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.
Similar content being viewed by others
References
Faraday, M., Phil. Trans. Royal Soc. London,121, 299–340 (1831).
Rayleigh, L., Phil. Trans Royal Soc. London,175, 1–21 (1883).
Schlichting, H., Phys. Z.33, 327–335 (1932).
Andres, J. M. and Ingard, U., J. Acous. Soc. Amer.,25, 928–938 (1953).
Stuart, J. T.,Unsteady boundary layer. In:Laminar Boundary Layers, Oxford University Press 1963
Stuart, J. T., J. Fluid Mech.,24, 673–687 (1966).
Riley, N., J. Inst. Maths. Applies.,3, 419–434 (1967).
Wang, C. Y., J. Fluid Mech.,32, 55–68 (1967).
Haddon, E. W. and Riley, N., Q. J. Mech. Appl. Maths.32, 265–282 (1979).
Davidson, B. J. and Riley, N., J. Fluid Mech.,53, 287–303 (1972).
Riley, N., Mathematika,12, 161–175 (1965).
Bertelsen, A., Svardal, A. and Tjotta, S., J. Fluid Mech.,59, 493–511 (1973).
Bertelsen, A. F., J. Fluid Mech.,64, 589–597 (1974).
Irani, M. B., Masters Thesis, Univ. of British Columbia 1982.
Pattani, P. G. and Olson, M. D., Int. J. Num. Methods in Fluids,7, 653–695 (1987).
Pattani, P. G. and Olson, M. D., Int. J. Num. Methods in Fluids,8, 519–536 (1988).
Kim, S. K. and Troesch, A. W., Phys. Fluids,A1, 975–985 (1989).
Zapryanov, Z., Kozhoukharova, Zh. and Iordanova, A., J. Appl. Maths. & Phys. (ZAMP),39, 204–220 (1988).
Tabakova, S. and Zapryanov, Z., J. Appl. Maths. & Phys. (ZAMP).33, 344–357 (1982).
Williamson, C. H. K., J. Fluid Mech.,155, 141–174 (1985).
Ingham, D. B., Tang, T. and Morton, B. R., J. Fluid Mech.,210, 281–303 (1990).
Ingham, D. B., Yan, B. and Morton, B. R., Computer & Fluids,21, 305–321 (1992).
Ingham, D. B. and Yan, B., Acta Mechanica,91, 27–46 (1992).
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).
Motz, H., Quart. Appl. Maths.,4, 371–377 (1946).
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.
Woods, L. C., Aero. Quart.5, 176–184 (1954).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ingham, D.B., Yan, B. Fluid flows around cascades. Z. angew. Math. Phys. 44, 53–72 (1993). https://doi.org/10.1007/BF00914353
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00914353