Transonic Flutter Analysis Using Euler Equation and Reduced Order Modeling Technique

Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071910

References:

[1] K. C. Hall, "Eigenanalysis of Unsteady Flows About Airfoil, Cascades, and Wing," AIAA Journal, Vol. 32, No. 12, 1994, pp. 2426-2432.
[2] E. H. Dowell, K. C. Hall, and M. C. Romanowski, "Eigenmode Analysis in Unsteady Aerodynamics; Reduced-Order Models," Applied Mechanics Review, Vol. 50, No. 6, 1997, pp. 371-386.
[3] M. C. Romanoski, "Reduced-Order Unsteady Aerodunamic and Aeroelastic Models Using Karhunen-Loeve Eigenmodes," AIAA-96-3981, AIAA Symp. On Multidisciplinary Anal. And Optim., Bellevue, WA.
[4] T. Kim, "Frequency-Domain Karhunen-Loeve Method and Its Application to Linear dynamic Systems," AIAA Journal, Vol.36, No. 11, 1998, pp. 2117-2123.
[5] K. Hall, J. P. Thomas, and E. Dowell, "Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows," AIAA Journal, Vol. 38, No. 10, 2000, pp. 1853-1862.
[6] T. Kim, and J. E. Bussoletti, "An Optimal Reduced-Order Aeroelastic Modeling Based on a Response-Based Modal Analysis of Unsteady CFD Models," AIAA-2001-1525, 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials conference, Seattle, WA, April 2001.
[7] W. A. Silva, "Application of Nonlinear Systems Theory to Transonic Unsteady Aerodynamic Responses," Journal of Aircraft, Vol. 30, No. 5, 1993, pp. 660-668.
[8] D. E. Raveh, "Identification of Computational Fluid Dynamic Based Unsteady Aerodynamic Models for Aeroelastic Analysis," Journal of Aircraft, Vol. 41, No. 3, 2004, pp. 620-632.
[9] T. Kim, M. Hong, K. G. Bhatia, and G. Sengupta, "Aeroelastic Model Reduction for Affordable Computational Fluid Dynamics-Based Flutter Analysis," AIAA Journal, Vol. 43, No. 12, 2005, pp. 2487-2495.
[10] K. K. Gupta, and C. Bach, "Systems Identification Approach for a Computational-Fluid-dynamics Based Aeroelastic Analysis," AIAA Journal, Vol. 45, No. 12, 2007, pp. 2820-2827.
[11] Kim, T., "New System Identification for Coupled Fluid-Structure Systems: Aerodynamics is Aeroelasticity minus Structure," IFASD-2009-073, International Forum on Aeroelasticity and Structural Dynamics, Seattle, WA, June 2009.
[12] Kim, T., "System Identification for Coupled Fluid-Structures: Aerodynamics is Aeroelasticity minus Structure," AIAA Journal, Volume 49, No. 3, 2011, pp. 503-512.