Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-29T21:31:44.562Z Has data issue: false hasContentIssue false
  • English
  • Français

Convection in a rotating, horizontal cylinder with radial and normal gravity forces

Published online by Cambridge University Press:  26 April 2006

Foluso Ladeinde  and
K. E. Torrance
Foluso Ladeinde
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA Present address: Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794, USA.
K. E. Torrance
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Convection driven by radial and normal gravity forces in a rotating, horizontal cylinder is examined. The cylinder is subjected to uniform volumetric heating and constant-temperature wall cooling. The parameters are the radial-gravity and normal-gravity Rayleigh numbers, Rar and Rag (with Rar, Rag ≤ 106), the rotational Reynolds number, Re = 2Ω r02/v (0 ≤ Re ≤ 250), and the Prandtl number (Pr = 7). Critical conditions for the radial-gravity rest state correspond to a two-cell flow in the azimuthal plane with Rar,c = 13738. Finite-amplitude transient and steady flows are obtained with a Galerkin finite element method for Rayleigh number ratios in the range 0.1 ≤ Rar/Rag ≤ 100. When radial gravity dominates the flows tend to be multicellular and, during transients, initial high-wavenumber forms evolve to lower-wavenumber forms. When normal gravity dominates the flows are bicellular. When radial and normal gravity forces are comparable, in the presence of rotation, complex time-dependent motions occur and the largest rates of fluid circulation and heat transfer are observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 361 - 385
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Busse, F. H. 1986 Asymptotic theory of convection in a rotating, cylindrical annulus. J. Fluid Mech. 173, 545–556.Google Scholar
Chen, M. M. & Whitehead, J. A. 1968 Evolution of two-dimensional periodic Rayleigh convection cells of arbitrary wave-numbers. J. Fluid Mech. 31, 1–15.Google Scholar
Daniels, P. G. 1984 Roll-pattern evolution in finite-amplitude Rayleigh–Bénard convection in a two-dimensional fluid layer bounded by distant sidewalls. J. Fluid Mech. 143, 125–152.Google Scholar
Fusegi, T., Farouk, B. & Ball, K. S. 1986 Mixed-convection flows within a horizontal concentric annulus with a heated rotating inner cylinder. Numer. Heat Transfer 9, 591–604.Google Scholar
Gollub, J. P., McCarriar, A. R. & Steinman, J. F. 1982 Convective pattern evolution and secondary instabilities. J. Fluid Mech. 125, 259–281.Google Scholar
Greenspan, H. P. 1969 The Theory of Rotating Fluids. Cambridge University Press.
Gresho, P. M., Lee, R. L. & Sani, R. L. 1980 On the time-dependent solution of the incompressible Navier—Stokes equation in two and three dimensions. Recent Advances in Numerical Methods in Fluids (ed. C. Taylor & K. Morgan), vol. 1. Swansea, UK: Pineridge Press Ltd.
Hide, R. 1967 Theory of axisymmetric thermal convection in a rotating fluid annulus. Phys. Fluids 10, 56–68.Google Scholar
Hide, R. & Mason, P. J. 1970 Baroclinic waves in a rotating fluid subject to internal heating. Phil. Trans. R. Soc. Lond. A 268, 201–232.Google Scholar
Hide, R. & Mason, P. J. 1974 Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100.Google Scholar
Hsui, A. T., Turcotte, D. L. & Torrance, K. E. 1972 Finite amplitude thermal convection within a self-gravitating fluid sphere. Geophys. Fluid Dyn. 3, 35–44.Google Scholar
Hutchins, J. & Marschall, E. 1989 Pseudosteady-state natural convection heat transfer inside spheres. Intl J. Heat Mass Transfer 32, 2047–2053.Google Scholar
Joseph, D. D. 1966 Nonlinear stability of the Boussinesq equations by the energy method. Arch. Rat. Mech. Anal. 22, 163–184.Google Scholar
Joseph, D. D. & Carmi, S. 1969 Stability of Poiseuille flow in pipes, annuli and channels. Q. Appl. Maths 26, 575–599.Google Scholar
Ladeinde, F. 1986 Design of a dual rotating system for thermal processing of canned fluid foods. M. Engng Rep. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA.
Ladeinde, F. 1988 Studies on thermal convection in self-gravitating and rotating horizontal cylinders in a vertical external gravity field. PhD thesis, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 346 pp.
Ladeinde, F. & Torrance, K. E. 1990 Galerkin finite element simulation of convection driven by rotation and gravitation. Intl J. Numer. Meth. Fluids 10, 47–77.Google Scholar
Lee, T. S. 1984 Numerical experiments with laminar fluid convection between concentric and essentric heated rotating cylinders. Numer. Heat Transfer 7, 77–87.Google Scholar
Lin, Y. S. & Akins, R. G. 1986 Pseudo-steady-state natural convection heat transfer inside a vertical cylinder. Trans. ASME C: J. Heat Transfer 108, 310–316.Google Scholar
Lopez, A. 1981 A Complete Course in Canning. Book 1. Basic Information on Canning. The Canning Trade, Baltimore, Maryland, USA.
Mori, Y. & Nakayama, W. 1967 Forced convective heat transfer in a straight pipe rotating about a parallel axis (laminar region). Intl J. Heat Mass Transfer 10, 1179–1194.Google Scholar
Ostrach, S. 1972 Natural convection in enclosures. Adv. Heat Transfer 8, 161–227.Google Scholar
Randriamampianina, A., Bontoux, P. & Roux, B. 1987 Ecoulements induits par la force gravifique dans une cavité cylindrique en rotation. Intl J. Heat Mass Transfer 30, 1275–1292.Google Scholar
Sabzevari, A. & Ostrach, S. 1974 Experimental studies of natural convection in a horizontal cylinder In Fifth Intl Heat Transfer Conf. Tokyo, Japan, vol. 8, pp. 100–104.
Takeuchi, M. & Cheng, K. C. 1976 Transient natural convection in horizontal cylinders with constant cooling rate. Warme-und-Stoffübertragung 9, 215–225.Google Scholar
Vahl Davis, G. De 1983 Natural convection of air in a square cavity: a benchmark numerical solution. Intl J. Numer. Meth. Fluids 3, 249–264.Google Scholar
Van Sant, J. H. 1969 Free convection of heat-generating liquids in a horizontal pipe. Nucl. Engng Design 10, 349–355.Google Scholar
Weir, A. D. 1976 Axisymmetric convection in a rotating sphere. Part I. Stress free surface. J. Fluid Mech. 75, 49–79.Google Scholar
Woods, J. L. & Morris, W. D. 1980 A study of heat transfer in a rotating cylindrical tube. Trans. ASME C: J. Heat Transfer 102, 612–616.Google Scholar
Yang, H. Q., Yang, K. T. & Lloyd, J. R. 1988 Rotational effects on natural convection in a horizontal cylinder AIChE J. 34, 1627–1633.Google Scholar