Small Disturbance Euler Equations: Efficient and Accurate Tool for Unsteady Load Prediction

Abstract

It is well known that the time-accurate solutions of the unsteady Euler equations are a reasonable but computationally expensive and time-consuming approach. Concerning aeroelastic applications, there is a need for efficient and accurate tools to determine the unsteady aerodynamic loads due to a variety of parameters. A numerical method based on an alternative approach, namely, on the solution of the small disturbance Euler equations (SDEu), is presented. These equations provide the following advantages: The unsteady problem is reduced to a steady-state problem for the perturbation part. The unsteady loads can be evaluated directly. Assuming harmonic behavior of unsteadiness, tire use of well-proven modal methods in aeroelastic analysis is supported. By application of this method, a substantial reduction of computational time is achieved. Results are presented for several airfoils and wings in pitching motion at subsonic, transonic, and supersonic Mach numbers. It is shown that for the most critical region, namely, the transonic region, the SDEu provide an excellent and fast means for the prediction of unsteady forces. The only remarkable differences between the nonlinear Euler solution and the SDEu solution can be observed in the pressure distribution in the vicinity of a shock, which is shown to have negligible influence on the integral contribution of the shock impulse to the generalized forces.