Skip to main content
SpringerLink
Log in

Underwater explosion in centrifuge part I: Validation and calibration of scaling laws

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Centrifuge is a promising tool for underwater explosion (UNDEX) research as both Mach and Froude similitudes could be satisfied with hyper-gravity in models, which would result in similarities in both shock wave and bubble oscillation. Scaling laws for UNDEX in centrifuge have been proposed based on dimensional analysis. Two dimensionless numbers, i.e., π3 and π4, are used to characterize shock wave and bubble oscillation, respectively. To validate scaling laws, 17 UNDEX tests are designed by varying accelerations or explosive weights and positions in centrifuge. The tests are classified into different groups to validate scaling laws as well as calibrate coefficients in empirical formulae for both shock wave and bubble oscillation. The results show that changes of gravity acceleration or hydrodynamic pressure almost has no influence on shock wave peak pressure and time constant as long as π3 is constant. The dimensionless bubble period and maximum radius agreed with each other when π4 is constant. Based on the research, an example is exhibited to suggest method for the computation of initial loading conditions for a submerged obstacle subjected to UNDEX.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Snay H G. Hydrodynamics of underwater explosions. In: Symposium on Naval Hydrodynamics. 1957, 515: 325

    Google Scholar 

  2. Cole R H. Underwater Explosions. New Jersey: Princeton University Press, 1948

    Book  Google Scholar 

  3. Zamyshlyaev B V, Yakovlev Y S. Dynamic Loads in Underwater Explosion. Naval Intelligence Support Center Washington DC Translation Div AD-757 183. 1973

    Google Scholar 

  4. Plesset M S, Chapman R B. Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J Fluid Mech, 1971, 47: 283–290

    Article  Google Scholar 

  5. Geers T L, Hunter K S. An integrated wave-effects model for an underwater explosion bubble. J Acoust Soc Am, 2002, 111: 1584–1601

    Article  Google Scholar 

  6. Wilkerson S. A boundary integral approach for three-dimensional underwater explosion bubble dynamics. Army Ballistic Research Lab Aberdeen Proving Ground Maryland AD-A252 412. 1992

    Google Scholar 

  7. Li Z, Sun L, Zong Z, et al. Some dynamical characteristics of a nonspherical bubble in proximity to a free surface. Acta Mech, 2012, 223: 2331–2355

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu M B, Liu G R, Lam K Y, et al. Smoothed particle hydrodynamics for numerical simulation of underwater explosion. Comp Mech, 2003, 30: 106–118

    Article  MATH  Google Scholar 

  9. Wang C, Khoo B C. An indirect boundary element method for threedimensional explosion bubbles. J Comp Phys, 2004, 194: 451–480

    Article  MATH  Google Scholar 

  10. Barras G, Souli M, Aquelet N, et al. Numerical simulation of underwater explosions using an ALE method. The pulsating bubble phenomena. Ocean Eng, 2012, 41: 53–66

    Article  Google Scholar 

  11. Zhang A M, Li S, Cui J. Study on splitting of a toroidal bubble near a rigid boundary. Phys Fluids, 2015, 27: 062102

    Article  Google Scholar 

  12. Jiang L, Ge H, Feng C L, et al. Numerical simulation of underwater explosion bubble with a refined interface treatment. Sci China-Phys Mech Astron, 2015, 58: 1–10

    Article  Google Scholar 

  13. Mahmadi K, Aquelet N. Euler–Lagrange simulation of high pressure shock waves. Wave Motion, 2015, 54: 28–42

    Article  MathSciNet  Google Scholar 

  14. Petrov N V, Schmidt A A. Multiphase phenomena in underwater explosion. Exp Thermal Fluid Sci, 2015, 60: 367–373

    Article  Google Scholar 

  15. Koukouvinis P, Gavaises M, Supponen O, et al. Numerical simulation of a collapsing bubble subject to gravity. Phys Fluids, 2016, 28: 032110

    Article  Google Scholar 

  16. Song G, Zu Z Y, Long Y, et al. Experimental and numerical investigation of the centrifugal model for underwater explosion shock wave and bubble pulsation. Ocean Eng, 2017, 142: 523–531

