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Research Papers

On the Self-Recovery Phenomenon for a Cylindrical Rigid Body Rotating in an Incompressible Viscous Fluid

[+] Author and Article Information
Dong Eui Chang

Department of Applied Mathematics,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: dechang@uwaterloo.ca

Soo Jeon

Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: soojeon@uwaterloo.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 25, 2014; final manuscript received June 1, 2014; published online September 10, 2014. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 137(2), 021005 (Sep 10, 2014) (5 pages) Paper No: DS-14-1092; doi: 10.1115/1.4027823 History: Received February 25, 2014; Revised June 01, 2014

The damping-induced self-recovery phenomenon is well understood for finite-dimensional mechanical systems. In this paper, we discover a self-recovery phenomenon in a composite system that consists of a cylindrical vessel and a surrounding fluid, where the vessel is equipped with an internal rotor and the fluid is incompressible and viscous. In the system dynamics, interactions between the vessel and the ambient fluid are fully taken into account. A combination of the Lyapunov method and the final-value theorem is applied for analysis of the dynamics. It is mathematically shown that after the spin of the rotor comes to a complete stop in finite time or exponentially as time tends to infinity, the vessel, which has deviated from its initial position due to the reaction to rotor spinning, converges back to its initial position as time tends to infinity, and so does every fluid particle. An experimental test is conducted to verify the occurrence of this phenomenon. The simultaneous self-recovery of the vessel and the fluid to the initial configuration is induced by the fluid viscosity as if the viscosity has a memory of the initial configuration. We envision that our discovery may be useful in designing and operating mechatronic systems interacting with fluids such as underwater vehicles.

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Figures

Grahic Jump Location
Fig. 1

A cylindrical vessel with an internal rotor immersed in a cylindrical region filled with an incompressible viscous fluid

Grahic Jump Location
Fig. 2

Experimental setup. (a) Cross-sectional view and (b) top view.

Grahic Jump Location
Fig. 3

Time trajectory of the inner cylinder assembly

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