21st Congress of International Council of the Aeronautical Sciences, Melbourne, Australia, 13-18 September, 1998
Paper ICAS-98-2.6.3

SMALL DISTURBANCE EULER EQUATIONS (SDEE) -AN EFFICIENT AND ACCURATE TOOL FOR UNSTEADY LOAD PREDICTIONS AT ALL MACH NUMBERS

Kreiselmaier E., Laschka B.
Technical University of Munich, Germany

Keywords: small disturbance euler equations (sdee), unsteady load predictions at all mach numbers

A numerical method is presented to predict unsteady loads for aero elastic calculations. It is well known that the time-accurate solutions of the unsteady Euler equations are a reasonable but expensive and time consuming approach, especially for transonic flows. An alternative approach are the small disturbance Euler equations (SDEE) applied to harmonic motion providing the following advantages: • The unsteady problem is formally reduced to a steady one for the perturbation. • The first harmonics of unsteady loads are evaluated directly by that supporting the use of well proven modal methods in aero elastic analysis. • Substantial reduce of computational time For an optimal evaluation of the airfoil boundary conditions a harmonically deforming grid is used. Results will be 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 SDEE provides an excellent and relatively quick mean for the prediction of unsteady forces. The only remarkable differences between the exact Euler solution and SDEE solution may be observed at the pressure distribution in the vicinity of the shock, which is of negligible influence for the coefficients.

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