Accurate Internal Ballistics Modeling and Testing of Rodless High Pressure Pneumatic Catapult Considering Leakage

doi:10.12382/bgxb.2022.0172

Abstract

Abstract:

The rodless high-pressure pneumatic catapult experiences a certain amount of leakage due to the inherent structure of the opening. In this study, a prototype leakage test is designed and conducted. Based on the standard dry air thermodynamic equation of state fitted by the experimental data, the leakage rate is calculated and compared under the hypothesis of ideal gas and real gas. The empirical formula of leakage rate varying with pressure and stroke is fitted. An accurate interior ballistic model considering dynamic leakage, real gas effects, and the real valve opening law is established. The two working conditions with and without leakage are solved numerically and compared. Then, the variation laws of thermodynamic parameters and load motion parameters in the ejection process with leakage are analyzed in detail and compared with the ejection test data and fluid simulation results. The results show that the leakage rate calculated under ideal gas assumption is about 4% lower than that under real gas assumption. Moreover, the calculated leakage rate shall not exceed 4%/s. The calculation results of the accurate interior ballistic model considering leakage are basically consistent with the ejection test data and the fluid simulation results, indicating high calculation accuracy.

Key words: rodless high pressure pneumatic catapult, real valve opening law, internal ballistics, leakage, real gas effects

WANG Xueqin, MA Wuning, MA Dawei, WANG Shanglong, ZHANG Zhendong. Accurate Internal Ballistics Modeling and Testing of Rodless High Pressure Pneumatic Catapult Considering Leakage[J]. Acta Armamentarii, 2023, 44(7): 1867-1880.

Figures/Tables 27

Fig.1 Schematic diagram of the double symmetrical rodless cylinder ejector

Fig.2 Schematic diagram of rodless cylinder ejector

Table 1 Reference parameters of dry air

参数	数值
最大冷凝温度T_m/K	132.6312
最大冷凝密度ρ_m/(kg·m^-3)	302.5654
最大冷凝压力p_m/MPa	3.7850
摩尔质量M/(kg·mol^-1)	0.0289586
空气理想气体常数R/(J·(kg·K)^-1)	287.0041

Fig.3 Schematic diagram of leakage test plan

Fig.4 Working fluid leakage process

Fig.5 Pressure time history curves

Fig.6 Temperature time history curve

Table 2 Leakage rate obtained using two calculation methods

l/m	p/MPa
	1.77		2.76		3.76
	理想气体	真实气体	理想气体	真实气体	理想气体	真实气体
0	2.77	2.85	2.62	2.73	2.41	2.50
1.11	2.85	2.95	2.77	2.88	2.47	2.57
2.18	2.95	3.05	2.87	2.98	2.76	2.85
3.24	3.05	3.14	3.00	3.10	2.85	2.93
4.18	3.12	3.20	3.06	3.16	2.89	2.98
5.18	3.27	3.38	3.13	3.23	2.95	3.03

Fig.7 Schematic diagram of the valve

Table 3 Relevant parameters of the model

参数	数值
活塞推力面积S/m²	0.0435
低压室初始容积V₀/m³	0.1
开口气缸数目n/个	2
高压室容积V_h/m³	2.5
发射角α/(°)	88
空气绝热系数γ	1.4
流量修正系数μ_x	0.96
阀门管道半径r/m	0.125
标准大气压力p_a/Pa	10132.5
弹射质量m_e/kg	16000

Table 4 Initial values of the variables

X₁/ (kg·m^-3)	X₂/ K	X₃/ kg	X₄/ (kg·m^-3)	X₅/ K	X₆/ m	X₇/ (m·s^-2)	X₈/ m
153	300	0.2354	1.177	300	0	0	0

