By coupling the Donnell–Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up.
Issue Section:
Research Papers
1.
Païdoussis
, M. P.
, 2004, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol. 2
, Elsevier
, London
.2.
Srinivasan
, A. V.
, 1971, “Flutter Analysis of Rotating Cylindrical Shells Immersed in a Circular Helical Flowfield of Air
,” AIAA J.
, 9
, pp. 394
–400
. 0001-14523.
Dowell
, E.
, Srinivasan
, A.
, McLean
, J.
, and Ambrose
, J.
, 1974, “Aeroelastic Stability of Cylindrical Shells Subjected to a Rotating Flow
,” AIAA J.
, 12
, pp. 1644
–1651
. 0001-14524.
Rayleigh
, Lord J. W.
, 1917, “Dynamics of Revolving Fluids
,” Proc. R. Soc. London, Ser. A
0950-1207, 93
, pp. 148
–154
.5.
Howard
, L. N.
, and Gupta
, A. S.
, 1962, “On the Hydrodynamic and Hydromagnetic Stability of Swirling Flows
,” J. Fluid Mech.
0022-1120, 14
, pp. 463
–476
.6.
Wang
, S.
, and Rusak
, Z.
, 1996, “On the Stability of an Axisymmetric Rotating Flow in a Pipe
,” Phys. Fluids
1070-6631, 8
, pp. 1007
–1016
.7.
Chow
, C. Y.
, 1969, “Swirling Flow in Tubes of Non-Uniform Cross-Sections
,” J. Fluid Mech.
, 38
, pp. 843
–854
. 0022-11208.
Yih
, C.-S.
, 1965, Dynamics of Nonhomogeneous Fluids
, Macmillan
, New York
.9.
Lai
, Y.-C.
, and Chow
, C.-Y.
, 1973, “Stability of a Rotating Thin Elastic Tube Containing a Fluid Flow
,” Z. Angew. Math. Mech.
, 53
, pp. 511
–517
. 0044-226710.
Chen
, T. L. C.
, and Bert
, C. W.
, 1977, “Dynamic Stability of Isotropic or Composite-Material Cylindrical Shells Containing Swirling Fluid Flow
,” ASME J. Appl. Mech.
, 44
, pp. 112
–116
. 0021-893611.
Cortelezzi
, L.
, Pong
, A.
, and Païdoussis
, M.
, 2004, “Flutter of Rotating Shells With a Co-Rotating Axial Flow
,” ASME J. Appl. Mech.
0021-8936, 71
, pp. 143
–145
.12.
Leissa
, A. W.
, 1973, “Vibration of Shells
,” NASA
Report No. SP-288.13.
Gosselin
, F.
, 2006, “Stability of a Rotating Cylindrical Shell Containing Axial Viscous Flow
,” M.Eng. thesis, McGill University, Montreal, Canada.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
