Aerodynamic center of an end-to-end wing at low Reynolds number

Two key parameters that govern the flow past an airfoil/wing are its angle of attack (α) to the free stream and Reynolds number defined as Re = U c/ν, where U is the free stream speed, c is its chord and ν the kinematic viscosity of air. Two important quantities that can be used to evaluate the performance of a wing/airfoil are the lift and drag coefficients. The pitching moment coefficient of the wing, although not directly indicative of the performance of a wing, is an important parameter to consider. It governs the static stability characteristics of the aircraft. The aerodynamic center is a point within the airfoil about which the pitching moment is invariant with the angle of attack. Owing to their small size and low speed, UAVs and MAVs operate in a low Reynolds number (Re) regime. The current study is focused on the low Re application of wings. The classical thin airfoil theory predicts, for inviscid flows, the quarter chord point to be the aerodynamic center as well as the center of pressure,i.e., for a thin symmetric airfoil. Flow past airfoils at high Re and low angle of attack are associated with a thin attached boundary layer, resulting in performance that is comparable to the predictions from the thin airfoil theory. Experiments by Abbott et al. at Re =3×10⁶, 9×10⁶ show that the quarter chord point is, in fact, the aerodynamic center for NACA 0012. This study investigates the aerodynamic characteristics of an end-to-end wing with NACA 0012 airfoil section for 100 ≤ Re ≤ 6000 by three-dimensional computations. The wingspan is equal to the chord length of the wing. The aerodynamic coefficients from the study are utilized to estimate the aerodynamic center. We try to answer the following question: At high Re, the aerodynamic center and the center of pressure are at the quarter chord. Is the location the same at low Re?

References:

[1] I. H. Abbott and A. E. Von Doenhoff, Theory of wing sections: including a summary of airfoil data