截锥形弹体在液体介质中运动速度衰减规律分析

孔祥韶; 石干; 王旭阳; 周红昌; 吴卫国

doi:10.11883/bzycj-2020-0075

截锥形弹体在液体介质中运动速度衰减规律分析

doi: 10.11883/bzycj-2020-0075

孔祥韶^{1, 2,},
石干^{1, 2},
王旭阳^{1, 2, 3},
周红昌^{1, 2},
吴卫国^{1, 2}

1.
武汉理工大学绿色智能江海直达船舶与邮轮游艇研究中心，湖北武汉 430063
2.
武汉理工大学交通学院，湖北武汉 430063
3.
西安航天动力研究所液体火箭发动机技术重点实验室，陕西西安 710100

基金项目: 装备预研教育部联合基金（青年人才）（6141A02033108）

详细信息

作者简介:
孔祥韶（1983－　），男，博士，教授，博士生导师，kongxs@whut.edu.cn

中图分类号: O353.4
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- 文章访问数: 601
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出版历程
- 收稿日期: 2020-03-20
- 修回日期: 2020-06-24
- 刊出日期: 2021-01-05

On velocity attenuation of a truncated cone-shaped projectile vertically penetrating through liquid

KONG Xiangshao^{1, 2
,},
SHI Gan^{1, 2},
WANG Xuyang^{1, 2, 3},
ZHOU Hongchang^{1, 2},
WU Weiguo^{1, 2}

1.
Green & Smart River-Sea-Going Ship, Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, Hubei, China
2.
School of Transportation, Wuhan University of Technology, Wuhan 430063, Hubei, China
3.
Science and Technology on Liquid Rocket Engine Laboratory, Xi’an Aerospace Propulsion Institute, Xi’an 710100, Shaanxi, China

摘要

摘要: 水面舰船被动防护体系中液舱的主要功能之一是阻止高速弹体（爆炸破片）对内部重要结构、设备和人员的威胁，高速弹体打击液舱的过程包含着复杂的能量传递与耗散。为了分析弹体形状对其在液体介质中运动速度衰减的影响, 开展了一系列不同头形因数的截锥形弹体在不同入水速度下弹体垂直侵彻液体介质过程的数值模拟，得到了垂直侵彻液体介质时弹体速度衰减特性，发现高速弹体在液体介质中运动的阻力因数与弹体形状和无量纲速度有关。基于对系列数值模拟计算结果的拟合分析，提出了计及头形因数的截锥形弹体垂直侵彻液体介质时的速度衰减经验公式，通过开展数值算例分析验证了公式计算结果的可靠性。本文中提出的经验公式可实现对高速弹体在液体介质中速度衰减的准确快速计算，为舰船防护液舱结构设计提供一定的参考。
- 截锥形弹体 /
- 头形因数 /
- 速度衰减 /
- 防护液舱
Abstract: One of the main functions of liquid tanks in the passive protective systems of surface warships is to prevent the damage by high-velocity projectiles (explosive fragments) to important internal structures, equipments and personnels. The process of high-velocity projectile penetrating through a liquid tank involves complex energy transfer and dissipation. To explore the influences of the head shape of a projectile and its water-entry velocity on the velocity attenuation of the projectile in fluid, a series of truncated cone-shaped projectiles with different head shape factors were developed to numerically simulate the processes of the truncated cone-shaped projectiles vertically penetrating through the fluid at different initial water-entry velocities. The velocity attenuation characteristics were obtained for the projectiles vertically penetrating through the fluid. The above results display that the resistance factor of a high-velocity projectile moving in the fluid is related with the projectile shape and the ratio of the instantaneous velocity of the projectile to its initial water-entry velocity. Based on the numerical simulations and the corresponding fitting results, an empirical formula was proposed by considering the projectile head factor to predict the velocity attenuation of the truncated cone-shaped projectiles vertically penetrating through the fluid. And a series of calculation examples were carried out to verify the formula. These calculation examples show that the formula is feasible and can be used to accurately calculate the velocity attenuation of high-velocity projectiles in fluid media and it is helpful for the structural design of the protective tanks of warships.
- truncated cone-shaped projectile /
- head shape factor /
- velocity attenuation /
- protective tank

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图 1 截锥形弹体示意图

Figure 1. Schematic diagram of a truncated cone-shaped projectile

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图 2 不同头形因数截锥形弹体有限元模型

Figure 2. Finite element models for truncated cone-shaped projectiles with different head type coefficients

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图 3 针对弹体直径为12.65 mm，长度为25.4 mm，入水初速度为603 m/s时，试验与数值计算的空泡尺寸

Figure 3. Comparison of cavitation sizes obtained experimentally and numerically for the projectile with the diameter of 12.65 cm and the length of 25.4 cm, water entering at 603 m/s

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图 4 长度为25.4 mm的弹体在两种入水速度工况下位移和速度的变化

Figure 4. Changes of displacement and velocity of the projectile with the length of 25.4 mm at two initial velocities of water entry

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图 5 长度为38.1 mm的弹体在两种入水速度工况下位移和速度的变化

Figure 5. Changes of displacement and velocity of the projectile with the length of 38.1 mm at two initial velocities of water entry

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图 6 不同头形因数的截锥形弹体在不同入水速度工况下速度随入水距离的衰减

