Download - Numerical simulation of air blast waves
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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 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 5
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 6
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.
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 7
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 8
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 9
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 . . . . . .
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 10
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 12
About blast waves
• Temporal profile of a blast wave :
~2 ms
Duration
td+
Duration
td-
∆P0
P(t)
Time of arrival
Pressure
Time
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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 !
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 15
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.
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 16
Comparison with exp & Autodyn
• 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)
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 17
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
Comparison with exp & Autodyn
• Duration of positive phase
Prediction between CONWEP and Kinney-Graham : magnitude is satisfying.
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 18
Comparison with exp & Autodyn
• 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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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
TNT equivalent is local !
Lateral blast wave (torical)
End blast wave
Bridge wave
(Ismail et al 1993)
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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 21
Experiments vs Simulations
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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 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 24
Any Questions ?
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 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:
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 26
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
2011 European HyperWorks Technology Conference, 7-9 November, Bonn 27
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