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Boundary layer growth on two circular cylinders

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Abstract

This paper deals with the problem of boundary layer growth on two circular cylinders in a flow with large Reynolds and Strouhal numbers. Analytic solutions for the stream function of the inner and outer flow field are obtained to the second order by using the method of matched asymptotic expansions. The dependence of the movement of the detachment points and the drag coefficients of the two cylinders on (i) the distance between them, (ii) the ratio of their radii, (iii) the Reynolds number and (iv) the acceleration parameter of the flow is investigated. The results obtained indicate that the mutual hydrodynamic interaction between two cylinders leads to some new relations and findings.

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References

  1. Lord Rayleigh, On the motion of solid bodies through viscous liquids, Philos. Mag. 21 (1911) 697–711.

    Google Scholar 

  2. L. Howarth, Rayleigh's problem for a semi-infinite plate, Proc. Cambridge Soc. 46 (1950) 127–140.

    Google Scholar 

  3. H. Hasimoto, Note on Rayleigh's problem for a bent flat plate, J. Phys. Soc. Japan 6 (1951) 400–401.

    Google Scholar 

  4. L. Sowerby and J. Cooke, The flow of fluid along corners and edges, Quart. Mech. Appl. Math. 6 (1953) 50–70.

    Google Scholar 

  5. H.S. Carslaw and J.C. Jaeger, The conduction of heat in solids, Oxford University Press, Oxford, England (1947).

    Google Scholar 

  6. G.K. Batchelor, The skin friction on infinite cylinders moving parallel to their length, Quart Mech. Appl. Math. 7 (1954) 179–192.

    Google Scholar 

  7. H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys. 56 (1908) 1–37.

    Google Scholar 

  8. S. Goldstein and L. Rosenhead, Boundary layer growth, Proc. Cambr. Phil. Soc. 32 (1936) 392–401.

    Google Scholar 

  9. H. Görtler, Verdrängungswirkung der laminaren Grenzschicht und Druckwiderstand, Ing. Arch. 14 (1944) 286–305.

    Google Scholar 

  10. E. Watson, Boundary layer growth, Proc. Roy. Soc. A231 (1955) 104–116.

    Google Scholar 

  11. C-Yi Wang, The flow past a circular cylinder which is started impulsively from rest, J. Math. and Phys. 46 (1967) 195–202.

    Google Scholar 

  12. C-Yi Wang, Separation and stall of an impulsively started elliptic cylinder, J. Appl. Mech. E34 (1967) 823–828.

    Google Scholar 

  13. Z. Zapryanov, Boundary layer growth around a parabolic cylinder, Theory, and Appl. Mech., BAS, 2 (1974) 19–28.

    Google Scholar 

  14. Sl. Slavchev, Boundary layer growth on a circular cylinder, Theor, and Appl. Mech., Bas. 4 (1975) 49–55.

    Google Scholar 

  15. Z.D. Zapryanov and P.G. Kalitzova-Kurteva, Boundary layer growth on a parabolic cylinder at angle of attack, University Annual, Appl, Math., XII (1976), book 3, 185–194.

    Google Scholar 

  16. G. Simeonov, On the motion from rest of a class of cylinders. Elliptic cylinder case, Theor. and Appl. Mech., BAS, 1 (1977) 64–75.

    Google Scholar 

  17. L.A. Belov, Interaction of non-uniform flows with obstacles, Mashinostroene, Leningrad (1983) (in Russian).

    Google Scholar 

  18. I.A. Belov and N.A. Kudriavtzev, Cross flow past two circular cylinders in line, (steady flow), Journal of Physical Engineering XLI (1981) 310–317.

    Google Scholar 

  19. S.S. Tabakova and Z. Zapryanov, On the hydrodysamic interaction of two spheres oscillating in a viscous fluid, I: Axisymmetrical case, ZAMP 33 (1982) 344–357.

    Google Scholar 

  20. S.S. Tabakova and Z. Zapryanov, On the hydrodynamic interaction of two spheres oscillating in a viscous fluid, II: Three dimensional case, ZAMP 33 (1982) 487–502.

    Google Scholar 

  21. D.P. Telionis, Unsteady viscous flows, Springer-Verlag, New York, Heidelberg, Berlin (1981).

    Google Scholar 

  22. J. Happel, H. Brenner, Low Reynolds number hydrodynamics, Prentice-Hall (1965).

  23. P.G. Kalitzova-Kurteva, Hydrodynamic interaction in unsteady viscous flow past two bodies, Ph.D. Thesis, Univ. of Sofia (1987).

  24. S.F. Shen, Unsteady separation according to the boundary-layer equation. In: Adv. Appl. Mech., ed. C.S. Yih: 18 (1978) 177–220.

  25. I. Proudman and K. Johnson, Boundary layer growth near a rear stagnation point. J. Fluid Mech, 12 (1962) 161–168.

    Google Scholar 

  26. S.C.R. Dennis and A.N. Staniforth, A numerical method for calculating the initial flow past a cylinder in a viscous fluid, Lecture Notes in Physics 8 (1970) 343–349.

    Google Scholar 

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Kalitzova-Kurteva, P.G., Zapryanov, Z.D. Boundary layer growth on two circular cylinders. J Eng Math 25, 207–221 (1991). https://doi.org/10.1007/BF00044331

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  • DOI: https://doi.org/10.1007/BF00044331

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