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Two mechanisms of modulation of very-large-scale motions by inertial particles in open channel flow

  • G. Wang (a1) and D. H. Richter (a1)


Very-large-scale motions (VLSMs) and large-scale motions (LSMs) coexist at moderate Reynolds numbers in a very long open channel flow. Direct numerical simulations two-way coupled with inertial particles are analysed using spectral information to investigate the modulation of VLSMs. In the wall-normal direction, particle distributions (mean/preferential concentration) exhibit two distinct behaviours in the inner flow and outer flow, corresponding to two highly anisotropic turbulent structures, LSMs and VLSMs. This results in particle inertia’s non-monotonic effects on the VLSMs: low inertia (based on the inner scale) and high inertia (based on the outer scale) both strengthen the VLSMs, whereas moderate and very high inertia have little influence. Through conditional tests, low- and high-inertia particles enhance VLSMs following two distinct routes. Low-inertia particles promote VLSMs indirectly through the enhancement of the regeneration cycle (the self-sustaining mechanism of LSMs) in the inner region, whereas high-inertia particles enhance the VLSM directly through contribution to the Reynolds shear stress at similar temporal scales in the outer region. This understanding also provides more general insight into inner–outer interaction in high-Reynolds-number, wall-bounded flows.


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Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re 𝜏 = 640. Trans. ASME J. Fluids Engng 126 (5), 835843.
Adrian, R. J. & Marusic, I. 2012 Coherent structures in flow over hydraulic engineering surfaces. J. Hydraul Res. 50 (5), 451464.
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, 4144.
Baker, L., Frankel, A., Mani, A. & Coletti, F. 2017 Coherent clusters of inertial particles in homogeneous turbulence. J. Fluid Mech. 833, 364398.10.1017/jfm.2017.700
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid. Mech. 42, 111133.10.1146/annurev.fluid.010908.165243
Balakumar, B. & Adrian, R. 2007 Large-and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665681.
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 8096.
Cameron, S., Nikora, V. & Stewart, M. 2017 Very-large-scale motions in rough-bed open-channel flow. J. Fluid Mech. 814, 416429.
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 131.
Capecelatro, J., Desjardins, O. & Fox, R. O. 2018 On the transition between turbulence regimes in particle-laden channel flows. J. Fluid Mech. 845, 499519.
Carter, D. W. & Coletti, F. 2018 Small-scale structure and energy transfer in homogeneous turbulence. J. Fluid Mech. 854, 505543.
Crowe, C. T. 2000 On models for turbulence modulation in fluid–particle flows. Intl J. Multiphase Flow 26 (5), 719727.
Dritselis, C. D. & Vlachos, N. S. 2008 Numerical study of educed coherent structures in the near-wall region of a particle-laden channel flow. Phys. Fluids 20 (5), 055103.
Elghobashi, S. & Truesdell, G. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification. Phys. Fluids A 5 (7), 17901801.10.1063/1.858854
Guala, M., Hommema, S. & Adrian, R. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M. 2013 Clustering and turbulence modulation in particle-laden shear flows. J. Fluid Mech. 715, 134162.10.1017/jfm.2012.503
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.10.1017/S0022112006003946
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708738.
Jiménez, J. 2011 Cascades in wall-bounded turbulence. Annu. Rev. Fluid. Mech. 44 (1), 27.
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842.10.1017/jfm.2018.144
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.10.1017/S0022112099005066
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Klinkenberg, J., Sardina, G., De Lange, H. & Brandt, L. 2013 Numerical study of laminar–turbulent transition in particle-laden channel flow. Phys. Rev. E 87 (4), 043011.
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80120.10.1017/S002211201000621X
Lee, M. & Moser, R. D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886938.10.1017/jfm.2018.903
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.
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283315.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Marusic, I. & Monty, J. P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid. Mech. 51, 4974.
Michael, D. 1964 The stability of plane Poiseuille flow of a dusty gas. J. Fluid Mech. 18 (1), 1932.
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22 (10), 103304.
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 118.
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng 131 (4), 229246.
Nezu, I. & Nakagawa, H.1993 Turbulence in open-channel flows. IAHR-Monograph. CRC Press.
Pan, Y. & Banerjee, S. 1995 A numerical study of free-surface turbulence in channel flow. Phys. Fluids 7 (7), 16491664.
Pan, Y. & Banerjee, S. 1996 Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8 (10), 27332755.
Park, H. J., O’Keefe, K. & Richter, D. H. 2018 Rayleigh–Bénard turbulence modified by two-way coupled inertial, nonisothermal particles. Phys. Rev. Fluids 3 (3), 034307.
Poelma, C. & Ooms, G. 2006 Particle–turbulence interaction in a homogeneous, isotropic turbulent suspension. Appl. Mech. Rev. 59 (2), 7890.
Rawat, S., Cossu, C., Hwang, Y. & Rincon, F. 2015 On the self-sustained nature of large-scale motions in turbulent Couette flow. J. Fluid Mech. 782, 515540.10.1017/jfm.2015.550
Reeks, M. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aero. Sci. 14 (6), 729739.
Richter, D. H. 2015 Turbulence modification by inertial particles and its influence on the spectral energy budget in planar Couette flow. Phys. Fluids 27 (6), 063304.10.1063/1.4923043
Richter, D. H. & Sullivan, P. P. 2014 Modification of near-wall coherent structures by inertial particles. Phys. Fluids 26 (10), 103304.
Saffman, P. 1962 On the stability of laminar flow of a dusty gas. J. Fluid Mech. 13 (1), 120128.10.1017/S0022112062000555
Sardina, G., Schlatter, P., Brandt, L., Picano, F. & Casciola, C. M. 2012 Wall accumulation and spatial localization in particle-laden wall flows. J. Fluid Mech. 699, 5078.10.1017/jfm.2012.65
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid. Mech. 43 (1), 353375.
Sumer, B. M. & Oguz, B. 1978 Particle motions near the bottom in turbulent flow in an open channel. J. Fluid Mech. 86 (1), 109127.
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101 (11), 114502.10.1103/PhysRevLett.101.114502
Toh, S. & Itano, T. 2005 Interaction between a large-scale structure and near-wall structures in channel flow. J. Fluid Mech. 524, 249262.
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.
Wang, G., Abbas, M. & Climent, E. 2018 Modulation of the regeneration cycle by neutrally buoyant finite-size particles. J. Fluid Mech. 852, 257282.
Wang, G. & Richter, D. 2019 Modulation of the turbulence regeneration cycle by inertial particles in planar Couette flow. J. Fluid Mech. 861, 901929.
Yamamoto, Y., Kunugi, T. & Serizawa, A. 2001 Turbulence statistics and scalar transport in an open-channel flow. J. Turbul. 2 (10), 116.
Zhao, L., Andersson, H. I. & Gillissen, J. J. 2013 Interphasial energy transfer and particle dissipation in particle-laden wall turbulence. J. Fluid Mech. 715, 3259.
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