Effect of the asymmetric geometry on the wake structures of a pitching foil

The two-dimensional wake produced by a time-periodic pitching foil with the asymmetric geometry is investigated in the present work. Through numerically solving nonlinear Navier–Stokes equations, we discuss the relationship among the kinematics of the prescribed motion, the asymmetric parameter K ranged as-1 ≤ K ≤ 1, and the types of the wakes including the mP+nS wake, the B′enard–von K′arm′an wake, the reverse B′enard–von K′arm′an wake, and the deviated wake.Compared with previous studies, we reveal that the asymmetric geometry of a pitching foil directly affects the foil's wake structures. The numerical results show that the reverse B′enard–von K′arm′an wake is easily deviated at K < 0, while the symmetry-breaking of the reverse B′enard–von K′arm′an wake is delayed at K > 0. Through the vortex dynamic method,we understand that the initial velocity of the vortex affected by the foil's asymmetry plays a key role in the deviation of the reverse B′enard–von K′arm′an wake. Moreover, we provide a theoretical model to predict the wake deviation of the asymmetric foil.