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On the unsteady characteristics of turbulent separations over a forward–backward-facing step

Published online by Cambridge University Press:  29 January 2019

Xingjun Fang Open the ORCID record for Xingjun Fang [Opens in a new window]  and
Mark F. Tachie
Xingjun Fang*
Affiliation:
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada
Mark F. Tachie
Affiliation:
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent separation bubbles over and behind a two-dimensional forward–backward-facing step submerged in a deep turbulent boundary layer are investigated using a time-resolved particle image velocimetry. The Reynolds number based on the step height and free-stream velocity is 12 300, and the ratio of the streamwise length to the height of the step is 2.36. The upstream turbulent boundary layer thickness is 4.8 times the step height to ensure a strong interaction of the upstream turbulence structures with the separated shear layers over and behind the step. The velocity measurements were performed in streamwise–vertical planes at the channel mid-span and streamwise–spanwise planes at various vertical distances from the wall. The unsteady characteristics of the separation bubbles and their associated turbulence structures are studied using a variety of techniques including linear stochastic estimation, proper orthogonal decomposition and variable-interval time averaging. The results indicate that the low-frequency flapping motion of the separation bubble over the step is induced by the oncoming large-scale alternating low- and high-velocity streaky structures. Dual separation bubbles appear periodically over the step at a higher frequency than the flapping motion, and are attributed to the inherent instability in the rear part of the mean separation bubble. The separation bubble behind the step exhibits a flapping motion at the same frequency as the separation bubble over the step, but with a distinct phase delay. At instances when an enlarged separation bubble is formed in front of the step, a pair of vertical counter-rotating vortices is formed in the immediate vicinity of the leading edge.

JFM classification

Boundary Layers: Boundary layer separation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 994 - 1030
Copyright
© 2019 Cambridge University Press 

