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Korea-Australia Rheology Journal, Vol.32, No.3, 213-231, August, 2020
Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method
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The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions- simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.
- Aharonov E, Rothman DH, Geophys. Res. Lett., 20, 679 (1993)
- Albensoeder S, Kuhlmann HC, Rath HJ, Theor. Comput. Fluid Dyn., 14, 223 (2001)
- Alleborn N, Raszillier H, Durst F, Int. J. Heat Mass Transf., 42(5), 833 (1999)
- Artoli A, Mesoscopic computational haemodynamic, Ph.D. Thesis, University of Amsterdam 2003.
- Balmforth NJ, Frigaard IA, Ovarlez G, Annu. Rev. Fluid Mech., 46, 121 (2014)
- Benzi R, Succi S, Vergassola M, Phys. Rep., 222, 145 (1992)
- Bhatnagar PL, Gross EP, Krook M, Phys. Rev., 94, 511 (1954)
- Bird RB, Dai GC, Yarusso BJ, Rev. Chem. Eng., 1, 1 (1983)
- Blohm CH, Kuhlmann HC, J. Fluid Mech., 450, 67 (2002)
- Buick JM, Chem. Eng. Sci., 64(1), 52 (2009)
- Cao ZL, Esmail MN, AIChE J., 41(8), 1833 (1995)
- Chai ZH, Shi BC, Guo ZL, Rong FM, J. Non-Newton. Fluid Mech., 166(5-6), 332 (2011)
- Chen S, Doolen GD, Annu. Rev. Fluid Mech., 30, 329 (1998)
- Cheng M, Hung KC, Comput. Fluids, 35, 1046 (2006)
- Chhabra RP, Bubbles, Drops, and Particles in non-Newtonian fluids, CRC Press, Boca Raton, FL 2007.
- Frey S, Silveira FS, Zinani F, Mech. Res. Commun., 37, 145 (2010)
- Frigaard IA, Nouar C, J. Non-Newton. Fluid Mech., 127(1), 1 (2005)
- Gabbanelli S, Drazer G, Koplik J, Phys. Rev. E, 72, 6312 (2005)
- Gaskell PH, Summers JLHM, Thompson MD, Theor. Comput. Fluid Dyn., 8, 415 (1996)
- Ginzburg I, Steiner K, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 360, 453 (2002)
- Hellebrand H, VCH Verlagsgesellschaft mbH, Weinheim 17A, 189-265 1996.
- He X, Luo LS, Dembo M, Physica A, 239, 276 (1997)
- Hedayat MM, Borghei MH, Fakhari A, Sadeghy K, J. Soc. Rheol. Jpn., 38, 201 (2010)
- Hou S, Zou Q, Chen S, Doolen G, Cogley AC, J. Comput. Phys., 118, 329 (1995)
- Kuhlmann HC, Wanschura M, Rath HJ, J. Fluid Mech., 336, 267 (1997)
- Kuhlmann HC, Wanschura M, Rath HJ, Eur. J. Mech., B. Fluids., 17, 561 (1998)
- Lallemand P, Luo LS, Phys. Rev. E, 61, 6546 (2000)
- Leong CW, Ottino JM, J. Fluid Mech., 209, 463 (1989)
- Mendu SS, Das PK, J. Non-Newton. Fluid Mech., 175, 10 (2012)
- Miller W, Phys. Rev. E, 51, 3659 (1995)
- Mitsoulis E, Rheol. Rev., 135 2007.
- Mitsoulis E, Zisis T, J. Non-Newton. Fluid Mech., 101(1-3), 173 (2001)
- Neofytou P, Adv. Eng. Software, 36, 664 (2005)
- Ohta M, Nakamura T, Yoshida Y, Matsukuma Y, J. Non-Newton. Fluid Mech., 166(7-8), 404 (2011)
- Papanastasiou TC, J. Rheol., 31, 385 (1987)
- Patil DV, Lakshmisha KN, Rogg B, Comput. Fluids, 35, 1116 (2006)
- Perumal DA, Das AK, WIT Trans. Eng. Sci., 59, 45 (2008)
- Perumal DA, Das AK, CFD Lett., 2, 13 (2010)
- Prashant, Derksen JJ, Comput. Chem. Eng., 35(7), 1200 (2011)
- Succi S, The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University Press, Oxford 2001.
- Sukop MC, Thorne DT, An introduction for Geoscientists and engineers, Springer, Heidelberg 2006.
- Sullivan SP, Gladden LF, Johns ML, J. Non-Newton. Fluid Mech., 133(2-3), 91 (2006)
- Syrakos A, Georgiou GC, Alexandrou AN, J. Non-Newton. Fluid Mech., 195, 19 (2013)
- Tang GH, Wang SB, Ye PX, Tao WQ, J. Non-Newton. Fluid Mech., 166(1-2), 145 (2011)
- Triantafillopoulos NG, Aidun CK, TAPPI J, 73, 127 (1990)
- Vikhansky A, J. Non-Newton. Fluid Mech., 155(3), 95 (2008)
- Vola D, Boscardin L, Latche JC, J. Comput. Phys., 187, 441 (2003)
- Wahba EM, Comput. Fluids, 38, 247 (2009)
- Wang CH, Ho JR, Physica A, 387, 4740 (2008)
- Wang C, Ho J, Comput. Math. Appl., 62, 75 (2011)
- Wu JS, Shao YL, Int. J. Numer. Methods Fluids, 46, 921 (2004)
- Xie CY, Zhang JY, Bertola V, Wang MR, J. Non-Newton. Fluid Mech., 234, 118 (2016)
- Zou Q, He X, Phys. Fluids, 9, 1591 (1997)