Lifting Line Framework for Optimization of Rotary Wing Systems

This paper describes a rotating lifting line framework used for the constrained design optimization of rotary wing systems. This method leverages a finite vortex element approach to represent the lifting line and shed circulation elements associated with the helical wake vortex system. An iterative approach is utilized to close the interdependency between the wake-induced velocities, the optimal distribution of bound circulation to the rotor, and the vortical wake shape. Using a closed-form expression for the wake-induced velocities on the lifting line, a Lagrangian function is derived and utilized to determine the blade circulation distributions that minimize the torque (or power) of the rotor, subject to a set of specified equality constraints (e.g., design thrust coefficient). Experiments were conducted to validate the optimization process and performance predictions of the associated design framework, based on acquired thrust and torque performance data. The four-bladed rotor assemblies were configured in a hover condition, having thrust coefficients of C_T = 0.01, 0.015, and 0.02. The thrust and torque predictions of the optimal designs were shown to be typically on the order of 5%, indicating the effectiveness of the analytical framework for conceptual design optimization studies.