Comparative analysis of flow patterns in off-design planar and conical nozzle

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Published: Mar 12, 2025
Updated: 2025-03-12
Versions:
2025-03-12 (3)
DOI: https://doi.org/10.17163/ings.n33.2025.10
Keywords:
Flow fluctuations, RANS model, SAS turbulence model, Shock wave, Flow patterns, Off-design nozzles

Main Article Content

San L. Tolentino
Universidad Nacional de Ingeniería
https://orcid.org/0000-0001-6320-6864
Jorge Mírez
Universidad Nacional de Ingeniería
https://orcid.org/0000-0002-5614-5853

Abstract

This study aims to analyze the behavior of Mach number and pressure field flow patterns in off-design planar and conical nozzles with a divergent half-angle of 10.85°. Numerical simulations of the flow field were conducted using the ANSYS-Fluent R16.2 software, employing the RANS model and the SAS turbulence model under transient flow conditions. The nozzle pressure ratios (NPR) ranged from 1.97 to 8.91. The results reveal differences in flow patterns, including Mach number and static pressure, between the two nozzle types. Notably, normal shock fronts exhibited varying positions for the same NPR values. The maximum peak flow fluctuation along the centerline of the conical nozzle's divergent section reached Mach 2.844, compared to Mach 2.011 in the planar nozzle, indicating lower flow velocity in the latter. At the nozzle outlet, the flow velocity of the conical nozzle was Mach 2.535, representing a 27.32% increase compared to the planar nozzle, which achieved Mach 1.991. Additionally, the throat area significantly influenced mass flow transit, with the planar nozzle having a larger throat area than the conical nozzle. These findings provide insights into the impact of nozzle geometry on flow characteristics under off-design conditions.

Article Details

Issue
No. 33 (2025): january-june
Section
Scientific Paper
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References

G. P. Sutton and O. Biblarz, Rocket Propulsion Elements. John Wiley & Sons, 2016. [Online]. Available: https://upsalesiana.ec/ing33ar10r1

G. Scarlatella, M. Tajmar, and C. Bach, “Advanced nozzle concepts in retro-propulsion applications for reusable launch vehicle recovery: a case study,” in 72nd International Astronautical Congress (IAC), Dubai, United Arab Emirates, 2021. [Online]. Available: https://upsalesiana.ec/ing33ar10r2

G. Hagemann, A. Preuss, J. Kretschmer, F. Grauer, M. Frey, R. Ryden, and R. Stark, Technology Investigation for High Area Ratio Nozzle Extensions. 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. [Online]. Available: https://doi.org/10.2514/6.2003-4912

F. J. Malina, “Characteristics of the rocket motor unit based on the theory of perfect gases,” Journal of the Franklin Institute, vol. 230, no. 4, pp. 433–454, 1940. [Online]. Available: https://doi.org/10.1016/S0016-0032(40)91348-5

S. Zivkovic, m. Milinovic, and N. Adamec, “Eksperimentalno i numericko istrazivanje supersonicnog ravanskog mlaznika sa vektorisanim potiskom mehanickim preprekama,” FME Transactions, vol. 42, no. 3, pp. 205–211, 2014. [Online]. Available: https://doi.org/10.5937/fmet1403205Z

C. A. Hunter, “Experimental investigation of separated nozzle flows,” Journal of Propulsion and Power, vol. 20, no. 3, pp. 527–532, 2004. [Online]. Available: https://doi.org/10.2514/1.4612

J. D. Anderson, Hypersonic and High-Temperature Gas Dynamics, Third Edition. AIAA Education Series, 2019. [Online]. Available: https://doi.org/10.2514/5.9781624105142.0000.0000

K. Q. Zaman and A. F. Fagan, Flow, noise and thrust of supersonic plug nozzles. AIAA SCITECH, 2024. [Online]. Available: https://doi.org/10.2514/6.2024-2305

J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics. Springer Berlin, Heidelberg, 2012. [Online]. Available: https://doi.org/10.1007/978-3-642-56026-2

H. Schlichting and K. Gersten, Boundary- Layer Theory. Springer Berlin, Heidelberg, 2016. [Online]. Available: https://doi.org/10.1007/978-3-662-52919-5

S. L. Tolentino, “Comparative analysis of 2d simulations and isentropic equations for compressible flow in experimental nozzles,” INCAS BULLETIN, vol. 15, pp. 111–125, 09 2023. [Online]. Available: https://doi.org/10.13111/2066-8201.2023.15.3.9

——, “Empirical equation of the mach number as a function of the stagnation pressure ratio for a quasi- one-dimensional compressible flow,” FME Transactions, vol. 51, 03 2023. [Online]. Available: http://dx.doi.org/10.5937/fme2302149T

J. Majdalani and B. Maicke, “Explicit inversion of stodola’s area-mach number equation,” Journal of Heat Transfer, vol. 133, p. 071702, 07 2011. [Online]. Available: http://dx.doi.org/10.1115/1.4002596

A. Ferrari, “Exact solutions for quasi-onedimensional compressible viscous flows in conical nozzles,” Journal of Fluid Mechanics, vol. 915, p. A1, 2021. [Online]. Available: https://doi.org/10.1017/jfm.2020.1158

S. L. Tolentino, J. Mírez Tarrillo, and S. Caraballo F., “Numerical analysis of the shock train in conical nozzles with straightcut throats,” FME Transactions, vol. 52, pp. 186–195, 01 2024. [Online]. Available: http://dx.doi.org/10.5937/fme2402186T

