Skip to main content
Log in

Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

The separated flow in an overexpanded nozzle featuring a restricted shock separation is investigated numerically using delayed detached eddy simulation and compared with the experimental data of Nguyen et al. (Int J Flow Turbul Combust 71(1):161–181, 2003). First, the enormous cost of a Large Eddy Simulation for such a nozzle flow is assessed before being performed to motivate the practical need for using an hybrid RANS/LES method. The calculation is then used to investigate the “end-effect” regime which involves a strong global unsteadiness with very large amplitude fluctuations of about 15–20% of nozzle divergent length. The flow regime is characterized by high wall pressure fluctuations which are hopefully nearly axisymmetric. The main properties (rms levels, amplitude of displacement of the separation) of the motion are rather well reproduced by DDES compared to the experiment. However, a major difference lies in the frequency of the computed motion which is higher than in the experiment. This major discrepancy is currently not explained by the author. The properties of the side-loads are also briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Reijasse, Ph., Morzenski, M., Naudin, P., Geneau, F.: Fluctuating side-load measurements in overexpanded subscale rocket-nozzles. AIAA Paper 2001-3557 (2001)

  2. Munier, D., Garcon, F., Champigny, P., Deck, S., Hallard, R.: Side load measurements on subscale launcher nozzles. In: Proceedings of the 4th International Conference on Launcher Technology ‘Space Launcher Liquid Propulsion’, Liège, Belgium (2002)

  3. Ostlund J., Damgaard T., Frey M.: Side-load phenomena in highly overexpanded rocket nozzles. AIAA J. Propuls. Power 20(4), 695–704 (2004)

    Article  Google Scholar 

  4. Nave, L.H., Coffey, G.A.: Sea level side loads in high-area-ratio rocket engines. AIAA Paper 73-1284, 9th AIAASAE Propulsion Conference, Las Vegas, Nevada, November 1973

  5. Mattson, J., Hogman, U., Torngren, L.: A sub scale test program on investigation of flow separation and side loads in rocket nozzles. In: Proceeding of the third European Symposium on Aerothermodynamics for Space Vehicles, Noordwijk, The Nederlands, pp. 273–378, November 1998

  6. Nguyen, A.T., Deniau, H., Girard, S., Alziary, de Roquefort, T.: Wall pressure fluctuations in an over-expanded supersonic nozzle. AIAA Paper 02-4001, 38th AIAA Joint Propulsion Conference and Exhibit, Indianapolis, IN (2002)

  7. Frey, M., Stark, R., Ciezki, H.K., Quessard, F., Kwan, W.: Subscale Nozzle Testing at the P6.2 Test Stand. AIAA Paper 00-3777, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, Alabama, 17–19 July 2000

  8. Hunter C.A.: Experimental investigation of separated nozzle flows. AIAA J. Propuls. Power 20(3), 527–532 (2004)

    Article  Google Scholar 

  9. Reijasse, Ph., Morzenski, M., Blacodon, D., Birkemeyer, J.: Flow separation experimental analysis in overexpanded subscale rocket-nozzles. AIAA Paper 2001-3556 (2001)

  10. Chen C.L., Chakravarthy S.R., Hung C.M.: Numerical investigation of separated nozzle flows. AIAA J. 32(9), 1836–1843 (1994)

    Article  Google Scholar 

  11. Onofri, M., Nasuti, F., Bongiorno, M.: Shock generated vortices and pressure fluctuations in propulsive nozzles. AIAA Paper 98-0777 (1998)

  12. Onofri, M., Nasuti, F.: The physical origins of side loads in rocket nozzles. AIAA Paper 99-2587, 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Los Angeles, California, 20–24 June 1999

  13. Nasuti F., Onofri M.: Viscous and inviscid vortex generation during startup of rocket nozzles. AIAA J. 36(5), 809–815 (1998)

