Generalized Aerodynamic Modeling of Dynamic Wake Curvature for Open Rotors With Slender Blades

Abstract

This paper elaborates on the theoretical development of an analytical approach, capable of modeling the effect of dynamic wake curvature on the aeroelastic response of open rotors with slender blades. The classical solution of incompressible, potential flow derived for a curved vortex tube of uniform vorticity strength is employed. The previously developed curved vortex tube analysis is mathematically generalized to account for arbitrary radial and circumferential variations of circulatory disk loading. An orthogonality analysis is carried out to obtain a finite set of inflow perturbation coefficients that describe the aerodynamic effect of wake curvature in a generalized manner. The end result is a set of integral expressions that provide the interharmonic coupling between the inflow perturbations on the rotor disk due to a curved trailing wake and the corresponding variations of disk loading. The obtained perturbation coefficients are subsequently superimposed upon an existing finite-state induced flow model that assumes a skewed, noncurved cylindrical wake. The developed mathematical approach for fluid mechanics is coupled with an unsteady blade element aerodynamics model, a rotor blade structural mechanics model, and a nonlinear rotor dynamics model. The combined formulation is implemented in an existing helicopter flight mechanics code. The overall method is initially employed to assess the effect of wake curvature on the dynamic response of a small-scale articulated rotor with a flap frequency ratio equal to unity. Subsequently, the integrated model is deployed to investigate the influence of wake curvature and inflow modeling fidelity on the predicted oscillatory blade loads and transient control response of a full-scale helicopter rotor. Comparisons are carried out with flight test measurements as well as with complex free-wake analysis methods. It is shown that including the effect of wake curvature is essential for predicting the transient control response of the investigated rotor. Good agreement is demonstrated between the proposed analytical model and nonlinear predictions carried out by resolving the complex wake geometry. The developed fluid mechanics formulation is a time-accurate method derived from first-principles and is applicable to both axial and nonaxial flow conditions.