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Aspect Ratio Effect on Multiple Flow Solutions in a Two-Sided Parallel Motion Lid-Driven Cavity

  • K.-T. Chen (a1), C.-C. Tsai (a1), W.-J. Luo (a2), C.-W. Lu (a3) and C.-H. Chen (a4)...

Abstract

A continuation method, accompanied with a linear stability analysis, is employed to investigate the bifurcation diagram of the flow solutions, as well as the multiple flow states in a cavity with different aspect ratios for parallel motion of two facing lids. The Reynolds number proportional to the wall velocity is used as the continuation parameter, and the evolution of the bifurcation diagrams in cases with different aspect ratios is illustrated. The induced flow patterns are highly dependent upon both the aspect ratios and the moving velocity of the walls. Three different types of bifurcation diagrams and their corresponding flow states are classified according to the aspect ratios. One stable symmetric flow state and one stable asymmetric flow state are identified. The stable asymmetric flow state is obtained at a high aspect ratio and a low Reynolds number. Meanwhile, the regions of stable and unstable flows are distinguished according to the different aspect ratios.

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*Corresponding author (wjluo@ncut.edu.tw)

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1.Pan, F. and Acrivos, A., “Steady Flows in Rectangular Cavities,” Journal of Fluid Mechanics, 28, pp. 643655 (1967).
2.Prasad, A. K. and Koseff, J. R., “Reynolds Number and End-Wall Effects on a Lid-Driven Cavity Flow,” Physics of Fluids A, 1, pp. 208218 (1989).
3.Ahlman, D., Söderlund, F., Jackson, J., Kurdila, A. and Shyy, W., “Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows,” Numerical Heat Transfer Part B-Fundamentals, 42, pp. 285306 (2002).
4.Croce, G., Comini, G. and Shyy, W., “Incompressible Flow and Heat Transfer Computations Using a Continuous Pressure Equation and Nonstaggered Grids,” Numerical Heat Transfer Part B-Fundamentals, 38, pp. 291307 (2000).
5.Kuhlmann, H. C., Wanschura, M. and Rath, H. J., “Flow in Two-Sided Lid-Driven Cavities: Non-Uniqueness, Instabilities, and Cellular Structures,” Journal of Fluid Mechanics, 336, pp. 267299 (1997).
6.Kuhlmann, H. C., Wanschura, M. H. and Rath, J., “Elliptic Instability in Two-Sided Lid-Driven Cavity Flow,” European Journal of Mechanics B/Fluids, 17, pp. 561569 (1998).
7.Albensoeder, S., Kuhlmann, H. C. and Rath, H. J., “Multiplicity of Steady Two Dimensional Flows in Two-Sided Lid-Driven Cavities,” Theoretical and Computational Fluid Dynamics, 14, pp. 223241 (2001).
8.Alleborn, N., Raszillier, H. and Durst, F., “Lid-Driven Cavity with Heat and Mass Transport,” International Journal of Heat and Mass Transfer, 42, pp. 833853 (1999).
9.Albensoeder, S. and Kuhlmann, H. C., “Linear Stability of Rectangular Cavity Flows Driven by Anti-Parallel Motion of Two Facing Walls,” Journal of Fluid Mechanics, 458, pp. 153180 (2002).
10.Blohm, C. and Kuhlmann, H. C., “The Two-Sided Lid-Driven Cavity: Experiments on Stationary and Time-Dependent Flows,” Journal of Fluid Mechanics, 450, pp. 6795 (2002).
11.Yang, R. J. and Luo, W. J., “Multiple Fluid Flow and Heat Transfer Solutions in a Two-Sided Lid-Driven Cavity,” International Journal of Heat and Mass Transfer, 50, pp. 23942405 (2007).
12.Albensoeder, S. and Kuhlmann, H. C., “Three-Dimensional Instability of Two Counter Rotating Vortices in a Rectangular Cavity Driven by Parallel Wall Motion,” European Journal of Mechanics B/Fluids, 21, pp. 307316 (2002).
13.Chen, K. T., Tsai, C. C., Luo, W. J. and Chen, C. N., “Multiplicity of Steady Solutions in a Two-Sided Lid-Driven Cavity with Different Aspect Ratios,” Theoretical and Computational Fluid Dynamics, 27, pp. 767776 (2013).
14.Cadou, J. M., Guevel, Y. and Girault, G., “Numerical Tools for the Stability Analysis of 2D Flows: Application to the Two- and Four-Sided Lid-Driven Cavity,” Fluid Dynamics Research, 44, pp. 031403 (2012).
15.Waheed, M. A., “Mixed Convective Heat Transfer in Rectangular Enclosures Driven by a Continuously Moving Horizontal Plate,” International Journal of Heat and Mass Transfer, 52, pp. 50555063 (2009).
16.Noor, D. Z., Kanna, P. R. and Chern, M. J., “Flow and Heat Transfer in a Driven Square Cavity with Double-Sided Oscillating Lids in Anti-Phase,” International Journal of Heat and Mass Transfer, 52, pp. 30093023 (2009).
17.Keller, H. B., Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems, In applications of Bifurcation Theory, Rabinowitz, P. Ed., Academic Press, New York, pp. 359384 (1977).
18.Sorensen, D. C., “Implicit Application of Polynomial Filters in a K-Step Arnoldi Method,” SIAM Journal of Matrix Analysis and Applications, 13, pp. 357367 (1992)
19.Saad, Y., Numerical Methods for Large Eigenvalues Problems, Halsted Press, New York (1992)
20.Yang, R. J. and Luo, W. J., “Flow Bifurcations in a Thin Gap Between Two Rotating Spheres,” Theoretical and Computational Fluid Dynamics, 16, pp. 115131 (2002).
21.Luo, W. J., Yarn, K. F. and Hsu, S. P.Analysis of Electrokinetic Mixing Using AC Electric Field and Patchwise Surface Heterogeneities,” Japan Journal of Applied Physics, 46, pp. 16081616 (2007).

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