zbMATH — the first resource for mathematics

Structure evolution at early stage of boundary-layer transition: simulation and experiment. (English) Zbl 07193492
Summary: The beginning of laminar-turbulent transition is usually associated with a wave-like disturbance, but its evolution and role in precipitating the development of other flow structures are not well understood from a structure-based view. Nonlinear parabolized stability equations (NPSE) were solved numerically to simulate the transition of K-regime, N-regime and O-regime. However, only the K-regime transition was examined experimentally using both hydrogen bubble visualization and time-resolved tomographic particle image velocimetry (tomo-PIV). Based on the ‘NPSE visualization’ and ‘tomographic visualization’, at least four common characteristics of the generic transition process were identified: (i) inflectional regions representing high-shear layers (HSL) that develop in vertical velocity profiles, accompanied by ejection-sweep behaviours; (ii) low-speed streak (LSS) patterns, manifested in horizontal timelines, that seem to consist of several three-dimensional (3-D) waves; (iii) a warped wave front (WWF) pattern, displaying multiple folding processes, which develops adjacent to the LSS in the near-wall region, prior to the appearance of \(\Lambda\)-vortices; (iv) a coherent 3-D wave front, similar to a soliton, in the upper boundary layer, accompanied by regions of depression along the flanks of the wave. It was determined that the amplification and lift-up of a 3-D wave causes the development of the HSL, WWF and multiple folding behaviour of material surfaces, that all contribute to the development of a \(\Lambda\)-vortex. The amplified 3-D wave is hypothesized as a soliton-like coherent structure. Based on our results, a path to transition is proposed, which hypothesizes the function of the WWF in boundary-layer transition.

76 Fluid mechanics
Full Text: DOI
[1] Acarlar, M. S. & Smith, C. R.1987aA study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech.175, 1-41.
[2] Acarlar, M. S. & Smith, C. R.1987bA study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech.175, 43-83.
[3] Adrian, R. J., Meinhart, C. D. & Tomkins, C. D.2000Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech.422, 1-54. · Zbl 0959.76503
[4] Bake, S., Fernholz, H. H. & Kachanov, Y. S.2000Resemblance of K- and N-regimes of boundary-layer transition at late stages. Eur. J. Mech. (B/Fluids)19, 1-22. · Zbl 0953.76502
[5] Berlin, S., Lundbladh, A. & Henningson, D.1994Spatial simulations of oblique transition in a boundary layer. Phys. Fluids6 (6), 1949-1951.
[6] Berlin, S., Wiegel, M. & Henningson, D. S.1999Numerical and experimental investigations of oblique boundary layer transition. J. Fluid Mech.393, 23-57. · Zbl 0944.76547
[7] Bertolotti, F. P., Herbert, T. & Spalart, P. R.1992Linear and nonlinear stability of the Blasius boundary-layer. J. Fluid Mech.242, 441-474.
[8] Bhaumik, S. & Sengupta, T. K.2014Precursor of transition to turbulence: spatiotemporal wave front. Phys. Rev. E89 (4), 043018.
[9] Boiko, A. V., Dovgal, A. V., Grek, G. R. & Kozlov, V. V.2012Nonlinear effects during the laminar-turbulent transition. In Physics of Transitional Shear Flows: Instability and Laminar-Turbulent Transition in Incompressible Near-Wall Shear Layers, pp. 223-242. Springer.
[10] Boiko, A. V., Westin, K. J. A., Klingmann, B. G. B., Kozlov, V. V. & Alfredsson, P. H.1994Experiments 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.
[11] Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Meyer, D. G. W., Rist, U., Lian, Q. X. & Lee, C. B.2002Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theor. Comput. Fluid Dyn.15 (5), 317-337. · Zbl 1057.76529
[12] Bose, R. & Durbin, P. A.2016Transition to turbulence by interaction of free-stream and discrete mode perturbations. Phys. Fluids28 (11), 114105.
[13] Chang, C.-L. & Malik, M. R.1994Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech.273, 323-360. · Zbl 0814.76040
[14] Chen, W.2013 Numerical simulation of boundary layer transition by combined compact difference method. PhD thesis, Nanyang Technological University.
[15] Chen, X., Zhu, Y. D. & Lee, C. B.2017Interactions between second mode and low-frequency waves in a hypersonic boundary layer. J. Fluid Mech.820, 693-735. · Zbl 1383.76315
[16] Chernoray, V. G., Kozlov, V. V., Löfdahl, L. & Chun, H. H.2006Visualization of sinusoidal and varicose instabilities of streaks in a boundary layer. J. Vis.9 (4), 437-444.
[17] Cohen, J., Breuer, K. S. & Haritonidis, J. H.1991On the evolution of a wave packet in a laminar boundary layer. J. Fluid Mech.225, 575-606.
