A New Approach to the Free Wake Problem for Hovering Rotors

A new approach to the free wake problem for a hovering rotor has been developed. An Influence coefficient solution method is used to find the rotor wake solution which is steady in a reference frame rotating with the blades. This solution scheme solves directly for the conditions of free wake equilibrium by a procedure which does not involve time stepping and the associated use of numerical damping or special convergence methods. The influence coefficient solution method was implemented into a hover wake computer program having a three-part wake model for the tip vortex. The free wake tip vortex is located using the new solution method. Below the free wake is an adaptive mid wake based on a free vortex sheet analysis for the final contraction. This mid wake provides a transition to a semi-infinite momentum theory far wake. All three wake regions are represented by the new Basic Curved Vortex Elements which are well suited for this application because of their efficiency and high accuracy. Sample hover calculations have been made for single and multi-bladed rotors. Converged solutions were obtained after only a few calculation cycles. The temporal stability of converged solutions was investigated using an eigenvalue analysis and a numerical simulation. It is clearly feasible to include additional wake features within the framework of this solution method.