Acta Mechanica Sinica

, 27:461 | Cite as

Flow structures of gaseous jets injected into water for underwater propulsion

  • Jia-Ning Tang
  • Ning-Fei Wang
  • Wei ShyyEmail author
Research Paper


Gaseous jets injected into water are typically found in underwater propulsion, and the flow is essentially unsteady and turbulent. Additionally, the high water-to-gas density ratio can result in complicated flow structures; hence measuring the flow structures numerically and experimentally remains a challenge. To investigate the performance of the underwater propulsion, this paper uses detailed Navier-Stokes flow computations to elucidate the gas-water interactions under the framework of the volume of fluid (VOF) model. Furthermore, these computations take the fluid compressibility, viscosity, and energy transfer into consideration. This paper compares the numerical results and experimental data, showing that phenomena including expansion, bulge, necking/breaking, and back-attack are highlighted in the jet process. The resulting analysis indicates that the pressure difference on the rear and front surfaces of the propulsion system can generate an additional thrust. The strong and oscillatory thrust of the underwater propulsion system is caused by the intermittent pulses of the back pressure and the nozzle exit pressure. As a result, the total thrust in underwater propulsion is not only determined by the nozzle geometry but also by the flow structures and associated pressure distributions.


Gaseous jets Underwater propulsion High density ratio Gas-water interactions 



Area of nozzle exit


Area of cross-section of propulsion system


Area of nozzle throat


Diameter of cross-section of propulsion system


Diameter of nozzle throat


Diameter of nozzle exit


Energy of gas


Energy of water




Enthalpy of gas


Enthalpy of water


Effective thermal conductivity, k eff = k + k t


Thermal conductivity of gas


Turbulent thermal conductivity


Thermal conductivity of water

Mass flow rate


Mach number




Normalized pressure


Stagnant pressure


Atmosphere pressure


Ambient pressure


Back pressure


Pressure at nozzle exit


Reference pressure


Prandtl number of gas


Prandtl number of water


Reynolds number




Normalized Axial-velocity


Reference velocity


Normal velocity at nozzle exit


Volume fraction of gas


Volume fraction of water


Ratio of specific heats of gas


Dynamic viscosity of gas


Dynamic viscosity of mixture


Dynamic viscosity of water


Density of gas


Density of liquid


Density of mixture


Reference density


Density of water


  1. 1.
    Linck, M., Gupta, A.K., Yu, K.: Submerged combustion and two-phase exhaust jet instabilities. Journal of Propulsion and Power 25(2), 522–532 (2009)CrossRefGoogle Scholar
  2. 2.
    Gulawani, S.S., Deshpande, S.S., Joshi, J.B.: Submerged gas jet into a liquid bath: A review. Industrial & Engineering Chemistry Research 46, 3188–3218 (2007)CrossRefGoogle Scholar
  3. 3.
    Petipas, F., Massoni, J., Saurel, R., et al.: Diffuse interface model for high speed cavitating underwater systems. International Journal of Multiphase Flow 35, 747–759 (2009)CrossRefGoogle Scholar
  4. 4.
    Yang, Q. X., Gustavsson, H., Burström, E.: Erosion of refractory during gas injection-a cavitation based model. Scandinavian Journal of Metallurgy 19, 127–136 (1990)Google Scholar
  5. 5.
    Gongwer, C. A.: Some aspects of underwater jet propulsion systems. ARS Journal 30(12), 1148–1151 (1960)Google Scholar
  6. 6.
    Wislicenus, G.F.: Hydrodynamics and propulsion of submerged bodies. ARS Journal 30(12), 1140–1148 (1960)Google Scholar
