A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations

This report contains a description of a Beddoes-Leishman type dynamic stall model in both a state-space and an indicial function formulation. The model predicts the unsteady aerodynamic forces and moment on an airfoil section undergoing arbitrary motionin heave, lead-lag, and pitch. The model includes the effects of shed vorticity from the trailing edge (Theodorsen Theory), and the effects of an instationary trailing edge separation point.

The governing equations of the model are nonlinear, and theyare linearized about a steady state for application in stability analyzes. A validation is carried out by comparing the response of the model with inviscid solutions and observing the general behavior of the model using known airfoil data as input.

Theproposed dynamic model gives results identical to inviscid solutions within the attached-flow region; and it exhibits the expected dynamic features, such as overshoot of the lift, in the stall region. The linearized model is shown to give identicalresults to the full model for small amplitude oscillations.

Furthermore, it is shown that the response of finite thichkness airfoils can be reproduced to a high accuracy by the use of specific inviscid response functions.