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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)
Abstract

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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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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