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Reynolds Number Influence on Dual-Bell Transition Phenomena

Published Online:https://doi.org/10.2514/1.B34734

An experimental investigation was conducted to study the Reynolds number influence on dual-bell transition behavior for tests inside a high-altitude simulation chamber. For the range of nozzle supply pressures tested, the nozzle Reynolds number is seen to gradually decrease from a relatively high value (of the order of 107 for tests in sea-level atmospheric conditions) toward the transitional range (lower side of 106 for tests inside the high-altitude chamber). This influences the width of the inflection region, which is seen to decrease with an increase in nozzle Reynolds number. Because of the smaller negative pressure gradient experienced during sneak transition with a decrease in nozzle Reynolds number, the separation point is seen to move into the region of wall inflection much earlier and tends to stay in the region of wall inflection for a relatively longer time. Although the time duration of final transition remains more or less constant for different nozzle supply pressure values, the time duration for the separation point to move from its location at the inflection point to the point of minimum wall pressure in nozzle extension shows a significant increase in value with a decrease in nozzle Reynolds number. These conditions are conducive in delaying the transition to higher nozzle pressure ratios with a decrease in nozzle supply pressure. The preceding study therefore indicates that the scaling effects can very strongly dominate the results of dual-bell tests conducted inside high-altitude test facilities.

References

  • [1] Liquid Rocket Engine Nozzles,” NASA Space Vehicle Design Criteria, NASA SP-8120, 1976. Google Scholar

  • [2] Hagemann G., Immich H., Nguyen T. V. and Dumnov G. E., “Advanced Rocket Nozzles,” Journal of Propulsion and Power, Vol. 14, No. 5, 1998, pp. 629–634. doi:https://doi.org/10.2514/2.5354 JPPOEL 0748-4658 LinkGoogle Scholar

  • [3] Kasuka K., Kumakawa A., Niino M., Konno A. and Atsumi M., “Experimental Study on Extendible and Dual-Bell Nozzles Under High Altitude Conditions,” AIAA Paper  2002-3303, 2002. Google Scholar

  • [4] Foster C. and Cowles F., “Experimental Study of Gas-Flow Separation in Overexpanded Exhaust Nozzles for Rocket Motors,” Jet Propulsion Lab., California Inst. of Technology, Progress Rept.  4-103, 1949. Google Scholar

  • [5] Horn M. and Fisher S., “Dual-Bell Altitude Compensating Nozzle,” NASA CR-194719, 1994. Google Scholar

  • [6] Rao G. V. R., “Recent Developments in Rocket Nozzle Configurations,” ARS Journal, Vol. 31, No. 11, 1961, pp. 1488–1494. doi:https://doi.org/10.2514/8.5837 ARSJAY 0097-4056 LinkGoogle Scholar

  • [7] Wasko R. A., “Performance of Annular Plug and Expansion-Deflection Nozzles Including External Flow Effects at Transonic Mach Numbers,” NASA TN-D-4462, April 1968. Google Scholar

  • [8] Ruf J. H. and McConnaughey P. K., “The Plume Physics Behind Aerospike Nozzle Altitude Compensation and Slipstream Effect,” AIAA Paper  1997-3217, 1997. LinkGoogle Scholar

  • [9] Kalinin E. M., Lapygin V. I., Pushkin R. M. and Aksenov L. A., “Gas Dynamics of Self-Adjustable Thruster with Zero-Length Central Plug,” European Space Research and Technology Centre, ESA-SP-426, 1998. Google Scholar

  • [10] Rao G. V. R., “The E-D Nozzle,” Astronautics, Vol. 5, No. 8, 1960, pp. 28–29, 50–51. Google Scholar

  • [11] Frey M. and Hagemann G., “Critical Assessment of Dual-Bell Nozzles,” Journal of Propulsion and Power, Vol. 15, No. 1, 1999, pp. 137–143. doi:https://doi.org/10.2514/2.5402 JPPOEL 0748-4658 LinkGoogle Scholar

  • [12] Dumonov G., Ponomaryov N. B. and Voinov A. L., “Dual-Bell Nozzles for Rocket Engines of Launch Vehicle Upper Stages and Orbital Transfer Vehicles,” AIAA Paper  1997-3089, 1997. Google Scholar

  • [13] Stark R., Boehm C., Haidn O. J. and Zimmermann H., “Cold Flow Testing of Dual-Bell Nozzles in Altitude Simulation Chambers,” European Conference for Aerospace Sciences, Torus Press, Russian Federation, July 2005. Google Scholar

  • [14] Génin C. and Stark R., “Side-Loads in Subscale Dual-Bell Nozzles,” Journal of Propulsion and Power, Vol. 27, No. 4, July–Aug. 2011, pp. 828–837. doi:https://doi.org/10.2514/1.54666 JPPOEL 0748-4658 LinkGoogle Scholar

