THERMAL SCIENCE

International Scientific Journal

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P. D. Towers

,

Stephen J. Garrett

SIMILARITY SOLUTIONS OF COMPRESSIBLE FLOW OVER A ROTATING CONE WITH SURFACE SUCTION

ABSTRACT
We present solutions of the laminar compressible boundary-layer flows over the family of rotating cones subject to surface mass flux. The work is a generalization of previous studies of the compressible rotating-disk flow and incompressible rotating-cone flow without surface mass flux. Transformations are used which lead to a system of generalized von Kármán equations with boundary conditions parameterized by half-angle and a mass-flux parameter. Results are discussed in terms of wall temperature and local Mach number in the particular case of air, although the formulation is readily extended to other fluids. It is suggested that suction acts a stabilizing mechanism, whereas increased wall temperature and local Mach number have destabilizing influences.
KEYWORDS
rotating cone, compressible boundary-layer flow, similarity solution, surface mass flux
PAPER SUBMITTED: 2013-04-08
PAPER REVISED: 2013-11-11
PAPER ACCEPTED: 2014-03-21
PUBLISHED ONLINE: 2014-04-05
DOI REFERENCE: https://doi.org/10.2298/TSCI130408032T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 2, PAGES [517 - 528]
REFERENCES
  1. Gregory, N., Stuart, J. T. and Walker, W. S. 1955, On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk., Phil. Trans. R. Soc. Lond. A 248, 155-199.
  2. Gregory, N. and Walker, W. S. 1960 Experiments on the effect of suction on the flow due to a rotating disk., Phil. Trans. R. Soc. Lond. 248, 225-234.
  3. Lingwood, R. J. 1995, Absolute instability of the boundary layer on a rotating disk., J. Fluid Mech. 299, 17-33.
  4. Lingwood, R. J. 1997, On the effects of suction and injection on the absolute instability of a rotating disk boundary layer., Phys. Fluids 9, 1317-1328.
  5. Kreith, F., Ellis, D. and Giesing, J. 1962, An experimental investigation of the flow engendered by a rotating cone., Appl. Sci. Res. A11, 430-440.
  6. Tien, C. L. and Campbell, D. T. 1963, Heat and mass transfer from rotating cones., J. Fluid Mech. 17, 105-112.
  7. Garrett, S. J. 2002, The stability and transition of the boundary layer on rotating bodies., PhD thesis, Cambridge University.
  8. Garrett, S. J. and Peake, N. 2007, The absolute instability of the boundary layer on a rotating cone., European. J. Mech. B. 26, 344-53.
  9. Garrett, S. J., Hussain, Z. and Stephen, S. O. 2009, The cross flow instability of the boundary layer on a rotating cone., J. Fluid Mech. 622, 209-232.
  10. Garrett, S.J. 2010, Linear growth rates of types I & II convective modes within the rotating-cone boundary layer,, Fluid Dyn. Res. 42, 025504
  11. Garrett, S.J., Hussain, Z. and Stephen, S.O. 2010, Boundary-layer transition on broad cones rotating in an imposed axial flow,, AIAA Journal, 48, No. 6, 1184-1194.
  12. Hussain, Z., Stephen, S.O. and Garrett, S.J. 2011, The centrifugal instability of a slender rotating cone,, Journal of Algorithms & Computational Technology, 6, No. 1.
  13. Turkyilmazoglu, M., Cole, J. W. and Gajjar, J. S. B. 2000, Absolute and convective instabilities in the compressible boundary layer on a rotating disk., Theor. Comput. Fluid Dyn. 14, 21-37.
  14. Turkyilmazoglu, M. and Uygun, N. 2004, Basic compressible flow over a rotating disk., Hace. J. Math. Stat. 33, 1-10.
  15. Turkyilmazoglu, M. 2005, Lower branch modes of the compressible boundary layer flow due to a rotating disk., Stud. Appl. Math. 114, 17-43.
  16. Turkyilmazoglu, M. 2007, Influence of finite amplitude disturbances on the non-stationary modes of a compressible boundary layer flow., Stud. Appl. Math. 118, 199-220.
  17. Lingwood, R. J. and Garrett, S. J. 2011, The effects of surface mass flux on the instability of the BEK system of rotating boundary-layer flows., European J. Mech. B., to appear.
  18. Ockendon, H. 1971, An asymptotic solution for steady flow above an infinite rotating disc with suction., Q. J. Mech. appl. Math., 25, 291-301.
  19. Bassom, A. P. and Seddougui, S. O. 1992, The effects of suction on the nonlinear stability of the three-dimensional boundary layer above a rotating disk., Proc. R. Soc. Lond. A, 436, 405-415.
  20. Dhanak, M. R. 1992, effects of uniform suction on the stability of flow on a rotating disk., Proc. R. Soc. Lond. A, 439, 431-440.
  21. Hussain, Z. 2009, Stability and transition of three dimensional rotating boundary layers., PhD Thesis, University of Birmingham.
  22. Stewartson, K. 1964 The theory of laminar boundary layers in compressible fluids. Oxford University Press.
  23. Riley, N. 1964, The heat transfer from a rotating disk., Q. J. Mech. Appl. Math. 17, 331-349.
  24. Towers, P.D. 2013, The stability and transition of the compressible boundary-layer flow over broad rotating cones, PhD thesis, University of Leicester.
  25. Hussain, Z., Garrett, S. J. and Stephen, S. O. 2011, Distinct transition mechanisms over slender and broad rotating cones, Proceedings of the 40th AIAA Fluid Dynamics Conference, Chicago, IL, USA, Paper AIAA-2010-4285.
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Similarity solutions of compressible flow over a rotating cone with surface suction

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