Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T19:37:02.176Z Has data issue: false hasContentIssue false
  • English
  • Français

The instantaneous structure of secondary flows in turbulent boundary layers

Published online by Cambridge University Press:  16 January 2019

C. Vanderwel Open the ORCID record for C. Vanderwel [Opens in a new window] ,
A. Stroh ,
J. Kriegseis ,
B. Frohnapfel  and
B. Ganapathisubramani Open the ORCID record for B. Ganapathisubramani [Opens in a new window]
C. Vanderwel*
Affiliation:
Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK
A. Stroh*
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany
J. Kriegseis
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany
B. Frohnapfel
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany
B. Ganapathisubramani
Affiliation:
Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK
*
†Email addresses for correspondence: c.m.vanderwel@soton.ac.uk, alexander.stroh@kit.edu
†Email addresses for correspondence: c.m.vanderwel@soton.ac.uk, alexander.stroh@kit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Secondary flows can develop in turbulent boundary layers that grow over surfaces with spanwise inhomogeneities. In this article, we demonstrate the formation of secondary flows in both experimental and numerical tests and dissect the instantaneous structure and topology of these secondary motions. We show that the formation of secondary flows is not very sensitive to the Reynolds number range investigated, and direct numerical simulations and experiments produce similar results in the mean flow as well as the dispersive and turbulent stress distributions. The numerical methods capture time-resolved features of the instantaneous flow and provide insight into the near-wall flow structures, that were previously obscured in the experimental measurements. Proper orthogonal decomposition was shown to capture the essence of the secondary flows in relatively few modes and to be useful as a filter to analyse the instantaneous flow patterns. The secondary flows are found to create extended regions of high Reynolds stress away from the wall that comprise predominantly sweeps similar to what one would expect to see near the wall and which are comparable in magnitude to the near-wall stress. Analysis of the instantaneous flow patterns reveals that the secondary flows are the result of a non-homogeneous distribution of mid-size vortices.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 845 - 870
Copyright
© 2019 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

Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290.Google Scholar
Amir, M. & Castro, I. P. 2011 Turbulence in rough-wall boundary layers: universality issues. Exp. Fluids 51 (2), 313–326.10.1007/s00348-011-1049-7Google Scholar
Anderson, W., Barros, J. M., Christensen, K. T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316–347.10.1017/jfm.2015.91Google Scholar
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13 (1), 131–156.Google Scholar
Awasthi, A. & Anderson, W. 2018 Numerical study of turbulent channel flow perturbed by spanwise topographic heterogeneity: amplitude and frequency modulation within low-and high-momentum pathways. Phys. Rev. Fluids 3 (4), 044602.10.1103/PhysRevFluids.3.044602Google Scholar
Bai, H. L., Kevin, Hutchins, N. & Monty, J. P. 2018 Turbulence modifications in a turbulent boundary layer over a rough wall with spanwise-alternating roughness strips. Phys. Fluids 30 (5), 055105.Google Scholar
Barros, J. M. & Christensen, K. T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.10.1017/jfm.2014.218Google Scholar
Benschop, H. & Breugem, W. 2017 Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow. J. Turbul. 18 (8), 717–759.10.1080/14685248.2017.1319951Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.Google Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19 (1), 53–74.10.1146/annurev.fl.19.010187.000413Google Scholar
Canton, J., Örlü, R., Chin, C., Hutchins, N., Monty, J. & Schlatter, P. 2016 On large-scale friction control in turbulent wall flow in low Reynolds number channels. Flow Turbul. Combust. 97 (3), 811–827.10.1007/s10494-016-9723-8Google Scholar
Castro, I. P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.10.1017/S0022112007006921Google Scholar
Chan-Braun, C., García-Villalba, M. & Uhlmann, M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441–474.10.1017/jfm.2011.311Google Scholar
Chatterjee, A. 2000 An introduction to the proper orthogonal decomposition. Curr. Sci. 78 (7), 808–817.Google Scholar
Cheng, H. & Castro, I. 2002 Near wall flow over urban-like roughness. Boundary-Layer Meteorol. 104 (2), 229–259.10.1023/A:1016060103448Google Scholar
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D.2007 Simson: a pseudo-spectral solver for incompressible boundary layer flows TRITA-MEK, KTH Mechanics, Stockholm, Sweden.Google Scholar
Coceal, O., Thomas, T., Castro, I. & Belcher, S. 2006 Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol. 121 (3), 491–519.10.1007/s10546-006-9076-2Google Scholar
Dai, Y., Huang, W., Xu, C. & Cui, G. 2015 Direct numerical simulation of turbulent flow in a rotating square duct. Phys. Fluids 27 (6), 065104.Google Scholar
De Marchis, M., Napoli, E. & Armenio, V. 2010 Turbulence structures over irregular rough surfaces. J. Turbul. 11, N3.10.1080/14685241003657270Google Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32 (1), 519–571.10.1146/annurev.fluid.32.1.519Google Scholar
Finnigan, J. J. 1979 Turbulence in waving wheat. Boundary-Layer Meteorol. 16 (3), 213–236.Google Scholar
Finnigan, J. J. & Shaw, R. 2008 Double-averaging methodology and its application to turbulent flow in and above vegetation canopies. Acta Geophys. 56 (3), 534–561.10.2478/s11600-008-0034-xGoogle Scholar
Flack, K. A. & Schultz, M. P. 2014 Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26 (10), 101305.10.1063/1.4896280Google Scholar
Forooghi, P., Stroh, A., Magagnato, F., Jakirlić, S. & Frohnapfel, B. 2017 Toward a universal roughness correlation. Trans. ASME J. Fluids Engng 139 (12), 121201.Google Scholar
Forooghi, P., Stroh, A., Schlatter, P. & Frohnapfel, B. 2018 Direct numerical simulation of flow over dissimilar, randomly distributed roughness elements: a systematic study on the effect of surface morphology on turbulence. Phys. Rev. Fluids 3 (4), 044605.Google Scholar
Goldstein, D., Handler, R. & Sirovich, L. 1993 Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105 (2), 354–366.10.1006/jcph.1993.1081Google Scholar
Goldstein, D. B. & Tuan, T.-C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115–151.Google Scholar
Hwang, H. G. & Lee, J. H. 2018 Secondary flows in turbulent boundary layers over longitudinal surface roughness. Phys. Rev. Fluids 3, 014608.10.1103/PhysRevFluids.3.014608Google Scholar
Kawahara, G., Uhlmann, M. & Van Veen, L. 2012 The significance of simple invariant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44, 203–225.10.1146/annurev-fluid-120710-101228Google Scholar
Kevin, K., Monty, J. P., Bai, H. L., Pathikonda, G., Nugroho, B., Barros, J. M., Christensen, K. T. & Hutchins, N. 2017 Cross-stream stereoscopic particle image velocimetry of a modified turbulent boundary layer over directional surface pattern. J. Fluid Mech. 813, 412–435.10.1017/jfm.2016.879Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.10.1063/1.4862918Google Scholar
