Extension of the subsonic doublet lattice method in transonic region using successive kernel

Abstract

The Doublet Lattice Method, a panel method, is a standard tool for calculating aerodynamic forces in flutter analysis. However, this method is only correct for subsonic flow conditions. The intention of this report is to investigate the successive kernel expansion method (SKEM), a method from literature, which promise a successful extension of the DLM into transonic regions. The kernel function is expanded as a Taylor series with respect to the reduced frequency about w*=0. The first element is representing the quasi steady part of the solution and is corrected by the difference of two steady CFD (Computational Fluid Dynamics) calculations with different angles of attack.

The main advantage over other so called reduced order methods is that no numerical simulations in the flow field are required. Pressure differences are directly calculated at the surface of the wing or aircraft. In contrast to the Transonic Doublet-Lattice Method (TDLM), in which terms are added obtained from one steady CFD simulation, SKEM extrapolates from a quasi steadysolution at w*=0 to the unsteady pressure differences.

In the method is only validated for very low frequencies and only two Taylor coefficients are taken into consideration. This restriction could be successfully disbanded by higher Taylor expansion. The Taylor series is computed using automatic differentiation techniques. Furthermore convergence properties are analyzed and an improved SKEM (iSKEM) is developed. Moreover the method is compared to nonlinear unsteady simulations in the time domain using the DLR TAU-Code and to measurement data of the AGARD LANN wing. Computed transonic cases include Euler calculations for various frequencies and RANS calculations with separation and inverse shock movement.