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Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

Published online by Cambridge University Press:  28 April 2016

Holger B. E. Kurz  and
Markus J. Kloker
Holger B. E. Kurz
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
Markus J. Kloker*
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The effects of a spanwise row of finite-size cylindrical roughness elements in a laminar, compressible, three-dimensional boundary layer on a wing profile are investigated by direct numerical simulations (DNS). Large elements are capable of immediately tripping turbulent flow by either a strong, purely convective or an absolute/global instability in the near wake. First we focus on an understanding of the steady near-field past a finite-size roughness element in the swept-wing flow, comparing it to a respective case in unswept flow. Then, the mechanisms leading to immediate turbulence tripping are elaborated by gradually increasing the roughness height and varying the disturbance background level. The quasi-critical roughness Reynolds number above which turbulence sets in rapidly is found to be $Re_{kk,qcrit}\approx 560$ and global instability is found only for values well above 600 using nonlinear DNS; therefore the values do not differ significantly from two-dimensional boundary layers if the full velocity vector at the roughness height is taken to build $Re_{kk}$. A detailed simulation study of elements in the critical range indicates a changeover from a purely convective to a global instability near the critical height. Finally, we perform a three-dimensional global stability analysis of the flow field to gain insight into the early stages of the temporal disturbance growth in the quasi-critical and over-critical cases, starting from a steady state enforced by damping of unsteady disturbances.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 158 - 194
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© 2016 Cambridge University Press 

