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On the water exit of supercavitating projectiles with different head shapes

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Abstract

In this paper, the water-exit phenomenon has been studied experimentally and numerically. Based on the volume-of-fluid model and the Schnerr–Sauer cavitation model, the water-exit supercavitation around different shapes of cavitator projectiles is investigated using a dynamic mesh technology and three-dimensional six-degree-of-freedom method. The numerical results are compared with the experimental results obtained in our laboratory. Next, the effects of the cavitator shape on the characteristics of the projectile motion, breaking of the free surface, supercavitation size, and hydrodynamics of the water-exit supercavitation are analyzed. It was found that the hemispherical-nose projectile holds the best storage capacity and the longest displacement. The blunt disk-shaped nose projectile generates the maximum diameter of supercavity. The cavitation diameters of the conical-nose projectile and the hemispherical-nose projectile are relatively small.

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References

  1. Logvinovich, G.V.: Hydrodynamics of Flows with Free Boundaries. Naukova Dumka, Kiev (1969)

    Google Scholar 

  2. Nair, V.V., Bhattacharyya, S.K.: Water entry and exit of axisymmetric bodies by CFD approach. J. Ocean Eng. Sci. 3, 156–174 (2018). https://doi.org/10.1016/j.joes.2018.05.002

    Article  Google Scholar 

  3. Erfanian, M.R., Anbarsooz, M., Rahimi, N., Zare, M., Moghiman, M.: Numerical and experimental investigation of a three dimensional spherical-nose projectile water entry problem. Ocean Eng 104, 397–404 (2015). https://doi.org/10.1016/j.oceaneng.2015.05.024

    Article  Google Scholar 

  4. Nguyen V.T., Ha C.T., Park W.G.: Multiphase flow simulation of water-entry and-exit of axisymmetric bodies. ASME 2013 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, California, USA (2013). https://doi.org/10.1115/IMECE2013-64691

  5. Zhang, J.Z., You, T.Q., He, Q.K., Wei, Y., Wang, C.: Numerical analysis of cavitation flow during vertical water exit of underwater vehicles. J. Adv. Mater. Res. 201–203, 2780–2784 (2011)

    Article  Google Scholar 

  6. Wu, Q.G., Ni, B.Y., Bai, X.L., Cui, B., Sun, S.L.: Experimental study on large deformation of free surface during water exit of a sphere. Ocean Eng. 140, 369–376 (2017). https://doi.org/10.1016/j.oceaneng.2017.06.009

    Article  Google Scholar 

  7. He, C.T., Wang, C., Min, J.X., Jin, D.Q., Huang, H.L.: Numerical simulation of early air-cavity of cylinder cone with vertical water-entry. J. Eng. Mech. 29(4), 237–243 (2012). (in Chinese)

    Google Scholar 

  8. Sun, Z., Cao, W., Wang, C.: Numerical investigations of hydrodynamic force acting on sphere during water entry. J. Vib. Shock 36(20), 165–172 (2017). https://doi.org/10.13465/j.cnki.jvs.2017.20.026. (in Chinese)

    Article  Google Scholar 

  9. Zhang, C.X., Li, X.L., Liu, Y.Q.: Numerical investigation of water-exit cavity flow of missile with complex configuration. J. Syst. Simul. 28(6), 1321–1328 (2016). https://doi.org/10.16182/j.cnki.joss.2016.06.010. (in Chinese)

    Article  Google Scholar 

  10. Kirschner, I.N., Fine, N.E., Uhlman, J.S., Gieseke, T.A., Kuklinski, R., Kring, D.C., Rosenthal, B.J., Varghese, A.N.: Supercavitation Research and Development. Undersea Defense Technologies, Waikiki, HI (2001)

  11. Cameron, P., Rogers, P., Doane, J., Gifford, D.: An experiment for the study of free-flying supercavitating projectiles. ASME J. Fluids Eng. 133, 021303-1–9 (2011). https://doi.org/10.1115/1.4003560

    Article  Google Scholar 

  12. Fedorenko, N.S., Kozenko, V.F., Kozenko, R.N.: Experiment study of the inertial motion of supercavitating models. In: Nesteruk, I. (ed.) Supercavitation, pp. 27–37. Springer (2011). https://doi.org/10.1007/978-3-642-23656-3_2

    Chapter  Google Scholar 

  13. Baradaran, F.M., Nikseresht, A.H.: Numerical simulation of unsteady 3D cavitating flows over axisymmetric cavitators. Sci. Iran B 19(5), 1258–1264 (2012). https://doi.org/10.1016/j.scient.2012.07.013

