Abstract:
We present a variational approach to the multipoint aerodynamic design optimization of conventional and coaxial helicopter rotors. The optimal design problem is cast as a variational statement that minimizes the weighted sum of induced and viscous power losses between two flight conditions for prescribed vehicle trim constraints at each flight condition. The resulting nonlinear constrained optimization problem is solved via Newton iteration and may be used to map the Pareto frontier, i.e., the set of rotor designs (radial twist and chord distributions and harmonic blade pitch inputs) for which it is not possible to improve upon the performance in one flight conditions without degrading performance in the other. The two flight conditions can represent different advance ratios (including hover), disk loadings, altitude, or other conditions of interest. For forward flight computations, the rotor control inputs are related to the circulation on the blades (and in the wake) through a lifting-line/vortex-lattice method that accounts for nonlinear sectional lift and drag polars. For hovering flight, the rotor performance is analyzed using Blade Element Momentum Theory. We map the Pareto frontier for both a cruise/cruise and hover/cruise multipoint optimization, and show that significant tradeoffs must be made in designing a rotor to balance performance between two flight conditions, particularly hover and high speed forward flight. We also show that higher harmonic control is capable of reducing rotor power and improving the Pareto frontier, particularly for coaxial rotors. Finally, we present a number of rotor designs that best balance performance between two flight conditions.