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References

Acarlar, M. S. & Smith, C. R. 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), 1–41.Google Scholar
Akervik, E., Brandt, L., Henningson, D. S., Hoepffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.Google Scholar
Bagheri, S., Schlatter, P., Schmid, P. J. & Henningson, D. S. 2009 Global stability of a jet in crossflow. J. Fluid Mech. 624, 33–44.Google Scholar
Baker, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95 (02), 347–367.Google Scholar
Balachandar, S., Streett, C. L. & Malik, M. R. 1992 Secondary instability in rotating-disk flow. J. Fluid Mech. 242, 323–347.Google 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.Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2012 Compressibility effects on roughness-induced boundary layer transition. Intl J. Heat Fluid Flow 35, 45–51.Google Scholar
Bernardini, M., Pirozzoli, S., Orlandi, P. & Lele, S. K. 2014 Parameterization of boundary-layer transition induced by isolated roughness elements. AIAA J. 52 (10), 2261–2269.CrossRefGoogle Scholar
Bonfigli, G. & Kloker, M. 2007 Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation. J. Fluid Mech. 583, 229–272.Google Scholar
Brynjell-Rahkola, M., Schlatter, P., Hanifi, A. & Henningson, D. S. 2015 Global stability analysis of a roughness wake in a Falkner–Skan–Cooke boundary layer. Procedia IUTAM 14, 192–200.Google Scholar
Buell, J. C. & Huerre, P. 1988 Inflow/outflow boundary conditions and global dynamics of spatial mixing layers. In Proceedings of 2nd Summer Prog., pp. 19–27. Stanford Univ. Cent. Turbul. Res.Google Scholar
Choudhari, M. & Duck, P. W. 1996 Nonlinear excitation of inviscid stationary vortex instabilities in a boundary-layer flow. In IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, pp. 409–422.Google Scholar
Choudhari, M. & Fischer, P.2005 Roughness-induced transient growth. AIAA Paper 2005-4765.CrossRefGoogle Scholar
Denissen, N. A. & White, E. B. 2008 Roughness-induced bypass transition, revisited. AIAA J. 46 (7), 1874–1877.Google Scholar
Denissen, N. A. & White, E. B. 2013 Secondary instability of roughness-induced transient growth. Phys. Fluids 25 (11), 114108.Google Scholar
Doolittle, C. J., Drews, S. D. & Goldstein, D. B. 2014 Near-field flow structures about subcritical surface roughness. Phys. Fluids 26 (12), 124106.Google Scholar
Drews, S. D., Downs, R., Doolittle, C., Goldstein, D. & White, E. B.2011 Direct numerical simulations of flow past random distributed roughness. AIAA Paper 2011-564.Google Scholar
Edwards, W. S., Tuckerman, L. S., Friesner, R. A. & Sorensen, D. C. 1994 Krylov methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 110 (1), 82–102.Google Scholar
Ergin, F. G. & White, E. B.2005 Multicomponent and unsteady velocity measurements of transient disturbances. AIAA Paper 2005-527.Google Scholar
Ergin, F. G. & White, E. B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 44 (11), 2504–2514.Google Scholar
Fischer, P. & Choudhari, M.2004 Numerical simulation of roughness-induced transient growth in a laminar boundary layer. AIAA Paper 2004-2539.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 (5), 054110.Google Scholar
Gaster, M., Grosch, C. E. & Jackson, T. L. 1994 The velocity field created by a shallow bump in a boundary layer. Phys. Fluids 6 (9), 3079–3085.Google Scholar
Gregory, N. & Walker, W. S.1956 The effect on transition of isolated surface excrescences in the boundary layer. Aero. Res. Counc. R&M 2779. London.Google Scholar
Groskopf, G., Kloker, M. J. & Marxen, O. 2010 Bi-global crossplane stability analysis of high-speed boundary-layer flows with discrete roughness. In Seventh IUTAM Symposium on Laminar-Turbulent Transition (ed. Schlatter, P. & Henningson, D. S.), IUTAM Bookseries, 18, pp. 171–176. Springer.Google Scholar
Hernandez, V., Roman, J. E. & Vidal, V. 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351–362.Google Scholar
Hosseini, S. M., Tempelmann, D., Hanifi, A. & Henningson, D. S. 2013 Stabilization of a swept-wing boundary layer by distributed roughness elements. J. Fluid Mech. 718, R1.Google Scholar
Joslin, R. D. & Grosch, C. E. 1995 Growth characteristics downstream of a shallow bump: computation and experiment. Phys. Fluids 7 (12), 3042–3047.CrossRefGoogle Scholar
Kendall, J. M. 1981 Laminar boundary layer velocity distortion by surface roughness: effect upon stability. AIAA Paper 81, 0195.Google Scholar
Klanfer, L. & Owen, P. R.1953 The effect of isolated roughness on boundary layer transition. RAE.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 (1), 101–187.Google Scholar
Kloker, M., Konzelmann, U. & Fasel, H. 1993 Outflow boundary conditions for spatial Navier–Stokes simulations of transition boundary layers. AIAA J. 31 (4), 620–628.CrossRefGoogle Scholar
Koch, W., Bertolotti, F. P., Stolte, A. & Hein, S. 2000 Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability. J. Fluid Mech. 406, 131–174.Google Scholar
