非均匀装药的复杂燃面退移与内弹道性能预示  

Complex burn-back analysis and internal ballistic performance prediction of non-uniform grain

作　　者：李文韬 何允钦[1] 张艺仪 梁国柱[1] LI Wentao;HE Yunqin;ZHANG Yiyi;LIANG Guozhu(School of Astronautics,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学宇航学院,北京100191

出　　处：《北京航空航天大学学报》2024年第8期2524-2537,共14页Journal of Beijing University of Aeronautics and Astronautics

摘　　要：非均匀装药的复杂燃面退移与内弹道性能预示是固体火箭发动机设计的核心问题。建立非均匀装药燃烧的燃面退移数学模型,提出一种采用有限元法通过求解泊松方程逼近程函方程黏滞解的新方法(PEF)。所提方法可将燃面退移问题转化为特殊的稳态热传导问题,实现对几何形状不规则且燃速分布复杂的三维装药燃面退移的计算。考虑燃烧室压力变化等实际因素,在平衡压力假设下,形成了内弹道性能预示的4种计算模型。完成了二维星型装药、三维翼柱型装药和含金属丝的双推进剂装药的计算。计算结果表明:所提方法不仅可以高精度地适应多种推进剂构成的复杂交界面,而且可以直接在商业有限元软件的稳态热传导模块上应用和求解,充分利用商业有限元软件成熟的计算机辅助设计(CAD)建模、前处理、后处理及二次开发能力,实现了复杂燃面退移与内弹道性能预示方法的通用化和实用化。The complex burn-back analysis and internal ballistic performance prediction of the non-uniform grain are the core issues in solid rocket motor design.A mathematical model of burn-back analysis of combustion with non-uniform grain was established.A new method,namely Poisson equation-eikonal equation-finite element method(PEF)was proposed to approach the viscous solution of the eikonal equation by solving a Poisson equation using the finite element method.The proposed method can transform the burn-back problem into a special stationary thermal conduction problem and realize the burn-back calculation of the 3D grain with irregular geometry and complicated burning rate distribution.Then,the actual factors such as the change in combustion chamber pressure were considered,and four calculation models for internal ballistic performance prediction were developed under the assumption of equilibrium pressure.The calculation of 2D star grain,3D finocyl grain,and dual propellant grain with metal wires embedded was completed.The calculation results show that the proposed method can precisely adapt to the complex interfaces of different propellants.The proposed method can be directly applied and solved in the stationary thermal conduction module of the commercial finite element software.It can fully utilize the mature capabilities of computeraided design(CAD)modeling,pre-processing,post-processing,and secondary development in commercial finite element software,achieving universality and practicality of the complex burn-back analysis and internal ballistic performance prediction method.

关 键 词：固体火箭发动机 燃面退移 内弹道性能预示 有限元法 程函方程 泊松方程 

分 类 号：V435.1[航空宇航科学与技术—航空宇航推进理论与工程]