1016/S0142-727X(99)00081-8
  8. Grunau D., Chen S. and Eggert K., (1993). A lattice Boltzmann model for multiphase fluid flows, Physics of Fluids, 10, 2557–2562, doi: https://doi.org/10.1063/1.858769
  9. Gunstensen A. K. and Rothman D. H., Lattice Boltzmann model of immiscible fluids (1991). Physical Review A, 43(8), 4320–4327, doi: https://doi.org/10.1103/PhysRevA.43.4320
  10. He X., Chen S. and Zhang R. (1999). A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability, Journal of computational physics, 152(2), 642-663, doi: https://doi.org/10.1006/jcph.1999.6257
  11. He X., Zhang R. and Chen S. (2000). Interface and surface tension in incompressible lattice Boltzmann multiphase model, Computer Physics Communications, 129(1-3), 121-130, doi: https://doi.org/10.1016/S0010-4655(00)00099-0
  12. Huang H., Thorne D. T., Schaap M. G. and Sukop M. C. (2007). Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models, Physical Review E, 76(6), 698-701, doi: https://doi.org/10.1103/PhysRevE.76.066701
  13. Huang H., Lu J. J., Yun X. and Sukop M. C. (2013). On simulations of high-density ratio flows using color-gradient multiphase lattice Boltzmann models, International Journal of Modern Physics C, 24.04, 1350021, doi: https://doi.org/10.1142/S0129183113500216
  14. Huang H., Huang J. J. and Lu X. Y. (2014). A mass-conserving axisymmetric multiphase lattice Boltzmann method and its application in simulation of bubble rising, Journal of Computational Physics, 269, 386-402, doi: https://doi.org/10.1016/j.jcp.2014.03.028
  15. Huang, H., Sukop, M. and Lu, X., (2015). Multiphase Lattice Boltzmann Methods: Theory and Application, John Wiley & Sons Ltd., Chichester,
  16. doi: https://doi.org/10.1002/9781118971451
  17. Inamuro T., Ogata T., Tajima S. and Konishi N. (2004). A lattice boltzmann method for incompressible two-phase flows with large density differences, Journal of Computational physics, 198(2), 628–644, doi: https://doi.org/10.1016/j.jcp.2004.01.019
  18. Lafarge, T., Boivin, P., Odier, N., and Cuenot, B. (2021). Improved color-gradient method for lattice Boltzmann modeling of two-phase flows, Physics of Fluids, 33(8), 082110, doi: https://doi.org/10.1063/5.0061638
  19. Latva-Kokko M. and Rothman D. H. (2005). Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids, Physical Review E, 71(5), 056702, doi: https://doi.org/10.1103/PhysRevE.71.056702
  20. Leclaire S., Reggio M. and Tr panier J. Y. (2012). Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model, Applied Mathematical Modelling, 36(5), 2237-2252, doi: https://doi.org/10.1016/j.apm.2011.08.027
  21. Mora P., Morra G. and Yuen D. A. (2021). Optimal surface-tension isotropy in the Rothman- Keller color-gradient lattice Boltzmann method for multiphase flow, Physical Review E, 103(3), 033302, doi: https://doi.org/10.1103/PhysRevE.103.033302
  22. Mora, P., Morra, G., Yuen, D. A., and Juanes, R. (2021). Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations, Transport in Porous Media, 1-28, doi: https://doi.org/10.1007/s11242-021-01629-8
  23. Moussaoui M. A., Jami M., Mezrhab A. and Naji H. (2010). MRT-Lattice Boltzmann simulation of forced convection in a plane channel with an inclined square cylinder, International Journal of Thermal Sciences, 49(1), 131-142, doi: https://doi.org/10.1016/j.ijthermalsci.2009.06.009
  24. Moussaoui M. A., Jami M., Mezrhab A. and Naji H. (2009). Convective heat transfer over two blocks arbitrary located in a 2D plane channel using a hybrid lattice Boltzmann-finite difference method, Heat and mass transfer, 45(11), 1373-1381, doi: https://doi.org/10.1007/s00231-009-0514-9
  25. Nie D., Jianzhong L., Limin Q. and Xiaobin Z. (2015). Lattice Boltzmann simulation of multiple bubbles motion under gravity, In Abstract and Applied Analysis, Hindawi, doi: https://doi.org/10.1155/2015/706034
  26. Rothman D. H. and Keller J. M. (1988). Immiscible Cellular Automaton Fluids, Journal of Statistical Physics, 52, 1119–1127, doi: https://doi.org/10.1007/BF01019743
  27. Sadeghi, M., Sadeghi, H., and Choi, C. E. (2021). A lattice Boltzmann study of dynamic immiscible displacement mechanisms in pore doublets, In MATEC Web of Conferences, 337(02011), EDP Sciences, doi: https://doi.org/10.1051/matecconf/202133702011
  28. Schneider M., Koos E., and Willenbacher N. (2016). Highly conductive, printable pastes from capillary suspensions, Sci. Rep., vol (6), p 31367. doi: https://doi.org/10.1038/srep31367
  29. Schneider M., Maurath J., Fischer S.B., Wei M., Willenbacher N. and Koos E. (2017). Suppressing crack formation in particulate systems by utilizing capillary forces, ACS Appl. Mater, Interfaces, 9, 11095–11105. doi: https://doi.org/10.1021/acsami.6b13624
  30. Shan X. and Chen H. (1993). Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E, 47(3), 1815, doi: https://doi.org/10.1103/PhysRevE.47.1815
  31. Sohankar A., Norberg C. and Davidson L. (1998). Low-Reynolds-number flow around a square cylinder at incidence: study of blockage onset of vortex shedding and outlet boundary condition, International journal for numerical methods in fluids, 26(1), 39-56, doi: https://doi.org/10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P
  32. Swift M. R., Osborn W. and Yeomans J. (1995). Lattice boltzmann simulation of nonideal fluids, Physical review letters, 75(5), 830, doi: https://doi.org/10.1103/PhysRevLett.75.830
  33. Ul-Islam S. and Zhou C. Y. (2009). Characteristics of flow past a square cylinder using the lattice Boltzmann method, Information Technology Journal, 8, 1094-1114, doi: https://doi.org/10.3923/itj.2009.1094.1114
  34. Zhu, X., Wang, S., Feng, Q., Zhang, L., Chen, L., and Tao, W. (2021). Pore-scale numerical prediction of three-phase relative permeability in porous media using the lattice Boltzmann method, International Communications in Heat and Mass Transfer, 126, 105403, doi: https://doi.org/10.1098/rsta.2012.0320
  35. Zou Q. and He X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model (1997), Physics of fluids, 9(6), 1591-1598, doi: https://doi.org/10.1063/1.869307

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