    Article  Google Scholar 

  14. Frey M., Hagemann G.: Restricted shock separation in rocket nozzles. AIAA J. Propuls. Power 16(3), 478–484 (2000)

    Article  Google Scholar 

  15. Hagemann G., Frey W., Koschel M.: Appearance of restricted shock separation in rocket nozzles. AIAA J. Propuls. Power 18(3), 577–584 (2002)

    Article  Google Scholar 

  16. Takayama K., Ben-Dor G.: The inverse Mach reflection. AIAA J. 43(12), 1853–1859 (1985)

    Article  MathSciNet  Google Scholar 

  17. Nguyen, A.T.: Décollement instationnaire et charges latérales dans les tuyères propulsives. PhD thesis, Université de Poitiers, Dpt Sciences de l’ingénieur, Poitiers, Juin 2005

  18. Nguyen A.T., Deniau H., Girard S., Alziaryde Roquefort T.: Unsteadiness of flow separation and end-effects regime in a thrust-optimized contour rocket nozzle. Int. J. Flow Turbul. Combust. 71(1), 161–181 (2003)

    Article  Google Scholar 

  19. Gross A., Weiland C.: Numerical simulation of separated cold gas nozzle flows. AIAA J. Propuls. Power 20(3), 509–519 (2004)

    Article  Google Scholar 

  20. Ostlund, J., Jaran, M.: Assessment of turbulence models in overexpanded rocket nozzle flow simulations. AIAA Paper 99-2583 (1999)

  21. Yonezawa, K., Yokota, K., Watanabe, Y., Tsujimoto, Y., Abe, T.: 2-D numerical simulation of side loads in rocket nozzles. In: 23rd International Symposium on Space Technology and Science, Matsue, Japan (2002)

  22. Takahashi, M., Ueda, S., Tomita, T., Takahashi, M., Tamura, H., Aoki, K.: Transient flow simulation of a compressed truncated perfect nozzle. AIAA Paper 01-34363, 37th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference, Salt Lake City, Utah, 8–11 July 2001

  23. Perigo, D., Schwane, R., Wong, H.: A numerical comparison of the flow in conventional and duall-bell nozzles in the presence of an unsteady external pressure environment. AIAA Paper 2003-4771 (2003)

  24. Alziary de Roquefort, T.: Low frequency fluctuations in separated turbulent compressible flows. Symposium on Advanced Fluid Information, Tokyo, Japan (2002)

  25. Nebbache A., Pilinski C.: Pulsatory phenomenon in a thrust-optimized contour nozzle. Aerosp. Sci. Technol. 10(4), 295–308 (2006)

    Article  Google Scholar 

  26. Deck S., Guillen Ph.: Numerical simulation of side loads in an ideal truncated nozzle. AIAA J. Propuls. Power 18(2), 261–269 (2002)

    Article  Google Scholar 

  27. Deck S., Garnier E., Guillen P.: Turbulence modelling applied to space launcher configurations. J. Turbul. 3(57), 1–21 (2002)

    Google Scholar 

  28. Yonezawa, K., Yokota, K., Tsujimoto, Y., Sakazume, N., Watanabe, Y.: Three-dimensionnal unsteady flow simulation of compressed truncated perfect nozzles. AIAA Paper 02-3991, 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Indianapolis, Indiana, 7–10 July 2002

  29. Deck S., Nguyen A.T.: Unsteady side loads in a thrust optimized contour nozzle at hysteresis regime. AIAA J. 42(9), 1878–1888 (2004)

    Article  Google Scholar 

  30. Shimizu T., Miyajima H., Kodera M.: Numerical study of restricted shock separation in a compressed truncated perfect nozzle. AIAA J. 44(3), 576–584 (2006)

    Article  Google Scholar 

  31. Wang, T.-S.: Transient three-dimensional analysis of side-load in liquid rocket engine nozzles. AIAA Paper 2003-4771 (2003)

