Application of Dorodnitsyn's Integral Method to Nonequilibrium Flows over Pointed Bodies
Dorodnitsyn's integral method is used to obtain an approximate solution to the supersonic nonequilibrium flow over pointed bodies with attached shock waves. The partial differential equations governing the flow are converted to an approximate set of ordinary equations, which are solved by numerical integration starting at the body tip. Detailed analytical and numerical results for the first approximation are presented, considering the vibrational relaxation of a diatomic gas over a wedge or cone. It is shown that the first approximation yields: (1) The exact flow-variable gradients at the wedge tip (2) Expressions for the flow-variable gradients at the cone tip which are in agreement with extrapolations of characteristics calculations (3) A good approximate algebraic solution for frozen or equilibrium conical flow (4) An approximate expression for the nonequilibrium-flow stream function which affords a means of obtaining variations across the shock layer of the temperature and vibrational energy. Numerical results for both the wedge and cone compare favorably with identical cases computed by the method of characteristics.