Simulation and Comparison of Non-Newtonian Fluid Models using LBM in a Cavity

Document Type : Full Length Research Article

Authors

1 Department of Mechanical Engineering, University of Kashan, Kashan, Iran.

2 university of Kashan

3 Mech. Eng. kashan university

Abstract

In this paper, simulation of non-Newtonian fluid flow in a two-dimension lid driven cavity is investigated. In this simulation Lattice Boltzmann method is used to solve computational fluid dynamics equations numerically. The particular approach of this research is to simulate non-Newtonian fluid flow by Sisko and Hershel Bulkley extended models for the first time beside other non-Newtonian models, by means of Lattice Boltzmann technique. The results of different models including x and y- velocity profiles and streamlines were presented. Then the simulation results of different non-Newtonian fluid flow by Sisko and Hershel Bulkley extended models have been compared with Power Law, Herschel Bulkley and Bingham plastic models. Also, the effect of the Reynolds Number and Power Law parameter (n) on the velocity profiles were studied. Increase of n parameter and Reynolds number leads to moving center of main vortex toward center of cavity. By increasing the parameter n, the maximum value of velocity increases and this indicates while n parameter is increased, vortex strength is excessed

Keywords

Main Subjects


[1] Hou , S., Zou, Q., Chen S., Doolen G. and Cogley A.C., 1995. Simulation of cavity flow by the Lattice Boltzmann Method. Comput. Phys. 118,pp. 329–347.
[2] Miller, W., 1995., Flow in the driven cavity calculated by the Lattice Boltzmann Method, Phys., 51,pp. 3659–3669.
[3] Wu, J.S. and Shao, Y.L., 2004. Simulation of lid-driven cavity flows by parallel Lattice Boltzmann Method using multi-relaxation-time scheme, Int. J. Numer. Meth. Fluids 46,pp. 921–937.
[4] Chai, Z.H., Shi, B.C. and Zheng, L.,2006., Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time Lattice Boltzmann Method, Chin. Phys. 15,pp. 1855–1862.
[5] Arumuga Perumal, D. and Das, A.K., 2008., Simulation of flow in two-sided lid-driven square cavities by the Lattice Boltzmann Method, WIT Trans. Eng. Sci. 59, pp.45–54.
[6] Yoshino, M. , Hotta, Y. Hirozane, T. and Endo, M.,2007. A numerical method for incompressible non-Newtonian fluid flows based on the Lattice Boltzmann Method, Journal of Non-Newton. Fluid Mechanics. 147, pp.69–78.
[7] Phillips, T.N. and Roberts, G.W.,2011. Lattice Boltzmann models for non-Newtonian flows, IMA J. Appl. Math. 76, pp.790–816.
[8] Jiang, D., Sun, D., Xiang, N., Chen, K. ,Yi, H. and Ni, Z.,2013. Lattice Boltzmann numerical simulation and experimental research of dynamic flow in an expansion- contraction microchannel, Biomirofluidics, 7.
[9] Gabanelli, S. and Drazer, G.,2005. Lattice Boltzmann Method for Non-Newtonian (Power Law) fluids, physical review E79.
[10] Azhdari heravi, A.,Talebi, F. and Valipour ,M.S.,2015. Investigation of pro-scale random porous media using lattice Boltzmann method. Journal of Heat and Mass Transfer Research.2,pp 1-12.
[11] Nazari, M. and Kayhani, M.S.,2016. A Comparative Solution of Natural Convection in an Open Cavity using Different Boundary Conditions via the Lattice Boltzmann Method. Journal of Heat and Mass Transfer Research.3,pp115-129.
[12] Shomali, M. and Rahmati,A.R.2020., Numerical Analysis of Gas Flows in a Microchannel Applying the Cascaded Lattice Boltzmann Method with Varying Bosanquet Parameter., Journal of Heat and Mass Transfer Research.7,pp 25-38.
