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Finite Element Analysis of Thermal Stress of Supersonic Missile Warhead
DOI: 10.12677/IJM.2021.101007, PDF, HTML, XML, 下载: 318  浏览: 911  国家自然科学基金支持

Abstract: The supersonic missile is faced with severe aerodynamic heating in flight, and the thermal stress analysis of the warhead is very important for its safety. In this paper, the geometric structure of missile warhead is designed, the tetrahedral element is used to discretize, and the material prop-erties of SiC ceramic varying with temperature is considered. The aerodynamic heat of environment when flighting at the speed of 4.3 Ma is used as the boundary condition. The thermal stress mathematical model is established, and the temperature field and stress field are calculated and analyzed. The results show that the aerodynamic heat of supersonic warhead has great influence on the stress and deformation of the structure. And the rapid rise of stagnation point temperature leads to the local stress concentration. This study can provide theoretical and data reference for the structural design of supersonic warhead.

1. 引言

2. 几何外形与材料

Figure 1. Outline drawing of blunt sphere cone warhead

Table 1. Physical properties of SiC ceramics

3. 数学模型

3.1. 热流边界条件

${q}_{s}=\frac{1105×{10}^{5}}{\sqrt{{R}_{N}}}{\left(\frac{{\rho }_{\infty }}{1.206}\right)}^{0.5}{\left(\frac{{v}_{\infty }}{7900}\right)}^{3.15}$ (1)

3.2. 温度场计算

$\rho c\frac{\partial T}{\partial t}=\lambda \frac{{\partial }^{2}T}{\partial {x}^{2}}+\lambda \frac{{\partial }^{2}T}{\partial {y}^{2}}+\lambda \frac{{\partial }^{2}T}{\partial {z}^{2}}$ (2)

${T|}_{t=0}={T}_{0}\left(x,y,z\right)$

${\left({\lambda }_{x}\frac{\partial T}{\partial x}{n}_{x}+{\lambda }_{y}\frac{\partial T}{\partial y}{n}_{y}+{\lambda }_{z}\frac{\partial T}{\partial z}{n}_{z}\right)|}_{s}={q}_{x}\left(x,y,z,t\right)$

${\left[C\right]}^{e}{\left\{\stackrel{˙}{T}\right\}}^{e}+{\left[K\right]}^{e}{\left\{T\right\}}^{e}={\left\{P\right\}}^{e}$ (3)

${C}_{ij}={\int }_{\Omega }^{e}\rho c{N}_{i}{N}_{j}\text{d}\Omega$

${K}_{ij}={\int }_{\Omega }^{e}\left({\lambda }_{x}\frac{\partial {N}_{i}}{\partial x}\frac{\partial {N}_{j}}{\partial x}+{\lambda }_{y}\frac{\partial {N}_{i}}{\partial y}\frac{\partial {N}_{j}}{\partial y}\right)\text{d}\Omega +{\int }_{{\Gamma }_{3}}^{e}h{N}_{i}{N}_{j}\text{d}\Gamma$

${P}_{i}={\int }_{{\Gamma }_{2}}^{e}{N}_{i}{q}_{s}\text{d}\Gamma +{\int }_{{\Gamma }_{3}}^{e}{N}_{i}h{T}_{f}\text{d}\Gamma$

$\frac{\partial T}{\partial t}=\frac{{T}_{t}-{T}_{t-\Delta t}}{\Delta t}$ (4)

$\left[\frac{C}{\Delta t}+K\right]{\left\{T\right\}}_{t}=\frac{\left[C\right]}{\Delta t}{\left\{T\right\}}_{t-\Delta t}+{\left\{P\right\}}_{t}$ (5)

3.3. 热应力计算

$\left\{\epsilon \right\}=\left\{{\epsilon }_{e}\right\}+\left\{{\epsilon }_{0}\right\}$ (6)

$\Pi =\frac{\text{1}}{\text{2}}\underset{e}{\sum }{\left\{\delta \right\}}^{e\text{T}}{\left[K\right]}^{e}{\left\{\delta \right\}}^{e}-\underset{e}{\sum }{\left\{\delta \right\}}^{e\text{T}}{\left\{{F}_{T}\right\}}^{e}$ (7)

