Toufik Zebbiche and ZineEddine Youbi
International Journal of Aeronautical and Space Sicences, vol. 7, no. 1, pp.13-26, 2006

Abstract : When the stagnation temperature of a perfect gas increases, the specific heat for constant pressure and ratio of the specefic heats do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, with exception that it will be named by calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios, and to study the supersonic flow at high temperature, lower than the threshold of dissociation. The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm for the numerical integration of the found integrals. A condensation of the nodes is used. Since, the functions to be integrated have a high gradient at the extremity of the interval of integration. The comparison is made with the calorifcally perfect gas to determine the error made by this last. The application is made for the air in a supersonic nozzle.

Keyword : Supersonic Flow, High Temperature, Supersonic Nozzle, Thermodynamics ratios, Stretching Function, Numerical Integration, Interpolation