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Axisymmetric compressible flow in a rotating cylinder with axial convection

Published online by Cambridge University Press:  20 April 2006

Marius Ungarish
Affiliation:
Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel
Moshe Israeli
Affiliation:
Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel

Abstract

The steady compressible flow of an ideal gas in a rotating annulus with thermally conducting walls is considered for small Rossby number ε and Ekman number E and moderate rotational Mach numbers M. Attention is focused on nonlinear effects which show up when σ and εM2 are not small (σ = ε/HE½, H is the dimensionless height of the container). These effects are not properly predicted by the classical linear perturbation analysis, and are treated here by quasi-linear extensions.

The extra work required by these extensions is only the numerical solution of one ordinary differential equation for the pressure.

Numerical solutions of the full Navier–Stokes equations in the nonlinear range are presented, and the validity of the present approach is confirmed.

Type
Research Article
Copyright
© 1985 Cambridge University Press

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References

Barcilon, V. 1970 Some inertial modifications of the linear viscous theory of steady rotating fluid flows. Phys. Fluids 13, 537544.Google Scholar
Barcilon, V. & Pedlosky, J. 1967 Linear theory of rotating stratified fluid motions. J. Fluid Mech. 23, 116.Google Scholar
Bark, F. H. & Bark, T. H. 1976 On vertical boundary layers in a rapidly rotating gas. J. Fluid Mech. 78, 749761.Google Scholar
Bark, F. H., Meijer, P. S. & Cohen, H. I. 1978 Spin up of a rapidly rotating gas. Phys. Fluids 21, 531539.Google Scholar
Bennetts, D. A. & Hocking, L. M. 1973 On nonlinear Ekman and Stewartson layers in a rotating fluid. Proc. R. Soc. Lond. A 333, 469489.Google Scholar
Conlisk, A. T., Foster, M. R. & Walker, J. D. A. 1982 Fluid dynamics and mass transfer in a gas centrifuge. J. Fluid Mech. 125, 283317.Google Scholar
Duncan, I. B. 1966 Axisymmetric convection between two rotating disks. J. Fluid Mech. 24, 417449.Google Scholar
Greenspan, H. P. 1969 The Theory of Rotating Fluids. Cambridge University Press.
Homsy, G. M. & Hudson, J. L. 1969 Centrifugally driven thermal convection in a rotating cylinder. J. Fluid Mech. 35, 3352.Google Scholar
Hudson, J. L. 1968a Non isothermal flow between rotating disks. Chem. Engng Sci. 23, 1007.Google Scholar
Hudson, J. L. 1968b Convection near a cooled disk rotating with its environment. Intl J. Heat Mass Transfer 11, 407.Google Scholar
Hultgren, L. S. 1978 Stability of axisymmetric gas flows in a rapidly rotating cylindrical container. Ph.D. thesis, MIT.
Hunter, C. 1967 The axisymmetric flow in a rotating annulus due to a horizontal applied temperature gradient. J. Fluid Mech. 27, 753778.Google Scholar
Israeli, M. & Ungarish, M. 1981 Improvement of numerical schemes by incorporation of approximate solutions applied to rotating compressible flows. In Proc. 7th Intl Conf. on Numerical Methods in Fluid Dynamics (ed. W. C. Reynolds & R. W. MacCormack). Lecture Notes in Physics, vol. 141, pp. 230235. Springer.
Israeli, M. & Ungarish, M. 1983 Laminar compressible flow between close rotating disks — an asymptotic and numerical study. Comp. Fluids 11, 145157.Google Scholar
Matsuda, T. & Hashimoto, K. 1978 The structure of the Stewartson layers in a gas centrifuge. Part 1. Insulated endplates. J. Fluid Mech. 85, 433442.Google Scholar
Matsuda, T., Sakurai, T. & Takeda, H. 1975 Source—sink flow in a gas centrifuge. J. Fluid Mech. 69, 197208.Google Scholar
Matsuda, T. & Takeda, H. 1978 The structure of the Stewartson layers in a gas centrifuge. Part 2. Insulated side wall. J. Fluid Mech. 85, 443457.Google Scholar
Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. R. Soc. Lond. A 264, 597634.Google Scholar
Riley, N. 1967 Thermally induced boundary-layer flows in a rotating environment. J. Fluid Mech. 29, 241257.Google Scholar
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine. J. Fluid Mech. 62, 727736.Google Scholar
Toren, M. 1976 Compressible isothermal flow over a stationary disk confined in a rotating cylindrical container. Ph.D. Thesis, Technion, Haifa, Israel.
Toren, M. & Solan, A. 1979 Laminar compressible flow over a stationary disk in a rotating cylinder. Trans. ASME I: J. Fluids Engng 101, 173180Google Scholar