Skip to main content
SpringerLink
Log in

Direct Numerical Simulation of an Accelerating Channel Flow

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Direct Numerical Simulation of a linearly accelerating channel flow starting from an initially statistically steady turbulent flow has been performed. It is shown that the response of the accelerating flow is fundamentally the same as that of the step-change transient flow described in He and Seddighi (J Fluid Mech 715:60–102, 2013). The flow structure again behaves like a boundary layer bypass transition undergoing three distinct phases, namely, (i) initially (pre-transition), the flow is laminar-like and the pre-existing turbulent structures are modulated resulting in elongated streaks leading to a strong and continuous increase in the streamwise fluctuating velocity but little changes in the other two components; (ii) it then undergoes transition when isolated turbulent spots are generated which spread and merge with each other, and (iii) they eventually cover the entire surface of the wall when the flow is fully turbulent. The similarity between the turbulence responses in the two flows is significant noting the contrasting features of the two types of mean flow unsteadiness: in the step-change flow, a sharp boundary layer is resulted in nearly instantly on the wall which closely resembles the spatially developing boundary layer, whereas the linear flow acceleration causes a continuing change of velocity gradient adjacent to the wall which propagates into the flow field with time, resulting in a gradually-developing boundary layer. There are, however, quantitative differences in the detailed behavior of the two flows and especially the transition is much delayed in the accelerating flow. It is also shown that the late pre-transition and early transition stages in both flows are characterised by significantly increased inwards sweep events in the wall region and ejection events in the outer layer. The flatness of the wall-normal velocity increases markedly near the wall around the time of onset of transition as a consequence of the huge intermittency of the velocity fluctuations. That is, there are long periods of quiescent flow coupled with occasional turbulent bursts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Vardy, A., Brown, J.: Approximation of turbulent wall shear stresses in highly transient pipe flows. J. Hydraul. Eng. 133(11), 1219–1228 (2007). doi:10.1061/(ASCE)0733-9429(2007)133:11(1219)

    Article  Google Scholar 

  2. Vardy, A.E., Bergant, A., He, S., Ariyaratne, C., Koppel, T., Annus, I., Tijsseling, A., Hou, Q.: Unsteady skin friction experimentation in a large diameter pipe. In: Paper Presented at the 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems

  3. Vardy, A.E., Brown, J.M.B.: Transient turbulent friction in smooth pipe flows. J. Sound Vib. 259(5), 1011–1036 (2003)

    Article  Google Scholar 

  4. Colombo, A.F., Lee, P., Karney, B.W.: A selective literature review of transient-based leak detection methods. J. Hydro Environ. Res. 2(4), 212–227 (2009)

    Article  Google Scholar 

  5. Van der A, D.A., O’Donoghue, T., Davies, A.G., Ribberink, J.S.: Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow. J. Fluid Mech. 684, 251–283 (2011)

    Article  MATH  Google Scholar 

  6. Ricco, P., Baron, A., Molteni, P.: Nature of pressure waves induced by a high-speed train travelling through a tunnel. J. Wind Eng. Ind. Aerodyn. 95(8), 781–808 (2007)

    Article  Google Scholar 

  7. Scotti, A., Piomelli, U.: Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13(5), 1367–1384 (2001)

    Article  Google Scholar 

  8. Tardu, S.F., Da Costa, P.: Experiments and modeling of an unsteady turbulent channel flow. AIAA J. 43(1), 140–148 (2005)

    Article  Google Scholar 

  9. Shemer, L., Wygnanski, I., Kit, E.: Pulsating flow in a pipe. J. Fluid Mech. 153, 313–337 (1985)

    Article  Google Scholar 

  10. Brereton, G.J., Mankbadi, R.R.: Review of recent advances in the study of unsteady turbulent internal flows. Appl. Mech. Rev. 48(4), 189–212 (1995)

    Article  Google Scholar 

  11. He, S., Jackson, J.D.: An experimental study of pulsating turbulent flow in a pipe. Eur. J. Mech. B/Fluids 28(2), 309–320 (2009)

    Article  MATH  Google Scholar 

  12. Gündoǧdu, M.Y., Çarpinlioǧlu, M.Ö.: Present state of art on pulsatile flow theory (Part 2: turbulent flow regime). JSME Int. J. Ser. B: Fluid Therm. Eng. 42(3), 398–410 (1999)

    Article  Google Scholar 

  13. Chung, Y.M.: Unsteady turbulent flow with sudden pressure gradient changes. Int. J. Numer. Methods Fluids 47(8–9), 925–930 (2005)

