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Transonic flutter is a pacing item in transport aircraft design in that it is crucial to characterize this phenomenon for each aircraft to prevent catastrophic failure. Aerodynamic study of flows around airfoils is a canonical problem that entails both experimental and computational approaches. While the transonic flutter prediction can be more accurate with high-fidelity Computational Fluid Dynamics (CFD) methods than with unsteady potential flow methods, the computational cost is high. Therefore, computationally efficient methods for transonic flutter prediction continue to be of high interest to the aircraft design community. NASA Ames has developed a novel method that eliminates the need for expensive calculations of aerodynamics of wing flutter, which typically takes tens of hours on a supercomputer. Such calculations are now replaced by machine-learning-based closed form solutions that provide the solution almost instantaneously. The technology presents a new approach to predict the flow around pitching NACA00 series airfoils. NACA airfoils are generally symmetric, and thus they do not possess camber. However, the invention can readily extend to wings with camber. This novel data modeling approach is orders of magnitude faster than the traditional CFD approach of predicting aerodynamic effects of transonic pitching airfoils. The data model is based on a subset of unsteady CFD simulations that train the model. The trained model then resolves the pitching airfoil in time for any other set on the order of a second, as compared with a complete CFD simulation that typically takes 30 hours on a supercomputer. The data model is demonstrated in this invention for transonic flow corresponding to Mach number of 0.755 over pitching NACA00 series airfoils for a reduced frequency range typical of flutter, i.e., k lies in the range 0.02 - 0.25.

This invention, developed under the Rotor Optimization for the Advancement of Mars eXploration (ROAMX) project, provides a method for optimizing airfoil geometries for aerial flight vehicles generally, and can also specifically optimize airfoil geometries for operating in Martian or other low Reynolds number environments. The method introduces a new “ROAMX parameterization” that defines geometric constraints, such as camber node count and the number and order of Bézier curve segments, to generate candidate airfoil shapes. A genetic algorithm evaluates these shapes against multiple objectives and iteratively selects the best-performing designs, converging on a Pareto-optimal front. This enables simultaneous optimization of metrics such as maximizing lift and minimizing drag. Using the ROAMX 1301 parameterization, the method produced an airfoil with lift to drag ratio improvements of up to 42% over the outboard airfoil used on the Mars Helicopter Ingenuity, representing a significant performance gain.