A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields

The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with small thickness ratio was solved by the linearized theory, which is first approximation at and near surface but fails far fields from body. Such problem W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This field disturbance reexamined this study using asymptotic expansion theory. A systematic approach adopted to obtain Burgers’ equation for fields. We also use similarity method solve boundary value (BVP) inviscid patterns, including jump condition shock wave. Secondly, transonic hypersonic equations were obtained stretching coordinate y direction considering an freestream Mach number terms parameters. mathematical structures supersonic, transonic, flows are unified be same. similar patterns positions parabolic airfoil regimes exemplified discussed.