Modular charges can form different structures within the chamber, offering flexibility, versatility, and high efficiency, and have therefore been widely used in large-diameter combustion and propulsion systems. To effectively enhance the performance of the propulsion system through optimizing the number of modules and charging methods, this study integrates the two-phase flow particle element method to analyze the performance variations of different combinations of module numbers and charging modes and employs multiple evaluation methods. Based on experimental verification, the numerical calculation shows that the varying number of modules significantly impacts on the flow process in the chamber. When the number of modules is low, the increased particle dispersion space results in notable pressure fluctuations in the ignition transfer process in the chamber, leading to low energy utilization efficiency. With increase in the number of modules, the energy utilization rate in the chamber also increases gradually, and the growth rate initially accelerates and then decelerates. The sequential charging mode can significantly improve the energy utilization efficiency and the charge utilization rate per unit chamber volume. Compared to the unordered charging mode, the charge amount increases by more than 9.5%, and the velocity increases by approximately 5%–8%.

1.
Z. S.
Wang
, “
Propelling charge and modular charge systems for the extended firing range
,”
J. Nanjing Univ. Sci. Technol.
27
(
5
),
466
472
(
2003
).
2.
K. L.
Zhang
,
G. Y.
Yu
, and
X.
Lu
, “
Interior ballistics simulation of modular charge gun system using Matlab
,”
Appl. Mech. Mater.
195-196
,
834
839
(
2012
).
3.
H. Y.
Qian
,
Y. G.
Yu
, and
J.
Liu
, “
Effects of module number and firing condition on charge thermal safety in gun chamber
,”
Def. Technol.
18
(
1
),
27
37
(
2022
).
4.
C. J.
Ma
and
X. B.
Zhang
, “
Interior ballistic modeling and simulation for different charge zones in modular charge system
,”
J. Appl. Mech.
80
(
3
),
031404
(
2013
).
5.
G.
Legeret
,
E.
Tayana
, and
D.
Boisson
, “
Study of the ignition of a large caliber modular charge, computation and validation
,” in
Proceedings of the 17th International Symposium of Ballistics Midrand: The South Africa Ballistics Organization
(
1998
), pp.
440
447
.
6.
B.
Yu
, “
Comprehensive review of modular charge technology
,”
J. Gun Launch Control
2002
(
3
),
52
55 + 60
.
7.
S. S.
Cheng
,
R. Y.
Tao
,
S.
Xue
,
X. G.
Lu
, and
H.
Wang
, “
Two-phase flow characteristics of different charging structure in ignition and flame-spreading
,”
Combust. Theor. Model.
25
(
4
),
751
764
(
2021
).
8.
S. S.
Cheng
et al, “
Visualization experiment on the ignition performance and flame-spreading in different charging structures
,”
Flow Meas. Instrum.
99
,
102656
(
2024
).
9.
X. G.
Yang
and
Y. G.
Yu
, “
Influence of rupture size on dispersion characteristics of propellant particles during ignition and flame spreading processes for modular charges
,”
J. Phys. Conf. Ser.
2460
(
1
),
012016
(
2023
).
10.
S.
Cheng
,
R.
Tao
,
X.
Lu
et al, “
Numerical simulation of interior ballistics two-phase flow in modular charge based on the particle element method
,”
Case Stud. Therm. Eng.
61
,
105121
(
2024
).
11.
A.
Chen
and
Y. G.
Yu
, “
Investigation of particle distribution after the energetic module broken in the ignition process of gun
,”
Case Stud. Therm. Eng.
41
,
102619
(
2023
).
12.
R. Y.
Tao
and
S. S.
Cheng
, “
Two-phase flow simulation of interior ballistic with different sequential charging structures
,” in
2nd International Conference on Computational Modeling, Simulation and Data Analysis (CMSDA)
, Zhuhai, China (
IEEE
,
2022
), pp.
106
109
.
13.
Y. J.
Li
,
Q. J.
Li
,
Z. P.
Han
et al, “
Optimization of artillery interior ballistic performance based on sequential loading of propellants
,”
J. Ordnance Equip. Eng.
44
(
8
),
154
161
(
2023
).
14.
H.
Miura
,
A.
Matsuo
, and
Y.
Nakamura
, “
Numerical prediction of interior ballistics performance of projectile accelerator using granular or tubular solid propellant
,”
Propellants Explos. Pyrotech.
