Aerodynamic Optimization of Delta Fin Configurations for Supersonic Flight: A Computational Investigation of Geometric Coupling Effects

Abstract

The aerodynamic performance of fin-stabilized projectiles operating in supersonic regimes is governed by complex interactions between geometric parameters that cannot be adequately captured through isolated variable analysis. This investigation presents a systematic computational study examining the coupled effects of leading-edge sweep angle, fin taper ratio, and tip chord modification on the aerodynamic coefficients of a fin-stabilized configuration at Mach 2.5. A response surface methodology was employed to evaluate sixteen distinct geometric configurations using three-dimensional Reynolds-Averaged Navier-Stokes simulations with the k-ω SST turbulence model. Results demonstrate that sweep angle exerts the dominant influence on drag characteristics, with a 15-degree increase in leading-edge sweep producing a 12.4% reduction in wave drag coefficient. The interaction between taper ratio and tip chord modification proved significant for lift generation, with configurations combining moderate taper (0.6) and extended tip chord yielding lift improvements of 18.7% compared to baseline geometry. An unexpected finding emerged regarding the non-monotonic relationship between aspect ratio and aerodynamic efficiency, where optimal performance occurred at intermediate aspect ratios rather than at extremes. Pressure distribution analysis revealed that configurations with gradual leading-edge curvature delayed shock detachment and maintained favorable pressure gradients across a wider range of angles of attack. The study provides quantitative guidance for supersonic fin design and demonstrates the utility of integrated geometric optimization approaches for high-speed aerodynamic applications.