Multi-fidelity and Multi-condition airfoil shape optimisation

  • Robledo Martín, Isaac (Instituto Nacional de Técnica Aeroespacial «E)
  • Vilariño, Alberto (Universidad Carlos III de Madrid)
  • Miró, Arnau (Barcelona Supercomputing Centre)
  • Lehmkuhl, Oriol (Barcelona Supercomputing Centre)
  • Sanmiguel Vila, Carlos (Instituto Nacional de Técnica Aeroespacial «E)
  • Castellanos, Rodrigo (Universidad Carlos III de Madrid)

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During preliminary aerodynamic design, parametric studies explore large design spaces, prioritising rapid iteration to identify promising regions for detailed analysis. This stage typically necessitates a trade-off between solver fidelity and computational cost, where reduced accuracy is accepted in exchange for speed. To enhance accuracy while ensuring high-quality evaluation metrics, we present a multi-fidelity airfoil shape optimisation framework employing our in-house Hybrid Genetic Optimiser (HyGO) \citep{robledo2025hygo}. This approach synergises the efficiency of the XFOIL potential-flow solver with the accuracy of high-resolution incompressible RANS simulations (using the Spalart--Allmaras turbulence model). By integrating these through a Gaussian Process Regressor (GPR) multi-fidelity model, the framework enables rapid aerodynamic characterisation with high-fidelity accuracy. The shape optimisation problem aims at maximising key aerodynamic performance metrics of airfoils defined by 12 CST parameters as design variables. The optimisation considers performance at two key angle of attack operating points: the design cruise condition, targeting aerodynamic efficiency ($E_{\alpha=2^\circ}=L/D$), and a critical off-design high-angle-of-attack condition, focusing on lift generation ($C_{L, \alpha=10^\circ}$), both at a realistic flight Reynolds number of $Re=6 \times 10^6$. Geometric constraints are enforced to ensure minimum thickness and structural feasibility. The GPR-based multi-fidelity model is initialised by training on the first generation of individuals, which are evaluated using both XFOIL and RANS to establish a correlated low- and high-fidelity dataset. From this initial surrogate, an active learning strategy is deployed during the subsequent generations. At each iteration, the GPR uncertainty is evaluated across the population, triggering the high-fidelity solver if the normalized standard deviation is above a threshold $\kappa$. These new samples are then assimilated to retrain the GPR, progressively refining the multi-fidelity mapping and improving prediction accuracy while controlling the number of expensive RANS calls. After only evaluating 12\% of the individuals in RANS, the optimised airfoil shape achieves a 41\% improvement in $E_{\alpha=2^\circ}$ and a 21\% improvement in $C_{L, \alpha=10^\circ}$, demonstrating the viability and potential of multi-condition global shape optimisation, further expedited through adaptive multi-fide