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Modulation of turbulence by saltating particles on erodible bed surface

Published online by Cambridge University Press:  07 May 2021

Xiaojing Zheng
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, Department of Mechanics, Lanzhou University, Lanzhou730000, PR China
Shengjun Feng
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, Department of Mechanics, Lanzhou University, Lanzhou730000, PR China
Ping Wang*
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, Department of Mechanics, Lanzhou University, Lanzhou730000, PR China
*
Email address for correspondence: [email protected]

Abstract

Large-eddy simulation of a particle-laden flow over an erodible bed is performed to investigate the effect of heavy, saltating particles on turbulence modulation, using the Eulerian–Lagrangian point-particle approach with two-way coupling. The flow into which the solid particles are introduced is a turbulent open channel flow with particle-free friction Reynolds numbers of 3730 and 4200. The inter-particle collisions are not considered, whereas the particle-bed collisions are described by splashing models. Simulation results show that the addition of particles reduces the mean streamwise fluid velocity. The streamwise fluctuating velocity and Reynolds stress are damped while the vertical and spanwise turbulence intensities are enhanced in the near-bed region. The turbulence intensities and Reynolds stress in the outer layer are apparently increased. These effects become more pronounced as the Reynolds number increases. Correlation scales of the turbulence structures increase in the near-bed region and decrease in the outer region. The modulation mechanism of turbulence is revealed. That is, the range and degree of turbulence enhancement by ascending particles in the near-bed region are much larger than those of turbulence attenuation by descending particles, which results in the redistribution of turbulent kinetic energy from the streamwise to the spanwise and vertical directions. This effect extends to the outer region via saltating particles by forming ‘active’ roughness elements. The premultiplied energy spectra of the streamwise velocity show that the enhancement of outer turbulent kinetic energy by saltating particles occurs in a wide range of wavelengths from the intermediate to very large scale.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abe, H., Kawamura, H. & Cho, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to $Re_{\tau } = 640$. J. Fluids Engng 126, 835843.CrossRefGoogle Scholar
Anderson, R.S. & Haff, P.K. 1991 Wind modification and bed response during saltation of sand in air. Acta Mechanica 1, 2151.CrossRefGoogle Scholar
Armenio, V. & Fiorotto, V. 2001 The importance of the forces acting on particles in turbulent flows. Phys. Fluids 13, 24372440.CrossRefGoogle Scholar
Bae, H.J., Lozano-Durán, A., Bose, S.T. & Moin, P. 2018 Turbulence intensities in large-eddy simulation of wall-bounded flows. Phys. Rev. Fluids 3, 014610.CrossRefGoogle ScholarPubMed
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Barati, R., Neyshabouri, S. & Ahmadi, G. 2019 Issues in Eulerian-Lagrangian modeling of sediment transport under saltation regime. Intl J. Multiphase Flow 33, 441461.Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to $Re_{\tau } = 4000$. J. Fluid Mech. 742, 171191.CrossRefGoogle Scholar
Caraman, N., Borée, J. & Simonin, O. 2003 Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: experimental and theoretical analysis. Phys. Fluids 15, 36023612.CrossRefGoogle Scholar
