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On the interaction and coalescence of spherical blast waves

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Abstract

The scaling and similarity laws concerning the propagation of isolated spherical blast waves are briefly reviewed. Both point source explosions and high pressure gas explosions are considered. Test data on blast overpressure from the interaction and coalescence of spherical blast waves emanating from explosives in the form of shaped charges of different strength placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure. The results point out the possibility of detecting source explosions from far-field pressure measurements.

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References

  1. Taylor, G.I.: The air wave surrounding an expanding sphere. Proc. R. Soc. A 186, 273 (1946)

    MathSciNet  MATH  Google Scholar 

  2. Taylor, G.I.: The formation of a blast wave by a very intense explosion, I. Proc. R. Soc. Ser. A 201, 159–174 (1950)

    MATH  Google Scholar 

  3. Taylor, G.I.: The formation of a blast wave by a very intense explosion, II. The atomic explosion of 1945. Proc. R. Soc. Ser. A. 201, 175 (1950)

    MATH  Google Scholar 

  4. Sedov, L.I.: Propagation of intense (strong) blast waves (in Russian). Prikl. Mat. Mek. (PMM) 10, 241 (1946)

    Google Scholar 

  5. Sedov, L.I.: Similarity and Dimensional Methods in Mechanics, Academic Press, New York, Chap. 4 (1959) (10th edn., CRC Press, London, 1993)

  6. Von Neumann, J.: The point source solution. National Defense Research Committee, Div. B Report AM-9 (see Collected Works of J. von Neumann, vol. VI, Pergamon Press, Oxford, p. 219, 1947)

  7. Sakurai, A.: On the propagation and the structure of the blast wave I. J. Phys. Soc. Jpn. 8, 662 (1953)

    Article  MathSciNet  Google Scholar 

  8. Sakurai, A.: On the propagation and the structure of the blast wave II. J. Phys. Soc. Jpn. 9, 256 (1954)

    Article  MathSciNet  Google Scholar 

  9. Oshima, K.: Blast waves produced by exploding wire. Rept. 358-26-9 Aeronautical Research Institute, University of Tokyo (1960)

  10. Goldstine, H.H., von Neumann, J.: Blast wave calculation. Commun. Pure Appl. Math. 8, 327–354 (1955)

    Article  MathSciNet  Google Scholar 

  11. Bach, G.G., Lee, J.H.S.: An analytical solution of blast waves. AIAA J. 8, 271 (1970)

    Article  Google Scholar 

  12. Whitham, G.B.: The propagation of spherical blast. Rept. 358, Aeronautical Research Institute, University of Tokyo, Tokyo (1960)

  13. Landau, L.D.: On shock waves at a large distance from the place of their origin. Soviet J. Phys. 9, 496 (1945)

    Google Scholar 

  14. Brode, H.L.: Numerical solutions for spherical blast waves. J. Appl. Phys. 26, 766–775 (1955)

    Article  MathSciNet  Google Scholar 

  15. Brode, H.L.: Blast wave from a spherical charge. Phys. Fluids 2(2), 217–229 (1959)

    Article  Google Scholar 

  16. Friedman, M.P.: A simplified analysis of spherical and cylindrical blast waves. J. Fluid Mech. 11, 1–15 (1961)

    Article  MathSciNet  Google Scholar 

  17. Liu, T.J., Khoo, B.C., Yeo, K.S.: The numerical simulations of explosion and implosion in air: use of a modified Harten’s TVD scheme. Int. J. Numer. Methods Fluids 31, 661–680 (1999)

    Article  MathSciNet  Google Scholar 

  18. Chen, H., Liang, S.M.: Planar blast/vortex interaction and sound generation. AIAA J. 40(11), 2298–2304 (2002)

    Article  Google Scholar 

  19. Sachdev, P.L.: Shock Waves and Explosions. Chapman & Hall/CRC, New York (2000)

    MATH  Google Scholar 

  20. Kinney, G.F, Graham, K.J.: Explosive Shocks in Air, 2nd edn. (see also 1st edn.) Springer, Heidelberg (1985)

  21. Starkenberg, J.K., Benjamin, K.J.: Predicting coalescence of blast waves from sequentially exploding ammunition stacks. Army Research Lab Report ARL-TR-645, December (1994)

