Numerical simulation of air blast waves

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  • 1. Numerical simulation of air blast waves M. Arrigoni, S. Kerampran, ENSTA Bretagne, France J.-B. Mouillet, Altair Engineering France B. Simoens, M. Lefebvre, S. Tuilard, Ecole Royal Militaire de Bruxelles, Belgium R. Fallet, France 2011 European HyperWorks Technology Conference, 7-9 November, Bonn
  • 2. IntroductionCylindrical charge Spherical charge 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 2
  • 3. Blast wave in air with RADIOSS• Problem : – Experimental data are not available close to the explosive (<1m). – Experimental data are available only for given shapes (spherical, hemispherical, …) and given explosives (TNT, C4, …) Challenge : Modeling blast wave in close range, with a FEM code, without sofisticated models (combustion, turbulences, real gas, …). 1) Check the JWL law for TNT. 2) Check RADIOSS simulations vs Literature (Kingery, Kinney-Graham, Baker, Autodyn, Blast X, CONWEP,…). 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 3
  • 4. Table of content• Check the ability of modelling the detonation of high explosives (TNT) with RADIOSS (JWL).• Check the ability of modelling the blast wave propagation in air (perfect gaz) with RADIOSS (2D axisym. Eulerian). Comparison with experiments and scaling laws (CONWEP, Kinney-Graham, …)• Comparison with AUTODYN 2D.• Application to the detonation in air of cylindrical charge (L/D = 1).• Conclusion and perspectives. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 4
  • 5. Numerical simulation of the TNT detonation• TNT : C7H5O6N3 molecular weight : 227 g/mol CJ state ρ0 g/cm3 PCJ Mbar ρCJ g/cm3 γCJ DCJ km/s Dobratz 85 1.63 0.21 2.23 2.727 6.930 Kury 97 1.a 1.624 0.19 2.193 2.855 6.849 Kury 97 1.b 1.624 0.18 2.193 2.855 6.849 Kury 1997 2.a 1.645 0.195 2.218 2.871 6.930 Kury 1997 2.b 1.645 0.185 2.218 2.871 6.930 Souers kury 1993 1.632 0.205 2.193 2.979 7.070• The Jones-Wilkins-Lee equation of state :     R1 V     R2 V E P  A  1   e   B  1   e    R1  V   R2  V  V A, B, R1, R2 and ω are the model parameters, V is the density ratio ρ0/ρ, E the internal energy per unit volume of explosive (E=ρ0×eint). JWL param. A GPa B GPa w R1 R2 E0 Gpa V à CJ P à CJ Dobratz 1985 371.21 3.23 0.3 4.15 0.95 7 0.731 19.9 Dobratz 1981 373.8 3.747 0.35 4.15 0.9 6 0.731 19.7 Kury 1997 1.a 673.1 21.988 0.3 5.4 1.8 7 0.741 18.7 Kury 1997 1.b 3394.889 63.7085 0.6 8.3 2.8 7 0.741 17.9 Kury 1997 2.a 673.1 25.1735 0.3 5.4 1.8 7 0.742 19.3 Kury 1997 2.b 3394.889 70.9736 0.6 8.3 2.8 7 0.742 18.5 Souers et kury 1993 524.4089 4.900052 0.23 4.579 0.85 7.1 0.744 20.0 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 5
  • 6. Cylinder test for determining JWL parameters• Livermore cylinder test on OFHC Copper for reaction products EOS of explosives : 15.24 mm• Cylindrical test (adapted for spherical situations ?)• Experimental data is fitted by 2D code. explosive u(t)• Does not take into account the ZND peak pressure.• Does not take into account the post-detonation combustion. 300 mm• Does not take into account the grain size effects. D• Does not take into account the non detonated matter.• Does not take into account turbulences and instabilities.• The validity domain is reduced. 12.7 mm 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 6
  • 7. Numerical simulation of high explosive detonation using JWL in a rod• Axisym. rod (1D), Eulerian square mesh with 1 elm, TNT (Dobratz 1985) Other mesh shape : H/L = 8 and H/L = 0.5 BCS/110 z DETPOIN• The analytical PCJ calculated by the EOS JWL, using Dobratz parameters is 199 kBar.• The Radioss computed peak pressure reaches 194.8 kBar (for H/L=8).  -2.2% of relative error with 5000 elts.• The DCJ velocity is well reproduced (err<1%).• But the peak pressure is flattened.• But the pressure pulse is about three time longer than in 2D. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 7
