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

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe industrial aerodynamic design of helicopter rotor blades needs to consider the two typical flight conditions of hover and forward flight simultaneously. Here, this multi-objective design problem is tackled by using a genetic algorithm, coupled to rotor performance simulation tools. The turn-around time of an optimization loop is acceptable in an industrial design loop when using low-cost, low-fidelity tools such as the comprehensive rotorcraft code HOST, but becomes excessively high when employing high-fidelity models like CFD methods. To incorporate high-fidelity models into the optimization loop while maintaining a moderate computational cost, a Multi-Fidelity Optimization (MFO) strategy is proposed: as a preliminary step, a HOST-based genetic algorithm optimization is used to reduce the parameter space and select a set of blade geometries used for initializing the high-fidelity stage. Secondly, the selected blades are re-evaluated by CFD and used to construct a high-fidelity surrogate model. Finally, a Surrogate Based Optimization (SBO) is carried out and the Pareto optimal individuals according to the SBO are recomputed by CFD for final performance evaluation. The proposed strategy is validated step by step. It is shown that an industrially acceptable number of CFD-simulations is sufficient to obtain blade designs with a significantly higher performance than the baseline and then SBO results issued from a standard Latin-Hypercube-Sampling initialization. The proposed MFO strategy represents an efficient method for the simultaneous optimization of rotor blade geometries in hover and forward flight.

Industrial aerodynamic design optimization of helicopter rotor blades requires employment of multi-objective optimization methods to account for the two distinct objectives in hover and forward flight. Genetic algorithms are preferred for finding the Pareto Optimal Front, as they allow the engineer to select out of optimal designs. An optimization loop is created, coupling the Dakota optimization library and two simulation methods for objective function evaluation: comprehensive rotor code HOST and CFD solver elsA. For low-cost rotor simulations by HOST, a genetic algorithm is employed to maximize hover and forward flight rotor performance in single-and two-point optimizations. Twist and chord laws of the 7A blade are optimized separately and simultaneously. As genetic algorithms require too many cost function evaluations for CFD-based optimizations, Surrogate Based Optimization (SBO) is employed. SBO is initialized by a preliminary Design of Experiment (DoE). The results are used to generate a metamodel for estimation of cost function evaluations in the optimization algorithm. The metamodel is updated using information from subsequent simulations. Validation of HOST-based SBO against full genetic algorithm optimizations shows that the Pareto Optimal Front is correctly represented by SBO, while requiring 88% less cost function simulations. Several sizes of initial DoE, number of update cycles and number of simulations added per cycle are tested. Then, a similar SBO optimization is carried out by replacing the HOST code by CFD for hover performance simulation. The results demonstrate the ability of both solvers and both optimization techniques to perform aerodynamic design optimization of helicopter rotor blades. NomenclatureHOST Helicopter Overall Simulation Tool GA Genetic Algorithm RSM Response Surface Method SBO Surrogate Based Optimization F.M.Figure of Merit (measure for rotor performance in hover) L/D Lift-over-Drag ratio (measure for rotor performance in forward flight)

This contribution relates to the simulation of the flow around the tip of a helicopter rotor blade in hovering flight conditions. We here propose a new methodology of framework adaptation, using a comprehensive rotor code and highfidelity numerical simulations. We construct an equivalent fixed-wing configuration from a rotating blade, in which centrifugal and Coriolis forces are neglected. The effect of this approximation on the solution is analysed. The method is validated by a detailed comparison with wind tunnel data from the literature, concerning aerodynamic properties and tip vortex roll-up. This validation also includes variations of the pitch angle and rotational speed, up to transonic tip velocities. Compared to previously published methods of framework adaptation, the new hybrid method is found to reproduce more accurately the flow around a rotating blade tip.

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