Aerodynamic Optimization of Helicopter Rotors using a Harmonic Balance Lifting Surface Technique

This thesis concerns the optimization of the aerodynamic performance of conventional helicopter rotors, given a set of design variables to control the rotor's pitching angle, twist and chord distributions. Two models are presented for use. The lifting line model is a vortex lattice model that uses assumptions on the size and shape of the blade to simplify the model, but is unable to account for unsteady and small aspect ratio effects. The lifting surface model removes these assumptions and allows for a wider variety of accurate solutions, at the cost of overall computational complexity. The lifting surface model is chosen for analysis, and then condensed using static condensation and harmonic balance. The final system is discretized and pertinent values of power, force, and moment calculated using Kelvin's theorem and the unsteady Bernoulli equation. This system is then optimized in one of two ways: using a direct linear solve if possible, or the open source package IPOPT where necessary. The results of single-point and multi-point optimization demonstrate for low speed forward flight, the lifting line model is sufficient for modeling purposes. As the speed of the rotor increases, more unsteady effects become prominent in the system, and therefore the lifting surface model becomes more necessary. When conducting a chord optimization on the rotor, hysteresis effects and local minima are calculated for the non-linear optimization. The global minima within the set of captured local minima can be found through simple data visualization, and the global minima is confirmed to have similar behavior to the results of lifting line; a large spike in induced power at a critical advance ratio, with a sharp decline in induced power as the rotor flies faster. Within the realm of practical forward flight speeds of a conventional rotor, smooth, continuous results are demonstrated.