  32. Péchier M., Guillen Ph., Caysac R.: Magnus effect over finned projectiles. AIAA J. Spacecr. Rockets 38(4), 542–549 (2001)

    Article  Google Scholar 

  33. Deck S., Duveau Ph., d’Espiney P., Guillen Ph.: Development and application of Spalart Allmaras one equation turbulence model to three-dimensional supersonic complex configurations. Aerosp. Sci. Technol. 6(3), 171–183 (2002)

    Article  Google Scholar 

  34. Spalart, P.R., Allmaras, S.R.: A one equation turbulence model for aerodynamic flows. La Recherche Aérospatiale, pp. 5–21 (1994)

  35. Spalart, P., Jou, W.H., Strelets, M., Allmaras, S.R.: Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. In: Proceedings of the 1st AFSOR International Conference on DNS/LES, Ruston, pp. 137–147 (1998)

  36. Shur, M., Spalart, P.R., Strelets, M., Travin, A.: Detached-eddy simulation of an airfoil at high angle of attack. In: 4th Interenational Symposium on Eng. Turb. Modelling and Measurements, pp. 669–678. Elsevier, Amsterdam (1999)

  37. Spalart P.R., Deck S., Shur M.L., Squires K.D., Strelets M., Travin A.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195 (2006)

    Article  Google Scholar 

  38. Deck S.: Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43(7), 1556–1566 (2005)

    Article  Google Scholar 

  39. Deck S.: Zonal-detached eddy simulation of the flow around a high-lift configuration. AIAA J. 43(11), 2372–2384 (2005)

    Article  Google Scholar 

  40. Simon F., Deck S., Guillen Ph., Sagaut P., Merlen A.: Numerical simulation of the compressible mixing layer past an axisymmetric trailing edge. J. Fluid Mech. 591, 215–253 (2007)

    Article  Google Scholar 

  41. Deck, S., Thorigny, P.: Unsteadiness of an axisymmetric separating flow. Phys. Fluids 19(065103) (2007)

  42. Simon F., Deck S., Guillen Ph., Sagaut P.: Reynolds averaged Navier Stokes/large eddy simulations of supersonic base flow. AIAA J. 44(11), 2578–2590 (2006)

    Article  Google Scholar 

  43. Chauvet N., Deck S., Jacquin L.: Zonal-detached-eddy simulation of a controlled propulsive jet. AIAA J. 45(10), 2458–2473 (2007)

    Article  Google Scholar 

  44. Trapier S., Deck S., Duveau Ph.: Delayed detached eddy simulation and analysis of supersonic inlet buzz. AIAA J. 46(1), 118–131 (2008)

    Article  Google Scholar 

  45. Sagaut, P., Deck, S., Terracol, M.: Multiscale and Multiresolution Approaches in Turbulence, p. 356. Imperial College Press, London (2006)

  46. Frey, M., Hagemann, G.: Status of Flow Separation Prediction in Rocket Nozzles. AIAA Paper 98-2619 (1998)

  47. Delcayre F., Dubief Y.: On coherent-vortex identification in turbulence. J. Turbul. 1(11), 1–22 (2000)

    MathSciNet  MATH  Google Scholar 

  48. Jeong J., Hussain F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

    Article  MathSciNet  Google Scholar 

  49. Verma S.B., Stark R., Haidn O.: Relation between shock unsteadiness and the origin of side-loads inside a thrust optimized parabolic rocket nozzle. Aerosp. Sci. Technol. 10(6), 474–483 (2006)

    Article  Google Scholar 

  50. Sandberg R.D., Fasel H.F.: Numerical investigation simulation of transitional supersonic axisymmetric wakes. J. Fluid Mech. 563, 1–41 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sébastien Deck.

Additional information

Communicated by A. Hadjadj.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deck, S. Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow. Shock Waves 19, 239–249 (2009). https://doi.org/10.1007/s00193-009-0199-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-009-0199-5

Keywords

PACS

Navigation