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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

2011 European HyperWorks Technology Conference, 7-9 November, Bonn 2

Introduction

Spherical charge Cylindrical charge


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,…).


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.


Numerical simulation of the TNT detonation

• TNT : C7H5O6N3 molecular weight : 227 g/mol

• The Jones-Wilkins-Lee equation of state :

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).

V

Ee

VRBe

VRAP

VRVR

21

21

11

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

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


Cylinder test for determining JWL parameters

• Livermore cylinder test on OFHC Copper for reaction products EOS of explosives :

30

0 m

m

15.24 mm

12.7 mm

explosive

D

u(t)

• Cylindrical test (adapted for spherical situations ?) • Experimental data is fitted by 2D code. • Does not take into account the ZND peak pressure. • Does not take into account the post-detonation combustion. • Does not take into account the grain size effects. • Does not take into account the non detonated matter. • Does not take into account turbulences and instabilities. • The validity domain is reduced.


Numerical simulation of high explosive detonation using JWL in a rod

• Axisym. rod (1D), Eulerian square mesh with 1 elm, TNT (Dobratz 1985)

• 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.

z BCS/110

DETPOIN

Other mesh shape : H/L = 8 and H/L = 0.5


Numerical simulation of high explosive detonation using JWL in a rod

• Axisym. rod (2D), Eulerian square mesh, TNT (Dobratz 1985)

• 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.

z BCS/110

DETPOIN

Other mesh shape : H/L = 8


Detonation of spherical charge of 1 kg of TNT

• 2 D axisym. sphere of TNT from Dobratz 1985

0,08

0,1

0,12

0,14

0,16

0,18

0,2

0 2 4 6 8 10

P m

ax M

Bar

abscisse cm

4500

30000

50000

112500

Nb elem

PCJ

PCJ is not reached (JWL not adapted for spherical geometry ?)

Mesh with 30 000 offers the best compromise time-cost vs accuracy.

nb elem Pcj Pcalc %err 4500 0.199 0.158 -20.6

30000 0.199 0.165 -17.1 50000 0.199 0.166 -16.6

112500 0.199 0.172 -13.6

BCS/001011

BC

S/0

10

00

0

DETPOIN (BCS/111000)

/MAT/EUL/1.0

. . . z

y . . . . . .


Effects of the JWL parameters set on detonation

0,1

0,11

0,12

0,13

0,14

0,15

0,16

0,17

0,18

0,19

0,2

0 2 4 6

P (

Mb

ar)

abscisse mm

kur2b

kur2a

kur1b

kur1a

sou93

dob81

dob85

PCJ

• 2 D axisym. sphere of TNT with 30 000 elements

PCJ is not reached for these mesh densities.

The Dobratz, 1985 JWL set of parameters provides the highest P.

PCJ Pcalc %err Dobratz 1985 0.1990 0.1647 -17.1 Dobratz 1981 0.1970 0.1648 -16.4 Kury 1997 1.a 0.1874 0.1515 -19.2 Kury 1997 1.b 0.1792 0.1415 -21.0 Kury 1997 2.a 0.1931 0.1587 -17.8 Kury 1997 2.b 0.1849 0.1566 -15.3 Souers 1993 0.2004 0.162 -19.2

BCS/001011

BC

S/0

10

00

0

DETPOIN

/MAT/EUL/1.0


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

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

C0 = 340 m/s P0 = 1 atm


About blast waves

• Temporal profile of a blast wave :

~2 ms

Duration

td+

Duration

td-

∆P0

P(t)

Time of arrival

Pressure

Time


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 !

Blast wave in air

Reduced dist. cm/kg1/3

without 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 10.5

Reduced dist. cm/kg1/3

without 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

• Max pressure (bar) in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985)

Same results Highest differences Closest to literature


Comparison with exp & Autodyn

• Pressure in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985), SUPG=0.02

0

50

100

150

200

250

300

350

400

0 50 100 150 200

Reduced distance (cm/kg1/3)

Ove

rpre

ssu

re (

Bar

)

Radioss 2D

Kinney-Graham

Autodyn 2D

CONWEP

Physics is not well known and overpressure varies a lot with reduced distance.

Radioss is about -17% below the Kinney-Graham prediction : The mesh is enlarged with the reduced distance.



• Time of arrival in free field, 2D axisym., 1kg TNT, JWL Dobratz (1985)

0

500

1000

1500

2000

2500

0 50 100 150 200

reduced distance (cm/kg1/3)

tim

e o

f ar

riva

l (µ

s) Radioss

Kinney-Graham

CONWEP

Good agreement in close range but diffusion when mesh is growing (far range)


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 50 100 150 200

Reduced distance (cm/kg1/3)

du

rati

on

of

po

siti

ve p

has

e (µ

s) Radioss

Kinney-Graham

CONWEP


• Duration of positive phase

Prediction between CONWEP and Kinney-Graham : magnitude is satisfying.



• Impulse of positive phase

0

100

200

300

400

500

600

700

0 50 100 150 200

Reduced distance (cm/Kg1/3)

Imp

luse

(b

ar.m

s)

Radioss Kinney-Graham

CONWEP autodyn 2D

Baker Blastx

Order of magnitude is satisfying and tendance in agreement with experiments


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

TNT equivalent is local !

Lateral blast wave (torical)

End blast wave

Bridge wave

(Ismail et al 1993)


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.


Experiments vs Simulations


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.


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.


Any Questions ?


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:

Conservation of momentum:

Conservation of energy:

Where h enthalpy, u material velocity, p hydrodynamic pressure, ρ=1/v density

1100 uu

2

111

2

000 upup

22

2

11

2

00

uh

uh


About detonations

• Combination of conservation equations :

• Thermodynamic states in the energetic material :

• The C-J state is a characteristic of the energetic material.

22

1

2

1

2

0

2

0

10

01 muupp

ZND point


About blast waves

• Scaling laws (Hopkinson-Cranz) : Spherical charge of TNT in air (in Kinney-Graham)

atm222

2

0 P

1.35

Z1

0.32

Z1

0.048

Z1

4.5

Z1808

ΔP

263

10

3

1d

6.9

Z1

0.74

Z1

0.02

Z1

0.54

Z1980

W

t

3

3

2

4

s

1.55

Z1Z

0.23

Z10.067

I

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