Extension of a discontinuous Galerkin finite element method to viscous rotor flow simulations

Heavy vibratory loading of rotorcraft is relevant for many operational aspects of helicopters, such as the structural life span of (rotating) components, operational availability, the pilot’s comfort, and the effectiveness of weapon targeting systems. A precise understanding of the source of these vibrational loads has important consequences in these application areas. Moreover, in order to exploit the full potential offered by new vibration reduction technologies, current analysis tools need to be improved with respect to the level of physical modeling of flow phenomena which contribute to the vibratory loads. In this paper, a computational fluid dynamics tool for rotorcraft simulations based on first-principles flow physics is extended to enable the simulation of viscous flows. Viscous effects play a significant role in the aerodynamics of helicopter rotors in high-speed flight. The new model is applied to three-dimensional vortex flow and laminar dynamic stall. The applications clearly demonstrate the capability of the new model to perform on deforming and adaptive meshes. This capability is essential for rotor simulations to accomodate the blade motions and to enhance vortex resolution. ∗Research funded by NLR’s basic research programme. †Research conducted in the STW project TWI.5541; the financial support from STW and NLR is gratefully acknowledged. Symbols and abbreviations a∞ freestream speed of sound α angle of attack BVI Blade-Vortex Interaction c chord CFD Computational Fluid Dynamics DG discontinuous Galerkin MTMG Multitime-Multigrid ω vorticity RANS Reynolds-averaged Navier-Stokes u velocity vector uj j-th component of a vector u,j ∂u ∂xj Û i j expansion coefficient for the j-th basis function and the i-th conservative variable ∇ ∇j = ∂ ∂xj ·T transpose of a vector