Kurz, H. B. E. & Kloker, M. J. 2014a Effects of a discrete medium-sized roughness in a laminar swept-wing boundary layer. In New Results in Numerical and Experimental Fluid Dynamics IX (ed. Dillmann, A. et al. ), Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 124, pp. 173–180. Springer.Google Scholar
Kurz, H. B. E. & Kloker, M. J. 2014b Receptivity of a swept-wing boundary layer to micron-sized discrete roughness elements. J. Fluid Mech. 755, 62–82.Google Scholar
Kurz, H. B. E. & Kloker, M. J. 2015a Discrete-roughness effects in a three-dimensional boundary layer on an airfoil by means of DNS. Procedia IUTAM 14, 163–172.CrossRefGoogle Scholar
Kurz, H. B. E. & Kloker, M. J. 2015b Near-wake behavior of discrete-roughness arrays in 2-d and 3-d laminar boundary layers. In High Performance Computing in Science and Engineering ’14 (ed. Nagel, W. E. et al. ), pp. 289–306. Springer.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (02), 243–251.CrossRefGoogle Scholar
Loiseau, J.-C., Cherubini, S., Robinet, J.-C. & Leriche, E. 2015 Influence of the shape on the roughness-induced transition. In Instability and Control of Massively Separated Flows, pp. 123–128. Springer.Google 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.Google Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.Google Scholar
Luchini, P. 2013 Linearized no-slip boundary conditions at a rough surface. J. Fluid Mech. 737, 349–367.Google Scholar
Mochizuki, M. 1961 Smoke observation on boundary layer transition caused by a spherical roughness element. J. Phys. Soc. Japan 16 (5), 995–1008.Google Scholar
Peplinski, A., Schlatter, P. & Henningson, D. S. 2015 Global stability and optimal perturbation for a jet in cross-flow. Eur. J. Mech. (B/Fluids) 49, 438–447.Google Scholar
Piot, E. & Casalis, G. 2009 Absolute stability mechanism of a swept cylinder laminar boundary layer with imposed spanwise periodic conditions. Phys. Fluids 21 (6), 064103.Google Scholar
Piot, E., Casalis, G. & Terracol, M.2007 Direct numerical simulation of the crossflow instabilities induced by a periodic roughness array on a swept cylinder: receptivity and stability investigations. AIAA Paper 2007-3976.Google 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.Google Scholar
Saric, W. S., Carrillo, R. B. Jr. & Reibert, M. S. 1998 Leading-edge roughness as a transition control mechanism. AIAA Paper 98-0781.Google Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (1), 5–28.Google Scholar
Sedney, R. 1973 A survey of the effects of small protuberances on boundary-layer flows. AIAA J. 11 (6), 782–792.Google Scholar
Shin, Y.-S., Rist, U. & Krämer, E. 2015 Stability of the laminar boundary-layer flow behind a roughness element. Exp. Fluids 56 (11), 1–18.Google Scholar
Stephani, K. A. & Goldstein, D. B.2009 DNS study of transient disturbance growth and bypass transition due to realistic roughness. AIAA.Google Scholar
Stewart, G. 2002 A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Applics. 23 (3), 601–614.Google Scholar
Tani, I. 1961 Effect of two-dimensional and isolated roughness on laminar flow. Boundary Layer Flow Control 2, 637–656.Google 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 (1), 319–352.Google Scholar
Tumin, A. & Reshotko, E. 2001 Spatial theory of optimal disturbances in boundary layers. Phys. Fluids 13 (7), 2097–2104.Google Scholar
Von Doenhoff, A. E. & Braslow, A. L. 1961 The effect of distributed surface roughness on laminar flow. Boundary Layer Control 2, 657–681.Google Scholar
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer. J. Fluid Mech. 456, 49–84.Google Scholar
White, E. B.2005 Experiments in transient growth and roughness-induced bypass transition. Tech. Rep. DTIC Document.Google Scholar
White, E. B. & Ergin, F. G.2003 Receptivity and transient growth of roughness-induced disturbances. AIAA Paper 2003-4243.Google Scholar
Zhou, Z., Wang, Z. & Fan, J. 2010 Direct numerical simulation of the transitional boundary-layer flow induced by an isolated hemispherical roughness element. Comput. Meth. Appl. Mech. Engng 199 (23–24), 1573–1582.Google Scholar

Kurz et al. supplementary movie

“Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer”. Movie to §6, 6.1.-6.3, figures 11-17, of the paper. Vortex visualization using λ2, the colour indicates the sign of the streamwise vorticity: red is for rotation sense in clockwise direction when looking downstream. Quasi-critical roughness case, Rekk=564. Phase 1: start from enforced steady state w/o controlled unsteady forcing; phase 2: controlled pulsing switched on; phase 3: controlled pulsing switched off.

Download Kurz et al. supplementary movie(Video)
Video 23 MB

Kurz et al. supplementary movie

“Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer”. Movie to §6, 6.4, figures 19-20, of the paper. Vortex visualization using λ2, the colour indicates the sign of the streamwise vorticity: red is for rotation sense in clockwise direction when looking downstream. Over-critical roughness case, Rekk=881. Start from enforced steady state w/o controlled unsteady forcing; convective instability is seen first, followed by appearance of global instability.

Download Kurz et al. supplementary movie(Video)
Video 13.2 MB