Hostname: page-component-5447f9dfdb-lxcff Total loading time: 0 Render date: 2025-07-28T22:26:33.172Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on critical Reynolds number and global instability in roughness-induced laminar–turbulent transition

Published online by Cambridge University Press:  13 April 2018

Dominik K. Puckert Open the ORCID record for Dominik K. Puckert [Opens in a new window]  and
Ulrich Rist
Dominik K. Puckert*
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70569 Stuttgart, Germany
Ulrich Rist
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70569 Stuttgart, Germany
*
†Email address for correspondence: puckert@iag.uni-stuttgart.de
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of isolated, cylindrical roughness elements on laminar–turbulent transition in a flat-plate boundary layer are investigated in a laminar water channel. Our experiments aim at providing a comparison to global linear stability theory (LST) by means of hot-film anemometry and particle image velocimetry. Although the critical Reynolds number from theory does not match the transition Reynolds number observed in experiments, there are distinct experimental observations indicating a changeover from purely convective to absolute/global instability very close to the critical Reynolds number predicted by theory. Forcing with a vibrating wire reveals the evolution of the system dynamics from an amplifier to a wavemaker when the critical Reynolds number is exceeded. The mode symmetry is varicose for thick roughness elements and a changeover from varicose to sinuous modes is observed at the critical Reynolds number for thin roughness elements. Therefore, most predictions by global LST can be confirmed, but additional observations in the physical flow demonstrate that not all features can be captured adequately by global LST.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability Instability: Transition to turbulence

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 878 - 904
Copyright
© 2018 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.)

