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Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

Published online by Cambridge University Press:  26 April 2006

Jae Min Hyun  and
Jun Sang Park
Jae Min Hyun
Affiliation:
Department of Mechanical Engineering, Korea Advanced Institute of Science & Technology, P.O. Box 150, Chong Ryang, Seoul, Korea
Jun Sang Park
Affiliation:
CAD/CAM, R & D Center, Sam Sung Electro-Mechanics, Suweon, Korea
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Abstract

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 413 - 434
Copyright
© 1992 Cambridge University Press

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References

Bark, F. H., Meijer, P. S. & Cohen, H. I. 1978 Spin-up of a rapidly rotating gas. Phys. Fluids 21, 531–539.Google Scholar
Choi, S., Kim, J. W. & Hyun, J. M. 1989 Transient free surface shape in an abruptly rotating, partially-filled cylinder. Trans. ASME I: J. Fluids Engng 111, 439–442Google Scholar
Greenspan, H. P. 1980 A note on the spin-up from rest of a stratified fluid. Geophys. Astrophys. Fluid Dyn. 15, 1–5.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Hanin, M. 1960 On Rayleigh's problem for a compressible fluid. Q. J. Mech. Appl. Maths 13, 184–198.Google Scholar
Harada, I. 1980a A numerical study of weakly compressible rotating flows in a gas centrifuge. Nucl. Sci. Engng 73, 73–225.Google Scholar
Harada, I. 1980b Computation of strongly compressible rotating flows. J. Comput. Phys. 38, 38–335.Google Scholar
Harlow, F. H. & Meixner, B. D. 1961 Motion of a viscous compressible gas adjacent to a sliding plate. Phys. Fluids 4, 1202–1206.Google Scholar
Howarth, L. 1951 Some aspects of Rayleigh's problem for a compressible fluid. Q. J. Mech. Appl. Maths 4, 157–169.Google Scholar
Hyun, J. M. 1983 Axisymmetric flows in spin-up from rest of a stratified fluid in a cylinder. Geophys. Astrophys. Fluid Dyn. 23, 127–141.Google Scholar
Hyun, J. M., Leslie, F., Fowlis, W. W. & Warn-Varnas, A. 1983 Numerical solutions for spin-up from rest in a cylinder. J. Fluid Mech. 127, 263–281.Google Scholar
Hyun, J. M. & Park, J. S. 1989 Some aspects of compressible Rayleigh's problem in a rotating cylinder. J. Phys. Soc. Japan 58, 159–166.Google Scholar
Kitchen, C. W. 1980 Navier-Stokes solutions for spin-up in a filled cylinder. AIAA J. 18, 929–934.Google Scholar
Park, J. S. & Hyun, J. M. 1989 Transient adjustment of a gas contained in a rapidly-rotating infinite cylinder. J. Phys. Soc. Japan 58, 3949–3959.Google Scholar
Park, J. K. & Hyun, J. M. 1990 Numerical solution for thermally driven compressible flows in a rapidly-rotating cylinder. Fluid Dyn. Res. 6, 139–153.Google Scholar
Park, J. K. & Hyun, J. M. 1991 Effects of thermal boundary conditions on rapidly-rotating gas flow. Fluid Dyn. Res. 7, 119–129.Google Scholar
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine. J. Fluid Mech. 62, 727–736.Google Scholar
Stewartson, K. 1955 On the motion of a flat plate at high speed in a viscous compressible fluid. Proc. Camb. Phil. Soc. 51, 202–219.Google Scholar
Ungarish, M. & Israeli, M. 1985 Axisymmetric compressible flow in a rotating cylinder with axial convection. J. Fluid Mech. 154, 121–144.Google Scholar
Warn-Varnas, A., Fowlis, W. W., Piacsek, S. & Lee, S. M. 1978 Numerical solutions and laser-Doppler measurements of spin-up. J. Fluid Mech. 85, 609–639.Google Scholar
Watkins, W. B. & Hussey, R. G. 1973 Spin-up from rest: limitations of the Wedemeyer model. Phys. Fluids 16, 1530–1531.Google Scholar
Watkins, W. B. & Hussey, R. G. 1977 Spin-up from rest in a cylinder. Phys. Fluids 20, 1596–1604.Google Scholar
Wedemeyer, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar
Weidman, P. D. 1976 On the spin-up and spin-down of a rotating fluid. J. Fluid Mech. 77, 685–708.Google Scholar