Large Eddy Simulation of Surging Airfoils at High Advance Ratio and Reynolds Number

Large eddy simulation (LES) is performed for a surging NACA 0012 airfoil at high advance ratios and Reynolds numbers. The airfoil is subjected to sinusoidal oscillations in the streamwise direction at a fixed frequency and angle of attack in a constant free-stream flow. Three Reynolds numbers of Re=40,000, 200,000 and 1,000,000 are considered together with two advance ratios of λ=1.0 and 1.2, i.e., six cases are considered in total. We note that at the higher advance ratio the relative flow velocity becomes negative and a reversed flow condition is reached.

Overall a similar trend is observed in the lift force among all cases. The peak normalized lift is about 9% lower for the highest Reynolds number case as compared to the lower Reynolds number cases for each advance ratio. On the other hand, the peak normalized lift is about 21% higher for the higher advance ratio case as compared to the lower advance ratio case for each Reynolds number, which is the difference in the peak dynamic pressure between the two advance ratios. Flow field also reveals a similar behavior among all cases with prominent features of flow separation near the (geometric) leading edge during the beginning of the retreating phase and formation of a dominant leading edge vortex (LEV). We observe that as the Reynolds number increases the LEV is formed later in the cycle (for a given advance ratio) while as the advance ratio increases it is formed earlier in the cycle (for a given Reynolds number). LEV evolution is also quantified based on its size and position. The central core of the LEV is found to fit the Rankine vortex model. As expected, a larger LEV is obtained for the lowest Reynolds number while LEV remains closest to the airfoil for the highest Reynolds number. At the higher advance ratio the LEV initially moves to the left past the geometric leading edge for each Reynolds number. This is expected since the relative flow velocity becomes negative (or a reversed flow condition is obtained). Further, the slope of the horizontal displacement in each case is remarkably close to the free-stream velocity, i.e., the LEV is advected in the horizontal direction at the free-stream velocity.