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Direct numerical simulation of controlled transition in a flat-plate boundary layer

Published online by Cambridge University Press:  26 April 2006

U. Rist  and
H. Fasel
U. Rist
Affiliation:
Institut für Aero- und Gasdynamik, Universität Stuttgart, D-70550 Stuttgart, Germany
H. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
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Abstract

The three-dimensional development of controlled transition in a flat-plate boundary layer is investigated by direct numerical simulation (DNS) using the complete Navier-Stokes equations. The numerical investigations are based on the so-called spatial model, thus allowing realistic simulations of spatially developing transition phenomena as observed in laboratory experiments. For solving the Navier-Stokes equations, an efficient and accurate numerical method was developed employing fourth-order finite differences in the downstream and wall-normal directions and treating the spanwise direction pseudo-spectrally. The present paper focuses on direct simulations of the wind-tunnel experiments by Kachanov et al. (1984, 1985) of fundamental breakdown in controlled transition. The numerical results agreed very well with the experimental measurements up to the second spike stage, in spite of relatively coarse spanwise resolution. Detailed analysis of the numerical data allowed identification of the essential breakdown mechanisms. In particular, from our numerical data, we could identify the dominant shear layers and vortical structures that are associated with this breakdown process.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 211 - 248
Copyright
© 1995 Cambridge University Press

