Design of an Optimal Wing-Body Configuration to Delay Onset of Vortex Asymmetry

Abstract

O NE important phenomenon associated with high-angle-ofattack aerodynamics is the sudden onset of vortex asymmetry on the forebody of an air vehicle in symmetric flight. One of the first observations of the onset of vortex asymmetry was reported in 1951 by Allen and Perkins [1]. Interest in the phenomenon has been intensified since the late 1970s as concepts for highly maneuverable aircraft have been developed. These high-performance aircraft are expected to operate routinely at angles of attack at which vortex asymmetry is likely to occur. When vortex asymmetry occurs, the aerodynamic, stability, and control characteristics of the vehicle change dramatically. In themeantime, the conventional aerodynamic controls become ineffective due to the vortex wakes generated by the forebody. The subject was reviewed by Hunt [2], Ericsson and Reding [3], and Champigny [4]. High-angle-of-attack flow control is most effective when applied in the region close to the tip of the forebody. The presence of two closely spaced vortices around the pointed forebody at high angles of attack enhances the effectiveness. Compared with that on wings, control on the forebody is required over a much smaller area; thus, physical requirements such as size and weight should be much smaller. The lengthy forebody of a modern fighter further enhances the control effectiveness by providing a long moment arm. Excellent reviews of this activity can be found in papers by Malcolm [5,6] and Williams [7]. Recently, Liu et al. [8] successfully demonstrated linear proportional control of the side forces over a slender circular cone using duty-cycled single-dielectric-barrier-discharge plasma actuators. One of the devices to suppress the flow asymmetry are the horizontal nose strakes. Coe et al. [9] showed, by wind-tunnel tests, the alleviating effects of horizontal and symmetrical strakes placed close to the apex of a slender ogive forebody and a slender circular cone. It is observed that the effect of the strakes is to produce a welldefined point of separation at the leading edges of the strakes, which results in a symmetrical flowfield over a wide range of high angles of attack. Two sharp side edges on an otherwise smooth body can also serve to define the point of separation. Siclari [10] used a Navier– Stokes solver to study the natural occurrence of separated flows over biparabolic and biwedge cones at a freestream Mach number of 1.8 and an angle of attack of 20 . As the thickness ratiowas increased, the originally symmetric vortex pair separated from the sharp side edges, becoming asymmetric at thickness ratios of 0.5 and 0.6 for the biparabolic and biwedge cones, respectively. Cai et al. developed a stability analysis method [11] and used it to study high angle-of-attack flow about slender conical wing and wing–body combinations [12,13]. The analytic method is based on an eigenvalue analysis on the motion of the vortices under small temporal perturbations. The theoretical results agree well with available experimental observations and are corroborated by numerical computations [14]. The aim of the present paper is to manipulate the aerodynamic configuration for the purpose of keeping the stationary symmetric vortex pair stable at high angles of attack. In the following sections, the analyticmethod in [11] is summarized and a numerical conformal mapping technique is described. A series of configurations are analyzed for the stability of the symmetric vortex pair. A most effective configuration of thewing–body combination is obtained by the analytic method and validated by an Euler solver. In the last section, conclusions are drawn.