Effects of aluminized charge structures on blast wave propagation and the parameters of partially confined explosions

Abstract

The composite charge structure may have the potential to enhance the overall damage capability of the weapon. In this regard, three-dimensional LS-DYNA simulation software (dynamics calculation software from LSTC) was used to simulate the explosion process of charges in a partially confined space. The effects of different aluminized charge structures on the propagation and parameters of blast waves in a cubic cabin structure with a pressure relief port were obtained. The results showed that the reflected waves generated local pressure convergence at the junction and corner areas of adjacent walls in the cabin structure. The numbers of significant reflections of the blast waves at the center and corners of the wall were 3 and 2, respectively. The overpressure of the reflected wave at the corner was more than 3.2 times that at the center of the sidewall. Moreover, the number of reflections, overpressure ratio, and charge structure were not directly related. The advantages of composite structure charges in enhancing the overpressure and wave velocity of incident waves and the overpressure and impulse of reflected waves were not significant. However, the internal and external composite charge structure had more advantages than did the upper and lower structures, and its impulse TNT equivalent reached more than 70% of that of a single-structure explosive. The results can provide theoretical support and technical guidance for the design of charge structures and cabin structures.

Full text

AIP Advances ARTICLE pubs.aip.org/aip/adv
Effects of aluminized charge structures on blast
wave propagation and the parameters of partially
confined explosions
Cite as: AIP Advances 14, 115216 (2024); doi: 10.1063/5.0223158
Submitted: 12 June 2024 •Accepted: 11 October 2024 •
Published Online: 12 November 2024
Feng Wang,1,2 Wei Xiao,2,a) Lili Tan,2Zongwei Liu,2Heng Wang,2and Zecheng Wang2
AFFILIATIONS
1School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
2Institute of Special Equipment, Chongqing Hongyu Precision Industrial Group Co., Ltd., Chongqing 402760, China
a)Author to whom correspondence should be addressed: iridescent_bubbles@163.com
ABSTRACT
The composite charge structure may have the potential to enhance the overall damage capability of the weapon. In this regard, three-
dimensional LS-DYNA simulation software (dynamics calculation software from LSTC) was used to simulate the explosion process of charges
in a partially confined space. The effects of different aluminized charge structures on the propagation and parameters of blast waves in a cubic
cabin structure with a pressure relief port were obtained. The results showed that the reflected waves generated local pressure convergence at
the junction and corner areas of adjacent walls in the cabin structure. The numbers of significant reflections of the blast waves at the center and
corners of the wall were 3 and 2, respectively. The overpressure of the reflected wave at the corner was more than 3.2 times that at the center
of the sidewall. Moreover, the number of reflections, overpressure ratio, and charge structure were not directly related. The advantages of
composite structure charges in enhancing the overpressure and wave velocity of incident waves and the overpressure and impulse of reflected
waves were not significant. However, the internal and external composite charge structure had more advantages than did the upper and lower
structures, and its impulse TNT equivalent reached more than 70% of that of a single-structure explosive. The results can provide theoretical
support and technical guidance for the design of charge structures and cabin structures.
©2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-
NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0223158
I. INTRODUCTION
Confined explosions and partially confined explosions, such as
those employed in caverns, construction, and cabins, have long been
the focus of research. Compared with that of free space, the reflection
of the wall surface complicates the confined explosion process. The
mixing of detonation products and metal fuel with air is accelerated
by reflected waves due to the limitations of confined environmen-
tal conditions. The energy release of explosions is further improved,
and the comprehensive damage ability is enhanced by promoting
the afterburning reaction.1Trzci´
nski et al. believed that the aerody-
namic process should be considered in confined explosions, and an
equilibrium state will be reached in the structure when heat released
in part is transferred to the wall.2Moreover, the temperature and
pressure of the gas mixture in the confined space increase through
the heat of the reaction.
