NUMERICAL-SOLUTION OF EULER EQUATIONS FOR AEROFOILS IN ARBITRARY UNSTEADY MOTION

This paper is part of a DLR research programme to develop a three-dime nsional Euler code for the calculation of unsteady flow fields around helicopter rotors in forward flight. The present research provides a c ode for the solution of Euler equations around aerofoils in arbitrary unsteady motion. The aerofoil is considered rigid in motion, and an O- grid system fixed to the moving aerofoil is generated once for all flo w cases. Jameson's finite volume method using Runge-Kutta time steppin g schemes to solve Euler equations for steady flow is extended to unst eady flow. The essential steps of this paper are the determination of inviscid governing equations in integral form for the control volume v arying with time in general, and its application to the case in which the control volume is rigid with motion. The implementation of an impl icit residual averaging with variable coefficients allows the CFL numb er to be increased to about 60. The general description of the code, w hich includes the discussions of grid system, grid fineness, farfield distance, artificial dissipation, and CFL number, is given. Code valid ation is investigated by comparing results with those of other numeric al methods, as well as with experimental results of an Onera two-blade d rotor in non-lifting flight. Some numerical examples other than peri odic motion, such as angle-of-attack variation, Mach number variation, and development of pitching oscillation from steady state, are given in this paper.