Pressure and temperature of the liquid rocket thrust chambers into which propellants are injected have been in an ascending trajectory to gain higher specific impulse. It is quite possible then that the thermodynamic condition into which liquid propellants are injected reaches or surpasses the critical point of one or more of the injected fluids. For example, in cryogenic hydrogen/oxygen liquid rocket engines, such as Space Shuttle Main Engine (SSME) or Vulcain (Ariane 5), the injected liquid oxygen finds itself in a supercritical condition. Very little detailed information was available on the behavior of liquid jets under such a harsh environment nearly two decades ago. The author had the opportunity to be intimately involved in the evolutionary understanding of injection processes at the Air Force Research Laboratory (AFRL), spanning sub- to supercritical conditions during this period. The information included here attempts to present a coherent summary of experimental achievements pertinent to liquid rockets, focusing only on the injection of nonreacting cryogenic liquids into a high-pressure environment surpassing the critical point of at least one of the propellants. Moreover, some implications of the results acquired under such an environment are offered in the context of the liquid rocket combustion instability problem. 1. Introduction In designs of chemical rocket engines, liquid fuel and oxidizer are often injected as round jets into a hot and elevated-pressure environment of the thrust chamber. The coaxial and impinging jets injectors are two of the well-established designs in liquid rocket engines (LREs). On the other hand, higher specific impulse is a major motivation for operating rocket thrust chambers at progressively higher pressures. Conditions therefore exist in which the injected liquid finds itself near or even above the thermodynamic critical point. Examples are Space Shuttle Main Engine and Vulcain (Ariane 5) with liquid H2/liquid O2. In such cases, major changes occur in some important and key properties of a substance as it approaches the thermodynamic critical point. For example, under thermodynamic equilibrium, the distinction between the liquid and gas phases disappears at and above the critical point and hence it is referred to as a “fluid.” Also, large changes in density occur near the critical point. The constant-pressure specific heat becomes very large and surface tension vanishes at and beyond the critical point. As the ambient pressure into which a liquid jet is injected increases, the importance of the solubility of
References
[1]
T. J. Bruno and J. F. Ely, Supercritical Fluid Technology: Review in Modern Theory and Applications, CRC Press, 1991.
[2]
R. S. Lazar and G. M. Faeth, “Bipropellant droplet combustion in the vicinity of the critical point,” in Proceedings of the 30th Symposium (International) on Combustion, p. 801, The Combustion Institute, 1971.
[3]
A. Umemura, “Supercritical droplet gasification combustion,” in Proceedings of the IUTAM Symposium on Theories Combustion on Droplets and Sprays, Taiwan, December 1994.
[4]
J. A. Newman and Brzustowski, “Behavior of a liquid jet near the thermodynamic critical region,” AIAA Journal, vol. 9, no. 8, pp. 1595–1602, 1971.
[5]
B. Chehroudi, D. Talley, and E. Coy, “Initial growth rate and visual characteristics of a round Jet into a sub- to supercritical environment of relevance to rocket, gas turbine, and diesel engines,” in Proceedings of the 37th AIAA Aerospace Science Meeting and Exhibit, Reno, NV, USA, January 1999, AIAA 99-0206.
[6]
W. Mayer, A. Schik, C. Schweitzer, and M. Schaffler, “Injection and mixing processes in high pressure LOX/GH2 rocket combustors,” in Proceedings of the 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Lake Buena Vista, Fla, USA, 1996, AIAA Paper no. 96-2620.
[7]
R. D. Reitz and F. B. Bracco, “On the dependence of spray angle and other spray parameters on nozzle design and operating condition,” in Proceedings of the SAE International Congress and Exposition, Detroit, MI, USA, February-March 1979, SAE Paper no. 790494.
[8]
W. Mayer, A. Ivancic, A. Schik, and U. Homung, “Propellant atomization in LOX/GH2 rocket combustors,” in Proceedings of the 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Cleveland, Ohio, USA, July 1998, Paper no. 98-3685.
[9]
A. Roy and C. Segal, “Experimental study of subcritical to supercritical jet mixing,” in Proceedings of the 47th AIAA ASM Meeting, Paper AIAA-2009-809, Orlando, Fla, USA, January 2008.
