An Unsteady Lifting-Line Model for Rotors in Forward Flight

This study presents a time-marching lifting-line algorithm to predict the unsteady aerodynamics of rotors. Validation studies employing purely harmonic and damped oscillatory wing and blade motions have demonstrated the solver’s ability to accurately and stably predict unsteady loads. Augmenting the free and prescribed wake solvers recently developed, this method extends their time-marching framework to rotary wing applications in forward flight. In the present formulation, wake-induced velocities are evaluated via a free-wake model, while sectional forces are computed via K¨ussner-Schwarz unsteady theory. The bound circulation is derived by an unsteady Kutta-Joukowski relation. From there, both load and circulation equations are cast into state-space form. A vital modification for rotating blades is the careful definition of the reduced frequency, dealing with the accuracy of the prediction of dynamic loads and circulation.