Oscillatory flow states in an enclosed cylinder with a rotating endwall

A combined experimental and numerical investigation is presented of the multiple oscillatory states that exist in the flows produced in a completely filled, enclosed, circular cylinder driven by the constant rotation of one of its endwalls. The flow in a cylinder of height to radius ratio 2.5 is interrogated experimentally using flow visualization and digitized images to extract quantitative temporal information. Numerical solutions of the axisymmetric Navier–Stokes equations are used to study the same flow over a range of Reynolds numbers where the flow is observed to remain axisymmetric. Three oscillatory states have been identified, two of them are periodic and the third is quasi-periodic with a modulation frequency much smaller than the base frequency. The range of Reynolds numbers for which the quasi-periodic flow exists brackets the switch between the two periodic states. The results from the combined experimental and numerical study agree both qualitatively and quantitatively, providing unambiguous evidence of the existence and robustness of these multiple time-dependent states.

[1]  J. Lopez.  Unsteady swirling flow in an enclosed cylinder with reflectional symmetry , 1995 .

[2]  J. Lopez,et al.  Axisymmetric vortex breakdown. Part 3 Onset of periodic flow and chaotic advection , 1992, Journal of Fluid Mechanics.

[3]  J. N. Sørensen,et al.  Direct Simulation of Flow Structures Initiated by a Rotating Cover in a Cylindrical Vessel , 1989 .

[4]  P. Buchhave,et al.  PIV Measurements of Turbulent and Chaotic Structures in a Rotating Flow Using an Optical Correlator , 1992 .

[5]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[6]  T. Mullin,et al.  An experimental observation of chaos arising from the interaction of steady and time-dependent flows , 1989, Nature.

[7]  S. Rosenblat,et al.  On Bifurcating Periodic Solutions at Low Frequency , 1977 .

[8]  Philip Holmes,et al.  The limited effectiveness of normal forms: a critical review and extension of local bifurcation studies of the Brusselator PDE , 1997 .

[9]  M. Thompson,et al.  Spiral streaklines in pre-vortex breakdown regions of axisymmetric swirling flows , 1995 .

[10]  N. Tsitverblit.  Vortex breakdown in a cylindrical container in the light of continuation of a steady solution , 1993 .

[11]  M. P. Escudier,et al.  Observations of the flow produced in a cylindrical container by a rotating endwall , 1984 .

[12]  Jens Nørkær Sørensen,et al.  Direct numerical simulation of rotating fluid flow in a closed cylinder , 1995 .

[13]  S. Wiggins,et al.  An analytical study of transport, mixing and chaos in an unsteady vortical flow , 1990, Journal of Fluid Mechanics.

[14]  Juan Lopez,et al.  Axisymmetric vortex breakdown Part 1. Confined swirling flow , 1990, Journal of Fluid Mechanics.

[15]  T. Mullin,et al.  An experimental study of oscillatory convection in liquid gallium , 1996, Journal of Fluid Mechanics.

[16]  G. Neitzel.  Streak-line motion during steady and unsteady axisymmetric vortex breakdown , 1988 .

[17]  H. Swinney,et al.  Onset of Turbulence in a Rotating Fluid , 1975 .

[18]  J. N. Sørensen,et al.  Low-dimensional representations of early transition in rotating fluid flow , 1993 .

[19]  Pinhas Z. Bar-Yoseph,et al.  Stability of confined swirling flow with and without vortex breakdown , 1996, Journal of Fluid Mechanics.

[20]  H. Lugt,et al.  Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid , 1987, Journal of Fluid Mechanics.

[21]  B. Cantwell,et al.  Experimental study of vortex breakdown in a cylindrical, swirling flow , 1996 .

[22]  Jie Shen,et al.  An Efficient Spectral-Projection Method for the Navier–Stokes Equations in Cylindrical Geometries: I. Axisymmetric Cases , 1998 .

[23]  T. Mullin,et al.  Low-dimensional bifurcation phenomena in Taylor–Couette flow with discrete azimuthal symmetry , 1994, Journal of Fluid Mechanics.