Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-01T00:06:35.188Z Has data issue: false hasContentIssue false
  • English
  • Français

On the disturbance evolution downstream of a cylindrical roughness element

Published online by Cambridge University Press:  08 October 2014

B. Plogmann ,
W. Würz  and
E. Krämer
B. Plogmann*
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
W. Würz
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
E. Krämer
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Roughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

JFM classification

Boundary Layers: Boundary layer stability Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 238 - 286
Copyright
© 2014 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

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.Google Scholar
Aizin, L. B. & Polyakov, N. F.1979 Acoustic generation of Tollmien–Schlichting waves over local unevenness of surfaces immersed in streams. Preprint 17, Akad. Nauk USSR, Siberian Div., Institute of Theoretical and Applied Mechanics, Novosibirsk.Google Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Bakchinov, A. A., Grek, G. R., Klingmann, B. G. B. & Kozlov, V. V. 1995 Transition experiments in a boundary layer with embedded streamwise vortices. Phys. Fluids 7, 820–832.Google Scholar
Borodulin, V. I., Kachanov, Y. S. & Koptsev, D. 2002a Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: III. Broadband disturbances. J. Turbul. 3 (64), 1–19.Google Scholar
Borodulin, V. I., Kachanov, Y. S., Koptsev, D. & Reschektayev, A. P. 2002b Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: II. Detuned resonance. J. Turbul. 3 (63), 1–32.Google Scholar
Breuer, K. S., Cohen, J. & Haritonidis, J. H. 1997 The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer. J. Fluid Mech. 340, 395–411.Google Scholar
Cebeci, T. & Egan, D. A. 1989 Prediction of transition due to isolated roughness. AIAA J. 27 (7), 870–875.Google Scholar
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic Press.Google Scholar
Choudhari, M. & Kerschen, E. J.1990 Instability wave patterns generated by interaction of sound waves with three-dimensional wall suction or roughness. AIAA Paper 90-119.Google Scholar
Conte, S. 1966 The numerical solution of linear boundary layer value problems. SIAM Rev. 8 (3), 309–321.Google Scholar
Corke, T. C. & Mangano, R. A. 1989 Resonant growth of three-dimensional modes in transitioning Blasius boundary layers. J. Fluid Mech. 209, 93–150.Google Scholar
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14, 57–60.Google Scholar
Cossu, C. & Brandt, L. 2004 On Tollmien–Schlichting-like waves in streaky boundary layers. Eur. J. Mech. (B/Fluids) 23, 815–833.Google Scholar
Crouch, J. D. 1997 Excitation of secondary instabilities in boundary layers. J. Fluid Mech. 336, 245–266.Google Scholar
Crouch, J. D., Kosorygin, V. S. & Ng, L. L. 2006 Modeling the effects of steps on boundary-layer transition. In 6th IUTAM Symposium on Laminar–Turbulent Transition (ed. Govindarajan, R.), pp. 37–44. Springer.Google Scholar
Délery, J. M. 2001 R. Legendre and H. Werle: toward the elucidation of three-dimensional separation. Annu. Rev. Fluid Mech. 33, 129–154.Google Scholar
von Doenhoff, A. E. & Braslow, A. L. 1961 The effect of distributed surface roughness on laminar flow. Boundary Layer Flow Control 2, 657–681.Google Scholar
Dovgal, A. V. & Kozlov, V. V. 1990 Hydrodynamic instability and receptivity of small scale separation regions. In IUTAM Symposium on Laminar–Turbulent Transition (ed. Arnal, D. & Michel, R.), pp. 523–531. Springer.Google Scholar
Drela, M. 1989 XFoil: An analysis and design system for low Reynolds number airfoils. In Low Reynolds Number Aerodynamics (ed. Mueller, T. J.), Lecture Notes in Engineering, vol. 54, pp. 1–12. Springer.Google Scholar
Dryden, H. L. 1953 Review of published data on the effect of roughness on transition from laminar to turbulent flow. J. Aeronaut. Sci. 477–482.Google Scholar
