Rapid design method and new contours for a class of three dimensional supersonic nozzle of arbitrary exit cross section

Toufik Zebbiche

doi:10.1051/meca/2018003

Abstract

The aim of this work is to develop a new and rapid numerical method for designing a new contour of the supersonic nozzle with arbitrary exit cross sections as a class of three dimensional nozzle extracted from the calculation of stationary flow solutions in axisymmetric nozzle. The application is made for nozzle giving a uniform and parallel flow at the exit section. The determination of the points of the axisymmetric nozzle contours in a non-dimensional manner with respect to the arbitrary throat radius is necessary. The exit section of the nozzle must be discretized at several points. The radii of the points of the throat section are determined by equalizing the ratio of the axisymmetric critical sections corresponding to each selected point of the exit section. Each point passes a contour of the nozzle to the throat where their position is determined by the multiplication of the non-dimensional positions of the axisymmetric nozzle point by the throat radius of this contour. A uniform portion is added at the end of each contour to compensate the decrease in its length. Longitudinal discretization of the nozzle is necessary. The flow properties of each point are the same as those of the points of the axisymmetric nozzle. The temperature and the deviation of the flow at each point of any section are determined by their interpolations between two successive points of each contour. The Mach number, the pressure and the density are determined accordingly. The application is made for air at high temperature lower than the dissociation threshold of the molecules.

Highlights

Numerical computing obliged us to think of developing efficient methods that meet the demands of convergence with high precision and in a smallest possible computer execution time
The methods developed for determining the contours of the three dimensional nozzles are based on the determination of the internal stream lines using the definition of the stream function [1–6]
The aim of this work is to solve the disadvantages found in the methods used for the design of the nozzles 3D presented in references [1–6], by developing a new very fast and efficient numerical method that can design the new contours of the nozzles 3D of arbitrary exit section in the HT model as a special class of Laval nozzle, only from the boundary axisymmetric nozzle wall, without going through the use of the stream function and storage of the internal meshing information, to derive the properties of the flow at all points of the wall of the nozzle 3D

Summary

Introduction

Numerical computing obliged us to think of developing efficient methods that meet the demands of convergence with high precision and in a smallest possible computer execution time. As the flow is considered as perfect and nonviscous, the stream lines can represent rigid surfaces and a wall shape of obstacles [7]. In our case these stream lines can represent the wall of the nozzle [1–6]. The use of these methods requires a very high computational time since the search of the points of the stream lines is based on the use of the segments in upward and downward characteristics from the developed internal mesh in the axisymmetric nozzle, which becomes impossible for fine

Objectives

Results

Conclusion