航行体垂向破冰数值分析与试验研究

doi:10.12382/bgxb.2024.0885

摘要/Abstract

摘要：

针对航行体与冰相互作用的强非线性问题,通过相似理论推导出影响航行体破冰的关键无量纲参数,进行航行体高速贯穿冰层的缩比模型试验。基于高斯拟合函数提出一个冰载荷预测公式;建立航行体破冰出水的流固耦合模型,通过改变航行体的头部形状、航行体撞击冰层的动能和冰层厚度,对破冰现象、冰载荷以及航行体运动特性进行分析。研究结果表明:在破冰过程中,航行体头部空泡的体积不断减小,肩部空泡的体积逐渐增大,空化效应越来越剧烈。当航行体初始速度为40m/s时,半球型、球锥型、尖锥型航行体的冰载荷极值分别为35700kN、33200kN、18600kN,尖锥型头部航行体破冰前后速度损失率最低,破冰效果最好;在冰层厚度为180mm、弹射压力分别为3MPa和5MPa的条件下,航行体破冰后速度分别由13.1m/s、17.8m/s降低至9.5m/s、13.4m/s;航行体破冰速度越大,速度损失率越低,动能损失越大;冰载荷极值和航行体速度损失率随着冰层厚度的增加而上升,航行体初速度对载荷特性和运动特性的影响效果随着冰层厚度的减小而弱化。

关键词: 航行体, 破冰, 冰载荷, 缩比试验, 预测模型

Abstract:

Aiming at the strong nonlinear problem of the interaction between underwater-launched projectile and ice, the key dimensionless parameters affecting the ice-breaking of projectile are derived by similarity theory. The scaled model test is carried out for the high-speed penetration of projectile through the ice layer. Based on the Gaussian fitting function, an ice load prediction formula is proposed. A fluid-solid coupling model of ice-breaking is established. The ice-breaking phenomenon, the ice load and the motion characteristics of projectile are analyzed by changing the nose shape of projectile, the kinetic energy of projectile and the thickness of ice layer. The results show that the volume of projectile nose cavitation decreases during ice-breaking, the volume of shoulder cavitation gradually increases, and the asymmetry of shoulder cavitation increases with the increase in ice thickness. When the initial speed of projectile is 40m/s, the extreme values of the ice loads on projectiles with hemispherical, spherical conical and pointed conical noses are 35700kN, 33200kN and 18600kN, respectively. The speed loss rate of projectile with pointed conical nose is the lowest, and its ice breaking effect is the best. Under the condition that the ice thickness is 180mm and the ejection pressure is 3MPa and 5MPa, respectively, the speeds of projectile after icebreaking are reduced from 13.1m/s and 17.8m/s to 9.5m/s and 13.4m/s. The greater the ice-breaking speed of projectile is, the lower the speed loss rate is, and the greater the kinetic energy loss is.The extreme value of ice load and the speed loss rate of projectile increase with the increase in ice thickness, and the effect of the initial speed of projectile on the load characteristics and motion characteristics weakens with the decrease in ice thickness.

Key words: underwater-launched projectile, vertical ice-breaking, ice loading, scaling test, predictive model

刁震霆, 方登建, 王少蕾. 航行体垂向破冰数值分析与试验研究[J]. 兵工学报, 2025, 46(5): 240885-.

DIAO Zhenting, FANG Dengjian, WANG Shaolei. Numerical Analysis and Experimental Study of a Underwater-launched Projectile Breaking Through Ice Vertically[J]. Acta Armamentarii, 2025, 46(5): 240885-.

图/表 37

图1 弹塑性模型应力-应变关系曲线

Fig.1 Stress-strain curve of elastoplastic model

表1 海冰本构模型材料

Table 1 Sea ice intrinsic model materials

材料属性	数值	材料属性	数值
密度/(kg·m^-3)	900	体积模量/GPa	5.26
剪切模量/GPa	2.20	塑性失效应变	0.35
屈服应力/MPa	2.12	截断压力/MPa	-4
塑性硬化模量/GPa	4.26

表2 参数的导出量纲

Table 2 Dimension of parameters

类型	物理量	符号参数	量纲
	长度	L	l
基本参数	质量	m	m
	时间	T	t
	密度	ρ_i,ρ_vh	m/l³
材料参数	泊松比	μ_i,μ_vh
	弹性模量	E_i,E_vh	m/(lt²)
	冰层厚度	h_i	l
几何参数	冰层特征尺寸	l_i,w_i	l
	航行体长度	l_vh	l
	航行体直径	d_vh	l
物理参数	时间	t	t
	初始速度	v₀	l/t
动态参数	速度	v_vh	l/t
	冰阻力	F_i	ml/t²

