Innovation with Computational Aerodynamics: The Divergent Trailing-Edge Airfoil

Introduction T aerodynamic design of airfoil sections continues today as an elegant yet practical engineering design problem. It is elegant in that the solution of any airfoil design problem, however complex, is nothing more than a two-dimensional closed contour. It is practical in that many, if not most, problems in aerodynamics involve the generation of lift, drag, and moment by airfoil sections. The airfoil design problem has received much attention in experimental, theoretical, and computational studies. Numerous volumes and documents have been compiled to summarize such studies. Reference 1 stands as a classic example of such documentation and provides an excellent summary of early airfoil research efforts. Early theoretical studies of airfoil design led to the decomposition of airfoil geometric characteristics into thickness, camber, and angle of attack, as shown in Fig. 1. Much of the early design studies dealt with the proper combination thickness shapes and camber shapes necessary to achieve some aerodynamic design goal. It is interesting to point out that few studies were focused on details associated with the airfoil trailing edge. Trailing-edge effects normally were of concern only when mechanical variations for high-lift systems or control systems were introduced.' Traditionally, airfoil closure has been accomplished by using trailingedge included angles typically in the 5to 15-deg range in conjunction with essentially zero trailing-edge thickness. Early trailing-edge design principles were that the trailing edge must be sharp to avoid drag penalties, and the trailing-edge included angle, as defined by e in Fig. 1, must be positive to allow for practical manufacture. These principles caused most early airfoil trailing-edge geometries to be wedge shaped. More recently, work by Whitcomb and others to develop the supercritical airfoil has shown the possibility of using a thin-trailing-edge geometry