Numerical analysis of the over-expanded flow in the experimental conical nozzle ULA-1B out of design

Authors

  • San Luis Baudilio Tolentino Masgo Centro de Estudios Energéticos, Universidad Nacional Politécnica "Antonio José de Sucre" Vice-Rectorado Puerto Ordaz, Bolívar, Venezuela. Grupo de Modelamiento Matemático y Simulación Numérica, Universidad Nacional de Ingeniería, Lima, Perú. http://orcid.org/0000-0001-6320-6864
  • Omar González Campos Universidad Nacional Hermilio Valdizán, Huánuco, Perú. Grupo de Modelamiento Matemático y Simulación Numérica, Universidad Nacional de Ingeniería, Lima, Perú. http://orcid.org/0000-0002-1399-1291

DOI:

https://doi.org/10.21501/21454086.3836

Keywords:

Oblique shock, Fluctuation, Over-expanded flow, Throat length, RANS model, Turbulence model, Flow pattern, Flow separation, Simulation, Conical nozzle.

Abstract

In supersonic nozzles, different flow patterns occur and their behavior is influenced by the geometries of the internal surfaces of the walls. In the present work, the over-expanded flow field is simulated in 2D in the experimental ULA-1B conical nozzle out of design, for two cases of throat lengths:Lg =15 mm and Lg= 1 mm; in order to analyze the field of Mach number, pressure and temperature. The ANSYS-Fluent code was used and the RANS model was applied; the governing equations: conservation of mass, momentum, energy, and state; as well as the Menter turbulence model and the Sutherland equation for the viscosity as a function of temperature. In the longest throat section, the results showed oblique shocks, speed, pressure and temperature fluctuations; for the shorter throat there were no fluctuations; for both cases, the flow in the divergent presented speed peaks in the range of 2,5 - 3 Mach. It is concluded that, for the shorter throat length, the flow accelerates without disturbances in said section; in the divergent there is a supersonic jet and flow separation.

Downloads

Download data is not yet available.

References

G. P. Sutton and O. Biblarz, Rocket propulsion elements, 9th ed., New York, USA: John Wiley & Sons, 2016.

J. D. Anderson, Fundamentals of aerodynamics, 6th ed., New York, USA: McGraw-Hill, 2017.

T. V. Karman, “The fundamentals of the statistical theory of turbulence”, Journal of the Aeronautical Sciences, vol. 4, no. 4, pp. 131–138, 1937, doi: https://doi.org/10.2514/8.350

H. Schlichting and G. Klaus, Boundary-layer theory, 9th ed., Berling Heidelberg, Germany: Springer-Verlag, 2017.

P. Krehl and S. Engemann, “August Toepler —the first who visualized shock waves”, Shock Waves, vol. 5, no. 1, pp. 1-18, 1995, doi: https://doi.org/10.1007/BF02425031

G. S. Settles, “Toma ultrarrápida de imágenes de ondas de choque, explosiones y disparos”. Revista Investigación y Ciencia, no. 356, pp. 74-83, may, 2006, http://www.investigacionyciencia.es/revistas/investigacion-y-ciencia/genes-de-la-longevidad-419/toma-ultrarrpida-de-imgenes-de-ondas-de-choque-explosiones-y-disparos-5828

J. Blazek, Computational fluid dynamics: principles and applications, 3rd ed., Oxford, United Kingdom: Butterworth-Heinemann, 2015.

B. Andersson, et al., Computational Fluid Dynamics, Engineers. Cambridge University Press, 2012.

V. Marcano, et al., “Progresos alcanzados en el proyecto universitario cohete sonda ULA”, Revista Universidad, Ciencia y Tecnología, vol. 13, no. 53, pp. 305–316, 2009, http://uct.unexpo.edu.ve/index.php/uct/article/view/109

L. Lacruz, M. A. Parco, R. Santos, C. Torres, J. Ferreira y P. Benítez, “Análisis experimental de las oscilaciones de presión interna en un motor de combustible sólido para cohete sonda”, Revista Ciencia y Tecnología, vol. 37, no. 2, pp. 81–88, 2016, http://erevistas.saber.ula.ve/index.php/cienciaeingenieria/article/view/7443

M. A. Parco, “Análisis experimental de temperaturas en la tobera de un motor de cohete de combustible sólido”. Trabajo de Grado de Maestría, dirigido por P. R. Benítez, Facultad de Ingeniería, Universidad de Los Andes, Mérida, Venezuela, 2014.

