Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T14:14:32.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanisms of instability growth, interaction and breakdown induced by a backward-facing step in a swept-wing flow

Published online by Cambridge University Press:  18 November 2021

Jenna L. Eppink Open the ORCID record for Jenna L. Eppink [Opens in a new window]
Jenna L. Eppink*
Affiliation:
Flow Physics and Control Branch, NASA Langley Research Center, Hampton, VA23681, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Time-resolved particle image velocimetry measurements were performed downstream of a swept backward-facing step. The measurements allow detailed analysis of the interactions between the unsteady instabilities and the stationary crossflow vortices. Different mechanisms are identified that lead to the modulation of the different families of unsteady instabilities that occur downstream of the step. For the low-frequency spanwise-travelling mode, the modulation occurs due to a redistribution of momentum when the instability encounters regions of large spanwise shear of the wall-normal and streamwise velocity. However, the higher-frequency streamwise-travelling instabilities undergo the familiar ‘lift-up’ mechanism when they encounter the regions of large vertical velocity due to the presence of the stationary crossflow vortices. The process leading to large velocity spikes, and ultimately to a laminar breakdown to turbulence, is identified as a constructive interaction between the different unsteady instabilities, coupled with an interaction with the stationary crossflow vortices when the phases align properly.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A1
Check for updates
Copyright
© National Aeronautics and Space Administration and The Author(s), 2021. To the extent this is a work of the US Government, it is not subject to copyright protection within the United States. Published by 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

