Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎LDRP Institute of Technology and Research‎, ‎Kadi Sarva Vishwavidyalaya‎, ‎Gandhinagar‎, ‎Gujarat‎, ‎India.

2 Department of Mathematics‎, ‎Sarvajanik College of Engineering and Technology‎, ‎Surat‎, ‎Gujarat Technological University‎, ‎Gujarat‎, ‎India.

Abstract

In the present study, numerical simulations of two-dimensional steady-state incompressible Newtonian fluid flow in one-sided square and two-sided deep lid driven cavities under the aspect ratio K = 1, 4, 6 are reported. For the one-sided lid driven cavity, the upper wall is moved to the right with up to 5000 Reynolds numbers under a grid size of up to 501×501. This lends support to previous findings in the literature with Ghia et al.s results. Three cases are used in this article for the two-sided deep lid driven square cavity specifically. In these cases, the top and lower walls are moved to the right, while the left and right walls remain fixed up to at high Reynolds numbers (5000) under the grid size of up to 201×201. All possible flow solutions are studied in the present article, and flow bifurcation diagrams are constructed as velocity profiles and streamline contours for the same Reynolds number using a finite volume SIMPLE technique. The work done in this paper includes flow properties such as the location of primary and secondary vortices, velocity components, and numerical values for benchmarking purposes, and it is in excellent agreement with previous findings in the literature. A PARAM Shavak, high-performance computing (HPC) computer, was used to execute the calculations.

