Large Eddy Simulation of Surging Airfoils with Moderate to Large Streamwise Oscillations

Abstract

A large eddy simulation (LES) based numerical investigation is carried out for flow over two surging airfoils with moderate to large streamwise oscillations. In each case, the airfoil is subjected to a sinusoidal surging motion with streamwise oscillation at a fixed angle of attack. The amplitude of the sinusoidal oscillation is varied within a moderate range as well as in the high range. The amplitude of oscillation is characterized by the advance ratio, which is defined as the ratio of the maximum relative velocity in excess to the mean relative velocity (or mean free-stream velocity) to the mean relative velocity. The relative velocity is defined between the airfoil and ambient fluid. For the moderate range, NACA 0018 airfoil at a mean Reynolds number of 300,000 and 4 • angle of attack is considered. Two advance ratios of 0.34 and 0.51 are considered to match with the experiments of Strangfeld et al. 1 For the high range, NACA 0012 airfoil at a mean Reynolds number of 40,000 and 6 • angle of attack is considered at three advance ratios of 0.8, 1.0 and 1.2 to match with the experiments of Granlund et al. 2 Note that the highest advance ratio case involves the reversed flow condition, where in a part of the surging cycle the relative flow becomes negative or is from the geometric trailing end of the airfoil to the leading end. Lift force is compared between the experiments and simulations. Overall a good agreement is obtained for the lift force in all cases. Additionally, for all cases flowfields from simulations are examined at different phases of the surge cycle. For the moderate advance ratio cases, a similar flow pattern is observed between the two advance ratios and no distinct vortex is shed from the airfoil. On the other hand, in all three high advance ratio cases a distinct vortex is shed near the (geometric) leading edge on the suction or upper side. This prominent leading-edge vortex is shed as the minimum velocity is reached in the surging cycle and advects downstream (in the horizontal direction) by roughly the mean free-stream velocity. The relative position of the shed vortex (with respect to the airfoil) varies significantly between the three high advance ratio cases; it crosses the leading edge before sweeping over the airfoil in the case with the highest advance ratio of 1.2 (i.e., in the case with the reverse flow regime).

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

“…Lift is normalized by its static counterpart, i.e., L 0 is the average or steady lift for the static airfoil at mean Reynolds number. This normalization was used in our previous study with Re=40,000 [17] to compare against the experimental data of [2], where a good agreement was shown between the experimental and simulation data. As noted earlier, data is phase averaged over 4 cycles.…”

“…The angle of attack of the airfoil is set to 6 • . Note that we considered the Reynolds number of Re=40,000 in previous study [17] that was selected in accordance with the experiments conducted in [2] where the airfoil was placed in a constant flow and oscillated in the streamwise direction. The six cases are summarized in Table 1.…”

Vortex formation on a pitching aerofoil at high surging amplitudes

“…More recent efforts have sought to expand the understanding of separated aerofoil flows to cases where the free-stream velocity is time varying (Choi, Colonius & Williams 2015;Granlund, Ol & Jones 2016;Kocher et al 2017;Kirk & Jones 2018). Of particular note, Dunne & McKeon (2015) considered the case of a NACA 0018 wing undergoing a simultaneous surging and pitching manoeuvre.…”