基于传热增广模型的轨迹优化与防热结构分析

doi:10.12305/j.issn.1001-506X.2022.03.25

摘要/Abstract

摘要：

在考虑飞行器结构温度约束的轨迹设计问题中, 采用一般约束热流密度的轨迹优化模型存在反复迭代、不能考虑轨迹、传热之间耦合关系等缺点。针对这些问题, 提出一种传热增广的轨迹优化模型。利用空间差分将传热方程转化为一阶微分方程组, 与运动方程组成传热增广的系统状态方程, 从而能在轨迹优化中对结构温度直接进行约束。算例仿真说明了基于增广模型求解的高效性与结果的合理性; 在此基础上分析了再入轨迹与防热结构之间的相互影响关系, 对方案设计阶段的防热结构设计提供参考。

关键词: 轨迹优化, 热传导, 防热结构, 高超声速

Abstract:

In the trajectory design problem considering the temperature constraint of aircraft structure, the trajectory optimization model with general constrained heat flux has some disadvantages, such as repeated iteration, unable to consider the coupling relationship between trajectory and heat transfer. To solve these problems, a trajectory optimization model of heat transfer expansion is proposed. The heat transfer equation is transformed into a set of first-order differential equations by using spatial difference, and the system state equation of heat transfer expansion is formed with the motion equation, so that the structure temperature can be directly constrained in the trajectory optimization. The simulation of an example shows the efficiency of the solution based on the augmented model and the rationality of the result. On this basis, the interaction between reentry trajectory and thermal structure is analyzed, which provides a reference for the design of thermal structure in the scheme design stage.

Key words: trajectory optimization, heat conduction, thermal protection structure, hypersonic

中图分类号:

V412

张腾飞, 龚春林, 粟华, 薛鹏飞. 基于传热增广模型的轨迹优化与防热结构分析[J]. 系统工程与电子技术, 2022, 44(3): 929-938.

Tengafei ZHANG, Chunlin GONG, Hua SU, Pengfei XUE. Trajectory optimization based on heat-augmented model and analysis of thermal protection structure[J]. Systems Engineering and Electronics, 2022, 44(3): 929-938.

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参数	防热层	隔热层
材料名称	PM1000	Saffil氧化铝纤维
厚度/m	0.025	0.095
密度/(kg/m³)	8 240	96
热导率/(W/mK)	k_f(T)	k_s(T)
比热/(JK/kg)	c_f(T)	c_s(T)
耐温极限/K	1 570	1 870(内表面不超过620)
表面辐射率	0.86	-
边界	热流密度/(W/m²)	q_s(t)
条件	环境温度/K	T_∞(t)

结构参数	值
质量/kg	907.2
参考面积/m²	0.484
气动力系数	拟合模型(见式(26))
材料尺寸/m	δ_f=0.024, δ_s=0.095(与第2.2节算例相同)

时刻	高度/km	速度/(m/s)	倾角/(°)	结构温度/K
初始状态	80	6 400	0	280
终端状态	20	760	-3	≤材料耐温极限

参数	模型
参数	一般模型	增广模型
迭代次数	17	1
计算耗时/s	49.2	10.6
内表面最高温度/K	619.98	620
外表面最高温度/K	1 562.87	1 566.90
航程角/(°)	103.56	106.15
热流约束/(W·m^-2)	4.05×10⁵	-

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