Journal of Engineering Mathematics

, Volume 33, Issue 3, pp 293–310 | Cite as

Unsteady slot Suction from a High-Reynolds-Number Cross-Flow

  • T. R. B. Lattimer
  • A. D. Fitt


The problem of unsteady suction from a high-Reynolds-number cross-flow into a slot is considered in the case where the suction is driven by a time-dependent slot pressure. The model uses linearised asymptotics based on a small parameter that defines the suction strength. An integro differential equation is derived for the mass flow into the slot and this is solved for various time-dependent slot pressures of practical interest. Closed-form expressions are also found for the shape of the shear layer dividing the external flow from the fluid in the slot. For a step function change in the slot pressure, a non-monotonic decay to the steady solution is observed, and for an oscillatory slot pressure there is a phase lag between the slot pressure and the mass flow. For rapidly changing slot pressures it is shown that slot injection can occur, even when the slot pressure remains below the free-stream pressure.

suction injection film cooling Hilbert transforms thin aerofoil theory. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. W. Chew, S. Dadkhah and A. B. Turner, Rim sealing of rotor-stator wheelspaces in the absence of external flow. J. Turbomachinery - Trans. ASME114 (1992) 433-438.Google Scholar
  2. 2.
    J. N. Dewynne, S. D. Howison, J. R. Ockendon, L. C. Morland, and E. J. Watson, Slot suction from inviscid channel flow. J. Fluid Mech. 200 (1989) 265-282.Google Scholar
  3. 3.
    J. H. Michell, On the theory of free stream lines. Phil. Trans. R. Soc. London A181 (1890) 389-431.Google Scholar
  4. 4.
    L. C. Morland, Mathematical Models for a Fluid Flow Arising in Turbine Blade Cooling Passages. D. Phil. Thesis, University of Oxford (1988) 114 pp.Google Scholar
  5. 5.
    M. Van Dyke, Perturbation Methods in Fluid Mechanics. Stanford, California: Parabolic Press (1975) 520 pp.Google Scholar
  6. 6.
    T. R. B. Lattimer, Singular Partial Integro-Differential Equations Arising in Thin Aerofoil Theory. Ph.D. Thesis, University of Southampton (1996) 159 pp.Google Scholar
  7. 7.
    N. I. Muskhelishvili, Singular Integral Equations. New York: Dover Publications (1992) 447 pp.Google Scholar
  8. 8.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications (1964) 946 pp.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • T. R. B. Lattimer
    • 1
  • A. D. Fitt
    • 2
  1. 1.The Mathematical InstituteOxfordUnited Kingdom
  2. 2.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonUnited Kingdom

Personalised recommendations