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References

Bertolotti, F. P. 1991 Linear and nonlinear stability of boundary layers with streamwise varying properties. Dissertation, Ohio State University.
Bertolotti, F. P., Herbert, Th. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.Google Scholar
Biringen, S. 1987 Three-dimensional vortical structures of transition in plane channel flows. Phys. Fluids 30, 3359–3368.Google Scholar
Cimbala, F. M., Nagib, H. M. & Roshko, A. 1988 Large structures in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265–298.Google Scholar
Fasel, H. F. 1976 Investigation of the stability of boundary layers by a finite-difference model of the Navier-Stokes equations. J. Fluid Mech. 18, 355–383.Google Scholar
Fasel, H. F. & 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
Fasel, H. F., Rist, U. & Konzelmann, U. 1990 Numerical investigation of the three-dimensional development in boundary-layer transition. AIAA J. 28, 29–37.Google Scholar
Caster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.Google Scholar
Gaster, M. 1965a On the generation of spatially growing waves in a boundary layer. J. Fluid Mech. 22, 433–441.Google Scholar
Gaster, M. 1965b The role of spatially growing waves in the theory of hydrodynamic stability. Prog. Aerospace Sci. 6, 251–270.Google Scholar
Gaster, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723–727.Google Scholar
Gaster, M. 1974 Nonparallel effects on boundary layer stability. J. Fluid Mech. 66, 465–480.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 341, 253–269.Google Scholar
Hama, F. R. 1962 Streaklines in a perturbed shear flow. Phys. Fluids 5, 644–650.Google Scholar
Hama, F. R. & Nutant, J. 1963 Detailed flow-field observations in the transition process in a thick boundary layer. In Proc. 1963 Heat Transfer and Fluid Mech. Inst., pp. 77–93. Stanford University Press.
Heisenberg, W. 1924 Über Stabilität und Turbulenz von Flüssigkeitsströmen. Ann. Phys. 74, 577–627.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20, 487–526.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Jordinson, R. 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. J. Fluid Mech. 43, 801.Google Scholar
Kachanov, Y. S. 1987 On the resonant nature of the breakdown of a laminar boundary layer. J. Fluid Mech. 184, 43–74.Google Scholar
Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y. 1977 Nonlinear development of a wave in a boundary layer. Izv. Akad. Nauk, SSSR Mech. Zhid Gaza 3 49–53 (in Russian); (transl. Fluid Dyn. 12, 1987, 383–390).Google Scholar
Kachanov, Y. S., Kozlov, V. V., Levchenko, V. V. & Ramazanov, M. P. 1984 Experimental study of K-regime of breakdown of laminar boundary layer. Preprint 9–84. Novosibirsk, ITPM SO AN SSSR (in Russian).
Kachanov, Y.S., Kozlov, V. V., Levchenko, V. Y. & Ramazanov, M. P. 1985 On the nature of K-breakdown of a laminar boundary-layer; new experimental data. In Laminar-Turbulent Transition (ed. V. V. Kozlov), pp. 61–73. Springer.
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
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
Kleiser, L. 1982 Numerische Simulation zum laminar-turbulenten Umschlagsprozeβ der ebenen Poiseuille-Strömung. Dissertation, University of Karlsruhe.
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Ann. Rev. Fluid Mech. 23, 495–537.Google Scholar
Kloker, M., Konzelmann, U. & Fasel, H. 1993 Outflow boundary conditions for spatial Navier-Stokes simulations of transitional boundary layers. AIAA J. 31, 620–628.Google Scholar
Konzelmann, U., Rist, R. & Fasel, H. 1987 Erzeugung dreidimensionaler, räumlich angefachter Störwellen durch periodisches Ausblasen und Absaugen in einer Plattengrenzschichtströmung. Z. Angew. Math. Mech. 67, T298–T300.Google Scholar
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. In Proc. 1962 Heat Transfer and Fluid Mech. Inst., pp. 1–26, Stanford University Press.
Kozlov, V. V. & Levchenko, V. Y. 1987 Laminar-turbulent transition controlled by localized disturbances. In Turbulence Management and Relaminarization (ed. H. W. Liepmann & R. Narasimha), pp. 249–269. Springer.
Krist, S. E. & Zang, T. A. 1987 Numerical simulation of channel flow transition. Resolution requirements and structure of the hairpin vortex. NASA TP 2667.
Laurien, E. & Kleiser, L. 1989 Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech. 199, 403–440.Google Scholar
Rai, M. M. & Moin, P. 1991 Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys. 96, 15–53.Google Scholar
Rai, M. M. & Moin, P. 1993 Direct simulations of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109, 169–192.Google Scholar
Rist, U. 1990 Numerische Untersuchung der räumlichen, dreidimensionalen Störungsentwicklung beim Grenzschichtumschlag. Dissertation, University of Stuttgart.
Roache, P. J. 1976 Computational Fluid Dynamics. Hermosa, Albuquerque.
Schlichting, H. 1933 Zur Entstehung der Turbulenz bei der Plattenströmung. Z. Angew. Math. Mech. 13, 171–174.Google Scholar
Schmidt, P. J. & Henningson, D. S. 1992 A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids A 4, 1986–1989.Google Scholar
Schubauer, G. B. & Skramstad, H. K. 1947 Laminar boundary layer oscillations and stability of laminar flow. J. Aeronaut. Sci. 14, 69–78.Google Scholar
Spalart, P. R. & Yang, K. S. 1987 Numerical study of ribbon-induced transition in Blasius flow. J. Fluid Mech. 118, 345–365.Google Scholar
Tollmien, W. 1929 Über die Entstehung der Turbulenz; 1. Mitteilung. Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse, pp. 21–44.
Williams, D. R., Fasel, H. F. & Hama, F. R. 1984 Experimental determination of the three-dimensional vorticity field in the boundary-layer transition process. J. Fluid Mech. 149, 179–203.Google Scholar
Wortmann, F. X. 1981 Boundary-layer waves and transition. In Advances in Fluid Mechanics (ed. E. Krause). Lecture Notes in Physics, vol. 148, pp. 268–279. Springer.
Wray, A. & Hussaini, M. Y. 1984 Numerical experiments in boundary-layer stability. Proc. R. Soc. Lond. A 392, 373–389.Google Scholar
Zang, T. A. & Hussaini, M. Y. 1987 Numerical simulation of nonlinear interactions in channel and boundary-layer transition. In Nonlinear Wave Interactions in Fluids (ed. R. W. Miksad, T. R. Akylas & T. Herbert), pp. 131–145. AMD-87, ASME.