NUMERICAL ANALSIS AND MULTI-OBJECTIVE OPTIMISATION OF THE NACA 2415 AIRFOIL USING A TAGUCHI-FUZZY FRAMEWORK

Abstract

Small fixed-wing unmanned aerial vehicles operating at chord Reynolds numbers of Re = 10⁵–5×10⁶ face a fundamental aerodynamic challenge: the gap between two dimensional section performance predicted by computational fluid dynamics and the drastically degraded efficiency of real, aspect-ratio-constrained three-dimensional wings. This study addresses that gap through a three-phase hierarchical investigation of the NACA 2415 aerofoil, integrating Taguchi design of experiments, Mamdani fuzzy multi-objective optimisation, steady-state Reynolds-Averaged Navier–Stokes simulation, and surrogate-assisted optimisation into a single systematic framework validated against NACA Technical Report 824 experimental data. Phase 1 deploys a Taguchi L25(5⁵) orthogonal array — reducing a 3,125-run full factorial to 25 balanced simulations — to simultaneously screen five RANS turbulence closures (Spalart–Allmaras, k-ε Realizable, k-ω SST, SST γ–Reθ, and Reynolds Stress Model), five Reynolds numbers (1–12×10⁶), five angles of attack (−4° to 16°), five turbulence intensities (0.05%–5.00%), and four surrogate optimisation strategies (RSM-Kriging, NSGA-II, Sparse RSM, and Neural Network Screening). Three conflicting aerodynamic responses — lift coefficient, drag coefficient, and lift-to-drag ratio — are unified into a scalar Multi-Performance Characteristic Index via a 27-rule Mamdani fuzzy inference system with corrected strict-inequality boundary membership evaluation, a previously unreported defect whose correction changes the turbulence model ANOVA contribution from a spurious 12.30% to the physically correct 1.83%. One-way ANOVA identifies angle of attack as the dominant factor (ρ = 80.99–85.70%), with Reynolds number second (ρ ≈ 8–10%). The k-ω SST model achieves the highest multi-objective η(MPCI) level mean (−9.202 dB) due to its Bradshaw adverse-pressure-gradient limiter and structural turbulence-intensity insensitivity via cross-diffusion. Sparse RSM achieves the highest Weighted Composite Score of 9.13/10, uniquely detecting the NACA 2415 drag-bucket interior minimum at α ≈ −0.75°, independently confirmed by Neural Network Screening at α ≈ −0.77°. Phase 2 deploys a Taguchi L9(3³) array exclusively with k-ω SST across a refined design space (Re = 6–12×10⁶, α = 4°–8°, TI = 0.05%–0.50%). The confirmed optimal configuration — Re = 12×10⁶, α = 8°, TI = 0.10° — yields CL = 1.038, CD = 0.015711, and |CL/CD| = 66.08, with a Taguchi additive model prediction error of only 0.26%, validating negligible factor interactions. Turbulence intensity contributes ρ ≈ 0.00% (F = 0.04) within the tested range, providing a practically significant result that eliminates TI as a source of CFD modelling uncertainty for this application. Phase 3 extends the Phase 2 optimum to a three-dimensional finite-wing RANS simulation at AR = 0.25 (b = 0.5 m, c = 2.0 m, A_ref = 1.0 m²). The aerodynamic outputs — CL = 0.12921, CD = 0.014899, |CL/CD| = 8.67, Lift = 607.908 N, Drag = 70.096 N — reveal an 86.9% efficiency collapse from the two-dimensional optimum, driven by a tip-vortex-induced downwash of ε ≈ 9.33° that reduces the effective angle of attack from +8° to approximately −1.43°. Three independent CFD visualisations — velocity pathlines, static pressure vectors, and velocity magnitude vectors — provide mutually corroborating topological, thermodynamic, and kinematic evidence confirming that the entire span lies within the tip-vortex induction zone and no two dimensional flow region exists. The study conclusively establishes that the binding aerodynamic limitation of the platform is planform geometry rather than section performance, motivating a redesign to AR = 6–8 to recover 75%–86% of the two dimensional efficiency ceiling.