    Article  Google Scholar 

  14. Kim, S., Kim, N.: Integrated dynamics modeling for supercavitating vehicle systems. Int. J. Nav. Archit. Ocean Eng. 7(2), 346–363 (2015). https://doi.org/10.1515/ijnaoe-2015-0024

    Article  Google Scholar 

  15. Shi, H.H., Hu, J.H., Zhou, H.L.: Experimental and theoretical analysis of water exit of a supercavity. Acta Aerodyn. Sin. 32(4), 544–550 (2014). https://doi.org/10.7638/kqdlxxb-2013.0008. (in Chinese)

    Article  Google Scholar 

  16. Shi, H.H., Hu, Q.Q., Chen, B., Jia, H.X.: Experimental study of supercavitating flows induced by oblique and vertical water entry of blunt bodies. Explos. Shock Waves 35(5), 617–624 (2015). https://doi.org/10.11883/1001-1455(2015)05-0617-08

    Article  Google Scholar 

  17. Shi, H.H., Zhou, Y.J., Jia, H.X., Zhu, B.B.: The effects of water depth and length-to-diameter ratio on drag coefficient and cavity shape of underwater supercavitating projectiles. Acta Armamentarii 37(11), 2029–2036 (2016). https://doi.org/10.3969/j.issn.1000-1093.2016.11.010. (in Chinese)

    Article  Google Scholar 

  18. Shi, H.H., Gao, J.R., Jia, H.X., Hu, J.H., Zhou, Y.J., Chen, B.: Cavitating gas-liquid two-phase flow pattern in water exit of a high-speed body. J. Univ. Chin. Acad. Sci. 33(2), 271–276 (2016). https://doi.org/10.7523/j.issn.2095-6134.2016.02.020. (in Chinese)

    Article  Google Scholar 

  19. Jia, H.X., Shi, H.H., Hu, J.H., Chen, B.: Experiments on water exit phenomenon of underwater launched projectiles with a supercavity. J. Ship Mech. 21(7), 814–820 (2017). https://doi.org/10.3969/j.issn.1007-7294.2017.07.003. (in Chinese)

    Article  Google Scholar 

  20. Smith, L.M., Woodruff, S.L.: Renormalization-group analysis of turbulence. Annu. Rev. Fluid Mech. 30(1), 275–310 (1998). https://doi.org/10.1146/annurev.fluid.30.1.275

    Article  MathSciNet  MATH  Google Scholar 

  21. Schnerr, G.H., Sauer, J.: Physical and numerical modeling of unsteady cavitation dynamics. Fourth International Conference on Multiphase Flow (Vol. 1), New Orleans, USA (2001)

  22. Zheng, Z.Y., Li, F.C., Li, Q., Kulagin, V.A.: Numerical study on the characteristics of natural supercavitation by planar symmetric wedge-shaped cavitators for rotational supercavitating evaporator. Sci. China Technol. Sci. 58(006), 1072–1083 (2015). https://doi.org/10.1007/s11431-015-5827-y

    Article  Google Scholar 

  23. Zhang, X.W., Li, Q., Huang, L.: Analysis of drag reduction on super-cavitation projectile based on 6DOF. J. Project. Rock. Missiles Guid. 36(05), 109-111+141 (2016). https://doi.org/10.15892/j.cnki.djzdxb.2016.05.028. (in Chinese)

    Article  Google Scholar 

  24. Lu, L.W.: Research on supercavitation flows’ characteristics of projectiles with complex structure in water exit and entry. Master Thesis, Zhejiang Sci-Tech University, Hangzhou, China (2019) (in Chinese)

  25. Kleefsman, K.M.T., Fekken, G., Veldman, A.E.P., Iwanowski, B., Buchner, B.: A volume-of-fluid based simulation method for wave impact problems. J. Comput. Phys. 206(1), 363–393 (2005). https://doi.org/10.1016/j.jcp.2004.12.007

    Article  MathSciNet  MATH  Google Scholar 

  26. Kleefsman, K.M.T., Fekken, G., Veldman, A.E.P., Iwanowski, B.: An improved volume-of-fluid method for wave impact problems. In: Proceedings of 14th International Offshore and Polar Engineering Conference, pp. 334–341. International Society of Offshore and Polar Engineering, California, USA (2004)

    MATH  Google Scholar 

  27. May, A.: Water entry and the cavity-running behavior of missiles. Final Technical Report, SEAHAC TR75-2, Naval Sea Systems Command, Arlington, VA, USA (1975)

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Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY16A020003).

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Correspondence to Y. Liu.

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Communicated by C.Y. Wen.

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Shi, H.H., Zhou, D.H., Lu, L.W. et al. On the water exit of supercavitating projectiles with different head shapes. Shock Waves 31, 597–607 (2021). https://doi.org/10.1007/s00193-021-01025-7

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