Unsteady thin airfoil theory revisited for a general deforming airfoil

Abstract

The unsteady thin airfoil theory of von Karman and Sears is extended to analyze the aerodynamic characteristics of a deforming airfoil. The von Karman and Sears approach is employed along with Neumark’s method for the unsteady load distribution. The wake-effect terms are calculated using either the Wagner or Theodorsen function, depending on the desired camberline deformation. The concept of separating the steady and damping terms in the camberline boundary condition is introduced. The influence of transient and sinusoidal airfoil deformations on the airfoil load distribution is examined. The general equations developed for the unsteady lift and load distribution are evaluated analytically for a morphing airfoil, which is defined here by two quadratic curves with arbitrary coefficients. This general camberline is capable of modeling a wide range of practical camberline shapes, including leading and trailing edge flaps. Results of the present model are shown for a variable camber, or morphing, airfoil configuration. The influence of transient and sinusoidal motion on the force coefficients and load distribution is addressed.