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A numerical and experimental investigation of the stability of spiral Poiseuille flow

Published online by Cambridge University Press:  20 April 2006

Donald I. Takeuchi  and
Daniel F. Jankowski
Donald I. Takeuchi
Affiliation:
Department of Mechanical and Energy Systems Engineering, Arizona State University, Tempe, Arizona 85281 Present address: AiResearch Manufacturing Company, Phoenix, Arizona.
Daniel F. Jankowski
Affiliation:
Department of Mechanical and Energy Systems Engineering, Arizona State University, Tempe, Arizona 85281
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Abstract

The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide-gap geometry. A three-dimensional disturbance is considered. Linear stability limits in the form of Taylor numbers TaL are computed for the rotation ratios μ, = 0, 0·2, and -0·5 and for values of the axial Reynolds number Re up to 100. Depending on the values of μ and Re, the disturbance which corresponds to TaL can have a toroidal vortex structure or a spiral form. Aluminium-flake flow visualization is used to determine conditions for the onset of a secondary motion and its structure at finite amplitude. The experimental results agree with the predicted values of TaL for μ [ges ] 0, and low Reynolds number. For other cases in which agreement is only fair, apparatus length is shown to be a contributing influence. The comparison between experimental and predicted wave forms shows good agreement in overall trends.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 101 - 126
Copyright
© 1981 Cambridge University Press

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References

Chandrasekhar, S. 1960 Proc. Nat. Acad. Sci. 46, 141–143.
Chandrasekhar, S. 1962 Proc. Roy. Soc. A 265, 188–197.
Chung, K. C. & Astill, K. N. 1977 J. Fluid Mech. 81, 641–655.
Coles, D. 1965 J. Fluid Mech. 21, 385–425.
Datta, S. L. 1965 J. Fluid Mech. 21, 635–640.
Davey, A. 1962 J. Fluid Mech. 14, 336–368.
DiPrima, R. C. 1960 J. Fluid Mech. 9, 621–631.
DiPrima, R. C. & Pridor, A. 1979 Proc. Roy. Soc. A 366, 555–573.
Elliott, L. 1973 Phys. Fluids 16, 577–580.
Gravas, N. & Martin, B. W. 1978 J. Fluid Mech. 86, 385–394.
Hasoon, M. A. & Martin, B. W. 1977 Proc. Roy. Soc. A 352, 351–380.
Hughes, T. H. & Reid, W. H. 1968 Phil. Trans. Roy. Soc. A 263, 57–91.
Joseph, D. D. & Munson, B. R. 1970 J. Fluid Mech. 43, 545–575.
Joseph, D. D. 1976 Stability of Fluid Motions I. Springer.
Krueger, E. R. & DiPrima, R. C. 1964 J. Fluid Mech. 19, 528–538.
Krueger, E. R., Gross, A. & DiPrima, R. C. 1966 J. Fluid Mech. 24, 521–528.
Kuester, J. L. & Mize, J. H. 1973 Optimization Techniques with FORTRAN McGraw-Hill.
Lance, G. N. 1959 J. Assoc. Comput. Mach. 6, 208–215.
Lessen, M., Singh, P. J. & Paillet, F. 1974 J. Fluid Mech. 63, 753–763.
Mackrodt, P.-A. 1976 J. Fluid Mech. 73, 153–164.
Martin, B. W. & Hasoon, M. A. 1976 J. Mech. Engng Sci. 18, 221–228.
Martin, R. W. & Payne, A. 1972 Proc. Roy. Soc. A 328, 123–141.
Maslowe, S. A. 1974 J. Fluid Mech. 64, 307–317.
Mavec, J. A. 1973 Spiral and toroidal secondary motions in swirling flows through an annulus at low Reynolds number. M.S.E. thesis, Illinois Institute of Technology.
Mott, J. E. & Joseph, D. D. 1968 Phys. Fluids 11, 2065–2073.
Muller, D. E. 1956 Math. Comp. 10, 208–215.
Nagib, H. M. 1972 On instabilities and secondary motions in swirling flows through annuli. Ph.D. thesis, Illinois Institute of Technology.
Roberts, P. H. 1965 Proc. Roy. Soc. A 283, 550–555.
Schwarz, K. W., Springett, B. E. & Donnelly, R. J. 1964 J. Fluid Mech. 20, 281–289.
Snyder, H. A. 1962 Proc. Roy. Soc. A 265, 198–214.
Snyder, H. A. 1965 Ann. Phys. 31, 292–313.
Snyder, H. A. 1969 J. Fluid Mech. 35, 273–298.
Sparrow, E. M. & Lin, S. H. 1964 Trans. A.S.M.E.D, J. Basic Engng, 86, 827–834.
Sparrow, E. M., Munro, W. D. & Jonsson, V. K. 1964 J. Fluid Mech. 20, 35–46.
Takeuchi, D. I. 1979 A numerical and experimental investigation of the stability of spiral Poiseuille flow. Ph.D. thesis, Arizona State University.
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