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Stability and receptivity characteristics of a laminar separation bubble on an aerofoil

Published online by Cambridge University Press:  07 April 2010

L. E. JONES ,
R. D. SANDBERG  and
N. D. SANDHAM
L. E. JONES*
Affiliation:
Aerodynamics And Flight Mechanics Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
R. D. SANDBERG
Affiliation:
Aerodynamics And Flight Mechanics Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
N. D. SANDHAM
Affiliation:
Aerodynamics And Flight Mechanics Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: ljones@soton.ac.uk
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Abstract

Stability characteristics of aerofoil flows are investigated by linear stability analysis of time-averaged velocity profiles and by direct numerical simulations with time-dependent forcing terms. First the wake behind an aerofoil is investigated, illustrating the feasibility of detecting absolute instability using these methods. The time-averaged flow around an NACA-0012 aerofoil at incidence is then investigated in terms of its response to very low-amplitude hydrodynamic and acoustic perturbations. Flow fields obtained from both two- and three-dimensional simulations are investigated, for which the aerofoil flow exhibits a laminar separation bubble. Convective stability characteristics are documented, and the separation bubble is found to exhibit no absolute instability in the classical sense; i.e. no growing disturbances with zero group velocity are observed. The flow is however found to be globally unstable via an acoustic-feedback loop involving the aerofoil trailing edge as a source of acoustic excitation and the aerofoil leading-edge region as a site of receptivity. Evidence suggests that the feedback loop may play an important role in frequency selection of the vortex shedding that occurs in two dimensions. Further simulations are presented to investigate the receptivity process by which acoustic waves generate hydrodynamic instabilities within the aerofoil boundary layer. The dependency of the receptivity process to both frequency and source location is quantified. It is found that the amplitude of trailing-edge noise in the fully developed simulation is sufficient to promote transition via leading-edge receptivity.