Chin, C., Ng, H.C.H., Blackburn, H.M., Monty, J.P. & Ooi, A. 2015 Turbulent pipe flow at $Re_{\tau } \approx 1000$: a comparison of wall-resolved large-eddy simulation, direct numerical simulation and hot-wire experiment. Comput. Fluids 122, 2633.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Phys. Fluids 24 (1), 011702.CrossRefGoogle Scholar
Creyssels, M., Dupont, P., El Moctar, A.O., Valance, A., Cantat, I., Jenkins, J.T., Pasini, J.M. & Rasmussen, K.R. 2009 Saltating particles in a turbulent boundary layer: experiment and theory. J. Fluid Mech. 625, 4774.CrossRefGoogle Scholar
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, 055103.CrossRefGoogle Scholar
Dritselis, C.D. & Vlachos, N.S. 2011 a Numerical investigation of momentum exchange between particles and coherent structures in low $Re$ turbulent channel flow. Phys. Fluids 23, 025103.CrossRefGoogle Scholar
Dritselis, C.D. & Vlachos, N.S. 2011 b Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases. Intl J. Multiphase Flow 37, 706721.CrossRefGoogle Scholar
Dupont, S., Bergametti, G., Marticorena, B. & Simoëns, S. 2013 Modeling saltation intermittency. J. Geophys. Res. 118, 71097128.CrossRefGoogle Scholar
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to $Re_{\theta } =8300$. Intl J. Heat Fluid Flow 47, 5769.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.CrossRefGoogle Scholar
Gore, R.A. & Crowe, C.T. 1991 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15, 279285.CrossRefGoogle Scholar
Hetsroni, G. 1989 Particle turbulence interaction. Intl J. Multiphase Flow 15, 735746.CrossRefGoogle Scholar
Ho, T.D., Walance, A., Dupont, P. & Ould El Moctar, A. 2011 Scaling laws in aeolian sand transport. Phys. Rev. Lett. 106, 094501.CrossRefGoogle ScholarPubMed
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.CrossRefGoogle Scholar
Ji, C.N, Munjiza, A., Avital, E., Xu, D. & Williams, J. 2014 Saltation of particles in turbulent channel flow. Phys. Rev. E 89, 052202.CrossRefGoogle ScholarPubMed
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.CrossRefGoogle Scholar
Johnson, P.L. 2020 Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles. Intl J. Multiphase Flow 124, 103182.CrossRefGoogle Scholar
Kaftori, D., Hetsroni, G. & Banerjee, S. 1998 The effect of particles on wall turbulence. Intl J. Multiphase Flow 24, 359386.CrossRefGoogle Scholar
Kiger, K.T. & Pan, C. 2002 Suspension and turbulence modification effects of solid particulates on a horizontal turbulent channel flow. J. Turbul. 3, N19.CrossRefGoogle Scholar
Kim, K., Baek, S.J. & Sung, H.J. 2002 An implicit velocity decoupling procedure for the incompressible Navier–stokes equations. Intl J. Numer. Meth. Fluids 38, 125138.CrossRefGoogle Scholar
Krogstad, P.A. & Antonia, R.A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450460.CrossRefGoogle Scholar
Kuerten, J.G.M. & Vreman, A.W. 2015 Effect of droplet interaction on droplet-laden turbulent channel flow. Phys. Fluids 27, 053304.CrossRefGoogle Scholar
Kulick, J.D., Fessler, J.R. & Eaton, J.K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109134.CrossRefGoogle Scholar
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33, 143159.CrossRefGoogle Scholar
Lämmel, M., Dzikowski, K., Oger, L. & Valance, A. 2017 Grain-scale modeling and splash parametrization for aeolian sand transport. Phys. Rev. E 95, 022902.CrossRefGoogle ScholarPubMed
Lee, J. & Lee, C. 2015 Modification of particle-laden near-wall turbulence: effect of Stokes number. Phys. Fluids 27, 023303.CrossRefGoogle Scholar
Lee, J. & Lee, C. 2019 The effect of wall-normal gravity on particle-laden near-wall turbulence. J. Fluid Mech. 873, 475507.CrossRefGoogle Scholar
Lee, S.H. & Sung, H.J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125146.CrossRefGoogle Scholar
