CFD Investigation of Asymmetric Three-Dimensional Supersonic Nozzle MLN for Rocket Engine

Authors

DOI:

https://doi.org/10.3849/aimt.02007

Keywords:

CFD, supersonic nozzle, streamline, Ansys-Fluent software, Method of Characteristics, high temperature model, minimum length nozzle

Abstract

This study focuses on the design of asymmetric supersonic nozzles to improve the performance of conventional axisymmetric propulsion systems. A numerical calculation program based on the Method of Characteristics (MOC) at high temperature was developed to design three-dimensional nozzles with arbitrary exit sections. The streamlines are obtained by integrating the axisymmetric flow function, and the three-dimensional geometry is generated by tracing the exit section parameters back to the throat. Five nozzle shapes were investigated: square, circular, hexagonal, rectangular, and elliptical. CFD simulations using Ansys-Fluent were performed to validate the designs for an exit Mach number of 4.00 with air as the working fluid. The results show very good agreement with the Fortran program calculations, confirming its accuracy and highlighting the influence of exit geometry on nozzle performance.

References

MALINA, F.J. Characteristics of the Rocket Motor Based on the Theory of Perfect Gases. Journal of the Franklin Institute, 1940, 230(4), pp. 433-450. https://doi.org/10.1016/ S00 16-0032(40) 91348-5.

SAUER, R. General Characteristics of the Flow Through Nozzles at Near Crit-ical Speeds [online]. 1947 [viewed 2025-04-09]. Available from: https://ntrs.nasa.gov/api/citations/20050019415/downloads/20050019415.pdf

RUPTASH, J. Supersonic Wind Tunnels-Theory, Design and Performance. Toronto: University of Toronto, 1952.

BECKWITH, I.E., H.W. RIDYARD and N. CROMER. The Aerodynamic Design of High Mach Number Nozzles Utilizing Axisymmetric Flow with Application to a Nozzle of Square Test Section [online]. 1952 [viewed 2025-04-20]. Availa-ble from: https://ntrs.nasa.gov/citations/19930083295

RAO, G.V.R. Exhaust Nozzle Contour for Optimum Thrust, Marquadt Aircraft Co. Journal of Jet Propulsion, 1958, 28(6), pp. 377-382. https://doi.org/10.2514/8.7324.

EVVARD, B.J.C. and S.H. MASLEN. Three-Dimensional Supersonic Nozzles and Inlets of Arbitrary Exit Cross Section [online]. 1952 [viewed 2025-04-10]. Available from: https://apps.dtic.mil/sti/tr/pdf/ADA380474.pdf

RAKICH, J.V. Three-Dimensional Flow Calculation by the Method of Charac-teristics. AIAA Journal, 1967, 5(10), pp. 1906-1908. https://doi.org/10.2514/ 3.4333.

CHUSHKIN, P.I. Numerical Method of Characteristics for Three-Dimensional Supersonic Flows. Progress in Aerospace Sciences, 1968, 9, pp. 41-122. https://doi.org/10.1016 / 0376-0421(68)90004-3.

RANSON, V.H., H.D. THOMPSON and J.D. HOFFMAN. Three-Dimensional Supersonic Nozzle Flow Field Calculation. Journal of Spacecraft and Rockets, 1970, 7(4), pp. 458-462. https://doi.org/10.2514/3.29963.

SIVELLS, J.C. A Computer Program for the Aerodynamic Design of Axisym-metric and Planar Nozzles for Supersonic and Hypersonic Wind Tunnels [online]. 1978 [viewed 2025-04-20]. Available from: https://apps.dtic.mil/sti/tr/pdf/ADA062944.pdf

SUTTON, G.P. Rocket Propulsion Elements. 6th ed. Hoboken: Wiley, 1992. ISBN 0-471-52938-9.

ARGROW, B.M. and G. EMANUEL. Comparison of Minimum Length Nozzles. Journal of Fluids Engineering, 1988, 110(3), pp. 283-288. https://doi.org/10.1115/1.3243546.