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References

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.10.1017/S0022112000001580Google Scholar
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear-flow. J. Fluid Mech. 190, 531–559.10.1017/S0022112088001442Google Scholar
Agelinchaab, M. & Tachie, M. F. 2008 PIV study of separated and reattached open channel flow over surface mounted blocks. Trans. ASME J. Fluids Engng 130 (6), 061206.10.1115/1.2911677Google Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.10.1017/S0022112099008976Google Scholar
Anand, K. & Sarkar, S. 2017 Features of a laminar separated boundary layer near the leading-edge of a model airfoil for different angles of attack: an experimental study. Trans. ASME J. Fluids Engng 139 (2), 021201.Google Scholar
Bergeles, G. & Athanassiadis, N. 1983 The flow past a surface-mounted obstacle. Trans. ASME J. Fluids Engng 105 (4), 461–463.10.1115/1.3241030Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575.10.1146/annurev.fl.25.010193.002543Google Scholar
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76 (1), 89–112.10.1017/S0022112076003145Google Scholar
Bogard, D. G. & Tiederman, W. G. 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 162, 389–413.10.1017/S0022112086002094Google Scholar
Bogard, D. G. & Tiederman, W. G. 1987 Characteristics of ejections in turbulent channel flow. J. Fluid Mech. 179, 1–19.10.1017/S002211208700140XGoogle Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.10.1017/S002211207400190XGoogle Scholar
Camussi, R., Felli, M., Pereira, F., Aloisio, G. & Di Marco, A. 2008 Statistical properties of wall pressure fluctuations over a forward-facing step. Phys. Fluids 20, 075113.10.1063/1.2959172Google Scholar
Castro, I. P. 1979 Relaxing wakes behind surface-mounted obstacles in rough wall boundary layers. J. Fluid Mech. 93 (4), 631–659.10.1017/S0022112079001968Google Scholar
Castro, I. P. & Haque, A. 1987 The structure of a turbulent shear layer bounding a separation region. J. Fluid Mech. 179, 439–468.10.1017/S0022112087001605Google Scholar
Cherry, N. J., Hillier, R. & Latour, M. E. M. P. 1984 Unsteady measurements in a separated and reattaching flow. J. Fluid Mech. 144, 13–46.10.1017/S002211208400149XGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.10.1017/S0022112001003512Google Scholar
Djilali, N. & Gartshore, I. S. 1991 Turbulent flow around a bluff rectangular plate. Part I. Experimental investigation. ASME J. Fluids Engng 113 (1), 51–59.10.1115/1.2926496Google Scholar
Driver, D. M., Seegmiller, H. L. & Marvin, J. G. 1987 Time-dependent behavior of a reattaching shear layer. AIAA J. 25 (7), 914–919.10.2514/3.9722Google Scholar
Eaton, J. K. & Johnston, J. P. 1982 Low frequency unsteadiness of a reattaching turbulent shear layer. In Turbulent Shear Flows 3 (ed. Bradbury, L. J. S., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), pp. 162–170. Springer.10.1007/978-3-642-95410-8_16Google Scholar
Essel, E. E. & Tachie, M. F. 2015 Roughness effects on turbulent flow downstream of a backward facing step. Flow Turbul. Combust. 94 (1), 125–153.10.1007/s10494-014-9549-1Google Scholar
Essel, E. E. & Tachie, M. F. 2017 Upstream roughness and Reynolds number effects on turbulent flow structure over forward facing step. Intl J. Heat Fluid Flow 66, 226–242.10.1016/j.ijheatfluidflow.2015.11.004Google Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2007 Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J. Fluid Mech. 585, 369–394.10.1017/S0022112007006799Google Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2009 Low-frequency dynamics of shocked induced separation in a compression ramp interaction. J. Fluid Mech. 636, 397–425.10.1017/S0022112009007952Google Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 57–80.10.1017/S0022112004002277Google Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.10.1017/S0022112002003270Google Scholar
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 53–64.10.1017/S0022112006000292Google Scholar
Hancock, P. E. 2000 Low Reynolds number two-dimensional separated and reattaching turbulent shear flow. J. Fluid Mech. 410, 101–122.10.1017/S0022112099007843Google Scholar
Hattori, H. & Nagano, Y. 2010 Investigation of turbulent boundary layer over forward-facing step via direct numerical simulation. Intl J. Heat Fluid Flow 31 (3), 284–294.10.1016/j.ijheatfluidflow.2010.02.027Google Scholar
Hudy, L. M., Naguib, A. M. & Humphreys, W. M. 2003 Wall-pressure-array measurements beneath a separating/reattaching flow region. Phys. Fluids 15 (3), 706–717.10.1063/1.1540633Google Scholar
Humble, R. A., Scarano, F. & van Oudheusden, B. W. 2009 Unsteady aspects of an incident shock wave/turbulent boundary layer interaction. J. Fluid Mech. 635, 47–74.10.1017/S0022112009007630Google Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.10.1017/S0022112006003946Google Scholar
Iftekhar, H. & Agelin-Chaab, M. 2016 Structure of turbulent flows over forward facing steps with adverse pressure gradient. ASME J. Fluids Engng 138 (11), 111202.10.1115/1.4033030Google Scholar
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26 (8), 2088–2097.10.1063/1.864413Google Scholar
Kiya, M. & Sasaki, K. 1983 Structure of a turbulent separation bubble. J. Fluid Mech. 137, 83–113.10.1017/S002211208300230XGoogle Scholar
