Method of characteristics design tool for nozzle contour

Abstract

The project’s principal objective is to generate a well-designed, highly versatile program that is capable of designing supersonic and even hypersonic nozzle contours to a high degree of accuracy. Various elements such as inclusion of real-gas effects will therefore be necessary if only to produce reliable results that closely resemble that of experiments done in the physical world. The method of characteristics (MOC) will be used as a tool to develop the compatibility equations and characteristics equations needed for use in the numerical computations in the program. In this final report, the program will possess the capacity to account for high temperature effects in hypersonic flows (Gordon and McBride, 1992) which involves molecule dissociation and hence the need to vary the specific heat ratio as a function of both pressure and temperature. This capability can be achieved by using the thermodynamic database provided by Gordon and McBride25 and has been looked into in the latter half of the project schedule.

To increase the flexibility of the program, the author has included various types of throat contours for the user to specify – (1) circular contour or, (2) cubic equation curvature. In addition, an option for conical nozzle design is also integrated into the program that can be connected to either a circular or cubic curvature. Such a feature will allow for reconstructing of nozzles where the user is limited by a certain nozzle curvature angle (obtained from an old nozzle). The program can calculate the length of the conical section needed in order to achieve the desired Mach number within the limits of the curvature provided. The second half of the project has also investigated the reliability and accuracy of the method of characteristics as a nozzle design tool. The author developed the rotational method of characteristics – a topic rarely elaborated in published text.9-16 Rotational MOC has expanded the competence of the program greatly as it can now account for non-uniform nozzle inflow. However, the complexity of the algorithm incremented the numerical errors substantially and this called for a superior numerical integration technique – (1) produces high precision solutions, (2) yet at minimal computational effort. The Modified Euler Predictor-Corrector Method was proposed to solve the differential equations in place of the conventional use of Euler’s Method in MOC programs.9-16 Various accuracy studies have also been conducted to validate the precision of the solutions obtained, including rigorous verification of solutions using the Chemical Equilibrium Analysis (CEA) code. A high precision and versatile MOC program is the end-product of this Final Year Project.