Figure 6. Velocity attenuation of truncated cone-shaped projectiles with different head coefficients with water-entry distance at different initial velocities of water entry

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图 7 不同入水速度下，$\psi = 0$的截锥形弹体阻力因数与${v_{\rm{b}}}/{v_0}$的关系

Figure 7. Resistance factor varying with ${v_{\rm{b}}}/{v_0}$ for the truncated cone-shaped projectile with $\psi = 0$ at different water-entry velocities

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图 8 对于头形因数不同的截锥形弹体，参数a₀和a₁与马赫数$Ma$的关系

Figure 8. Changes of parameters a₀ and a₁ with Mach number $Ma$ for the truncated cone-shaped projectiles with different head shape factors

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图 9 $a$系列参数与头形因数$\psi $的关系

Figure 9. Series parameters of a varyied with head shape factor $\psi $

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图 10 入水速度为400 m/s，头形因数不同的弹丸，速度随入水距离衰减的模拟结果与公式计算结果的比较

Figure 10. Comparison of velocity attenuation with distance between numerical simulation and formula calculation for the projectiles with different head shape factors at the initial water-entry velocity of 400 m/s

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图 11 头形因数为1/6，入水速度不同的弹丸，速度随入水距离衰减的模拟结果与公式计算结果的比较

Figure 11. Comparison of velocity attenuation with distance between numerical simulation and formula calculation for the projectile with the head shape factor of 1/6 at different initial water-entry velocities

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表 1 水的状态方程各项参数^[14]

Table 1. Parameters of equation of state for water^[14]

${A_1}{\rm{/GPa}}$	${A_{\rm{2}}}{\rm{/GPa}}$	${A_3}{\rm{/GPa}}$	${B_0}$	${B_1}$	${T_1}{\rm{/GPa}}$	${T_2}{\rm{/GPa}}$	$ {\rho }_{0}\rm{/(kg}·{\rm{m}}^{\rm{-3}}\rm{)}$
2.2	9.54	14.57	0.28	0.28	2.2	0	1 000

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表 2 数值计算工况

Table 2. Numerical calculation conditions

工况	$\psi $	v₀/(m·s⁻¹)	工况	$\psi $	v₀/(m·s⁻¹)	工况	$\psi $	v₀/(m·s⁻¹)	工况	$\psi $	v₀/(m·s⁻¹)
1-1	0	400	2-1	1/3	400	3-1	2/3	400	4-1	1	400
1-2	0	650	2-2	1/3	650	3-2	2/3	650	4-2	1	650
1-3	0	900	2-3	1/3	900	3-3	2/3	900	4-3	1	900
1-4	0	1 150	2-4	1/3	1 150	3-4	2/3	1 150	4-4	1	1 150
1-5	0	1 400	2-5	1/3	1 400	3-5	2/3	1 400	4-5	1	1 400

下载: 导出CSV

表 3 不同工况下的参数${a_0}$和${a_1}$的数值

Table 3. Values of parameters ${a_0}$ and ${a_1}$ under different working conditions

$\psi $	拟合参数	v₀/(m·s⁻¹)
$\psi $	拟合参数	400	650	900	1150	1400
0	a₀	0.617	0.612	0.633	0.587	0.367
0	a₁	−0.217	−0.212	−0.223	−0.153	0.128
1/3	a₀	0.329	0.459	0.477	0.440	0.288
1/3	a₁	−0.019	−0.158	−0.168	−0.113	0.077
2/3	a₀	0.768	0.707	0.784	0.714	0.553
2/3	a₁	−0.387	−0.297	−0.394	−0.289	−0.082
1	a₀	1.216	1.204	1.527	1.382	1.416
1	a₁	−0.344	−0.345	−0.823	−0.580	−0.640

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表 4 参数${a_0}$、${a_1}$的拟合结果

Table 4. Fitting results of parameters ${a_0}$ and ${a_1}$

$\psi $	a₀₁	a₀₂	a₀₃	a₀₄	a₀₅	a₁₁	a₁₂	a₁₃	a₁₄	a₁₅
0	0.847	−1.459	2.575	−0.707	−0.887	−0.376	0.918	−1.096	−1.059	1.743
1/3	−0.611	6.078	−13.025	12.901	5.055	1.060	−7.042	15.285	−15.196	5.971
2/3	2.810	−15.067	37.573	−38.342	13.579	−3.246	21.137	−52.932	54.463	−19.504
1	8.033	−53.017	141.081	−153.418	58.737	−10.547	79.685	−213.159	232.929	−89.548

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表 5 ${a_{ij}}$系列参数的拟合结果

Table 5. Fitting results of ${a_{ij}}$ series parameters

${a_{ij}}$	${a_{ij}}_0$	${a_{ij}}_1$	${a_{ij}}_2$
${a_0}_1$	0.693	−7.536	15.031
${a_{02}}$	−0.864	49.585	−102.332
${a_{03}}$	1.908	−128.117	267.957
${a_{04}}$	−0.654	136.681	−289.498
${a_{05}}$	0.814	−32.000	88.221
${a_1}_1$	−0.239	9.212	−19.657
${a_1}_2$	0.628	−70.273	149.620
${a_1}_3$	−1.463	185.983	−397.312
${a_1}_4$	0.187	−201.803	433.298
${a_1}_5$	1.001	77.280	−167.088

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