Skip to main content Accesibility Help
×
×
Home

Multiple bifurcations of the flow over stalled airfoils when changing the Reynolds number

  • E. Rossi (a1), A. Colagrossi (a1) (a2), G. Oger (a1) and D. Le Touzé (a1)
Abstract

In the present study, the sudden changes of the flow field past stalled airfoils for small variations of the Reynolds number are investigated numerically. A vortex particle method has been used for the simulations in a two-dimensional framework. The most critical configurations found with this solver are verified through the comparison with the solution given by a mesh-based finite volume solver. The airfoils considered are the NACA0010 and a narrow ellipse with the same thickness. The angle of attack is fixed to $\unicode[STIX]{x1D6FC}=30^{\circ }$ for which complex dynamics of the flow can take place in the different viscous regimes inspected. The Reynolds number ranges between $Re=100$ and $Re=3000$ and, within this interval, numerous bifurcations of the solution are observed in terms of mean lift and drag coefficients, Strouhal number and downstream wake. An analysis of these bifurcations is provided and links are made between the wake structures observed. On this base the flow patterns can be classified in different modes similarly to the analysis by Kurtulus (Intl J. Micro Air Vehicles, vol. 7(3), 2015, pp. 301–326; vol. 8(2), 2016, pp. 109–139). A discussion of the vortical evolution of the flow in the vicinity of the suction side of the airfoil is also provided.

Copyright
Corresponding author
Email address for correspondence: andrea.colagrossi@cnr.it
References
Hide All
Abdessemed, N., Sherwin, S. J. & Theofilis, V. 2009 Linear instability analysis of low-pressure turbine flows. J. Fluid Mech. 628, 5783.
Alam, M. M., Zhou, Y., Yang, H. X., Guo, H. & Mi, J. 2010 The ultra-low Reynolds number airfoil wake. Exp. Fluids 48 (1), 81103.
Anand, K. & Sarkar, S. 2017 Features of a laminar separated boundary layer near the leading-edge of a model airfoil for different angles of attack: an experimental study. Trans. ASME J. Fluids Engng 139 (2), 021201.
Anyoji, M., Nonomura, T., Aono, H., Oyama, A., Fujii, K., Nagai, H. & Asai, K. 2014 Computational and experimental analysis of a high-performance airfoil under low-Reynolds-number flow condition. J. Aircraft 51 (6), 18641872.
Barba, L. A., Leonard, A. & Allen, C. B.2003 Numerical investigations on the accuracy of the vortex method with and without remeshing. AIAA Paper 2003-3426.
Benson, M. G., Bellamy-Knights, P. G., Gerrard, J. H. & Gladwell, I. 1989 A viscous splitting algorithm applied to low Reynolds number flows round a circular cylinder. J. Fluids Struct. 3 (5), 439479.
Berger, M., Aftosmis, M. J. & Allmaras, S.2012 Progress towards a cartesian cut-cell method for viscous compressible flow. AIAA Paper 2012-1301.
Bigay, P., Oger, G., Guilcher, P.-M. & Touzé, D. L. 2017 A weakly-compressible Cartesian grid approach for hydrodynamic flows. Comput. Phys. Commun. 220 (Supplement C), 3143.
Chatelain, P., Curioni, A., Bergdorf, M., Rossinelli, D., Andreoni, W. & Koumoutsakos, P. 2008 Billion vortex particle direct numerical simulations of aircraft wakes. Comput. Meth. Appl. Mech. Engng 197 (13), 12961304.
Chorin, A. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57 (04), 785796.
Chorin, A. 1978 Vortex sheet approximation of boundary layers. J. Comput. Phys. 27 (3), 428442.
Colagrossi, A., Bouscasse, B., Antuono, M. & Marrone, S. 2012 Particle packing algorithm for SPH schemes. Comput. Phys. Commun. 183 (2), 16411683.
Colagrossi, A., Graziani, G. & Pulvirenti, M. 2014 Particles for fluids: SPH versus vortex methods. J. Math. Mech. Complex Syst. 2 (1), 4570.
Colagrossi, A., Rossi, E., Marrone, S. & Le Touzé, D. 2016 Particle methods for viscous flows: analogies and differences between the SPH and DVH methods. Commun. Comput. Phys. 20 (3), 660688.
Counsil, J. N. & Goni Boulama, K. 2013 Low-Reynolds-number aerodynamic performances of the NACA 0012 and Selig–Donovan 7003 airfoils. J. Aircraft 50 (1), 204216.
Durante, D., Rossi, E., Colagrossi, A. & Graziani, G. 2016 Numerical simulations of the transition from laminar to chaotic behaviour of the planar vortex flow past a circular cylinder. Commun. Nonlinear Sci. Numer. Simul. 48, 1838.
Galbraith, M. C. & Visbal, M. R.2009 Implicit large eddy simulation of low-Reynolds-number transitional flow past the sd7003 airfoil. PhD thesis, University of Cincinnati.
Gioria, R. S., He, W. & Theofilis, V. 2015 On global linear instability mechanisms of flow around airfoils at low Reynolds number and high angle of attack. Procedia IUTAM 14, 8895.
He, W., Gioria, R. S., Pérez, J. M. & Theofilis, V. 2017 Linear instability of low Reynolds number massively separated flow around three NACA airfoils. J. Fluid Mech. 811, 701741.
Hoarau, Y., Braza, M., Ventikos, Y. & Faghani, D. 2006 First stages of the transition to turbulence and control in the incompressible detached flow around a NACA0012 wing. Intl J. Heat Fluid Flow 27 (5), 878886.
Hoarau, Y., Braza, M., Ventikos, Y., Faghani, D. & Tzabiras, G. 2003 Organized modes and the three-dimensional transition to turbulence in the incompressible flow around a NACA0012 wing. J. Fluid Mech. 496, 6372.
Hu, H. & Yang, Z. 2008 An experimental study of the laminar flow separation on a low-Reynolds-number airfoil. Trans. ASME J. Fluids Engng 130 (5), 051101.
Huang, R. F. & Lin, C. L. 1995 Vortex shedding and shear-layer instability of wing at low-Reynolds numbers. AIAA J. 33 (8), 13981403.
Huang, R. F., Wu, J. Y., Jeng, J. H. & Chen, R. C. 2001 Surface flow and vortex shedding of an impulsively started wing. J. Fluid Mech. 441, 265292.
Jung, J., Yee, K., Misaka, T. & Jeong, S. 2017 Low Reynolds number airfoil design for a mars exploration airplane using a transition model. Trans. Japan Soc. Aeronaut. Space Sci. 60 (6), 333340.
