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Direct numerical simulation of passive control of three-dimensional phenomena in boundary-layer transition using wall heating

Published online by Cambridge University Press:  26 April 2006

L. D. Kral  and
H. F. Fasel
L. D. Kral
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA Present address: McDonnell Douglas Aerospace, PO Box 516, MC 106-4126, St Louis, MO 63166, USA.
H. F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
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Abstract

A numerical model is presented for investigating control of the three-dimensional boundary-layer transition process. Control of a periodically forced, spatially evolving boundary layer in water is studied using surface heating techniques. The Navier–Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. The Navier–Stokes equations are used in vorticity–velocity form and are coupled with the energy equation through the viscosity dependence on temperature. Passive control of small amplitude two-dimensional waves and three-dimensional oblique waves is numerically simulated with either uniform or non-uniform wall heating applied. Both amplitude levels and amplification rates are strongly reduced with heating applied. Comparison is made with parallel and non-parallel linear stability theory and experiments. Control of the early stages of the nonlinear breakdown process is also investigated using uniform wall heating. Both control of the fundamental and subharmonic routes to turbulence are investigated. For both breakdown processes, a strong reduction in amplitude levels and growth rates results. In particular, the high three-dimensional growth rates that are characteristic of the secondary instability process are significantly reduced below the uncontrolled levels.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 264 , 10 April 1994 , pp. 213 - 254
Copyright
© 1994 Cambridge University Press

