A Far Field Boundary and Initial Condition for the Simulation of Hovering Rotors based on Turbulent Jets

The far field flow induced by a hovering rotor is revisited as it relates to considerations in computational fluid dynamics, drawing on classical empirical knowledge of turbulent jets and recently published theory. A mathematical model based on axi-symmetric potential flow, with appropriate treatments for the wake, is presented in full and discussed in terms of implementation as a far field boundary condition in a compressible Navier-Stokes solver. A regularization of the model in the near field is also given as a simple initial condition with the aim of faster convergence. Steady Navier-Stokes solutions of an isolated rotor in a rotating frame are used to validate the new model. Key qualitative results show advantages over other boundary conditions in terms of an axi-symmetric and irrotational far field and demonstrate the dominance of the jet entrainment. Definitive statements of boundary and domain size effects on Figure of Merit and far wake details were complicated by oscillatory convergence and anomalous behaviors of the turbulence models in the rotating frame. The far wake problem is postulated to be caused by a 1st-order differencing of the turbulence transport equation, and limited results with a 3rd-order scheme show much better agreement with theory