Optimal airfoil’s shapes by high fidelity CFD

Purpose - There is an increasing interest in airfoils that modify their shape to adapt at the flow conditions. As an example of application, we search the optimal 4-digit NACA airfoil that maximises the lift-over-drag ratio for a constant lift coefficient of 0.6, from Re = 104 to 3 × 106.

Design/methodology/approach - We consider a γ − Reθt transition model and a κ − ω SST turbulence model with a covariance matrix adaptation evolutionary optimisation algorithm. The shape is adapted by radial basis functions mesh morphing using four parameters (angle of attack, thickness, camber, maximum camber position). The objective of the optimisation 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, while the observation of efficient biological fliers suggests that the thickness increases monotonically with Re, we find that it is constant but for a 1.5% step increase at Re = 3 × 105.

Practical implications - We propose and validate an efficient high fidelity method for the shape optimisation of airfoils that can be adopted to define robust and reliable industrial design procedures.

Originality/value - We show that the difference in the numerical error between 2D and 3D simulations is negligible, and that the numerical uncertainty of the 2D simulations is sufficiently small to confidently predict the aerodynamic forces across the investigated range of Re.