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Swept wing boundary-layer receptivity to localized surface roughness

Published online by Cambridge University Press:  20 September 2012

David Tempelmann ,
Lars-Uve Schrader ,
Ardeshir Hanifi ,
Luca Brandt  and
Dan S. Henningson
David Tempelmann
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden
Lars-Uve Schrader
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden
Ardeshir Hanifi
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden Swedish Defence Research Agency, FOI, Stockholm, SE-164 90, Sweden
Luca Brandt
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden
Dan S. Henningson
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden
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Abstract

The receptivity to localized surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolized stability equations (PSEs). The DNS is laid out to reproduce wind tunnel experiments performed by Saric and coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSEs is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE methods are 40 % of those measured in the experiments. Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability

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Papers
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Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 516 - 544
Copyright
Copyright © Cambridge University Press 2012

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References

1. Airiau, C. 2000 Non-parallel acoustic receptivity of a Blasius boundary layer using an adjoint approach. Flow Turbul. Combust. 65, 347–367.CrossRefGoogle Scholar
2. Airiau, C., Walther, S. & Bottaro, A. 2002 Boundary layer sensitivity and receptivity. C. R. Mécanique 330, 259–265.CrossRefGoogle Scholar
3. Andersson, P., Henningson, D. S. & Hanifi, A. 1998 On a stabilization procedure for the parabolic stability equations. J. Engng Math. 33 (3), 311–332.CrossRefGoogle Scholar
4. Bertolotti, F. P. 2000 Receptivity of three-dimensional boundary-layers to localized wall roughness and suction. Phys. Fluids 12 (7), 1799–1809.CrossRefGoogle Scholar
5. Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.CrossRefGoogle Scholar
6. Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerosp. Sci. 35, 363–412.CrossRefGoogle Scholar
7. Carpenter, A. L., Saric, W. S. & Reed, H. L. 2009 In-flight receptivity experiments on a 30-degree swept-wing using micron-sized discrete roughness size influence. AIAA Paper 2009-590.CrossRefGoogle Scholar
8. Carpenter, M. H., Choudhari, M., Li, F., Streett, C. L. & Chang, C.-L. 2010 Excitation of crossflow instabilities in a swept wing boundary layer. AIAA Paper 2010-378.CrossRefGoogle Scholar
9. Chang, C.-L. & Choudhari, M. 2005 Boundary-layer receptivity and integrated transition prediction. AIAA Paper 2005-0526.CrossRefGoogle Scholar
10. Chang, C.-L., Malik, M. R., Erlebacher, G. & Hussaini, M. Y. 1991 Compressible stability of growing boundary layers using parabolized stability equations. AIAA Paper 1991-1636.CrossRefGoogle Scholar
11. Choudhari, M. 1994 Roughness-induced generation of crossflow vortices in three-dimensional boundary layers. Theoret. Comput. Fluid Dyn. 6, 1–30.CrossRefGoogle Scholar
12. Collis, S. S. & Lele, S. K. 1999 Receptivity to surface roughness near a swept leading edge. J. Fluid Mech. 380, 141–168.CrossRefGoogle Scholar
13. Crouch, J. D. 1993 Receptivity of three-dimensional boundary layers. AIAA Paper 93-0074.CrossRefGoogle Scholar
14. Deyhle, H. & Bippes, H. 1996 Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions. J. Fluid Mech. 316, 73–113.CrossRefGoogle Scholar
15. Dobrinsky, A. 2002 Adjoint analysis for receptivity prediction. PhD thesis, Rice University.Google Scholar
16. Eliasson, P. 2002 EDGE: a Navier–Stokes solver for unstructured grids. In Proceedings to Finite Volumes for Complex Applications III (ed. Kroner, D. & Herbin, R. ), pp. 527–534. Hemre Penton Science London.Google Scholar
17. Fedorov, A. V. 1988 Excitation of waves of instability of the secondary flow in the boundary layer on a swept wing. J. Appl. Mech. Tech. Phys. 29, 643–648.CrossRefGoogle Scholar
18. Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G. 2008 Nek5000 Web page. http://nek5000.mcs.anl.gov.Google Scholar
19. Haj-Hariri, H. 1994 Characteristics analysis of the parabolized stability equations. Stud. Appl. Math. 92, 41–53.CrossRefGoogle Scholar
20. Hanifi, A., Henningson, D. S., Hein, S., Bertolotti, F. P & Simen, M. 1994 Linear non-local instability analysis: the linear NOLOT code. FFA TN 1994-54.Google Scholar
21. Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8 (3), 826–837.CrossRefGoogle Scholar
22. Haynes, T. S. & Reed, H. L. 2000 Simulation of swept-wing vortices using nonlinear parabolized stability equations. J. Fluid Mech. 405, 325–349.CrossRefGoogle Scholar
23. Hein, S., Hanifi, A. & Casalis, G. 2000 Nonlinear transition prediction. In Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering.Google Scholar
