Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T21:27:43.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer

Published online by Cambridge University Press:  26 August 2009

OLAF MARXEN ,
MATTHIAS LANG ,
ULRICH RIST ,
ORI LEVIN  and
DAN S. HENNINGSON
OLAF MARXEN*
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
MATTHIAS LANG
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
ULRICH RIST
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
ORI LEVIN
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
*
†Present address: Center for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady linear three-dimensional disturbances are investigated in a two-dimensional laminar boundary layer. The boundary layer is subject to a streamwise favourable-to-adverse pressure gradient and eventually undergoes separation. The separating flow corresponds to the first part of a pressure-induced laminar-separation bubble on a flat plate. Streamwise disturbance development in such a flow is studied by means of direct numerical simulation, a water-tunnel experiment and an adjoint-based parabolic theory suited to study spatial optimal growth. A complete overview of the disturbance evolution in various areas of the favourable-to-adverse pressure gradient laminar boundary layer is given. Results from all investigation methods show overall good agreement with respect to disturbance growth and shape within the entire domain. In the favourable pressure-gradient region and, again, slightly downstream of separation, transient growth caused by the lift-up effect dominates disturbance behaviour. In the adverse pressure-gradient region, a modal instability is observed. Evidence is presented that this instability is of Görtler type.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 165 - 189
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.CrossRefGoogle Scholar
Boiko, A. V. 2002 Development of a stationary streak in a local separation bubble. Tech Rep. IB 224–2002 A04. German Aerospace Center (DLR), Institute for Fluid Mechanics.Google Scholar
Bottaro, A. & Luchini, P. 1999 Görtler vortices: are they amenable to local eigenvalue analysis? Eur. J. Mech. B 18 (1), 47–65.CrossRefGoogle Scholar
Cossu, C., Chomaz, J.-M., Huerre, P. & Costa, M. 2000 Maximum spatial growth of Görtler vortices. Flow Turbul. Combust. 65, 369–392.CrossRefGoogle Scholar
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487–488.Google Scholar
Floryan, J. M. & Saric, W. S. 1982 Stability of Görtler vortices in boundary layers. AIAA. J. 20 (3), 316–324.CrossRefGoogle Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2004 Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer. Phys. Fluids 16 (10), 3627–3638.Google Scholar
Görtler, H. 1941 Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen. ZAMM 21 (4), 250–252.CrossRefGoogle Scholar
Inger, G. R. 1987 Spanwise-periodic three-dimensional disturbances in the wake of a slightly stalled wing. Paper 87-0456. AIAA.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.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
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
Kloker, M. 1998 A robust high-resolution split-type compact FD scheme for spatial direct numerical simulation of boundary-layer transition. Appl. Sci. Res. 59, 353–377.Google Scholar
Landahl, M. T. 1975 Wave breakdown and turbulence. SIAM J. Appl. Math 28 (4), 735–756.CrossRefGoogle Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.CrossRefGoogle Scholar
Lang, M. 2005 Experimentelle Untersuchungen zur Transition in einer laminaren Ablöseblase mit Hilfe der Laser-Doppler-Anemometrie und der Particle Image Velocimetry. Dissertation, Universität Stuttgart, Stuttgart, Germany.Google Scholar
Lang, M., Rist, U. & Wagner, S. 2004 Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV. Exp. Fluids 36, 43–52.Google Scholar
Lee, K. & Liu, J. T. C. 1992 On the growth of mushroomlike structures in nonlinear spatially developing Goertler vortex flows. Phys. Fluids A 4 (1), 95–103.CrossRefGoogle Scholar
Levin, O., Chernoray, V. G., Löfdahl, L. & Henningson, D. S. 2005 A study of the Blasius wall jet. J. Fluid Mech. 539, 313–347.CrossRefGoogle Scholar
Levin, O. & Henningson, D. S. 2003 Exponential vs algebraic growth and transition prediction in boundary layer flow. Flow Turbul. Combust. 70, 183–210.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.Google Scholar
Luchini, P. & Bottaro, A. 1998 Görtler vortices: a backward-in-time approach to the receptivity problem. J. Fluid Mech. 363, 1–23.Google Scholar
Marxen, O. 2005 Numerical studies of physical effects related to the controlled transition process in laminar separation bubbles. Dissertation, Universität Stuttgart, Stuttgart, Germany.Google Scholar
Marxen, O., Rist, U. & Henningson, D. 2006 Steady three-dimensional streaks and their optimal growth in a laminar separation bubble. In New Results in Numerical and Experimental Fluid Mechanics V (ed. Rath, H. J., Holze, C., Heinemann, H.-J., Henke, R. & Hönlinger, H.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol. 92, pp. 233–240. Springer.CrossRefGoogle Scholar
Marxen, O., Rist, U. & Wagner, S. 2004 Effect of spanwise-modulated disturbances on transition in a separated boundary layer. AIAA J. 42 (5), 937–944.CrossRefGoogle Scholar
Pauley, L. L. 1994 Response of two-dimensional separation to three-dimensional disturbances. J. Fluids Engng 116, 433–438.CrossRefGoogle Scholar
Rist, U. 1998 Zur Instabilität und Transition in laminaren Ablöseblasen. Habilitation, Universität Stuttgart, Stuttgart, Germany.Google Scholar
Rist, U. 2002 On instabilities and transition in laminar separation bubbles. In Proceedings of the CEAS Aerospace Aerodynamics Research Conference, Cambridge, UK.Google Scholar
Rist, U. 2003 Instability and transition mechanisms in laminar separation bubbles. In VKI/RTO-LS ‘Low Reynolds Number Aerodynamics on Aircraft Including Applications in Emerging UAV Technology’, pp. 1–29. Van Kármán Institut.Google Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44 (10), 2217–2223.Google Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, 1st edn. Springer.CrossRefGoogle Scholar
Spalart, P. R. & Strelets, M. K. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Watmuff, J. H. 1999 Evolution of a wave packet into vortex loops in a laminar separation bubble. J. Fluid Mech. 397, 119–169.CrossRefGoogle Scholar
Wilson, P. G. & Pauley, L. L. 1998 Two- and three-dimensional large-eddy simulations of a transitional separation bubble. Phys. Fluids 10 (11), 2932–2940.Google Scholar