| Citation: | LI W T，HE Y Q，ZHANG Y Y，et al. Complex burn-back analysis and internal ballistic performance prediction of non-uniform grain[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（8）：2524-2537 （in Chinese） doi: 10.13700/j.bh.1001-5965.2022.0669
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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 computer-aided 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.
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