Topologically assisted optimization for rotor design

Abstract

We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit ($FM$). This topologically assisted optimization (TAO) contains two steps. First a global evolutionary optimization is performed for the shape parameters and then a topological analysis reveals the local and global extrema of the objective function directly from the data. This non-dimensional objective function compares the achieved thrust with the required torque. Rotor blades have a decisive contribution to the performance of quadcopters. A two-blade rotor with pre-defined chord length distribution is chosen as the baseline model.The simulation is performed in a moving reference frame with a $k-\omega$ turbulence model for the hovering condition.The rotor shape is parameterized by the twist angle distribution.The optimization of this distribution employs a genetic algorithm. The local maxima are distilled from the data using a novel topological analysis inspired by discrete scalar-field topology. We identify one global maximum to be located in the interior of the data and five further local maxima related to errors from non-converged simulations.The interior location of the global optimum suggests that small improvements can be gained from further optimization.The local maxima have a small persistence, i.e., disappear under a small $\varepsilon$ perturbation of the figure of merit values. In other words, the data may be approximated by a smooth mono-modal surrogate model. Thus, the topological data analysis provides valuable insights for optimization and surrogate modeling.