Kiya, M., Sasaki, K. & Arie, M. 1982 Discrete-vortex simulation of a turbulent separation bubble. J. Fluid Mech. 120, 219–244.10.1017/S0022112082002742Google Scholar
Lander, D. C., Letchford, C. W., Amitay, M. & Kopp, G. A. 2016 Influence of the bluff body shear layers on the wake of a square prism in a turbulent flow. Phys. Rev. Fluids 1, 044406.10.1103/PhysRevFluids.1.044406Google Scholar
Lanzerstorfer, D. & Kuhlmann, H. C. 2012 Three-dimensional instability of the flow over a forward-facing step. J. Fluid Mech. 695, 390–404.10.1017/jfm.2012.28Google Scholar
Largeau, J. F. & Moriniere, V. 2007 Wall pressure fluctuations and topology in separated flows over a forward-facing step. Exp. Fluids 42, 21–40.10.1007/s00348-006-0215-9Google Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.10.1017/S0022112096003941Google Scholar
Lee, I. & Sung, H. J. 2002 Multiple-arrayed pressure measurement for investigation of the unsteady flow structure of a reattaching shear layer. J. Fluid Mech. 463, 377–402.10.1017/S002211200200890XGoogle Scholar
Lim, H. C., Castro, I. P. & Hoxey, R. P. 2007 Bluff bodies in deep turbulent boundary layers: Reynolds-number issues. J. Fluid Mech. 571, 97–118.10.1017/S0022112006003223Google Scholar
Luchik, T. S. & Tiederman, W. G. 1987 Timescale and structure of ejections and bursts in turbulent channel flows. J. Fluid Mech. 174, 529–552.10.1017/S0022112087000235Google Scholar
Marquillie, M., Ehrenstein, U. & Laval, J.-P. 2011 Instability of streaks in wall turbulence with adverse pressure gradient. J. Fluid Mech. 681, 205–240.10.1017/jfm.2011.193Google Scholar
Marquillie, M., Laval, J.-P. & Dolganov, R. 2008 Direct numerical simulation of a separated channel flow with a smooth profile. J. Turbul. 9 (1), 1–23.10.1080/14685240701767332Google Scholar
Meyer, K. E., Pedersen, J. M. & Özcan, O. 2007 A turbulent jet in crossflow analysed with proper orthogonal decomposition. J. Fluid Mech. 583, 199–227.10.1017/S0022112007006143Google Scholar
Mohammed-Taifour, A. & Weiss, J. 2016 Unsteadiness in a large turbulent separation bubble. J. Fluid Mech. 799, 383–412.10.1017/jfm.2016.377Google Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.10.1017/S0022112009007423Google Scholar
Moss, W. D. & Baker, S. 1980 Re-circulating flows associated with two-dimensional steps. Aero. Q. 31 (3), 151–172.10.1017/S0001925900008878Google Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.10.1017/S0022112098009987Google Scholar
Pearson, D. S., Goulart, P. J. & Ganapathisubramani, B. 2013 Turbulent separation upstream of a forward-facing step. J. Fluid Mech. 724, 284–304.10.1017/jfm.2013.113Google Scholar
Piirto, M., Saarenrinne, P., Eloranta, H. & Karvinen, R. 2003 Measuring turbulence energy with PIV in a backward-facing step flow. Exp. Fluids 35 (3), 219–236.10.1007/s00348-003-0607-zGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.10.1017/CBO9780511840531Google Scholar
Prandtl, L. 1925 Bericht über die Entstehung der Turbulenz. Z. Angew. Math. Mech. 5, 136–139.Google Scholar
Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry. Springer.Google Scholar
Samimy, M. & Lele, S. K. 1991 Motion of particles with inertia in a compressible free shear layer. Phys. Fluids A 3 (8), 1915–1923.10.1063/1.857921Google Scholar
Samson, A. & Sarkar, S. 2016 Effects of free-stream turbulence on transition of a separated boundary layer over the leading-edge of a constant thickness airfoil. ASME J. Fluids Engng 138, 021202.Google Scholar
Sherry, M., Lo Jacono, D. & Sheridan, J. 2010 An experimental investigation of the recirculation zone formed downstream of a forward facing step. J. Wind Engng Ind. Aerodyn. 98 (12), 888–894.10.1016/j.jweia.2010.09.003Google Scholar
Simpson, R. L. 1989 Turbulent boundary-layer separation. Annu. Rev. Fluid Mech. 21, 205–234.10.1146/annurev.fl.21.010189.001225Google Scholar
Spazzini, P. G., Iuso, G., Onorato, M., Zurlo, N. & Di Cicca, G. M. 2001 Unsteady behavior of back-facing step flow. Exp. Fluids 30 (5), 551–561.10.1007/s003480000234Google Scholar
Stüer, H., Gyr, A. & Kinzelbach, W. 1999 Laminar separation on a forward facing step. Eur. J. Mech. (B/Fluids) 18, 675–692.10.1016/S0997-7546(99)00104-1Google Scholar
Thacker, A., Aubrun, S., Leroy, A. & Devinant, P. 2013 Experimental characterization of flow unsteadiness in the centerline plane of an Ahmed body rear slant. Exp. Fluids 54, 1479.10.1007/s00348-013-1479-5Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.10.1017/S0022112003005251Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Volina, R. J., Schultz, M. P. & Flack, K. A. 2009 Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75–101.10.1017/S0022112009007617Google Scholar
Wilhelm, D., Härtel, C. & Kleiser, L. 2003 Computational analysis of the two-dimensional-three-dimensional transition in forward-facing step flow. J. Fluid Mech. 489, 1–27.10.1017/S0022112003004440Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41 (2), 327–361.10.1017/S0022112070000630Google Scholar
Yang, Z. & Voke, P. R. 2001 Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature. J. Fluid Mech. 439, 305–333.10.1017/S0022112001004633Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.10.1017/S002211209900467XGoogle Scholar