[18] Cornelius, K., Takeuchi, K. & Deutsch, S.1979Turbulent flow visualization-technique for extracting accurate quantitative information. In 5th Biennial Symposium on Turbulence (ed. Patterson, G. K. & Zakin, J. L.), pp. 287-293. University of Missouri-Rolla.
[19] Elofsson, P.1998 Experiments on oblique transition in wall bounded shear flows. PhD thesis, KTH Royal Institute of Technology, Department of Mechanics.
[20] Goldstein, M. E. & Choi, S.-W.1989Nonlinear evolution of interacting oblique waves on two-dimensional shear layers. J. Fluid Mech.207, 97-120. · Zbl 0681.76053
[21] Guo, H., Borodulin, V. I., Kachanov, Y. S., Pan, C., Wang, J. J., Lian, Q. X. & Wang, S. F.2010Nature of sweep and ejection events in transitional and turbulent boundary layers. J. Turbul.11 (34), 1-51.
[22] Guo, X. & Tang, D.2010Nonlinear stability of supersonic nonparallel boundary layer flows. Chin. J. Aeronaut.23 (3), 283-289.
[23] Haidari, A. H. & Smith, C. R.1994The generation and regeneration of single hairpin vortices. J. Fluid Mech.277, 135-162.
[24] Hama, F. R.1962Streaklines in a perturbed shear flow. Phys. Fluids5 (6), 644-650.
[25] Hama, F. R., Long, J. D. & Hegarty, J. C.1957On transition from laminar to turbulent flow. J. Appl. Phys.28 (4), 388-394.
[26] Hama, F. R. & Nutant, J.1963Detailed flow-field observations in the transition process in a thick boundary layer. In Proceedings of the Heat Transfer and Fluid Mechanics Institute, pp. 77-93. Stanford University Press. · Zbl 0114.41802
[27] Hellström, L. H. O. & Smits, A. J.2017Structure identification in pipe flow using proper orthogonal decomposition. Trans. R. Soc. Lond. A375 (2089), 20160086.
[28] Herbert, T.1984 Analysis of the subharmonic route to transition in boundary layers. AIAA Paper 84-0009.
[29] Herbert, T.1988Secondary instability of boundary layers. Annu. Rev. Fluid Mech.20 (1), 487-526.
[30] Herbert, T.1997Parabolized stability equations. Annu. Rev. Fluid Mech.29 (1), 245-283.
[31] Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research Report.
[32] Jiang, X. Y.2019aLagrangian identification of coherent structures in wall-bounded flows. Adv. Appl. Maths Mech.11, 640-652.
[33] Jiang, X. Y.2019bRevisiting coherent structures in low-speed turbulent boundary layers. Appl. Maths Mech. - Engl. Edn40 (2), 261-272.
[34] Kachanov, Y. S.1987On the resonant nature of the breakdown of a laminar boundary layer. J. Fluid Mech.184 (1), 43-74.
[35] Kachanov, Y. S.1991The mechanisms of formation and breakdown of soliton-like coherent structures in boundary layers. In Advances in Turbulence 3 (ed. Johansson, A. V. & Alfredsson, P. H.), pp. 42-51. Springer.
[36] Kachanov, Y. S.1994Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech.26 (1), 411-482.
[37] Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y.1977Nonlinear development of a wave in a boundary layer. Fluid Dyn.12 (3), 383-390.
[38] Kachanov, Y. S. & Levchenko, V. Y.1984The resonant interaction of disturbances at laminar turbulent transition in a boundary-layer. J. Fluid Mech.138, 209-247.
[39] Kachanov, Y. S., Ryzhov, O. S. & Smith, F. T.1993Formation of solitons in transitional boundary layers: theory and experiment. J. Fluid Mech.251, 273-297.
[40] Kim, H., Kline, S. J. & Reynolds, W. C.1971The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech.50, 133-160.
[41] Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M.1962The three-dimensional nature of boundary-layer instability. J. Fluid Mech.12, 1-34. · Zbl 0131.41901
[42] Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W.1967The structure of turbulent boundary layers. J. Fluid Mech.30 (4), 741-773.
[43] Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. D1962Detailed flow field in transition. In Proceedings of the Heat Transfer and Fluid Mechanics Institute, pp. 1-26. Stanford University Press.
[44] Laurien, E. & Kleiser, L.1989Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech.199, 403-440.
[45] Lee, C. B.1998New features of CS solitons and the formation of vortices. Phys. Lett. A247 (6), 397-402.
[46] Lee, C. B.2000Possible universal transitional scenario in a flat plate boundary layer: measurement and visualization. Phys. Rev. E62 (3), 3659-3670.
[47] Lee, C. B. & Chen, S. Y.2006Dynamics of transitional boundary layers. In Transition and Turbulence Control (ed. Ged-El Hak, M. & Tsai, H. M.), pp. 39-85. World Scientific. · Zbl 1180.76002
[48] Lee, C. B. & Fu, S.2001On the formation of the chain of ring-like vortices in a transitional boundary layer. Exp. Fluids30 (3), 354-357.
