Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-11T15:03:01.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Rapid gust response simulation of large civil aircraft using computational fluid dynamics

Published online by Cambridge University Press:  21 September 2017

P. Bekemeyer ,
R. Thormann  and
S. Timme
P. Bekemeyer*
Affiliation:
School of Engineering, University of Liverpool, United Kingdom
R. Thormann
Affiliation:
School of Engineering, University of Liverpool, United Kingdom
S. Timme
Affiliation:
School of Engineering, University of Liverpool, United Kingdom
*
philipp.bekemeyer@liverpool.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Several critical load cases during the aircraft design process result from atmospheric turbulence. Thus, rapidly performable and highly accurate dynamic response simulations are required to analyse a wide range of parameters. A method is proposed to predict dynamic loads on an elastically trimmed, large civil aircraft using computational fluid dynamics in conjunction with model reduction. A small-sized modal basis is computed by sampling the aerodynamic response at discrete frequencies and applying proper orthogonal decomposition. The linear operator of the Reynolds-averaged Navier-Stokes equations plus turbulence model is then projected onto the subspace spanned by this basis. The resulting reduced system is solved at an arbitrary number of frequencies to analyse responses to 1-cos gusts very efficiently. Lift coefficient and surface pressure distribution are compared with full-order, non-linear, unsteady time-marching simulations to verify the method. Overall, the reduced-order model predicts highly accurate global coefficients and surface loads at a fraction of the computational cost, which is an important step towards the aircraft loads process relying on computational fluid dynamics.

Keywords

ROMCFDGust responsePODlarge civil aircraft
Type
Research Article
Information
The Aeronautical Journal , Volume 121 , Issue 1246 , December 2017 , pp. 1795 - 1807
Copyright
Copyright © Royal Aeronautical Society 2017 

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

This paper first appeared at the RAeS Applied Aerodynamics Conference, 19-21 July 2016, Bristol, UK.

