An innovative algorithm to accurately solve the Euler equations for rotary wing flow

Abstract

Due to the ability of Euler methods to treat rotational, nonisentropic flows and also to correctly transport on the rotation embedded in the flow field it is possible to correctly represent the inflow conditions on the blade in the stationary hovering flight of a helicopter, which are significantly influenced by the tip vortices (blade-vortex interaction) of all blades. It is shown that also the very complex starting procedure of a helicopter rotor can be very well described by a simple Euler method that is to say without a wake model. The algorithm based on the procedure is part of category upwind schemes, in which the difference formation orientates to the actual, local flow state that is to say to the typical distrubance expansion direction. Hence, the artificial dissipation required for the numerical stability is included in a natural way adapted to the real flow state over the break-up error of the difference equation and has not to be included from outside. This makes the procedure robust. An implicit solution algorithm is used, where the invertation of the coefficient matrix is carried out by means of a Point-Gauss-Seidel relaxation.