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Effect of Suction on the Stability of Flow on a Rotating Disk

  • Manhar R Dhanak
Part of the ICASE NASA LaRC Series book series (ICASE/NASA)

Abstract

The effect of distributed suction on the cross-flow instability of the boundary layer on a rotating disk is considered. A vorticity-velocity formulation is used to obtain exact linear equations governing the development of infinitesimal disturbances to the steady flow on a rotating disk. A parallel flow approximation is made as a first step in determining the effect of suction on the instability. It is shown that suction has a stabilizing effect on the flow while blowing is destabilizing. Small values of the suction parameter are found to significantly increase the critical Reynolds number associated with stationary modes of disturbances. The wave-angle of the spiral vortices which precede turbulent flow is estimated from critical conditions and is shown to decrease with increase in suction rate. This is shown to be consistent with prediction based on an inviscid analysis (cf Stuart in Gregory et. al 1955). The corresponding estimate of the expected number of vortices is shown to increase with suction. Suction appears to make the second minimum on the neutral curve (Malik 1986) more pronounced suggesting possible increase in the relative importance of the associated low wavenumber mode of disturbance.

Keywords

Critical Reynolds Number Neutral Curve Stationary Disturbance Suction Parameter Disk Flow 
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References

  1. Balakumar P and Malik, M R. 1990. “Traveling disturbances in rotating disk flow.” Report. High Technology Corporation.- Hampton, Virginia.Google Scholar
  2. Davey, A. 1973. “A simple numerical method for solving Orr Sommerfeld problems.” Q. J. Mech. Appl. Math., 26, p401.MATHCrossRefGoogle Scholar
  3. Dhanak M R. 1990. “Transition prediction on swept wings. Progress Report: Eigenvalue Evaluation.” Engineering Department, Cambridge.Google Scholar
  4. Gaster, M 1974. “On the effect of boundary-layer growth on flow instability.” J Fluid Mech., 66, 465.ADSMATHCrossRefGoogle Scholar
  5. Gregory, N., Stuart, J.T. 1955. “On the stability of three dimensional boundary layers with application to the flow due to a rotating disk.” Phil. Tran. Roy. Soc. (A) 248, 155.MathSciNetADSMATHCrossRefGoogle Scholar
  6. Hall, P, Malik, M R, Poll, D I A 1984. “On the stability of an infinite swept attachment line boundary layer.” Proc. Roy. Soc. Lond. A 395, 229.MathSciNetADSCrossRefGoogle Scholar
  7. Hall P. 1986. “An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc.” Proc. Roy. Soc. Lond. A 406, 93.ADSMATHCrossRefGoogle Scholar
  8. Malik M R, Wilkinson, S P, and Orszag, S A 1981. “Instability and transition on a rotating disk flow.” AIAA L. 19, 1131.ADSCrossRefGoogle Scholar
  9. Malik, M R. 1986. “The neutral curve for stationary disturbance in rotating-disk flow.” J.Fluid Mech. 164, p275.MathSciNetADSMATHCrossRefGoogle Scholar
  10. Pfenninger, W and Bacon J W 1969. “Amplified laminar boundary layer oscillations and transition at the front attachment line of 45° swept flat-nosed wing with and without boundary layer suction.” Viscous Drag Reduction. Ed. C S Wells. p85., London: Plenum Press.Google Scholar
  11. Stuart, J T 1954. “Effects of uniform suction on steady flow.” Quart. J. Mech. 7, 446.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Manhar R Dhanak
    • 1
  1. 1.Florida Atlantic UniversityBoca RatonUSA

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