Lift characteristics of two tandem airfoils in the globally unstable wake of a heated cylinder

Abstract

In this numerical study, we use two-dimensional scale-adaptive simulations to investigate the lift characteristics of two tandem airfoils in the globally unstable wake of a cylinder at a Reynolds number of 104, with and without cylinder heating. Both airfoils have NACA 0012 profiles and are at the same angle of attack (α = 10°), implying zero decalage. We find that the lift characteristics of both airfoils depend strongly on the streamwise distance (X) between the trailing point of the cylinder and the leading edge of the fore airfoil. At the conditions of this study (1 ≤ X/D ≤ 5, where D is the cylinder diameter), both airfoils experience periodic limit-cycle oscillations in their lift coefficients (Cl) at the same frequency. However, when X/D < 3, abrupt decreases occur in both the Cl amplitude of the fore airfoil and the Cl oscillation frequency of both airfoils. We attribute these decreases to the fore airfoil entering the wavemaker region of the self-excited cylinder wake and altering its global instability properties. Heating the cylinder to a temperature above that of the free-stream leads to monotonic decreases in the oscillation frequency and amplitude of Cl for both airfoils. For the purpose of harvesting the maximum energy from two tandem airfoils behind a cylinder, our findings suggest that (i) the airfoils should be positioned as close as possible to the cylinder without disrupting the wavemaker of the globally unstable wake and (ii) the cylinder should be prevented from heating up.