Multi-objective optimization of a turbopump turbine disk using NSGA-II and CAD-free geometric modeling

In this study, the turbopump turbine disk of a liquid-propellant rocket engine is optimized using the multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II). A 2D turbopump turbine disk template and a CAD-free geometric modeling method, which removes dependence on external CAD software, are introduced. Physical disk features serve as design parameters. Disk geometries are constructed using line-edge and arc-center points whose coordinates are expressed in terms of design parameters. Known point coordinate relations are used to systematically detect and exclude infeasible disk shapes from the optimization process. A parameter-bounding strategy is introduced to discretize the design space by adjusting parameter ranges and allowable values. Multi-objective optimization minimizes disk mass and maximum stress. Two stress solvers are employed: a 1D finite difference (FD) solver and a 2D finite element (FE) solver. Initial comparisons of the FD- and FE-based Pareto frontiers suggest moderate agreement; however, a detailed cross-solver evaluation, in which FD-based Pareto-optimal disks are reanalyzed with the FE solver, reveals a critical limitation. The FD solver severely underestimates maximum stress in some disks, allowing them to persist across generations and produce misleading Pareto frontiers. The findings indicate that the FD solver is unsuitable for optimizing critical turbomachinery disks, even for rapid design space exploration, whereas the FE solver reliably predicts stresses and produces accurate, informative Pareto frontiers.