Aerodynamics of helicopter rotor in hover: The lifting-vortex line method applied to dihedral tip blades

There are various methods for predicting the aerodynamic performance of helicopter rotors. In this study, the vortex method, which schematizes the blades and the rotational flow areas on the basis of a distribution of vortices, has been used to calculate the air flow around a rotor in hover. This method is an application to helicopter rotors of the Prandtl's lifting-vortex line theory for aircraft wings. It assumes perfect incompressible fluid with non-rotational outside the vortex sheets. The induced velocities are determined using Biot and Savart's law, and the circulation distribution by Kutta-Joukowski's law. Data on initial wake geometry and aerodynamic characteristics, the latter being obtained by bidimensional wind tunnel tests, are necessary for implementing this method. On this theoretical basis, a numerical computational program has been developed to determine rotor performance at hover with stabilisation of the vortex sheet. The rigid blades with a flapping hinge are represented by a lifting-vortex line, angled or rectilinear, located in the leading quarter of the chord; the wake is discretized into a finite number of vortex lines. Comparisons of computational and experimental test results are presented on the overall magnitudes: figure of merit and pitch angle. The tests were carried out at Aerospatiale using rotors fitted with blades with either rectangular or dihedral tip planform. In the latter case, the lifting-vortex line, no more rectilinear, takes into account the actual shape of the blades. The results obtained in this study show a good correlation between computations and tests, for both blades with classical geometry or with non-rectilinear quarter line and non-rectangular planform.