Abstract
This paper presents a newly developed spectral collocation method for the study of the unsteady annular flow between two eccentric cylinders. In order to predict the stability of a system in a confined flow, the formulae and results of added mass and fluid damping are provided in the present paper when a cylinder undergoes oscillatory motion in the plane of symmetry and normal to the plane of symmetry in an eccentric annulus. The potential flow theory has been developed to obtain the added mass for incompressible, inviscid and irrotational fluid. For the viscous fluid, the added mass and the viscous damping are presented. This method is validated by comparison with the available analytical solutions obtained for the unsteady potential flow in the eccentric annular space. Excellent agreement was found between the solutions obtained with the present spectral method and the available analytical solutions. In the present study, the viscous effect on the added mass can be evaluated, comparing the results obtained by potential flow theory with those obtained by the viscous flow theory, and viscous damping is investigated.
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References
Au-Yang, M. K., 1976, “Free Vibration of Fluid-Coupled Coaxial Cylindrical Shells of Different Lengths,” Journal of Applied Mechanics, Vol. 43, pp. 480–484.
Chen, S. S., Wambsganss, M. W. and Jendrzejczyk, J. A., 1976, “Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluid,” Journal of Applied Mechanics, Vol. 43, pp. 325–329.
Chung, H. and Chen, S. S., 1977, “Vibration of a Group of a Circular Cylinders in a Confined Filuid,” Journal of Applied Mechanics, Vol. 44, pp. 213–217.
Fritz, R. J., 1972, “The Effect of Liquids on the Dynamic Motions of Immersed Solids,” ASME Journal of Engineering for Industry, Vol. 94, pp. 167–173.
Hobson, D. E. and Jedwab, M., 1990, “Investigations of the Effect of Eccentricity on the Unsteady Fluid Forces on the Centrebody of an Annular Diffuser,” Journal of Fluids and Structures, Vol. 4, pp. 155–169.
Mateescu, D., Païdoussis, M. P. and Bélanger, E., 1989, “A Theoretical Model Compared with Experiments for the Unsteady Pressure on a Cylinder Oscillating in a Turbulent Annular Flow,” Journal of Sound and Vibration, Vol. 135(3), pp. 487–498.
Mateescu, D., Païdossis, M. P. and Bélanger, F., 1991, “Computational Solutions Based on a Finite Difference Formulation for Unsteady Internal Flow,” AIAA 29th Aerospace Science Meeting. Reno. AIAA Paper No. 91-0724.
Muga, B. J. and Wilson, J. F., 1970. “Dynamic Analysis of Ocean Structures,” Plenum Press, New York-London.
Mulcahy, T. M., 1980, “Fluid Forces on Rods Vibrating in Finite Length Annular Regions,” Journal of Applied Mechanics, Vol. 47, pp. 234–240.
Païdoussis, M. P. and Ostoja-Starzewski, M., 1981, “Dynamics of a Flexible Cylinder in Subsonic Axial Flow,” AIAA Journal, Vol. 19(11), pp. 1467–1475.
Païdoussis, M. P., Mateescu, D. and Sim, W.-G., 1990, “Dynamics and Stability of a Flexible Cylinder in a Narrow Coaxial Cylindrical Duct Subjected to Annular Flow,” Journal of Applied Mechanics, Vol. 57, pp. 232–240.
Stokes, G. G. 1843, “On Some Cases of Fluid Motion,” Proceedings of the Cambridge Philosophical Society, Vol. 8, pp. 105–137.
Yeh, T. T. and Chen, S. S. 1977, “Dynamics of a Cylindrical Shell System Coupled by Viscous Fluid,” Journal of the Acoustical Society of America, Vol. 62(2), pp. 262–270.
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Sim, W.G., Cho, Y.C. Unsteady potential and viscous flows between eccentric cylinders. KSME Journal 7, 55–69 (1993). https://doi.org/10.1007/BF02953145
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DOI: https://doi.org/10.1007/BF02953145