Blast wave overpressure and quasistatic pressure are the main
indices used to evaluate the inner load action performance of con-
fined explosions or partially confined explosions. Zyskowski et al.
obtained the action law of TNT explosions in small chamber struc-
tures,3and Pennetier et al. mastered the blast wave propagation
law and waveform characteristics of underground tunnel explosions
through a combination of explosion tests and simulation calcula-
tions.4Wu et al. found that the peak pressure of axial blast waves
was greater than that of radial blast waves through explosion tests of
cylindrical and spherical charges with different masses in confined
spaces.5Sauvan et al. obtained key performance parameters such
as the blast wave overpressure peak value, impulse value, and blast
wave arrival time in confined explosions through a series of chamber
explosion experiments.6
Tzci´
nski and Paszila believed that reflected waves had a short
duration and were not the main source of damage to container
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walls.7The average pressure was fitted after averaging the pressure
curves, and the re-exponential factor of the exponential decreased as
the quasistatic pressure was obtained. In addition, they believed that
this quasistatic pressure wave, which lasts for a long time, can be
regarded as the actual load on the wall. Later, Lee et al. regarded the
pressure immediately following the initial blast wave as a quasistatic
pressure.8However, Ames et al. calculated the quasistatic pressure
by averaging the pressure over a period of time.9In addition, Lee
et al. found that there was a relationship between the quasistatic
pressure and total combustion heat of explosives based on a series
of tests in confined explosions.8Zhou et al. also reported that the
pressure curve first undergoes a violent oscillation of ∼20 ms when a
blast wave propagates in a confined space.10
Many valuable studies have been achieved via confined explo-
sions and partially confined explosions of single structure charges.
However, few research papers on confined explosions and partially
confined explosions of composite structure charges have been pub-
lished. Considering its importance in enhancing weapon damage,
confined explosions and partially confined explosions of composite
structure charges should be explored further.
The partially confined explosion process of two composite
structure charges and three single structure charges was simu-
lated through LS-DYNA software (dynamics calculation software
from LSTC), and the distribution and action mode of explosive
impact loads of different charges were determined in this paper.
At the same time, the characteristics of partially confined explo-
sions of composite charges were determined, and the influence
of the charge structure on blast wave propagation was obtained
through combination with explosion parameters such as blast
wave overpressure and quasistatic pressure. The research results
of this work can be used to provide theoretical support and tech-
nical guidance for the design of charge structures and explosive
vessels.
II. NUMERICAL SIMULATION PREFERENCES
AND MODELING
A. State equation preferences
In this work, the explosion processes for five types of charges
were simulated, including TNT, an HMX-based pressed PBX explo-
sive, a DNAN-based melt-cast explosive, and two composite struc-
ture charges. The diameter of the five charges was 50 mm, and
the mass was 200 g. Three single-structure charges are shown in
Fig. 1(a), and the structures of the two composite charges are shown
in Figs. 1(b) and 1(c). The two types of composite charges were
divided into upper-lower and inner-outer forms according to their
structure; they were all composed of HMX-based pressed explosive
and DNAN-based melt-cast explosives with a mass ratio of 1:1.
As a commonly used elemental explosive, the pressure para-
meter P of TNT after explosion can be determined by the JWL
state equation. As a commonly used type of non-ideal explosive,
explosives containing aluminum have significant afterburning reac-
tion effects. Therefore, the blast wave pressure during the explosion
process of explosives containing aluminum needs to be calculated
using the JWL–Miller equation. This equation fully considers the
afterburning reaction energy of non-ideal components (such as
aluminum powder) in thermobaric explosives, and it can phe-
nomenologically describe this process. The JWL state equation
FIG. 1. Schematic diagram of the charge structure: (a) single-structure charge, (b)
upper-lower charge, and (c) inner-outer charge.
and JWL–Miller state equation are shown in Eqs. (1) and (2),
respectively,
P=A⋅1−ω
R1V⋅e−R1V+B⋅1−ω
R2V−R2V+ωE
V, (1)
P=A⋅1−ω
R1V⋅e−R1V+B⋅1−ω
R2V−R2V+ω(E+λQ)
V. (2)
In Eqs. (1) and (2),Pis the pressure of the explosive product,
MPa; Qis the amount of heat contained in non-ideal components, kJ
m−3;V=ρ0/ρis the relative specific volume of the explosive product,
and ρ0is the initial density of the explosive product; Eis the specific
internal energy of explosive products per unit volume; A,B,C,R1,
R2, and ωare constants calibrated in cylindrical tests; and λis the
reactivity of non-ideal components.
