A hybrid spectral/finite difference method is developed in this paper for the analysis of three-dimensional unsteady viscous flows between concentric cylinders subjected to fully developed laminar flow and executing transverse oscillations. This method uses a partial spectral collocation approach, based on spectral expansions of the flow parameters in the transverse coordinates and time, in conjunction with a finite difference discretization of the axial derivatives. The finite difference discretization uses central differencing for the diffusion derivatives and a mixed central-upwind differencing for the convective derivatives, in terms of the local mesh Reynolds number. This mixed scheme can be used with coarser as well as finer axial mesh spacings, enhancing the computational efficiency. The hybrid spectral/finite difference method efficiently reduces the problem to a block-tridiagonal matrix inversion, avoiding the numerical difficulties otherwise encountered in a complete three-dimensional spectral-collocation approach. This method is used to compute the unsteady fluid-dynamic forces, the real and imaginary parts of which are related, respectively, to the added-mass and viscous-damping coefficients. A parametric investigation is conducted to determine the influence of the Reynolds and oscillatory Reynolds (or Stokes) numbers on the axial variation of the real and imaginary components of the unsteady forces. A semi-analytical method is also developed for the validation of the hybrid spectral method, in the absence of previous accurate solutions or experimental results for this problem. Good agreement is found between these very different methods, within the applicability domain of the semi-analytical method.
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September 1995
Technical Papers
Three-Dimensional Viscous Flows Between Concentric Cylinders Executing Axially Variable Oscillations: A Hybrid Spectral/Finite Difference Solution
D. Mateescu,
D. Mateescu
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
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M. P. Paidoussis,
M. P. Paidoussis
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
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W.-G. Sim
W.-G. Sim
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
Search for other works by this author on:
D. Mateescu
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
M. P. Paidoussis
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
W.-G. Sim
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 2K6, Canada
J. Appl. Mech. Sep 1995, 62(3): 667-673 (7 pages)
Published Online: September 1, 1995
Article history
Received:
October 25, 1993
Revised:
May 4, 1994
Online:
October 30, 2007
Citation
Mateescu, D., Paidoussis, M. P., and Sim, W. (September 1, 1995). "Three-Dimensional Viscous Flows Between Concentric Cylinders Executing Axially Variable Oscillations: A Hybrid Spectral/Finite Difference Solution." ASME. J. Appl. Mech. September 1995; 62(3): 667–673. https://doi.org/10.1115/1.2895998
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