    Article  MATH  Google Scholar 

  14. He, S., Ariyaratne, C.: Wall shear stress in the early stage of unsteady turbulent pipe flow. J. Hydraul. Eng. 137(5), 606–610 (2011)

    Article  Google Scholar 

  15. He, S., Jackson, J.D.: A study of turbulence under conditions of transient flow in a pipe. J. Fluid Mech. 408, 1–38 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Greenblatt, D., Moss, E.A.: Rapid temporal acceleration of a turbulent pipe flow. J. Fluid Mech. 514, 65–75 (2004)

    Article  MATH  Google Scholar 

  17. He, S., Ariyaratne, C., Vardy, A.E.: A computational study of wall friction and turbulence dynamics in accelerating pipe flows. Comput. Fluids 37(6), 674–689 (2008)

    Article  MATH  Google Scholar 

  18. Seddighi, M., He, S., Orlandi, P., Vardy, A.E.: A comparative study of turbulence in ramp-up and ramp-down unsteady flows. Flow Turbulence Combust. 86(3–4), 439–454 (2011)

    Article  MATH  Google Scholar 

  19. Greenblatt, D., Moss, E.A.: Pipe-flow relaminarization by temporal acceleration. Phys. Fluids 11(11), 3478–3481 (1999)

    Article  MATH  Google Scholar 

  20. Jung, S.Y., Chung, Y.M.: Large-eddy simulation of accelerated turbulent flow in a circular pipe. Int. J. Heat Fluid Flow 33(1), 1–8 (2012)

    Article  Google Scholar 

  21. Maruyama, T., Kuribayashi, T., Mizushina, T.: Structure of the turbulence in transient pipe flows. J. Chem. Eng. Jpn 9(6), 431–439 (1976)

    Article  Google Scholar 

  22. He, S., Ariyaratne, C., Vardy, A.E.: Wall shear stress in accelerating turbulent pipe flow. J. Fluid Mech. 685, 440–460 (2011)

    Article  MATH  Google Scholar 

  23. Ariyaratne, C., He, S., Vardy, A.E.: Wall friction and turbulence dynamics in decelerating pipe flows. J. Hydraul. Res. 48(6), 810–821 (2010)

    Article  Google Scholar 

  24. He, S., Seddighi, M.: Turbulence in transient channel flow. J. Fluid Mech. 715, 60–102 (2013). doi:10.1017/jfm.2012.498

    Article  MathSciNet  Google Scholar 

  25. Jacobs, R., Durbin, P.: Simulations of bypass transition. J. Fluid Mech. 428(1), 185–212 (2001)

    Article  MATH  Google Scholar 

  26. Kleiser, L., Zang, T.A.: Numerical simulation of transition in wall-bounded shear flows. Ann. Rev. Fluid Mech. 23(1), 495–537 (1991)

    Article  Google Scholar 

  27. Morkovin, M.V.: On the many faces of transition. In: Wells, C. S. (ed.) Viscous Drag Reduction, pp. 1–31. Plenum Press (1969)

  28. Kenneth, B., Takeo, K.: Bypass transition in two- and three-dimensional boundary layers. In: 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference. Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (1993)

  29. Schmid, P.J., Henningson, D.S.: Stability and Transition in Shear Flows. Springer, New York (2001)

    Book  MATH  Google Scholar 

  30. Saric, W.S., Reed, H.L., Kerschen, E.J.: Boundary-layer receptivity to freestream disturbances. Ann. Rev. Fluid Mech. 34, 291–319 (2002)

    Article  MathSciNet  Google Scholar 

  31. Durbin, P., Wu, X.: Transition beneath vortical disturbances. Ann. Rev. Fluid Mech. 39(1), 107–128 (2007). doi:10.1146/annurev.fluid.39.050905.110135

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. 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)

    Article  MATH  MathSciNet  Google Scholar 

  35. Andersson, P., Brandt, L., Bottaro, A., Henningson, D.S.: On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  36. 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). doi:10.1017/jfm.2011.177

    Article  MATH  Google Scholar 

  37. Nolan, K.P., Walsh, E.J.: Particle image velocimetry measurements of a transitional boundary layer under free stream turbulence. J. Fluid Mech. 702, 215–238 (2012)

    Article  MATH  Google Scholar 

  38. Schlatter, P., Deusebio, E., De Lange, R., Brandt, L.: Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks. Int. J. Flow Control 2(4), 259–288 (2010)

