Stagnation Temperature Effect on the Prandtl Meyer Function

摘要

For an error lower than 5%, a study on the supersonic flow is presented by using the PG relations, if T_0 < 1000 K for any value of Mach number, or when M < 2.00 for any value of T_0 up to approximately 3000 K. The PG model is presented by a simple and explicit relation, and does not require high time to make calculation, unlike the proposed model, which requires the resolution of a nonlinear algebraic Eq. (4) and integration of a complex analytical function (3). It takes more time for calculation and data processing. The presented relation is valid for any interpolation form chosen for the function C_P(T). The essential is that the selected one gives small error. Another substance instead of air can be chosen. It is necessary to have its table of variation of C_P with the temperature and to make a suitable interpolation. The PG model relations can be obtained starting from the HT model ones by annulling all constants of interpolation except the first. It becomes a particular case of the HT model. The PM function can be used to solve problems of external flows, in particular around a supersonic pointed airfoil. It leads us to develop a new mathematical model of the Method of Characteristics to concept and design various supersonic nozzles shapes at high temperature.