  • [15] Génin C. N. and Stark R., “Flow Transition in Dual Bell Nozzles,” Shock Waves, Vol. 19, No. 3, 2009, pp. 265–270. doi:https://doi.org/10.1007/s00193-008-0176-4 SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [16] Nasuti F., Onofri M. and Martelli E., “Role of Wall Shape on the Transition in Axisymmetric Dual-Bell Nozzles,” Journal of Propulsion and Power, Vol. 21, No. 2, 2005, pp. 243–250. doi:https://doi.org/10.2514/1.6524 JPPOEL 0748-4658 LinkGoogle Scholar

  • [17] Martelli E., Nasuti F. and Onofri M., “Numerical Parametric Analysis of Dual Bell Nozzle Flows,” AIAA Journal, Vol. 45, No. 3, 2007, pp. 640–650. doi:https://doi.org/10.2514/1.26690 AIAJAH 0001-1452 LinkGoogle Scholar

  • [18] Miyazawa M. and Otsu H., “An Analytical Study on Design and Performance of Dual-Bell Nozzles,” AIAA Paper  2004-380, 2004. LinkGoogle Scholar

  • [19] Verma S. B., Stark R., Génin C. and Haidn O., “Flow Separation Characteristics of a Dual-Bell Nozzle During Its Transition Modes,” Shock Waves, Vol. 20, No. 3, 2010, pp. 191–203. doi:https://doi.org/10.1007/s00193-010-0259-x SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [20] Verma S. B., Stark R., Génin C. and Haidn O., “Cold Gas Dual-Bell Transition Tests in a High Altitude Simulation Chamber,” Shock Waves, Vol. 21, No. 2, 2011, pp. 131–140. doi:https://doi.org/10.1007/s00193-011-0302-6 SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [21] Génin C. N. and Stark R., “Hot Flow Testing of a Film Cooled Dual Bell Nozzle,” AIAA Paper  2011-5614, 2011. Google Scholar

  • [22] Tomita T., Takahashi M. and Sasaki M., “Control of Transition Between Two Working Modes of a Dual-Bell Nozzle by Gas Injection,” AIAA Paper  2009-4952, 2009. LinkGoogle Scholar

  • [23] Annamalai K., Visvanathan K., Sriramulu V. and Bhaskaran K. A., “Evaluation of the Performance of Supersonic Exhaust Diffuser Using Scaled Down Models,” Experimental Thermal and Fluid Science, Vol. 17, No. 3, 1998, pp. 217–229. doi:https://doi.org/10.1016/S0894-1777(98)00002-8 ETFSEO 0894-1777 CrossrefGoogle Scholar

  • [24] Annamalai K., Satyanarayana T. N. V., Sriramulu V. and Bhaskaran K. A., “Development of Design Methods for Short Cylindrical Supersonic Exhaust Diffuser,” Experiments in Fluids, Vol. 29, No. 4, 2000, pp. 305–308. doi:https://doi.org/10.1007/s003489900071 EXFLDU 0723-4864 CrossrefGoogle Scholar

  • [25] Park B. H., Lim J. W. and Yoon W., “Fluid Dynamics in Starting and Terminating Transients of Zero-Secondary Flow Ejector,” International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 327–339. doi:https://doi.org/10.1016/j.ijheatfluidflow.2007.06.008 IJHFD2 0142-727X CrossrefGoogle Scholar

  • [26] Park B. H., Lim J. W. and Yoon W., “Studies on the Starting Transient of a Straight Cylindrical Supersonic Exhaust Diffuser: Effects of Diffuser Length and Pre-Evacuation State,” International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1369–1379. doi:https://doi.org/10.1016/j.ijheatfluidflow.2008.04.006 IJHFD2 0142-727X CrossrefGoogle Scholar

  • [27] Verma S. B. and Haidn O., “Cold Gas Testing of Thrust-Optimized Parabolic Nozzle in a High-Altitude Test Facility,” Journal of Propulsion and Power, Vol. 27, No. 6, 2011, pp. 1238–1246. doi:https://doi.org/10.2514/1.B34320 JPPOEL 0748-4658 LinkGoogle Scholar

  • [28] Stark R. and Wagner B., “Experimental Study of Boundary Layer Separation in Truncated Ideal Contour Nozzles,” Shock Waves, Vol. 19, No. 3, 2009, pp. 185–191. doi:https://doi.org/10.1007/s00193-008-0174-6 SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [29] Hadjadj A. and Onofri M., “Nozzle Flow Separation,” Shock Waves, Vol. 19, No. 3, 2009, pp. 163–169. doi:https://doi.org/10.1007/s00193-009-0209-7 SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [30] Donaldson C. and Lange R. H., “Study of Pressure Rise Across Shock Waves Required to Separate Laminar and Turbulent Boundary Layers,” NACA TN-2770, 1952. Google Scholar

  • [31] Shapiro A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 2, Ronald, New York, 1954, p. 1157. Google Scholar