  • 8. Numerical simulation of high explosive detonation using JWL in a rod• Axisym. rod (2D), Eulerian square mesh, TNT (Dobratz 1985) Other mesh shape : H/L = 8 BCS/110 z DETPOIN• The calculed PCJ by the EOS JWL, using Dobratz parameters is 199 kBar.• The DCJ velocity is well reproduced (err<1%).• The Radioss computed peak pressure reaches 193.1 kBar for H/L=8.  -3.0% of relative error with 5000 elts along z axis (40 000 elts). • Peak pressure and time duration are realistic (few µs).  Radioss is able to handle the JWL in a rod. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 8
  • 9. Detonation of spherical charge of 1 kg of TNT z . .. /MAT/EUL/1.0 .. BCS/010000• 2 D axisym. sphere of TNT from Dobratz 1985 0,2 PCJ .. . . y BCS/001011 0,18 DETPOIN (BCS/111000) 0,16 P max MBar Nb elem 0,14 nb elem Pcj Pcalc %err 4500 4500 0.199 0.158 -20.6 0,12 30000 30000 0.199 0.165 -17.1 50000 50000 0.199 0.166 -16.6 0,1 112500 0.199 0.172 -13.6 112500 0,08 0 2 4 6 8 10 abscisse cm PCJ is not reached (JWL not adapted for spherical geometry ?) Mesh with 30 000 offers the best compromise time-cost vs accuracy. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 9
  • 10. Effects of the JWL parameters set on detonation /MAT/EUL/1.0 BCS/010000• 2 D axisym. sphere of TNT with 30 000 elements 0,2 0,19 PCJ kur2b BCS/001011 0,18 kur2a DETPOIN 0,17 kur1b 0,16 P (Mbar) kur1a PCJ Pcalc %err 0,15 Dobratz 1985 0.1990 0.1647 -17.1 sou93 0,14 Dobratz 1981 0.1970 0.1648 -16.4 dob81 Kury 1997 1.a 0.1874 0.1515 -19.2 0,13 dob85 Kury 1997 1.b 0.1792 0.1415 -21.0 0,12 Kury 1997 2.a 0.1931 0.1587 -17.8 0,11 Kury 1997 2.b 0.1849 0.1566 -15.3 0,1 Souers 1993 0.2004 0.162 -19.2 0 2 4 6 abscisse mm PCJ is not reached for these mesh densities. The Dobratz, 1985 JWL set of parameters provides the highest P. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 10
  • 11. Detonation of Spherical charge of 1 kg of TNT in air• 2 D axisym. sphere of TNT with 30 000 elements in air (Law6 perfect gas). Variable Value C0 = 340 m/s P0 = 1 atm ρ0 1.225e-03 g/cm3 γ 1.4 ν 1.5e-5 cm/µs Ref. Temp. 288 °K E0 2.5e-03 kbar Specific Heat 0.000718 kJ/gK 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 11
  • 12. About blast waves• Temporal profile of a blast wave : Pressure ∆P0 P(t) Time ~2 ms Time of arrival Duration Duration td+ td- 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 12
  • 13. Numerical simulation of blast wave• Free field, 2D axisym.• 1 kg spherical charge of TNT, JWL Dobratz 1985• Air is perfect gas.• UPWIND Petrov-Galerkin (SUPG) or Taylor-Galerkin (TG) as flux limiter [F. Perie IRUC 1995] : « the information for each characteristic variable is obtained by looking in the direction from which this information should be coming. » 0 ≤ UPWIND ≤ 1 must respect the CFL condition, usually UPWIND = 1/Mach CAUTION : Only available for EUL ! 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 13
  • 14. Blast wave in air• Max pressure (bar) in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985)Reduceddist. withoutcm/kg1/3 UPWIND supg=1 supg=0.5 supg=0.2 supg=0.1 supg=0.05 supg=0.02 supg=0.01 12 271.4 392.9 395.8 367.5 382.2 390.1 394.8 396.8 24 106 130.6 130.7 125.5 127.7 129.7 130.6 130.8 48 34.7 45.1 45.3 42.4 43.7 44.4 45.1 45.1 96 7.6 10.4 10.5 9.6 10.1 10.2 10.4 10.5Reduceddist. withoutcm/kg1/3 UPWIND Tg=1 Tg=0.5 Tg=0.2 Tg=0.1 Tg=0.05 Tg=0.02 Tg=0.01 12 271.3 392.9 395.8 397.4 397.7 398.4 398.4 398.4 24 106.6 130.6 130.7 131 131.2 131.2 131.2 131.2 48 34.7 45.1 45 45.5 45.5 45.5 45.6 err 96 7.6 10.4 10.5 10.5 10.5 10.5 10.5 err Same results Highest differences Closest to literature
  • 15. Comparison with exp & Autodyn• Pressure in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985), SUPG=0.02 400 350 Radioss 2D Radioss is about -17% below the 300 Kinney-Graham Kinney-Graham prediction : The Overpressure (Bar) 250 mesh is enlarged with the reduced Autodyn 2D distance. 200 150 CONWEP 100 50 0 0 50 100 150 200 Reduced distance (cm/kg1/3)Physics is not well known and overpressurevaries a lot with reduced distance. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 15