For the JWL state equation preferences of TNT explo-
sives, Lee et al. have provided information in their published
papers.11 The JWL–Miller state equation preferences for HMX-
based pressed charge and DNAN-based melt-cast explosives were
obtained through previous rounds of tests. The state equation pref-
erences of the three explosives are listed in Table I. In this work,
the explosion process was simulated under air conditions. The ideal
gas state equation preferences for the ideal air medium are listed in
Table II.
B. Pressure cloud of explosion
In this work, the explosion characteristics of charges were
obtained in a partially confined cabin structure. The partially con-
fined cabin is a cubic structure, as shown in Fig. 2(a). The side length
of the cabin is 1.5 m, and the material is Q235 steel with a thickness
of 25 mm. In addition, a circular hole with a diameter of 100 mm
is designed in the upper surface of the partially confined cabin. This
circular hole can be used to simulate the real environment and can
also be used to conveniently place the charges into the cabin during
the experiment.
Considering the symmetry of the partially confined cabin struc-
ture and charge, a three-dimensional axisymmetric 1/8 simulation
model was established. The cabin uses a Lagrange mesh, while the
air domain and explosives use an Euler mesh. The ideal air domain
has a length of 800 mm, a width of 800 mm, and a height of 1000 mm,
and a gradient size grid with a size of 5 ×5×5 mm3was used. The
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TABLE I. State equation preferences of three types of explosives.
ρ0(g cm−3)D(m s−1)A(GPa) B(GPa) C (GPa) R1R2ω
TNT 1.63 6930 373.77 3.747 1.045 4.15 0.90 0.35
Pressed 1.860 7344 655 2.13 1.58 4.5 1.1 0.42
Melt-cast 1.893 8003 1030 5.9 0.45 4.8 1.1 0.25
TABLE II. Air medium preferences and state equation preferences.
ρ(g cm−3)γTemperature (K) Specific heat (J g−1)e(J kg−1)
1.225 1.40 288.2 717.6 2.068×105
internal dimensions of the cabin were 1500 ×1500 ×1500 mm3, and
the dimensions of the wall mesh were 5 ×5×5 mm3. The size of the
explosive was described in Sec. II A, with a grid size of 5 ×5×5 mm3.
In addition, the boundaries of the air domain were set as a flow-out
boundary model to simulate an infinite air domain. The charge was
filled in the air domain, and the connection between the air and the
cabin wall was determined by Euler–Lagrange fluid structure cou-
pling. Pressure monitoring points (1#, 2#, 3#, 4#, 5#, 6#, and 7#) are
set at 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.75 m away from the explosion
center, respectively. At the same time, pressure monitoring points
(8#and 9#) are set in the corner and the edge of the pressure relief
port.
III. RESULTS AND DISCUSSION
A. Explosion process
The difference and rule of pressure cloud images were explored
by comparing the pressure cloud images of typical single structure
charges at different times during the explosion process. A pressure
cloud image of a typical explosive is shown in Fig. 3. As shown in
Fig. 3, after the explosive was detonated, the high-temperature and
high-pressure products rapidly expanded and compressed the air
and formed an explosion blast wave in the cabin. The blast wave first
FIG. 2. Model size and location of the explosive. (a) Partially confined cabin
structure and gauges and (b) simulation model.
undergoes three-dimensional axisymmetric expansion, and the out-
ermost edge of the red area is the wavefront of the incident blast
wave. The charges were placed at the center of the cabin, at the same
distance from the six walls of the cabin. Because of the symmetrical
expansion of the blast wave, the pressure cloud image in the chamber
is also symmetrical.
As the explosion blast wave continued to propagate forward,
positive reflection occurred when it first reached the center of the
wall. Afterward, the rest of the points on the cabin wall began to be
loaded by the blast wave, and normal oblique reflection and Mach
reflection occurred sequentially. Over time, the explosion blast wave
underwent multiple reflections in the cabin space due to the con-
straints of the surrounding walls. During the propagation of this
explosive wave, significant Mach waves were formed due to irregular
reflections on the wall. Subsequently, the initial blast wave converged
with the Mach reflection wave from the wall, and the pressure acted
for a longer time after convergence.
