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固体火箭发动机三维装药的逆向设计与形状优化

3D grain reverse design and shape optimization for solid rocket motor
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摘要 固体火箭发动机装药逆向设计是指寻求最优的装药形状以匹配给定的内弹道性能曲线,可用于指导新型装药的设计。装药逆向设计正从尺寸优化阶段迈向形状优化与拓扑优化阶段。形状优化问题往往自由度大且高度非线性,这就对燃面退移的计算效率提出了极高的要求,而现有的椭圆算法难以满足需要。为此有必要开发燃面退移的高效椭圆算法,并将其应用于三维装药的逆向设计。首先,将程函方程线性化,推导出亥姆霍兹方程和泊松方程,形成了一系列求解燃面退移的快速热传导(Fast Heat Conduction,FHC)方法。其中f-FHC方法采用空腔体积分数分布来描述不规则装药,使用LDL分解法求解线性方程组,实现了“一次分解,处处回代”,显著提高了计算效率。然后,系统地分析了三维装药逆向设计的关键问题,包括目标函数的选取、待优化自变量的取值范围、孤立孔洞识别、浇铸工艺性要求等。运用进化神经网络方法开发了装药逆向智能设计(Grain Reverse and Intelligent Design,GRID)系统。计算结果表明,fFHC方法可以将三维装药燃面退移的计算时间缩短至1 s以内。以双推力装药的燃面变化规律或内弹道性能曲线为目标,GRID系统成功设计出含有复杂三维内孔的新型装药。所得装药符合浇铸工艺条件,芯模可采用3D打印工艺制造。所提出的算法和开发的软件系统可以为新型装药的设计提供支撑。 The solid rocket motor grain reverse design,an effort to seek the optimal grain shape to match a given internal ballistic curve,can be used to guide the conceptual design of brand-new grains.Grain reverse design is now progressing from the size optimization level towards the shape optimization and even topology optimization level.Shape optimization problems tend to have large degrees of freedom and high nonlinearity,placing extremely high demands on the computational efficiency of burn-back analysis.However,existing elliptic algorithms for burn-back analysis fail to meet the requirement.It is necessary to develop an efficient elliptic algorithm for burn-back analysis and apply it to the 3-dimensional(3D)grain reverse design.Firstly,the eikonal equation is linearized to a Helmholtz equation and a Poisson equation,forming a series of Fast Heat Conduction(FHC)methods for burn-back analysis.Among them,the f-FHC method,describing the grain geometry by cavity fraction distribution,uses the LDL decomposition method to solve the linear equations.With the principle of"once decomposition,back substitution everywhere",the computational efficiency can be significantly improved.Secondly,the key issues of 3D grain reverse design are systematically analyzed,including the selection of objective function,the range of independent variables that need to be optimized,isolated holes identification,and casting requirements.With the aid of the evolutionary neural network,the Grain Reverse and Intelligent Design(GRID)system is developed.The calculation results show that the f-FHC method can reduce the calculation time of 3D grain burn-back analysis into less than 1 s.Targeting at the burning surface curve or internal ballistic curve of the dual-thrust grain,the GRID system successfully designs a series of new grains containing complex 3D internal cavities.The resulting grains meet the casting requirements,and their mandrels can be manufactured by 3D-print.The proposed algorithm and the developed software can provide support for the conceptual design of brand-new grains.
作者 李文韬 何允钦 李文博 张艺仪 梁国柱 LI Wentao;HE Yunqin;LI Wenbo;ZHANG Yiyi;LIANG Guozhu(School of Astronautics,Beihang University,Beijing 102206,China;School of Aerospace Engineering,Tsinghua University,Beijing 100084,China)
出处 《航空学报》 EI CAS CSCD 北大核心 2024年第11期196-214,共19页 Acta Aeronautica et Astronautica Sinica
基金 国家级项目。
关键词 固体火箭发动机 装药逆向设计 形状优化 拓扑优化 燃面退移 程函方程 进化神经网络 solid rocket motor grain reverse design shape optimization topology optimization burn-back analysis eikonal equation evolutionary neural networks
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