Article purchase

Temporarily unavailable

References

Acarlar, M. & Smith, C. 1987 A study of hairpin vortices in a laminar boundary-layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.10.1017/S0022112087000272Google Scholar
Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.10.1063/1.2211705Google Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 2005 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.10.1063/1.869908Google Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.10.1017/S0022112000002421Google Scholar
Asai, M., Minagawa, M. & Nishioka, M. 2002 The instability and breakdown of a near-wall low-speed streak. J. Fluid Mech. 455, 289–314.10.1017/S0022112001007431Google Scholar
Bagheri, S., Akervik, E., Brandt, L. & Henningson, D. S. 2009 Matrix-free methods for the stability and control of boundary layers. AIAA J. 47 (5), 1057–1068.10.2514/1.41365Google Scholar
Brandt, L., Cossu, C., Chomaz, J.-M. & Huerre, P. 2003 On the convectively unstable nature of optimal streaks in boundary layers. J. Fluid Mech. 485, 221–242.10.1017/S0022112003004427Google Scholar
Bucci, M. A., Puckert, D. K., Andriano, C., Loiseau, J.-C., Cherubini, S., Robinet, J.-C. & Rist, U. 2018 Roughness-induced transition by quasi-resonance of a varicose global mode. J. Fluid Mech. 836, 167–191.10.1017/jfm.2017.791Google Scholar
Carmichael, B. H.1958 Prediction of critical Reynolds numbers for single three-dimensional roughness elements. Tech. Rep. N.A.I.-58-412 (BLC109), Northrop Aircraft Inc.Google Scholar
Cherubini, S., De Tullio, M. D., De Palma, P. & Pascazio, G. 2013 Transient growth in the flow past a three-dimensional smooth roughness element. J. Fluid Mech. 724, 642–670.10.1017/jfm.2013.177Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.10.1146/annurev.fluid.37.061903.175810Google Scholar
Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84, 119–144.10.1002/sapm1991842119Google Scholar
Denissen, N. A. & White, E. B. 2013 Secondary instability of roughness-induced transient growth. Phys. Fluids 25 (11), 114108.10.1063/1.4829482Google Scholar
von Doenhoff, A. E. & Braslow, A. L. 1961 The effect of distributed surface roughness on laminar flow. Boundary Layer Control 2, 657–681.10.1016/B978-1-4832-1323-1.50005-1Google Scholar
Ergin, F. G. & White, E. B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 44 (11), 2504–2514.10.2514/1.17459Google Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2005 Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 17 (5), 054110.10.1063/1.1897377Google Scholar
Gondret, P., Ern, P., Meignin, L. & Rabaud, M. 1999 Experimental evidence of a nonlinear transition from convective to absolute instability. Phys. Rev. Lett. 82, 1442–1445.10.1103/PhysRevLett.82.1442Google Scholar
Gregory, N. & Walker, W. S.1956 The effect on transition of isolated surface excrescence in the boundary layer. ARC Reports & Memoranda no. 2779, Aeronautical Research Council. HMSO, London.Google Scholar
Halstead, D. E., Wisler, D. C., Okiishi, T. H., Walker, G. J., Hodson, H. P. & Shin, H. W. 1995 Boundary layer development in axial compressors and turbines. Part 2. Compressors. In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers.Google Scholar
Hernon, D., Walsh, E. J. & McEligot, D. M. 2007 Experimental investigation into the routes to bypass transition and the shear-sheltering phenomenon. J. Fluid Mech. 591, 461–479.10.1017/S0022112007008336Google Scholar
Huerre, P. & Monkewitz, P. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.10.1146/annurev.fl.22.010190.002353Google Scholar
Kachanov, Y. S. & Michalke, A. 1994 Three-dimensional instability of flat-plate boundary layers: theory and experiment. Eur. J. Mech. (B/Fluids) 13, 401–422.Google Scholar
Klanfer, L. & Owen, P. R.1953 The effect of isolated roughness on boundary layer transition. RAE Tech. Memo. 355, Royal Aircraft Establishment.Google Scholar
Klebanoff, P. S., Cleveland, W. G. & Tidstrom, K. D. 1992 On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element. J. Fluid Mech. 237, 101–187.10.1017/S0022112092003379Google Scholar
Klebanoff, P. S., Schubauer, G. B. & Tidstrom, K. D. 1955 Measurements of the effect of two-dimensional and three-dimensional roughness elements on boundary-layer transition. J. Aero. Sci. 22.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1–34.10.1017/S0022112062000014Google Scholar
Kurz, H. B. E. & Kloker, M. J. 2016 Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer. J. Fluid Mech. 796, 158–194.10.1017/jfm.2016.240Google Scholar
Landahl, M. T. 1990 On sublayer streaks. J. Fluid Mech. 212, 593–614.10.1017/S0022112090002105Google 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 (1), 43–52.Google Scholar
Lingwood, R. J. 1996 An experimental study of absolute instability of the rotating-disk boundary-layer flow. J. Fluid Mech. 314, 373–405.10.1017/S0022112096000365Google Scholar
Loftin, K. L.1946 Effects of specific types of surface roughness on boundary-layer transition. Tech. Rep. A.C.R. L5J29a, National Aeronautics and Space Administration.Google Scholar
Loiseau, J. C., Cherubini, S., Robinet, J. C. & Leriche, E. 2014 Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations. J. Fluid Mech. 760, 175–211.10.1017/jfm.2014.589Google Scholar
de Luca, L. 1999 Experimental investigation of the global instability of plane sheet flows. J. Fluid Mech. 399, 355–376.10.1017/S0022112099006564Google Scholar
