VM-LSDYNA-SOLVE-037

VM-LSDYNA-SOLVE-037
Adiabatic Expansion of High Explosive Detonation Products Using Lagrangian 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.
Analysis Type(s): S-ALE
Element Type(s): 2D axisymmetric using Lagrangian approach
Input Files:Link to Input Files Download Page

Test Case

The setup 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, a 2D axisymmetric model with Eulerian formulation for the explosive and a Lagrangian modeling technique for the cylinder wall are used.

Figure 132: 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 133: Problem Setup

Problem Setup

Since the model is axisymmetric, to simplify the process, a 2D axisymmetric structure has been considered. TNT explosive is detonated with a booster explosive generating a planar shockwave hitting the TNT, therefore, for simplification, detonation points are defined close enough to generate a planar detonation wave. For copper, the Gruneisen-Gamma EOS (Equation Of State) has been used. The values can be seen in Table 13.

Table 13: Gruneisen-Gamma EOS card

*EOS_GRUNEISEN_(TITLE) (1)
EOSIDCS1S2S3GAMMA0AEO
23940.00001.48900000.00.01.97000000.47000000.0
 
V0UNUSEDLCID 
1.0000000 0

For TNT, the Jones-Wilkins-Lee EOS is used. The values can be seen in Table 14.

Table 14: 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 15.

Table 15: Jones-Wilkins-Lee 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 16: Multi-material card.

Table 16: Multi-material card

*ALE_STRUCTURED_MULTI-MATERIAL_GROUP_AXISM (4)
AMMGNMMIDEOSIDUNUSEDUNUSEDUNUSEDUNUSEDPREF
COPPER32    0.0

The mesh part overlaps the Eulerian domain and FSI is required to interact Eulerian domain with the Lagrangian part. The mesh model is shown in Figure 134 and the FSI card is shown in Table 17. The mesh size is 0.26 mm.

Figure 134: Mesh model

Mesh model

Table 17: FSI card

*ALE_STRUCTURED_FSI (1)
COUPID 
0
 
LSTRSIDALESIDLSTRSTYPALESTYP   MCOUP
2100011   -1
 
STARTENDPFACFRIC FLIP 
0.01.000E+101.00.0 0

Results Comparison

The results obtained by LS-DYNA 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 135: 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-DYNASolverError (%)
R-R0 (mm) at observation point for time 16.05 ms 1918.781.17