Numerical simulation of the under-expanded flow in the experimental conical nozzle helios-x

Main Article Content

San Luis B. Tolentino Masgo
Richard Nakka
Simón Caraballo
Jorge Mírez


Numerical studies of the flow field for convergent-divergent nozzles with throat length, have reported fluctuations of the flow with oblique shock waves in the throat section, for the over-expanded flow condition. However, for other flow conditions, for the same type of nozzle, knowledge is limited. In the present work, the objective is to determine the behavior of the flow in the throat length and in the divergent, for an experimental conical nozzle classified as Helios-X, for the under-expanded flow condition. 2D numerical simulations of the flow field were performed with the ANSYS-Fluent version 12.1 code, applying the RANS model. The governing equations for compressible flow, conservation of mass, momentum, energy, and state were used; as well as, for turbulence, the Menter model SST  and for the viscosity as a function of temperature the Sutherland equation. In the section of the throat, adjacent to the wall, the flow presented fluctuations, in the axial symmetry the flow presented a stepped acceleration; in the divergent section, the flow slowed in a certain region, however, the flow exited the nozzle at a supersonic speed slightly greater than Mach 3. It is concluded that in the throat length section there is a flow pattern, as well as, in the divergent section.
Abstract 229 | PDF (Español (España)) Downloads 127 PDF Downloads 35


[1] G. P. Sutton and O. Biblarz, Rocket propulsion elements. John Wiley & Sons, 2016. [Online]. Available:
[2] J. Blazek, Computational fluid dynamics: principles and applications. Butterworth-Heinemann, 2015. [Online]. Available:
[3] B. Andersson, R. Andersson, L. Hakansson, M. Mortensen, R. Sudiyo, and B. van Wachem, Computational Fluid Dynamics Engineers. Cambridge University Press, 2011. [Online]. Available:
[4] J. D. Anderson, Fundamentals of aerodynamics. McGraw-Hill international editions. Mechanical engineering series, 1984. [Online]. Available:
[5] F. M. White, Fluid Mechanics. McGraw-Hill series in mechanical engineering, 2011. [Online]. Available:
[6] P. Krehl and S. Engemann, “August toepler – the first who visualized shock waves,” Shock Waves, vol. 5, no. 1, pp. 1–18, Jun. 1995. [Online]. Available:
[7] V. Karman, “The fundamentals of the statistical theory of turbulence,” Journal of the Aeronautical Sciences, vol. 4, no. 4, pp. 131–138, 1937. [Online]. Available:
[8] F. White, Viscous fluid flow. McGraw-Hill series in Aeronautical and Aerospace Engineering, 1974. [Online]. Available:
[9] H. Schlichting and K. Gersten, Boundary-Layer Theory. Springer, 2016. [Online]. Available:
[10] D. C. Wilcox, Turbulence Modeling for CFD. DCW Industries, Incorporated, 1994. [Online]. Available:
[11] A. L. Tolentino, J. Ferreira, M. Parco, L. Lacruz, and V. Marcano, “Simulación numérica del flujo sobre-expandido en la tobera cónica experimental ULA-1A XP,” Unviversidad, Ciencia y Tecnología, vol. 21, no. 84, pp. 126–133, 2017. [Online]. Available:
[12] V. Marcano, P. Benitez, C. La Rosa, L. La Cruz, M. A. Parco, J. Ferreira, R. Andrenssen, A. Serra Valls, M. Peñaloza, L. Rodríguez, J. E. Cárdenas, V. Minitti, and J. J. Rojas, “Progresos alcanzados en el proyecto universitario cohete sonda ULA,” Universidad, Ciencia y Tecnología, vol. 13, no. 53, pp. 305–316, 2009. [Online]. Available:
[13] L. Lacruz-Rincón, M. A. Parco-Brizuela, R. Santos-Luque, C. Torres-Monzón, J. Ferreira- Rodríguez, and P. Benítez-Díaz, “Análisis experimental de las oscilaciones de presión interna en un motor de combustible solido para cohete sonda,” Ciencia e Ingeniería, vol. 13, no. 53, 2016. [Online]. Available:
[14] Universidad de los Andes. Programa espacial ULA. [Online]. Available:
[15] S. L. Tolentino Masgo and R. Nakka, “Simulación del flujo supersónico en la tobera del motor cohete Helios-X de categoría amateur,” in Jornadas de Investigación, 2019. [Online]. Available:
[16] R. Nakka. Richard Nakka’s experimental rocketry web site. [Online]. Available:
[17] F. R. Menter, “Two equation eddy-viscosity turbulence models for engineering applications,” Aerospace Research Central, vol. 32, no. 8, pp. 1598–1605, 2012. [Online]. Available:
[18] A. Balabel, A. M. Hegab, M. Nasr, and S. M. El-Behery, “Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle,” Applied Mathematical Modelling, vol. 35, no. 7, pp. 3408–3422, 2011. [Online]. Available:
[19] S. L. Tolentino Masgo, “Evaluación de modelos de turbulencia para el flujo de aire en una tobera plana,” INGENIUS, no. 22, pp. 25–37, 2019. [Online]. Available:
[20] Y. Liu, J. Wu, and L. Lu, “Performance of turbulence models for transonic flows in a diffuser,” Modern Physics Letters B, vol. 30, no. 25, p. 1650326, 2016. [Online]. Available:
[21] S. L. B. Tolentino Masgo, “Evaluación de modelos de turbulencia para el flujo de aire en un difusor transónico,” Revista Politécnica, vol. 45, no. 1, pp. 25–38, abr. 2020. [Online]. Available:
[22] Y. Zhang, H. Chen, M. Zhang, M. Zhang, Z. Li, and S. Fu, “Performance prediction of conical nozzle using navier–stokes computation,” Journal of Propulsion and Power, vol. 31, no. 1, pp. 192–203, 2015. [Online]. Available:
[23] R. Jia, Z. Jiang, and W. Zhang, “Numerical analysis of flow separation and side loads of a conical nozzle during staging,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 230, no. 5, pp. 845–855, 2016. [Online]. Available:
[24] H. Ding, C. Wang, and G. Wang, “Transient conjugate heat transfer in critical flow nozzles,” International Journal of Heat and Mass Transfer, vol. 104, pp. 930–942, 2017. [Online]. Available:
[25] A. K. Mubarak and P. S. Tide, “Design of a double parabolic supersonic nozzle and performance evaluation by experimental and numerical methods,” Aircraft Engineering and Aerospace Technology, vol. 91, no. 1, pp. 145–156, Dec. 2020. [Online]. Available:
[26] R. H. Pletcher, J. C. Tannehill, and D. Anderson, Computational Fluid Mechanics and Heat Transfer. CRC Press, 2012. [Online]. Available:
[27] D. Munday, E. Gutmark, J. Liu, and K. Kailasanath, Flow Structure of Supersonic Jets from Conical C-D Nozzles. [Online]. Available:
[28] J. Östlund and B. Muhammad-Klingmann, “Supersonic Flow Separation with Application to Rocket Engine Nozzles ,” Applied Mechanics Reviews, vol. 58, no. 3, pp. 143–177, 05 2005. [Online]. Available: