Comparative Supersonic Airfoil Analysis and Adjoint-Based Shape Optimization Using SU2

This study compares airfoil families for supersonic flight and applies adjoint-based shape optimization to reduce drag at a constant lift coefficient. The work supports the design of thin supersonic wings that must retain thickness for structure and fuel while keeping wave drag low. The study focuses on three parts: a comparison of seven airfoil families (Diamond, Double Wedge, Biconvex, Modified Wedge, and NACA 0012, 2412, and 64-206) using the two-dimensional, steady, inviscid Euler equations in the open-source solver SU2 at Mach 1.2 to 3.0 and angles of attack from -5° to 10°; a controlled test that rounds the Double Wedge's leading edge at fixed thickness; and gradient-based reshaping of the three sharp-edged sections at a fixed lift coefficient of 0.15. This effort is challenging due to three factors: slow convergence at low Mach numbers and high angles, which required identical solver settings and three-level grid refinement for every family; the fixed-lift objective, which required combining drag and lift adjoint gradients verified against finite differences; and thickness and area constraints that prevent drag reduction by simple thinning. At the design lift, the 6%-thick NACA 64-206 and the 10%-thick Diamond had the highest lift-to-drag ratios (4.08 and 3.97), while rounding the Double Wedge's nose lowered its ratio by 7–24%. All 15 optimizations met the optimizer's convergence criterion, reducing drag by 11.5–18.9% at Mach 1.2 but only 0.25–5.8% at Mach 1.5 to 3.0, with grid-to-grid variation of at most 1.3 percentage points. Ongoing work is extending the analysis to viscous flow.