表3 不同工况的参数

Table 3 Parameters of different working conditions

参数	工况1	工况2
h_i/m	0.1	0.12
l_vh/m	1	1.2
v₀/(m·s^-1)	20	25
ρ_vh/(m·s^-3)	7850	5024
$h i l v h$	0.1	0.1
$v 0 E i / ρ v h$	0.009	0.009

表3 不同工况的参数

Table 3 Parameters of different working conditions

参数	工况1	工况2
h_i/m	0.1	0.12
l_vh/m	1	1.2
v₀/(m·s^-1)	20	25
ρ_vh/(m·s^-3)	7850	5024
$h i l v h$	0.1	0.1
$v 0 E i / ρ v h$	0.009	0.009

图2 两种工况计算结果对比

Fig.2 Comparison of calculated results under two working conditions

图3 航行体贯穿冰层模型

Fig.3 The model of projectile breaking through ice

图4 球锥形(左)、半球形(中)、尖锥形(右)头部模型

Fig.4 Projectile models with conical (left), hemispherocal (middle), pyramidal (right) noses

图5 网格无关性检验

Fig.5 Grid-independence test

图6 不同网格密度冰层的裂纹扩展现象

Fig.6 Crack extension in ice layers with different grid densities

图7 三点弯曲仿真模型

Fig.7 Three-point bending simulation model

图8 冰载荷和位移关系

Fig.8 Relationship between ice load and displacement

图9 裂纹扩展现象(上为仿真结果,下为实验结果)

Fig.9 Crack extension phenomenon (top: figure shows the simulation result, bottom: figure shows the experimental result)

图10 试验装置示意图

Fig.10 Schematic diagram of experimental setup

图11 储气罐

Fig.11 Gas canister

图12 弹射筒(左)和航行体(右)

Fig.12 Launch tubes(left) and projectile(right)

图13 弹射压力3MPa、冰层厚度180mm的破冰过程

Fig.13 Ice-breaking process with ejection pressure of 3MPa and ice thickness of 180mm

图14 弹射压力5MPa、冰层厚度180mm的破冰过程

Fig.14 Ice-breaking process with ejection pressure of 5MPa and ice thickness of 180mm

表4 不同工况破冰前后速度变化

Table 4 Velocity changes before and after ice breaking under different working conditions

工况序号	压力/MPa	冰层厚度/mm	破冰前速度/(m·s^-1)	破冰后速度/(m·s^-1)	速度损失率/%	动能损失量/J
1	3	160	12.8	10.2	20.93	152.49
2	3	180	13.1	9.5	27.48	207.47
3	3	200	13.2	8.4	36.36	264.38
4	5	160	18.1	14.8	18.23	276.85
5	5	180	17.8	13.4	24.72	350.06
6	5	200	18.0	11.8	34.44	471.14

图15 航行体高速破冰数值计算模型

Fig.15 Numerical computational modeling of high-speed ice-breaking of a projectile

图16 航行体高速破冰速度对比

Fig.16 Comparison of ice-breaking speeds of projectiles

表5 不同算法的计算时间

Table 5 Computational time of different algorithms

算法	冰模型	水、空气模型	计算时间
1(本文算法)	FEM	S-ALE	8h32min
2	FEM	ALE	12h41min
3	SPH	SPH	20h08min
4	SPH	ALE	16h26min
5	FEM-SPH	ALE	14h22min
6	PD	ALE	9h15min
7	SPG-FEM	S-ALE	11h15min

图17 不同算法下的航行体速度变化

Fig.17 Velocity variations of projectiles

图18 v=35m/s时球锥形航行体破冰过程的流场演化

Fig.18 Evolution of flow field during ice-breaking of projectile with spherical conical nose for v=35m/s

图19 v=40m/s时不同头形航行体破冰的冰载荷变化曲线

Fig.19 Ice load curves of projectiles with different noses for v=40m/s

图20 v=40m/s时,半球形、球锥形、尖锥形头部航行体破冰过程等效应力云图

Fig.20 Equivalent force cloud maps of projectiles with different noses during ice-breaking for v=40m/s

