Aerodynamic force and flow structures of two airfoils in flapping motions

Aerodynamic force and flow structures of two airfoils in a tandem configura tion in flapping motions axe studied, by solving the Navier-Stokes equation s in moving overset grids. Three typical phase differences between the fore - and aft-airfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertic al 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; th e time average of the horizontal force coefficient is 1.97, which is also l arge. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the "pitching-up" motion n ear the end of the stroke. (2) In the cases of two-airfoils, the time-varia tions of the force and moment coefficients on each airfoil are broadly simi lar to that of the single airfoil in that the vertical force is mainly prod uced in downstroke and the horizontal force in upstroke, but very large dif ferences 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 decreas ed. As a result, the magnitude of the resultant force is almost unchanged b ut it inclines less forward. (4) For counter stroking, the major difference s 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 resultan t force is decreased by about 20 percent but its direction is almost unchan ged. (5) For 90 degrees -phase-difference stroking, the major differences a xe that the vertical force on AA in downstroke and the horizontal force on FA in upstroke axe decreased greatly and the horizontal force on AA in upst roke increased. As a result, the magnitude of the resultant force is decrea sed by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also t he largest resultant force); the 90 degrees -phase-difference flapping resu lts in the largest horizontal force, but the smallest resultant force.