Abstract
We present an adaptive finite element method for time-resolved simulation of aerodynamics without any turbulence-model parameters, which is applied to a benchmark problem from the HiLiftPW-3 workshop to compute the flow past a JAXA Standard Model (JSM) aircraft model at realistic Reynolds numbers. The mesh is automatically constructed by the method as part of an adaptive algorithm based on a posteriori error estimation using adjoint techniques. No explicit turbulence model is used, and the effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of a skin friction. In the case of very high Reynolds numbers, we approximate the small skin friction by zero skin friction, corresponding to a free-slip boundary condition, which results in a computational model without any model parameter to be tuned, and without the need for costly boundary-layer resolution. We introduce a numerical tripping-noise term to act as a seed for growth of perturbations; the results support that this triggers the correct physical separation at stall and has no significant pre-stall effect. We show that the methodology quantitavely and qualitatively captures the main features of the JSM experiment—aerodynamic forces and the stall mechanism—with a much coarser mesh resolution and lower computational cost than the state-of-the-art methods in the field, with convergence under mesh refinement by the adaptive method. Thus, the simulation methodology appears to be a possible answer to the challenge of reliably predicting turbulent-separated flows for a complete air vehicle.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- \(C_l\) :
-
lift coefficient (dimensionless)
- \(C_d\) :
-
drag coefficient (dimensionless)
- \(C_p\) :
-
pressure coefficient (dimensionless)
- h :
-
diameter of tetrahedron in finite element mesh (m)
- k :
-
time step (s)
- \(\mathbf {n}\) :
-
normal unit vector (dimensionless)
- P :
-
computed pressure (Pa)
- p :
-
pressure (Pa)
- q :
-
pressure test function (Pa)
- Re :
-
Reynolds number (dimensionless)
- t :
-
time variable (s)
- T :
-
end time (s)
- \(\mathbf {U}\) :
-
computed velocity (\({\mathrm{m}\,\mathrm{s}^{-1}}\))
- \(\mathbf {u}\) :
-
velocity (\({\mathrm{m}\,\mathrm{s}^{-1}}\))
- \(\mathbf {v}\) :
-
velocity test function (\({\mathrm{m}\,\mathrm{s}^{-1}}\))
- \(\mathbf {x}\) :
-
space variable (m)
- \(\alpha \) :
-
angle of attack (dimensionless)
- \(\beta \) :
-
friction parameter (\({\mathrm{kg}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}}\))
- \(\nu \) :
-
kinematic viscosity (\({\mathrm{m}^{2}\,\mathrm{s}^{-1}}\))
- \(\mathbf {\tau }\) :
-
tangent unit vector (dimensionless)
References
FEniCS (2003) Fenics project. http://www.fenicsproject.org
Hoffman, J.: Computation of mean drag for bluff body problems using adaptive dns/les. SIAM J. Sci. Comput. 27(1), 184–207 (2005)
Hoffman, J.: Adaptive simulation of the turbulent flow past a sphere. J. Fluid Mech. 568, 77–88 (2006)
Hoffman, J.: Efficient computation of mean drag for the subcritical flow past a circular cylinder using general galerkin g2. Int. J. Numer. Meth. Fluids 59(11), 1241–1258 (2009)
Hoffman, J., Jansson, N. (2010) A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions. Ercoftac series, vol. 16. Springer, Dordrecht
Hoffman, J., Johnson, C.: Computational Turbulent Incompressible Flow: Applied Mathematics Body and Soul, vol. 4. Springer, Berlin (2006)
Hoffman, J., Johnson, C.: A new approach to computational turbulence modeling. Comput. Methods Appl. Mech. Eng. 195, 2865–2880 (2006)
Hoffman, J., Johnson, C.: Computational turbulent incompressible flow. In: Applied Mathematics: Body and Soul, vol. 4. Springer, Berlin (2007)
Hoffman, J., Johnson, C.: Resolution of d’alembert’s paradox. J. Math. Fluid Mech., 10 Dec 2008. (Published Online First at www.springerlink.com)
Hoffman, J., Jansson, J., Jansson, N.: Fenics-hpc: automated predictive high-performance finite element computing with applications in aerodynamics. In: Proceedings of the 11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015. Lecture Notes in Computer Science (2015)
Hoffman, J., Jansson, J., Stöckli, M.: Unified continuum modeling of fluid-structure interaction. Math. Models Methods Appl. Sci. (2011)
Hoffman, J., Jansson, J., de Abreu, R.V., Degirmenci, N.C., Jansson, N., Müller, K., Nazarov, M., Spühler, J.H.: Unicorn: parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry. Comput. Fluids 80, 310–319 (2013)
