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Investigation of conjugate circular arcs in rocket nozzle contour design

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Abstract

The use of conjugate circular arcs in rocket nozzle contour design has been investigated by numerically comparing three existing sub-scale nozzles to a range of equivalent arc-based contour designs. Three performance measures were considered when comparing nozzle designs: thrust coefficient, nozzle exit wall pressure, and a transition between flow separation regimes during the engine start-up phase. In each case, an equivalent arc-based contour produced an increase in the thrust coefficient and exit wall pressure of up to 0.4 and 40% respectively, in addition to suppressing the transition between a free and restricted shock separation regime. A general approach to arc-based nozzle contour design has also been presented to outline a rapid and repeatable process for generating sub-scale arc-based contours with an exit Mach number of 3.8–5.4 and a length between 60 and 100% of a 15\(^{\circ }\) conical nozzle. The findings suggest that conjugate circular arcs may represent a viable approach for producing sub-scale rocket nozzle contours, and that a further investigation is warranted between arc-based and existing full-scale rocket nozzles.

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References

  1. Vuillermoz, P., Weiland, C., Hagemann, G., Aupoix, B., Grosdemange, H., Bigert, M.: Nozzle design and optimization. In: Yang, V., Habiballah, M., Hulka, J., Popp, M. (eds.) Progress in Astronautics and Aeronautics: Liquid Rocket Thrust Chambers, pp. 469–492. American Institute of Aeronautics and Astronautics, Reston (2004). https://doi.org/10.2514/5.9781600866760.0469.0492

    Google Scholar 

  2. Shapiro, A.: Nozzles for supersonic flow without shock fronts. J. Appl. Mech. 11(2), 93–100 (1944)

    Google Scholar 

  3. Ahlberg, J., Hamilton, S., Migdal, D., Nilson, E.: Truncated perfect nozzles in an optimum nozzle design. ARS J. 31(5), 614–620 (1961). https://doi.org/10.2514/8.5577

    Article  Google Scholar 

  4. Gogish, L.: A study of short supersonic nozzles. Fluid Dyn. 1(2), 122–126 (1966). https://doi.org/10.1007/bf01013838

    Article  Google Scholar 

  5. Watanabe, Y., Sakazume, N., Yonezawa, K., Tsujimoto, Y.: LE7A engine nozzle flow separation phenomena and a method of RSS suppression with a step inside nozzle. J. Jpn. Soc. Aeronaut. Space Sci. 55(645), 474–482 (2007). https://doi.org/10.2322/jjsass.55.474

    Google Scholar 

  6. Guderley, G., Hantsch, E.: Beste Formen fur Aschsensymmetrische Uberschallschubdusen. Zeitschrift fur Flugwissenschaften 3, 305–313 (1955)

    MATH  Google Scholar 

  7. Rao, G.: Exhaust nozzle contour for optimum thrust. Jet Propuls. 28(6), 377–382 (1958). https://doi.org/10.2514/8.7324

    Article  Google Scholar 

  8. Rao, G.: Approximation of optimum thrust nozzle contour. ARS J. 30(6), 561 (1960)

    Google Scholar 

  9. Nave, L., Coffey, G.: Sea level side loads in high-area-ratio rocket engines. In: 9th AIAA Joint Propulsion Conference, AIAA Paper 73-1284 (1973). https://doi.org/10.2514/6.1973-1284

  10. Sutton, G.: History of Liquid Propellant Rocket Engines, pp. 91–92. American Institute of Aeronautics and Astronautics, Reston (2006). https://doi.org/10.2514/4.868870

    Book  Google Scholar 

  11. Sternin, L.: Analysis of the thrust characteristics of jet nozzles designed by various methods. Fluid Dyn. 35(1), 123–131 (2000). https://doi.org/10.1007/bf02698797

    Article  MATH  Google Scholar 

  12. Davis, D.: Investigation of optimization techniques for solid rocket motor nozzle contours. In: 18th AIAA Joint Propulsion Conference, AIAA Paper 82-1188 (1982). https://doi.org/10.2514/6.1982-1188

  13. Sutton, G., Biblarz, O.: Rocket Propulsion Elements, pp. 27–102. Wiley, Hoboken (2010)

    Google Scholar 

  14. Schomberg, K., Doig, G., Olsen, J.: Design of high area nozzle contours using circular arcs. J. Propul. Power 32(1), 188–195 (2016). https://doi.org/10.2514/1.b35640

    Article  Google Scholar 

  15. Schomberg, K., Olsen, J., Neely, A., Doig, G.: Suppressing restricted shock separation in thrust-optimized rocket nozzles using contour geometry. J. Propul. Power 32(5), 1298–1301 (2016). https://doi.org/10.2514/1.b36059

    Article  Google Scholar 

  16. Stark, R., Hagemann, G.: Current status of flow prediction for separated nozzle flows. In: 2nd European Conference for Aerospace Sciences, pp. 1–8 (2007)

  17. Ostlund, J.: Flow Processes in Rocket Engine Nozzles with Focus on Flow Separation and Side-Loads. Royal Institute of Technology, Stockholm (2002)

    Google Scholar 

  18. Nguyen, A., Deniau, H., Girard, S., Alziary De Roquefort, T.: Unsteadiness of flow separation and end-effects regime in a thrust-optimized contour rocket nozzle. Flow Turbul. Combust. 75, 161–181 (2003). https://doi.org/10.1023/b:appl.0000014927.61427.ad

    Article  MATH  Google Scholar 

  19. Spalart, P., Allmaras, S.: A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale 1(5), 5–21 (1992)

    Google Scholar 

  20. Sutherland, W.: The viscosity of gases and molecular force. Philos. Mag. 36, 507–531 (1893). https://doi.org/10.1080/14786449308620508

    Article  MATH  Google Scholar 

  21. Roache, P.J.: Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid Mech. 29, 123–160 (1997). https://doi.org/10.1146/annurev.fluid.29.1.123

    Article  MathSciNet  Google Scholar 

  22. Meijer, J., Van Beek, C.: Analysis of Ariane 5 Base Flow Measurements in the NLR/PHST and FFA/T1500 Wind Tunnels, NLR-CR 99449, National Aerospace Laboratory (1999)

  23. Wang, T., Guidos, M.: Transient three-dimensional side-load analysis of a film-cooled nozzle. J. Propul. Power 25(6), 1272–1280 (2009). https://doi.org/10.2514/1.41025

    Article  Google Scholar 

  24. Software Engineering Associates (SEA) Inc., Two-Dimensional Kinetics (TDK) Nozzle Performance Computer Program Users Manual, pp. 4–19 (2007)

  25. Schomberg, K., Olsen, J., Neely, A., Doig, G.: Design of an arc-based thrust-optimized nozzle contour. In: 6th European Conference for Aerospace Sciences, pp. 1–8 (2015)

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Correspondence to K. Schomberg.

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Communicated by H. Olivier and A. Higgins.

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Schomberg, K., Olsen, J., Neely, A. et al. Investigation of conjugate circular arcs in rocket nozzle contour design. Shock Waves 29, 401–413 (2019). https://doi.org/10.1007/s00193-018-0834-0

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