[10]
B. Chehroudi, D. Talley, and E. Coy, “Visual characteristics and initial growth rates of round cryogenic jets at subcritical and supercritical pressures,” Physics of Fluids, vol. 14, no. 2, pp. 850–861, 2002.
[11]
C. J. Chen and W. Rodi, Vertical Turbulent Buoyant Jets: A Review of Experimental Data, Pergamon Press, 1980.
[12]
P. N. Papanicolaou and E. J. List, “Investigations of round vertical turbulent buoyant jets,” Journal of Fluid Mechanics, vol. 195, pp. 341–391, 1988.
[13]
R. Branam and W. Mayer, “Characterization of cryogenic injection at supercritical pressure,” Journal of Propulsion and Power, vol. 19, no. 3, pp. 342–355, 2003.
[14]
G. N. Abramovich, The Theory of Turbulent Jets, MIT Press, Cambridge, UK, 1963.
[15]
G. L. Brown and A. Roshko, “On density effects and large structure in turbulent mixing layers,” Journal of Fluid Mechanics, vol. 64, no. 4, pp. 775–816, 1974.
[16]
G. Brown, “The entrainment and large structure in turbulent mixing layers,” in Proceedings of the 5th Australian Conference on Hydraulics and Fluid Mechanics, pp. 352–359, 1974.
[17]
D. Papamoschou and A. Roshko, “The compressible turbulent shear layer: an experimental study,” Journal of Fluid Mechanics, vol. 197, pp. 453–477, 1988.
[18]
P. E. Dimotakis, “Two-dimensional shear-layer entrainment,” AIAA Journal, vol. 24, no. 11, pp. 1791–1796, 1986.
[19]
C. D. Richards and W. M. Pitts, “Global density effects on the self-preservation behaviour of turbulent free jets,” Journal of Fluid Mechanics, vol. 254, pp. 417–435, 1993.
[20]
B. Chehroudi, R. Cohn, D. Talley, and A. Badakhshan, “Raman scattering measurements in the initial region of sub- and supercritical jets,” in Proceedings of the 36th Joint Propulsion Conference, Huntsville, AL, USA, 2000, AIAA 2000-3392.
[21]
M. Oschwald and M. M. Micci, “Spreading angle and centerline variation of density of supercritical nitrogen jets,” Atomization and Sprays, vol. 12, no. 1–3, pp. 91–106, 2002.
[22]
B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, San Francisco, Calif, USA, 1983.
[23]
K. R. Sreenivasan and C. Meneveau, “The fractal facets of turbulence,” Journal of Fluid Mechanics, vol. 173, pp. 357–386, 1986.
[24]
J. J. Taylor and J. W. Hoyt, “Water jet photography—techniques and methods,” Experiments in Fluids, vol. 1, no. 3, pp. 113–120, 1983.
[25]
B. Chehroudi, D. Talley, and E. Coy, “Fractal geometry and growth rate of cryogenic jets near critical point,” in Proceedings of the 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Los Angeles, Calif, USA, June 1999, AIAA Paper 99-2489.
[26]
B. Chehroudi and D. Talley, “The fractal geometry of round turbulent cryogenic nitrogen jets at subcritical and supercritical pressures,” Atomization and Sprays, vol. 14, no. 1, pp. 81–91, 2004.
[27]
B. Chehroudi, S.-H. Chen, F. V. Bracco, and Y. Onuma, “On the intact core of full-cone sprays,” SAE Transaction 850126, 1985.
[28]
M. Oschwald and A. Schik, “Supercritical nitrogen free jet investigated by spontaneous Raman scattering,” Experiments in Fluids, vol. 27, no. 6, pp. 497–506, 1999.
[29]
I. Wygnanski and H. E. Fiedler, “The two-dimensional Mixing region,” Journal of Fluid Mechanics, vol. 41, no. 2, pp. 327–361, 1970.
[30]
R. M. C. So, J. Y. Zhu, M. V. ？tügen, and B. C. Hwang, “Some measurements in a binary gas jet,” Experiments in Fluids, vol. 9, no. 5, pp. 273–284, 1990.
[31]
N. Zong, H. Meng, S.-Y. Hsieh, and V. Yang, “A numerical study of cryogenic fluid injection and mixing under supercritical conditions,” Physics of Fluids, vol. 16, no. 12, pp. 4248–4261, 2004.