    Article  Google Scholar 

  39. Bagheri, S., Hanifi, A.: The stabilizing effect of streaks on Tollmien–Schlichting and oblique waves: a parametric study. Phys. Fluids 19, 078103 (2007)

    Article  Google Scholar 

  40. Fransson, J.H.M., Brandt, L., Talamelli, A., Cossu, C.: Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 17(5), 1–15 (2005)

    Article  Google Scholar 

  41. Fransson, J.H.M., Talamelli, A., Brandt, L., Cossu, C.: Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501 (2006)

    Article  Google Scholar 

  42. Boiko, A.V., Westin, K.J.A., Klingmann, B.G.B., Kozlov, V.V., Alfredsson, P.H.: Experiments in a boundary layer subjected to free stream turbulence. Part 2. The role of TS-waves in the transition process. J. Fluid Mech. 281, 219–245 (1994)

    Article  Google Scholar 

  43. Kendall, J.M.: Boundary layer receptivity to freestream turbulence. AIAA Paper 1504, 90–1504 (1990)

    Google Scholar 

  44. Wu, X., Choudhari, M.: Linear and nonlinear instabilities of a Blasius boundary layer perturbed by streamwise vortices. Part 2. Intermittent instability induced by long-wavelength Klebanoff modes. J. Fluid Mech. 483, 249–286 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  45. Cossu, C., Brandt, L.: Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14(8), L57–L60 (2002)

    Article  Google Scholar 

  46. Cossu, C., Brandt, L.: On Tollmien–Schlichting-like waves in streaky boundary layers. Eur. J. Mech. B/Fluids 23(6), 815–833 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  47. Durbin, P.A., Zaki, T.A., Liu, Y.: Interaction of discrete and continuous boundary layer modes to cause transition. Int. J. Heat Fluid Flow 30(3), 403–410 (2009). doi:10.1016/j.ijheatfluidflow.2008.12.008

    Article  Google Scholar 

  48. 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 (2008)

    Article  Google Scholar 

  49. Liu, Y., Zaki, T.A., Durbin, P.A.: Boundary-layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 199–233 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  51. Goldstein, M.E., Sescu, A.: Boundary-layer transition at high free-stream disturbance levels—beyond Klebanoff modes. J. Fluid Mech. 613, 95–124 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  52. Ovchinnikov, V., Choudhari, M.M., Piomelli, U.: Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence. J. Fluid Mech. 613, 135 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  53. Reddy, S.C., Schmid, P.J., Baggett, J.S., Henningson, D.S.: On stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269–303 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  54. Schlatter, P., Brandt, L., de Lange, H., Henningson, D.S.: On streak breakdown in bypass transition. Phys. Fluids 20, 101505 (2008)

    Article  Google Scholar 

  55. Cossu, C., Brandt, L., Bagheri, S., Henningson, D.S.: Secondary threshold amplitudes for sinuous streak breakdown. Phys. Fluids 23, 074103 (2011)

    Article  Google Scholar 

  56. Elofsson, P.A., Kawakami, M., Alfredsson, P.H.: Experiments on the stability of streamwise streaks in plane Poiseuille flow. Phys. Fluids 11(4), 915–930 (1999)

    Article  MATH  Google Scholar 

  57. Narasimha, R.: The laminar-turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22(1), 29–80 (1985)

    Article  Google Scholar 

  58. Fernholz, H.H., Warnack, D.: The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329–356 (1998). doi:10.1017/S0022112097008513

    Article  MATH  Google Scholar 

  59. Warnack, D., Fernholz, H.H.: The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 2. The boundary layer with relaminarization. J. Fluid Mech. 359, 357–381 (1998). doi:10.1017/S0022112097008501

    Article  Google Scholar 

  60. Bourassa, C., Thomas, F.O.: An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359–404 (2009). doi:10.1017/S0022112009007289

    Article  MATH  Google Scholar 

  61. Corke, T.C., Gruber, S.: Resonant growth of three-dimensional modes in Falkner–Skan boundary layers with adverse pressure gradients. J. Fluid Mech. 320, 211–233 (1996)

    Article  Google Scholar 

  62. Goldstein, M.E., Lee, S.S.: Fully coupled resonant-triad interaction in an adverse-pressure-gradient boundary layer. J. Fluid Mech. 245, 523–551 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  63. Liu, C., Maslowe, S.A.: A numerical investigation of resonant interactions in adverse-pressure-gradient boundary layers. J. Fluid Mech. 378, 269–289 (1999)

    Article  Google Scholar 

  64. Alam, M., Sandham, N.D.: Direct numerical simulation of ’short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28 (2000)

    Article  MATH  Google Scholar 

  65. Spalart, P.R., Strelets, M.K.: Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349 (2000)

    Article  MATH  Google Scholar 

  66. 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(5), 213–228 (1980)

    Article  Google Scholar 

  67. Zaki, T.A., Durbin, P.A.: Continuous mode transition and the effects of pressure gradient. J. Fluid Mech. 563, 357–388 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  68. Hodson, H.P., Howell, R.J.: Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Ann. Rev. Fluid Mech. 37, 71–98 (2005)

    Article  Google Scholar 

  69. Lardeau, S., Leschziner, M., Zaki, T.: Large Eddy Simulation of transitional separated flow over a flat plate and a compressor blade. Flow Turbulence Combust. 88(1–2), 19–44 (2012)

    Article  MATH  Google Scholar 

  70. Wissin, J.G., Rodi, W.: Direct numerical simulations of transitional flow in turbomachinery. J. Turbomach. 128(4), 668–678 (2006)

    Article  Google Scholar 

  71. Wissink, J.G., Rodi, W.: Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes. J. Fluid Mech. 569, 209–247 (2006). doi:10.1017/S002211200600262X

    Article  MATH  Google Scholar 

  72. Zaki, T.A., Wissink, J.G., 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)

    Article  MATH  Google Scholar 

  73. Henderson, A.D., Walker, G.J., Hughes, J.D.: Unsteady transition phenomena at a compressor blade leading edge. J. Turbomach. 130, 021013 (2008)

    Article  Google Scholar 

  74. Seddighi, M.: Study of turbulence and wall shear stress in unsteady flow over smooth and rough wall surfaces. University of Aberdeen (2011)

  75. Orlandi, P.: Fluid Flow Phenomena: A Numerical Toolkit. Springer, Heidelberg (2000)

    Book  Google Scholar 

  76. Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  MATH  Google Scholar 

  77. Fransson, J.H.M., Matsubara, M., Alfredsson, P.H.: Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25 (2005)

    Article  MATH  Google Scholar 

  78. Mandal, A., Venkatakrishnan, L., Dey, J.: A study on boundary-layer transition induced by free-stream turbulence. J. Fluid Mech. 660, 114–146 (2010)

    Article  MATH  Google Scholar 

  79. Landahl, M.T.: (Fluid Mechanics) A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98(2), 243–251 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  80. Zaki, T.A., Durbin, P.A.: Mode interaction and the bypass route to transition. J. Fluid Mech. 531(1), 85–111 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  81. Wu, X., Moin, P.: Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630(1), 5–41 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  82. Nolan, K.P., Walsh, E.J., McEligot, D.M.: Quadrant analysis of a transitional boundary layer subject to free-stream turbulence. J. Fluid Mech. 658, 310–335 (2010)

    Article  MATH  Google Scholar 

  83. Hunt, J.C.R., Carruthers, D.J.: Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532 (1990). doi:10.1017/S0022112090002075

    Article  MATH  MathSciNet  Google Scholar 

  84. Phillips, O.M.: Shear-flow turbulence. Ann. Rev. Fluid Mech. 1(1), 245–264 (1969). doi:10.1146/annurev.fl.01.010169.001333

    Article  Google Scholar 

  85. Lu, S.S., Willmarth, W.W.: Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60(03), 481–511 (1973). doi:10.1017/S0022112073000315

    Article  Google Scholar 

  86. Alfredsson, P.H., Johansson, A.V.: On the detection of turbulence-generating events. J. Fluid Mech. 139, 325–345 (1984)

    Article  Google Scholar 

  87. Tardu, S.: Characteristics of single and clusters of bursting events in the inner layer—Part 1: vita events. Exp. Fluids 20(2), 112–124 (1995)

    Article  Google Scholar 

  88. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11(4), 943–945 (1999)

    Article  MATH  Google Scholar 

  89. Davidson, P.A.: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, London (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD, UK

    M. Seddighi & S. He

  2. Division of Civil Engineering, University of Dundee, Dundee, DD1 4HN, UK

    A. E. Vardy

  3. Dipartimento di Meccanica e Aeronautica, Universita’ di Roma “La Sapienza”, Rome, Italy

    P. Orlandi

Authors
  1. M. Seddighi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Vardy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Orlandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. He.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Seddighi, M., He, S., Vardy, A.E. et al. Direct Numerical Simulation of an Accelerating Channel Flow. Flow Turbulence Combust 92, 473–502 (2014). https://doi.org/10.1007/s10494-013-9519-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-013-9519-z

Keywords

Search

Navigation