Topic
The aerodynamic model which has received widespread application for aeroelasticity is the Doublet-Lattice method. This model is based on potential theory and its main advantage is speed of computation. However, potential flow cannot represent important flow physics. In addition, the assessment of the impact of the modelling assumptions on the aeroelastic predictions is likely to be important for practical application and physical insight. Structural model sensitivity is relatively easy to evaluate if the structural model uncertainty is assumed to be due to parametric uncertainty. Methods for considering uncertainty introduced by the model form are much less clear.
Several methods have been considered to attack this problem. Efforts were made to parametrise the influence of aerodynamic structures through POD modes. The next attempt tried to use coupled models (eg full potential model + shock model + boundary layer model) to expose parameters related to individual physical features (see D2.1). Finally, the method fixed upon uses the Schur eigenvalue framework to evaluate sensitivity to matrix elements and to update matrix elements using different model levels.
The example being investigated is to use the simplest model possible being able to predict shock waves. The model of choice is the full potential equation. This baseline model is coupled with an integral boundary layer model to correct for viscous effects such as the displacement effect of the boundary layer as well as shallow separation. Besides the integral boundary layer formulation, a Clebsch variable model to correct for entropy and vorticity effects caused by strong shock waves violating the isentropic assumption of the full potential formulation is a future possibility. Euler and RANS codes are available for higher level models.
Progress
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A preliminary study was carried out into setting up the eigenvalue based aeroelastic prediction tools for aerofoils moving in pitching and plunging motion. This work exposed an interesting oscillation in the instability boundary. A detailed investigation of this phenomenon has been written up and presented at the ECCOMAS conference.
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The full potential formulation has been coupled with the structural model of a two degree of freedom aerofoil.
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An integral boundary layer formulation has been coupled in a fully-simultaneous fashion to the full potential formulation to correct the predictions for viscous effects.
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The approximation of the Schur interaction matrix is based on sampling and interpolation using kriging (previously used for flight dynamics aerodynamic model generation). The matrix terms can be approximated by low order methods (like FP) and then updated where necessary using higher order methods. This topic has been investigated in detail for aerofoil cases and was presented at the SDM 2010 conference.
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The approximation of the Schur interaction matrix to represent the aerodynamic influence on the aeroelastic stability problem has been formulated and tested for realistic aircraft models. The kriging interpolation has been exploited to search large parameter spaces for transonic aeroelastic instability using risk-based sampling. The risk-based sampling allows the use of computational fluid dynamics in the analysis to explore large parameter spaces for aeroelastic instability. This topic has been investigated in detail and was presented at the AFM 2010 conference.
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An alternative to the kriging interpolation, namely artificial neural networks, has been discussed for the approximation of the Schur interaction matrix. The search for aeroelastic instability using risk-based sampling and the different interpolation tools has been demonstrated for aerofoil and wing cases. This work was presented at the 2010 RAeS Aerodynamics Conference.
References
- Timme, S. and Badcock, K.J., Computational Aeroelasticity based on Bifurcation Theory, presented at
5th European Congress on Computational Methods in Applied Sciences and Engineering, Venice, 30 June-
4 July, 2008 - presentation
- Timme, S. and Badcock, K.J., Oscillatory Behavior of Transonic Aeroelastic Instability Boundaries,
AIAA Journal, Vol. 47, No. 6, 2009, pp. 1590-1592. (doi: 10.2514/1.40497)
- Timme, S., Formulation of Model Hierarchy - presentation
- Timme, S., Schur Method and Model Hierarchy - D2.3.pdf
- Timme, S. and Badcock, K. J., Searching for Transonic Aeroelastic Instability Using an Aerodynamic Model Hierarchy, AIAA Paper 2010-3048,
Presented at the 51st AIAA/ ASME/ ASCE/ AHS/ ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, 2010.
- Timme, S., Marques, S. and Badcock, K. J., Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation, AIAA Paper 2010-8228, Presented at the AIAA Atmospheric Flight Mechanics Conference, Toronto, Canada, 2010.
- Timme, S., Rampurawala, A. and Badcock, K. J., Applying Interpolation Techniques to Search for Transonic Aeroelastic Instability: ANN vs Kriging, Paper, Presented at the 2010 RAeS Aerodynamics Conference, Bristol, United Kingdom, 2010.
- Timme, S., Transonic Aeroelastic Instability Searches Using a
Hierarchy of Aerodynamic Models, Ph.D. thesis, School of Engineering, University of Liverpool, United Kingdom, 2010.
Contact
Sebastian Timme
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