Numerical Analysis and Experimental Study of a Underwater-launched Projectile Breaking Through Ice Vertically

doi:10.12382/bgxb.2024.0885

Abstract

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

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-.

Figures/Tables 37

Fig.1 Stress-strain curve of elastoplastic model

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

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

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

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

Fig.2 Comparison of calculated results under two working conditions

Fig.3 The model of projectile breaking through ice

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

Fig.5 Grid-independence test

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

Fig.7 Three-point bending simulation model

Fig.8 Relationship between ice load and displacement

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

Fig.10 Schematic diagram of experimental setup

Fig.11 Gas canister

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

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

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

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

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

Fig.16 Comparison of ice-breaking speeds of projectiles

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

Fig.17 Velocity variations of projectiles

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

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

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

Fig.21 Schematic diagram of interaction between projectile and ice

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

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

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

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

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

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

Fig.27 Comparison of results of three working conditions

Fig.28 Gaussian fitting curve for ice load

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

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

Fig.29 Comparison of simulated and predicted results

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

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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