HADDAD, A. and J.B. MOSS. Aerodynamic Design for Supersonic Nozzles of Arbitrary Cross Section. Journal of Propulsion and Power, 1990, 6(6), pp. 740-746. https://doi.org/10.2514/3.23280.

ANDERSON, J.D. Modern Compressible Flow with Historical Perspective. 2nd ed. New York: McGraw-Hill Book Company, 1982. ISBN 0-07-001673-9.

PETERSON, C.R. and P.G. HILL. Mechanics and Thermodynamics of Propul-sion. New York: Addison-Wesley Longman, 2010. ISBN 0-13-246548-5.

YU, T., X. WU, Y. YU, R. LI and H. ZHANG. Establishment and Validation of a Relationship Model Between Nozzle Experiments and CFD Results Based on Convolutional Neural Network. Aerospace Science and Technology, 2023, 142, 108694. https://doi.org/10.1016/j.ast.2023.108694.

LI, D., G. WANG, J. CHENG and H. YANG. On the Thrust Vector Performance Optimization and Modeling of Supersonic Split Line Nozzles. International Journal of Heat and Mass Transfer, 2025, 236, 126245. https://doi.org/10.1016/j.ijheat masstransfer.2024. 126245.

LEON-CARDONA, D., et al. Assessment of RANS Turbulence Models for the Simulation of Turbulent Compressible Flows in Convergent-Divergent Noz-zles. Chemical Engineering Transactions, 2024, 111, pp. 505-510. https://doi.org/10.3303/CET24111085.

HOUSMAN, J.A., G.D. STICH and C.C. KIRIS. Jet Noise Prediction using Hy-brid RANS/LES with Structured Overset Grids. In: 23rd AIAA/CEAS Aeroacous-tics Conference. Denver: AIAA, 2017. https://doi.org/10.2514/6.2017-3213.

ZORE, K., C. ALIAGA, J. SELVA, L. ZORI and B. MAKAROV. High-Fidelity SBES Simulations for Supersonic Nozzle Exhaust Flows. In: AIAA SCITECH 2024 Forum. Orlando: AIAA, 2024. https://doi.org/10.2514/6.2024-0753.

FAN, Z., L. WANG, F. XU, X. ZHANG, B. XIE, Y. WEN, H. LI and S. AMINIAN. Influence of the Non-Equal Aligned Nozzles for Fuel Injection Inside the Su-personic Combustion Chamber. Scientific Reports, 2024, 14, 12812. https://doi.org/10.1038/s41598-024-63544-4.

ABADA, O., H. KBAB and S. HAIF. Transonic Flow Field Analysis of a Mini-mum Nozzle Length Rocket Engine. Incas Bulletin, 2024, 16(2), pp. 3-15. https://doi.org/10.13111/ 2066-8201.2024.16.2.1.

ABADA, O., A. ABADA and A. ABDALLAH EL-HIRTSI. Effect of Bipropellant Combustion Products on the Rocket Nozzle Design. Mechanics & Industry, 2020, 21, 515. https://doi.org/10.1051/meca/2020064.

ABADA, O., T. ZEBBICHE and A. ABDALLAH EL-HIRTSI. Three-Dimensional Supersonic Minimum Length Nozzle Design at High Temperature for Arbitrary Exit Cross Section. Arabian Journal for Science and Engineer-ing, 2014, 39, pp. 8233-8245. https://doi.org/10.1007/s13369-014-1377-z.

Downloads

Published

24-05-2026

Issue

Section

Original research article

Categories

How to Cite

ABADA, O., Abada, A., Kbab, H., & Bekhti, A. (2026). CFD Investigation of Asymmetric Three-Dimensional Supersonic Nozzle MLN for Rocket Engine. Advances in Military Technology, 21(1), 277-293. https://doi.org/10.3849/aimt.02007

Similar Articles

1-10 of 455

You may also start an advanced similarity search for this article.