    Article  Google Scholar 

  17. Snay H G. The scaling of underwater explosion phenomena. Naval Ordnance Lab White Oak MD. 1962

    Book  Google Scholar 

  18. Gaspin J B. Depth scaling of underwater explosion source levels. Naval Surface Weapons Center White Oak Lab Silver Spring Maryland. 1975

    Google Scholar 

  19. Gel’fand B E, Takayama K. Similarity criteria for underwater explosions. Combust Explosion Shock Waves, 2004, 40: 214–218

    Article  Google Scholar 

  20. Goertner J F. Scaling Underwater Explosion shock waves for differences in ambient sound speed and density. Naval Surface Weapons Center Silver Spring Maryland AD-A102 366. 1980

    Book  Google Scholar 

  21. Goertner JF. Vacuum tank studies of gravity migration of underwater explosion bubbles. Navord Technical Report 3902. 1956

    Google Scholar 

  22. Gong S W, Ohl S W, Klaseboer E, et al. Scaling law for bubbles induced by different external sources: Theoretical and experimental study. Phys Rev E, 2010, 81: 056317

    Article  Google Scholar 

  23. Osborne M F M, Taylor A H. Non-linear propagation of underwater shock waves. Phys Rev, 1946, 70: 322–328

    Article  Google Scholar 

  24. Slifko J F. Pressure-pulse characteristics of deep explosions as functions of depth and range. Naval Ordnance Lab White Oak Maryland AD 661 804. 1967

    Book  Google Scholar 

  25. Kira A, Fujita M, Itoh S. Underwater explosion of spherical explosives. J Mater Proc Tech, 1999, 85: 64–68

    Article  Google Scholar 

  26. Klaseboer E, Hung K C, Wang C, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J Fluid Mech, 2005, 537: 387–413

    Article  MATH  Google Scholar 

  27. Wang B, Zhang Y P, Wang Y P. Experimental study on bubble oscillation formed during underwater explosions (in Chinese). Explosion Shock Waves, 2009, 28: 572–576

    Google Scholar 

  28. Hung C F, Hwangfu J J. Experimental study of the behaviour of minicharge underwater explosion bubbles near different boundaries. J Fluid Mech, 2010, 651: 55–80

    Article  MATH  Google Scholar 

  29. Chahine G L, Frederick G S, Lambrecht C J, et al. Spark-generated bubbles as laboratory-scale models of underwater explosions and their use for validation of simulation tools. In: SAVIAC Proceedings of the 66th Shock and Vibrations Symposium. Biloxi, 1995. 256–276

    Google Scholar 

  30. Cui J. Experimental study on underwater explosion bubble loads and damage on the structure nearby (in Chinese). Dissertation for the Doctoral Degree. Harbin: Harbin Engineering University, 2013

    Google Scholar 

  31. Ma K, Chu Z, Wang K H, et al. Experimental research on bubble pulse of small scale charge exploded under simulated deep water (in Chinese). Explosion Shock Waves, 2015, 35: 320–325

    Google Scholar 

  32. Zhang S, Wang S P, Zhang A M. Experimental study on the interaction between bubble and free surface using a high-voltage spark generator. Phys Fluids, 2016, 28: 032109

    Article  Google Scholar 

  33. Schmidt R M, Holsapple K A. Theory and experiments on centrifuge cratering. J Geophys Res, 1980, 85: 235–252

    Article  Google Scholar 

  34. Schmidt R M, Housen K R. Some recent advances in the scaling of impact and explosion cratering. Int J Impact Eng, 1987, 5: 543–560

    Article  Google Scholar 

  35. Fan Y, Chen Z, Liang X, et al. Geotechnical centrifuge model tests for explosion cratering and propagation laws of blast wave in sand. J Zhejiang Univ-Sci A, 2012, 13: 335–343

    Article  Google Scholar 

  36. Price R S. Underwater explosion tests in a preliminary high-gravity tank accelerated by a centrifuge. Naval Ordnance Lab White Oak Maryland. 1961

    Google Scholar 

  37. Price R S, Zuke W G, Infosino C. A study of underwater explosions in a high gravity tank. Naval Ordnance Lab White Oak Maryland AD352 834. 1964

    Book  Google Scholar 

  38. Snay H G. Migration of explosion bubbles in a rotating test tank. Naval Ordnance Laboratory White Oak Maryland NOLTER 61–145. 1962