38
(
2
),
204
213
(
2013
).
15.
S. S.
Cheng
,
K.
Jiang
,
S.
Xue
et al, “
Performance analysis of internal ballistic multiphase flow of composite charge structure
,”
Energies
16
(
5
),
2127
2127
(
2023
).
16.
D.
Xiaoli
,
R.
Xiaoting
, and
L.
Chao
, “
Interior ballistic two-phase flow model and its calculation for a mixed charge structure
,”
Int. Commun. Heat Mass Transfer
144
,
106788
(
2023
).
17.
C.
Woodley
, “
On the use of accurate ignition and combustion models in internal ballistics gun codes
,”
Chin. J. Explos. Propellants
41
(
2
),
117
121
(
2018
).
18.
S. Y.
Sen
,
H.
Wang
, and
R. Y.
Tao
, “
Numerical simulation and characteristics analysis on ignition and flame-propagation process of modular charge based on CE/SE method
,”
Chin. J. Energ. Mater.
30
(
7
),
744
751
(
2022
).
19.
C.
Cheng
and
X.
Zhang
, “
Numerical investigation on the transient ignition behavior using CFD-DEM approach
,”
Combust. Sci. Technol.
186
(
9
),
1115
1137
(
2014
).
20.
C.
Cheng
and
X.
Zhang
, “
Modeling of interior ballistic gas-solid flow using a coupled computational fluid dynamics-discrete element method
,”
J. Appl. Mech.
80
(
3
),
031403
(
2013
).
21.
M.
Sakai
,
H.
Takahashi
,
C. C.
Pain
et al, “
Study on a large-scale discrete element model for fine particles in a fluidized bed
,”
Adv. Powder Technol.
23
(
5
),
673
681
(
2012
).
22.
M.
Sakai
,
M.
Abe
,
Y.
Shigeto
et al, “
Verification and validation of a coarse grain model of the DEM in a bubbling fluidiz ed bed
,”
Chem. Eng. J.
244
,
33
43
(
2014
).
23.
C. S.
Hu
,
K.
Luo
,
S.
Wang
et al, “
Influences of operating parameters on the fluidized bed coal gasification process: A coarse-grained CFD-DEM study
,”
Chem. Eng. Sci.
195
,
693
706
(
2019
).
24.
S. S.
Cheng
,
R. Y.
Tao
,
S.
Xue
, and
X. G.
Lu
, “
The particle element method to obtain parameter distributions of two-phase reactive flow in a propulsion combustion system
,”
Combust. Sci. Technol.
196
(
5
),
730
752
(
2024
).
25.
S. S.
Cheng
,
R. Y.
Tao
,
X. G.
Lu
,
S.
Xue
, and
K.
Jiang
, “
Efficient two-dimension particle element method of interior ballistic two-phase flow
,”
Combust. Theor. Model.
27
(
4
),
558
583
(
2023
).
26.
S. S.
Cheng
,
H.
Wang
,
S.
Xue
, and
R. Y.
Tao
, “
Application and research of the particle element model in ignition process of large-particle high-density charge
,”
Combust. Sci. Technol.
194
(
9
),
1850
1871
(
2022
).
27.
S.
Cheng
,
X.
Lu
,
R.
Tao
et al, “
Modeling multiphase flow characteristics and particle behavior of mixed charge structure using the particle element method
,”
Phys. Fluids
36
(
10
),
103312
(
2024
).
28.
M.
Gao
,
X. Y.
Shi
, and
Z. S.
Wang
, “
The feasibility study on uni-modular charges in the modular propellant charge system
,”
J. Ballist.
2003
(
3
),
14
18
.
29.
Y. X.
Yuan
and
X. B.
Zhang
,
Multiphase Hydrokinetic Foundation of High Temperature and High Pressure
(
Publishing Company of Harbin Institute of Technology
,
Harbin
,
2005
).
30.
C.
Cheng
and
X. B.
Zhang
, “
Two-dimensional numerical simulation of gas-solid reactive flow with moving boundary
,”
Combust. Sci. Technol.
187
(
7–9
),
977
998
(
2015
).
31.
T. Y.
Ma
,
R. Y.
Tao
,
S. Y.
Zhou
et al, “
Experimental and numerical simulation study of short-barrel gun with modular charges
,”
J. Ballist.
36
(
2
),
44
52
(
2024
).
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