[13] Ghia, U., Ghia, K.N., Shin, T.,1982,. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of computational physics, 48, pp. 387-411.
[14] Thohura, S., Molla, M. and Sarker, M.A. 2019. Numerical solution of non-Newtonian Power Law fluid flow in a lid driven skewed cavity, international journal of applied and computational mathematics.
[15] Dalal, S., Tomar, G. and Dutta, P., 2016. Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities, Journal of Non_Newtonian fluid mechanics.
[16] Mahmood, R., Kousar, N., Yaqob, M., Jabeen, K., 2017.Numerical solutions of the square lid driven cavity flow of Bingham fluids using nonconforming finite element coupled with a direct solver, advances in mathematical physics.
[17] Furtado, G.M., Frey, S., Naccache, M.F., Souza mendes, P.R.,2018., Numerical simulation of an elasto-viscoplastic fluid flow inside the cavity, thermal engineering, vol. 17, pp. 73-79.
[18] Sousa, R.G., Poole, R.J., Afonso, A.M., Pinho, F.T., Oliviera, P.J., Moronzov A. and Alves, M.A., 2016. Lid driven cavity flow of viscoelastic liquids, Journal of Non_Newtonian fluid mechanics, 234,pp. 129-138.
[19] Li, Q., Hong, N., Shi, B. and Chai, Z., 2014. Simulation of power law fluid flows in two dimensional square cavity using multi relaxation time Lattice Boltzmann method, commun. comput. Phys., 15(1),pp. 265-284.
[20] Wang, C. and Ho, J.,2011. A Lattice Boltzmann approach for the non-Newtonian effect in the blood flow, computers and mathematics with applications, 62,pp. 75-86.
[21] Buick, J. and Boyd, J.,2007. Simulation of non-Newtonian fluid mixing using the lattice Boltzmann model. 4th WSEAS international conference on fluid mechanics, Queensland, Australia.
[22] Poursharifi, Z. and Sadeghy, K.,2017. On the use of lattice Boltzmann Method for simulating peristaltic flow if viscopelastic fluids in a closed cavity, Journal of Non_Newtonian fluid mechanics.
[23] Ashrafizadeh, M. and Bakhshaei, H., 2009. A comparison of non-Newtonian models for Lattice Boltzmann blood flow simulations, computers and mathematics with applications, 58, 1045-1054.
[24] Rahmati, A.R. and Ashrafizadeh, M.,2009.A generalized Lattice Boltzmann method for
124 A.R.Mehdizadeh/ JHMTR 8 (2021) 115- 125
three-dimensional incompressible fluid flow simulation, journal of applied fluid mechanics, 2(1), 71-95.
[25] Tang, G.H. Wang, S.B. Ye, P.X. and Tao, W.Q. , 2011. Bingham Fluid Simulation with the incompressible Lattice Boltzmann method, journal of non-Newtonian fluid mechanics, 166, 145-151.
[26] Gokhale, M.Y. and Fernandes, I.,2014. Lattice Boltzmann simulation of non-Newtonian fluid flow in a lid driven cavity, international journal of mechanical engineering and technology, 5(8), pp. 20-33.
[27] Perumal, D., 2017. Lattice Boltzmann computation of multiple solution in a double-sided square and rectangular cavity flows. thermal science and engineering progress.
[28] Mendo, S. S. and Das, P. K.,2012. Flow of power Law fluids in a cavity driven by the motion of two facing lids – A simulation by Lattice Boltzmann method. journal of non-Newtonian fluid mechanics, 175,pp. 10-24.
[29] Mendo, S. S. and Das, P. K., 2013. Fluid flow in a cavity driven by oscillating lid – A simulation by Lattice Boltzmann method. European journal of mechanic’s b/fluid mechanics, 39, pp. 59-70.
[30] Bisht, M. and Patil, D. V. ,2017. Power Law fluid flow in driven enclosures with undulation using MRT-Lattice Boltzmann method. computers and mathematics with applications.