Ergin, F. G. & White, E. B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 44 (11), 2504–2514.Google Scholar
Fage, A.1943 The smallest size of a spanwise surface corrugation which affects boundary layer transition on an aerofoil. Aeronautical Research Council, Reports and Memoranda (2120).Google Scholar
Foken, T. 2006 Angewandte Meteorologie. Springer.Google Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2004 Experimental and theoretical investigation of the nonmodal growth of steady streaks in flat plate boundary layer. Phys. Fluids 16, 3627–3638.Google 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, 054110.Google Scholar
Gaster, M., Grosch, C. E. & Jackson, T. L. 1994 Velocity field created by a shallow bump in a boundary layer. Phys. Fluids 6, 2104–3079.Google Scholar
Goldstein, M. E. 1985 Scattering of sound waves into Tollmien–Schlichting waves by small streamwise variations in surface geometry. J. Fluid Mech. 154, 509–529.Google Scholar
Gregory, N. & Walker, W. S.1956 The effect on transition of isolated surface excrescences in the boundary layer. Aeronautical Research Council, Reports and Memoranda (2779).Google Scholar
Herr, Stefan.2004 Experimental investigation of airfoil boundary-layer receptivity and a method for the characterization of the relevant free-stream disturbances. PhD thesis, University of Stuttgart.Google Scholar
Jacobs, E. N.1939 Preliminary report on laminar-flow airfoils and new methods adopted for airfoil and boundary-layer investigations. Tech. Rep. 345. NACA WR L.Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–482.Google Scholar
Kachanov, Y. S. 2000 Three-dimensional receptivity of boundary layers. Eur. J. Mech. (B/Fluids) 19, 723–744.Google Scholar
Kendall, J. M.1981 Laminar boundary layer velocity distortion by surface roughness: effect upon stability. AIAA Paper 1981-0195.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.Google Scholar
Klebanoff, P. S. & Tidstrom, K. D. 1972 Mechanism by which a two-dimensional roughness element induces boundary-layer transition. Phys. Fluids 15 (17), 1173–1188.CrossRefGoogle Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.Google Scholar
Masad, J. A. & Lyer, V. 1994 Transition prediction and control in subsonic flow over hump. Phys. Fluids 6, 313–327.Google Scholar
Matheis, B. D., Huebsch, W. W. & Rothmayer, A. P.2004 Separation and unsteady vortex shedding from leading edge surface roughness. Paper published in RTO-MP-AVT-111.Google 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. Phys. Soc. Japan 16, 995–1008.Google Scholar
Morkovin, M. V. 1990 On roughness-induced transition: facts, views and speculations. In Instability and Transition (ed. Hussaini, M. Y. & Voigt, R. G.), vol. 1, pp. 281–295. Springer.Google Scholar
Nayfeh, A. H., Ragab, S. A. & Al-Maaitah, A. 1988 Effect of bulges on the stability of boundary layers. Phys. Fluids 31, 796–806.Google Scholar
de Paula, I. B., Würz, W., Krämer, E., Borodulin, V. I. & Kachanov, Y. S.2010 Generation of seeds of subharmonic resonance in an airfoil boundary-layer transition initiated by modulated TS waves. International Conference on Methods of Aerophysical Research, Novosibirsk.Google Scholar
de Paula, I. B., Würz, W., Krämer, E., Borodulin, V. I. & Kachanov, Y. S. 2013 Weakly non-linear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves. J. Fluid Mech. 732, 571–615.Google Scholar
de Paula, I. B., Würz, W. & Medeiros, M. A. F. 2008 Experimental study of a Tollmien–Schlichting wave interacting with a shallow 3D roughness element. J. Turbul. 9, 1–23.Google Scholar
Piot, E., Casalis, G. & Rist, U. 2008 Stability of the laminar boundary layer flow encountering a row of roughness elements: biglobal stability approach and DNS. Eur. J. Mech. (B/Fluids) 27, 684–706.Google Scholar
Plogmann, B. & Würz, W. 2013 Aeroacoustic measurements on a NACA 0012 applying the coherent particle velocity method. Exp. Fluids 54 (7), 1556.Google Scholar