[49] Lee, C. B. & Li, R. Q.2007Dominant structure for turbulent production in a transitional boundary layer. J. Turbul.8 (55), 1-34.
[50] Lee, C. B. & Wu, J. Z.2008Transition in wall-bounded flows. Appl. Mech. Rev.61, 030802. · Zbl 1146.76601
[51] Lefauve, A., Partridge, J. L., Zhou, Q., Dalziel, S. B., Caulfield, C. P. & Linden, P. F.2018The structure and origin of confined Holmboe waves. J. Fluid Mech.848, 508-544.
[52] Lu, L. J. & Smith, C. R.1985Image processing of hydrogen bubble flow visualization for determination of turbulence statistics and bursting characteristics. Exp. Fluids3 (6), 349-356.
[53] Lynch, K. P. & Scarano, F.2015An efficient and accurate approach to MTE-MART for time-resolved tomographic PIV. Exp. Fluids56 (3), 66.
[54] Meyer, D. G. W., Rist, U., Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Lian, Q. X. & Lee, C. B.2000Late-stage transitional boundary-layer structures: direct numerical simulation and experiment. In Laminar-Turbulent Transition (ed. Fasel, H. F. & Saric, W. S.), pp. 167-172. Springer.
[55] Moin, P. & Moser, R. D.1989Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech.200, 471-509. · Zbl 0659.76062
[56] Nishioka, M., Asai, M. & Iida, S.1981Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. Meyer, R. E.), pp. 113-126. Academic Press.
[57] Rist, U. & Fasel, H.1995Direct numerical simulation of controlled transition in a flat-plate boundary layer. J. Fluid Mech.298, 211-248. · Zbl 0850.76392
[58] Sandham, N. D. & Kleiser, L.1992The late stages of transition to turbulence in channel flow. J. Fluid Mech.245, 319-348. · Zbl 0825.76312
[59] Sayadi, T., Hamman, C. W. & Moin, P.2013Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech.724, 480-509. · Zbl 1287.76138
[60] Sayadi, T., Schmid, P. J., Nichols, J. W. & Moin, P.2014Reduced-order representation of near-wall structures in the late transitional boundary layer. J. Fluid Mech.748, 278-301.
[61] Scarano, F.2013Tomographic PIV: principles and practice. Meas. Sci. Technol.24 (1), 012001.
[62] Schmid, P. & Henningson, D.1992A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids4 (9), 1986-1989.
[63] Schmid, P. J. & Henningson, D. S.2001Transition to turbulence. In Stability and Transition in Shear Flows, pp. 401-475. Springer. · Zbl 0966.76003
[64] Smith, C. R.1984A synthesized model of the near-wall behavior in turbulent boundary layers. In Proceedings of the 8th Symposium of Turbulence (ed. Patterson, G. K. & Zakin, J. L.), pp. 1-27. University of Missouri-Rolla.
[65] Smith, C. R. & Paxson, R. D.1983A technique for evaluation of three-dimensional behavior in turbulent boundary layers using computer augmented hydrogen bubble-wire flow visualization. Exp. Fluids1 (1), 43-49.
[66] Smyth, W. D. & Peltier, W. R.1991Instability and transition in finite-amplitude Kelvin-Helmholtz and Holmboe waves. J. Fluid Mech.228, 387-415. · Zbl 0723.76044
[67] White, F. M.2006Viscous Fluid Flow, 3rd edn. McGraw-Hill.
[68] Williams, D. R. & Hama, F. R.1980Streaklines in a shear layer perturbed by two waves. Phys. Fluids23 (3), 442-447.
[69] Wortmann, F. X.1981Boundary-layer waves and transition. In Advances in Fluid Mechanics (ed. Krause, E.), pp. 268-279. Springer.
[70] Zelman, M. B. & Maslennikova, I. I.1993Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition. J. Fluid Mech.252, 449-478. · Zbl 0777.76033
[71] Zhao, Y., Yang, Y. & Chen, S.2016Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech.793, 840-876. · Zbl 1382.76132
[72] Zhou, M. D. & Liu, T. S.1987Stability investigation in nominally two-dimensional laminar boundary layers by means of heat pulsing. In Perspectives in Turbulence Studies (ed. Meier, H. U. & Bradshaw, P.), pp. 47-70. Springer.
[73] Zhu, H. Y., Wang, C. Y., Wang, H. P. & Wang, J. J.2017Tomographic PIV investigation on 3D wake structures for flow over a wall-mounted short cylinder. J. Fluid Mech.831, 743-778.
[74] Zhu, Y., Lee, C., Chen, X., Wu, J., Chen, S. & Gad-El Hak, M.2018Newly identified principle for aerodynamic heating in hypersonic flows. J. Fluid Mech.855, 152-180. · Zbl 1415.76288
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.