Optimal airfoil’s shapes by high fidelity CFD

Abstract

Purpose There is an increasing interest in airfoils that modify their shape to adapt at the flow conditions. As an example of application, the authors search the optimal 4-digit NACA airfoil that maximizes the lift-over-drag ratio for a constant lift coefficient of 0.6, from Re = 104 to 3 × 106. Design/methodology/approach The authors consider a γ−Reθt transition model and a κ – ω SST turbulence model with a covariance matrix adaptation evolutionary optimization algorithm. The shape is adapted by radial basis functions mesh morphing using four parameters (angle of attack, thickness, camber and maximum camber position). The objective of the optimization is to find the airfoil that enables a maximum lift-over-drag ratio for a target lift coefficient of 0.6. Findings The computation of the optimal airfoils confirmed the expected increase with Re of the lift-over-drag ratio. However, although the observation of efficient biological fliers suggests that the thickness increases monotonically with Re, the authors find that it is constant but for a 1.5 per cent step increase at Re = 3 × 105. Practical implications The authors propose and validate an efficient high-fidelity method for the shape optimization of airfoils that can be adopted to define robust and reliable industrial design procedures. Originality/value The authors show that the difference in the numerical error between two-dimensional and three-dimensional simulations is negligible, and that the numerical uncertainty of the two-dimensional simulations is sufficiently small to confidently predict the aerodynamic forces across the investigated range of Re.