Blunt Body Flow - The Transonic Region

For supersonic flow of an ideal gas over planar and axisymmetric bodies we consider the transonic region bounded by the sonic line, the body surface, the downstream surface of the shock wave and the limiting characteristics. Using curved shock theory, we establish the conditions under which the shock surface is (type I), or is not (type II), a boundary of the transonic region. It is found that the existence of type I or type II flow is determined solely by the values of free stream Mach number, specific heat ratio of the gas and transverse-to-longitudinal curvature of the shock surface. When the curvature ratio is grater than 1, only type II flow is possible irrespective of the specific heat ratio. When the curvature ratio is less than -2/(gamma-1) then only type I is realized. When the curvature ratio is between 1 and -2/(gamma-1) the appearance of type I or type II is determined by the free stream Mach number which for planar flow. With proper choice of curvatures the results apply to general, three dimensional, shock waves as well