A Theory of Entropy Layers and Nose Bluntness in Hypersonic Flow
Department of Aeronautical Engineering, Stanford University., 1961 - Aerodynamics, Hypersonic - 154 pages
The method of inner and outer expansions was used in obtaining uniforml -valid solutions far downstream from the blunt nose of slender bodies in hypersonic flow. Application of this technique on the inverse problem, which prescribes the shock wave leaving the body to e determined, results in a unique treatment of the flow field. The influence of nose (shock) bluntness on the flow field and body shape is found to be significant due to the formation of a layer of low density, high entropy air enveloping the body. This entropy layer i in many respects analogous to Prandtl's viscous boundary layer. Analytical solutions, which assume an inviscid perfect gas and infinite Mach number were obtained for hyperbolic and power-law shock wave shapes. The hyperbolic shocks correspond to flows past bl nted wedges and cones in two an three dimensions, respectively. The second-order result for these two case yield a displacement thickness due to t e entropy layer. The lunt body that produces a paraboloidal shock is found to grow as a small power of the distance. (Author).
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analogy analytical approach approximation asymptotic behavior asymptotic expansions axisymmetric blast-wave theory blunt nose blunted cone bluntness and entropy boundary conditions boundary layer complete outer equations COMPOSITE EXPANSIONS constant coordinate system cylindrical coordinates defined density displacement thickness Doctor of Philosophy effects of bluntness effects of nose expressed finite flow past flow quantities given hyperbolic shock inner and outer inner expansions inner limit inner region inner variables integral inverse problem limit process matching conditions method of inner normalized with respect nose bluntness nose section numerical obtained ordinary differential equations outer expansions outer limit outer region outer variables p/p becomes plane power-law pressure distribution result second inner equations second outer equations second outer solutions second-order Sedov's sharp wedge shock asymptote shock conditions shock layer shock nose radius sions slender bodies stream function streamlines third inner equations transverse flow field transverse pressure gradient two-term uniformly-valid valid velocity