[31] Hussain, M.A. and Huq, M.,2014. Numerical Investigation of fluid flow over the lid driven square cavity, International conference of mechanical, industrial and energy engineering.
[32] Subrahmanyam, S., and Dasp, K., 2012. Flow Of Power-law Fluids In a Cavity driven by the motion of two facing lids-A Simulation By Lattice Boltzmann Method. Journal of Non-Newtonian Fluid Mechanics, 175, pp. 10-24.
[33] Chai, Z., Shi, B., Gou, Z. and Rong, F.,2011. Multiple-Relaxation-Time Lattice Boltzmann Model For generalized Newtonian Fluids Flow. Journal of Non-Newtonian Fluid Mechanics, 166, pp. 332-342.
[34] El-Borhamy, M.,2018. Numerical Study of the Stationary Generalized Visco-Plastic Fluid Flows. Alexandria Engineering journal, 57, pp. 2007-2018.
[35] Sidiki, M.D., Mamun Molla, M.D., Thohura, S. and Saha, C.,2018.Lattice Boltzmann Simulation of Non-Newtonian Power Law Fluid Flows in a Bifurcated channel. AIP Conference Proceedings.
[36] Yapici, K., Karasozen,B. and Uludag, Y.,2009.
Finite volume simulation of viscoelastic laminar flow in a lid-driven cavity. Non-Newtonian Fluid Mechanics, 164 (1), pp. 51-65.
[37] Yapici, K. and Uludag, Y., 2013.
Computational analysis of hydrodynamics of shear-thinning viscoelastic fluids in a square lid-driven cavity flow. Korea-Aust. Rheology Journal, 25, (4),pp. 243-260.
[38] Li ,Q., Hong , N., Shi ,B. and Chai, Z.,2014.Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation Time Lattice Boltzmann Method. Communications in Computational Physics, 15, (1),pp. 265-284.
[39] Madlener, K., Frey, B. and Ciezky, H. K. 2009.Generaliezed Reynolds Number For Non-Newtonian Fluids. Progress in Propulsion Physics, 1, pp. 237-250.
[40] Santos, P. H. S. Carignano, M. A. and Companella, O.,2017. Effect of Shear History on Rheology of Time-Dependent Colloidal Silica Gels. Gels, 3, 45, pp. 1-12.
[41] Ghasemi Kafarvedi, S., Hashemabadi, S. H. and Alboghobesh, F., 22012. CFD Simulation of Two phase Flow of Drilling Mud And Cutting Using Extended Herschel Bulkley Model. International conference of Oil, Gas , Petrochemical and Power Plant.
[42] Mohamad,A.A.,2011., Lattice Boltzmann Method, fundamentals and engineering applications with computer codes, springer.
[43] Benzi, R. and Succi, S., Vergassola, M.,19922.,The Lattice Boltzmann equation: theory and applications, Phys. Rep., 222, pp. 145–197.
[44] Chen, S. and Doolen, G.D.1998., Lattice Boltzmann Method for fluid flows, Annu. Rev. Fluid Mech. 30, pp. 329–364.
[45] Boyd, J. Buick, J. and Green, S.,2006. A second-order accurate lattice Boltzmann Non-Newtonian flow model. Journal of physics A: Mathematical and General, 39,pp. 14241-14247.
[46] Xiea, C., Zhang, J.,Bertolac, V. and Wanga, M.,2016. Lattice Boltzmann modeling for multiphase viscoplastic fluid flow. J. Non-Newtonian Fluid Mechanics, 234, pp.118-128.
[47] Papanastasiou, C.,1987.Flows of materials with yield. Journal of Rheology, 31, 385.
[48] Kefayati, GH. R.,2019.Lattice Boltzmann Method for natural convection of a Bingham fluid in a porous cavity. Physica, 521, pp.146-172.
[49] He, X.Y. and Luo, L.S.,1997.Lattice Boltzmann model for the incompressible Navier–Stokes equation. Stat. Phys. 88 , 927.
First Author / JHMTR 8 (2021) 115-125 125
[50] Han, S., Koo, J. and Moon, H.,2020. Morphological classification of disintegration behavior of viscoelastic simulant gel propellant in coaxial streams. Journal of the Visualization Society of Japan , 23, pp. 287-298.
[51] Neofytou, P.,2005. A 3rd order upwind finite volume method for generalized Newtonian fluid flows. Advances in Engineering Software, 36, pp. 664-680.