[32]
M. Oschwald, A. Schik, M. Klar, and W. Mayer, “Investigation of coaxial LN2/GH2-injection at supercritical pressure by spontaneous raman scattering,” in Proceedings of the 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Los Angeles, Calif, USA, June 1999.
[33]
L.-K. Tseng, G. A. Ruff, P.-K. Wu, and G. M. Faeth, “Continuous- and dispersed-phase structure of pressure-atomized sprays,” in Proceedings of the Progress in Astronautics and Aeronautics: Recent Advances in Spray Combustion, 1995.
[34]
N. Zong and V. Yang, “Cryogenic fluid jets and mixing layers in transcritical and supercritical environments,” Combustion Science and Technology, vol. 178, no. 1-3, pp. 193–227, 2006.
[35]
J. C. Oefelein and V. Yang, “Comprehensive review of liquid-propellant combustion instabilities in F-1 engines,” Journal of Propulsion and Power, vol. 9, no. 5, pp. 657–677, 1993.
[36]
B. Chehroudi and D. Talley, “Interaction of acoustic waves with a cryogenic nitrogen jet at sub- and supercritical pressures,” in Proceedings of the 40th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 2002, AIAA 2002-0342.
[37]
D. O. Rockwell, “External excitation of planar jets,” Journal of Applied Mechanics, vol. 39, no. 4, pp. 883–891, 1972.
[38]
H. A. Becker and T. A. Massaro, “Vortex evolution in a round jet,” Journal of Fluid Mechanics, vol. 31, pp. 435–448, 1968.
[39]
Y. V. Vaslov and A. S. Ginevskiy, “Acoustic effects on aerodynamic characteristics of a turbulent jet,” Tech. Rep. FTD-MT-24-232-68, Foreign Technology Division, Air Force Systems Command, 1968.
[40]
J. Hulka and J. J. Hutt, “Instability phenomena in liquid oxygen/hydrogen propellant rocket engines,” in Liquid Rocket Engine Combustion Instability, V. Yang and W. E. Anderson, Eds., AIAA Progress in Astronautics and Aeronautics, pp. 39–71, 1995.
[41]
J. Telaar, G. Schneider, and W. Mayer, Experimental Investigation of Breakup of Turbulent Liquid Jets, ILASS-Europe 2000, Darmstadt, Germany, 2000.
[42]
D. Davis and B. Chehroudi, “The effects of pressure and acoustic field on a cryogenic coaxial jet,” in Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, pp. 10741–10759, January 2004.
[43]
D. Davis and B. Chehroudi, “Behaviour of a rocket-Like coaxial injector in an acoustic field, ILAS america,” in Proceedings of the 19th Annual Conference on Liquid Atomization and Spray Systems, Toronto, Canada, May 2006.
[44]
D. W. Davis, On the behavior of a shear-coaxial Jet, spanning sub- to super-critical pressures, with and without an externally imposed transverse acoustic field [Ph.D. thesis], Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 2006.
[45]
M. Oschwald, J. J. Smith, R. Branam et al., “Injection of fluids into supercritical environments,” Combustion Science and Technology, vol. 178, no. 1–3, pp. 49–100, 2006.
[46]
M. Favre-Marinet and E. B. Camano Schettini, “Density field of coaxial jets with large velocity ratio and large density differences,” International Journal of Heat and Mass Transfer, vol. 44, no. 10, pp. 1913–1924, 2001.
[47]
H. Eroglu, N. Chigier, and Z. Farago, “Coaxial atomizer liquid intact lengths,” Physics of Fluids A, vol. 3, no. 2, pp. 303–308, 1991.
[48]
C. Englebert, Y. Hardalupas, and J. H. Whitlaw, “Article usage statistics center,” Proceedings of the Royal Society A, vol. 451, pp. 189–229, 1995.
[49]
Z. Faragó and N. Chigier, “Morphological classification of disintegration of round liquid jets in a coaxial air stream,” Atomization and Sprays, vol. 2, pp. 137–153, 1992.
[50]
R. D. Woodward, Primary atomization of liquid jets issuing from rocket engine coaxial Injectors [Ph.D. thesis], Pennsylvania State University, Department of Mechanical Engineering, University Park, Pa, USA, 1993.
