Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero-order (M->∞) and first-order (small but nonvanishing values of 1/(Mδ)2) solutions are presented, where M is free-stream Mach number and δ is a characteristic slope. These solutions are compared with exact numerical integrations of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Advances in Applied Mechanics

The exact 'constant-energy' solution of strong blast waves is expanded in powers of the density ratio across the shock wave; physical quantities are expressed directly as functions of the similitude parameter. The range of validity for t.;e application of this solution to hypersonic flow is then studied as a function of the density ratio. The general similar solution of the strong blast wave is found in the Newtonian approximation. The results are applied to power-law bodies in hypersonic flow using the equivalence principle. The pressure distribution on slender bodies of arbitrary shape is obtained and agrees with the Newton-Busemann pressure formula. Higher-order approximations are derived for the cases in which the shock layer is thin. A simple pressure formula is obtained and some of its applications are shown. (Author).

Unified, self-contained view of nonequilibrium effects, body geometries, and similitudes available in hypersonic flow and thin shock layer; appropriate for graduate-level courses in hypersonic flow theory. 1966 edition.