VM-LSDYNA-SOLVE-036

VM-LSDYNA-SOLVE-036
Adiabatic Expansion of High Explosive Detonation Products Using Eulerian Approach

Overview

Reference: Lee, E.L., Hornig, H.C., & Kury, J.W. (1968). Adiabatic expansion of high explosive detonation products. Lawrence Radiation Laboratory, 1(1), 1-12.

https://digital.library.unt.edu/ark:/67531/metadc1059048/

Analysis Type(s): S-ALE
Element Type(s): 2D axisymmetric using Eulerian approach
Input Files:Link to Input Files Download Page

Test Case

The test case involves a copper cylinder containing TNT explosive. Detonation begins at the base of the explosive using a planar detonation wave which then travels along the axis of the cylinder. The radial expansion of the copper cylinder is measured at a specific point on its external surface (z = 24.48 cm). To measure the radial expansion, the setup uses a 2D axisymmetric model with a Eulerian formulation for the explosive and a Eulerian modeling technique for the cylinder wall.

Figure 128: Problem Sketch

Problem Sketch

Geometric PropertiesMaterial Properties

L = 30.5 cm

Do = 3.06 cm

Di= 2.54 cm

Copper:

ρ = 8.96 x 10-6 g/m3

G = 45.926 GPa

ν = 0.35

 

TNT:

ρ = 1,63 x 10-6 g/m3

D = 6930 m/s

PCJ = 21 GPa

 

Air:

ρ = 1 x 10-9 g/m3

where

ρ is the material density
G is the shear stress
ν is the Poisson's ratio
D is the detonation velocity
PCJ is the Chapman-Jouget pressure

Analysis Assumptions and Modeling Notes

Figure 129: Problem setup

Problem setup

Since the model is axisymmetric, a 2D axisymmetric structure is used to simplify the calculations. The TNT explosive is detonated with a booster explosive which generates a planar shockwave hitting the TNT. For simplification, the detonation points are defined close enough to generate a planar detonation wave. For copper, the Gruneisen-Gamma EOS (equation of state) is used. The values can be seen in Table 7.

Table 7: Gruneisen-Gamma EOS card

*EOS.GRUNEISEN_TITLE) (1)
EOSIDCS1S2S3GAMMA()AE0
23940.00001.48900000.00.01.97000000.4700000 0.0
 
V0UNUSEDLCID 
1 0

For TNT, the Jones-Wilkins-Lee EOS is used. The values can be seen in Table 8.

Table 8: Jones-Wilkins-Lee EOS card

*EOS_JWL_(TITLE) (1)
EOSIDABR1R2OMEGE0VO
1371.209993.72300004.15000010.95000000.30000007.00000000.0

For air, the Linear Polynomial EOS is used. The values can be seen in Table 9.

Table 9: Gruneisen-Gamma EOS card

*EOS_LINEAR_POLYNOMIAL_(TITLE) (1)
EOSIDC0C1C2C3C4C5C6
30.00.00.00.00.40000000.40000000.0
 
E0V0 
2.500E-040.0

Copper material must be defined like a multi-material. See Table 10.

Table 10: Multi-material card

*ALE_STRUCTURED_MULTI-MATERIAL_GROUP_AXISYM (4)
AMMGNMMIDEOSIDUNUSEDUNUSEDUNUSEDUNUSEDPREF
COPPER32    0.0

The Eulerian domain is filled solely with a rigid dummy part similar to the TNT, so there is no need for Fluid-Structure Interaction (FSI). See Table 11.

Table 11: ALE_STRUCTURED_MESH_VOLUME_FILLING card

*ALE_STRUCTURED_MESH_VOLUME_FILLING
MSHIDUNUSEDAMMGTOUNUSEDNSAMPLEUNUSEDUNUSED-VID
1 2 3  0
 
GEOMIN/OUTPIDE2E3E4E5 
PART020.0000

Also, as the MAT Johnson-Cook (015) allows failure, a Vacuum material must be defined. See Table 12.

Table 12: Vacuum material card

*ALE_STRUCTURED_MULTI-MATERIAL_GROUP_AXISYM (4)
AMMGNMMIDEOSIDUNUSEDUNUSEDUNUSEDUNUSEDPREF
vacuum50    0.0
*MAT_VACUUM_(TITLE) (140) (1)
MIDRHO 
51.000E-09

Figure 130: Mesh model

Mesh model

Results Comparison

The results obtained by the LS-DYNA application are almost identical to the experimental results for R-R0—the radial expansion for the observation point at z = 24.48 cm from the moment expansion begins.

Figure 131: Radial expansion of copper cylinder for observation point at z = 24.48 cm

Radial expansion of copper cylinder for observation point at z = 24.48 cm

ResultsTarget LS-DYNA SolverError (%)
R-R0 (mm) at observation point for time 16.05 ms 1918.711.55