Numerical solution of Euler equations for aerofoils in arbitrary unsteady motion

Abstract

This paper is part of a DLR research programme to develop a three-dimensional Euler code for the calculation of unsteady flow fields around helicopter rotors in forward flight. The present research provides a code for the solution of Euler equations around aerofoils in arbitrary unsteady motion. The aerofoil is considered rigid in motion, and an 0-Grid system fixed to the moving aerofoil is generated once for all flow cases. Jameson's finite volume method using Runge-Kutta time stepping scheme to solve Euler equations for steady flow is extended to unsteady flow. The essential steps of this paper are the determination of inviscid governing equations in integral form for the control volume varying with time in general, and its application to the case in which the control volume is rigid in motion. The implementation of an implicit residual averaging with variable coefficients allows the CFL number to be increased to about 60. The general description of the code, which includes the discussion of grid system, grid fineness, farfield distance, artificial dissipation, and CFL number, is given. Code validation is investigated by comparing results with those of other numerical methods, as well as with experimental results of an ONERA two-blade rotor in non-lifting flight. Some numerical examples other than periodic motion, such as angle-of-attack variation, Mach number variation, and development of pitching oscillation from steady state, are given in this paper.