FLOW DYNAMICS OF LID-DRIVEN CAVITIES WITH OBSTACLES OF VARIOUS SHAPES AND CONFIGURATIONS USING THE LATTICE BOLTZMANN METHOD

Year 2021, , 83 - 102, 01.02.2021

Isac Rajan D. Arumuga Perumal

https://doi.org/10.18186/thermal.869135

Cited By: 5

Abstract

This work implements the emerging computational technique namely the Lattice Boltzmann Method (LBM) to a fluid flow problem of single sided lid-driven cavities with various shapes of obstacles placed in it. The numerical methodology employs the Single-Relaxation-Time (SRT) model applicable to low Mach number hydrodynamic problem for incompressible flow regime. Three geometrical shapes of the obstacles considered are circular, square, and elliptic. Cavity with obstacles exhibited remarkable circulation zones and structures in contrast to the classical lid driven cavity. The flow mechanics and the vortex dynamics are studied for various values of Reynolds Number (Re = 100, 400, and 1000). Due to the introduction of the obstacles, a strong induced vortex forms close to the obstacles and its size changes interestingly with the variation of Reynolds number, which is captured by LBM. Further the study is extended to examine the vortex phenomena induced by changing the position of the obstacles within the cavity. It is observed that the flow structures change dramatically with little change in the position of obstacle inside the cavity which helps to identify position with enhanced mixing characteristics.

Keywords

Lid Driven Cavity, Lattice Boltzmann Method, Circular Obstacle, Square Obstacle, Elliptic Obstacle

References

• [1] Succi, S. The Lattice Boltzmann Method for Fluid Dynamics and Beyond. United Kingdom: Oxford University Press; 2001.
• [2] Shankar P. N, and Deshpande M.D, Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics 2000; 32: 93-136. https://doi.org/10.1146/annurev.fluid.32.1.93
• [3] Sthavistha Bhopalam R, Perumal, D.A. Yadav, A.K., Computation of fluid flow in double sided cross-shaped lid-driven cavities using Lattice Boltzmann Method. European Journal of Mechanics-B/Fluids. 2018; 70:46–72. https://doi.org/10.1016/j.euromechflu.2018.01.006
• [4] Burgraff, O.R. Analytical and numerical studies of the structure of steady separated flows, Journal of Fluid Mechanics. 1966; 24(1): 113-151. https://doi.org/10.1017/S0022112066000545
• [5] Pan F. and Acrivos, A. Steady flows in rectangular cavities. Journal of Fluid Mechanics. 1967; 28(4): 643-655. https://doi.org/10.1017/S002211206700237X
• [6] Ghia, U. Ghia K.N. and Shin, C.T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics. 1982; 48 (3): 387-411. https://doi.org/10.1016/0021-9991(82)90058-4
• [7] Xu, G. X. Li, E. Tan V. and Liu, G.R. Simulation of steady and unsteady incompressible flow using gradient smoothing method (GSM). Computers & Structures. 2012; 90: 131-144. https://doi.org/10.1016/j.compstruc.2011.10.001
• [8] Jiang, Y. Mei L. and Wei, H. A finite element variational multiscale method for incompressible flow. Applied Mathematics and Computation. 2015; 266: 374-384. https://doi.org/10.1016/j.amc.2015.05.055
• [9] Xie B. and Xiao, F. A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows. Journal of Computational Physics. 2016; 327: 747-778. https://doi.org/10.1016/j.jcp.2016.09.054
• [10] Hu, Z. Zheng, X. Ma Q-W and Duan, W-Y. Fluid flow in a cavity driven by an oscillating lid by an improved incompressible SPH. Procedia Engineering 2015; 126: 275-279. https://doi.org/10.1016/j.proeng.2015.11.241
• [11] Perumal, D. A. Dass, A.K. A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer. Alexandria Engineering Journal. 2015; 54: 955-971. https://doi.org/10.1016/j.aej.2015.07.015
• [12] Hou, S. Zou, Q. Chen, S. Doolen, G. Cogley, A.C. Simulation of cavity flow by the lattice Boltzmann method. Journal of Computational Physics. 1995; 118(2): 329–347. https://doi.org/10.1006/jcph.1995.1103
• [13] Perumal, D.A. Lattice Boltzmann computation of multiple solutions in a double-sided square and rectangular cavity flows. Thermal Science and Engineering Progress. 2018; 6: 48-56. https://doi.org/10.1016/j.tsep.2017.10.009
• [14] Oztop, H.F. Zhao, Z. Yu. B. Fluid flow due to combined convection in lid-driven enclosure having a circular body. International Journal of Heat and Fluid Flow. 2009; 30: 886–901. https://doi.org/10.1016/j.ijheatfluidflow.2009.04.009
• [15] Rahman, M.M. Alim, M.A. Sarker, M.M.A. Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity. International Communications in Heat and Mass Transfer. 2010; 37: 524–534. https://doi.org/10.1016/j.icheatmasstransfer.2009.12.012
• [16] Gangawane, K.M. Computational analysis of mixed convection heat transfer characteristics in lid-driven cavity containing triangular block with constant heat flux: Effect of Prandtl and Grashof numbers. International Journal of Heat and Mass Transfer. 2017; 105: 34-57. https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.061
• [17] Gangawane, K.M. Oztop, H.F. Abu-Hamdeh, N. Mixed convection characteristic in a lid-driven cavity containing heated triangular block: Effect of location and size of block. International Journal of Heat and Mass Transfer. 2018; 124: 860-875. https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.079
• [18] Hammami, F. Souayeh, B. Ben-Cheikh N., Ben-Beya, B. Computational analysis of fluid flow due to a two-sided lid driven cavity with a circular cylinder. Computers & Fluids. 2017; 156: 317-328. https://doi.org/10.1016/j.compfluid.2017.07.017
• [19] Zou Q. and He, X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids. 1997; 9(6): 1591-1598. https://doi.org/10.1063/1.869307
• [20] Abbassi, M.A. Ridha, D. Kamel, G. Effects of heater dimensions on nanofluid natural convection in a heated incinerator shaped cavity containing a heated block, Journal of Thermal Engineering. 2018; 4(3): 2018-2036. https://doi.org/10.18186/journal-of-thermal-engineering.411434
• [21] Hussein, A.K. Hussain, S.H. Characteristics of magnetohydrodynamic mixed convection in a parallel motion two-sided lid-driven differentially heated parallelogrammic cavity with various skew angles, Journal of Thermal Engineering. 2015; 1(3): 221-235. https://doi.org/10.18186/jte.66113
• [22] Taghikhani, M.A. Magnetic Field Effect on the Heat Transfer in a Nanofluid Filled Lid Driven Cavity with Joule Heating, Journal of Thermal Engineering. 6(4) (2020) 521-543. 10.18186/thermal.764225