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Transitional flow between contra-rotating disks

Published online by Cambridge University Press:  26 April 2006

M. Kilic ,
X. Gan  and
J. M. Owen
M. Kilic
Affiliation:
School of Mechanical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK Present address: Uludag Universitesi, Mühendislik-Mimarlik Fakultesi, Makina Bolumu, Bursa, Turkey.
X. Gan
Affiliation:
School of Mechanical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK
J. M. Owen
Affiliation:
School of Mechanical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK
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Abstract

This paper describes a combined computational and experimental study of the flow between contra-rotating disks for – 1 ≤ Γ ≤ 0 and Reϕ = 105, where Γ is the ratio of the speed of the slower disk to that of the faster one and Reϕ is the rotational Reynolds number of the faster disk. For Γ = 0, the rotor-stator case, laminar and turbulent computations and experimental measurements show that laminar Batchelor-type flow occurs: there is radial outflow in a boundary layer on the rotating disk, inflow on the stationary disk and a rotating core of fluid between. For Γ = – 1, the laminar computations produce Batchelor-type flow: there is radial outflow on both disks and inflow in a free shear layer in the mid-plane, on either side of which is a rotating core of fluid. The turbulent computations and the velocity measurements for Γ = – 1 show Stewartson-type flow: radial outflow occurs in laminar boundary layers on the disks and inflow occurs in a non-rotating turbulent core between the boundary layers. For intermediate values of Γ, transition from Batchelor-type flow to Stewartson-type flow is associated with a two-cell structure, the two-cells being separated by a streamline that stagnates on the slower disk; Batchelor-type flow occurs radially outward of the stagnation point and Stewartson-type flow radially inward. The turbulent computations are mainly in good agreement with the measured velocities for Γ = 0 and Γ = – 1, where either Batchelor-type flow or Stewartson-type flow occurs; there is less good agreement at intermediate values of Γ, particularly for Γ = – 0.4 where the double transition of Batchelor-type flow to Stewartson-type flow and laminar to turbulent flow occurs in the two-cell structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 281 , 25 December 1994 , pp. 119 - 135
Copyright
© 1994 Cambridge University Press

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References

Batchelor, G. K. 1951 Note on a class of solutions of the Navier–Stokes equations representing steady rotationally-symmetric flow. Q. J. Mech. Appl. Maths 4, 333–354.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Dijkstra, D. & Heijst, G. J. F. Van 1983 The flow between two finite rotating disks enclosed by a cylinder. J. Fluid Mech. 128, 123–154.Google Scholar
Doormaal, J. P. Van & Raithby, G. D. 1984 Enhancement of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer 7, 147–163.Google Scholar
Gan, X., Kilic, M. & Owen, J. M. 1993 Flow between contra-rotating discs. ASME Intl Gas Turbine and Aeroengine Congress, Cincinnati, Paper 93-GT-286. (To appear in J. Turbomachinery.)
Iacovides, H. & Toumpanakis, P. 1993 Turbulence modelling of flow in axisymmetric rotor-stator systems. Proc. 5th Intl Symp. on Refined Flow Modelling and Turbulence Measurements, Paris, September, 1993
Itoh, M., Yamada, Y. & Nishioka, K. 1985 Transition of the flow due to an enclosed rotating disk. Trans. Japan Soc. Mech. Engrs 51, 452–460 (in Japanese).Google Scholar
Karman, Th. Von 1921 Über laminare und turbulente reibung. Z. Angew. Math. Mech. 1, 233–252.Google Scholar
Kilic, M. 1993 Flow between contra-rotating discs. PhD thesis, University of Bath, UK.
Launder, B. E. & Sharma, B. I. 1974 Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1, 131–138.Google Scholar
Lonsdale, G. 1988 Solution of a rotating Navier–Stokes problem by a nonlinear multigrid algorithm, J. Comput. Phys. 74, 177–190.Google Scholar
Morse, A. P. 1988 Numerical prediction of turbulent flow in rotating cavities. J. Turbomachinery 110, 202–215.Google Scholar
Morse, A. P. 1991a Assessment of laminar-turbulent transition in closed disc geometries. J. Turbomachinery 113, 131–138.Google Scholar
Morse, A. P. 1991b Application of a low Reynolds number k-e turbulence model to high speed rotating cavity flows. J. Turbomachinery 113, 98–105.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Schlichting, H. 1979 Boundary-Layer Theory. McGraw Hill.
Stewartson, K. 1953 On the flow between two rotating coaxial disks. Proc. Camb. Phil. Soc. 49, 333–341.Google Scholar
Vaughan, C. M., Gilham, S. & Chew, J. W. 1989 Numerical solutions of rotating disc flows using a non-linear multigrid algorithm. Proc. 6th Intl Conf. Numer. Meth. Laminar Turbulent Flow, Swansea, pp. 66–73. Pineridge.
Zandbergen, P. J. & Dijkstra, D. 1987 Von Karman swirling flows. Ann. Rev. Fluid Mech. 19, 465–491.Google Scholar