  7. 7.
    Yang, Q.X., Gustavsson, H.: Effects of gas jet instability on refractory wear—a study by high-speed photography. Scandinavian Journal of Metallurgy 21, 15–26 (1992)Google Scholar
  8. 8.
    Brady, J.F.: Underwater propulsion. AIAA and office of naval research, symposium on deep submergence propulsion and marine systems, forest park, ill. AIAA-1966-2408. 204–225 (1966)Google Scholar
  9. 9.
    Rogers, K.W.: A theoretical and experimental investigation of the transient phase of underwater rocket motor firing. University of Southern California Engineering Center Report (1962)Google Scholar
  10. 10.
    Wang, X.H., Chen, Y.L., Li, Q., et al.: Nozzle flows of the launching under water. Journal of Propulsion Technology 22(1), 61–64 (2001) (in Chinese)MathSciNetGoogle Scholar
  11. 11.
    Labotz, R. J.: Hydrodynamic consideration and limitations in submerged rocket firings. Journal of Spacecraft and Rocket 2(3), 320–324 (1965)CrossRefGoogle Scholar
  12. 12.
    Zhang, Y.W., Wang, X.H., Yang, J.X.: Study on working thrust for underwater engine using the spherical bubble model. Journal of Hydrodynamics 20(5), 636–640 (2005) (in Chinese)Google Scholar
  13. 13.
    Tang, J.N., Li, S.P., Wang, N.F., et al.: Flow structures of gaseous jet injected into liquid for underwater propulsion. 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN. AIAA-2010-6911 (2010)Google Scholar
  14. 14.
    Chen, K., Richter, H.J.: Instability analysis of the transition from bubbling to jetting in a gas injected into a liquid. International Journal of Multiphase Flow 23(4), 699–712 (1997)zbMATHCrossRefGoogle Scholar
  15. 15.
    Longuet-Higgins, M.S., Kerman, B.R., Lunde, K.: The release of air bubbles from an underwater nozzle. Journal of Fluid Mechanics 230, 365–390 (1991)zbMATHCrossRefGoogle Scholar
  16. 16.
    Siamas, G.A., Jiang, X, Wrobel, L.C.: Dynamics of annular gas-liquid two-phase swirling jets. International Journal of Multiphase Flow 35, 450–467 (2009)CrossRefGoogle Scholar
  17. 17.
    Koria, S.C.: Principles and applications of gas injection in steelmaking practice. Scandinavian Journal of Metallurgy 22, 271–279 (1993)Google Scholar
  18. 18.
    Lindau, J.W., Venkateswaran, S., Kunz, R.F., et al.: Multiphase computations for underwater propulsive flows. 16th AIAA Computational Fluid Dynamics Conference, Orlando, Florida. AIAA 2003-4105(2003)Google Scholar
  19. 19.
    Surin, V.A., Evchenko, V.N., Rubin, V.M.: Propagation of a gas jet in a liquid. Journal of Engineering Physics 45, 1091–1101 (1983)CrossRefGoogle Scholar
  20. 20.
    Hoefele, E.O., Brimacombe, J.K.: Flow regimes in submerged gas injection. Metallurgical Transactions B 10B, 631–648 (1979)CrossRefGoogle Scholar
  21. 21.
    Engh, T.A., Nilmani, M.: Bubbling at high flow rates in inviscid and viscous liquids (slags). Metallurgical Transactions B 19B, 83–94 (1988)CrossRefGoogle Scholar
  22. 22.
    Loth E, Faeth G.M.: Structure of underexpanded round air jets submerged in water. International Journal of Multiphase Flow 15(4), 589–603 (1989)CrossRefGoogle Scholar
  23. 23.
    Qi, L.X., Cao, Y., Wang, B.Y.: Experimental study of under-expanded sonic air jets in water. Acta Mechanica Sinica 32(6), 667–675 (2000) (in Chinese)Google Scholar
  24. 24.
    Irie, T., Yasunobu, T., Kashimura, H., et al.: Characteristics of the Mack Disk in the under-expanded jet in which the back pressure continuously changes with time. Journal of Thermal Science 12(2), 132–137 (2003)CrossRefGoogle Scholar
  25. 25.
    Chang, K. S., Kim, J.K.: Numerical investigation of inviscid shock wave dynamics in an expansion tube. Shock Waves 5, 33–45 (1995)zbMATHCrossRefGoogle Scholar