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References

Asrar, W. & Nayfeh, A. H. 1985 Nonparallel stability of heated two-dimensional boundary layers. Phys. Fluids 28, 1263–1272.Google Scholar
Barker, S. J. 1979 Experiments on heat-stabilized boundary layers in a tube. Proc. 12th Symp. on Naval Hydrodyn., pp. 77–85. National Academy of Sciences, Washington, DC.
Barker, S. J. & Jennings, C. 1977 The effect of wall heating upon transition. Proc. AGARD Symp. on Laminar-Turbulent Transition, Copenhagen, pp. 19-1–19-9.
Bestek, H., Dittrich, P. & Fasel, H. 1987 Einfluß der Wandtemperatur auf die Entwicklung von Tollmien–Schlichting–Wellen in Grenzschichströmungen. Z. angew. Math. Mech. 67, 256–258.Google Scholar
Bushnell, D. M. 1983 Turbulent drag reduction for external flows. AIAA paper 83-0227.
Bushnell, D. M. & Hefner, J. N. (eds) 1990 Viscous drag reduction in boundary layers. In Prog. Astronaut. Aeronaut. 123 (ed. A. R. Seebass). AIAA.
El-Hady, N. M. & Nayfeh, A. H. 1979 Nonparallel stability of two-dimensional heated boundary layer flows. Proc. 12th Symp. on Naval Hydrodyn., pp. 53–62. National Academy of Sciences, Washington, DC.
Fasel, H. 1976 Investigation of the stability of boundary layers by a finite-difference model of the Navier–Stokes equations. J. Fluid Mech. 78, 355–383.Google Scholar
Fasel, H. 1989 Numerical simulation of instability and transition in boundary layer flows. Proc. 3rd IUTAM Symp. on Laminar–Turbulent Transition, Toulouse, pp. 587–598.Google Scholar
Fasel, H. & Bestek, H. 1980 Investigation of nonlinear, spatial disturbance amplification in plane Poiseuille flow. Proc. IUTAM Symp. on Laminar–Turbulent Transition, Stuttgart, pp. 173–185.Google Scholar
Fasel, H., Bestek, H. & Schefenacker, R. 1977 Numerical simulation studies of transitional phenomena in incompressible, two-dimensional flows. Proc. AGARD Symp. on Laminar–Turbulent Transition, Copenhagen, pp. 14-1–14-8.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
Fasel, H., Rist, U. & Konzelmann, U. 1990 Numerical investigation of the three-dimensional development in boundary layer transition. AIAA J. 28, 29–37.Google Scholar
Gazley, C. & Wazzan, A. R. 1985 Control of water boundary layer stability and transition by surface temperature distribution. Proc. 2nd IUTAM Symp. on Laminar–Turbulent Transition, Novosibirsk, pp. 153–162.Google Scholar
Hama, F. R. & Nutant, J. 1963 Detailed flow observation in the transition process in a thick boundary layer. Proc. Heat Transfer and Fluid Mech. Inst. 77. Stanford University Press.
Hardy, R. C. & Cottington, R. C. 1949 J. Res. NBS 42, 573.
Hauptmann, E. G. 1968 The influence of temperature dependent viscosity on laminar boundary-layer stability. Intl J. Heat Mass Transfer 11, 1049–1052.Google Scholar
Kachanov, Yu. S. & Levchenko, V. Ya. 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, 1–41.Google Scholar
Kloker, M., Konzelmann, U. & Fasel, H. 1993 Outflow boundary conditions for spatial Navier–Stokes simulations of transition boundary layers. AIAA J. 31, 620–628.Google Scholar
Konzelmann, U., Rist, U. & Fasel, H. 1987 Erzeugung Dreidimensionaler, Räumlich Angefachter Störwellen Durch Periodisches Ausblasen und Absaugen in einer Plattengrenzschichtströmung. Z. angew. Math. Mech. 67, 298–300.Google Scholar
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. Proc. Heat Transfer Fluid Mech. Institute, pp. 1–26.Google Scholar
Kral, L. D. 1988 Numerical investigation of transition control of a flat plate boundary layer. Dissertation, University of Arizona.
Kral, L. D. & Fasel, H. F. 1991 Numerical investigation of three-dimensional active control of boundary layer transition. AIAA J. 29, 1407–1417.Google Scholar
Liepmann, H. W., Brown, G. L. & Nosenchuck, D. M. 1982 Control of laminar–instability waves using a new technique. J. Fluid Mech. 118, 187–200.Google Scholar
Liepmann, H. W. & Fila, G. H. 1946 Investigations of effects of surface temperature and single roughness elements on boundary-layer transition. NACA Rep. 890, 587–598.
Lowell, R. L. 1974 Numerical study of the stability of a heated, water boundary layer. Dissertation, Case Western Reserve University.
Nayfeh, A. H. & El-Hady, N. M. 1980 Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows. Phys. Fluids 23, 10–18.Google Scholar
Nosenchuck, D. M. 1982 Passive and active control of boundary layer transition. Dissertation, California Institute of Technology.
Saric, W. S., Kozlov, V. V. & Levchenko, V. Ya. 1984 Forced and unforced subharmonic resonance in boundary-layer transition. AIAA paper 84-0007.
Saric, W. S. & Thomas, A. S. W. 1983 Experiments on the subharmonic route to turbulence in boundary layers. Proc. IUTAM Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, pp. 117–122.Google Scholar
Strazisar, A. J. & Reshotko, E. 1978 Stability of heated laminar boundary layers in water with nonuniform surface temperature. Phys. Fluids 21, 727–735.Google Scholar
Strazisar, A. J., Reshotko, E. & Prahl, J. M. 1977 Experimental study of the stability of heated laminar boundary layers in water. J. Fluid Mech. 83, 225–247.Google Scholar
Swindells, J. F. 1982 NBS, unpublished results. From CRC Handbook of Chemistry and Physics, 63rd edn, 1982–83, F-40, CRC Press.
Wazzan, A. R., Okamura, T. T. & Smith, A. M. O. 1968 The stability of water flow over heated and cooled flat plates. Trans. ASME C: J. Heat Transfer, February, 109–114.Google Scholar
Wazzan, A. R., Okamura, T. T. & Smith, A. M. O. 1970a The stability of incompressible flat plate laminar boundary layer in water with temperature dependent viscosity. Proc. Southeastern Seminar on Thermal Sciences, pp. 184–201.Google Scholar
Wazzan, A. R., Okamura, T. T. & Smith, A. M. O. 1970b The stability and transition of heated and cooled incompressible laminar boundary layers. Proc. 4th Intl Heat Transfer Conf., FC 1.4, pp. 1–11.
Zang, T. A. & Hussaini, M. Y. 1985a Numerical experiments on subcritical transition mechanism. AIAA paper 85-0296.
Zang, T. A. & Hussaini, M. Y. 1985b Numerical experiments on the stability of controlled shear flows. AIAA paper 85-1698.