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Implicit method for the time marching analysis of flutter

Part of: 75 year anniversary of Aeronautical Engineering at Glasgow University

Published online by Cambridge University Press:  04 July 2016

G. S. L. Goura ,
K. J. Badcock ,
M. A. Woodgate  and
B. E. Richards
G. S. L. Goura
Affiliation:
Aerospace Engineering Department , University of Glasgow, UK
K. J. Badcock
Affiliation:
Aerospace Engineering Department , University of Glasgow, UK
M. A. Woodgate
Affiliation:
Aerospace Engineering Department , University of Glasgow, UK
B. E. Richards
Affiliation:
Aerospace Engineering Department , University of Glasgow, UK
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Abstract

This paper evaluates a time marching simulation method for flutter which is based on a solution of the Euler equations and a linear modal structural model. Jameson’s pseudo time method is used for the time stepping, allowing sequencing errors to be avoided without incurring additional computational cost. Transfinite interpolation of displacements is used for grid regeneration and a constant volume transformation for inter-grid interpolation. The flow pseudo steady state is calculated using an unfactored implicit method which features a Krylov subspace solution of an approximately linearised system. The spatial discretisation is made using Osher’s approximate Riemann solver with MUSCL interpolation. The method is evaluated against available results for the AGARD 445.6 wing. This wing, which is made of laminated mahogany, was tested at NASA Langley in the 1960s and has been the standard test case for simulation methods ever since. The structural model in the current work was built in NASTRAN using homogeneous plate elements. The comparisons show good agreement for the prediction of flutter boundaries. The solution method allows larger time steps to be taken than other methods.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 105 , Issue 1046 , April 2001 , pp. 199 - 214
Copyright
Copyright © Royal Aeronautical Society 2001 

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References

1. Melville, R.B., Morton, S.A. and Rizzetta, D.P. Implementation of a fully-implicit aeroelastic Navier-Stokes solver, 13th computational fluid dynamics conference, 29 June-2 July, 1997, Snowmass Village, CO, AIAA paper 97-2039.Google Scholar
2. Morton, S.A. and Beran, P.S. Hopf bifurcation analysis applied to deforming airfoils at transonic speeds, 13th computational fluid dynamics conference, 29 June-2 July, 1997, Snowmass, CO, AIAA paper 97-1772.Google Scholar
3. Jameson, A. Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings, 1991, technical report, AIAA 91-1596.Google Scholar
4. Badcock, K.J., Goura, G.S.L. and Richards, B.E. Investigation of sequencing effects on the simulation of fluid-structure interaction, High Performance Computing, Allan, R.J. et al (Eds), 1998, pp 385–394, Plenum Publishing Corp.Google Scholar
5. Dubuc, L., Cantariti, F., Woodgate, M., Gribben, B., Badcock, K.J. and Richards, B.E. A grid deformation technique for unsteady flow computations, Int J Num Meth Fluids, 2000, 32, pp 285–311.Google Scholar
6. Nakahashi, K. and Deiwert, G.S. Self adaptive grid method with application to airfoil flow, AIAA J, 1987, 25, pp 513–520.Google Scholar
7. Harder, R.L. and Desmarais, R.N. Interpolation using surface splines, J Aircr, 1972,9, (2), pp 189–191.Google Scholar
8. Appa, K. Finite-surface spline, J Aircr, 1989, 26, (5), pp 495–496.Google Scholar
9. Hounjet, M.H.L. and Meijer, J.J. Evaluation of elastomechanical and aerodynamic data transfer methods for non-planar configurations in computational aeroelastic analysis, Proceedings of International Forum on Aeroelasticity and Structural Dynamics, RAeS, 1995, pp 10.1–10.25.Google Scholar
10. Chen, P.C. and Jadic, I. Interfacing of fluid and structural models via innovative boundary element method, AIAA J, 1998, 36, pp 282–287.Google Scholar
11. Goura, G.S.L., Badcock, K.J. and Richards, B.E. Tools for investigation of fluid-structure interaction, CEAS/AIAA/ICASE/NASA meeting on aeroelasticity and structural dynamics, June 1999, Norfolk, VA, USA.Google Scholar
12. Yates, E.C. AGARD standard aeroelastic configurations for dynamic response I: Wing 445.6, AGARD Report 765, 1988.Google Scholar
13. ZAERO Applications Manual, Version 3.2. Zona Technology, Arizona.Google Scholar
14. Da Silva, R.G.A and De Faria Mello, O.A. Prediction of transonic flutter using Nastran with aerodynamic coefficients tuned to Navier Stokes computations. CEAS/AIAA/ICASE/NASA meeting on aeroelasticity and structural dynamics, June 1999, Norfolk, VA, USA.Google Scholar
15. Batina, J.T., Bennett, R.M., Seidel, D.A., Cunningham, H.J. and Bland, S. Recent advances in transonic computational aeroelasticity, Computers and Fluids, 1998, 30, (172), pp 29–37.Google Scholar
16. Edwards, J.T. Calculated viscous and scale effects on transonic aeroelasticity, presented at AGARD SMP meeting on numerical unsteady aerodynamic and aeroelastic simulation, October 1997, Aalborg, Denmark, AGARD R-822.Google Scholar
17. Gupta, K.K. Development of a finite element aeroelastic analysis capability, J Aircr, 1996, 33, (5), pp 995-1,002.Google Scholar
18. Rausch, R.D., Batina, J.T. and Yang, H.T. Three-dimensional time- marching aeroelastic analyses using an unstructured-grid Euler method, AIAA J, 1993, 31, (9), pp 1,626-1,633.Google Scholar
19. Lesoinne, M. and Farhat, C. High order subiteration-free staggered algorithm for nonlinear transient aeroelastic problems, AIAA J, 1998, 36, (9), pp 1,754-1,757.Google Scholar
20. Osher, S. and Chakravarthy, S.R. Upwind schemes and boundary conditions with applications to Euler equations in general coordinates, J Computational Physics, 1983, 50, pp 447–481.Google Scholar
21. Cantariti, F., Dubuc, L., Gribben, B., Woodgate, M., Badcock, K.J. and Richards, B.E. Approximate Jacobians for the solution of the Euler and Navier-Stokes equations, Aerospace Engineering Report 5, 1997, Glasgow University, UK.Google Scholar
22. Badcock, K.J., Porter, S. and Richards, B.E. Unfactored multiblock methods: part I initial method development, Aerospace Engineering Report 11, 1995, Glasgow University, UK.Google Scholar
23. Gordon, W.J. and Hall, C.A., Construction of curvilinear coordinate systems and applications to mesh generation, Int J Num Meth Engr, 1973,7, pp 461–477.Google Scholar
24. Thomas, P.D. and Lombard, C.K. Geometric conservation law and its application to flow computations on moving grids, AIAA J, 1979, 17, pp 1,030-1,037.Google Scholar
26. Tidjeman, H. and Van-Nunen, J.W.G. Results of transonic wind tunnel meaurements on an oscillating wing with external store (data report), 1978, technical report 78030, NLR.Google Scholar
27. Van Nunen, J.W.G. and Tidjeman, H. Transonic wind tunnel tests of an oscillating wing with external store (parts i-iv), 1978, technical report 78106, NLR.Google Scholar
28. Geurts, E.G.M. F-5 wing and F5-wing + tip store, Verification and Validation Data for Computational Unsteady Aerodynamics, 2000, RTO-TR-26.Google Scholar
29. Badcock, K.J., Woodgate, M, Cantariti, F. and Richards, B. Solution of the unsteady Euler equations in three dimensions using a fully unfactored method, 2000, AIAA paper 2000-0919.Google Scholar
30. Cantariti, F., Woodgate, M., Badcock, K.J. and Richards, B.E. Solution of the Euler equations in three dimensions using a fully unfactored method, Aerospace Engineering Report 7, 1999, Glasgow University, Glasgow, UK. Google Scholar
31. Kolonay, R. M. Unsteady Aeroelastic Optimization in the Transonic Regime, December 1996, PhD dissertation, Purdue University.Google Scholar