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Fluid flows around cascades

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Abstract

Flows induced by the small-amplitude and high frequency harmonic oscillations of a cascade of bodies in an unbounded fluid which is otherwise at rest are investigated theoretically. In the theoretical study we separate the flow into inner and outer regions. The flow in the inner region is governed by the Stokes boundary-layer equation. The first-order outer flow is governed by the potential solution which is found by using a conformai mapping technique. The second-order outer flow is governed by the full Navier-Stokes equation and the steady streaming flow has been obtained using a modified central-difference scheme for cascades with square cylinders and flat plates for values of the streaming Reynolds number,R s , up to 70. These results show a complicated flow structure.

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References

  1. Faraday, M., Phil. Trans. Royal Soc. London,121, 299–340 (1831).

    Google Scholar 

  2. Rayleigh, L., Phil. Trans Royal Soc. London,175, 1–21 (1883).

    Google Scholar 

  3. Schlichting, H., Phys. Z.33, 327–335 (1932).

    Google Scholar 

  4. Andres, J. M. and Ingard, U., J. Acous. Soc. Amer.,25, 928–938 (1953).

    Google Scholar 

  5. Stuart, J. T.,Unsteady boundary layer. In:Laminar Boundary Layers, Oxford University Press 1963

  6. Stuart, J. T., J. Fluid Mech.,24, 673–687 (1966).

    Google Scholar 

  7. Riley, N., J. Inst. Maths. Applies.,3, 419–434 (1967).

    Google Scholar 

  8. Wang, C. Y., J. Fluid Mech.,32, 55–68 (1967).

    Google Scholar 

  9. Haddon, E. W. and Riley, N., Q. J. Mech. Appl. Maths.32, 265–282 (1979).

    Google Scholar 

  10. Davidson, B. J. and Riley, N., J. Fluid Mech.,53, 287–303 (1972).

    Google Scholar 

  11. Riley, N., Mathematika,12, 161–175 (1965).

    Google Scholar 

  12. Bertelsen, A., Svardal, A. and Tjotta, S., J. Fluid Mech.,59, 493–511 (1973).

    Google Scholar 

  13. Bertelsen, A. F., J. Fluid Mech.,64, 589–597 (1974).

    Google Scholar 

  14. Irani, M. B., Masters Thesis, Univ. of British Columbia 1982.

  15. Pattani, P. G. and Olson, M. D., Int. J. Num. Methods in Fluids,7, 653–695 (1987).

    Google Scholar 

  16. Pattani, P. G. and Olson, M. D., Int. J. Num. Methods in Fluids,8, 519–536 (1988).

    Google Scholar 

  17. Kim, S. K. and Troesch, A. W., Phys. Fluids,A1, 975–985 (1989).

    Google Scholar 

  18. Zapryanov, Z., Kozhoukharova, Zh. and Iordanova, A., J. Appl. Maths. & Phys. (ZAMP),39, 204–220 (1988).

    Google Scholar 

  19. Tabakova, S. and Zapryanov, Z., J. Appl. Maths. & Phys. (ZAMP).33, 344–357 (1982).

    Google Scholar 

  20. Williamson, C. H. K., J. Fluid Mech.,155, 141–174 (1985).

    Google Scholar 

  21. Ingham, D. B., Tang, T. and Morton, B. R., J. Fluid Mech.,210, 281–303 (1990).

    Google Scholar 

  22. Ingham, D. B., Yan, B. and Morton, B. R., Computer & Fluids,21, 305–321 (1992).

    Google Scholar 

  23. Ingham, D. B. and Yan, B., Acta Mechanica,91, 27–46 (1992).

    Google Scholar 

  24. Yan, B., Ingham, D. B. and Morton, B. R.,Streaming flow induced by an oscillating cascade of cylinders, to appear in J. Fluid Mech. (1992).

  25. Motz, H., Quart. Appl. Maths.,4, 371–377 (1946).

    Google Scholar 

  26. Dennis, S. C. R. and Hudson, J. D., Proc. 1st Int. Conf. Num. Methods in Laminar & Turbulent Flow, pp. 69–80, Pineridge Press, Swansea (U.K.) 1978.

    Google Scholar 

  27. Woods, L. C., Aero. Quart.5, 176–184 (1954).

    Google Scholar 

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Authors and Affiliations

  1. Dept of Applied Mathematical Studies, University of Leeds, LS2 9JT, Leeds, England

    D. B. Ingham & B. Yan

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  1. D. B. Ingham
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  2. B. Yan
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Ingham, D.B., Yan, B. Fluid flows around cascades. Z. angew. Math. Phys. 44, 53–72 (1993). https://doi.org/10.1007/BF00914353

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  • DOI: https://doi.org/10.1007/BF00914353

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