Synthesis of a Variable Geometry Trailing Edge Control Surface

Abstract

This paper describes the synthesis of a twodimensional airfoil with a chordwise variable geometry trailing edge control surface. Sequential unconstrained minimization techniques are applied to the control surface camberline representation to determine the optimal deflected shape. In addition to a continuous fourth order equation, a series of segments are used to describe the change in camber of the control surface, and viability of the two models is considered. Design variables consist of parameters which change the camberline including the control surface “hinge” location. The typical aeroelastic airfoil section is modelled with vertical and torsional springs to account for the flexibility of the system. Thin airfoil theory is used to model the pressure differential along the complete airfoil section, and determine aeroelastic performance parameters. The lift, moment imparted by the aerodynamic pressures on the control surface about its effective “hinge” point, and the energy necessary for the variable geometry control surface to overcome the aerodynamic forces as it changes positions are utilized as behavior functions. These behavior functions can be used in combination to provide objectives and constraints to the design process. Preand post-roll reversal cases are studied. 1 American Institute of Aero *Member AIAA †Associate Fellow AIAA ‡Professor, Fellow AIAA s declared a work of the U.S. Government and is not subject to copyright prote Nomenclature = , where is an integer = , where is an integer Aerodynamic Parameters = Density of Air = Freestream Velocity of Air = Dynamic Pressure = Initial Angle of Attack (AoA) = Change in AoA due to flexibility = Pressure Differential = Lift of Airfoil = Change in Energy at TECS = Aerodynamic Moment about Shear Center = “Hinge” Moment at Location = Lift Coefficient of 2-D Section = Slope of the Coefficient of Lift w.r.t. AoA = Moment Coefficient about Shear Center = Pressure Coefficient Differential