Shape and material optimization of problems with dynamically evolving interfaces applied to solid rocket motors

This paper studies design problems where the performance is dominated by the dynamic evolution of interfaces due to chemical processes. Considering the representative example of a solid rocket motor, the shape of the interface between the solid fuel and the gas inside the combustion chamber at the beginning of the burn process and the reference burn rate of a functionally graded propellant are optimized to achieve a desired thrust over time. The initial fuel–gas interface is described by a level set function parameterized by geometric primitives and B-splines. The reference burn rate distribution is discretized by multi-variate B-splines. The thrust is predicted by a semi-analytical approach that requires modeling the recession of the fuel–gas interface. To this end, a stabilized finite element formulation of the Hamilton–Jacobi equation is used to describe the evolution of the level set function during the burn process. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are evaluated by the adjoint method. The proposed optimization approach is studied with numerical examples in 2D and 3D, involving configurations with more than 6 × 10 ⁴ optimization variables and 12 × 10 ⁶ state variables. The optimization results show that this approach provides a promising design tool for problems with dynamically evolving interfaces due to surface reactions. However, the results also reveal that the simplicity of the recession and thrust models requires limiting the design freedom through a carefully chosen design parameterization. Furthermore, additional constraints need to be imposed to prevent unphysical designs.