Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T20:56:40.841Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatial simulation of channel flow instability and control

Published online by Cambridge University Press:  04 December 2013

Alec Kucala  and
Sedat Biringen
Alec Kucala
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA
Sedat Biringen*
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A direct numerical simulation is performed on the full time-dependent three-dimensional Navier–Stokes equations in a spatially developing plane-channel flow at a Reynolds number of 10 000. Two-dimensional eigenfunctions based on the solution of the Orr–Sommerfeld equation are introduced at the inflow with random noise added to simulate a vibrating ribbon transition experiment. The flow is allowed to choose a natural path to secondary instability, either K-type (after Klebanoff) or H-type (after Herbert), depending on the amplitude of the two-dimensional disturbance. For low-amplitude two-dimensional disturbances (1 % of the centreline velocity), H-type modes are found to dominate, while a doubling of the amplitude (2 % of the centreline velocity) produces a mixed H-type/K-type disturbance field with explosive growth of the secondary modes. In addition, the use of a suction/blowing slot that is phase lagged with respect to a fixed wall pressure signal is demonstrated to significantly reduce the energy in the primary mode owing to the destruction of phase between the streamwise and wall-normal velocity components. The use of forward finite-time Lyapunov exponents to generate Lagrangian coherent structures as a means of flow visualization is also presented, showing qualitative agreement with previous experimental visualizations, and represents a viable means of identifying characteristic vortical flow structures.

JFM classification

Flow Control: Flow Control Flow Control: Instability control Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 738 , 10 January 2014 , pp. 105 - 123
Copyright
©2013 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

Ashpis, D. & Reshotko, E. 1990 The vibrating ribbon problem revisited. J. Fluid Mech. 213, 531–547.Google Scholar
Barkley, D. 1990 Theory and predictions of finite-amplitude waves in two-dimensional plane Poiseuille flow. Phys. Fluids A 6, 955–970.Google Scholar
Baumann, M. & Nitsche, W. 1996 Investigation of active control of Tollmien–Schlichting waves on a wing. Trans. Bound. Layer Aeronaut. 46, 89–98.Google Scholar
Biringen, S. 1984 Active control of transition by periodic suction–blowing. Phys. Fluids 27 (6), 1345–1347.Google Scholar
Biringen, S., Nutt, W. E. & Caruso, M. J. 1987 Numerical study of transition control by periodic suction blowing. AIAA J. 25 (2), 239–244.Google Scholar
Borodulin, V. I., Kachanov, Y. S. & Koptsev, D. B. 2002 Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: I. Tuned resonances. J. Turbul. 3, N62.CrossRefGoogle Scholar
Chang, Y., Collis, S. & Ramakrishnan, S. 2002 Viscous effects in control of near-wall turbulence. Phys. Fluids 14, 4069–4080.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.Google Scholar
Danabasoglu, G., Biringen, S. & Streett, C. L. 1991 Spatial simulation of instability control by periodic suction blowing. Phys. Fluids A 3 (9), 2138–2147.Google Scholar
Erdmann, R., Patzold, A., Engert, M., Peltzer, I. & Nitsche, W. 2011 On active control of laminar–turbulent transition on two-dimensional wings. Phil. Trans. R. Soc. Lond. A 369, 1382–1395.Google Scholar
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14, 1851–1861.CrossRefGoogle Scholar
Herbert, T. 1983 Secondary instability of plane channel flow to subharmonic three-dimensional disturbances. Phys. Fluids 26, 871–874.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y. 1978 Nonlinear development of a wave in a boundary layer. Fluid Dyn. 12, 383–390.Google Scholar
Kachanov, Y. S. & Levchenko, V. Y. 1984 The resonant interaction of disturbances at laminar–turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247.Google Scholar
Kim, J. & Moser, R. D. 1989 On the secondary instability in plane Poiseuille flow. Phys. Fluids A 1 (5), 775–777.CrossRefGoogle 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.Google Scholar
Kozlov, V. V. & Ramazanov, M. P. 1983 Development of finite-amplitude disturbances in Poiseuille flow. J. Fluid Mech. 147, 149–157.Google Scholar
Kruse, M. & Wagner, S. 1998 Visualization and laser Doppler measurements of the development of Lambda vortices in laminar–turbulent transition. Meas. Sci. Technol. 9, 659–669.Google Scholar
Lipinski, D. & Mohseni, K. 2010 A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures. Chaos 20, 017504.Google Scholar
May, C. L. & Kleiser, L. 1985 Numerical simulation of subharmonic transition in plane Poiseuille flow. Bull. Am. Phys. Soc. 30, 1748.Google Scholar
Nishioka, M., Asai, M. & Iida, S. 1980 An experimental investigation of the secondary instability. In Laminar–Turbulent Transition: Proc. IUTAM Symp., Stuttgart, West Germany, 16–22 September 1979 (ed. Eppler, R. & Fasel, H.), pp. 37–46. Springer.Google Scholar
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731–751.Google Scholar
Ramazanov, M. P. 1985 Development of finite-amplitude disturbances in Poiseuille flow. In Laminar–Turbulent Transition: Proc IUTAM Symp., Novosibirsk, USSR, 9–13 July 1984 (ed. Kozlov, V. V.), pp. 183–190. Springer.CrossRefGoogle Scholar
Reynolds, W. C. 1969 Orrsom: A Fortran-IV program for solution of the Orr–Sommerfeld equation. Tech. Rep. FM-4. Stanford University.Google Scholar
Saiki, E. M., Biringen, S., Danabasoglu, G. & Streett, C. L. 1993 Spatial simulation of secondary instability in plane channel flow: comparison of K- and H-type disturbances. J. Fluid Mech. 253, 485–507.CrossRefGoogle Scholar
Saric, W. S., Kozlov, V. V. & Levchenko, V. Y. 1984 Forced and unforced subharmonic resonance in boundary layer transition. AIAA Paper 84-0007.Google Scholar
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.Google Scholar
Shadden, S. C., Lekien, F. & Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271–304.Google Scholar
Shadden, S. C., Lekien, F., Paduan, J. D., Chavez, F. P. & Marsden, J. E. 2009 The correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay. Deep-Sea Res. II 56, 161–172.Google Scholar
Singer, B. A. 1987 Numerical simulation studies of laminar–turbulent transition in the plane channel. PhD thesis, Stanford University, CA.Google Scholar
Singer, B. A., Reed, H. L. & Ferziger, J. H. 1989 The effects of streamwise vortices on transition in the plane channel. Phys. Fluids 1, 1960–1971.Google Scholar
Spalart, P. R. & Yang, K. S. 1987 Numerical study of ribbon-induced transition in Blasius flow. J. Fluid Mech. 178, 345–365.Google Scholar
Voth, G. A., Haller, G. & Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88, 254501.CrossRefGoogle ScholarPubMed
Waggy, S., Biringen, S. & Sullivan, P. P. 2013 Direct numerical simulation of top-down and bottom-up diffusion in the convective boundary layer. J. Fluid Mech. 724, 581–606.Google Scholar
Zang, T. A. & Krist, S. E. 1989 Numerical experiments on stability and transition in plane channel flow. Theor. Comput. Fluid Dyn. 1, 41–64.Google Scholar