  • 16. Comparison with exp & Autodyn• Time of arrival in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985) 2500 Radioss time of arrival (µs) 2000 Kinney-Graham 1500 CONWEP 1000 500 0 0 50 100 150 200 reduced distance (cm/kg1/3)Good agreement in close range but diffusion when mesh is growing (far range) 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 16
  • 17. Comparison with exp & Autodyn• Duration of positive phase 5000 4500 duration of positive phase (µs) Radioss 4000 Kinney-Graham 3500 CONWEP 3000 2500 2000 1500 1000 500 0 0 50 100 150 200 Reduced distance (cm/kg1/3)Prediction between CONWEP and Kinney-Graham : magnitude is satisfying. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 17
  • 18. Comparison with exp & Autodyn• Impulse of positive phase 700 Radioss Kinney-Graham 600 Impluse (bar.ms) 500 CONWEP autodyn 2D 400 Baker Blastx 300 200 100 0 0 50 100 150 200 Reduced distance (cm/Kg1/3)Order of magnitude is satisfying and tendance in agreement with experiments 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 18
  • 19. Cylindrical charge• Radioss is in agreements with exp. for blast waves from spherical detonation of TNT.• What about blast waves from cylindrical charges (land mines, …) ? – Experiments with emulsion (Simoens et al 2010) – L/D = 1 Lateral blast wave (torical) Bridge wave End blast wave (Ismail et al 1993) TNT equivalent is local ! 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 19
  • 20. Experiments vs simulations• Cylindrical charge of emulsion L/D =1 x L/D=1, 110cm Experiments Mesh size and shape sensitive Order of magnitude and Tendancy are respected. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 20
  • 21. Experiments vs Simulations2011 European HyperWorks Technology Conference, 7-9 November, Bonn 21
  • 22. Conclusion• Radioss is able to handle JWL law (err < 1% in 1D).• Discrepancies are persisting due to the modeling (perfect gas, no turbulence, no instabilities, simple detonation law JWL, no grain size effects, no partial detonation, …), but not more 18 % vs Kinney-Graham.• Radioss also gives orders of magnitudes and tendencies in agreements with experiments in the case of a cylindrical detonation in air (L/D=1), for : – Pmax – Time of arrival – Duration time – Positive impulse• Radioss results are comparable with Autodyn. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 22
  • 23. Perspectives• Considere real gas in Radioss.• Compare with Polytropic law, Lee Tarver, Sesame laws also available in RADIOSS.• Compare with other explosives (C4, HMX, RDX, PETN, …).• Implement another detonation law ? (BKW, …)• Try other cylindrical configuration (L/D = 8,3).• Deduce a local TNT equivalent from experiments. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 23
  • 24. Any Questions ?2011 European HyperWorks Technology Conference, 7-9 November, Bonn 24
  • 25. About detonations• Detonation : supersonic exothermic chemical decomposition (< 1µs) of an energetic molecule provoking a shock wave.• Chapman-Jouget detonation : the reactive area and the shock front are merged.• 1D case : Conservation of mass: 0u0  1u1 Conservation of momentum: p0   0 u0  p1  1u12 2 2 Conservation of energy: u0 u12 h0   h1  2 2 Where h enthalpy, u material velocity, p hydrodynamic pressure, ρ=1/v density 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 25
  • 26. About detonations p1  p0• Combination of conservation equations :  0 u0  12u12  m 2 2 2   0  1• Thermodynamic states in the energetic material : ZND point• The C-J state is a characteristic of the energetic material. 2011 European HyperWorks Technology Conference, 7-9 November, Bonn 26
  • 27. About blast waves • Scaling laws (Hopkinson-Cranz) : Spherical charge of TNT in air (in Kinney-Graham)   Z 2    Z   10 808 1     980 1    ΔP    4.5   Patm td    0.54   0 1 2 2 2   Z   1   Z   1   Z  3 6 2 1 Z  1 Z  1 Z  W3       1           0.048   0.32  1.35    0.02     0.74    6.9  4 0.067 1   Z     0.23  Is   3 Z 231   Z    1.55  2011 European HyperWorks Technology Conference, 7-9 November, Bonn 27