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The initial flow past an impulsively started sphere at high Reynolds numbers

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Summary

A solution for the early flow around an impulsively started sphere in a viscous fluid has been developed in powers of the time from the start of the motion. The boundary-layer solution considered by E. Boltze has been extended and solutions of this type have been developed to include the effect of finite Reynolds numbers. For high Reynolds numbers the time series is valid past the time when separation occurs and a number of characteristic flow properties can be calculated with reasonable accuracy.

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References

  1. E. Boltze, Grenzschichten an Rotationskörpern in Flüssigkeiten mit kleiner Reibung,Thesis, Göttingen (1908).

  2. S. Goldstein and L. Rosenhead, Boundary Layer Growth,Proc. Camb. Phil. Soc., 32 (1936) 392–401.

    Google Scholar 

  3. L. C. Squire, Boundary Layer Growth in Three Dimensions,Phil. Mag. (7), 45 (1954) 1272–83.

    Google Scholar 

  4. H. Wundt, Wachstum der laminaren Grenzschicht an schräg angeströmten Zylindern bei Anfahrt aus der Ruhe,Ing.-Arch., 23 (1955) 212.

    Google Scholar 

  5. C.-Y. Wang. The Impulsive Starting of a Sphere,Quart. Appl. Math., 27 (1969) 273–277.

    Google Scholar 

  6. M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions, Dover, New York (1968).

    Google Scholar 

  7. L. Fox,Numerical solution of Two-Point Boundary Problems in Ordinary Differential Equations, Oxford (1957).

  8. J. B. Rosser, The Direct Solution of Difference Analogs of Poisson's equation,TSR No. 797 Mathematics Research Centre, Madison, Wisconsin (1967).

    Google Scholar 

  9. W. G. Bickley, Formulae for Numerical Differentiation,Math. Gaz., 25 (1941) 19–27.

    Google Scholar 

  10. J. D. A. Walker, The Flow of a Viscous Fluid Past a Sphere,Ph. D. Thesis, University of Western Onatrio, London, Ontario (1971).

    Google Scholar 

  11. H. Schlichting,Boundary Layer Theory, Pergamon Press (1955).

  12. Y. Rimon and S. I. Cheng, Numerical Solution of a Uniform Flow over a Sphere at Intermediate Reynolds Numbers,Physics of Fluids, 12 (1969) 949–959.

    Google Scholar 

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Dennis, S.C.R., Walker, J.D.A. The initial flow past an impulsively started sphere at high Reynolds numbers. J Eng Math 5, 263–278 (1971). https://doi.org/10.1007/BF01548244

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  • DOI: https://doi.org/10.1007/BF01548244

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