Numerical Assessment of Turbulent Flow Driving in a Two-Sided Lid-Driven Cavity with Antiparallel Wall Motion

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In this paper, the case of the steady two-dimensional flow in a two-sided lid-driven square cavity is numerically investigated by the finite volume method (FVM). The flow motion is due to the top and bottom horizontal walls sliding symmetrically in the opposite direction with equal velocities, UT and UB, obtained through three respective Reynolds numbers, Re1,2=10000, 15000, and 20000. Due to the lack of availability of experimental results in this Reynolds number margin for this type of flow, the problem is first examined by considering that the flow is turbulent with the inclusion of four commonly used RANS turbulence models: Omega RSM, SST k-ω, RNG k-ε and Spalart-Allmaras (SA). Next, the regime is considered being laminar in the same range of Reynolds numbers. A systematic evaluation of the flow characteristics is performed in terms of stream-function contour, velocity profiles, and secondary vortices depth. Examination of the calculation results reveals the existence of a great similarity of the predicted flow structures between the Omega RSM model and those from the laminar flow assumption. On the other hand, the computed flow with the SST k-ω model, the RNG k-ε model, and the SA model reveals a remarkable under-prediction which appears clearly in the size and number of secondary vortices in the near-wall regions. Various benchmarking results are presented in this study.

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133-148

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January 2021

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[1] N. Shankar, M.D. Deshpande, Fluid mechanics in the driven cavity, Annu. Rev. Fluid. Mech. 32 (2000) 93–136.

DOI: 10.1146/annurev.fluid.32.1.93

Google Scholar

[2] H. C. Kuhlmann, F. Romanò, The lid-driven cavity, in: A. Gelfgat, (Ed.), Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, Springer, Cham, 2019, pp.233-309.

DOI: 10.1007/978-3-319-91494-7_8

Google Scholar

[3] H. F. Oztop, I. Dagtekin, Mixed Convection in Two-Sided Lid-Driven Differentially Heated Square Cavity, Int. J. Heat. Mass. Transf. 47 (2004), 1761-1769.

DOI: 10.1016/j.ijheatmasstransfer.2003.10.016

Google Scholar

[4] A.K. Hussein, S. Hussain, Mixed convection through a lid-driven air–filled square cavity with a hot wavy wall, Int. J. Mech. Mater. Eng. 5 (2010) 222-235.

Google Scholar

[5] S. Sivasankaran, V. Sivakumar, A.K Hussein, Numerical study on mixed convection in an inclined lid-driven cavity with discrete heating, Int. Commun. Heat. Mass. Transf. 46 (2013) 112-125.

DOI: 10.1016/j.icheatmasstransfer.2013.05.022

Google Scholar

[6] M. A. Ismael, I. Pop, A. J. Chamkha, Mixed Convection in a Lid-Driven Square Cavity with Partial Slip, Int. J. Therm. Sci. 82 (2014) 47-61.

DOI: 10.1016/j.ijthermalsci.2014.03.007

Google Scholar

[7] S. Sivasankaran, V. Sivakumar, A.K. Hussein, P. Prakash. Mixed convection in a lid-driven two-dimensional square cavity with corner heating and internal heat generation, Numer. Heat Transf. A. 65 (2014) 269-286.

DOI: 10.1080/10407782.2013.826017

Google Scholar

[8] S. Hussain, Characteristics of magnetohydrodynamic mixed convection in a parallel motion two-sided lid- driven differentially heated parallelogrammic cavity with various skew angles, J. Therm. Eng. 1 (2015) 221-235.

DOI: 10.18186/jte.66113

Google Scholar

[9] J.R. Koseff, R.L. Street, Visualization studies of a shear driven three-dimensional recirculating flow, J. Fluids. Eng. 106 (1984) 21-29.

DOI: 10.1115/1.3242393

Google Scholar

[10] U. Ghia, K.N. Ghia, C. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys. 48 (1982) 387–411.

DOI: 10.1016/0021-9991(82)90058-4

Google Scholar

[11] R. Schreiber, H. Keller, Driven cavity flows by efficient numerical techniques, J. Comput. Phys. 49 (1983) 310–333.