Medjnoun, T. S., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516–543.Google Scholar
Mejia-Alvarez, R. & Christensen, K. T. 2013 Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25 (11), 115109.Google Scholar
Meyer, K., Pedersen, J. & Özcan, O. 2007 A turbulent jet in crossflow analysed with proper orthogonal decomposition. J. Fluid Mech. 583, 199–227.10.1017/S0022112007006143Google Scholar
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng ASCE 131 (4), 229–246.Google Scholar
Ni, W., Lu, L., Fang, J., Moulinec, C. & Yao, Y. 2018 Large-scale streamwise vortices in turbulent channel flow induced by active wall actuations. Flow Turbul. Combust. 100 (3), 651–673.10.1007/s10494-017-9871-5Google Scholar
Okino, S. & Nagata, M. 2012 Asymmetric travelling waves in a square duct. J. Fluid Mech. 693, 57–68.10.1017/jfm.2011.455Google Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107–122.10.1017/S0022112009992242Google Scholar
Placidi, M. & Ganapathisubramani, B. 2018 Turbulent flow over large roughness elements: effect of frontal and plan solidity on turbulence statistics and structure. Boundary-Layer Meteorol. 167 (1), 99–121.10.1007/s10546-017-0317-3Google Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. Hafner.Google Scholar
Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363–382.10.1017/S0022112081002164Google Scholar
Reynolds, W. & Hussain, A. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.10.1017/S0022112072000679Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part i. Coherent structures. Q. Appl. Maths 45 (3), 561–571.10.1090/qam/910462Google Scholar
Stroh, A., Hasegawa, Y., Kriegseis, J. & Frohnapfel, B. 2016 Secondary vortices over surfaces with spanwise varying drag. J. Turbul. 17 (12), 1142–1158.10.1080/14685248.2016.1235277Google Scholar
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186–217.Google Scholar
Uhlmann, M., Kawahara, G. & Pinelli, A. 2010 Travelling-waves consistent with turbulence-driven secondary flow in a square duct. Phys. Fluids 22 (8), 084102.10.1063/1.3466661Google Scholar
Uhlmann, M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162.10.1017/S0022112007007604Google Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, 1–12.10.1017/jfm.2015.292Google Scholar
Vanderwel, C. & Tavoularis, S. 2011 Coherent structures in uniformly sheared turbulent flow. J. Fluid Mech. 689, 434–464.10.1017/jfm.2011.423Google Scholar
Vanderwel, C. & Tavoularis, S. 2016 Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel. J. Fluid Mech. 17 (7), 633–650.Google Scholar
Vermaas, D., Uijttewaal, W. & Hoitink, A. 2011 Lateral transfer of streamwise momentum caused by a roughness transition across a shallow channel. Water Resour. Res. 47 (2), W02530.10.1029/2010WR010138Google Scholar
Wang, Z.-Q. & Cheng, N.-S. 2006 Time-mean structure of secondary flows in open channel with longitudinal bedforms. Adv. Water Resour. 29 (11), 1634–1649.10.1016/j.advwatres.2005.12.002Google Scholar
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26 (2), 025111.Google Scholar
Wu, X. & Moin, P. 2009 Forest of hairpins in a low-Reynolds-number zero-pressure-gradient flat-plate boundary layer. Phys. Fluids 21 (9), 091106.10.1063/1.3205471Google Scholar
Xie, Z.-T. & Fuka, V. 2018 A note on spatial averaging and shear stresses within urban canopies. Boundary-Layer Meteorol. 167 (1), 171–179.10.1007/s10546-017-0321-7Google Scholar
Yang, J. & Anderson, W. 2018 Numerical study of turbulent channel flow over surfaces with variable spanwise heterogeneities: topographically-driven secondary flows affect outer-layer similarity of turbulent length scales. Flow Turbul. Combust. 100 (1), 1–17.Google Scholar

Vanderwel et al. supplementary movie 1

Video of sequential snapshots of the instantaneous flow field from the experiment recorded at 2 frames per second.

Download Vanderwel et al. supplementary movie 1(Video)
Video 1.3 MB

Vanderwel et al. supplementary movie 2

Time-resolved video of the instantaneous flow field from the numerical simulation.

Download Vanderwel et al. supplementary movie 2(Video)
Video 6.3 MB

Vanderwel et al. supplementary movie 3

Complete instantaneous flow field with its POD-reconstructed counterpart (upper row) and the corresponding velocity fluctuations (lower row). In the upper row, the colour code corresponds to the streamwise velocity component and the arrows indicate the in-plane motion, whereas in the bottom row, the color code represents the instantaneous deviation of the streamwise velocity component from (y).

Download Vanderwel et al. supplementary movie 3(Video)
Video 19.3 MB

Vanderwel et al. supplementary movie 4

Instantaneous structure of the flow visualized using isosurfaces of $\lambda_2$-criterion ($\lambda_2$ = −0.005) and colored by their rotational direction.

Download Vanderwel et al. supplementary movie 4(Video)
Video 67.8 MB