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Perspectives on the Phenomenology and Modeling of Boundary Layer Transition

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Abstract

This article is a perspective review of boundary layer transition. Both orderly and bypass transition are discussed, but with a decided emphasis on bypass routes. The focus is on transition in a natural, perturbed environment. Then orderly transition occurs through Λ vortices, that develop locally on instability waves. The precursors to bypass transition are boundary layer ‘streaks’. Transition proceeds through inner and outer mode secondary instability, leading to patches of turbulence: in zero pressure gradient, bypass transition develops through local, undulatory, outer mode breakdown; in sufficiently adverse pressure gradient, bypass transition proceeds through inner mode instability, which may be of varicose or of helical form. Phenomenology of the creation, growth and breakdown of streaks is surveyed. Theories of shear sheltering, transient and optimal growth, and Orr-Sommerfeld continuous mode resonance are summarized. Recent developments in predictive modeling are summarized. These include laminar fluctuation, and intermittency models. Some open questions are discussed, as are needs for further research.

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  1. modulo Squire’s transformation

References

  1. Saric, W.S., Reed, H.L., White, E.B.: Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440 (2003). doi:10.1146/annurev.fluid.35.101101.161045

    Article  MathSciNet  MATH  Google Scholar 

  2. Bose, R., Durbin, P.A.: Helical modes in boundary layer transition. Phys. Rev. Fluids 1, 073,602 (2016a). doi:10.1103/PhysRevFluids.1.073602

    Article  Google Scholar 

  3. Zaki, T.A., Durbin, P.A.: Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111 (2005). doi:10.1017/S0022112005003800

    Article  MathSciNet  MATH  Google Scholar 

  4. Drazin, P.G.: Introduction to Hydrodynamic Stability. Cambridge University Press (2002)

  5. White, F.M.: Viscous Fluid Flow, 2nd edn. McGraw-Hill, Inc (1991)

    Google Scholar 

  6. Grosch, C.E., Salwen, H.: The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and the eigenfunctions. J. Fluid Mech. 68, 33–54 (1978)

    Article  MATH  Google Scholar 

  7. Durbin, P.A., Wu, X.: Transition beneath vortical disturbances. Annu. Rev. Fluid Mech. 39, 107–128 (2007). doi:10.1146/annurev.fluid.39.050905.110135

    Article  MathSciNet  MATH  Google Scholar 

  8. Hama, F.R.: Progressive deformation of a curved vortex filament by its own induction. Phys. Fluids 5(10), 1156–1162 (1962). doi:10.1063/1.1706500

    Article  MATH  Google Scholar 

  9. Herbert, T.: Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526 (1988). doi:10.1146/annurev.fl.20.010188.002415

    Article  Google Scholar 

  10. Rist, U., Fasel, H.: Direct numerical simulation of controlled transition in a flat-plate boundary layer. JFM 298, 211–248 (1995). doi:10.1017/S0022112095003284

    Article  MATH  Google Scholar 

  11. Schlatter, P., Li, Q., Brethouwer, G., Johansson, A.V., Henningson, D.S.: Structure of a turbulent boundary layer studied by DNS. In: Kuerten, H., Geurts, B., Armenio, V., Fröhlich, J. (eds.) Direct and Large-Eddy Simulation VIII, pp. 9–14. Springer Netherlands, Dordrecht (2011). doi:10.1007/978-94-007-2482-2_2

    Chapter  Google Scholar 

  12. Liu, Y., Zaki, T.A., Durbin, P.A.: Boundary layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 199–233 (2008a). doi:10.1017/S0022112008001201

    Article  MathSciNet  MATH  Google Scholar 

  13. Reshotko, E.A.: Boundary layer stability and transition. Annu. Rev. Fluid Mech. 8, 311–349 (1976)

    Article  Google Scholar 

  14. Brandt, L.: The lift-up effect: The linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. B. Fluids 47, 80–96 (2014). http://www.sciencedirect.com/science/article/pii/S0997754614000405

    Article  MathSciNet  MATH  Google Scholar 

  15. Zaki, T.A.: From streaks to spots and on to turbulence: Exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91(3), 451–473 (2013). doi:10.1007/s10494-013-9502-8

