Multi-Point Geometric Optimization of NACA Airfoils Across Multiple Reynolds Numbers and Angles of Attack

Abstract

Single-point airfoil optimization targets one operating condition, which limits how reliably a design performs across real flight conditions. This study presents a multi-point optimization of a NACA 4-digit airfoil, maximizing lift-to-drag ratio and lift coefficient while minimizing drag coefficient, by varying maximum thickness, camber and camber position across five Reynolds numbers (1 × 10⁵ to 2 × 10⁶) and angles of attack from 0° to 12° in 2° increments. A benchmark was first selected from NACA 0012, 2412 and 4412 using TOPSIS, which identified NACA 4412 as the baseline. Two rounds of optimization followed. Latin Hypercube Sampling generated candidate geometries, which were ranked with TOPSIS, and the rankings were tested for robustness against weighting assumptions using Monte Carlo and one-at-a-time sensitivity analyses. The round 1 optimum, airfoil_29 (maximum thickness 11.28%, maximum camber 4.57%, camber position 37.21%), achieved the highest TOPSIS score (0.6143) in a final combined evaluation against the round 2 optimum, refine_13 (0.6049), and NACA 4412 (0.5989), and was the most robust under sensitivity analysis. Relative to NACA 4412, airfoil_29 performed better at Reynolds numbers of 3 × 10⁵ and 1 × 10⁶, while NACA 4412 performed better at 1 × 10⁵, 5 × 10⁵ and 2 × 10⁶

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