Khalid, M. S. U. & Akhtar, I. 2012 Characteristics of flow past a symmetric airfoil at low Reynolds number: a nonlinear perspective. In ASME 2012 International Mechanical Engineering Congress & Exposition, pp. 167175. American Society of Mechanical Engineers.
Kojima, R., Nonomura, T., Oyama, A. & Fujii, K. 2013 Large-eddy simulation of low-Reynolds-number flow over thick and thin NACA airfoils. J. Aircraft 50 (1), 187196.
Kunz, P. & Kroo, I.2000 Analysis, design, and testing of airfoils for use at ultra-low Reynolds numbers. Conference Paper, Conference on Fixed and Flapping Flight at Low Reynolds Numbers, 5–7 June, University of Notre Dame, IN, pp. 349–372.
Kurtulus, D. F. 2015 On the unsteady behavior of the flow around NACA 0012 airfoil with steady external conditions at ℜ = 1000. Intl J. Micro Air Vehicles 7 (3), 301326.
Kurtulus, D. F. 2016 On the wake pattern of symmetric airfoils for different incidence angles at ℜ = 1000. Intl J. Micro Air Vehicles 8 (2), 109139.
Lee, D., Nonomura, T., Oyama, A. & Fujii, K. 2015 Validation of numerical analysis to estimate airfoil aerodynamic characteristics at low Reynolds number region. In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference, pp. V01AT13A005V01AT13A005. American Society of Mechanical Engineers.
Lee, D., Nonomura, T., Oyama, A. & Fujii, K. 2017 Comparative studies of numerical methods for evaluating aerodynamic characteristics of two-dimensional airfoil at low Reynolds numbers. Intl J. Comput. Fluid Dyn. 31 (1), 5767.
Lissaman, P. B. S. 1983 Low-Reynolds-number airfoils. Annu. Rev. Fluid Mech. 15 (1), 223239.
Liu, Y., Li, K., Zhang, J., Wang, H. & Liu, L. 2012 Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation. Commun. Nonlinear Sci. Numer. Simul. 17 (8), 34273434.
Liu, X.-D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes iii. J. Comput. Phys. 115, 200212.
Mateescu, D. & Abdo, M. 2010 Analysis of flows past airfoils at very low Reynolds numbers. Proc. Inst. Mech. Engrs 224 (7), 757775.
Mesnard, O. & Barba, L. A.2016 Reproducible and replicable CFD: it’s harder than you think. Preprint, arXiv:1605.04339.
Mueller, T. J. & Delaurier, J. D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35 (1), 89111.
Oger, G., Marrone, S., Touzé, D. L. & de Leffe, M. 2016 SPH accuracy improvement through the combination of a quasi-Lagrangian shifting transport velocity and consistent ALE formalisms. J. Comput. Phys. 313, 7698.
Pulliam, T. H. & Vastano, J. A. 1993 Transition to chaos in an open unforced 2D flow. J. Comput. Phys. 105 (1), 133149.
Rodríguez, D. & Theofilis, V. 2011 On the birth of stall cells on airfoils. Theor. Comput. Fluid Dyn. 25 (1), 105117.
Rossi, E., Colagrossi, A., Bouscasse, B. & Graziani, G. 2015a The diffused vortex hydrodynamics method. Commun. Comput. Phys. 18 (2), 351379.
Rossi, E., Colagrossi, A., Durante, D. & Graziani, G. 2016 Simulating 2D viscous flow around geometries with vertices through the diffused vortex hydrodynamics method. Comput. Meth. Appl. Mech. Engng.
Rossi, E., Colagrossi, A. & Graziani, G. 2015b Numerical simulation of 2D-vorticity dynamics using particle methods. Comput. Math. Appl. 69 (12), 14841503.
Sun, P. N., Colagrossi, A., Marrone, S., Antuono, A. & Zhang, A. M. 2018 Multi-resolution Delta-plus-SPH with tensile instability control: towards high Reynolds number flows. Comput. Phys. Commun. 224, 6380.
Sun, P. N., Colagrossi, A., Marrone, S. & Zhang, A. M. 2017 The 𝛿-plus-SPH model: simple procedures for a further improvement of the SPH scheme. Comput. Meth. Appl. Mech. Engng 315 (Supplement C), 2549.
Titarev, V. A. & Toro, E. F. 2004 Finite-volume WENO schemes for three dimensional conservation laws. J. Comput. Phys. 201, 238260.
Uranga, A., Persson, P.-O., Drela, M. & Peraire, J. 2011 Implicit large eddy simulation of transition to turbulence at low Reynolds numbers using a discontinuous Galerkin method. Intl J. Numer. Meth. Engng 87 (1–5), 232261.
Zdravkovich, M. M. 1997 Flow around circular cylinders. Fundamentals 1.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Type Description Title
VIDEO
Movie

Rossi et al. supplementary movie
Wakes shedding downstream a NACA0010 profile with angle of attack 30 degrees for Re numbers equal to Re=900.

 Video (90.3 MB)
90.3 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed