A new design method for high conditions applied to minimum length nozzles

Abstract

This present work focused on new nozzles design method, based on the characteristics method, which is a technique method to reduce a partial differential equation to linear differential equations along which the solution can be integrated from initial conditions. The latter is developed under the real gas theory, because when the both pressure and temperature of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect, and it becomes a real gas. The presented equations of the characteristics remain valid whatever area or field of study. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The resolution has been made by the finite differences method using the corrector predictor algorithm. As result, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature HT models on the one hand and our results by the real gas theory on the other of nozzles are made. An important gain of length and weight can rise up to 40% and 20% respectively. It is in this context that Minimum Length Nozzle (MLN) nozzles for aerospace engines based on real gas theory were developed to achieve maximum thrust with the smallest possible nozzle weight (minimum length).