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Numerical simulation of flow fields induced by a supersonic projectile moving in tubes

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Abstract

Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.

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References

  1. Jiang Z., Huang Y.H., Takayama K.: Wave dynamic processed induced by a supersonic projectile discharging from a shock tube. Phys. Fluids 15(6), 1665–1675 (2003)

    Article  Google Scholar 

  2. Sun M., Takayama K.: The formation of a secondary shock wave behind a shock wave diffracting at a convex corner. Shock Waves 7(5), 287–295 (1997)

    Article  MATH  Google Scholar 

  3. Sun M., Siato T., Takayama K.: Unsteady drag on a sphere by shock loading. Shock Waves 14(1–2, 221), 3–9 (2005)

    Article  MATH  Google Scholar 

  4. Kim H.D., Setoguchi T.: Study of the discharge of wave shocks from an open end of a duct. J. Sound Vib. 226(5), 1011–1028 (1999)

    Article  Google Scholar 

  5. Bagabir A., Drikakis D.: Numerical experiments using high resolution schemes for unsteady, invisid compressible flows. Comput. Methods Appl. Mech. Eng. 193, 4675–4705 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Rajesh G., Kim H.D., Matsuo S., Setoguchi T.: A study of the unsteady projectile aerodynamics using a moving coordinates method. J. Aerosp. Eng. 221(5), 691–706 (2007)

    Google Scholar 

  7. Settles, G.S., Grumstrup, T.P., Miller, J.D. Hargather, M.J., Dodson, L.J., Gatto, J.A.: Full-scale high-speed ‘Edgerton’ retroreflective shadowgraphy of explosions and gunshots. In: 5th Pacific Symposium on Flow Visualization and Image Processing, 27–29th September, Australia (2005)

  8. Glass I.I.: Shock Waves and Man. The University of Toronto Press, Toronto (1974)

    Google Scholar 

  9. Matsummura T., Funabashi S., Taitoh T., Takayama K.: A holographic interferometric study of the axisymmetric supersonic flow around a cylindrical projectile. Rep. Ins. Fluid Sci. Tohoku Univ. 5, 89–97 (1993)

    Google Scholar 

  10. Jiang Z., Takayama K.: Numerical study on blast flow fields induced by supersonic projectiles discharged from shock tubes. Phys. Fluids 10(1), 277–288 (1998)

    Article  Google Scholar 

  11. Jiang X.H., Chen Z.H., Fan B.C., Li H.Z.: Numerical simulation of blast flow fields induced by a high-speed projectile. Shock Waves 18(3), 205–212 (2008)

    Article  MATH  Google Scholar 

  12. Cler, D.L., Chevaugeon, N., Shephard M.S., Remacle, J.F.: CFD application to gun muzzle blast-a validation case study. AIAA Paper, No. 2003–1142 (2003)

  13. Rajesh G., Kim H.D., Setotuchi T.: Projectile aerodynamics overtaking a shock wave. J. Spacecr. Rockets 45(6), 1251–1261 (2008)

    Article  Google Scholar 

  14. Jiang G.S., Shu C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126(1), 202–228 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sussman M., Smereka P., Osher S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146–159 (1994)

    Article  MATH  Google Scholar 

  16. Osher S., Sethian J.: A Fronts propagating with curvature-dependent speed: algorithm as based on Hamilton–Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fedkiw R., Aslam T., Merriman B., Osher S.: A non-oscillatory Eulerian approach to interfaces in multi-material flows (the Ghost Fluid Method). J. Comput. Phys. 152(2), 457–492 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sod G.A.: A numerical study of a converging cylindrical shock. J. Fluid Mech. 83(4), 785–794 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shu C.W., Osher S.: Eifficient implementation of essentially non-oscillatory shock-capturing shceme. J. Comput. Phys. 77(2), 439–471 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu X.D., Osher S., Chan T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115(1), 200–212 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shanghai Jiaotong University, Shanghai, 200240, China

    B. Zhang, H. Liu & F. Chen

  2. Department of Aerospace Engineering, Harbin Engineering University, Harbin, 150001, China

    G. Wang

Authors
  1. B. Zhang
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  2. H. Liu
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  3. F. Chen
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  4. G. Wang
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Correspondence to B. Zhang.

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Communicated by O. Igra.

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Zhang, B., Liu, H., Chen, F. et al. Numerical simulation of flow fields induced by a supersonic projectile moving in tubes. Shock Waves 22, 417–425 (2012). https://doi.org/10.1007/s00193-012-0389-4

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  • DOI: https://doi.org/10.1007/s00193-012-0389-4

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