24. Hellsten, A. 2005 New advanced k-$\omega $ turbulence model for high-lift aerodynamics. AIAA J. 43 (9), 1857–1869.CrossRefGoogle Scholar
25. Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.CrossRefGoogle Scholar
26. Hill, D. C. 1995 Adjoint systems and their role in the receptivity problem for boundary layers. J. Fluid Mech. 292, 183–204.CrossRefGoogle Scholar
27. Hill, D. C. 1997 Receptivity in non-parallel boundary layers. In Proceedings of the 1997 ASME Fluids Engineering Division Summer Meeting. ASME.Google Scholar
28. Maday, Y. & Patera, A. T. 1989 Spectral element methods for the Navier–Stokes equations. In State of the Art Surveys in Computational Mechanics (ed. Noor, A. K. ). pp. 71–143. ASME.Google Scholar
29. Malik, M. R., Li, F., Choudhari, M. M. & Chang, C.-L. 1999 Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85–115.CrossRefGoogle Scholar
30. Manuilovich, S. V. 1989 Disturbances of a three-dimensional boundary layer generated by surface roughness. Fluid Dyn. 24, 764–769.CrossRefGoogle Scholar
31. Ng, L. L. & Crouch, J. D. 1999 Roughness-induced receptivity to crossflow vortices on a swept wing. Phys. Fluids 11 (2), 432–438.CrossRefGoogle Scholar
32. Nishino, T. & Shariff, K. 2009 Direct numerical simulation of a swept-wing boundary layer with an array of discrete roughness elements. In Proceedings 7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden. Springer.Google Scholar
33. Ohlsson, J., Schlatter, P., Fischer, P. F. & Henningson, D. S. 2011 Stabilization of the spectral-element method in turbulent flow simulations. In Spectral and High Order Methods for Partial Differential Equations (ed. Hesthaven, J. S. & Rønquist, E. M. ), pp. 449–458. Springer.CrossRefGoogle Scholar
34. Patera, A. T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468–488.CrossRefGoogle Scholar
35. Piot, E., Content, C. & Casalis, G. 2008 Receptivity of crossflow instabilities to a periodic roughness array on a swept cylinder: investigation of the roughness size influence. AIAA Paper 2008-502.CrossRefGoogle Scholar
36. Reibert, M. S. 1996 Nonlinear stability, saturation, and transition in crossflow-dominated boundary layers. PhD thesis, Arizona State University.Google Scholar
37. Reibert, M. S., Saric, W. S., Carillo, R. B. & Chapman, K. L. 1996 Experiments in nonlinear saturation of stationary crossflow vortices in a swept-wing boundary layer. AIAA Paper 96-0184.CrossRefGoogle Scholar
38. Rizzetta, D. P., Visbal, M. R., Reed, H. L. & Saric, W. S. 2010 Direct numerical simulation of discrete roughness on a swept-wing leading edge. AIAA J. 48 (11).CrossRefGoogle Scholar
39. Sakov, P. 2011 gridgen-c: an orthogonal grid generator based on the CRDT algorithm (by conformal mapping). http://code.google.com/p/gridgen-c/.Google Scholar
40. Saric, W. S. Jr, Carillo, R. B. & Reibert, M. S. 1998a Leading-edge roughness as a transition control mechanism. AIAA Paper 98-0781.CrossRefGoogle Scholar
41. Saric, W. S. Jr, Carillo, R. B. & Reibert, M. S. 1998b Nonlinear stability and transition in 3-D boundary layers. Meccanica 33, 469–487.CrossRefGoogle Scholar
42. Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.CrossRefGoogle Scholar
43. Schlichting, H. 1979 Boundary-Layer Theory, seventh edition. McGraw-Hill.Google Scholar
44. Schrader, L. U., Amin, S. & Brandt, L. 2010 Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence. J. Fluid Mech. 646.CrossRefGoogle Scholar
45. Schrader, L. U., Brandt, L. & Henningson, D. S. 2009 Receptivity mechanisms in three-dimensional boundary layer flows. J. Fluid Mech. 618, 209–241.CrossRefGoogle Scholar
46. Schrader, L.-U., Tempelmann, D., Brandt, L., Hanifi, A. & Henningson, D. S. 2011 Excitation of cross-flow vortices by surface roughness on a swept wing. In Proceedings of CASI AERO 2011 Conference.Google Scholar
47. Simen, M. 1992 Local and non-local stability theory of spatially varying flows. In Instability, Transition and Turbulence, pp. 181–195. Springer.CrossRefGoogle Scholar
48. Somers, D. M. & Horstmann, K.-H. 1985 Design of a medium-speed, natural laminar-flow aerofoil for commuter aircraft applications. DLR-IB. 129-85/26.Google Scholar
49. Tempelmann, D., Hanifi, A. & Henningson, D. S. 2010 Spatial optimal growth in three-dimensional boundary layers. J. Fluid Mech. 646, 5–37.CrossRefGoogle Scholar
50. Tempelmann, D., Hanifi, A. & Henningson, D. S. 2012 Spatial optimal growth in three-dimensional compressible boundary layers. J. Fluid Mech. 704, 251–279.CrossRefGoogle Scholar
51. Tufo, H. M. & Fischer, P. F. 2001 Fast parallel direct solvers for coarse grid problems. J. Parallel Distrib. Comput. 61 (2), 151–177.Google Scholar
52. Wallin, S. & Johansson, A. 2000 An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403, 89–132.CrossRefGoogle Scholar
53. Weideman, J. A. & Reddy, S. C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Soft. 26 (4).CrossRefGoogle Scholar