Reynolds Number Scaling of the Propulsive Performance of a Pitching Airfoil

Simulations of symmetrical NACA airfoils pitching about their quarter chord point are presented to investigate the scaling of their performance metrics, especially their dependence on Reynolds number. Variations in the Reynolds number (500≤Re≤32,000), pitch amplitude (2°≤θ0≤10°), and thickness ratio (6≤t/c≤30) consistently show that the scaling for thrust, power, and efficiency derived in a recent study of heaving and pitching teardrop airfoils applies unchanged for the present case. The empirically determined coefficients in these scaling relationships are found to depend on the square root of Reynolds number, suggesting laminar flow scaling. The thrust and power are relatively insensitive to Reynolds numbers greater than about 16,000, but the efficiency continues to show a significant Reynolds number influence because it is strongly influenced by the drag on the airfoil.