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Application of the triple-deck theory of viscous-in viscid interaction to bodies of revolution

  • Ming-Ke Huang (a1) (a2) and G. R. Inger (a1)

The general triple-deck theory of laminar viscous-inviscid interaction is extended to axisymmetric bodies. With body radius/length ratios scaled in terms of Reynolds number as $Re^{\frac{1}{8}\beta} (\beta > 0)$, it is found that for β < 3 the only three-dimensional effect is that on the incoming undisturbed boundary-layer profile as accounted for by the Mangler transformation. When β = 3, however, an explicit axisymmetric effect on the interaction equations also enters: the upper-deck flow is governed by the equation of axisymmetric potential disturbance flow, whereas the middle and lower decks are still governed by equations of two-dimensional form. When β > 3, the body is so slender that transverse curvature effects become important and the lower decks too are explicitly influenced by three-dimensional effects. A detailed example application of this theory is given for weak interactions on a flared cylinder and cone in supersonic flow with β [Lt ] 3. The three-dimensional effects on the interactive pressure and shear-stress distributions are shown to relieve the strength of the interaction and reduce its upstream influence, as expected. Correspondingly, it is found that the smallest flow deflection angle provoking incipient separation increases with increasing axisymmetric body slenderness. These results are shown to be in qualitative agreement with several experimental studies.

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Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. National Bureau of Standards.
Burggraf, O. 1975 Asymptotic theory of separation and reattachment of a laminar boundary layer on a compression ramp. AGARD. CP-168 on Flow Separation, pp. 101 109.
Davis, R. T. & Werle, M. J. 1976 Numerical methods for interacting boundary layers. In Proc. Heat Transfer Fluid Mech. Inst., pp. 317339. Stanford University Press.
Duck, P. W. 1981 Laminar flow over a small unsteady three-dimensional hump Z. angew. Math. Phys. 32, 6279.
Duck, P. W. 1983 The effect of a surface discontinuity on an axisymmetric boundary layer. Q. J. Math. Appl. Mech. (To be published.)
Ginoux, J. 1969 High speed flows over wedges and flares with emphasis on a method of detecting transition. In Viscous Interaction Phenomena in Supersonic and Hypersonic Flows, pp. 523538. University of Dayton Press.
Inger, G. R. 1980 Upstream influence and skin friction in non-separating shock-turbulent boundary layer interactions. A.I.A.A. Paper 80–1411.
Jenson, R., Burggraf, O. & Rizzetta, D. 1975 Asymptotic solution for supersonic viscous flow past a compression corner. In Proc. 4th Int. Conf. on Num. Meth. Fluid Dyn. (ed. R. D. Richtmyer), Lecture Notes in Physics, vol. 35. Springer.
Kuehn, D. M. 1962 Laminar boundary layer separation induced by flares on cylinders at zero angle of attack. NASA. Tech. Rep. R-146.
Lighthill, M. J. 1953 On boundary layers and upstream influence. II. Supersonic flows without separation. Proc. R. Soc. Lond. A 217, 478507.
Lighthill, M. J. 1954 Higher approximations. In General Theory of High Speed Aerodynamics, vol. vi, §E. Princeton University Press.
Messiter, A. F. 1970 Boundary layer flow near the trailing edge of a flat plate SIAM. J. Appl. Math. 18, 241247.
Neiland, V. Ya. 1969 Contribution to a theory of separation of a laminar boundary layer in supersonic stream. Izv. Akad. Nauk SSSR., Mekh. Zhid. i Gaza 4, 5357 (in Russian).
Ryzhov, O. S. 1980 Unsteady three-dimensional boundary layer, freely interacting with an outer stream. Prik. Mat. Mekh. 44, 10351052 (in Russian).
Smith, F. T. 1973 Laminar flow over a small hump on a flat plate J. Fluid Mech. 57, 803829.
Smith, F. T., Sykes, R. I. & Brighton, P. W. M. 1977 A two-dimensional boundary layer encountering a three-dimensional hump J. Fluid. Mech. 83, 163176.
Stewartson, K. 1971 On laminar boundary layers near corners. Q. J. Mech. Appl. Math. 23, 137152 [Corrections and addition. 24, 387–389].
Stewartson, K. 1974 Multistructured boundary layers on plates and related bodies Adv. Appl. Mech. 14, 146239.
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 313, 181206.
Stollery, J. L. 1975 Laminar and turbulent boundary layer separation at supersonic and hypersonic speeds. AGARD. CP-168 on Flow Separation, pp. 20–1–20–10.
Tu, K. M. & Weinbaum, S. 1976 A non-asymptotic triple-deck model for supersonic boundary layer interaction A.I.A.A. J. 14, 767775.
Ward, G. N. 1955 Linearized Theory of Steady High-Speed Flow. Cambridge University Press.
White, F. M. 1974 Viscous Fluid Flow. McGraw-Hill.
Williams, P. G. 1975 A reverse flow computation in the theory of self-induced separation. In Proc. 4th Int. Conf. Num. Meth. Fluid Dyn. (ed. R. D. Richtmyer), Lecture Notes in Physics, vol. 35. Springer.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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