# Aeroservoelastisches Modell zur Beschreibung der instationären Aerodynamik für nichtlineare beliebige Eingangsgrößen im Zeitbereich

- Aeroservoelastic model describing the unsteady aerodynamics for non-linear arbitrary input in time domain

Wang, Wen; Ballmann, Josef (Thesis advisor)

*Aachen : Publikationsserver der RWTH Aachen University (2006)*

Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2006

Abstract

In this thesis an aeroservoelastic model for an airfoil-rudder-system with three degrees of freedom is established in time domain. This leads to the design of control laws for active flutter suppression. The response of the unsteady aerodynamics and the system behav-iour with respect to a non-linear time dependent doublet deflection of the rudder and the angle of attack are calculated. An integrated areoservoelastic model in time domain is set up by means of the indicial concept. The unsteady aerodynamics in incompressible and compressible flow for arbi-trary movements is approximated by indicial functions using the following approach: 1. The aerodynamic forces and moments are derived in integral form from the lin-earized potential theory.2. The indicial functions are validated for compressible and incompressible flow in frequency and time domain.3. The lift system for arbitrary variations of angle of attack, pitching and rate of rud-der deflection is derived from DUHAMEL-superposition integral.4. The transfer function of the lift system is derived by LAPLACE transformation.5. The state space equation for the airfoil-rudder-system for unsteady aerodynamics in compressible and incompressible flow are set up.6. The differential equations of motion of the airfoil-rudder-system are expressed by the LAGRANGE equations of second kind and combined with the aerodynamic equations to the aeroelastic system.7. The validation of the aeroelastic is carried out by comparison of the flutter speed using the root locus method according U-g-method, p-k-method and g-method from literature. The three most important results of this work are three new formulas for the approxima-tion of the unsteady aerodynamics for incompressible and compressible flow: 1. A new and better constant for the approximation of the WAGNER function in in-compressible flow. The indicial function is validated by comparison with the THEODORSEN function in LAPLACE domain. Compared to other approximations this procedure yields better imaginary parts of the indicial lift. This results in a better prediction of the flutter speed.2. The two other formulas are related to the time constants KaM and KaM1/4, which are used for the approximation of the non-circulatory indicial moments relative to the elastic axis and the 1/4-chord in compressible flow. Therefore, the explicit start and end values of the indicial response according to LOMAX are used. In particular, the constants KaM, which are related to the elastic axis, are important for the aeroelastic modelling. The substantial effects for the unsteady aerodynamic due to non-harmonic motion or disturbances can be calculated in a very fast and efficient way in time domain. This al-lows the simultaneous consideration of the flexibility of the lift system within the aerody-namic system and the set-up of an integrated model including the control laws and the flight mechanic system.

### Identifier

- URN: urn:nbn:de:hbz:82-opus-17277
- RWTH PUBLICATIONS: RWTH-CONV-123216