REFERENCES

Balakumar, P., King, R.A. & Eppink, J.L. 2014 Effects of forward- and backward-facing steps on the crossflow receptivity and stability in supersonic boundary layers. AIAA Paper 2014-2639.CrossRefGoogle Scholar
Barkley, D., Gomes, M.G.M. & Henderson, R.D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerosp. Sci. 35 (4), 363–412.CrossRefGoogle Scholar
Bonfigli, G., Kloker, M. & Wagner, S. 2003 3-D-boundary-layer transition induced by superposed steady and traveling crossflow vortices. In High Performance Computing in Science and Engineering’02, pp. 255–271. Springer.CrossRefGoogle Scholar
Cooke, E. 2020 Modelling the effect of step and roughness features on swept wing boundary layer instabilities. PhD thesis, Imperial College London.Google Scholar
Crouch, J.D., Kosorygin, V.S. & Ng, L.L. 2006 Modeling the effects of steps on boundary-layer transition. In IUTAM Symposium on Laminar-Turbulent Transition (ed. R. Govindarajan), pp. 37–44. Springer.CrossRefGoogle Scholar
Diwan, S.S. 2009 Dynamics of early stages of transition in a laminar separation bubble. PhD thesis, Indian Institute of Science, Bangalore, India.Google Scholar
Drake, A., Bender, A.M., Korntheuer, A.J., Westphal, R.V., McKeon, B.J., Gerashchenko, S., Rohe, W. & Dale, G. 2010 Step excrescence effects for manufacturing tolerances on laminar flow wings. AIAA Paper 2010-375.CrossRefGoogle Scholar
Duncan, G.T. Jr., Crawford, B.K. & Saric, W.S. 2013 Effects of step excrescences on swept-wing transition. AIAA Paper 2013-2412.CrossRefGoogle Scholar
Duncan, G.T. Jr., Crawford, B.K., Tufts, M.W., Saric, W.S. & Reed, H.L. 2014 Effects of step excrescences on a swept wing in a low-disturbance wind tunnel. AIAA Paper 2014-0910.CrossRefGoogle Scholar
Eppink, J.L. 2019 Validation and uncertainty analysis of stereo time-resolved PIV measurements for boundary-layer transition research. AIAA Paper 2019-1825.CrossRefGoogle Scholar
Eppink, J.L. 2020 a Effect of step shape on transition over a swept backward-facing step. AIAA Paper 2020-3051.CrossRefGoogle Scholar
Eppink, J.L. 2020 b Mechanisms of stationary cross-flow instability growth and breakdown induced by forward-facing steps. J. Fluid Mech. 897, A15.CrossRefGoogle Scholar
Eppink, J.L., Wlezien, R.W., King, R.A. & Choudhari, M. 2018 Interaction of a backward-facing step and crossflow instabilities in boundary-layer transition. AIAA J. 56 (2), 497–509.CrossRefGoogle ScholarPubMed
Eppink, J.L., Wlezien, R.W., King, R.A. & Choudhari, M. 2019 Influence of a backward-facing step on swept-wing boundary-layer transition. AIAA J. 57 (1), 267–278.CrossRefGoogle ScholarPubMed
Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.CrossRefGoogle Scholar
Gartling, D.K. 1990 A test problem for outflow boundary conditions – flow over a backward-facing step. Intl J. Numer. Meth. Fluids 11 (7), 953–967.CrossRefGoogle Scholar
Gresho, P.M., Gartling, D.K., Torczynski, J.R., Cliffe, K.A., Winters, K.H., Garratt, T.J., Spence, A. & Goodrich, J.W. 1993 Is the steady viscous incompressible two-dimensional flow over a backward-facing step at $Re= 800$ stable? Intl J. Numer. Meth. Fluids 17 (6), 501–541.CrossRefGoogle Scholar
Hammond, D.A. & Redekopp, L.G. 1998 Local and global instability properties of separation bubbles. Eur. J. Mech. B/Fluids 17 (2), 145–164.CrossRefGoogle Scholar
Hedley, T.B. & Keffer, J.F. 1974 Turbulent/non-turbulent decisions in an intermittent flow. J. Fluid Mech. 64 (4), 625–644.CrossRefGoogle Scholar
Hildebrand, N., Choudhari, M. & Paredes, P. 2020 Predicting boundary-layer transition over backward-facing steps via linear stability analysis. AIAA J. 58 (9), 3728–3734.CrossRefGoogle Scholar
Holmes, B.J., Obara, C.J., Martin, G.L. & Domack, C.S. 1985 Manufacturing tolerances for natural laminar flow airframe surfaces. SAE Paper 850863.CrossRefGoogle Scholar
Hosseinverdi, S. & Fasel, H.F. 2018 Role of Klebanoff modes in active flow control of separation: direct numerical simulations. J. Fluid Mech. 850, 954–983.CrossRefGoogle Scholar
Hu, W., Hickel, S. & Van Oudheusden, B. 2020 Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step. Phys. Fluids 32 (5), 056102.Google Scholar
Kaltenbach, H.-J. & Janke, G. 2000 Direct numerical simulation of flow separation behind a swept, rearward-facing step at $Re$ $h= 3000$. Phys. Fluids 12 (9), 2320–2337.CrossRefGoogle Scholar
Kuan, C.L. & Wang, T. 1990 Investigation of the intermittent behavior of transitional boundary layer using a conditional averaging technique. Expl Therm. Fluid Sci. 3 (2), 157–173.CrossRefGoogle Scholar
Loiseau, J.-C., Robinet, J.-C., Cherubini, S. & Leriche, E. 2014 Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations. J. Fluid Mech. 760, 175–211.CrossRefGoogle Scholar
Malik, M.R., Crouch, J.D., Saric, W.S., Lin, J.C. & Whalen, E.A. 2016 Application of drag reduction techniques to transport aircraft. In Encyclopedia of Aerospace Engineering, p. 1–10. John Wiley and Sons.CrossRefGoogle Scholar
Perraud, J. & Seraudie, A. 2000 Effects of steps and gaps on 2D and 3D transition. In European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, 11–14 Sept. 2000. ECCOMAS.Google Scholar
Rani, H.P. & Sheu, T.W.H. 2006 Nonlinear dynamics in a backward-facing step flow. Phys. Fluids 18 (8), 084101.CrossRefGoogle Scholar
Rani, H.P., Sheu, T.W.H. & Tsai, E.S.F. 2007 Eddy structures in a transitional backward-facing step flow. J. Fluid Mech. 588, 43–58.CrossRefGoogle Scholar
Saeed, T.I., Mughal, M.S. & Morrison, J. 2016 The interaction of a swept-wing boundary layer with surface excrescences. AIAA Paper 2016-2065.CrossRefGoogle Scholar
Saric, W.S. & Reshotko, E. 1998 Review of flow quality issues in wind tunnel testing. AIAA Paper 1998-2613.CrossRefGoogle Scholar
Schäfer, F., Breuer, M. & Durst, F. 2009 The dynamics of the transitional flow over a backward-facing step. J. Fluid Mech. 623, 85–119.CrossRefGoogle Scholar
Schmidt, O.T. & Colonius, T. 2020 Guide to spectral proper orthogonal decomposition. AIAA J. 58 (3), 1023–1033.CrossRefGoogle Scholar
Schmidt, O.T. & Schmid, P.J. 2019 A conditional space–time pod formalism for intermittent and rare events: example of acoustic bursts in turbulent jets. J. Fluid Mech. 867, R2.CrossRefGoogle Scholar
Schneider, S.P. 1995 Improved methods for measuring laminar-turbulent intermittency in boundary layers. Exp. Fluids 18 (5), 370–375.CrossRefGoogle Scholar
Schröder, A., Schanz, D., Heine, B. & Dierksheide, U. 2013 Investigation of transitional flow structures downstream of a backward-facing-step by using 2D-2C- and high resolution 3D-3C-TOMO-PIV. In New Results in Numerical and Experimental Fluid Mechanics VIII (ed. A. Dillmann et al. ), pp. 219–226. Springer.CrossRefGoogle Scholar
Serpieri, J. & Kotsonis, M. 2016 Three-dimensional organisation of primary and secondary crossflow instability. J. Fluid Mech. 799, 200–245.CrossRefGoogle Scholar
Theodorsen, T. 1955 The structure of turbulence. In 50 Jahre Grenzschichtforschung (ed. H. Görtler and W. Tollmien), pp. 55–62. Springer.CrossRefGoogle Scholar
Tufts, M.W., Reed, H.L., Crawford, B.K., Duncan, G.T. Jr & Saric, W.S. 2017 Computational investigation of step excrescence sensitivity in a swept-wing boundary layer. J. Aircraft 54 (2), 602–626.CrossRefGoogle Scholar
Wang, Y.X. & Gaster, M. 2005 Effect of surface steps on boundary layer transition. Exp. Fluids 39 (4), 679–686.CrossRefGoogle Scholar
Wassermann, P. & Kloker, M. 2005 Transition mechanisms in a three-dimensional boundary-layer flow with pressure-gradient changeover. J. Fluid Mech. 530, 265–293.CrossRefGoogle Scholar
Wörner, A., Rist, U. & Wagner, S. 2002 Influence of humps and steps on the stability characteristics of a 2D laminar boundary layer. AIAA Paper 2002-0139.CrossRefGoogle Scholar
Zhang, D.H., Chew, Y.T. & Winoto, S.H. 1996 Investigation of intermittency measurement methods for transitional boundary layer flows. Expl Therm. Fluid Sci. 12 (4), 433–443.CrossRefGoogle Scholar

