Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-27T09:05:57.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient aerodynamic derivative calculation in three-dimensional transonic flow

Published online by Cambridge University Press:  10 July 2017

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

Abstract

One key task in computational aeroelasticity is to calculate frequency response functions of aerodynamic coefficients due to structural excitation or external disturbance. Computational fluid dynamics methods are applied for this task at edge-of-envelope flow conditions. Assuming a dynamically linear response around a non-linear steady state, two computationally efficient approaches in time and frequency domain are discussed. A non-periodic, time-domain function can be used, on the one hand, to excite a broad frequency range simultaneously giving the frequency response function in a single non-linear, time-marching simulation. The frequency-domain approach, on the other hand, solves a large but sparse linear system of equations, resulting from the linearisation about the non-linear steady state for each frequency of interest successively. Results are presented for a NACA 0010 aerofoil and a generic civil aircraft configuration in very challenging transonic flow conditions with strong shock-wave/boundary-layer interaction in the pre-buffet regime. Computational cost savings of up to 1 order of magnitude are observed in the time domain for the all-frequencies-at-once approach compared with single-frequency simulations, while an additional order of magnitude is obtained for the frequency-domain method. The paper demonstrates the readiness of computational aeroelasticity tools at edge-of-envelope flow conditions.

Type
Research Article
Information
The Aeronautical Journal , Volume 121 , Issue 1244 , October 2017 , pp. 1464 - 1478
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.)

