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.

1.
Au-Yang
M. K.
,
1976
, “
Free Vibration of Fluid-Coupled Coaxial Cylindrical Shells of Different Lengths
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
43
, pp.
480
484
.
2.
Au-Yang
M. K.
, and
Galford
J. E.
,
1981
, “
A Structural Priority Approach to Fluid-Structure Interaction Problems
,”
ASME Journal of Pressure Vessel Technology
, Vol.
103
, pp.
142
150
.
3.
Brenneman
B.
, and
Au-Yang
M. K.
,
1992
, “
Fluid-Structure Dynamics with a Modal Hybrid Method
,”
ASME Journal Pressure Vessel Technology
, Vol.
114
, pp.
133
138
.
4.
Chen
S. S.
,
Wambsganss
M. W.
, and
Jendrzejczyk
J. A.
,
1976
, “
Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluid
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
43
, pp.
325
329
.
5.
Chen
S. S.
,
1981
, “
Fluid Damping for Circular Cylindrical Structures
,”
Nuclear Engineering and Design
, Vol.
63
, pp.
81
100
.
6.
Hobson, D. E., 1982, “Fluid-Elastic Instabilities Caused by Flow in an Annulus,” Proceedings of the BNES Third International Conference on Vibration in Nuclear Plant, Keswick, U.K., pp. 440–463.
7.
Mateescu
D.
, and
Pai¨doussis
M. P.
,
1985
, “
The Unsteady Potential Flow in an Axially Variable Annulus and its Effects on the Dynamics of the Oscillating Rigid Centrebody
,”
ASME Journal of Fluids Engineering
, Vol.
107
, pp.
421
427
.
8.
Mateescu
D.
, and
Pai¨doussis
M. P.
,
1987
, “
Unsteady Viscous Effects on the Annular-Flow-Induced Instabilities of a Rigid Cylindrical Body in a Narrow Duct
,”
Journal of Fluids and Structures
, Vol.
1
, pp.
197
215
.
9.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Be´langer
F.
,
1988
, “
Unsteady Pressure Measurements on an Oscillating Cylinder in Narrow Annular Flow
,”
Journal of Fluids and Structures
, Vol.
2
, pp.
615
628
.
10.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Belanger
F.
,
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
, pp.
487
498
.
11.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Sim
W.-G.
,
1990
, “
CFD Solutions for Steady Viscous and Unsteady Potential Flows Between Eccentric Cylinders
,”
Proceedings of the ASME International Symposium on Nonsteady Fluid Dynamics, Toronto
, FED-Vol.
92
, pp.
235
242
.
12.
Mateescu, D., Pai¨doussis, M. P., and Be´langer, F, 1991, “Computational Solutions Based on a Finite Difference Formulation for Unsteady Internal Flows,” 29th Aerospace Sciences Meeting, Reno, Nevada, AIAA Paper 91–0724.
13.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Sim
W.-G.
,
1994
a, “
A Spectral Collocation Method for Confined Unsteady Flows with Oscillating Boundaries
,”
Journal of Fluids and Structures
, Vol.
8
, pp.
157
181
.
14.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Be´langer
F.
,
1994
b, “
A Time-Integration Method Using Artificial Compressibility for Unsteady Viscous Flows
,”
Journal of Sound and Vibration
, Vol.
117
, pp.
197
203
.
15.
Mateescu
D.
,
Pai¨doussis
M. P.
, and
Sim
W.-G.
,
1994
c, “
Spectral Solutions for Unsteady Annular Flows Between Eccentric Cylinders Induced by Transverse Oscillations
,”
Journal of Sound and Vibration
, Vol.
117
, pp.
635
649
.
16.
Mulcahy
T. M.
,
1980
, “
Fluid Forces on Rods Vibrating in Finite Length Annular Regions
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
47
, pp.
234
240
.
17.
Pai¨doussis
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
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
57
, pp.
232
240
.
18.
Spalding
D. B.
,
1972
, “
A Novel Finite Difference Formulation for Differential Expressions Involving both First and Second Derivatives
,”
International Journal for Numerical Methods in Engineering
, Vol.
4
, pp.
551
559
.
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