Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows
Publication: Journal of Aerospace Engineering
Volume 25, Issue 4
Abstract
A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range , .
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Acknowledgments
This research has been partially supported by Airbus Operations under Contract No. A8208636G. The work by José M. Vega has also been supported by the Spanish Ministry of Education, under Grant No. TRA2010-18054. We are indebted to two anonymous referees for some useful comments on an previous version of the paper.
References
Akima, H. (1978). “A method of bivariate interpolation and smooth surface fitting for irregular distributed data points.” ACM Trans. Math. Softw., 4(2), 148–159.
Alonso, D., Vega, J. M., and Velazquez, A. (2010). “Reduced-order model for viscous aerodynamic flow past an airfoil.” AIAA J., 48(9), 1946–1958.
Alonso, D., Velazquez, A., and Vega, J. M. (2009). “A method to generate computationally efficient reduced order models.” Comput. Methods Appl. Mech. Eng., 198(33–36), 2683–2691.
Bache, E., Vega, J. M., and Velazquez, A. (2010). “Model reduction in the back step fluid–thermal problem with variable geometry.” Int. J. Therm. Sci., 49(12), 2376–2384.
Ben Kheli, S., Gervois, J. L., Carrier, G., Moens, F., and Viscat, P. (2002). “Assessment of ELSA software through civil transport aircraft configurations.” Proc., EAS Aerospace Aerodynamics Research Conf., Engineering and Applied Science, Cambridge, U.K.
Cambier, L. and Gazaix, M. (2002). “ELSA: An efficient object-oriented solution to CFD complexity.” 40th AIAA Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, Reston, VA.
Couplet, M., Basdevant, C., and Sagaut, P. (2005). “Calibrated reduced-order POD-Galerkin system for fluid flow modelling.” J. Comput. Phys., 207(1), 192–220.
Dowell, E. H., and Hall, K. C. (2001). “Modeling of fluid-structure interaction.” Annu. Rev. Fluid Mech., 33, 445–490.
Edwards, J. R., and Chandra, S. (1996). “Comparison of eddy viscosity-transport turbulence models for three-dimensional, shock-separated flow fields.” AIAA J., 34(4), 756–763.
LeGresley, P. A., and Alonso, J. J. (2001). “Investigation of non-linear projection for POD based reduced order models for aerodynamics.” 39th AIAA Aerospace Sciences Meeting & Exhibit, American Institute of Aeronautics and Astronautics, Reston, VA.
Lieu, T., Farhat, C., and Lesoinne, M. (2006). “Reduced-order fluid/structure modeling of a complete aircraft configuration.” Comput. Methods Appl. Mech. Eng., 195(41–43), 5730–5742.
Lorente, L. (2009).“Generation and post-process of aerodynamic databases via SVD/POD methods.” Ph.D. thesis, Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain.
Lucia, D. J., Beran, P. S., and Silva, W. A. (2004). “Reduced-order modeling: New approaches for computational physics.” Prog. Aerosp. Sci., 40(1–2), 51–117.
Rapun, M. L., and Vega, J. M. (2010). “Reduced order models based on local POD plus Galerkin projection.” J. Comput. Phys., 229(8), 3046–3063.
Rempfer, D. (2003). “Low dimensional modeling and numerical simulation of transition in a simple shear flow.” Annu. Rev. Fluid Mech., 35, 229–265.
Shepard, D. (1968). “A two-dimensional interpolation function for irregularly-spaced data.” Proc., 1968 ACM National Conf., Association for Computing Machinery, New York.
Sirisup, S., and Karniadakis, G. E. (2005). “Stability and accuracy of periodic flow solutions obtained by POD-penalty method.” Physica D, 202(3–4), 218–237.
Sirisup, S., Karniadakis, G. E., Xiu, D., and Kevrekidis, I. G. (2005). “Equation-free/Galerkin-free POD-assisted computation of incompressible flows.” J. Comput. Phys., 207(2), 568–587.
Spalart, P. R., and Allmaras, S. R. (1992). “A one-equation turbulence model for aerodynamic flows.” 30th AIAA Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reston, VA.
Tannehill, J. C., Anderson, D. A., and Pletcher, R. H. (1997). Computational fluid mechanics and heat transfer, Taylor & Francis, Philadelphia.
Thomas, J. P., Dowell, E. H., and Hall, K. C. (2010). “Using automatic differentiation to create nonlinear reduced-order-model aerodynamic solver.” AIAA J., 48(1), 19–24.
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© 2012 American Society of Civil Engineers.
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Received: Dec 13, 2010
Accepted: Jun 24, 2011
Published online: Jun 27, 2011
Published in print: Oct 1, 2012
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