  26. 26.
    Abate, G., Shyy, W.: Dynamic structure of confined shocks undergoing sudden expansion. Progress in Aerospace Sciences 38, 23–42 (2002)CrossRefGoogle Scholar
  27. 27.
    Jiang, Z., Takayama, K., Babinsky, H., et al.: Transient shock wave flows in tubes with a sudden change in cross section. Shock Waves 7, 151–162 (1997)CrossRefGoogle Scholar
  28. 28.
    Liang, S. M., Chen, H.: Numerical simulation of underwater blast-wave focusing using a high-order scheme. AIAA Journal 37(8), 1010–1013 (1999)CrossRefGoogle Scholar
  29. 29.
    Dai, Z.Q., Wang, B.Y., Qi, L.X., et al.: Experimental study on hydrodynamic behaviors of high-speed gas jet in still water. Acta Mechanica Sinica 22, 443–448 (2006)CrossRefGoogle Scholar
  30. 30.
    Shi, H.H., Wang, B.Y., Qi, L.X.: A submerged supersonic gas jet. In: Proc. 7th National Congress on Hydrodynamics and 19th National Symposium on Hydrodynamics. Beijing: Ocean Press, 75–81 (2005) (in Chinese)Google Scholar
  31. 31.
    Shi, H.H., Wang, B.Y., Dai, Z.Q.: Research on the mechanics of underwater supersonic gas jets. Science China 53(3), 527–535 (2010)Google Scholar
  32. 32.
    Wang, B.Y., Dai, Z.Q., Qi, L.X., et al.: Experimental study on back-attack phenomenon in underwater supersonic gas jets. Chinese Journal of Theoretical and Applied Mechanics 39(2), 267–272 (2007) (in Chinese)Google Scholar
  33. 33.
    Cao, J.Y., Lu, C.J., Li, J., et al.: Research on dynamic characteristics of underwater supersonic gas jets. Chinese Journal of Hydrodynamics 24(5), 575–582 (2009) (in Chinese)Google Scholar
  34. 34.
    Kerrebrock, J.L.: Aircraft Engines and Gas Turbines. The MIT Press, Cambridge, Massachusetts, and London (1987)Google Scholar
  35. 35.
    Shan, X.S., Yang, R.G., Ye, Q.Y.: Fluid force on a vehicle with control system of vectorial thrust. Journal of Shanghai Jiaotong University 35(4), 625–629 (2001) (in Chinese)Google Scholar
  36. 36.
    Wang, C., Ye, Q.Y., He, Y.S.: Calculation of an exhausted gas cavity behind an under-water vehicle. Chinese Journal of Applied Mechanics 14(3), 1–7 (1997) (in Chinese)Google Scholar
  37. 37.
    Shi, H.H., Guo, Q., Wang, C., et al.: Oscillation flow induced by underwater supersonic gas jets. Shock Waves 20, 347–352 (2010)zbMATHCrossRefGoogle Scholar
  38. 38.
    Wei, J.H., Ma, J.C., Fan, Y.Y.: Back-attack phenomena of gas jets with submerged horizontally blowing and effects on erosion and water of refractory. ISIJ International 39(8), 779–786 (1999)CrossRefGoogle Scholar
  39. 39.
    Lu, C.J., Chen. F., Fan, H., et al.: The fluid dynamic research on the underwater ignition. Acta Aeronautica et Astronautica Sinica 13(4), B124–B130 (1992) (in Chinese)Google Scholar
  40. 40.
    Ju, Y.T., Wu, X.X., Zhu, F.Y.: The study of air flow characteristic in nozzle and the thrust computation method in higher surrounding pressure. Journal of Ballistics 15(3), 66–69 (2003) (in Chinese)Google Scholar
  41. 41.
    Aoki, T, Masuda, S, Hatano, A.: Characteristics of submerged gas jets and a new type bottom blowing tuyere. In: Injection Phenomena in Extraction and Refining. Wraith, A.E., ed. Newcastle: Department of Metallurgy and Engineering Materials (University of Newcastle upon Tyne), A1–A36 (1982)Google Scholar
  42. 42.
    Anderson, J.D.: Fundamentals of Aerodynamics. McGraw-Hill, New York (1991)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA
  3. 3.Department of Mechanical EngineeringHong Kong University of Science and TechnologyKowloon, Hong KongChina

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