S. L. Tolentino, J. Ferreira, M. A. Parco, L. Lacruz y V. Marcano, “Simulación numérica del flujo sobre-expandido en la tobera cónica experimental ULA-1A XP”, Revista Universidad, Ciencia y Tecnología, vol. 21, no. 84, pp. 126–133, 2017, http://www.uct.unexpo.edu.ve/index.php/uct/article/view/803

S. L. Tolentino, M. A. Parco, S. Caraballo, L. Lacruz, V. Marcano, J. Ferreira y J. Mírez, “Análisis numérico del comportamiento del flujo en la sección de la garganta de una tobera cónica experimental”, Revista Enfoque UTE, vol. 12, no. 1, pp. 12-28, 2021, doi: https://doi.org/10.2909/enfoqueute.676

S. L. Tolentino, y J. Mírez, “Análisis numérico del flujo sobrexpandido en la tobera cónica experimental ULA-2 fuera de diseño”, Lámpsakos, no 24, pp. 33-47, 2020, doi: https://doi.org/10.21501/214540863707

C. A. Hunter, “Experimental, theoretical, and computational investigation of separated nozzle flows”, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference  exhibit, Cleveland, OH, July 1998. Disponible en: https://doi.org/10.2514/6.1998-3107

S. Verma, M. Chidambaranatathan and A. Hadjadj, “Analysis of shock unsteadiness in a supersonic over-expanded planar nozzle”, European Journal of Mechanics/B Fluids, vol. 68, pp. 55-65, 2018, doi: https://doi.org/10.1016/j.euromechflu.2017.11.005

E. Martelli, P. P. Ciottoli, L. Saccoccio, F. Nasuti, M. Valorani and M. Bernardini, “Characterization of unsteadiness in an overexpanded planar nozzle”, AIAA Journal, vol. 57, no. 1, pp. 239-251, 2019, doi: https://doi.org/10.2514/1.J057162

P. P. Nair, A. Suryan and H. Dong, “Computational study on reducing flow asymmetry in over-expanded planar nozzle by incorporating double divergence”, Aerospace Science and Technology, vol. 100, pp. 1-18, 2020, doi: https://doi.org/10.1016/j.ast.2020.105790

ANSYS, “Ansys Fluent 2019 R1: Theory guide”, [Online]. Available: https://go-pdf.online/out/2BE079D/ansys-fluent-theory-guide.pdf, [consultado el 5 de julio de 2020].

F. White, Fluids Mechanics, 8th ed., New York, USA: McGraw-Hill Education, 2016.

J. Anderson, Hipersonic and high temperature gas dynamics, Virginia, USA: AIAA, 2019.

W. Sutherland, “The viscosity of gases and molecular force”, Philosophical Magazine series 5, vol. 36, no. 223, pp. 507–531, 1893, doi: https://doi.org/10.1080/14786449308620508

F. R. Menter, “Two equation eddy-viscosity turbulence models for engineering applications”, AIAA Journal, vol. 32, no. 8, pp. 1598–1605, 1994, doi: https://doi.org/10.2514/3.12149

S. L. Tolentino, “Evaluation of turbulence models for the air flow in a planar nozzle”, Revista INGENIUS, no. 22, pp. 25–37, 2019, doi: https://doi.org/10.17163/ings.n22.2019.03

S. L. Tolentino, “Evaluación de modelos de turbulencia para el flujo de aire en un difusor transónico”, Revista Politécnica, vol. 45, no. 1, pp. 25-38, 2020, doi: https://doi.org/10.33333/rp.vol45n1.03

Y. A. Cengel and J. M. Cimbala, Fluid mechanics: Fundamentals and applications, 4th ed., New York, USA: McGraw-Hill, 2017.

C. Génin, A. Gernoth and R. Stark, “Experimental and numerical study of heat flux in dual bell nozzles”, Journal of Propulsion and Power, vol. 29, no. 1, pp. 21-26, 2013, doi: https://doi.org/10.2514/1.B34479

H. Ding, C. Wang and G. Wang, “Transient conjugate heat transfer in critical flow nozzle”, International Journal of Heat and Mass transfer, vol. 104, pp. 930-942, 2017, doi: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.09.021

R. Arora, and R. Vaidyanathan, “Experimental investigation of flow through planar double divergent nozzles”. Acta Astronautica, vol. 112, pp. 200-216, 2015, doi: https://doi.org/10.1016/j.actaastro.2015.03.020

B. Zebiri, A. Piquet, and A. Hadjadj, “Analysis of shock-wave unsteadiness in conical supersonic nozzle”, Aerospace Science and Technology, vol. 105, pp. 1-15, 2020, doi: https://doi.org/10.1016/j.ast.2020.106060

J. Östlund and B. Muhammed, “Supersonic flow separation with application to rocket engine nozzles”, ASME, Applied Mechanics Reviews, vol. 58, no. 3, pp. 143-177, 2005, doi: https://doi.org/10.1115/1.1894402

S. L. Tolentino, R. Nakka, S. Caraballo y J. Mírez, “Numerical simulation of the flow under-expanded flow in the experimental conical nozzle helios-x”, Revista INGENIUS, no. 25, pp. 81-93, 2021, doi: https://doi.org/10.17163/ings.n25.2021.08

Published

2021-04-21

How to Cite

Tolentino Masgo, S. L. B., & González Campos, O. (2021). Numerical analysis of the over-expanded flow in the experimental conical nozzle ULA-1B out of design. Lámpsakos, (25), e–3836. https://doi.org/10.21501/21454086.3836

Issue

Section

Articles of scientific and technological research