EVALUATION OF THE PRINCIPLE OF AERODYNAMIC SUPERPOSITION IN FORCED RESPONSE CALCULATIONS

Stefan Schmitt

German Aerospace Center Institute of Propulsion Technology Cologne, Germany stefan. schmitt@dlr. de

Dirk Nurnberger

German Aerospace Center Institute ofPropulsion Technology Cologne, Germany dirk. nuernberger@dlr. de

Volker Carstens

German Aerospace Center Institute ofAeroelasticity Gottingen, Germany volker. carstens@dlr. de

Abstract The validity of the principle of superposition for forced response analysis is evaluated by its application to a research propfan stage. The counter-rotating propfan features transonic fbw conditions and aerodynamic interaction between the blade rows. The computed unsteady aerodynamics are verified by compar­ison with rig measurements. A forced response analysis based on the principle of superposition is conducted, similar to the current practice in turbomachinery design. For reference, a fully coupled simulation of the propfan forced response is undertaken. This simulation does not rely on the principle of superposition, and the model can also resolve non-linear interaction effects beyond the valid­ity of the linear superposition principle. The comparison shows a full validity of the superposition principle for the present case: Computed blade vibration amplitudes, as well as the unsteady aerodynamics inside the blade passages, are correct, even in quantitative terms. This supports the application of the superpo­sition principle for forced response analysis within the industrial design process.

133

K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 133-144. © 2006 Springer. Printed in the Netherlands.

Introduction

Important goals in today’s aeroengine design are the reduction of fuel con­sumption, engine weight and production effort. A contribution to lower weight and production costs is a reduction of the number of blades, and a closer axial spacing of the blade rows. The use of less blades leads to an increase in blade loading, while the reduced axial spacing increases the amount of interaction between adjacent blade rows. The aerodynamic interaction between the blades can excite the blades to vibrate causing a forced response problem.

The forced response problem is characterized by the interference of the ex­ternal aerodynamic forces arising from up – or downstream excitation on the one hand, and the aerodynamic damping forces of the oscillating blades on the other hand. Current methods mostly rely on a linear superposition of these forces (Chiang and Kielb, 1993, Green and Marshall, 1999), where the re­sponse amplitudes are computed from the balance of excitation and damping forces.

The use of a non-linear aeroelastic method using fliid-structure coupling in the time domain enables a computation of the blade response amplitudes without the application of the rather restrictive superposition principle. Some directly coupled forced response calculations on turbomachinery stages have been presented in recent years: Wakeley and Potts calculated the excitation of a steam turbine stage due to partial admission (Wakeley and Potts, 1996). He calculated the forced response in a two-stage-compressor (He, 1999). Gottfried and Fleeter investigated an inlet-guide-vane/rotor research fan stage combina­tion (Gottfried and Fleeter, 2000). The research group at Imperial College presented forced response calculations of a low pressure turbine (Sayma et al, 1998), a high pressure turbine, as well as a fan stage (Vahdati et al, 2000).

Unfortunately the results of the computations mentioned above do not yield definite information about the dependence of the numerical data on the use of either a coupled or a linear method. The authors conclude that at present it is not sufficiently clear in which cases fluid-structure coupling methods are necessary for forced response predictions.