Abstract
In a linear setting we examine the stability of the flow of a viscous incompressible liquid between eccentric cylinders, the inner cylinder rotating and the outer cylinder fixed. We consider the case of a narrow gap between the cylinders, which is characteristic for problems in lubrication theory. The main flow, perturbations, and the critical Reynolds number are found in the form of expansions in powers of the eccentricity ɛ to within O (ɛ3). The results obtained agree with the known experimental data for 0 ≤ ɛ ≤ 0.5 and confirm the stabilizing influence of the eccentricity.
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M. M. Kamal, “Separation in the flow between eccentric rotating cylinders,” Trans. ASME, Ser. D. J. Basic Engng.,88, No. 4 (1966).
J. H. Vohr, “An experimental study of Taylor vortices and turbulence in flow between eccentric rotating cylinders,” Trans. ASME, Ser. F. J. Lubr. Technol.,90, No. 4 (1968).
J. A. Cole, “Taylor vortices with eccentric rotating cylinders,” Nature,221, No. 5177 (1969).
P. L. Versteegen and D. F. Jankowski, “Experiments on the stability of viscous flow between eccentric rotating cylinders,” Phys. Fluids,12, No. 6 (1969).
P. Castle, F. R. Mobbs, and P. H. Markho, “Visual observations and torque measurements in the Taylor vortex regime between eccentric rotating cylinders,” Trans. ASME, Ser. F. J. Lubr. Technol.,93, No. 1 (1971).
R. C. Di Prima, “A note on the stability of flow in loaded journal bearings,” ASLE Trans.,6, No. 3 (1963).
G. S. Ritchie, “On the stability of viscous flow between eccentric rotating cylinders,” J. Fluid Mech.,32, Pt. 1 (1968).
R. L. Urban and E. R. Krueger, “On the stability of viscous flow between two rotating nonconcentric cylinders,” J. Franklin Inst.,293, No. 3 (1972).
L. G. Stepanyants, “An account of the inertia terms in hydrodynamic lubrication theory,” Trudy Leningr. Politekhn. Inst., Tekhn. Gidromekhan., No. 198 (1958).
E. S. Kulinski and S. Ostrach, “Journal-bearing velocity profiles for small eccentricity and moderate modified Reynolds numbers,” Trans. ASME, Ser. E. J. Appl. Mech.,89, No. 1 (1967).
R. L. Urban, “Viscous flow between two rotating nonconcentric cylinders for small eccentricity,” Appl. Sci. Res.,24, No. 2, 3 (1971).
R. C. Di Prima and J. T. Stuart, “Flow between eccentric rotating cylinders,” Trans. ASME, J. Lubr. Technol., Ser. F, Paper No. 72 (1972).
G. I. Bodyakov and L. A. Oganesyan, “Method of a small parameter for determining the motion of a viscous incompressible liquid in a support bearing,” Prikl. Matem. i Mekhan.,30, No. 4 (1966).
M. P. Kravchuk, Application of the Method of Moments for Solving Linear Differential and Integral Equations [in Russian], Vols. 1 and 2, Vid-vo. Vseukr. Akad. Nauk, Kiev (1932–1935).
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961).
R. C. Di Prima and J. T. Stuart, “Stability and growth of Taylor vortices in the flow between eccentric rotating cylinders,” in: Proc. of the 13th Intern. Congress on Theoretical and Applied Mechanics [in Russian], Nauka, Moscow (1972).
R. C. Di Prima and J. T. Stuart, “Nonlocal effects in the stability of flow between eccentric rotating cylinders,” J. Fluid Mech.,54, Pt. 3 (1972).
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 101–106, May–June, 1973.
The author wish to thank N. P. Artemenko, A. D. Myshkis, and R. Di Prima for a useful discussion of the problem.
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Babskii, V.G., Sklovskaya, I.L. & Sklovskii, Y.B. Emergence of taylor vortices between rotating eccentric cylinders. J Appl Mech Tech Phys 14, 378–382 (1973). https://doi.org/10.1007/BF00850953
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DOI: https://doi.org/10.1007/BF00850953