Stagnation pressure effect on Prandtl Meyer function for air

Abstract

When the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not stay perfect. Its state equation change and it becomes for a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. The aim of this work is developing a new form of Prandtl Meyer function based on those assumptions; and determining the effect of stagnation pressure on this function. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The application is for air. A computation of error was made in this case to give a limit of the perfect gas and the high temperature models compared to the real gas model.

Keywords

Supersonic flow perfect gas model high temperature model real gas Berthelot’s state equation condensation’s function stagnation pressure Simpson’s integration Newton’s method numerical derivation Prandtl Meyer function

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