P. Krehl and S. Engemann, “August toepler aE” the first who visualized shock waves,” Shock Waves, vol. 5, no. 1, pp. 1–18, Jun 1995. [Online]. Available: https://doi.org/10.1007/BF02425031

C. Génin, R. Stark, and S. Karl, “Shock system deformation in high mach number rocket nozzles,” in 31st International Symposium on Shock Waves 2, A. Sasoh, T. Aoki, and M. Katayama, Eds. Cham: Springer International Publishing, 2019, pp. 543–549. [Online]. Available: https://doi.org/10.1007/978-3-319-91017-8_69

S. B. Verma and C. Manisankar, “Origin of flow asymmetry in planar nozzles with separation,” Shock Waves, vol. 24, no. 2, pp. 191–209, Mar 2014. [Online]. Available: https://doi.org/10.1007/s00193-013-0492-1

J. O¨stlund and B. Muhammad-Klingmann, “Supersonic flow separation with application to rocket engine nozzles,” Applied Mechanics Reviews, vol. 58, no. 3, pp. 143–177, May 2005. [Online]. Available: https://doi.org/10.1115/1.1894402

V. Zmijanovic, A. Chpoun, and B. Rasuo, “Flow separation modes and side phenomena in an overexpanded nozzle,” FME Transactions, vol. 40, pp. 111–118, 06 2012. [Online]. Available: https://upsalesiana.ec/ing33ar10r21

A. Hadjadj, O. Ben-Nasr, M. Shadloo, and A. Chaudhuri, “Effect of wall temperature in supersonic turbulent boundary layers: A numerical study,” International Journal of Heat and Mass Transfer, vol. 81, pp. 426–438, 2015. [Online]. Available: https://doi.org/10.1016/j.ijheatmasstransfer.2014.10.025

R. Zangeneh, “Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer,” International Journal of Heat and Fluid Flow, vol. 92, p. 108876, 2021. [Online]. Available: https://doi.org/10.1016/j.ijheatfluidflow.2021.108876

S. L. Tolentino, J. Mírez, and O. González, “Numerical analysis of the flow field in a planar nozzle for different divergent angles,” Journal of Mechanical Enginnering and Sciences (JMES), vol. 16, no. 4, pp. 9241–9252, 2022. [Online]. Available: https://doi.org/10.15282/jmes.16.4.2022.07.0731

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

S. L. Tolentino, J. Mírez, and S. A. Caraballo, “Numericka analiza evolucije udarnog voza u planarnim mlaznicama sa duzinom grla,” FME Transactions, vol. 51, no. 4, pp. 595–605, 2023. [Online]. Available: https://doi.org/10.5937/fme2304595T

M. L. Mason, L. E. Putnam, and R. J. Re, The effect of throat contouring on two-dimensional converging-diverging nozzles at static conditions. NASA Technical Paper 1704, 1980. [Online]. Available: https://upsalesiana.ec/ing33ar10r27

S. L. Tolentilo and J. Mirez, “Efekat dužine grla na obrasce protoka u konusnim mlaznicama van dizajna,” FME Transactions, vol. 50, no. 2, pp. 271–280, 2022. [Online]. Available: https://doi.org/10.5937/fme2201271T

B. Wagner and S. Schlechtriem, Numerical and Experimental Study of the Flow in a Planar Expansion-Deflection Nozzle. 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2011. [Online]. Available: https://doi.org/10.2514/6.2011-5942

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, Nov 2005. [Online]. Available: https://doi.org/10.1007/s00193-005-0269-2

M. Faheem, A. Khan, R. Kumar, S. Afghan Khan, W. Asrar, and A. M. Sapardi, “Experimental study on the mean flow characteristics of a supersonic multiple jet configuration,” Aerospace Science and Technology, vol. 108, p. 106377, 2021. [Online]. Available: https://doi.org/10.1016/j.ast.2020.106377

(ANSYS-Fluent). (2023) Ansys fluent theory guide 2020r1. Ansys Innovation Space. [Online]. Available: https://upsalesiana.ec/ing33ar10r32

F. M. White, Fluid Mechanics. Mc-Graw Hill, 2011. [Online]. Available: https://upsalesiana.ec/ing33ar10r33

Y. Egorov, F. R. Menter, R. Lechner, and D. Cokljat, “The scale-adaptive simulation method for unsteady turbulent flow predictions. part 2: Application to complex flows,” Flow, Turbulence and Combustion, vol. 85, no. 1, pp. 139–165, Jul 2010. [Online]. Available:

https://doi.org/10.1007/s10494-010-9265-4

P. R. Spalart, S. Deck, M. L. Shur, K. D. Squires, M. K. Strelets, and A. Travin, “A new version of detached-eddy simulation, resistant to ambiguous grid densities,” Theoretical and Computational Fluid Dynamics, vol. 20, no. 3, pp. 181–195, Jul 2006. [Online]. Available: https://doi.org/10.1007/s00162-006-0015-0

F. Menter, M. Kuntz, and R. B. Langtry, “Ten years of industrial experience with the sst turbulence model,” Heat and Mass Transfer, vol. 4, 01 2003. [Online]. Available: https://upsalesiana.ec/ing33ar10r36

S. Tsan-Hsing, W. L. William, S. Aamir, Y. Zhigang, and Z. Jiang, “A new k-E eddy viscosity model for high reynolds number turbulent flows,” Computers & Fluids, vol. 24, no. 3, pp. 227–238, 1995. [Online]. Available: https://doi.org/10.1016/0045-7930(94)00032-T