Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T03:58:14.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of surface corrugation on the stability of a zero-pressure-gradient boundary layer

Published online by Cambridge University Press:  12 February 2014

Mochamad Dady Ma’mun ,
Masahito Asai  and
Ayumu Inasawa
Mochamad Dady Ma’mun
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, Asahigaoka 6-6, Hino, Tokyo 191-0065, Japan
Masahito Asai*
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, Asahigaoka 6-6, Hino, Tokyo 191-0065, Japan
Ayumu Inasawa
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, Asahigaoka 6-6, Hino, Tokyo 191-0065, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of surface corrugation with small amplitude on the growth of Tollmien–Schlichting (T–S) waves were examined experimentally in a zero-pressure-gradient boundary layer. Two- and three-dimensional corrugations of sinusoidal geometry with wavelengths of the same order as that of the two-dimensional T–S wave were considered. The corrugation amplitudes were one order of magnitude smaller than the boundary-layer displacement thickness. Streamwise growth of T–S waves on the corrugated walls was compared with that in the boundary layer on the smooth surface. A distinct difference was found in the destabilizing effect between the two- and three-dimensional corrugations. The two-dimensional corrugation significantly enhanced the growth of two-dimensional T–S waves even when the corrugation amplitude was only ∼10% of the displacement thickness. On decreasing the corrugation amplitude, the growth rate of two-dimensional T–S waves asymptotically approached that in the smooth-wall case. On the other hand, the three-dimensional corrugation had only a small influence on the growth of two-dimensional T–S waves even when the corrugation amplitude was as large as 20% of the displacement thickness. For three-dimensional corrugations, however, a pair of oblique waves was generated and developed by an interaction between the two-dimensional T–S wave and the corrugation-induced mean-flow distortion for the corrugation wavelength considered. On increasing the corrugation amplitude, the oblique waves generated were increased in amplitude and thus significantly influenced the secondary instability process.

JFM classification

Boundary Layers: Boundary layer stability Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , pp. 228 - 251
Copyright
© 2014 Cambridge University Press 

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

Asai, M. & Floryan, J. M. 2006 Experiments on the linear instability of flow in a wavy channel. Eur. J. Mech. (B/Fluids) 25, 971–986.CrossRefGoogle Scholar
Bertolotti, F. P., Herbert, Th. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 411–474.Google Scholar
Corke, T. C., Bar-Sever, A. & Morkovin, M. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids 29, 3199–3213.Google Scholar
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude streaks in the Blasius boundary layer. Phys. Fluids 14, L57–L60.Google Scholar
Fasel, H. & Konzelmann, U. 1990 Non-parallel stability of a flat-plate boundary layer using the complete Navier–Stokes equations. J. Fluid Mech. 221, 311–347.Google Scholar
Floryan, J. M. 2005 Two-dimensional instability of flow in a rough channel. Phys. Fluids 17, 044101.Google Scholar
Floryan, J. M. & Asai, M. 2011 On the transition between distributed and isolated surface roughness and its effect on the stability of channel flow. Phys. Fluids 23, 104101.Google Scholar
Fransson, J. H. M., Talamelli, A., Brandt, L. & Cossu, C. 2006 Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501.CrossRefGoogle ScholarPubMed
Gaster, M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465–480.Google Scholar
Goldstein, M. E. & Hultgren, L. S. 1989 Boundary layer receptivity to long-wave free-stream disturbances. Annu. Rev. Fluid Mech. 21, 137–166.Google Scholar
Görtler, H. 1948 Einfluss einer schwachen Wadwelligkeit auf den Verlawf den laminaren Grenzschichten. Z. Angew. Math. Mech. 25/27, 233–244.Google Scholar
Herbert, Th. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Kachanov, Yu. S., Kozlov, V. V., Kotjolkin, JU. D., Levchenko, V. Ya. & Rudnitsky, A. L. 1975 Laminar boundary layer on a wavy surface. Acta Astronaut. 2, 557–559.Google Scholar
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1974 Experimental study of the stability of boundary layer on a wavy wall. Zv. Sib. Otd. Akad. Nauk, SSSR, Tekh. Nauk 3, 3–6.Google Scholar
Kendall, J. M. 1990 The effect of small-scale roughness on the mean flow profile of a laminar boundary layer. In Instability and Transition (ed. Hussaini, M. Y. & Voigt, R. G.), vol. 1, pp. 296–302. Springer.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–34.CrossRefGoogle Scholar
Lessen, M. & Gangwani, S. T. 1976 Effect of small amplitude wall waviness upon the stability of the laminar boundary layer. Phys. Fluids 19, 510–513.Google Scholar
Levchenko, V. Ya & Solovev, A. S. 1972 Stability of boundary layer on wavy surface. Izv. Akad. Nauk, SSSR, Mekh. Zhidk. Gaza 3, 11–16.Google Scholar
Morkovin, M. V. 1990 On roughness-induced transition: facts, views and speculations. In Instability and Transition (ed. Hussaini, M. Y. & Voigt, R. G.), vol. 1, pp. 281–295. Springer.Google Scholar
Nishioka, M. & Asai, M. 1985 Three-dimensional wave disturbances in plane Poiseuille flow. In Laminar Turbulent Transition (ed. Kozlov, V. V.), pp. 173–182. Springer.Google Scholar
Radeztsky, R. H. Jr., Reibert, M. S. & Saric, W. S. 1999 Effect of isolated micron-sized roughness on transition in swept-wing flows. AIAA J. 37, 1371–1377.Google Scholar
Reshotko, E. 1984 Disturbances in a laminar boundary layer due to distributed surface roughness. In Turbulence and Chaotic Phenomena in Fluids (ed. Tatsumi, T.), pp. 39–46. North-Holland.Google Scholar
Saric, W. S., Carrillo, B. C. Jr. & Reibert, M. S. 1998 Leading-edge roughness as a transition control mechanism. AIAA Paper 98–0781.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to free stream disturbances.. Annu. Rev. Fluid Mech. 34, 291–319.Google Scholar
Saric, W. S. & Thomas, A. S. W. 1984 Experiments on the subharmonic route to turbulence in boundary layers. In Turbulence and Chaotic Phenomena in Fluids (ed. Tatsumi, T.), pp. 117–122. North-Holland.Google Scholar
Tao, J. 2009 Critical instability and friction scaling of fluid flows through pipes with rough inner surfaces. Phys. Rev. Lett. 103, 264502.Google Scholar
Wie, Y.-S. & Malik, M. R. 1998 Effect of surface waviness on boundary-layer transition in two-dimensional flows. Comput. Fluids 27, 157–181.Google Scholar