Keywords

References

  • [1]          J. D. Anderson and J. Wendt, Computational fluid dynamics, Springer, 1995.
  • [2]          E. F. Anley and Z. Zheng, Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients, Symmetry, 12 (2020), 485.
  • [3]          A. R. Appadu, J. K. Djoko, and H. Gidey, A computational study of three numerical methods for some advection- diffusion problems, Applied Mathematics and Computation, 272 (2016), 629–647.
  • [4]          E. F. Anley, Numerical solutions of elliptic partial differential equations by using finite volume method, Pure and Applied Mathematics Journal, 5 (2015), 120–129.
  • [5]          S. Arun and A. Satheesh, Analysis of flow behaviour in a two sided lid driven cavity using lattice boltzmann technique, Alexandria Engineering Journal, 54 (2015), 795–806.
  • [6]          V. Aswin, A. Awasthi, and C. Anu, A comparative study of numerical schemes for convection-diffusion equation, Procedia Engineering, 127 (2015), 621–627.
  • [7]          P. Ding, Solution of lid-driven cavity problems with an improved SIMPLE algorithm at high Reynolds numbers, International Journal of Heat and Mass Transfer, 115 (2017), 942–954.
  • [8]          I. Demirdˇzi´c,  Lilek Zˇ, and M. Peri´c,  Fluid  flow  and  heat  transfer  test  problems  for  non-orthogonal  grids:  bench-mark solutions, International Journal for Numerical Methods in Fluids, 15 (1992), 329–354.
  • [9]          E. Erturk, Discussions on driven cavity flow, International journal for numerical methods in fluids, 60 (2009), 275–294.
  • [10]        E.  Erturk,  T.  C,  Corke,  and  C.  G¨ok¸c¨ol,  Numerical  solutions  of  2-D  steady  incompressible  driven  cavity  flow  at high Reynolds numbers, International journal for Numerical Methods in fluids, 48 (2005), 747–774.
  • [11]        E. Erturk and C. G¨ok¸c¨ol, Fourth-order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids, 50 (2006), 421–436.
  • [12]        E. Erturk and O. Gokcol, Fine grid numerical solutions of triangular cavity flow, The European Physical Journal- Applied Physics, 38 (2007), 97–105.
  • [13]        J. Ferziger and M. Peric, Computational methods for fluid dynamics: Springer Science & Business Media, 2012.
  • [14]        U. Ghia, K. N. Ghia, and C. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of computational physics, 48 (1982), 387–411.
  • [15]        D. Gismalla, Matlab software for iterative methods and algorithms to solve a linear system, International Journal of Engineering and Technical Research (IJETR), (2014), 2321–0869.
  • [16]        M. M. Gupta and J. C. Kalita A new paradigm for solving Navier–Stokes equations: streamfunction–velocity formulation, Journal of Computational Physics, 207 (2005), 52–68.
  • [17]        S. Hou, Q. Zou, S. Chen, G. Doolen, and A. C. Cogley, Simulation of cavity flow by the lattice Boltzmann method, Journal of computational physics, 118 (1995), 329–347.
  • [18]        J. V. Indukuri and R. Maniyeri, Numerical simulation of oscillating lid driven square cavity, Alexandria engineer- ing journal, 57 (2018), 2609–2625.
  • [19]        P. K. Kundu and I. M. Cohen, Fluid mechanics, 2002.
  • [20]        A. G. Kamel, E. H. Haraz, and S. N. Hanna, Numerical simulation of three-sided lid-driven square cavity, Engi- neering Reports, 2 (2020), e12151.
  • [21]        S. Mazumder, Numerical methods for partial differential equations: finite difference and finite volume methods, Academic Press,(2015).
  • [22]        F. Moukalled, L. Mangani, and M. Darwish, The finite volume method in computational fluid dynamics, Springer, 113 (2016).
  • [23]        M. N. Ozisik, Heat transfer: a basic approach,McGraw-Hill New York,1985.
  • [24]        H. F. Peng, K. Yang, M. Cui, and X. W. Gao, Radial integration boundary element method for solving two- dimensional unsteady convection–diffusion problem, Engineering Analysis with Boundary Elements, 102 (2019), 39–50.
  • [25]        M. R. Patel and J. U. Pandya, Numerical study of a one and two-dimensional heat flow using finite volume, Materials Today: Proceedings, 51 (2021), 4857.
  • [26]        M. R. Patel and J. U. Pandya, A research study on unsteady state convection diffusion flow  with  adoption  of  the  finite volume technique, Journal of Applied Mathematics and Computational Mechanics, 20 (2021), 65–76.
  • [27]        D. Patil, K. Lakshmisha, and B. Rogg, Lattice  Boltzmann simulation of lid-driven flow in deep  cavities, Computers  & fluids, 35 (2006), 1116–1125.
  • [28]        O. Satbhai, S. Roy, and S. Ghosh, Direct numerical  simulation  of  a  low  Prandtl  number  RayleighBrd  convection  in a square box, Journal of Thermal Science and Engineering Applications, 11 (2019).
  • [29]        P. Suhas, Numerical heat transfer and fluid flow, Hemisphere publishing corporation, Etas-Unis dAm´erique, 1980.
  • [30]        S. Som, Introduction to heat transfer, PHI learning Pvt. Ltd.,2008.
  • [31]        G. D. Smith, Numerical solution of partial differential equations: finite difference methods,Oxford university press, 1985.
  • [32]        S. S. Sastry, Introductory methods of numerical analysis, PHI Learning Pvt. Ltd., 2012.
  • [33]        D. A. Von Terzi, Numerical investigation of transitional and turbulent backward-facing step flows, PhD thesis. The University of Arizona, 2004.
  • [34]        H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: the finite volume method,Pearson education, 2007.
  • [35]        M. Xu, A modified finite volume method for convection-diffusion-reaction  problems, International Journal of Heat and Mass Transfer, 117 (2018), 658–668.
  • [36]        A. Yaghoubi, High Order Finite Difference Schemes for Solving Advection-Diffusion Equation.
Computational Methods for Differential Equations
Volume 10, Issue 4
October 2022
Pages 986-1006

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History

  • Receive Date: 11 January 2022
  • Revise Date: 21 March 2022
  • Accept Date: 01 April 2022

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