Eppink supplementary movie 1

See word file for movie caption

Download Eppink supplementary movie 1(Video)
Video 8.2 MB

Eppink supplementary movie 2

See word file for movie caption

Download Eppink supplementary movie 2(Video)
Video 13.3 MB

Eppink supplementary movie 3

See word file for movie caption

Download Eppink supplementary movie 3(Video)
Video 13.9 MB

Eppink supplementary movie 4

See word file for movie caption

Download Eppink supplementary movie 4(Video)
Video 15 MB

Eppink supplementary movie 5

See word file for movie caption

Download Eppink supplementary movie 5(Video)
Video 12.9 MB

Eppink supplementary movie 6

See word file for movie caption

Download Eppink supplementary movie 6(Video)
Video 9.1 MB

Eppink supplementary movie 7

See word file for movie caption

Download Eppink supplementary movie 7(Video)
Video 5.5 MB

Eppink supplementary movie 8

See word file for movie caption

Download Eppink supplementary movie 8(Video)
Video 5.8 MB

Eppink supplementary movie 9

See word file for movie caption

Download Eppink supplementary movie 9(Video)
Video 9.8 MB

Eppink supplementary movie 10

See word file for movie caption

Download Eppink supplementary movie 10(Video)
Video 5 MB
Supplementary material: File

Eppink supplementary material

Captions for movies 1-10

Download Eppink supplementary material(File)
File 46.6 KB