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Papers
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Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 257 - 296
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750–756.CrossRefGoogle Scholar
Carpenter, M. H., Nordström, J. & Gottlieb, D. 1999 A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148 (2), 341–365.CrossRefGoogle Scholar
Deng, S., Jiang, L. & Liu, C. 2007 DNS for flow separation control around an airfoil by pulsed jets. Comp. Fluids 36 (6), 1040–1060.CrossRefGoogle Scholar
Desquesnes, G., Terracol, M. & Sagaut, P. 2007 Numerical investigation of the tone noise mechanism over laminar airfoils. J. Fluid Mech. 591, 155–182.CrossRefGoogle Scholar
Drazin, P. G. & Reed, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Drela, M. & Giles, M. B. 1987 Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25 (10), 1347–1355.CrossRefGoogle Scholar
Erturk, E. & Corke, T. C. 2001 Boundary layer leading-edge receptivity to sound at incidence angles. J. Fluid Mech. 444, 383–407.CrossRefGoogle Scholar
Ffowcs Williams, J. E. & Hall, L. H. 1970 Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half-plane. J. Fluid Mech. 40 (4), 657–670.CrossRefGoogle Scholar
Gaster, M. 1963 On stability of parallel flows and the behaviour of separation bubbles. PhD thesis, University of London, London.Google Scholar
Gaster, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723–727.CrossRefGoogle Scholar
Gaster, M. 1978 Series representation of the eigenvalues of the Orr–Sommerfeld equation. J. Comput. Phys. 29, 147–162.CrossRefGoogle Scholar
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.CrossRefGoogle Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.CrossRefGoogle Scholar
Haddad, O. M., Erturk, E. & Corke, T. C. 2005 Acoustic receptivity of the boundary layer over parabolic bodies at angles of attack. J. Fluid Mech. 536, 377–400.CrossRefGoogle Scholar
Hammerton, P. W. & Kerschen, E. J. 1996 Boundary-layer receptivity for a parabolic leading edge. J. Fluid Mech. 310, 243–267.CrossRefGoogle Scholar
Hammond, D. A. & Redekopp, L. G. 1998 Local and global instability properties of separation bubbles. Eur. J. Mech. B 17 (2), 145–164.CrossRefGoogle Scholar
Hannemann, K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88.CrossRefGoogle Scholar
Herbert, Th. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.CrossRefGoogle Scholar
Horton, H.P. 1968 Laminar separation in two- and three-dimensional incompressible flow. PhD thesis, University of London, London.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10, 2006–2011.CrossRefGoogle Scholar
Jones, L. E. 2007 Numerical studies of the flow around an airfoil at low Reynolds number. PhD thesis, University of Southampton, Southampton, UK.Google Scholar
Jones, L. E., Sandberg, R. S. & Sandham, N. D 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175–207.CrossRefGoogle Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411–482.CrossRefGoogle Scholar
Lam, S. H. & Rott, N. 1960 Theory of Linearized Time-Dependent Boundary Layers. Graduate School of Aeronautical Engineering, Cornell University.Google Scholar
Lee, C. B. & Wu, J. Z. 2008 Transition in wall-bounded flows. Appl. Mech. Rev. 61, 1–32.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Lowson, M. V., Fiddes, S. P. & Nash, E. C. 1994 Laminar boundary layer aeroacoustic instabilities. Paper 94-0358. AIAA.CrossRefGoogle Scholar
Marquillie, M. & Ehrenstein, U. W. E. 2003 On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169–188.CrossRefGoogle Scholar
McAlpine, A., Nash, E. C. & Lowson, M. V. 1999 On the generation of discrete frequency tones by the flow around an airfoil. J. Sound Vib. 222 (5), 753–779.CrossRefGoogle Scholar
Morkovin, M. 1984 Bypass transition to turbulence and research desiderata. In Transition in Turbines (ed. Graham, R.), NASA Conf. Pub. 2386, pp. 161–204.Google Scholar
Morkovin, M., Reshotko, E. & Herbert, T. 1994 Transition in open flow systems – a reassessment. Bull. Am. Phys. Soc. 39 (9), 1882.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.CrossRefGoogle Scholar
Radespiel, J. W. & Scholz, U. 2007 Numerical and experimental flow analysis of moving airfoils with laminar separation bubbles. AIAA J. 45 (6), 1346–1356.CrossRefGoogle Scholar
Rossiter, J. E. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aeronaut. Res. Counc. Rep. Memo 3838.Google Scholar
Sandberg, R. D., Jones, L. E., Sandham, N. D. & Joseph, P. F. 2009 Direct numerical simulations of tonal noise generated by laminar flow past airfoils. J. Sound Vib. 320, 838–858.CrossRefGoogle Scholar
Sandberg, R. D. & Sandham, N. D. 2008 Direct numerical simulation of turbulent flow past a trailing-edge and the associated noise generation. J. Fluid Mech. 596, 353–385.CrossRefGoogle Scholar
Sandberg, R. D., Sandham, N. D. & Joseph, P. F. 2007 Direct numerical simulations of trailing-edge noise generated by boundary-layer instabilities. J. Sound Vib. 304, 677–690.CrossRefGoogle Scholar
Sandham, N. D. 2008 Transitional separation bubbles and unsteady aspects of aerofoil stall. Aeronaut. J. 112 (1133), 395–404.CrossRefGoogle Scholar
Sandham, N. D. & Kleiser, L. 1992 The late stages of transition to turbulence in channel flow. J. Fluid Mech. 245, 319–347.CrossRefGoogle Scholar
Sandham, N. D., Li, Q. & Yee, H. C. 2003 Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178, 307–322.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to free stream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291–319.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and transition in shear flows. Springer.CrossRefGoogle Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Progr. Aerosp. Sci. 39, 249–315.CrossRefGoogle Scholar
Torres, G. E. & Mueller, T. J. 2001 Aerodynamic characteristics of low aspect ratio wings at low Reynolds numbers. In Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications (ed. Mueller, T. J.), pp. 115–141, AIAA.Google Scholar
Wanderley, J. B. V. & Corke, T. C. 2001 Boundary layer receptivity to free-stream sound on elliptic leading edges of flat plates. J. Fluid Mech. 429, 1–21.CrossRefGoogle Scholar
White, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.Google Scholar
Yang, Z. & Voke, P. R. 2001 Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature. J. Fluid Mech. 439, 305–333.CrossRefGoogle Scholar
Yee, H. C., Sandham, N. D. & Djomehri, M. J. 1999 Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150 (1), 199–238.CrossRefGoogle Scholar
Yuan, W., Khalid, M., Windte, J., Scholz, U. & Radespiel, R. 2007 Computational and experimental investigations of low-Reynolds-number flows past an aerofoil. Aeronaut. J. 111 (1115), 17–29.CrossRefGoogle Scholar
Zhang, W., Hain, R. & Kähler, C. J. 2008 Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil. Exp. Fluids 45 (4), 725–743.CrossRefGoogle Scholar