References

REFERENCES

1. Albano, E. and Rodden, W.P. A doublet lattice method for calculating lift distribution on oscillating surfaces in subsonic flow, AIAA J, 1969, 2, (7), pp 279-285.Google Scholar
2. Giesing, J.P., Rodden, W.P. and Stahl, B. Sears function and lifting surface theory for harmonic gust fields, J Aircr, 1970, 7, pp 252-255.Google Scholar
3. Kier, T. Comparison of unsteady aerodynamic modelling methodologies with respect to flight loads analysis, AIAA Atmospheric Flight Mechanics Conference and Exhibit, 2005, AIAA 2005-6027, San Francisco, CA, US.CrossRefGoogle Scholar
4. Dimitrov, D. and Thormann, R. DLM-correction methods for aerodynamic gust response prediction, International Forum on Aeroelasticity and Structural Dynamics (IFASD), 2013, IFASD 2013-24C, Bristol, England.Google Scholar
5. Raveh, D.E. CFD-based models of aerodynamic gust response, J Aircr, 2007, 44, (3), pp 888-897.CrossRefGoogle Scholar
6. Reimer, L., Ritter, M., Heinrich, R. and Krüger, W. CFD-based gust load analysis for a free-flying flexible passenger aircraft in comparison to a DLM-based approach, 22nd AIAA Computational Fluid Dynamics Conference, 2015, AIAA 2015-2455, Dallas, TX, US.Google Scholar
7. Clark, W.S. and Hall, K.C. A time-linearized analysis of stall flutter, J Turbomachinery, 2000, 122, (3), pp 467-476.Google Scholar
8. Weishäupl, C. and Laschka, B. Small disturbance euler simulations for delta wing unsteady flows due to harmonic oscillations, J Aircr, 2004, 41, (4), pp 782-789.Google Scholar
9. Thormann, R. and Widhalm, M. Linear-frequency-domain predictions of dynamic-response data for viscous transonic flows, AIAA J, 2013, 51, (11), pp 2540-2557.Google Scholar
10. Bekemeyer, P., Thormann, R. and Timme, S. Frequency-domain gust response simulation using computational fluid dynamics, AIAA J, 2017, 55, (7), pp 2174-2185.Google Scholar
11. Lucia, D.J., Beran, P.S. and Silva, W.A. Reduced-order modeling: New approaches for computational physics, Progress in Aerospace Sciences, 2004, 40, (1-2), pp 51-117.CrossRefGoogle Scholar
12. Taira, K., Brunton, S.L., Dawson, S.T.M., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. and Ukeiley, L.S. Model analysis of fluid flows: An overview, AIAA J, 2017, accepted for publication.CrossRefGoogle Scholar
13. Lumley, J.L. The structures of inhomogeneous turbulent flow, Atmospheric Turbulence and Radio Wave Propagation, 1967, pp 166-178.Google Scholar
14. Kim, T. Frequency-domain Karhunen-Loève method and its application to linear dynamic systems, AIAA J, 1998, 36, (11), pp 2117-2123.Google Scholar
15. Hall, K.C., Thomas, J.P. and Dowell, E.H. Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows, AIAA J, 2000, 38, (10), pp 1853-1862.Google Scholar
16. Bekemeyer, P. and Timme, S. Reduced order gust response simulation using computational fluid dynamics, 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2016, AIAA 2016-1485, San Diego, CA, US.Google Scholar
17. Thormann, R., Bekemeyer, P. and Timme, S. Reduced order modelling of gust analysis using computational fluid dynamics, European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 2016, ECCOMAS 2016–5441, Crete, Greece.Google Scholar
18. Bekemeyer, P. and Timme, S. Reduced order transonic aeroelastic gust response simulation of large aircraft, 35th AIAA Applied Aerodynamics Conference, 2017, AIAA Paper 2017-4361, Denver, CO.CrossRefGoogle Scholar
19. Rodden, W.P. Theoretical and Computational Aeroelasticity, 1st ed., 2011, Crest Publishing.Google Scholar
20. Bekemeyer, P., Thormann, R. and Timme, S. Linearised frequency domain gust response analysis of large civil aircraft, European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 2016, ECCOMAS 2016-5316, Crete, Greece.Google Scholar
21. Holmes, P., Lumley, J.L., Berkooz, G. and Rowley, C.W. Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd ed., 2012, Cambridge Univ. Press.Google Scholar
22. Berkooz, G., Holmes, P. and Lumley, J.L. The proper orthogonal decomposition in the analysis of turbulent flows, Annual Review of Fluid Mech, 1993, 25, pp 539-575.Google Scholar
23. Sirovich, L. Turbulence and the dynamics of coherent structures, Parts I-III, Quarterly of Applied Mathematics, 1987, XLV, pp 561-590.Google Scholar
24. Schwamborn, D., Gerhold, T. and Heinrich, R. The DLR TAU-code: Recent applications in research and industry, European Conference on Computational Fluid Dynamics, 2006, ECCOMAS CFD, Egmond aan Zee, The Netherlands.Google Scholar
25. Spalart, P.R. and Allmaras, S.R. A one-equation turbulence model for aerodynamic flows, Recherche Aerospatiale, 1994, 1, pp 5-21.Google Scholar
26. Parameswaran, V. and Baeder, J.D. Indicial aerodynamics in compressible flow-direct computational fluid dynamic calculations, J Aircr, 1997, 34, (1), pp 131-133.Google Scholar
27. Jameson, A., Schmidt, W. and Turkel, E. Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, 14th Fluid and Plasma Dynamic Conference, 1981, AIAA Paper 1981-1259, Palo Alto, CA, US.Google Scholar
28. Dwight, R. An implicit LU-SGS scheme for finite-volume discretizations of the Navier-Stokes equations on hybrid grids, DLR-FB-2005-05, 2006, Braunschweig, Germany.Google Scholar
29. Xu, S., Timme, S. and Badcock, K.J. Enabling off-design linearised aerodynamics analysis using Krylov subspace recycling technique, Comput. Fluids, 2016, 140, pp 385-396.Google Scholar
30. Saad, Y. Iterative Methods for Sparse Linear Systems, 2nd ed., 2003, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, US.Google Scholar
31. Broyden, C.G. A class of methods for solving nonlinear simultaneous equations, Mathematics of Computation (American Mathematical Society), 1965, 19, pp 577-593.Google Scholar
32. European Aviation Regulations. Certification Specifications for Large Aeroplanes (CS-25), European Aviation Safety Agency (EASA), 2015, pp 63-65.Google Scholar
33. Pagliuca, G., Bekemeyer, P., Thormann, R. and Timme, S. Model reduction for gust load analysis of free-flying aircraft, International Forum on Aeroelasticity and Structural Dynamics (IFASD), 2017, IFASD-2017-148, Como, Italy.Google Scholar