Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T07:43:50.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence

Published online by Cambridge University Press:  25 April 2008

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
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at Rec=5×104 and incidence 5° are presented. Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to self-sustain, with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the two-dimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 175 - 207
Copyright
Copyright © Cambridge University Press 2008

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

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. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Carpenter, M. H., Nordström, J. & Gottlieb, D. 1999 A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148, 341–365.Google Scholar
Corcos, G. M. & Lin, S. J. 1984 The mixing layer: Deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech. 139, 67–95.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, 1347–1355.CrossRefGoogle Scholar
Gaster, M. 1967 The structure and behaviour of separation bubbles. Aero. Res. Counc. R&M 3595. Aerodynamics Division NPL.Google Scholar
Gaster, M. 1978 Series representation of the eigenvalues of the Orr-Sommerfeld equation. J. Comput. Phys. 29, 147–162.Google Scholar
Gault, D. E. 1957 A correlation of low-speed airfoil-section stalling characteristics with Reynolds number and airfoil geometry. NACA TN 3963. Washington.Google Scholar
Hammond, D. A. & Redekopp, L. G. 1998 Local and global instability properties of separation bubbles. Eur. J. Mech. B/Fluids 17, 145–164.Google Scholar
Hannemann, K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88.Google Scholar
Horton, H. P. 1969 A semi-empirical theory for the growth and bursting of laminar separation bubbles. Aero. Res. Counc. Current Paper 1073.Google Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2006 Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44, 1541–1549.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.CrossRefGoogle Scholar
Kerho, M., Hutcherson, S., Blackwelder, R. F. & Liebeck, R. H. 1993 Vortex generators used to control laminar separation bubbles. J. Aircraft 30, 315–319.Google Scholar
Kerswell, R. R. 2002 Elliptical Instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
Lang, M., Rist, U. & Wagner, S. 2004 Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV. Exps. Fluids 36, 43–52.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 a Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.Google Scholar
Leweke, T. & Williamson, C. H. K. 1998 b Three-dimensional instabilities in wake transition. Eur. J. Mech. B/Fluids 17, 571–586.CrossRefGoogle Scholar
Marxen, O., Lang, M., Rist, U. & Wagner, S. 2003 A combined experimental/numerical study of unsteady phenomena in a laminar separation bubble. Flow, Turbulence Combust. 71, 133–146.Google Scholar
Marxen, O., Rist, U. & Wagner, S. 2004 Effect of spanwise-modulated disturbances on transition in a separated boundary layer. AIAA J. 42, 937–944.Google Scholar
Maucher, U., Rist, U. & Wagner, S. 1997 Secondary instabilities in a laminar separation bubble. In New Results in Numerical and Experimental Fluid Dynamics (ed. Körner, H. & Hilbig, R.), pp. 229–236. Vieweg.Google Scholar
Maucher, U., Rist, U. & Wagner, S. 1998 Transitional structures in a laminar separation bubble. New Results in Numerical and Experimental Fluid Mechanics II, Proc. 11th STAB/DGLR Symposium, Berlin (ed. Nitsche, W., Heinemann, H. J. & Hilbig, R.), vol. 72, pp. 307–314.Google Scholar
Pauley, L. L. 1994 Response of two-dimensional separation to three-dimensional disturbances. Trans. ASME: J. Fluids Engng 116, 433–438.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.Google Scholar
Rist, U. 1994 {Nonlinear effects of 2D and 3D disturbances on laminar separation bubbles}. Proc. IUTAM Symp. on Nonlinear Instability of Nonparallel Flows, pp. 324–333. Springer.CrossRefGoogle Scholar
Rist, U. & Maucher, U. 2002 Investigations of time-growing instabilities in laminar separation bubbles. Eur. J. Mech. B/Fluids 21, 495–509.CrossRefGoogle Scholar
Sandberg, R. D. & Sandham, N. D. 2006 Nonreflecting zonal characteristic boundary condition for direct numerical simulation of aerodynamic sound. AIAA J. 44, 402–405.Google 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.Google Scholar
Sandham, N. D., Li, Q. & Yee, H. C. 2002 Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178, 307–322.Google Scholar
Sandhu, H. S. & Sandham, N. D. 1994 Boundary conditions for spatially growing compressible shear layers. Rep. QMW-EP-1100. Faculty of Engineering, Queen Mary and Westfield College, University of London.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.Google Scholar
Spalart, P. R. & Strelets, M. K. H. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
von Terzi, D. A. 2004 Numerical investigation of transitional and turbulent backward-facing step flows. PhD thesis, The University of Arizona.Google Scholar
Theofilis, V. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. 358, 3229–3246.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerospace Sci. 39, 249–315.Google Scholar
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607–616.Google Scholar
Waleffe, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A 2, 76.Google Scholar
Williamson, C. H. K. 1992 The natural and forced formation of spot-like'vortex dislocations' in the transition of a wake. J. Fluid Mech. 243, 393–441.Google Scholar
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar