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Receptivity mechanisms in three-dimensional boundary-layer flows

Published online by Cambridge University Press:  10 January 2009

LARS-UVE SCHRADER ,
LUCA BRANDT  and
DAN S. HENNINGSON
LARS-UVE SCHRADER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
LUCA BRANDT*
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
DAN S. HENNINGSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: luca@mech.kth.se
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Abstract

Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 209 - 241
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Berlin, S. & Henningson, D. S. 1999 A nonlinear mechanism for receptivity of free-stream disturbances. Phys. Fluids 11, 3749–3760.CrossRefGoogle Scholar
Bertolotti, F. P. 1997 Response of the Blasius boundary layer to free-stream vorticity. Phys. Fluids 9, 2286–2299.CrossRefGoogle Scholar
Bertolotti, F. P. 2000 Receptivity of three-dimensional boundary-layers to localized wall roughness and suction. Phys. Fluids 12 (7), 1799–1809.CrossRefGoogle Scholar
Bertolotti, F. P. & Kendall, J. M. 1997 Response of the Blasius boundary layer to Controlled free-stream vortices of axial form. AIAA Paper 97-2018.CrossRefGoogle Scholar
Bippes, H. & Deyhle, H. 1992 Das receptivity-problem in Grenzschichten mit längswirbelartigen Störungen. Z. Flugwiss. Weltraumforschung 16, 34–41.Google Scholar
Brandt, L., Henningson, D. S. & Ponziani, D. 2002 Weakly non-linear analysis of boundary layer receptivity to free-stream disturbances. Phys. Fluids 14, 1426–1441.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Buter, T. A. & Reed, H. L. 1994 Boundary layer receptivity to free-stream vorticity. Phys. Fluids 6 (10), 3368–3379.CrossRefGoogle Scholar
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007 A pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. Royal Institute of Technology (KTH), Dept of Mechanics, Stockholm.Google Scholar
Choudhari, M. 1994 Roughness-induced generation of crossflow vortices in three-dimensional boundary layers. Theor. Comput. Fluid Dyn 6, 1–30.CrossRefGoogle Scholar
Choudhari, M. & Streett, C. L. 1992 A finite Reynolds number approach for the prediction of boundary layer receptivity in localized regions. Phys. Fluids A 4, 2495–2514.CrossRefGoogle Scholar
Collis, S. S. & Lele, S. K. 1999 Receptivity to surface roughness near a swept leading edge. J. Fluid Mech. 380, 141–168.CrossRefGoogle Scholar
Crouch, J. D. 1992 Localized receptivity of boundary layers. Phys. Fluids A 4 (7), 1408–1414.CrossRefGoogle Scholar
Crouch, J. D. 1993 Receptivity of three-dimensional boundary layers. AIAA Paper 93-0074.CrossRefGoogle Scholar
Crouch, J. D. & Spalart, P. R. 1995 A study of non-parallel and nonlinear effects on the localized receptivity of boundary layers. J. Fluid Mech. 290, 29–37.CrossRefGoogle Scholar
Fransson, J. H. M., Matsubara, M. & Alfredsson, P. H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.CrossRefGoogle Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.CrossRefGoogle Scholar
Goldstein, M. E. 1985 Scattering of acoustic waves into Tollmien–Schlichting waves by small streamwise variations in surface geometry. J. Fluid Mech. 154, 509–529.CrossRefGoogle Scholar
Grosch, C. E. & Salwen, H. 1978 The continuous spectrum of the Orr–Sommerfeld equation. Part 1. The spectrum and the eigenfunctions. J. Fluid Mech. 87, 33–54.CrossRefGoogle Scholar
Högberg, M. & Henningson, D. 1998 Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers. J. Fluid Mech. 368, 339–357.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10 (8), 2006–2011.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Kendall, J. M. 1998 Experiments on boundary-layer receptivity to freestream turbulence. AIAA Paper 98-0530.CrossRefGoogle Scholar
Lin, N., Reed, H. & Saric, W. 1992 Effect of leading edge geometry on boundary-layer receptivity to freestream sound. In Instability, Transition and Turbulence (ed. Hussaini, M., Kumar, A. & Streett, C.). Springer.Google Scholar
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1985 A spectral collocation method for the Navier–Stokes equations. J. Comput. Phys. 61, 64–88.CrossRefGoogle Scholar
Maslowe, S. A. & Spiteri, R. J. 2001 The continuous spectrum for a boundary layer in a streamwise pressure gradient. Phys. Fluids 13 (5), 1294–1299.CrossRefGoogle Scholar
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
Nordström, J., Nordin, N. & Henningson, D. S. 1999 The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. SIAM J. Sci. Comput. 20, 1365–1393.CrossRefGoogle Scholar
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
Ruban, A. I. 1985 On the generation of Tollmien–Schlichting waves by sound. Fluid Dyn. 19, 709–716.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.CrossRefGoogle Scholar
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
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn.McGraw-Hill.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2006 Continuous mode transition and the effects of pressure gradient. J. Fluid Mech. 563, 357–388.CrossRefGoogle Scholar
Zavol'skii, N. A., Reutov, V. P. & Ryboushkina, G. V. 1983 Generation of Tollmien–Schlichting waves via scattering of acoustic and vortex perturbations in boundary layer on wavy surface. J. Appl. Mech. Tech. Phys. 24 (3), 355–361.CrossRefGoogle Scholar