Meanwhile, the explosion blast wave will generate local pres-
sure convergence at the junction of adjacent walls. This type of
pressure will continue to propagate along the prism direction, caus-
ing a sharp increase in overpressure (2870 μsinFig. 3). When the
blast wave reaches the endpoint of the prism, it will once again form
a converging pressure in the corner area (3245 μsinFig. 3). After
that, the pressure in the chamber is concentrated toward the explo-
sion center (4000 μs in Fig. 3). In addition, a continuous pressure
relief process begins at the opening on the top surface of the cabin,
as can be observed from Fig. 3, after the incident wave first contacts
the side wall.
Meanwhile, the explosion blast wave generated local pressure
convergence at the junction of adjacent walls. This type of pressure
continued to propagate along the prism direction, causing a sharp
increase in overpressure (2870 μsinFig. 3). When the blast wave
reached the endpoint of the prism, it once again formed a converging
pressure in the corner area (3245 μs in Fig. 3). After that, the pressure
in the chamber was concentrated toward the explosion center (4000
μs in Fig. 3). In addition, a continuous pressure relief process began
at the opening on the top surface of the cabin, as shown in Fig. 3,
after the incident wave first contacted the sidewall.
B. Incident wave
After explosive blasting in the cabin, the first incident wave
generated by the compressed air of the detonation product propa-
gated outward from the blast center and created a positive reflection
when it touched the center of the cabin wall (which means that a
reflected wave was formed). The incident wave pressure signals at
different distances were obtained through setting pressure gauges
(1#–6#in Fig. 2) during the simulation process. The typical incident
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FIG. 3. Pressure cloud images of a
typical explosive.
wave overpressure-time curves of the pressed explosive are shown in
Fig. 4.
Figure 4 shows that the overpressure of the wavefront decreased
rapidly due to energy loss caused by continuous work in the pro-
cess of strongly compressed air. The positive pressure action time
of the incident wave increased gradually with increasing distance,
indicating that the smaller the pressure of the wavefront was, the
slower the attenuation. It is worth noting that the overpressure-time
curves at R =0.1–0.6 m all exhibited a distinct plateau caused by the
energy released from the postcombustion reaction of the aluminum-
containing explosive enhancing the back pressure of the wavefront.
In this regard, the incident wave power level of the high-pressure
effect can be characterized by the impulse of the positive pressure
interval, as shown in the square in Fig. 4.
Figure 4 shows that the gauges located further away from
the blast center had higher impulse values. The positive pressure
action time at 0.1 m was the smallest, but its overpressure peak
was the highest, resulting in a higher impulse value within the first
wave peak. Overall, considering both the postcombustion reaction
FIG. 4. Typical overpressure-time curve of explosive incident waves.
FIG. 5. Peak overpressure of five types of explosives incident waves.
and the duration of action, the incident wave exhibited significant
high-pressure effects.
In this partially confined explosion, the blast wave can be con-
sidered to propagate in free space before the incident wave touches
the wall. Therefore, according to the explosion similarity theory,12
the Sadovsky empirical formula can be used to represent the over-
pressure of the incident wave at different distances, as shown in
Eq. (3),
ΔP=a1
R+b1
R2+c1
R3, (3)
R=R
3
√W, (4)
where Ris the comparison distance; Ris the distance from the pres-
sure test point to the center of the explosion, m; Wis the mass of the
sample, kg; and a,b, and care constants.
The peak overpressure values of the five types of charge inci-
dent waves are depicted in Fig. 5. At the same time, nonlinear fitting
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curves for the incident wave overpressure of each type of charge
were obtained by using empirical formula (1). The coefficients a,
b, and cin Eq. (1), as well as the fitting accuracy R2, are all listed
in Fig. 5.Figure 5 shows that the incident wave overpressure of the
five charges rapidly decays exponentially. From Fig. 5. At a distance
of R<0.6 m, aluminized explosives had a greater pressure advan-
tage than did TNT. Afterward, the difference in peak overpressure
between the two types of charges gradually narrowed. In addition,
the overpressure of both composite charges was lower than that of
the two single charges. The results indicated that using composite
structure charges could not significantly increase the high-pressure
effect of the incident wave under the same mass conditions.
To further clarify the propagation characteristics of incident
waves, the average velocity (wave velocity) of five types of charge
incident waves passing through each pressure gauge was calculated,
and the results are shown in Fig. 6. The curves in Fig. 6 show that the
incident wave velocities of the five charges exhibited similar expo-
nential decay trends. The wave velocity at R=0.1 m is greater than
5000 m s−1;atR=0.75 m, the wave velocity is close to 1000 m s−1.