[51]
B. Chehroudi, D. Davis, and D. Talley, “Initial results from a cryogenic coaxial injector in an acoustic field,” in Proceedings of the 41st Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 2003, AIAA 2003-1339.
[52]
I. A. Leyva, J. I. Rodriguez, B. Chehroudi, and D. Talley, “Preliminary results on coaxial jet spread angles and the effects of variable phase transverse acoustic fields,” in Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nv, USA, January 2008.
[53]
J. C. Lasheras and E. J. Hopfinger, “Liquid jet instability and atomization in a coaxial gas stream,” Annual Review of Fluid Mechanics, vol. 32, pp. 275–308, 2000.
[54]
J. I. Rodriguez, I. A. Leyva, B. Chehroudi, and D. Talley, in Proceedings of the 21st Annual Conference on Liquid Atomization and Spray Systems (ILASS '08), Orlando, Fla, USA, May 2008.
[55]
J. I. Rodriguez, Acoustic excitation of liquid fuel droplets and coaxial jets [Ph.D. thesis], University of California at Los Angeles, 2009.
[56]
B. Chehroudi, “Physical hypothesis for the combustion instability in cryogenic liquid rocket engines,” Journal of Propulsion and Power, vol. 26, no. 6, pp. 1153–1160, 2010.
[57]
W. E. Anderson, H. M. Ryan, R. J. Santoro, and R. A. Hewitt, “Combustion instability mechanisms in liquid rocket engines using impinging jet injectors,” in Proceedings of the 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, San Diego, Calif, USA, July 1995, Paper AIAA-95-2357.
[58]
T. D. Harrje and H. F. Reardon, “Propellant rocket combustion instability,” NASA Report, 1972, NASA SP-194.
[59]
“Liquid rocket engine combustion instability,” in Proceedings of the AIAA Progress in Astronautics and Aeronautics, V. Yang and W. E. Anderson, Eds., vol. 169, p. 577, 1995.
[60]
L. Rayleigh, “The explanation of certain acoustical phenomena,” in Proceedings of the Royal Institution, vol. 8, pp. 536–542, London, UK, 1878.
[61]
M. F. Heidemann and J. F. Groeneweg, “Analysis of the dynamic response of liquid Jet atomization to acoustic oscillations,” NASA Technical Note, 1969, NASA TN D-5339.
[62]
T. Kiwata, A. Okajima, and H. Ueno, “Effects of excitation on plane and coaxial jets,” in Proceedings of the 3rd Joint ASME/JSME Fluid Engineering Conference, pp. 18–22, San Francisco, Calif, USA, 1999.
[63]
D. W. Davis and B. Chehroudi, “Measurements in an acoustically-driven coaxial jet under supercritical conditions,” Journal of Propulsion and Power, vol. 23, no. 2, pp. 364–374, 2007.
[64]
D. W. Davis and B. Chehroudi, “Shear-coaxial jets from a rocket-like injector in a transverse acoustic field at high pressures,” in Proceedings of the 44th AIAA Aerospace Sciences Meeting, pp. 9173–9190, Reno, Nv, USA, January 2006, Paper No. AIAA-2006-0758.
[65]
I. A. Leyva, B. Chehroudi, and D. Talley, “Dark core analysis of coaxial injectors at sub-, near-, and supercritical pressures in a transverse acoustic field,” in Proceedings of the 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp. 4342–4359, Cincinnati, Ohio, USA, July 2007.
[66]
R. D. Woodward, S. Pal, S. Farhangi, G. E. Jensen, and R. J. Santoro, “LOX/GH2 shear coaxial injector atomization studies: effect of recess and non-concentricity,” in Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, pp. 6925–6946, Reno, Nv, USA, January 2007.
[67]
B. Yang, C. Francesco, L. Wang, and M. Oschwald, “Experimental investigation of reactive liquid Oxygen/CH4 coaxial sprays,” Journal of Propulsion and Power, vol. 23, no. 4, pp. 763–771, 2007.
[68]
J. J. Smith, M. Bechle, D. Suslov, M. Oschwald, O. J. Haidn, and G. M. Schneider, “High pressure LOx/H2 combustion and flame dynamics preliminary results,” in Proceedings of the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Fort Lauderdale, Fla, USA, July 2004, AIAA-2004-3376.
