Concurrent Aerodynamic Optimization of Rotor Blades Using a Nash Game Method

A multi-objective strategy adapted to the aerodynamic concurrent optimization of helicopter rotor blades is developed. The present strategy is based on Nash Games from game theory, where the objective functions are minimized by virtual players involved in a non-cooperative concurrent game. A method is presented to split the design vector into two sub-spaces, defined to be the strategies of the players in charge of the minimization of the primary and the secondary objective functions respectively. This split of territory allows the optimization of the secondary function while causing the least possible degradation of the first one. This methodology is applied to the model rotor ERATO, seeking to maximize the Figure of Merit in hover while minimizing the required rotor power in forward flight. An initial constrained optimization in hover is conducted using a previously developed adjoint-based technique using the 3D Navier-Stokes solver elsA along with the gradient-based CONMIN algorithm. The chord, twist and sweep distributions of the baseline blade are parametrized using Bézier and cubic splines for a total of 16 design variables. The obtained optimized rotor is then used as a starting point to launch constrained and unconstrained Nash games. The comprehensive rotor code HOST is used to evaluate forward flight performance and a surrogate model is built to obtain the hover performance at low computational cost. Twist and sweep distribution laws are optimized independently at first and then a final joint optimization involving twist, sweep and chord is performed. The results demonstrate the potential of this technique to obtain helicopter rotor designs realizing interesting trade-offs between strongly antagonistic objectives.