Methods for the Design and Analysis of Jet-Flapped Airfoils

Methods for solving both the direct and inverse jet flap airfoil potential flow problems are described. The direct airfoil analysis method is a completely nonlinear iterative method which is applicable to either thick or thin airfoils of arbitrary shape. The very general surface singularity formulation has been extended to include multielement airfoils, ground effects, nonuniform freestreams, inlet flows, jet entrainment effects, etc. Comparisons are given with the results of previous linear and nonlinear methods as well as with experimental data. The inverse (design) method is a more approximate method in which camber and thickness distributions are designed separately. Section shapes are shown for several airfoils designed to have only very small regions of adverse pressure gradient. Nomenclature c = length of airfoil chord cp = coefficient of pressure d = coefficient of lift cu = coefficient of jet momentum h = height of airfoil leading edge above ground plane R = radius of curvature of the jet sheet s = coordinate along the jet sheet t = airfoil thickness V = local flow speed V = average flow speed across a vortex sheet Vj - jet flow speed Vn = component of velocity normal to a surface V = freestream flow speed x = coordinate parallel to the freestream = coordinate perpendicular to the freestream = jet deflection angle at the trailing edge relative to the airfoil chord line 7 = strength of a vortex sheet 0 = local angle of inclination of the jet sheet relative to the freestream 0 = velocity potential