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.CrossRefGoogle Scholar
2. Brink-Spalink, J. and Bruns, J.M. Correction of unsteady aerodynamic influence coefficients using experimental or CFD data, International Forum on Aeroelasticity and Structural Dynamics (IFASD), IFASD-2001-034, 2001, Madrid, Spain.CrossRefGoogle Scholar
3. Thormann, R. and Dimitrov, D. Correction of aerodynamic influence matrices for transonic flow, CEAS Aeronautical J, 2014, 1, (1), pp 1-12.Google Scholar
4. Rodden, W. Theoretical and Computational Aeroelasticity, chap. 7.4, Crest Publishing, 5th ed, 2013.Google Scholar
5. Seidel, D.A., Bennet, R.M. and Whitlow, W. An exploratory study of finite-difference grids for transonic unsteady aerodynamics, AIAA 1983-0503, 1983, Reno, USA.CrossRefGoogle Scholar
6. Silva, W. and Raveh, D.E. Development of unsteady aerodynamic state-space models from CFD-based pulse responses, AIAA-2001-1213, 2001, Anaheim, USA.CrossRefGoogle Scholar
7. Thormann, R. and Widhalm, M. Forced motion simulations using a linear frequency domain solver for a generic transport aircraft, International Forum on Aeroelasticity and Structural Dynamics (IFASD), IFASD-2013-17A, 2013, Royal Aeronautical Society, Bristol, UK.Google Scholar
8. Hall, K.C. and Clark, W.S. Linearized euler predictions of unsteady aerodynamic loads in cascades, AIAA J, 1993, 31, (3), pp 540-550.CrossRefGoogle Scholar
9. Clark, W.S. and Hall, K.C. A time-linearized analysis of stall flutter, J of Turbomachinery, 2000, 122, (3), pp 467-476.CrossRefGoogle Scholar
10. Dufour, G., Sicot, F., Puigt, G., Liauzun, C. and Dugeai, A. Contrasting the harmonic balance and linearized methods for oscillating-flap simulations. AIAA J, April 2010, 48, (4), pp 788-797.CrossRefGoogle Scholar
11. Thormann, R., Nitsche, J. and Widhalm, M. Time-linearized simulation of unsteady transonic flows with shock-induced separation, European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 2012, Vienna, Austria.Google Scholar
12. Pechloff, A. and Laschka, B. Small disturbance Navier-Stokes computations for low-aspect-ratio wing pitching oscillations. J Aircr, 2010, 47, (3), pp 737-753.CrossRefGoogle Scholar
13. 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.CrossRefGoogle Scholar
14. Revalor, Y., Daumas, L. and Forestier, N. Industrial use of CFD for loads and aero-servo-elastic stability computations at dassault aviation, International Forum on Aeroelasticity and Structural Dynamics (IFASD), IFASD-2011-061, June 2011, Paris, France.Google Scholar
15. Widhalm, M., Thormann, R. and Hübner, A.R. Linear frequency domain predictions of dynamic derivatives for the DLR F12 wind tunnel model, Proceedings of the 6th European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2012, September 2012, Vienna, Austria.Google Scholar
16. Lee, B.H.K. Self-sustained shock oscillations on airfoils at transonic speeds, Progress in Aerospace Sciences, February 2001, 37, (2), pp 147-196.CrossRefGoogle Scholar
17. Xu, S., Timme, S. and Badcock, K.J. Enabling off-design linearised aerodynamics analysis using Krylov subspace recycling technique, Computers & Fluids, 2016, 140, pp 385-396.CrossRefGoogle Scholar
18. McCracken, A.J., Ronch, A.D., Timme, S. and Badcock, K.J. Solution of linear systems in Fourier-based methods for aircraft applications, Int J of Computational Fluid Dynamics, 2013, 27, (2), pp 79-87.CrossRefGoogle Scholar
19. Gerhold, T., Galle, M., Friedrich, O. and Evans, J. Calculation of complex three-dimensional configurations employing the DLR TAU-Code, AIAA-1997-0167, 1997, Reno, USA.CrossRefGoogle Scholar
20. Schwamborn, D., Gerhold, T. and Heinrich, R. The DLR TAU-Code: Recent applications in research and industry, Proceedings of the 3rd European Conference on Computational Fluid Dynamics, ECCOMAS CFD, 2006, Egmond aan Zee, Netherlands.Google Scholar
21. Jameson, A., Schmidt, W. and Turkel, E. Numerical solutions of the euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA-1981-1259, 1981, Palo Alto, USA.CrossRefGoogle Scholar
22. Spalart, P.R. and Allmaras, S.R. A one-equation turbulence model for aerodynamic flows, Recherche Aerospatiale, 1994, (1), pp 5-21.Google Scholar
23. Jameson, A. Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings, AIAA-1991-1596, 1991, Honolulu, USA.CrossRefGoogle Scholar
24. Theodorsen, T. General theory of aerodynamic instability and the mechanism of flutter, NACA Report, 1935, (496), pp 413-433.Google Scholar
25. Nitzsche, J. A numerical study on aerodynamic resonance in transonic separated flow, International Forum on Aeroelasticity and Structural Dynamics (IFASD), IFASD-2009-126, 2009, Seattle, USA.Google Scholar
26. Iovnovich, M. and Raveh, D. Transonic unsteady aerodynamics in the vicinity of shock-buffet instability, J of Fluids and Structures, 2012, 29, pp 131-142.CrossRefGoogle Scholar
27. Lawson, S., Greenwell, D. and Quinn, M. K. Characterisation of buffet on a civil aircraft wing, AIAA-2016-1309, 2016, San Diego, USA.CrossRefGoogle Scholar
28. Timme, S. and Thormann, R. Towards three-dimensional global stability analysis of transonic shock buffet, AIAA-2016-3848, 2016, Washington, USA.CrossRefGoogle Scholar
29. Martineau, D.G.S., Stokes, S., Munday, S.J., Jackson, A., Gribben, B.J. and Verhoeven, N. Anisotropic hybrid mesh generation for industrial RANS applications, AIAA-2006-534, 2006, Reno, USA.CrossRefGoogle Scholar
30. Sartor, F. and Timme, S. Reynolds-averaged Navier-Stokes simulations of shock buffet on half wing-body configuration, AIAA-2015-1939, 2015, Kissimmee, USA.CrossRefGoogle Scholar