${\left[K\right]}^{e}={\int }_{{V}^{e}}{\left[B\right]}^{\text{T}}\left[D\right]\left[B\right]\text{d}v$

${\left\{{F}_{T}\right\}}^{e}={\int }_{{V}^{e}}{\left[B\right]}^{\text{T}}\left[D\right]\left\{{\epsilon }_{0}\right\}\text{d}v$

${\left[K\right]}^{e}{\left\{\delta \right\}}^{e}={\left\{{F}_{T}\right\}}^{e}$ (8)

4. 有限元分析

4.1. 有限元分析步骤

Figure 2. Process of finite element analysis

4.2. 三维建模及网格划分

Figure 3. Schematic diagram: three-dimensional model

Figure 4. Schematic diagram: finite element mesh

4.3. 边界条件的施加

Figure 5. Heat flux boundary condition

Figure 6. Curve: distribution of surface heat flux

5. 结果分析

5.1. 温度场分析

Figure 7. Temperature field of external surface

Figure 8. Curve: variation of outer surface temperature along y-axis

Figure 9. Temperature field of inner surface

Figure 10. Curve: temperature of stagnation point from 0 to 400 s

5.2. 热应力分析

Figure 11. Cloud chart: von Mises stress

Figure 12. Cloud chart: overall displacement

Figure 13. Stress: X direction

Figure 14. Stress: Y direction

Figure 15. Stress: Z direction

6. 结论

NOTES

*通讯作者。

 [1] 徐世南, 吴催生. 高超声速导弹流场与结构温度场耦合数值分析[J]. 弹箭与制导学报, 2019, 39(5): 121-124+128. [2] 徐世南, 吴催生. 高超声速导弹多场耦合仿真[J]. 宇航学报, 2019, 40(7): 768-775. [3] 张超, 刘洪泉, 赵泽华, 王记妃, 胡东阳, 张玺, 翟北北. 高超声速钝锥体热环境仿真计算[J]. 弹箭与制导学报, 2018, 38(6): 43-46. [4] 高翔. 攻角下高超声速弹头气动热和温度场的计算与研究[D]: [硕士学位论文]. 南京: 南京理工大学, 2015. [5] 王志超, 张龙, 姚琳. 高速飞行器结构气动热计算与温度场模拟[J]. 四川兵工学报, 2015, 36(11): 49-52. [6] 李凰立. 再入弹头的气动加热及热响应分析[D]: [硕士学位论文]. 西安: 西北工业大学, 2001. [7] 王琳. 导弹复合材料头罩设计与结构强度研究[D]: [硕士学位论文]. 北京: 国防科学技术大学, 2012. [8] 易龙, 孙秦, 彭云. 复合材料头锥结构气动热应力分析方法研究[J]. 机械强度, 2007(4): 686-690. [9] 胡雨濛. 近空间高超声速气动热的数值模拟[D]: [博士学位论文]. 北京: 北京交通大学, 2018. [10] Zander, F., Gollan, R.J., Jacobs, P.A. and Morgan, R.G. (2014) Hypervelocity Shock Standoff on Spheres in Air. Shock Waves, 24, 171-178. https://doi.org/10.1007/s00193-013-0488-x [11] 黄强. 磨削过程中硬质合金材料热应力的有限元分析[D]: [硕士学位论文]. 武汉: 武汉理工大学, 2007. [12] 黄海明, 郭然. 计算固体力学[M]. 北京: 科学出版社, 2014. [13] Meng, Y.S., Yan, L., Huang, W. and Tong, X.Y. (2020) Numerical Investigation of the Aerodynamic Characteristics of a Missile. IOP Conference Series: Materials Science and Engineering, 887, Article ID: 012001. https://doi.org/10.1088/1757-899X/887/1/012001 [14] 王志超. 高速飞行器结构的热响应特性分析研究[D]: [硕士学位论文]. 南京: 南京理工大学, 2016.