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The authors of this paper develop a computational program to determine the effects of gaseous imperfections on calculations of the Prandtl Meyer function. Which is often applied to minimum length nozzle (MLN) design. The aim is to improve the design parameters of supersonic nozzles when using a gas propellant for cold propulsion or heated thruster systems under a high pressure and temperature. We considered H 2 , O 2 , Cl 2 , N 2 , CO, NO, and air to this end. The Prandtl–Meyer function depends on the stagnation temperature, pressure, Mach number, and the gas used as non-flammable fuel. As values of the parameters of stagnation of the gases increased, their specific heats as well and ratio began to vary, and the ideal gas began behaving as a real gas. This can be explained by Berthelot’s correction of the terms of the equation of state related to a perfect gas, because the co-volume and intermolecular forces of attraction of the gas influenced system. We calculated differences in values of the Prandtl–Meyer function for different gases and air. The results showed that the use of H 2 , N 2 , and CO led to a significant reduction in the weight, length, and volume of the MLN, and it yielded better performance in terms of the manufacture of aerospace propulsion systems that can attain the maximum thrust than when air was used. The performance of the system when the above gases were used was 16% better than when air was used.

In this study, a method for designing supersonic nozzles with axisymmetric plugs at high temperature has been proposed. The approach is based on the theory of Prandtl-Mayer expansion at high temperatures using the method of characteristics. For this purpose, a code in FORTRAN language was developed in order to obtain the nozzle design. Once the latter was obtained, we were interested in the evolution of the thermodynamic parameters of the flow such as pressure, temperature, and Mach number. The results achieved were confronted with those obtained for a perfect gas model. Regarding the design parameters (length, section ratio, thrust coefficient and mass coefficient), we found that the PG model gives very satisfactory results for values of and 0 below 2.00 and 1000 , respectively. As and 0 increase, this affects performance, requiring the use of our HT model to correct the calculations. In order to minimize the weight of this nozzle, this research is investigating the truncation of the Plug nozzle to increase its performances. All calculations were performed for air.

The aim of this work is to develop a new numerical calculation program to determine the effect of the stagnation temperature on the calculation of the supersonic flow around a pointed airfoils using the equations for oblique shock wave and the Prandtl Meyer expansion, under the model at high temperature, calorically imperfect and thermally perfect gas, lower than the dissociation threshold of the molecules. The specific heat at constant pressure does not remain constant and varies with the temperature. The new model allows making corrections to the perfect gas model designed for low stagnation temperature, low Mach number, low incidence angle and low airfoil thickness. The stagnation temperature is an important parameter in our model. The airfoil should be pointed at the leading edge to allow an attached shock solution to be seen. The airfoil is discretized into several panels on the extrados and the intrados, placed one adjacent to the other. The distribution of the flow on the panel in question gives a compression or an expansion according to the deviation of the flow with respect to the old adjacent panel. The program determines all the aerodynamic characteristics of the flow and in particular the aerodynamic coefficients. The calculation accuracy depends on the number of panels considered on the airfoil. The application is made for high values of stagnation temperature, Mach number and airfoil thickness. A comparison between our high temperature model and the perfect gas model is presented, in order to determine an application limit of the latter. The application is for air.

This work is to develop a new computational program to determine the effect of using gas propellant of the combustion chamber at high temperature on the calculation of the value of the Prandtl Meyer function and application to supersonic nozzles design. The selected gases are the H2, O2, N2, CO, CO2, H2O, NH3, CH4 and air. Prandtl Meyer function depends on the stagnation temperature, Mach number and the gas used. The specific heat at constant pressure and the enthalpy of the gases vary with the temperature and the selected gas. The gas is still considered as perfect and it will be calorically imperfect and thermally perfect below the threshold of dissociation of molecules. A calculation of the difference between the Prandtl Meyer function for different gases with the air is made for the purpose of comparison. The application is made for designing the supersonic MLN nozzle at high temperature.