DOI: 10.1016/0021-9991(83)90129-8

Google Scholar

[12] M.M. Gupta, J.C. Kalita, A new paradigm for solving NavierStokes equations: streamfunction–velocity formulation, J. Comput. Phys. 207 (2005) 52–68.

DOI: 10.1016/j.jcp.2005.01.002

Google Scholar

[13] Y-H. Peng, Y-H. Shiau, R.R. Hwang, Transition in a 2-D lid-driven cavity flow, Comput. Fluids. 32 (2003) 337–352.

DOI: 10.1016/s0045-7930(01)00053-6

Google Scholar

[14] J.R. Murdock, J.C. Ickes, S.L. Yang, Transition flow with an incompressible lattice Boltzmann method, Adv. Appl. Math. Mech. 9 (2017) 1271–1288.

DOI: 10.4208/aamm.oa-2016-0103

Google Scholar

[15] A.N. Nuriev, A.G. Egorov, O.N. Zaitseva, Bifurcation analysis of steady-state flows in the lid-driven cavity, Fluid. Dyn. Res. 48 (2016) 061405–1–06140515.

DOI: 10.1088/0169-5983/48/6/061405

Google Scholar

[16] B. AN, F. Mellibovsky, J.M. Bergadà, W.M. Sang, Towards a better understanding of wall-driven square cavity flows using the Lattice Boltzmann method, Appl. Math. Model. 82 (2020) 469-486.

DOI: 10.1016/j.apm.2020.01.057

Google Scholar

[17] F. Auteri, N. Parolini, L. Quartapelle, Numerical investigation on the stability of singular driven cavity flow, J. Comput. Phys. 183 (2002) 1–25.

DOI: 10.1006/jcph.2002.7145

Google Scholar

[18] E. Erturk, Discussions on driven cavity flow, Int. J. Numer. Meth. Fluids. 60 (2009) 275–294.

DOI: 10.1002/fld.1887

Google Scholar

[19] E. Erturk, T.C. Corke, C. Gokcol, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, Int J. Numer. Method. Fluids. 48 (2005) 747–774.

DOI: 10.1002/fld.953

Google Scholar

[20] E.M. Wahba. Steady flow simulations inside a driven cavity up to Reynolds number 35000, J. Comput. Fluids. 66 (2012) 85–97.

DOI: 10.1016/j.compfluid.2012.06.012

Google Scholar

[21] E.A. Azzouz, S. Houat, O. Benhizia, Numerical study of steady flow inside a lid-driven square cavity for Reynolds number up to 50000, 23 rd French Mechanical Congress, Lille, French, (2017).

Google Scholar

[22] B. An, J.M. Bergadà, F. Mellibovsky, W.M. Sang, New applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers, Comput. Math. Appl. 79 (2019) 1718-1741.

DOI: 10.1016/j.camwa.2019.10.002

Google Scholar

[23] H.C. Kuhlmann, M. Wanschura, and H.J. Rath, Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures, J. Fluid. Mech. 336 (1997) 267–299.

DOI: 10.1017/s0022112096004727

Google Scholar

[24] H.C. Kuhlmann, M. Wanschura, and H.J. Rath, Elliptic instability in two-sided lid-driven cavity flow, Eur J. Mech. B/Fluids. 17 (1998) 561–569.

DOI: 10.1016/s0997-7546(98)80011-3

Google Scholar

[25] S. Albensoeder, H. Kuhlmann, H. Rath, Multiplicity of steady two-dimensional flows in two-sided lid-driven cavities, J. Theor. Comput. Fluid. Dyn. 14 (2001) 223–41.

DOI: 10.1007/s001620050138

Google Scholar

[26] K.T. Chen, C.C. Tsai, W.J. Luo, C.N. Chen, Multiplicity of Steady Solutions in a Two-Sided Lid-Driven Cavity with Different Aspect Ratios, J. Theor. Comput. Dyn. 27(2013) 767-776.