图21 航行体与冰层作用示意图

Fig.21 Schematic diagram of interaction between projectile and ice

图22 v=35m/s时不同头部形状航行体破冰的冰载荷变化曲线

Fig.22 Ice load curves of projectiles with different noses for v=35m/s

图23 半球形、球锥形、尖锥形航行体破冰的速度变化曲线

Fig.23 Velocity change curves of projectiles with different noses after ice breaking

图24 不同材料密度的航行体破冰速度变化

Fig.24 Changes in speeds for projectiles of different material densities

图25 不同材料密度的航行体破冰载荷变化

Fig.25 Changes in loads for projectiles of different material densities

表6 v=40m/s时不同冰层厚度航行体破冰过程云图

Table 6 Processes of projectiles breaking different thick ices for v=40m/s

图26 不同冰层厚度下航行体破冰的冰载荷极值和速度损失率

Fig.26 Ice load variations and velocity losses in projectile breaking different thick ices

图27 3种工况结果对比

Fig.27 Comparison of results of three working conditions

图28 冰载荷的高斯拟合曲线

Fig.28 Gaussian fitting curve for ice load

表7 冰载荷曲线拟合参数

Table 7 Parameters for ice load curve fitting

序号	$v 0 E i / ρ v h$	$h i l v h$	a	b	c	R²
1	0.0390	0.08	1.5696×10⁷	0.0061	0.0069	0.9217
2	0.0446	0.08	1.7788×10⁷	0.0056	0.0059	0.9200
3	0.0502	0.08	1.9454×10⁷	0.0052	0.0053	0.9241
4	0.0390	0.10	1.6117×10⁷	0.0073	0.0074	0.9485
5	0.0446	0.10	1.8128×10⁷	0.0067	0.0065	0.9521
6	0.0502	0.10	1.9765×10⁷	0.0062	0.0057	0.9505
7	0.0390	0.12	1.6671×10⁷	0.0070	0.0067	0.9519
8	0.0446	0.12	1.8950×10⁷	0.0064	0.0056	0.9555
9	0.0502	0.12	2.0635×10⁷	0.0059	0.0050	0.9550

表7 冰载荷曲线拟合参数

Table 7 Parameters for ice load curve fitting

序号	$v 0 E i / ρ v h$	$h i l v h$	a	b	c	R²
1	0.0390	0.08	1.5696×10⁷	0.0061	0.0069	0.9217
2	0.0446	0.08	1.7788×10⁷	0.0056	0.0059	0.9200
3	0.0502	0.08	1.9454×10⁷	0.0052	0.0053	0.9241
4	0.0390	0.10	1.6117×10⁷	0.0073	0.0074	0.9485
5	0.0446	0.10	1.8128×10⁷	0.0067	0.0065	0.9521
6	0.0502	0.10	1.9765×10⁷	0.0062	0.0057	0.9505
7	0.0390	0.12	1.6671×10⁷	0.0070	0.0067	0.9519
8	0.0446	0.12	1.8950×10⁷	0.0064	0.0056	0.9555
9	0.0502	0.12	2.0635×10⁷	0.0059	0.0050	0.9550

图29 仿真结果与预测公式结果对比

Fig.29 Comparison of simulated and predicted results

表8 预测值与实际值对比

Table 8 Comparison of predicted and actual values

序号	$v 0 E i / ρ v h$	$h i l v h$	预测值/Pa	实际值/Pa	误差/%
1	0.0700	0.06	2.81×10⁷	2.92×10⁷	3.77
2	0.0669	0.10	3.48×10⁷	3.26×10⁷	6.75
3	0.0585	0.12	2.44×10⁷	2.34×10⁷	4.27
4	0.0675	0.11	2.97×10⁷	3.11×10⁷	4.50
5	0.0558	0.08	2.13×10⁷	2.26×10⁷	6.02

表8 预测值与实际值对比

Table 8 Comparison of predicted and actual values

序号	$v 0 E i / ρ v h$	$h i l v h$	预测值/Pa	实际值/Pa	误差/%
1	0.0700	0.06	2.81×10⁷	2.92×10⁷	3.77
2	0.0669	0.10	3.48×10⁷	3.26×10⁷	6.75
3	0.0585	0.12	2.44×10⁷	2.34×10⁷	4.27
4	0.0675	0.11	2.97×10⁷	3.11×10⁷	4.50
5	0.0558	0.08	2.13×10⁷	2.26×10⁷	6.02

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