Aerodynamic force and flow structures of two airfoils in flapping motions

Aerodynamic force and flow structures of two airfoils in a tandem configuration in flapping motions are studied, by solving the Navier-Stokes equations in moving overset grids. Three typical phase differences between the fore- and aftairfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertical force coefficient over the downstroke is 2.74, which is about 3 times as large as the maximum steady-state lift coefficient of a dragonfly wing; the time average of the horizontal force coefficient is 1.97, which is also large. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the “pitching-up” motion near the end of the stroke. (2) In the cases of two-airfoils, the time-variations of the force and moment coefficients on each airfoil are broadly similar to that of the single airfoil in that the vertical force is mainly produced in downstroke and the horizontal force in upstroke, but very large differences exist due to the interaction. (3) For in-phase stroking, the major differences caused by the interaction are that the vertical force on FA in downstroke is increased and the horizontal force on FA in upstroke decreased. As a result, the magnitude of the resultant force is almost unchanged but it inclines less forward. (4) For counter stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased. As a result, the magnitude of the resultant force is decreased by about 20 percent but its direction is almost unchanged. (5) For 90°-phase-difference stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased greatly and the horizontal force on AA in upstroke increased. As a result, the magnitude of the resultant force is decreased by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also the largest resultant force); the 90°-phase-difference flapping results in the largest horizontal force, but the smallest resultant force.