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Prediction Of Unsteady States In Lid-Driven Cavities Filled With An Incompressible Viscous Fluid

Author

Listed:
  • FAYÇAL HAMMAMI

    (Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El-Manar II, Tunisia)

  • NADER BEN-CHEIKH

    (Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El-Manar II, Tunisia)

  • ANTONIO CAMPO

    (Department of Mechanical Engineering, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA)

  • BRAHIM BEN-BEYA

    (Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El-Manar II, Tunisia)

  • TAIEB LILI

    (Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El-Manar II, Tunisia)

Abstract

In this work, a numerical study devoted to the two-dimensional and three-dimensional flow of a viscous, incompressible fluid inside a lid-driven cavity is undertaking. All transport equations are solved using the finite volume formulation on a staggered grid system and multi-grid acceleration. Quantitative aspects of two and three-dimensional flows in a lid-driven cavity for Reynolds numberRe= 1000show good agreement with benchmark results.An analysis of the flow evolution demonstrates that, with increments in Re beyond a certain critical value Rec, the steady flow becomes unstable and bifurcates into unsteady flow. It is observed that the transition from steadiness to unsteadiness follows the classical Hopf bifurcation. The time-dependent velocity distribution is studied in detail and the critical Reynolds number is localized for both 2D and 3D cases.Benchmark solutions for 2D and 3D lid-driven cavity flows are performed forRe= 1500and 6000.

Suggested Citation

  • Fayçal Hammami & Nader Ben-Cheikh & Antonio Campo & Brahim Ben-Beya & Taieb Lili, 2012. "Prediction Of Unsteady States In Lid-Driven Cavities Filled With An Incompressible Viscous Fluid," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-13.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:04:n:s0129183112500301
    DOI: 10.1142/S0129183112500301
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    References listed on IDEAS

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    1. Van Loef, J.J. & Cohen, E.G.D., 1989. "Transport coefficients of simple fluids in a density range from the solid to the dilute gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 156(1), pages 522-533.
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