Li, B.L. & McKenna Neuman, C. 2012 Boundary-layer turbulence characteristics during aeolian saltation. Geophys. Res. Lett. 39, L11402.CrossRefGoogle Scholar
Li, D., Luo, K. & Fan, J. 2016 Modulation of turbulence by dispersed solid particles in a spatially developing flat-plate boundary layer. J. Fluid Mech. 802, 359394.CrossRefGoogle Scholar
Li, J., Wang, H., Liu, Z., Chen, S. & Zheng, C. 2012 An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow. Exp. Fluids 53, 13851403.CrossRefGoogle Scholar
Li, Y., Mclaughlin, J.B., Kontomaris, K. & Portela, L. 2001 Numerical simulation of particle-laden turbulent channel flow. Phys. Fluids 13, 29572976.CrossRefGoogle Scholar
Liljegren, L.M. & Vlachos, N.S. 1990 Laser velocimetry measurements in a horizontal gas-solid pipe flow. Exp. Fluids 9, 205212.CrossRefGoogle Scholar
Lilly, D. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_{\tau } = 4200$. Phys. Fluids 26 (1), 011702.CrossRefGoogle Scholar
Mallouppas, G. & Van Wachem, B. 2013 Large eddy simulations of turbulent particle-laden channel flow. Intl J. Multiphase Flow 54, 6575.CrossRefGoogle Scholar
Marchioli, C. 2017 Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mechanica 228 (3), 741771.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283315.CrossRefGoogle Scholar
Marusic, I., Mckeon, B.J., Monkewitz, P.A., Nagib, H.M., Smiths, A.J. & Sreenivasan, K.R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Meneveau, C., Lund, T.S. & Cabot, W.H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319 (1), 353385.CrossRefGoogle Scholar
Owen, P.R. 1964 Saltation of uniform grains in air. J. Fluid Mech. 20 (2), 225242.CrossRefGoogle Scholar
Pähtz, T., Clark, A.H., Valyrakis, M. & Durán, O. 2020 The physics of sediment transport initiation, cessation, and entrainment across aeolian and fluvial environments. Rev. Geophys. 58, e2019RG000679.CrossRefGoogle Scholar
Pähtz, T. & Durán, O. 2017 Fluid forces or impacts: what governs the entrainment of soil particles in sediment transport mediated by a Newtonian fluid? Phys. Rev. Fluids 2, 074303.CrossRefGoogle Scholar
Pähtz, T., Kok, J.F. & Herrmann, H.J. 2011 The apparent surface roughness of moving sand transported by wind. New J. Phys. 14 (4), 043035.CrossRefGoogle Scholar
Pan, Y. & Banerjee, S. 1996 Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8, 27332755.CrossRefGoogle Scholar
Rashidi, M., Hetsroni, G. & Banerjee, S. 1990 Particle-turbulence interaction in a boundary layer. Intl J. Multiphase Flow 16, 935949.CrossRefGoogle Scholar
Revil-Baudard, T., Chauchat, J., Hurther, D. & Eiiff, O. 2016 Turbulence modifications induced by the bed mobility in intense sediment-laden flows. J. Fluid Mech. 808, 469484.CrossRefGoogle Scholar
Rice, M.A., Willetts, B.B. & Mcewan, I.K. 1995 An experimental study of multiple grain-size ejecta produced by collisions of saltating grains with a flat bed. Sedimentology 42, 695706.CrossRefGoogle Scholar
Richter, D.H. & Sullivan, P.P. 2013 Momentum transfer in a turbulent, particle-laden Couette flow. Phys. Fluids 25, 053304.CrossRefGoogle Scholar
Richter, D.H. & Sullivan, P.P. 2014 Modification of near-wall coherent structures by inertial particles. Phys. Fluids 26 (10), 103304.CrossRefGoogle Scholar
Righetti, M. & Romano, G.P. 2004 Particle-fluid interactions in a plane near-wall turbulent flow. J. Fluid Mech. 505, 93121.CrossRefGoogle Scholar
Roger, C.B. & Eaton, J.K. 1991 The effect of small particles on fluid turbulence in a flat-plate, turbulent boundary layer in air. Phys. Fluids A 3, 928937.CrossRefGoogle Scholar
Schiller, L. & Nauman, A. 1933 Uber die grundlegenden Gerechnungen bei der Schwerkraftaufbereitung. Z. Verein. Deutsch. Ing. 77, 318321.Google Scholar
