Effect of Deep-Stall Wing Dynamics on Forebody-Induced Wing Rock

Abstract

Introduction A RECENT review 1 of wing rock of advanced aircraft, such as X-29A, X-31, and F-18 HARV, showed that wing rock occurs Ž rst at moderate angles of attack through dynamic stall of outer wing panels with moderately swept leading edges. This is illustrated by the experimental results for the X-29A aircraft (Fig. 1). When this type of wing rock was suppressed by the use of the  aperons, forebody-induced wing rock occurred at higher angles of attack, a > 35 deg (Fig. 1b). The driving  ow mechanism for the wing rock at these high angles of attack is the moving wall effect on the forebody cross ow separation at a > uA, where uA is the forebody apex half-angle. The wing rock reaches its maximum amplitude at an angle of attack just below that for which static asymmetric cross ow separation occurs, i.e., at a 2uA, the moving wall effect has to overcome the static cross ow asymmetry. This is the reason for the rapid decrease of the limit cycle amplitude for a > 55 deg in Fig. 1b. In the analysis in Ref. 1 of the experimentally observed wing rock of a generic aircraft model (Fig. 2), a certain roll-damping value had to be assumed to obtain a limit-cycle oscillation. In the wind-tunnel test bearing friction could have supplied the needed roll damping. However, in free  ight, the roll damping has to be generated by other means to obtain an oscillation of the limit-cycle type. As discussed in Ref. 1, the only source of this roll damping at high angles of attack is the deep-stall damping-in-plunge of the outboard wing sections. The wing on the generic aircraft model (Fig. 2) has a  atplate airfoil section. It and the inverted 7.4% Clark Y airfoil have very similar deep-stall cl(a) characteristics 9 (Fig. 3). Judging by the deep-stall characteristics for the NACA 0012 and NACA 0015 airfoil sections (Fig. 4), the mean cl(a) slope at a > 8 deg in Fig. 3 should give a conservative estimate for the  at-plate airfoil section, i.e., cla ’ 0.95. As the tangential force is negligibly small, cna ’ 0.95/cos a. For the plunging wing section during wing rock, the sectional normal force at the spanwise location y = hb/2, where b is the wing span, is