Journal of Hydrodynamics

, Volume 18, Issue 1, pp 481–486 | Cite as

Mathematical modeling of fluid flows for underwater missile launch

  • Yong-sheng Cheng
  • Hua Liu
Session A8


The gas and water flows during an underwater missile launch are numerically studied. For the gas flow, the explicit difference scheme of Non-oscillation and Non-free-parameter Dissipation (NND) is utilized to solve the Euler equations for compressible fluids in the body-fitted coordinates. For the water flow, the Hess-Smith method is employed to solve the Laplace equation for the velocity potential of irrotational water flows based on the potential theory and boundary element method. The hybrid Eulerian-Lagrangian formulation for the free boundary conditions is used to compute the changes of the free surface of the exhausted gas bubble in time stepping. On the free surface of the exhausted gas bubble, the matched conditions of both normal velocities and pressures are satisfied. From the numerical simulation, it is found that the exhausted gas bubble grows more rapidly in the axial direction than in the radial direction and the bubble will shrink at its ‘neck’ finally.

Key words

exhausted gas bubble Laval nozzle missile launched underwater shock wave gas jet 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Loth, E., Faeth, GM. Structure of Plane Underexpanded Air Jets into Water[J]. AIChE, 1990, 36(6):818–826.CrossRefGoogle Scholar
  2. [2]
    Loth, E., Faeth, GM. Structure of Underexpanded Round Air Jets Submerged in Water[J]. International Journal of Multiphase Flow, 1989, 15(4):589–603.CrossRefGoogle Scholar
  3. [3]
    Qi, L., Chao, Y. and Wang, B., Experimental Study of Underexpanded Sonic Air Jets in Water[J]. Acta Mechanica Sinica, 2000, 32(6):667–675. (in Chinese)Google Scholar
  4. [4]
    Pan, Z., Wang, B. and Song, Z. Research on Underwater Rocket Separation Performance[J]. Journal of Ship Research, 2004, 8(4): 22–26. (in Chinese)Google Scholar
  5. [5]
    Lu, CJ., Chen, F., Fan, H., et al. The Fluid Dynamic Research On the Under-Water Ignition Of Missile[J]. Acta Aeronautica Et Astronautica Sinica, 1992, 13(4): B124–B130. (in Chinese)Google Scholar
  6. [6]
    Huang, JC., Ye, QY and Zhu, SQ. Gas-Water Dynamic Calculation for the Underwater Ignition of a Missile at Different Depths[J]. Chinese Journal of Applied Mechanics, 1994, 11(3): 19–24. (in Chinese)Google Scholar
  7. [7]
    Wang, C., Ye, QY. and He YS. Calculation of an Exhausted Gas Cavity behind an Under-water Launched Missile[J]. Chinese Journal of Applied Mechanics, 1997, 14(3): 1–7. (in Chinese)Google Scholar
  8. [8]
    Zhong F., Lu X. and Zhuang L. Numerical Simulation of the Complex Flowfield for Rocket Launch Underwater[J]. Journal of Astronautics, 2000, 21(2): 1–7. (in Chinese)Google Scholar
  9. [9]
    Shan X., Yang R. and Ye QY. Fluid Forces on a Missile with Control System of Vectorial Thrust [J]. Journal of Shanghai Jiao Tong University, 2001, 35(4): 625–629. (in Chinese)Google Scholar
  10. [10]
    Wang, X., Chen, Y. and Liu C. Nozzle Flows of the Missile Launching Under Water[J]. Journal of Propulsion Technology. 2001, 22(1):61–64. (in Chinese)Google Scholar
  11. [11]
    Yi, S., Xu, S., Yan, K., Chen, J. Numerical Simulation of the Initial Stage of Noncondensing High-speed Gas Jet in Liquid[J]. Journal of Hydrodynamics, 2002, Ser. A, 17(4): 448–453. (in Chinese)Google Scholar
  12. [12]
    He, X., Ma, H. and Ji, C. Numerical Simulation of Gas Jets in Water[J]. Journal of Hydrodynamics, 2004, Ser. A, 19(2): 207–212. (in Chinese)Google Scholar
  13. [13]
    Zhai, D., Li, X. and An, Y. A Method Designed For Complex Phase Mixing Jet-flow[J]. Journal of Hydrodynamics, 2004, Ser. A, 19, Supplement: 833–837. (in Chinese)Google Scholar
  14. [14]
    Xu, X., Deng J., Ren A., Lu CJ. The Research on High-Speed Gas Jet of Nozzle Underwater [J]. Journal of Hydrodynamics, 2005, Ser. B, 17(2): 204–208.Google Scholar
  15. [15]
    Zhang, H. Non-oscillatory and Non-free-parameter Dissipation Difference Scheme[J]. Acta Aerodynamica Sinica, 1988, 6(2): 143–164. (in Chinese)Google Scholar
  16. [16]
    Hess, JL. and Smith, AMO. Calculation of Potential Flow About Arbitrary Bodies[J]. Progress in Aeronautical Sceence, 1967, 1-138.CrossRefGoogle Scholar
  17. [17]
    Longuet-Higgins, MS., Cokelet, E D. The Deformation of Steep Surface Waves on Water[J], (I) A Numerical Method of Computation. Proc. Roy. Soc. London, 1976, Series A, 350:1–26.MathSciNetCrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  • Yong-sheng Cheng
    • 1
  • Hua Liu
    • 1
  1. 1.Department of Engineering MechanicsShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations