Numerical Investigations of the Blade-tip Vortex of a Rotor with Axial Inflow

Abstract

Numerical computations using DLR's finite-volume compressible-flow solver TAU are conducted to investigate the tip vortex of a helicopter blade. The computations comprise unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and detached-eddy simulations (DES). In all computations, a Mach-scaled rotor with a radius of R = 0.65 m is simulated with a constant flow perpendicular to the rotor axis. The chord length c = 0.072 m of the DSA-9A airfoil leads to a Mach number of M_tip = 0.28 and a Reynolds number of Re_tip = 470 000 at the tip. Both two-bladed and four-bladed configurations under various constant and sinusoidal pitch conditions are examined. In the expected path of the blade-tip vortex, a fine resolution of a hexahedral block is implemented to reduce numerical dissipation. The URANS simulations using the shear-stress transport (SST) turbulence model on the two-bladed configuration demonstrate good prediction regarding the generation and early development of the blade-tip vortex. The numerical dissipation, however, inhibits realistic results at more advanced wake ages. Therefore, a zonal approach with a large-eddy simulations (LES) model is employed on the four-bladed configuration to reduce numerical dissipation and to improve physical modeling of the vortex development. Algorithms deriving the vortex position, shape, swirl velocity, circulation, and core radius are implemented. The analysis shows that the position of the rotor-blade trailing-edge mainly drives the vertical location of the vortex core. Furthermore, the high cyclic pitch case predicts a strong hysteresis between up- and downstroke and a very elliptic vortex core. This elliptical vortex shape rotates with approximately half the solid-body rotation speed of the core. The vortex of the attached pitching case can be modeled as an assembly of the static vortex states. Additionally, the vorticity in the vortex is well predicted by the maximum circulation on the blade. The simulations are validated by wind tunnel experiments featuring a complete pitching cycle at the rotor test facility in Göttingen (RTG). Thrust trimmed comparisons show a qualitative and quantitative agreement in the swirl velocity.