The average difference in the wave velocity between these two dis-
tances is five times greater. This indicated that the propagation of
an incident wave is positively correlated with its own energy level
under the same medium conditions, and rapid attenuation of over-
pressure also reduces its propagation speed. In addition, the wave
velocity of TNT was at the bottom of the five curves. The wave veloc-
ity curves of two single charges were at the top, followed closely by
two composite charges. Overall, the results correspond to Figs. 4
and 5, indicating once again that a single type of aluminized explo-
sive had an advantage in improving the incident wave propagation
speed in air compared to composite structure charges, even if this
advantage was weak.
C. Reflected wave
The incident wave will reflect after touching the cabin wall, and
a sharp increase in pressure will cause damage to the cabin wall.
The overpressure-time curves of five charges at the center of the
FIG. 6. The wave velocity of five types of explosive incident waves.
sidewall (gauge 7#) are plotted in Fig. 7 based on the simulation
results. As shown in Fig. 7, the overpressure of the positive reflected
waves suddenly reached its peak in a short period of time and then
rapidly decreased. Afterward, the blast wave continuously reflected,
stacked, and converged inside the cabin space due to the constraints
of the cabin boundary. During this process, the blast wave under-
went multiple reflections in disturbed air (with significant multipeak
characteristics), forming a highly complex fluctuating pressure load
with continuously decreasing peak pressure until the pressure inside
the cabin stabilized at atmospheric pressure. Unlike in a confined
explosion, in a partially confined cabin, the reflected waves tend to
attenuate to atmospheric pressure after experiencing three signifi-
cant peaks (i.e., three reflections) due to pressure relief. Moreover,
the number of reflections is not directly related to the charge
structure.
The blast wave in the cabin not only undergoes positive
reflection but also exhibits more complex irregular reflections
(oblique reflection, Mach reflection, etc.). The incident wave further
converges and causes the overpressure to increase sharply after
reflecting on the three walls. A sharp increase in pressure at the
corners is the main cause of cabin damage.13 Therefore, it is nec-
essary to understand the pressure variation law of reflected waves at
corners. The overpressure vs time curves of the five charges at the
corners are shown in Fig. 8. The overpressure at the corner decays to
atmospheric pressure after two significant convergences due to the
rapid loss of pressure inside the cabin. The attenuation process only
lasts ∼5 ms, especially the macroscopic pulsation of the blast wave
in the later stage, which is not significant. However, the overpres-
sure time curve showed that the overpressure that formed after the
first convergence was very high (with sharp peaks). Moreover, the
attenuation trends and patterns of the five types of blast waves at the
corners are similar.
The degree of cabin damage caused by an explosion inside the
cabin is positively correlated with the power of the charge and cabin
structural strength. Among them, the overpressure of the blast wave
is one of the key parameters characterizing the power level of the
FIG. 7. Overpressure-time curves of five explosives at the center of the sidewall.
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FIG. 8. Overpressure-time curves of the five explosives at the corners.
charge. Because the center and corner of the cabin wall sustain the
maximum overpressure, the peak overpressure at these two locations
should be given special consideration. The peak overpressure val-
ues of the five charges at the center and corners of the sidewall are
shown in Fig. 9. The diamond shape in the figure represents the ratio
of the peak overpressure at the corner to that at the center of the
wall, α(α>1). The peak overpressure of the five types of charges
tends to be 1 MPa at the center of the wall, while it approaches 4
MPa at the corners. The value of αindicated that the peak over-
pressure of the reflected wave at the corner was more than 3.2 times
that of the center of the sidewall. Moreover, the composite charge
FIG. 9. Peak overpressure of the five explosives at the sidewalls and corners.
FIG. 10. Impulse-time curves of five explosives on the sidewalls.
structure did not exhibit a significant change in the αvalue, indi-
cating that there was no significant correlation between the two
parameters.
