Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-25T22:47:57.288Z Has data issue: false hasContentIssue false

A pulse size estimation method for reduced-order models*

Published online by Cambridge University Press:  21 November 2016

L.M. Griffiths
Affiliation:
University of Bristol, Department of Aerospace Engineering, Bristol, UK
A.L. Gaitonde
Affiliation:
University of Bristol, Department of Aerospace Engineering, Bristol, UK
D.P. Jones*
Affiliation:
University of Bristol, Department of Aerospace Engineering, Bristol, UK
M.I. Friswell
Affiliation:
University of Swansea, College of Engineering, Swansea, UK

Abstract

Model-Order Reduction (MOR) is an important technique that allows Reduced-Order Models (ROMs) of physical systems to be generated that can capture the dominant dynamics, but at lower cost than the full order system. One approach to MOR that has been successfully implemented in fluid dynamics is the Eigensystem Realization Algorithm (ERA). This method requires only minimal changes to the inputs and outputs of a CFD code so that the linear responses of the system to unit impulses on each input channel can be extracted. One of the challenges with the method is to specify the size of the input pulse. An inappropriate size may cause a failure of the code to converge due to non-physical behaviour arising during the solution process. This paper addresses this issue by using piston theory to estimate the appropriate input pulse size.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Electronic supplementary information (ESI) available: Figure data can be found in a data repository (DOI: 10.5523/bris.mjzvu4runkof1eb3sy8sd28j8)

References

REFERENCES

1. Dowell, E.H. and Hall, K.C. Modelling of fluid-structure interaction, Annual Review Fluid Mechanics, 2001, 33, pp 445490.Google Scholar
2. Antoulas, A.C. Approximation of Large-Scale Dynamical Systems, 2005, Advances in Design and Control, SIAM, Philadelphia, Pennsylvania, US.Google Scholar
3. Juang, J-N. and Pappa, R.S. An eigensystem realization algorithm for modal parameter identification and model reduction, J Guidance, Control and Dynamics, 1985, 8, (5), pp 620627.Google Scholar
4. Kung, S.-Y. A new identification and model reduction algorithm via singular value decomposition, Proceedings of the 12th Asilomar Conference on Circuits, Systems and Computers, 1978.Google Scholar
5. Silva, W.A. Discrete-Time Linear and Nonlinear Aerodynamic Impulse Responses for Efficient CFD Analyses, PhD Thesis, 1997, Department of Applied Science, College of William and Mary, Virginia, US.Google Scholar
6. Silva, W.A. and Raveh, D.E. Development of unsteady aerodynamic state-space models from CFD-based pulse responses, 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Paper No AIAA-2001-1213, 2001.Google Scholar
7. Gaitonde, A.L. and Jones, D.P. Reduced order state-space models from the pulse responses of a linearised CFD scheme, Int J Numerical Methods in Fluids, 2003, 42, pp 581606.CrossRefGoogle Scholar
8. Ma, Z., Ahuja, S. and Rowley, C. Reduced order models for control of fluids using the Eigensystem Realization Algorithm, Theoretical and Computational Fluid Dynamics, 2011, 25, pp 233247.Google Scholar
9. Wales, C.J., Gaitonde, A.L. and Jones, D.P. Stabilisation of reduced order models via restarting, Int J Numerical Methods in Fluids, 2013, 83, pp 578599.Google Scholar
10. Griffiths, L. Reduced Order Model Updating, PhD Thesis, 2014, University of Bristol, Bristol, UK.Google Scholar
11. Jameson, A., Schmidt, W. and Turkel, E. Numerical solution of the Euler equations by finite volume method using Runge-Kutta time-stepping schemes, AIAA 14th Fluid and Plasma Dynamic Conference, Paper No AIAA-1981-1259, 1981.Google Scholar
12. Kroll, N. and Jain, R.K. Solution of two-dimensional Euler equations - Experience with a finite volume code, Forschungsbericht, DFVLR-FB 87-41, 1987, Braunschweig, Germany.Google Scholar
13. Gaitonde, A.L. A dual time method for the solution of the unsteady Euler equations, Aeronautical J, 1994, 98, Article 978.Google Scholar
14. Jameson, A.J. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings, Paper No AIAA-91-1596 1991.CrossRefGoogle Scholar
15. Arnone, A., Liou, M.S. and Povinelli, L. Integration of Navier-Stokes equations using dual time stepping and a multigrid method, AIAA J, 1995, 33.Google Scholar
16. Gaitonde, A.L. and Jones, D.P. Study of linear response identification techniques and reduced order model generation for a 2D CFD scheme, Int J Numerical Methods in Fluids, 2006, 52, (12), pp 13611402.Google Scholar
17. Gaitonde, A.L. and Jones, D.P. Solutions of the 2D linearised unsteady Euler equations on moving meshes, Proceedings of the Institution of Mechanical Engineering, Part G, J Aerospace Engineering, 2002, 216, pp 89104.Google Scholar
18. Wales, C., Gaitonde, A.L. and Jones, D.P. Stabilisation of reduced order models via restarting. Int J Numerical Methods Fluids, 2013, 73, (6), pp 78599.Google Scholar
19. Jones, D., Roberts, I. and Gaitonde, A. Identification of limit-cycles for piecewise non-linear aeroelastic systems, J Fluids and Structures, 2007, 23, (7).Google Scholar
20. Aplevich, J.D. The Essentials of Linear State-Space Systems, 2000, Wiley, New York, US.Google Scholar
21. Conner, M., Virgin, L. and Dowell, E. Accurate numerical integration of state-space models for aeroelastic systems with freeplay, AIAA J, 1996, 34, pp 22022205.Google Scholar
22. Lin, W. and Cheng, W. Nonlinear flutter of loaded lifted surfaces (i) & (ii), J Chinese Society of Mechanical Engineers, 1993, 14, pp 446466.Google Scholar
23. Gaitonde, A.L. and Jones, D.P. Calculations with ERA based reduced order aerodynamic models, AIAA 24th Applied Aerodynamics Conference, Paper No AIAA-2006-2999, 2006.Google Scholar
24. Griffiths, L., Jones, D. and Friswell, M. Pulse sizing for constructing reduced order models of the Euler equations, International Forum on Aeroelasticity and Structural Dynamics conference, IFASD-2011-195, 2011.Google Scholar
25. Ashley, H. and Zartarian, G., Piston theory - a new aerodynamic tool for the aeroelastician, J Aeronautical Sciences, 1956, 23, pp 11091118.Google Scholar
26. Lighthill, M.J. Oscillating airfoils at high Mach number, J Aeronautical Sciences, 1953, 20, (6), pp 402406.CrossRefGoogle Scholar
27. Van Dyke, M.D. Supersonic flow past oscillating airfoils including nonlinear thickness effects, NACA Technical Note 2982, 1953.Google Scholar
28. Zhang, W., Ye, Z., Zhang, C. and Liu, F. Supersonic flutter analysis based on a local piston theory, AIAA J, 2009, 47, (10), pp 23212328.Google Scholar
29. Landahl, M., Mollo-Christensen, E.L. and Ashley, H. Parametric studies of viscous and nonviscous unsteady flows, O.S.R. Technical Report 55-13, 1955.Google Scholar