Modeling for Unsteady Aerodynamics of Rectangular Wing in Incompressible Flow Using Step Responses

Abstract

This paper considers approximating unsteady aerodynamic forces acting on a rectangular wing in the time domain. Time responses of the aerodynamic forces caused by a step movement of a rectangular wing in incompressible flow are calculated by using the time domain vortex element method. Transient characteristics in the step responses can be represented by one decreasing function regardless of wing motions. By approximating the decreasing function with a set of exponential functions and by calculating apparent mass coefficients and steady state forces, a mathematical model for the aerodynamic forces in the form of 1st-order linear time-invariant differential equations (the state equations) is obtained. The results obtained for the example problems show that a good fit to the aerodynamic forces can be achieved with two exponential functions approximating the decreasing function.