    Article  Google Scholar 

  16. Jacobs, R.G., Durbin, P.A.: Shear sheltering and the continuous spectrum of the Orr-Sommerfeld equation. Phys. Fluids 10(8), 2006–2011 (1998). doi:10.1063/1.869716

    Article  MathSciNet  MATH  Google Scholar 

  17. Moffatt, H.K.: In: Proceedings URSI-IUGG International Colloquium on Atmospheric Turbulence and Radio Wave Propagation, Moscow: Nauka, pp. 139–154 (1967)

  18. Landahl, M.T.: A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251 (1980). doi:10.1017/S0022112080000122

    Article  MathSciNet  MATH  Google Scholar 

  19. Butler, K.M., Farrell, B.F.: Three-dimensional optimal perturbations in viscous flow. Phys. Fluids 4(8), 1637–1650 (1992)

    Article  Google Scholar 

  20. Schmid, P.J., Brandt, L.: Analysis of fluid systems: stability, receptivity, sensitivity. Appl. Mech. Rev. 66, 024,803–024,803–21 (2014). doi:10.1115/1.4026375

    Article  Google Scholar 

  21. Andersson, P., Berggren, M., Henningson, D.S.: Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11(1), 134–150 (1999). doi:10.1063/1.869908

    Article  MathSciNet  MATH  Google Scholar 

  22. Luchini, P.: Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bose, R., Durbin, P.A.: Transition to turbulence by interaction of free-stream and discrete mode perturbations. Phys. Fluids 28(11), 114,105 (2016b). doi:10.1063/1.4966978

    Article  Google Scholar 

  24. Brinkerhoff, J.R., Yaras, M.I.: Numerical investigation of transition in a boundary layer subjected to favourable and adverse streamwise pressure gradients and elevated free stream turbulence. J. Fluid Mech. 781, 52–86 (2015). doi:10.1017/jfm.2015.457

    Article  MathSciNet  MATH  Google Scholar 

  25. Rao, V.N., Jefferson-Loveday, R., Tucker, P.G., Lardeau, S.: Large eddy simulations in turbines: Influence of roughness and free-stream turbulence. Flow Turbul. Combust. 92(1-2), 543–561 (2014)

    Article  Google Scholar 

  26. Gostelow, J.P., Blunden, A.R., Walker, G.J.: Effects of free-stream turbulence and adverse pressure gradients on boundary layer transition. J. Turbomach. 116, 392–404 (1994). doi:10.1115/1.2929426

    Article  Google Scholar 

  27. Walker, G.J., Gostelow, J.P.: Effects of adverse pressure gradients on the nature and length of boundary layer transition. J. Turbomach. 112, 196–205 (1989)

    Article  Google Scholar 

  28. Zaki, T.A., Wissink, J., Rodi, W., Durbin, P.A.: Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence. J. Fluid Mech. 665, 57–98 (2010). doi:10.1017/S0022112010003873

    Article  MATH  Google Scholar 

  29. Bose, R.: Mixed Mode Transition to Turbulence in Boundary Layers. Iowa State University, PhD thesis (2016)

    Google Scholar 

  30. Hack, M.J.P., Zaki, T.A.: Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech. 741, 280–315 (2014). http://journals.cambridge.org/article_S0022112013006770

    Article  MathSciNet  Google Scholar 

  31. Lardeau, S., Leschziner, M.A., Zaki, T.A.: Large eddy simulation of transitional separated flow over a flat plate and a compressor blade. Flow Turbul. Combust. 88 (1-2), 19–44 (2012). doi:10.1007/s10494-011-9353-0

    Article  MATH  Google Scholar 

  32. Nagarajan, S., Lele, S.K., Ferziger, J.H.: Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471–504 (2007). doi:10.1017/S0022112006001893

    Article  MATH  Google Scholar 

  33. Westin, K.J.A., Henkes, R.A.W.M.: Application of turbulence models to bypass transition. J. Fluids Eng. 119(4), 859–866 (1997). doi:10.1115/1.2819509

    Article  Google Scholar 

  34. Alfredsson, P.H., Matsubara, M.: Streaky structures in transition. In: Henkes, R.A.W.M., van Ingen, J.L. (eds.) Transitional Boundary Layers in Aeronautics, pp. 374–386. Elsevier Science Pub. (1996)

  35. Jacobs, R.G., Durbin, P.A.: Bypass transition phenomena studied by computer simulation. Report no. TF-77, Stanford University, Department of Mechanical Engineering (2000a)

  36. Goldstein, M.E.: Boundary-layer receptivity to long-wave free-stream disturbances. Annu. Rev. Fluid Mech. 21(1), 137–166 (1989). doi:10.1146/annurev.fl.21.010189.001033

    Article  MathSciNet  MATH  Google Scholar 

  37. Leib, S.J., Wundrow, D.W., Goldstein, M.E.: Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  38. Bertolotti, F.P.: Response of the Blasius boundary layer to free-stream vorticity. Phys. Fluids 9(8), 2286–2299 (1997)

    Article  Google Scholar 

  39. Kendall, J.M.: Experiments on boundary-layer receptivity to freestream turbulence. 36th AIAA Aerospace Sciences Meeting and Exhibit AIAA-98-0530, 10.2514/6.1998-530 (1998)

  40. Westin, K.J.A., Boiko, A.V., Klingmann, B.G.B., Kozlov, V.V., Alfredsson, P.H.: Experiments in a boundary layer subjected to freestream turbulence. Part I. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193–218 (1994)

    Article  Google Scholar 

  41. Hunt, J.C.R., Durbin, P.A.: Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24, 375–404 (1999). doi:10.1016/S0169-5983(99)00009-X

    Article  MathSciNet  MATH  Google Scholar 

  42. Zaki, T.A., Saha, S.: On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. J. Fluid Mech. 626, 111–147 (2009). doi:10.1017/S0022112008005648

    Article  MathSciNet  MATH  Google Scholar 

  43. Bhaskaran, R., Lele, S.K.: Large eddy simulation of free-stream turbulence effects on heat transfer to a high-pressure turbine cascade. J. Turbul. 11. doi:10.1080/14685241003705756 (2010)

  44. Brandt, L., Schlatter, P., Henningson, D.S.: Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  45. Jacobs, R.G., Durbin, P.A.: Simulations of bypass transition. J. Fluid Mech. 428, 185–212 (2000b). doi:10.1017/S0022112000002469

    Article  MATH  Google Scholar 

  46. Durbin, P.A., Pettersson Reif, B.A.: Statistical Theory and Modeling for Turbulent Flows, 2nd edn. John Wiley & Sons, Chichester, U.K.; New York, U.S.A. (2010). ISBN: 978-0-470-68931-8

    Book  MATH  Google Scholar 

  47. Landahl, M.T.: Wave breakdown and turbulence. SIAM J. Appl. Math. 28, 735 (1975)

    Article  MATH  Google Scholar 

  48. Matsubara, M., Alfredsson, P.: Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168 (2001)

    Article  MATH  Google Scholar 

  49. Wu, X., Jacobs, R.G., Durbin, P.A., Hunt, J.C.R.: Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109–153 (1999). doi:10.1017/S0022112099006205

    Article  MATH  Google Scholar 

  50. Schlatter, P., Brandt, L., de Lange, H.C., Henningson, D.S.: On streak breakdown in bypass transition. Phys. Fluids 20(10), 101,505 (2008). doi:10.1063/1.3005836

    Article  MATH  Google Scholar 

  51. Vaughan, N.J., Zaki, T.A.: Stability of zero-pressure-gradient boundary layer distorted by unsteady klebanoff streaks. J. Fluid Mech. 681, 116–153 (2011). http://journals.cambridge.org/article_S0022112011001777

    Article  MATH  Google Scholar 

  52. Andersson, P., Brandt, L., Bottaro, A., Henningson, D.S.: On the breakdown of boundary layers streaks. J. Fluid Mech. 428, 29–60 (2001). doi:10.1017/S0022112000002421

