Design of Rocket Engine Nozzle Using Method of Characteristics

Abstract

This report focuses on the design of a 2D theoretical layout of a rocket engine nozzle. Convergent and divergent are to be designed separately with the focus on divergent part for a minimum length nozzle. The divergent part is to be designed using method of characteristics with left and right running characteristics using the known (sonic) values at the throat of the convergent-divergent nozzle. These characteristics would be pressure, density, velocity and temperature. A computer code has been designed to calculate the values of these characteristics and the end characteristics at the exit. CFD analysis has also been carried out on the designed nozzle using commercial software ANSYS.

Introduction

V. RESULT AND DISCUSSION

We have successfully applied the method of characteristics to generate the contour for a minimum length nozzle. The resulting nozzle points can be imported into any CAD environment for further refinement and manufacturing processes. It is highly recommended to use this method with an iterative design process to achieve the best results according to the input specifications. Additionally, it is crucial to select an optimal number of characteristics; the number should be sufficiently large to produce a smooth, bell-shaped contour using straight lines. The overall effectiveness of the method of characteristics can be enhanced by running multiple iterations of our algorithm with small variations in the input parameters. The nozzle design gave us Mach 3.79 at the nozzle exit from the MATLAB code at an exit length of 3.56m. The nozzle design when imported in a simulation software for 2D flow analysis  gave us Mach 3.693 at the nozzle exit, which is close the results obtained from the code as well. This helps us verify that our calculations have been precise and accurate in calculating the Mach no. obtained from the method of characteristics. The Mach no. produced by the flow at the nozzle exit expands further according to the Prandtl-Meyer expansion theory. Since there is a difference between the exit nozzle pressure and the ambient pressure at the higher altitude, this thrust increases further with increasing operating altitude. These results are in accordance with the original design as our design is able to produce thrust and impulse close to the original design of 725 kN.  Since there is not much change in the y co-ordinates of the nozzle design after nozzle length of 3.03m, we can truncate the length of the nozzle to 3.03m giving us the precise thrust and Mach no.

Conclusion

The design of a minimum length supersonic nozzle focuses on minimizing its length by eliminating the expansion section. As the expansion section contracts, the overall length of the nozzle decreases. In design, the supersonic nozzle achieves minimum length due to the minimized expansion section, which contracts to a point at the throat\'s end. Previously, it was noted that the nozzle is optimized for the desired exit Mach number. It\'s important to remember that the flow streamlines diverge from the axis and then converge back towards it in the diverging section. This divergence of streamlines occurs in the expansion section, and the angle of divergence depends on the local Mach number. Hence, the final local and maximum divergence angles crucially determine the exit Mach number. Supersonic nozzles find applications in diverse fields such as rocket engine propulsion and wind tunnels, where they encounter intricate flow patterns. While this design approximation simplifies these complex flow patterns, the method of characteristics remains the most suitable for supersonic nozzle design. To address real-world conditions accurately, factors like viscous effects, changes in pressure difference concerning back pressure, heat conduction, and others must be considered. The design presented here serves as a benchmark for comparison with similar nozzle designs under similar conditions. We achieved comparable Mach numbers and thrust while significantly reducing the nozzle\'s length. Maintaining the nozzle\'s area ratio ensures similar flow conditions and expansion as the original design.

References

[1] Md Akhtar Khan, Sanjay Kumar Sardiwal, M. V. Sai Sharath, D. Harika Chowdary (2013): Design of a Supersonic Nozzle using Method of Characteristics.(IJERT) [2] Tiago Fernandes, Alain Souza, Frederico Afonso (2023): A Shape Design Optimization Methodology based on the Method of Characteristics for Rocket Nozzles. (CEAS Space Journal) [3] Andrew C. Also, Brian M. Agrow: Supersonic Minimum Length Nozzle Design for Dense Gases. (Department of Aerospace Engineering Sciences, University of Colorado) [4] Thomas J. Benson: An Interactive Method of Characteristics Java Applet to Design and Analyze Supersonic Aircraft Nozzles. (NASA Glenn Research Centre) [5] Md Hasan Ali, Mohammad Mashud, Abdullah Al Bari, Muhammad Misbah-Ul-Islam (2012): Numerical Solution for the Design of Minimum length Supersonic Nozzle. (ARPN Jornal of Engineering and Applied Sciences) [6] Anuj Kumar, Sudhanshu G. Ogalpur (2021): Design of Minimum Length Nozzle by Method of Characteristics. (RIET-IJSET)

Copyright

Copyright © 2024 Dr. R. S. Tarnacha , Mehak Virmani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.