D. Quasistatic pressure
The continuous reflection of explosive waves forms a
continuously decaying wave. The continuous reflection of explosive
waves forms a continuous decaying fluctuation pressure, and its
average value is the quasistatic pressure.14 In an explosion in a par-
tially confined cabin space, the quasistatic pressure monotonically
decayed due to the continuous pressure relief of the cabin struc-
ture. Therefore, the peak pressure of the quasistatic pressure can be
defined as the pressure after the third reflection of the blast wave.15
Regarding the pressure relief port situation in the partially con-
fined cabin in this work, the ratio of the pressure relief port to the
wall area is ∼0.014, resulting in a higher pressure relief speed. The
overpressure-time curve in Fig. 7 indicates that the quasistatic pres-
sure peak defining method mentioned earlier is not suitable under
the operating conditions of this work. Due to the relatively long pro-
cess of quasistatic pressure attenuation within the cabin, continuous
loading of gas pressure considering a time scale can more accu-
rately predict the load situation inside the cabin.16 Based on this, the
impulses of the reflected waves on the sidewalls of five charges were
calculated, and the results are shown in Fig. 10.
Figure 10 shows that the impulses of the five charges on the
sidewall surface generally increase. However, the rate of increase in
the TNT explosive impulse is significantly lower than that of the
aluminized charges. Based on the first positive pressure range phe-
nomenon exhibited by the four aluminized charges in Fig. 7, all their
overpressure-time curves exhibit a significant plateau hindering the
reduction in overpressure. This local increase in the overpressure of
the blast wave was precisely caused by the release of energy from the
postcombustion reaction of the aluminized explosives because TNT
did not exhibit this phenomenon. The postcombustion reaction has
a slower rate but a longer action time, and it continuously releases
a large amount of gas and heat, forming a quasistatic gas pressure
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that acts on the cabin structure. Therefore, aluminized explosives
have a stronger destructive ability than TNTs in terms of damag-
ing cabin structures. Notably, all five curves showed a slight decrease
in impulse, which was due to the pressure decreasing to negative
pressure caused by strong and sparse waves propagating in opposite
directions after the first reflection of the blast wave.
In addition, the total impulse of both single charges was greater
than that of the two composite charges. The impulse TNT equiv-
alents of the four aluminized explosives were 2.48, 2.13, 1.57, and
1.92, respectively, based on the impulses of the TNT explosives. The
results indicated that the composite structure charge was weaker
than that of single-structure explosives in enhancing the quasistatic
pressure damage ability. However, the internal and external compos-
ite structure charge had more advantages in increasing the impulse
of the quasistatic pressure compared to the upper and lower compos-
ite structures. The impulse TNT equivalent could reach more than
70% of the single structure charge.
IV. CONCLUSION
The partially confined explosion processes of charges were sim-
ulated for a blast in a cubic cabin with a pressure relief port diameter
of 100 mm by using three-dimensional LS-DYNA in this work. The
following conclusions were obtained:
(1) During a partially confined explosion, the blast wave will gen-
erate local pressure convergence at the junction and corner
areas of adjacent walls in the cabin structure due to wave
reflection. Moreover, the pressure relief port has a significant
impact on the reflection frequency of the blast waves inside
the cabin.
(2) In a partially confined cube cabin, the blast wave signif-
icant reflections were three times and two times greater
at the center and corners of the wall, respectively, and
their reflection times were not directly related to the charge
structure.
(3) Under the same quality conditions, the advantages of com-
posite structure charges in enhancing incident wave over-
pressure, wave velocity, and reflected wave overpressure were
not significant. The overpressure of the reflected wave at the
corner was more than 3.2 times that at the center of the side-
wall, and there was no significant correlation between the
overpressure ratio and the charge structure.
(4) Impulse parameters that consider the time scale can more
accurately predict the quasistatic pressure load in a partially
confined explosion. Compared with that of single explosives,
the composite charge structure did not significantly improve
the damage caused by quasistatic pressure. The internal and
external composite charge structure has more advantages
than the upper and lower structures, and its impulse TNT
equivalent can reach more than 70% of that of a single
explosive.
ACKNOWLEDGMENTS
This article was created by the joint efforts of the authors. We
acknowledge Wei Xiao for his contribution to the writing of the
paper and Lili Tan and Heng Wang for their help in the simulation
calculations. We also acknowledge Zongwei Liu and Zecheng Wang
for beautifying the language of the paper.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Feng Wang: Writing – review & editing (equal). Wei Xiao: Writ-
ing – original draft (equal). Lili Tan: Software (equal). Zongwei Liu:
Writing – review & editing (equal). Heng Wang: Software (equal).
Zecheng Wang: Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
within the article.
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