Numerical analysis of the flow field in a planar nozzle for different divergent angles

Authors

  • S. L. Tolentino Faculty of Mechanical Engineering, National Experimental Polytechnic University “AJS” Vice-Rectorate (UNEXPO) Puerto Ordaz, Bolívar, Venezuela
  • J. Mírez Group of Mathematical Modelling and Numerical Simulation (GMMNS), Faculty of Oil, Natural Gas and Petrochemical Engineering, Universidad Nacional de Ingeniería (UNI), Lima, Peru https://orcid.org/0000-0002-5614-5853
  • O. González Faculty of Civil Engineering, National University Hermilio Valdizán (UNHEVAL), Huánuco, Perú https://orcid.org/0000-0002-1399-1291

DOI:

https://doi.org/10.15282/jmes.16.4.2022.07.0731

Keywords:

Cold flow, Internal shock, Mach number, Numerical simulation, Planar nozzle, RANS model, Turbulence model

Abstract

In the present work, the flow field is analysed for Mach number, pressure and temperature in 2D computational domains for a planar nozzle of symmetrical geometry as used in the experimental tests for cold (air) flow. The study has been considered for three mean angles of the divergent section: α = 9°, α = 11.01° and α = 13°, and for four pressure ratios: NPR = 2.412, NPR = 3.413, NPR = 5.423 and NPR = 8.78. For the numerical simulation of the turbulence in the presence of shock waves, the RANS model, the Sutherland equation and the Spalart-Allmaras turbulence model were used in the ANSYS-Fluent R16.2 code. The results obtained show fluctuations at the intersections of the internal shocks in the divergent, and the fluctuation decreases as the angle of the divergent increases. For NPR = 3.413, NPR = 5.423 and NPR = 8.78, the Mach number at the nozzle exit is the same, where for α = 11.01° Mach 2.00 was obtained, and based on this reference, for α = 13° there is an increase in velocity of 4.15% and for α = 9° a decrease in velocity of 3.78%. The lowest pressure and temperature drop occurs at the nozzle outlet for α = 13°.

References

G. P. Sutton, and O. Biblarz, Rocket propulsion elements. John Wiley and Sons, New York, 2016.

H. Schlichting, and K. Gersten, Boundary-layer theory, Berlin Heidelberg, Germany, Springer Verlag, 9th ed., 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.

J. D. Anderson, Fundamentals of aerodynamics, McGraw-Hill Education, New York, 2017.

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.

C. Génin, and R. Stark, "Hot Flow Testing of Dual Bell Nozzles," In 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. pp. 1-8, 2011.

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, 2005.

S. Ristić, M. Kozić, and M. Puharić, "Experimental and numerical investigation of flow separation in a supersonic nozzle," Journal of Russian Laser Research, vol 29, no. 4, pp. 377–389, 2008.

L. Li, and T. Saito, "Numerical and experimental investigations of fluidic thrust vectoring mechanism," International Journal of Aerospace Innovations, vol. 4, pp. 53–64, 2012.

M. Sajben, T. Bogar, and J. Kroutil, "Forced oscillation experiments in supercritical diffuser flows with application to ramjet instabilities," 17th Joint Propulsion Conference, pp.1-12, july 21-29, 1981.

P. Krehl and S. Engemann, “August toepler —the first who visualized shock waves,” Shock Waves, vol. 5, no. 1, pp. 1–18, Jun 1995.

A. Shapiro, The dynamics and thermodynamics of compressible fluid flow, John Wiley and Sons, Volume I, 1953.

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

D. C. Wilcox, Turbulence modeling for CFD. C., California, USA: DCW Industries, 2006.

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.

S. L. Tolentino, "Evaluation of turbulence models for the air flow in a planar nozzle," INGENIUS, no. 22, pp. 25–37, 2019.

A. B. M. Toufique Hasan, “Characteristics of overexpanded nozzle flows in imposed oscillating condition,” International Journal of Heat and Fluid Flow, vol. 46, pp. 70–83, 2014.

V. M. K. Kotteda and S. Mittal, “Flow in a planar convergent–divergent nozzle,” Shock Waves, vol. 27, no. 3, pp. 441–455, May 2017.

