A Distributed Doublet-Based Method for Unsteady Aerodynamic Analysis with Relaxed Wakes

A novel potential flow-based method for unsteady aerodynamic analysis with relaxed wakes is presented. This method models aerodynamic surfaces and wakes using distributed doublet elements (DDEs) of parabolic strength in both the spanwise and streamwise directions. Due to the nature of the method, the velocities induced by a DDE-based system are bounded everywhere, meaning there are no non-physical or infinite induced velocities in the velocity field, as opposed to lower-order filament-based potential flow methods. In addition to providing a robust velocity field, the use of DDEs provides a degree of stability in predicting unsteady forces that is unachievable with conventional lower-order methods.

The DDE-based method was validated through a series of four studies. The first study predicted the span efficiency of various planar elliptical wings, which agreed with the classical lifting line solution to within 3%. The second study predicted the unsteady lift response to an airfoil passing through a sharp-edged gust, which matched the analytical solution provided by the Küssner function, illustrating the stability of the unsteady force calculations within the DDE-based method. The third study predicted the unsteady time-averaged thrust force produced by a small, rigid rotor at various tip-path plane angles and advance ratios, matching experimentally-obtained data to within 10%. The final study compared the transient sectional thrust of a small, rigid rotor blade operating under unsteady conditions to those obtained via a CFD-based analysis. The comparison agreed well in magnitude and azimuthal location.

Two exploratory studies focusing on small, rigid rotors were performed to demonstrate potential applications of the DDE-based method. The first study quantified the impacts of rolling maneuvers on the time-averaged thrust and moments of a rigid rotor, with the results indicating that a rolling maneuver can have a significant effect on the thrust and roll moment coefficients. The second study predicted the transient thrust of two rotors operating under multiple tip-path plane angles and advance ratios, showing transient thrust oscillations of up to 60% of the mean thrust output in some cases. The thrust output of individual rotor blades oscillated by up to 90% of the mean total rotor thrust under certain conditions.