  22. Shapiro, A.: The Dynamics and Thermodynamics of Compressible Fluid Flow. Wiley, New York (1953)

    Google Scholar 

  23. Liepmann, H.W., Roshko, A.: Elements of Gas Dynamics. Wiley, p. 63 (1953)

  24. Taylor, J.L.: An exact solution of the spherical blast wave problem. Philos. Mag. 46, 317 (1955)

    Article  MathSciNet  Google Scholar 

  25. Sakurai, A.: Exploding wires based on a conf. Exploding wire phenomena. In: Chace W.G., Moore H.K. (eds.) I. Plenum Press, New York (1959)

  26. Higashino, F., Henderson, L.F., Shimizu, F.: Experiments on the interaction of a pair of cylindrical weak blast waves in air. Shock Waves 1, 275–284 (1991)

    Article  Google Scholar 

  27. Sakurai, A.: Blast wave theory. In: Holt, M. (eds) Basic Developments in Fluid Dynamics. Academic Press, New York pp. 309–375 (1965)

    Google Scholar 

  28. Von Neumann, J., Richtmyer, R.D.: A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232–237 (1950)

    Article  MathSciNet  Google Scholar 

  29. Wyle Laboratories, Sonic and vibration environments for ground facilities—A design manual, Report No. WR 68–2 (1968) (L.C. Sutherland, Principal Author and Editor)

  30. Liang, S.M., Wang, J.S., Chen, H.: Numerical study of spherical blast-wave propagation and reflection. Shock Waves 12, 59–68 (2002)

    Article  Google Scholar 

  31. Freeman, R.A.: Variable energy blast waves. Brit. J. App. Phys. (J. Physics D), ser 2. 1, 1697–1710 (1968)

    Article  Google Scholar 

  32. Dabora, E.: Variable energy blast waves. AIAA J. 10(10), 1384–1386 (1972)

    Article  Google Scholar 

  33. Merlen, A., Dyment, A.: Similarity and asymptotic analysis for gun-firing aerodynamics. J. Fluid Mech. 225, 497–528 (1991)

    Article  Google Scholar 

  34. Merlen, A., Dyment, A.: Anisotropic blast waves and explosions in a moving gas. Eur. J. Mech. B/Fluids 11(2), 161–198 (1992)

    MathSciNet  MATH  Google Scholar 

  35. Merlen, A.: Generalization of the muzzle wave similarity rules. Shock Waves 9(5), 341–352 (1999)

    Article  Google Scholar 

  36. Jiang, Z., Takayama, K., Skews, B.W.: Numerical study on blast flowfields induced by supersonic projectiles discharged from shock tubes. Phys. Fluids 10(1), 277–288 (1988)

    Article  Google Scholar 

  37. Hikida, S., Needham, L.E.: Low Altitude Multiple Burst (LAMB) Model. S-cubed Final Report, S-CUBED-R-81-5067 (1981)

  38. Zaker, T.A.: Farfield overpressure from closely spaced sequential detonations. 11th Explosive Safety (1969)

  39. von Neumann, J., Oblique reflection of shocks. Expl. Res. Rept. 12, Dept. Navy, Washington DC, 1943 (see also Collected Works 6:238–299, Oxford Pergamon, 1963)

  40. Colela, P., Henderson, L.F.: The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213, 71–94 (1990)

    Article  MathSciNet  Google Scholar 

  41. NASA White Sands Test Facility.: STAR 48B Full Scale Demonstration Test. Special Test Report WSTF # 02-36952 (October 29, 2002)

  42. Kandula, M., Freeman, R.: On the interaction and propagation of spherical blast waves. AIAA-2007-4117 (2007)

  43. Diaci, J., Mozina, J.: A study of blast wave forms detected simultaneously by a microphone and a laser probe during laser ablation. Appl. Phys. A 55, 352–358 (1992)

    Article  Google Scholar 

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Correspondence to M. Kandula.

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Communicated by A. Merlen.

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Kandula, M., Freeman, R. On the interaction and coalescence of spherical blast waves. Shock Waves 18, 21–33 (2008). https://doi.org/10.1007/s00193-008-0134-1

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