    Article  MathSciNet  MATH  Google Scholar 

  53. Schoppa, W., Hussain, F.: Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108 (2002). doi:10.1017/S002211200100667X

    Article  MathSciNet  MATH  Google Scholar 

  54. Hœpffner, J, Brandt, L., Henningson, D.S.: Transient growth on boundary layer streaks. J. Fluid Mech. 537, 91–100 (2005). doi:10.1017/S0022112005005203

    Article  MathSciNet  MATH  Google Scholar 

  55. Cossu, C., Brandt, L.: On Tollmien-Schlichting like waves in streaky boundary layers. Eur. J. Mech. B. Fluids 23, 815–833 (2004). http://www.sciencedirect.com/science/article/pii/S0997754604000469

    Article  MathSciNet  MATH  Google Scholar 

  56. Kachanov, Y.S.: Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–482 (1994). doi:10.1146/annurev.fl.26.010194.002211

    Article  MathSciNet  Google Scholar 

  57. Liu, Y., Zaki, T.A., Durbin, P.A.: Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien-Schlichting waves. Phys. Fluids 20(124102). doi:10.1017/S0022112008001201 (2008b)

  58. Chau-Lyan, C., Choudhari, M.: Boundary-layer receptivity and integrated transition prediction. AIAA, paper 2005–0526 (2005)

  59. Reed, H.L., Saric, W.S., Arnal, D.: Linear stability theory applied to boundary layers. Annu. Rev. Fluid Mech. 28, 389–428 (1996)

    Article  MathSciNet  Google Scholar 

  60. Herbert, T.: Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283 (1997). doi:10.1146/annurev.fluid.29.1.245

    Article  MathSciNet  Google Scholar 

  61. Abu-Ghannam, B.J., Shaw, R.: Natural transition of boundary layers – the effects of turbulence, pressure gradient, and flow history. J. Mech. Eng. Sci. 22, 213–228 (1980)

    Article  Google Scholar 

  62. Praisner, T., Clark, J.: Predicting transition in turbomachinery—part i: a review and new model development. J. Turbomach. 129, 1–13 (2007). doi:10.1115/1.2366513

    Article  Google Scholar 

  63. Suzen, Y.B., Huang, P.G.: Modeling of flow transition using an intermittency transport equation. J. Fluids Eng. 122, 273–284 (1999)

    Article  Google Scholar 

  64. Praisner, T.J., Grover, E.A., Rice, M.J., Clark, J.P.: Predicting transition in turbomachinery—part ii: Model validation and benchmarking. J. Turbomach. 129, 14–22 (2004). doi:10.1115/1.2366528

    Article  Google Scholar 

  65. Savill, A.M.: One Point Closures Applied to Transition. In: Hallbäck, M. et al. (eds.) Turbulence and Transition, Kluwer Academic Publishers, pp. 233–268 (1999)

    Google Scholar 

  66. Pecnik, R., Pieringer, P., Sanz, W.: Numerical Investigation of the Secondary Flow of a Transonic Turbine Stage Using Various Turbulence Closures. Tech. Rep. GT2005-68754 ASME Turbo Expo 2005: Power for Land, Sea and Air (2005)

  67. Wu, X., Durbin, P.A.: Boundary layer transition induced by periodic wakes. J. Turbomach. 122(3), 442–449 (2000)

    Article  Google Scholar 

  68. Wilcox, D.C.: Simulation of transition with a two-equation turbulence model. AIAA J. 32(2), 247–255 (1994)

    Article  MATH  Google Scholar 

  69. Lopez, M., Walters, D.K.: Prediction of transitional and fully turbulent flow using an alternative to the laminar kinetic energy approach. J. Turbul. 17(3), 253–273 (2016)

    Article  MathSciNet  Google Scholar 

  70. Walters, D.K., Cokljat, D.: A three-equation eddy-viscosity model for Reynolds-averaged Navier-Stokes simulations of transitional flow. J. Fluids Eng. 130, 121,401–1–14 (2008)

    Article  Google Scholar 

  71. Walters, D.K., Leylek, J.H.: A new model for boundary layer transition using a single-point RANS approach. J. Turbomach. 126, 193–202 (2004)

