Page 25 - 《含能材料》2018年优秀论文

Experimental Study and Numerical Simulation of CL‑20‑Based Aluminized Explosive in Underwater Explosion 691

well as gas bubble and pulsation period prolongs. 4.3 Equation of State for Water
Polynomial equation of state is used for water，
4 Simulation of the Shock Wave and Bubbles and it is given by

2
3
ìp = A 1 μ + A 2 μ + A 3 μ + (B 0 + B 1 μ ) ρ 0 e μ > 0
4.1 Simulation Model í （10）
î p = T 1 μ + T 2 μ 2 + B 0 ρ 0 e μ < 0
Numerical analysis was based on the explicit fi‑
- 1 ；A ，A ，A ，B ，B ，T ，T
Where μ = ρ/ρ
0
1
ref
2
1
3
1
nite element program ANSYS AUTODYN. In this arti‑ are EOS constants. Materials parameters of polyno‑ 2
cle，multi ‑ material Euler solver was used for all of
mial EOS for water are shown in Table 4 ［41］ .
the numerical models including multiple material：
the water，air and explosive charges. The model was Table 4 Material parameters of polynomial EOS for water
established based on the actual situation. The dimen‑ A1/Pa A2/Pa A3/Pa B0 B1
sions of the water region were set as 2.0 m×1.6 m× 2.2×10 9 9.54×10 9 1.457×10 9 0.28 0.28
2.0 m and those of the air region as 2.0 m × 0.4 m × T1/Pa T2/Pa ρ/kg·m -3 e/J·kg -1
2.0 m using the numerical model. For the portion of 2.2×10 9 0 1.0×10 3 361.875
the charge and the water near the charge，the mesh 4.4 Equation of State for Explosion Products
size was millimeter magnitude. For the water far To describe the effects of the energy release of
from the charge and the portion of the air，the mesh
the secondary reaction，a time‑dependent JWL EOS，
size was centimeter magnitude. The method of tran‑ in which the late energy released λ Q and yielding
sitional mesh division was used in the middle part of ω（E + λQ）/V are added to the energy of the prod‑
the model to reduce the amount of model's nodes and ucts，is used ［25，42］ ，to make it as an improved form
shorten the time of computation. Boundary conditions to fit for an aluminized explosive. The JWL EOS with
of the calculation model were“pressure outflow”. The Miller extension used for the explosion products is
simulation of explosion charge was located at a 0.8 m
as follows：
water depth. The booster charges and electric detona‑ ω ω ω(E + λQ )
tor were also taken into consideration. They were p = A(1 - R 1 V ) e -R 1 V + B (1 - R 2 V ) e -R 2 V + V （11）
converted into explosive energy，which were used Where p is the pressure，MPa；V is relative vol‑
in computation program. Hydrostatic pressure gradi‑ ume，m ；E is relative internal energy of the detona‑
3
ent depending on water depth was given to all over tion products，J·m ；A，B，R ，R ，and ω are con‑
-3
2
1
region of water. The effects of atmospheric pressure， stants，Q and λ are additional specific energy and
gravitational acceleration during bubble pulsation its reaction rate，J·m .
-3
were also applied to the numerical model. dλ m n
4.2 Equation of State for Air dt = a ( 1 - λ ) p （12）
Ideal gas equation of state is used for air，and it Where a is the energy release constant，m is the
is given by energy release exponent and n is the pressure expo‑
p = ( γ - 1) ρe （9） nent，λ is the fraction reacted of aluminum powder，
Where e is the specific internal energy of air， these parameters are related to the particle size and
J·kg ；ρ is the density of air，kg·m ；γ is equal to specific surface area of aluminum powders ［42］ . The
-3
-1
1.4 in general. Materials parameters of ideal gas EOS material parameters are shown in Table 5 ［43］ .
for air are shown in Table 3 ［41］ . 4.5 Numerical Analysis Cases
Because of the limitation of AUTODYN itself，
Table 3 Material parameters of ideal gas EOS for air
AUTODYN can't show intuitive interface when alu‑
ρ/kg·m -3 γ e/J·kg -1 minum reacts with explosion products. The simula‑
1.225 1.4 2.068×10 8
tion results of the bubble of the CL‑20‑based alumi‑

CHINESE JOURNAL OF ENERGETIC MATERIALS 含能材料 2018 年 第 26 卷 第 8 期 （686-695）