Fig.8 Temperature curves in the high and low pressure chamber

Fig.9 Pressure curves in the high pressure chamber

Fig.10 Pressure curves in the low pressure chamber

Fig.11 Load kinematics parameter curves

Fig.12 Mass flow rate curves from high pressure chamber to low pressure chamber

Fig.13 Leakage mass flow rate curve

Fig.14 Spool displacement curve

Fig.15 Valve opening area curve

Fig.16 Pressure curves in the high and low pressure chamber considering leakage

Fig.17 Schematic diagram of the ejection test system

Fig.18 Photo of the ejection test field

Fig.19 Pressure curves in the low pressure chamber

Fig.20 Pressure curves in the high pressure chamber

Fig.21 Load kinematics parameter curves

Fig.22 Computational grid

Fig.23 Pressure contours at t=0.375s

References 21

[1]	谭大成. 弹射内弹道学[M]. 北京: 北京理工大学出社, 2015.
	TAN D C. Interior ballistics of catapults[M]. Beijing: Beijing Institute of Technology Press, 2015. (in Chinese)
[2]	芮守祯, 邢玉明. 几种导弹弹射动力系统内弹道性能比较[J]. 北京航空航天大学学报, 2009, 5(6):766-770.
	RUI S Z, XING Y M. Comparative studies of interior-ballistic performance among several missile eject power systems[J]. Journal of Beijing Aerospace University, 2009, 5(6):766-770. (in Chinese)
[3]	姚琳, 马大为, 任杰, 等. 无杆式气缸弹射装置内弹道仿真与优化设计[J]. 振动与冲击, 2017, 36(6):122-127.
	YAO L, MA D W, REN J, et al. Internal ballistics simulatinon and improving of rodless cylinder cold launching device[J]. Vibration and Shock, 2017, 36(6):122-127. (in Chinese)
[4]	杨风波, 马大为, 杨帆, 等. 高压弹射装置内弹道建模与计算[J]. 兵工学报, 2013, 4(5):527-534.
	YANG F B, MA D W, YANG F, et al. Interior ballistics modeling and calculation of high-pressure ejection device[J]. Acta Armamentarii, 2013, 4(5):527-534. (in Chinese)
[5]	SOAVE G. Equilibrium constants from a modified redlieh-kwong equation of state[J]. Chemical Engineering Science, 1972, 27:1197-1203. doi: 10.1016/0009-2509(72)80096-4 URL
[6]	PENG D Y, ROBINSON D. A new two-constant equation of state[J]. Industrial & Engineering Chemistry Fundamentals, 1976, 15(l):59-64.
[7]	LEMMON E W, JACOBSEN R T, PENONCELLO S G, et al. Thermodynamic properties of air and mixtures of nitrogen 2000 K at pressure to 2000MPa[J]. Journal Chemical Reference, 2000, 29(3):331-385.
[8]	李悦, 裴锦华. 无人机气液压发射动力学数值仿真[J]. 机械工程学报, 2011, 47(8):183-190.
	LI Y, PEI J H. Dynamic Numerical simulation of the pneumatic and hydraulic launching of UAV[J]. Journal of Mechanical Engineering, 2011, 47(8):183-190. (in Chinese)
[9]	田兵, 王树宗, 练永庆. 水下蓄能式发射装置结构优化[J]. 兵工学报, 2011, 32(9):1094-1098.
	TIAN B, WANG S Z, LIAN Y Q. Structure optimization for underwater energy-accumulated launcher[J]. Acta Armamentarii, 2011, 32(9):1094-1098. (in Chinese)
[10]	赫雷, 尚兴超, 周克栋, 等. 一种压缩空气驱动的武器发射过程动力学分析[J]. 振动与冲击, 2014, 33(21):202-206.
	HE L, SHANG X C, ZHOU K D, et al. Dynamic analyis for launching process of a compressed air-driving weapon[J]. Vibration and Shock, 2014, 33(21):202-206. (in Chinese)
[11]	卢伟, 马晓平, 周明. 无人机气动弹射动力学仿真与优化[J]. 西北工业大学学报, 2014, 32(6):865-871.
	LU W, MA X P, ZHOU M. Dynamic simulation and optimization of UAV pneumatic launching[J]. Journal of Northwestern Polytechnical University, 2014, 32(6):865-871. (in Chinese)
[12]	刘少刚, 刘刚, 赵丹, 等. 气动发射灭火炮伴随式击发装置研究[J]. 兵工学报, 2013, 34(10):1318-1323. doi: 10. 3969/ j. issn. 1000-1093. 2013. 10. 019
	LIU S G, LIU G, ZHAO D, et al. Research on the associated-tube type firing mechanism for pneumatic Fire-extinguishing cannon[J]. Acta Armamentarii, 2013, 34(10):1318-1323. (in Chinese)
[13]	牛清勇, 李天匀, 朱翔, 等. 水下气动发射装置发射性能参数灵敏度分析[J]. 哈尔滨工程大学学报, 2015, 36(7):877-881.
	NIU Q Y, LI T Y, ZHU X, et al. Sensitivity analysis of the performance parameters of an underwater pneumatic launcher[J]. Journal of Harbin Engineering University, 2015, 36(7):877-881. (in Chinese)
[14]	李博平, 李国庆, 张笈玮, 等. 压缩空气弹射系统内弹道特性[J]. 兵工学报, 2021, 42(12):2606-2616. doi: 10.3969/j.issn.1000-1093.2021.12.008
	LI B P, LI G Q, ZHANG J W, et al. Ballistics of submarine ballistic missile launch system[J]. Acta Armamentarii, 2021, 42(12):2606-2616. (in Chinese)
[15]	REN J, YANG F B, MA D W, et al. Pneumatic performance study of a high pressure ejection device based on real specific energy and specific enthalpy[J]. Energy, 2014, 16(9):4801-4817.
[16]	杨风波, 马大为, 杨帆, 等. 高压弹射装置内弹道建模与计算[J]. 兵工学报, 2013, 4(5):527-534.
	YANG F B, MA D W, YANG F, et al. Interior ballistics modeling and calculation of high-pressure ejection device[J]. Acta Armamentarii, 2013, 4(5):527-534. (in Chinese)
[17]	YANG F B, MA D W, LE G G. Real thermodynamic energy and enthalpy on high pressure pneumatic system based on improved virial equation[J]. Advanced Materials Research, 2013, 694:734-738.
[18]	任锐, 马大为, 姚琳, 等. 多级气动液压弹射装置建模及性能研究[J]. 兵工学报, 2016, 7(8):1365-1372.
	REN R, MA D W, YAO L, et al. Theoretical modeling and performance research on multi-stage pneumatic and hydraulic catapult device[J]. Acta Armamentarii, 2016, 7(8): 1365-1372. (in Chinese)
[19]	GU S W, LI Y X, Teng L. An experimental study on the flow characteristics during the leakage of high pressure CO₂ pipelines[J]. Process Safety and Environmental Protection, 2019, 125:92-101. doi: 10.1016/j.psep.2019.03.010 URL
[20]	TU R, XIE Q Y, YI J X, et al. An experimental study on the leakage process of high pressure CO₂ from a pipeline transport system[J]. Greenhouse Gases: Science and Technology, 2014(4):777-784.
[21]	姚琳, 马大为, 任杰, 等. 高速无杆气缸作动器密封圈润滑性能分析[J]. 浙江大学学报(工学版), 2017, 51(8):1568-1574.
	YAO L, MA D W, REN J, et al. Lubrication performance analysis of high-speed rod-less cylinder seal[J]. Journal of Zhejiang University (Engineering Science), 2017, 51(8):1568-1574. (in Chinese)