DOI: 10.1007/s00162-013-0296-z

Google Scholar

[27] K.T. Chen, C.C. Tsai, C.W. Lu, W.J. Luo, C.H. Chen, Aspect ratio effect on multiple flows solution in a two-sided parallel motion lid-driven cavity, J. Mech. 31 (2015) 153-160.

DOI: 10.1017/jmech.2014.51

Google Scholar

[28] D.A. Perumal, A.K. Dass, Simulation of incompressible flows in two-sided lid– driven square cavities. Part I. FDM, CFD. Lett. 2 (2010) 13–24.

Google Scholar

[29] D.A. Perumal, A.K. Dass, Simulation of incompressible flows in two-sided lid– driven square cavities. Part II. LBM, CFD. Lett. 2 (2010) 25–38.

Google Scholar

[30] D.A. Perumal, Simulation of flow in Two-Sided Lid-Driven deep cavities by finite difference method, J. Appl. Sci. Thermodyn. Fluid. Mech. 6 (2012) 1–6.

Google Scholar

[31] D.A. Perumal, Lattice Boltzmann Computation of Multiple Solutions in a Double Sided Square and Rectangular Cavity Flows, J. Therm. Sci. 6 (2018) 48-56.

DOI: 10.1016/j.tsep.2017.10.009

Google Scholar

[32] S. Arun, A. Satheesh, Analysis of flow behaviour in a two sided lid driven cavity using lattice Boltzmann technique, J. Alexandria. Eng. 54 (2015) 795-806.

DOI: 10.1016/j.aej.2015.06.005

Google Scholar

[33] C. Prasad, A.K. Dass, Use of an HOC scheme to determine the existence of multiple steady states in the antiparallel lid-driven flow in a two-sided square cavity, J. Comput. Fluids. 140 (2016) 297-307.

DOI: 10.1016/j.compfluid.2016.10.013

Google Scholar

[34] T. Lemée, G. Kasperski, G. Labrosse, R. Narayanan, Multiple stable solutions in the 2d symmetrical two-sided square lid-driven cavity, J. Comput. Fluids. 119 (2015) 204–212.

DOI: 10.1016/j.compfluid.2015.05.022

Google Scholar

[35] J.O. Hinze, Turbulence, McGraw-Hill Publishing Co., New York, (1975).

Google Scholar

[36] P.R. Spalart, S.R. Allmaras, A one-equation turbulence model for aerodynamics flows, La Rech. Aerosp. 1 (1994) 5–21.

Google Scholar

[37] S.A. Orszag, V. Yakhot, W.S. Flannery, F. Boysan, D. Choudhury, J. Maruzewski, and B. Patel, Renormalization Group Modeling and Turbulence Simulations, International Conference on Near-Wall Turbulent Flows, Tempe, Arizona, (1993).

Google Scholar

[38] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605.

DOI: 10.2514/3.12149

Google Scholar

[39] M.M. Gibson, B.E. Launder, Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer, J. Fluid. Mech. 86 (1978) 491–511.

DOI: 10.1017/s0022112078001251

Google Scholar

[40] B.E. Launder, Second-Moment Closure: Present... and Future, Inter J. Heat. Fluid. Flow. 10 (1989) 282–300.

DOI: 10.1016/0142-727x(89)90017-9

Google Scholar

[41] B.E. Launder, G.J. Reece, and W. Rodi, Progress in the Development of a Reynolds-Stress Turbulence Closure, J. Fluid. Mech. 68 (1975) 537–566.

DOI: 10.1017/s0022112075001814

Google Scholar

[42] D.C. Wilcox, Turbulence Modeling for CFD, DCW Industries, Inc., La Canada, California, (1998).

Google Scholar

[43] J.H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, Third ed., Springer Verlag, Berlin, (2002).

Google Scholar

[44] A. Ghobadian, S.A. Vasquez, A General Purpose Implicit Coupled Algorithm for the Solution of Eulerian Multiphase Transport Equation, International Conference on Multiphase Flow, Leipzig, Germany, (2007).

Google Scholar