3D grain reverse design and shape optimization for solid rocket motor

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.