Plogmann, B., Würz, W. & Krämer, E.2012a Interaction of a laminar boundary layer with a cylindrical roughness element near an airfoil leading edge. 42nd AIAA Fluid Dynamic Conference, New Orleans, AIAA Paper 2012-3077.Google Scholar
Plogmann, B., Würz, W. & Krämer, E.2012b Interaction of a three-dimensional roughness element with a TS-wave near an airfoil leading edge. 16th International Conference on Methods of Aerophysical Research—ICMAR, Kazan.Google Scholar
Plogmann, B., Würz, W. & Krämer, E. 2014 Interaction of a cylindrical roughness element and a two-dimensional TS-wave. In New Results in Numerical and Experimental Fluid Mechanics IX (ed. Dillmann, A., Heller, G., Krämer, E., Kreplin, H. P., Nitsche, W. & Rist, U.), pp. 163–172. Springer.Google Scholar
Rist, U. & Jäger, A. 2004 Unsteady disturbance generation and amplification in the boundary-layer flow behind a medium sized roughness element. In 6th IUTAM Symposium on Laminar–Turbulent Transition (ed. Govindarajan, R.), pp. 293–298. Springer.Google Scholar
Ruban, A. I.1984 On the generation of Tollmien–Schlichting waves by sound. Translated from Izv. Akad. Nauk SSSR, Mech. Zhidk. i Gaza, No. 5, pp. 44–52.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.Google Scholar
Saric, W. S., Hoos, J. A. & Radezsky, R. H. 1991 Boundary layer receptivity of sound with roughness. In Boundary Layer Stability and Transition to Turbulence; Proceedings of the Symposium, ASME and JSME Joint Fluids Engineering Conference, 1st, Portland, OR, June 23–27, 1991 (ed. Reda, D. C., Reed, H. L. & Kobayashi, R.), pp. 17–22. American Society of Mechanical Engineers.Google Scholar
Tadjfar, M. & Bodonyi, R. J. 1992 Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances. J. Fluid Mech. 242, 701–720.Google Scholar
Tani, I. 1961 Effect of two-dimensional and isolated roughness on laminar flow. Boundary Layer Flow Control Pergamon Press 2, 637–656.Google Scholar
Tani, I. 1969 Boundary-layer transition. Annu. Rev. Fluid Mech. 1, 169–196.Google Scholar
Tani, I. & Hama, R.1940 On the permissible roughness in the laminar boundary layer. Report Aeronautical Research Institute of Tokyo Imperial University 199 pp. 419–429.Google Scholar
Terentev, E. D. 1981 Linear problem for a vibrator in subsonic boundary layer. Prikl. Mat. Mekh. 45, 1049–1055.Google Scholar
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Annu. Rev. Fluid Mech. 14, 61–85.Google Scholar
Ustinov, M. V. 1995 Secondary instability modes generated by a Tollmien–Schlichting wave scattering from a bump. Theor. Comput. Fluid Dyn. 7, 341–354.Google Scholar
Wang, Y. X.2004 Instability and transition of boundary layer flows disturbed by steps and bumps. PhD thesis, Queen Mary College, University of London, UK.Google Scholar
Wortmann, F. X. & Althaus, D. 1964 Der Laminarwindkanal des Instituts für Aero- und Gasdynamik an der Technischen Hochschule Stuttgart. Z. Flugwiss. 12 (4), 129–134.Google Scholar
Wu, X. & Hogg, L. W. 2006 Acoustic radiation of Tollmien–Schlichting waves as they undergo rapid distortion. J. Fluid Mech. 550, 307–347.Google Scholar
Wu, X. & Luo, J. 2003 Linear and nonlinear instabilities of a Blasius boundary layer perturbed by streamwise vortices. Part 1. Steady streaks. J. Fluid Mech. 483, 225–248.Google Scholar
Wu, X. & Stuart, P. 1996 Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances. J. Fluid Mech. 316, 335–372.Google Scholar
Wu, X., Stuart, P. & Cowley, S. J. 2007 On the catalytic role of the phase-locked interaction of Tollmien–Schlichting waves in boundary layer transition. J. Fluid Mech. 590, 265–294.Google Scholar
Würz, W., Herr, S., Wörner, A., Rist, U., Wagner, S. & Kachanov, Y. S. 2003 Three-dimensional acoustic receptivity of a boundary-layer on an airfoil: experiments and direct numerical simulations. J. Fluid Mech. 478, 135–163.Google Scholar
Würz, W., Sartorius, D., Kloker, M., Borodulin, V. I., Kachanov, Y. S. & Smorodsky, B. V. 2012 Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: experiments, DNS and theory. Eur. J. Mech. (B/Fluids) 31, 102–128.Google Scholar