Vertical Taylor–Couette flow with free surface at small aspect ratio

Acta Mechanica - Tập 223 - Trang 347-353 - 2011
T. Watanabe1, Y. Toya2
1Graduate School of Information Science, Nagoya University, Nagoya, Japan
2Department of Mechanical Engineering, Nagano National College of Technology, Nagano, Japan

Tóm tắt

The free surface flow between two concentric cylinders with vertical axes is investigated using numerical and experimental approaches. The bottom end wall of the cylinders and the outer cylinder are stationary and fixed, and the inner cylinder is allowed to rotate. In such a case, an odd number of Taylor vortices is usually formed (normal mode). However, we found that anomalous modes with outer flow near the bottom end wall or inner flow at the free surface appear in some conditions. Further, we determined bifurcation diagrams between the normal three-cell mode and normal one-cell mode and between the normal five-cell mode and the normal three-cell mode.

Tài liệu tham khảo

Taylor G.I.: Stability of a viscous liquid contained between two rotating cylinders. Philos. Trans. Roy. Soc. Lond. Ser A 223, 289 (1923)

Benjamin T.B.: Application of Leray-Schauder degree theory to problems of hydrodynamics stability. Math Proc. Camb. Phil. Soc. 79, 373 (1976)

Benjamin T.B.: Bifurcation phenomena in steady flows of a viscous fluid, I theory, II, experiments. Proc. Royal Soc. Lond. A 359, 1 (1978)

Tagg R.: The Couette-Taylor problem. Nonlinear Science Today 4–3, 2–25 (1994)

Koschmieder E.L.: Bénard Cells and Taylor Vortices. Cambridge University Press, Victoria (1993)

Toya Y., Yamashita S., Ueki Y.: An experiment on a Taylor vortex in a gap with a small aspect ratio—Bifurcation of flows in an asymmetric system. Acta Mech. 102, 137 (1994)

Linek M., Ahlers G.: Boundary limitation of wave numbers in Taylor-vortex flow. Phys. Rev. E 58, 3168 (1998)

Ammar M., Bouabdallah A., Skali S.E.: Effect of free surface and aspect ratio on the transition of the Taylor-Couette flow. Comptes Refunds Mecanique 331, 245 (2003)

Ammar M., Bouabddallah A., Skali S.E.: Ècoulemnent de Taylor-Couette en Géométrie fine et à surface libre. Can. J. Chem. Eng. 83, 652 (2005)

Batchelor G.K.: An Introduction of Fluid Dynamics, Chap. 1. Cambridge University Press, London (1967)

Abshagen J., Lopez J.M., Marques F., Pfister G.: Mode competition of rotating waves in reflection-symmetric Taylor-Couette flow. J. Fluid Mech. 540, 269 (2005)

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Thông tin xuất bản

Acta Mechanica

Tập 223

347-353

Thông tin tác giả