    Google Scholar 

  39. Liu W T, Yao X L, Li S, et al. Experimental principle and numerical study of scaled-down underwater explosion model on a centrifuge apparatus (in Chinese). Explosion Shock Waves, 2016, 36: 789–796

    Google Scholar 

  40. Vanadit-Ellis W, Davis L K. Physical modeling of concrete gravity dam vulnerability to explosions. In: Waterside Security Conference (WSS), 2010 International. IEEE, 2010. 1–11

    Google Scholar 

  41. De A, Niemiec A, Zimmie T F. Physical and numerical modeling to study effects of an underwater explosion on a buried tunnel. J Geotech Geoenviron, 2017: 04017002

    Google Scholar 

  42. Zhang X D, Hou Y J, Liang X Q, et al. Centrifuge modeling research on the influence of underwater blasting on a dam (in Chinese). Chin Northwestern Seismol J, 2011, 33: 234–236

    Google Scholar 

  43. Snay H G. Model tests and scaling. Naval Ordnance Lab White Oak Maryland AD357501. 1964

    Book  MATH  Google Scholar 

  44. Buckingham E. On physically similar systems: Illustrations of the use of dimensional equations. Phys Rev, 1914, 4: 345–376

    Article  Google Scholar 

  45. Swisdak J M. Explosion effects and properties: Part II-explosion effects in water. Naval Surface Weapons Center Silver Spring Maryland TR76-116. 1978

    Book  Google Scholar 

  46. Iffenegger C R. Revised similitude equations for the underwater shock-wave performance of pentolite and hbx-1. Naval Ordnance Lab White Oak Maryland. 1961

    Book  Google Scholar 

  47. Coleburn N L, Roslund L A, Heathcote T B, et al. Improvements in underwater explosion systems: Field tests, phase I. Naval Ordnance Lab White Oak Maryland. 1966

    Google Scholar 

  48. Coleburn N L, Roslund L A, Heathcote T B, et al. Improvements in underwater explosion systems: Field tests, phase II. Naval Ordnance Lab White Oak Maryland. 1966

    Google Scholar 

  49. Li J H, Zhao J B, Tan D W, et al. Underwater shock wave performances of explosives (in Chinese). Explosion, Shock Waves, 2009, 29: 172–176

    Google Scholar 

  50. Plesset M S, Prosperetti A. Bubble dynamics and cavitation. Annu Rev Fluid Mech, 1977, 9: 145–185

    Article  MATH  Google Scholar 

  51. Vernon T A. Whipping response of ship hulls from underwater explosion bubble loading. Defence Research Establishment Atlantic Canada 86/225. 1986

    Google Scholar 

  52. Snay H G. Underwater explosion phenomena: The parameters of migrating bubbles. Naval Ordnance Laboratory White Oak Maryland NAVORD 4185. 1962

    Google Scholar 

  53. Snay H G, Tipton R V. Charts for the parameters of migrating explosion bubbles. Naval Ordnance Laboratory White Oak Maryland NOLTR 62–184. 1963

    Book  Google Scholar 

  54. Wang B, Zhang G S, Gao N, et al. Application of high-speed photography in bubble oscillation at underwater explosion (in Chinese). Chin J Energ Mater, 2010, 18: 102–106

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. China Institute of Water Resources and Hydropower Research, Beijing, 100048, China

    Jing Hu, ZuYu Chen, XueDong Zhang, YingQi Wei, XiangQian Liang & JianHui Liang

  2. School of Transportation Science and Engineering, Beihang University, Beijing, 100083, China

    Jing Hu & ZuYu Chen

  3. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, 100124, China

    GuoWei Ma & QiuSheng Wang

  4. College of Field Engineering, PLA University of Science and Technology, Nanjing, 210007, China

    Yuan Long

Authors
  1. Jing Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ZuYu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. XueDong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. YingQi Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. XiangQian Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. JianHui Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. GuoWei Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. QiuSheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Yuan Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ZuYu Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, J., Chen, Z., Zhang, X. et al. Underwater explosion in centrifuge part I: Validation and calibration of scaling laws. Sci. China Technol. Sci. 60, 1638–1657 (2017). https://doi.org/10.1007/s11431-017-9083-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-017-9083-0

Keywords

Search

Navigation