Luo, J. W., Bai, J. & Shao, J. H. 2006 Application of the wavelet transforms on axial strain calculation in ultrasound elastography. Prog. Nat. Sci. 16 (9), 942–947.Google Scholar
Manneville, P. 2004 Instabilities, Chaos and Turbulence: An Introduction to Nonlinear Dynamics and Complex Systems. Imperial College Press.10.1142/p349Google Scholar
Miranda-Barea, A., Fabrellas-Garcia, C., Parras, L. & del Pino, C. 2016 Spin-down in rotating Hagen–Poiseuille flow: a simple criterion to detect the onset of absolute instabilities. J. Fluid Mech. 793, 316–334.10.1017/jfm.2016.122Google Scholar
Mochizuki, M. 1961a Hot wire investigations of smoke patterns caused by a spherical roughness element. Nat. Sci. Rep. Ochanomizu Univ. 12 (2), 87–101.Google Scholar
Mochizuki, M. 1961b Smoke observation on boundary layer transition caused by a spherical roughness element. J. Phy. Soc. Japan 16, 995–1008.10.1143/JPSJ.16.995Google Scholar
Monkewitz, P., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.10.1017/S0022112093003313Google Scholar
Peterson, J. B. Jr & Horton, E. A. 1959 An investigation of the effect of a highly favorable pressure gradient on boundary-layer transition as caused by various types of roughnesses on a 10-foot-diameter hemisphere at subsonic speeds. Memo 2–8-59L, National Aeronautics and Space Administration.Google Scholar
Puckert, D. K., Dieterle, M. & Rist, U. 2017 Reduction of freestream turbulence at low velocities. Exp. Fluids 58 (5), 45.10.1007/s00348-017-2333-yGoogle Scholar
Puckert, D., Subasi, A., Rist, U. & Gunes, H. 2015 Experimental investigations of critical roughness heights in a laminar boundary layer. In The 13th International Symposium on Fluid Control, Measurement and Visualization, FLUCOME2015, Doha, Qatar.Google Scholar
Puckert, D. K. & Rist, U. 2016 Transition downstream of an isolated cylindrical roughness element on a flat plate boundary layer. In New Results in Numerical and Experimental Fluid Mechanics XI (ed. Dillmann, A., Heller, G., Krämer, E., Radespiel, R. & Wagner, C.), Springer.Google Scholar
Puckert, D. K. & Rist, U. 2018 Global instability in a laminar boundary layer perturbed by an isolated roughness element. Exp. Fluids 59 (3), 48.10.1007/s00348-018-2510-7Google Scholar
Reshotko, E. 2001 Transient growth: a factor in bypass transition. Phy. Fluids 13 (5), 1067–1075.10.1063/1.1358308Google Scholar
Rizzetta, D. P. & Visbal, M. R. 2007 Direct numerical simulations of flow past an array of distributed roughness elements. AIAA J. 45 (8), 1967–1976.10.2514/1.25916Google Scholar
Schiller, L. 1932 Strömung in Rohren. Handbuch Experiment. 4.Google Scholar
Schwartzberg, M. A. & Braslow, A. L.1952 Experimental study of the effects of finite surface disturbances and angle of attack on the laminar boundary layer of an NACA 64A010 airfoil with area suction. Tech. Rep. 2796, National Aeronautics and Space Administration.Google Scholar
Shin, Y. S., Rist, U. & Krämer, E. 2015 Stability of the laminar boundary-layer flow behind a roughness element. Exp. Fluids 56 (1), 11.10.1007/s00348-014-1878-2Google Scholar
Shrestha, K., Parras, L., Del Pino, C. & Sanmiguel-Rojas, E. 2012 Experimental evidence of convective and absolute instabilities in rotating Hagen–Poiseuille flow. J. Fluid Mech. 716, 103–126.Google Scholar
Smith, A. M. O. & Clutter, D. W.1957 The smallest height of roughness capable of affecting boundary-layer transition in low speed flow. Tech. Rep. ES 26803, Douglas Aircraft Co.Google Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J. 1987 Hopf bifurcation, Landau equation and vortex shedding behind circular cylinders. In Proc. Forum Unsteady Flow Sep. (ed. Ghia, K. N.), vol. 52, pp. 1–13. American Society for Mechanical Engineers, Fluids Engineering Division.Google Scholar
Stotz, S., Wakelam, C. T., Guendogdu, Y. & Niehuis, R.2014 Detection of boundary layer transition on a low pressure turbine airfoil without separation using a Preston tube and hot film anemometry. In 15th International Symposium of Transport Phenomena and Dynamics of Rotating Machinery: ISROMAC-15.10.1115/GT2014-25908Google Scholar
Taira, K., Brunton, S. L., Dawson, S., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S.2017 Modal analysis of fluid flows: an overview. arXiv:1702.01453.10.2514/1.J056060.c1Google Scholar
Tani, I. 1961 Effect of two-dimensional and isolated roughness on laminar flow. Boundary Layer Flow Control 2, 637–656.10.1016/B978-1-4832-1323-1.50004-XGoogle Scholar
Tani, I., Komoda, H., Komatsu, Y. & Iuchi, M. 1962 Boundary-layer transition by isolated roughness. Aeron. Res. Inst. Univ. Tokyo Rep. 375, 129–143.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.10.1146/annurev-fluid-122109-160705Google Scholar
White, E. B. 2002 Transient growth of stationary disturbances in a flat plate boundary layer. Phys. Fluids 14 (12), 4429–4439.10.1063/1.1521124Google Scholar
Wiegand, T.1996 Experimentelle Untersuchungen zum laminar-turbulenten Transitionsprozess eines Wellenzugs in einer Plattengrenzschicht. PhD thesis, Universität Stuttgart.Google Scholar
Zhang, J., Xu, M., Pollard, A. & Mi, J. 2013 Effects of external intermittency and mean shear on the spectral inertial-range exponent in a turbulent square jet. Phys. Rev. E 87 (5), 053009.Google Scholar

Puckert et al. supplementary movie

Time-resolved PIV measurements of the $xz$-plane sampled at 10 Hz with $eta=1$, $x_k=166.4$ at increasing freestream velocity.

Download Puckert et al. supplementary movie(Video)
Video 31.5 MB