    Article  Google Scholar 

  72. Kubacki, S., Dick, E.: An algebraic model for bypass transition in turbomachinery boundary layer flows. Int. J. Heat Fluid Flow 58, 68–83 (2016). doi:10.1016/j.ijheatfluidflow.2016.01.001

    Article  Google Scholar 

  73. Lardeau, S., Leschziner, M.A., Li, N.: Modelling bypass transition with low-Reynolds-number nonlinear eddy-viscosity closure. Flow Turbul. Combust. 73(1), 49–76 (2004). doi:10.1023/B:APPL.0000044367.24861.b7

    Article  MATH  Google Scholar 

  74. Lardeau, S., Leschziner, M.A.: Modeling of wake-induced transition in linear low-pressure turbine cascades. AIAA J. 44(8), 1854–1865 (2006). doi:10.2514/1.16470

    Article  Google Scholar 

  75. Steelant, J., Dick, E.: Modeling of bypass transition with conditioned navier-stokes equations coupled to an intermittency transport equation. Int. J. Numer. Methods Fluids 23, 193–220 (1996). doi:10.1002/(SICI)1097-0363(19960815)23:3<193::AID-FLD415>3.0.CO;2-2

    Article  MATH  Google Scholar 

  76. Dhawan, S., Narasimha, R.: Some properties of boundary layer during the transition from laminar to turbulent flow motion. J. Fluid Mech. 3, 418–436 (1958)

    Article  MATH  Google Scholar 

  77. Lodefier, K., Merci, B., DeLanghe, C., Dick, E.: Transition modelling with the k − ω turbulence model and an intermittency transport equation. J of Thermal Science pp. 220–225 (2003)

  78. Menter, F.R., Langtry, R.B., Völker, S.: Transition modeling for general purpose CFD codes. Flow Turbul. Combust. 77, 277–303 (2006)

    Article  MATH  Google Scholar 

  79. Langtry, R.B., Menter, F.R.: Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J. 47, 2894–2906 (2009)

    Article  Google Scholar 

  80. Suluksna, K., Dechaumphai, P., Juntasaro, E.: Correlations for modeling transitional boundary layers under influences of free stream turbulence and pressure gradient. Int. J. Heat Fluid Flow 30, 66–72 (2009)

    Article  Google Scholar 

  81. Medida, S., Baeder, J.: Numerical Prediction of Static and Dynamic Stall Phenomena Using the Γ − R 𝜃 Transition Model American Helicopter Society 67Th Annual Forum, Virginia Beach, VA, pp. 432–454 (2011)

    Google Scholar 

  82. Durbin, P.A.: An intermittency model for bypass transition. Int. J. Heat Fluid Flow 36, 1–6 (2012). doi:10.1016/j.ijheatfluidflow.2012.03.001

    Article  Google Scholar 

  83. Ge, X., Arolla, S., Durbin, P.A.: A bypass transition model based on the intermittency function. Flow Turbul. Combust. 93(1), 37–61 (2014)

    Article  Google Scholar 

  84. Ge, X., Durbin, P.A.: An intermittency model for predicting roughness induced transition. Int. J. Heat Fluid Flow 54, 55–64 (2015)

    Article  Google Scholar 

  85. Menter, F.R., Smirnov, P.E., Liu, T., Avancha, R.: A one-equation local correlation-based transition model. Flow Turbul. Combust. 95(4), 583–619 (2015)

    Article  Google Scholar 

  86. Wang, L., Fu, S.: Development of an intermittency equation for the modeling of the supersonic/hypersonic boundary layer flow transition. Flow Turbul. Combust. 87, 165–187 (2011). doi:10.1007/s10494-011-9336-1

    Article  MATH  Google Scholar 

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The author’s work was supported by the National Science Foundation, Air Force Office of Scientific Research and Office of Naval Research.

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    Paul A. Durbin

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Durbin, P.A. Perspectives on the Phenomenology and Modeling of Boundary Layer Transition. Flow Turbulence Combust 99, 1–23 (2017). https://doi.org/10.1007/s10494-017-9819-9

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