Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors

A harmonic balance technique for the analysis of unsteady flows about helicopter rotors in forward flight and hover is presented in this paper. The aerodynamics of forward flight are highly nonlinear, with transonic flow on the advancing blade, subsonic flow on the retreating blade, and stalled flow over the inner portion of the rotor. Nevertheless, the unsteady flow is essentially periodic in time making it well suited for frequency domain analysis. The present method uses periodic boundary conditions that allows one to model the flow field on a computational grid around a single helicopter blade, no matter the actual blade count. Using this approach, we compute several solutions, each one corresponding to one of several instants in time over one period. These time levels are coupled to each other through a spectral time derivative operator in the interior of the computational domain and through the far-field and periodic boundary conditions around the boundary of the domain. In this paper, we apply the method to the three-dimensional Euler equations (although the method can also be applied to three-dimensional viscous flows), and examine the steady and unsteady aerodynamics about wings and rotors.