Hoffman, J., Jansson, J., Degirmenci, C., Jansson, N., Nazarov, M.: Unicorn: A Unified Continuum Mechanics Solver, Chap. 18. Springer, Berlin (2012)
Hoffman, J., Jansson, J., Jansson, N., Abreu, R.V.D.: Towards a parameter-free method for high reynolds number turbulent flow simulation based on adaptive finite element approximation. Comput. Methods Appl. Mech. Eng. 288, 60–74 (2015)
Hoffman, J., Jansson, J., Jansson, N., Nazarov, M.: Unicorn: a unified continuum mechanics solver. In: Automated Solutions of Differential Equations by the Finite Element Method. Springer, Berlin (2011)
Hoffman, J., Jansson, J., Jansson, N., Johnson, C., de Abreu, R.V.: Turbulent flow and fluid-structure interaction. In: Automated Solutions of Differential Equations by the Finite Element Method. Springer, Berlin (2011)
Hoffman, J., Jansson, J., Jansson, N., De Abreu, R.V., Johnson, C.: Computability and adaptivity in CFD. In: Stein, E., de Horz, R., Hughes, T.J.R. (eds.) Encyclopedia of Computational Mechanics (2016)
Houzeaux, G., Vázquez, M., Aubry, R., Cela, J.: A massively parallel fractional step solver for incompressible flows. J. Comput. Phys. 228(17), 6316–6332 (2009)
Huang, L., Huang, P.G., LeBeau, R.P.: Numerical study of blowing and suction control mechanism on naca 0012 airfoil. AIAA J. Aircr. (2004)
Hunt, J.C., Wray, A.A., Moin, P.: Eddies, streams, and convergence zones in turbulent flows (1988)
Jansson, N., Hoffman, J., Jansson, J.: Framework for massively parallel adaptive finite element computational fluid dynamics on tetrahedral meshes. SIAM J. Sci. Comput. 34(1), C24–C41 (2012)
Kirby, R.C.: FIAT: Numerical Construction of Finite Element Basis Functions, Chap. 13. Springer, Berlin (2012)
Logg, A., Mardal, K.-A., Wells, G.N., et al.: Automated Solution of Differential Equations by the Finite Element Method. Springer, Berlin (2012)
Logg, A., Ølgaard, K.B., Rognes, M.E., Wells, G.N.: FFC: The FEniCS Form Compiler, Chap. 11. Springer, Berlin (2012)
Mellen, C.P., Frölich, J., Rodi, W.: Lessons from lesfoil project on large-eddy simulation of flow around an airfoil. AIAA J. 41, 573–581 (2003)
Moin, P., You, D.: Active control of flow separation over an airfoil using synthetic jets. J. Fluids Struct. 24(8), 1349–1357 (2008)
Piomelli, U., Balaras, E.: Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–374 (2002)
Rumsey, C.: 3rd AIAA CFD High Lift Prediction Workshop (HiLiftPW-2) (2017). http://hiliftpw.larc.nasa.gov/
Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer, Berlin (2005)
Schlatter, P., Orlu, R.: Turbulent boundary layers at moderate reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 534 (2012)
Shan, H., Jiang, L., Liu, C.: Direct numerical simulation of flow separation around a naca 0012 airfoil. Comput. Fluids 34, 10961114 (2005)
Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., Mavriplis, D.: Cfd vision 2030 study: a path to revolutionary computational aerosciences (2014)
Spalart, P.R.: Detached-eddy simulation. Annu Rev. Fluid Mech. 41, 181–202 (2009)
Vilela de Abreu, R., Jansson, N., Hoffman, J.: Adaptive computation of aeroacoustic sources for a rudimentary landing gear. Int. J. Numer. Meth. Fluids 74(6), 406–421 (2014)
Witherden, F.D., Jameson, A.: Future directions of computational fluid dynamics. In: 23rd AIAA Computational Fluid Dynamics Conference, p. 3791 (2017)
Acknowledgements
This research has been supported by the European Research Council, the H2020 MSO4SC grant, the Swedish Research Council, the Swedish Foundation for Strategic Research, the Swedish Energy Agency, the Basque Excellence Research Center (BERC 2014–2017) program and ELKARTEK GENTALVE project by the Basque Government, the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation SEV-2013-0323 and the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2013–40824 and La Caixa. We acknowledge the Swedish National Infrastructure for Computing (SNIC) at PDC—Center for High-Performance Computing for granting us access to the supercomputer resources Beskow.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Jansson, J., Krishnasamy, E., Leoni, M., Jansson, N., Hoffman, J. (2018). Time-Resolved Adaptive Direct FEM Simulation of High-Lift Aircraft Configurations. In: López Mejia, O., Escobar Gomez, J. (eds) Numerical Simulation of the Aerodynamics of High-Lift Configurations. Springer, Cham. https://doi.org/10.1007/978-3-319-62136-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-62136-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62135-7
Online ISBN: 978-3-319-62136-4
eBook Packages: EngineeringEngineering (R0)