A study of wall effect on the flow over a delta wing

Abstract

A study is described of the flow over a large-size semispan 76-deg delta wing in a low-speed wind tunnel. The flow was surveyed extensively at an angle of attack of 20.4 deg and a Reynolds number of 3.8 million. A consequence of the large-size wing is that the interaction of the model flowfield with the tunnel walls can significantly increase the angle of attack of the wing. This wall effect was examined from solutions of the threedimensional Euler equations developed for the flow over the wing in the existing tunnel, in an imaginary tunnel with a larger cross-sectional geometry, and in free air. The solutions show the effect of the tunnel walls on the leading-edge vortex flow and the forces acting on the wing. The solution for the flow about the wing in the existing tunnel was also compared with experimental data. The computed flowfield is shown to underestimate the magnitude of the velocities and pressures in the core of the leading edge vortex, but to reasonably well predict the wing surface pressure when secondary separation is prescribed. Nomenclature B tunnel span (computational space) b wing span C Cu drag coefficient CL lift coefficient C, C,, M freestream Mach number P static pressure Pt total pressure p, freestream static pressure qw freestream dynamic pressure Rb bIB Re root chord length, = 2.220 m static pressure coefficient, = ( p pm)/qm total pressure coefficient, = ( p t pm)/qm Reynolds number, based on root chord *Research Scientist, Member AlAA t Research Scientist 1Ph.D. Student Copyright 0 1 9 9 6 by N.G. Verhaagen. can Institute of Aeronautics and Astronautics. Inc. with permission. Published by the Anierilength S local wing semispan u, v, w velocity components in wing axes system U freestream velocity z, y, z coordinates of wing axes system, origin at apex N angle of attack Introduction Thin slender delta wings with relatively sharp leading edges are employed for several modern peace keeping aircraft and for design concepts of high-speed civil transport. At moderate and high angles of attack the flow over such wings separates at the sharp leading edges, forming a so-called primary or leading-edge vortex. This vortex is characterized by a free shear layer that rolls up in a spiral fashion into the vortex core. Since vorticity is continuously shed along the leading edges, the circulation of the primary vortex increases with distance from the apex of the wing. The circulation increases also with the angle of attack and vortex lift is responsible for a nonlinear increase of lift with the angle of attack. The vortex structure remains steady and stable over a large range of angles of attack. At high angles of attack vortex breakdown occurs upstream of the wing trailing edge, resulting in a decrease of circulation and a loss of suction on the wing downstream of the breakdown location. The present study focusses on the flow over a delta wing at moderate angle of attack and low subsonic speed, conditions typical of takeoff and approach. Detailed flowfield data for such conditions were obtained in an earlier study, reported by Verhaagen, et al, in Ref. [ l ] . This study was carried out in a subsonic wind tunnel on a large semispan delta wing at a constant angle of attack of 20.4 deg (Fig. 1). The wing had a leading-edge sweep of 76 deg, a chord length of 2.22 m and was attached vertically to a reflection plate at the top of the test section to avoid direct influence of the tunnel wall boundary layer. A relatively large wing was chosen in order to acquire detailed data of the vortex flow and, in particular, of the American Institute of Aeronautics and Astronautics