Schlatter, P., Li, Q., Brethouwer, G., Johansson, A.V. & Henningson, D.S. 2010 Simulations of spatially evolving turbulent boundary layers up to $Re_{\theta } =4300$. Intl J. Heat Fluid Flow 31, 251261.CrossRefGoogle Scholar
Schultz, M.P. & Flack, K.A. 2013 Reynolds-number scaling of turbulent channel flow. Phys. Fluids 25, 025104.CrossRefGoogle Scholar
Shao, X., Wu, T. & Yu, Z. 2012 Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number. J. Fluid Mech. 693, 319344.CrossRefGoogle Scholar
Smits, A.J., Mckeon, B.J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.CrossRefGoogle Scholar
Squires, K.D. & Eaton, J.K. 1990 Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 2, 11911203.CrossRefGoogle Scholar
Tanaka, T. & Eaton, J.K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101, 114502.CrossRefGoogle ScholarPubMed
Tay, G.F.K., Kuhn, D.C.S. & Tachie, M.F. 2015 Effects of sedimenting particles on the turbulence structure in a horizontal channel flow. Phys. Fluids 27 (2), 025106.CrossRefGoogle Scholar
Tsuji, Y. & Morikawa, Y. 1982 LDV measurements of an air-solid two-phase flow in a horizontal pipe. J. Fluid Mech. 120, 385409.CrossRefGoogle Scholar
Vowinckel, B., Kempe, T. & Fröhlich, J. 2014 Fluid-particle interaction in turbulent open channel flow with fully resolved mobile beds. Adv. Water Resour. 72, 3244.CrossRefGoogle Scholar
Vreman, A.W. 2007 Turbulence characteristics of particle-laden pipe flow. J. Fluid Mech. 584, 235279.CrossRefGoogle Scholar
Wang, G., Park, J.H. & Richter, D.H. 2020 Effect of computational domain size on inertial particle one-point statistics in open channel flow. Intl J. Multiphase Flow 125, 103195.CrossRefGoogle Scholar
Wang, G.Q. & Richter, D.H. 2019 Two mechanisms of modulation of very-large-scale motions by inertial particles in open channel flow. J. Fluid Mech. 868, 538559.CrossRefGoogle Scholar
Wang, P., Feng, S.J., Zheng, X.J. & Sung, H.J. 2019 The scale characteristics and formation mechanism of aeolian sand streamers based on large eddy simulation. J. Geophys. Res. 124, 1137211388.CrossRefGoogle Scholar
Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji, Y. 2001 Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303334.CrossRefGoogle Scholar
Yang, X.I.A. & Griffin, K.P. 2021 Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation. Phys. Fluids 33, 015108.CrossRefGoogle Scholar
Zhang, W., Wang, Y. & Lee, S.J. 2008 Simultaneous PIV and PTV measurements of wind and sand particle velocities. Exp. Fluids 45, 241256.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Zhao, L.H., Andersson, H.I. & Gillissen, J.J.J. 2010 Turbulence modulation and drag reduction by spherical particles. Phys. Fluids 22, 081702.CrossRefGoogle Scholar
Zheng, X.J. 2009 Mechanics of Wind-blown Sand Movement. Springer.CrossRefGoogle Scholar
Zheng, X.J., Cheng, N. & Xie, L. 2008 A three-dimensional analysis on lift-off velocities of sand grains in wind-blown sand flux. Earth Surf. Process. Landf. 33, 18241838.CrossRefGoogle Scholar
Zheng, X.J., Jin, T. & Wang, P. 2020 The influence of surface stress fluctuation on saltation sand transport around threshold. J. Geophys. Res. 125, e2019JF005246.Google Scholar
Zheng, X.J., Zhang, J.H., Wang, G.H., Liu, H.Y. & Zhu, W. 2013 Investigation on very large scale motions (VLSMs) and their influence in a dust storm. Sci. China Phys. Mech. 56 (2), 306314.CrossRefGoogle Scholar
Zhu, H.Y., Pan, C., Wang, J.J., Liang, Y.R. & Ji, X.C. 2019 Sand-turbulence interaction in a high-Reynolds-number turbulent boundary layer under net sedimentation conditions. Intl J. Multiphase Flow 119, 5671.CrossRefGoogle Scholar