S. Asbury, C. Gunther, and C. Hunter, "A passive cavity concept for improving the off-design performance of fixed-geometry exhaust nozzles," 32nd Joint Propulsion Conference and Exhibit. pp.1-31, july, 1996.

J. A. Owczarek, and D. O. Rockwell, (1972). "An Experimental Study of Flows in Planar Nozzles," Journal of Basic Engineering, vol. 94, no. 3, pp. 682-688, 1972.

A. Bourgoing, and P. Reijasse, "Experimental analysis of unsteady separated flows in a supersonic planar nozzle," Shock Waves, vol 14, no. 4, pp. 251–258, 2005.

D. Papamoschou, and A. Zill, "Fundamental Investigation of Supersonic Nozzle Flow Separation," 42nd AIAA Aerospace Sciences Meeting and Exhibit. pp.1-17, january 5-8, 2004.

S. B. Verma, and C. Manisankar, "Origin of flow asymmetry in planar nozzles with separation," Shock Waves, vol. 24, no. 2, pp. 191–209, 2014, doi: 10.1007/s00193-013-0492-1.

R. Arora, and A. Vaidyanathan, "Experimental investigation of flow through planar double divergent nozzles," Acta Astronautica, vol. 112, pp. 200–216, 2015.

O. Kostić, Z. A. Stefanović, and I. A. Kostić, "CFD modeling of supersonic airflow generated by 2D nozzle with and without an obstacle at the exit section," FME Transactions, vol. 43, no. 2, pp. 107-113, 2015.

B. Wagner, R. Stark, and S. Schlechtriem, "Experimental study of a planar expansion deflection nozzle," Progress in Propulsion Physics, vol. 2, pp. 641-654, 2011.

P. P. Nair, A. Suryan, and H. D. Kim, "Computational study on reducing flow asymmetry in over-expanded planar nozzle by incorporating double divergence," Aerospace Science and Technology, pp. 1-18, 2020.

ANSYS, Ansys Fluent 12.0 Theory guide, https://www.afs.enea.it/project/neptunius/docs/fluent

P. R. Spalart, and S. R. Allmaras, "A one-equation turbulence model for aerodynamic flows,” 30th Aerospace Sciences Meeting and Exhibit, 06 January, Reno, NV, U.S.A, pp. 1-22, 1992.

W. Sutherland, "LII. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical," Magazine and Journal of Science, vol. 36, no. 223, pp. 507–531, 1893.

D. C. Wilcox, “Reassessment of the scale determining equation for advanced turbulence models,” AIAA Journal, vol. 26, no. 11, pp. 1299–1310, 1988.

F. R. Menter, "Two-equation eddy-viscosity turbulence models for engineering applications," AIAA Journal, vol. 32, no. 8, pp. 1598–1605, 1994.

B. E. Launder, G. J. Reece, and W. Rodi, "Progress in the development of a Reynolds-stress turbulence closure," Journal of Fluid Mechanics, vol. 68, no. 3, pp. 537-566, 1975.

S. L. Tolentino, and J. Mírez, "Numerical analysis of over-expanded flow in the experimental ULA-2 conical nozzle out of design," Lámpsakos, no 24, pp. 33-47, 2020, (in Spanish).

S. L. Tolentino, M. A. Parco, S. Caraballo, L. Lacruz, V. Marcano, J. Ferreira, and J. Mírez, "Numerical analysis of the flow behavior in the throat section of an experimental conical nozzle," Enfoque UTE, vol. 12, no. 1, pp. 1228, 2021, (in Spanish).

S. L. Tolentino, and O. González, "Numerical analysis of the over-expanded flow in the experimental conical nozzle ULA-1B out of design," Lámpsakos, no. 24, pp. 33-47, 2021, (in Spanish).

S. L. Tolentino, and J. Mírez, “Throat length effect on the flow patterns in off-design conical nozzles,” FME Transactions, vol. 50, no. 2, pp. 271-282, 2022.

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Published

2022-12-27

How to Cite

[1]
San Luis Tolentino, J. Mírez, and O. González, “Numerical analysis of the flow field in a planar nozzle for different divergent angles”, J. Mech. Eng. Sci., vol. 16, no. 4, pp. 9241–9252, Dec. 2022.

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