Hostname: page-component-cb9f654ff-h4f6x Total loading time: 0 Render date: 2025-08-17T12:30:45.270Z Has data issue: false hasContentIssue false
  • English
  • Français

Settling of finite-size particles in homogeneous isotropic turbulence: the influence of particle inertia and a unified predictive model

Published online by Cambridge University Press:  07 August 2025

Cheng Peng Open the ORCID record for Cheng Peng [Opens in a new window] ,
Kairzhan Karzhaubayev ,
Lian-Ping Wang Open the ORCID record for Lian-Ping Wang [Opens in a new window] ,
Songying Chen  and
Zhongguo Niu
Cheng Peng*
Affiliation:
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
Kairzhan Karzhaubayev
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, PR China
Lian-Ping Wang
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, PR China
Songying Chen
Affiliation:
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
Zhongguo Niu
Affiliation:
AVIC Aerodynamics Research Institute, Low Speed High Reynolds Numerical Aeronautical Key Laboratory, Harbin 150001, PR China
*
Corresponding author: Cheng Peng, pengcheng@sdu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work, we conduct particle-resolved direct numerical simulations to investigate the influence of particle inertia on the settling velocity of finite-size particles at low volume fraction in homogeneous isotropic turbulence across various settling numbers. Our results for finite-size particles show only reductions of settling velocity in turbulence compared to the corresponding laminar case. Although increased particle inertia significantly reduces the lateral motion of particles and fluctuations in settling velocity, its effect on the mean settling velocity is not pronounced, except when the settling effect is strong, where increased particle inertia leads to a noticeable reduction. Mechanistically, the nonlinear drag effect, which emphasises contributions from large turbulent scales, cannot fully account for the reduction in settling velocity. The influence of small-scale turbulence, particularly through interactions with the particle boundary layer, should not be overlooked. We also analyse the dependency of turbulence’s modification on particle settling velocity within a broader parameter space, encompassing both sub-Kolmogorov point particles and finite-size particles. Additionally, we develop a qualitative model to predict whether turbulence enhances or retards the settling velocity of particles.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A63
Check for updates
Copyright
© The Author(s), 2025. Published by 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.)

Article purchase

Temporarily unavailable

References

Abdelsamie, A.H. & Lee, C. 2012 Decaying versus stationary turbulence in particle-laden isotropic turbulence: turbulence modulation mechanism. Phys. Fluids 24 (1), 015016.Google Scholar
Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J.C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.Google Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bec, J., Homann, H. & Ray, S.S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112 (18), 184501.Google ScholarPubMed
Bhattacharjee, S., Tom, J., Carbone, M. & Bragg, A.D. 2024 Investigating the parametric dependence of the impact of two-way coupling on inertial particle settling in turbulence. J. Fluid Mech. 987, A17.10.1017/jfm.2024.322CrossRefGoogle Scholar
Byron, M. 2015 The Rotation and Translation of Non-Spherical Particles in Homogeneous Isotropic Turbulence. University of California.Google Scholar
Chouippe, A., Kidanemariam, A.G., Derksen, J., Wachs, A. & Uhlmann, M. 2023 Results from particle-resolved simulations. In Modeling Approaches and Computational Methods for Particle-Laden Turbulent Flows, pp. 185–216. Elsevier.CrossRefGoogle Scholar
Chouippe, A. & Uhlmann, M. 2015 Forcing homogeneous turbulence in direct numerical simulation of particulate flow with interface resolution and gravity. Phys. Fluids 27 (12), 123301.Google Scholar
Chouippe, A. & Uhlmann, M. 2019 On the influence of forced homogeneous-isotropic turbulence on the settling and clustering of finite-size particles. Acta Mech. 230 (2), 387–412.CrossRefGoogle Scholar
Clift, R., Grace, J.R. & Weber, M.E. 2013 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Davila, J. & Hunt, J.C.R. 2001 Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117–145.10.1017/S0022112001004694CrossRefGoogle Scholar
Di Felice, R. 1999 The sedimentation velocity of dilute suspensions of nearly monosized spheres. Intl J. Multiphase Flow 25 (4), 559–574.Google Scholar
Eswaran, V. & Pope, S.B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16 (3), 257–278.CrossRefGoogle Scholar
Fornari, W., Picano, F. & Brandt, L. 2016 a Sedimentation of finite-size spheres in quiescent and turbulent environments. J. Fluid Mech. 788, 640–669.Google Scholar
Fornari, W., Picano, F., Sardina, G. & Brandt, L. 2016 b Reduced particle settling speed in turbulence. J. Fluid Mech. 808, 153–167.CrossRefGoogle Scholar
Friedman, P.D. & Katz, J. 2002 Mean rise rate of droplets in isotropic turbulence. Phys. Fluids 14 (9), 3059–3073.10.1063/1.1497377CrossRefGoogle Scholar
Good, G.H., Ireland, P.J., Bewley, G.P., Bodenschatz, E., Collins, L.R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.Google Scholar
Homann, H., Bec, J. & Grauer, R. 2013 Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer. J. Fluid Mech. 721, 155–179.Google Scholar
Ireland, P.J., Bragg, A.D. & Collins, L.R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects. J. Fluid Mech. 796, 659–711.Google Scholar
Kidanemariam, A.G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.10.1088/1367-2630/15/2/025031CrossRefGoogle Scholar
Ladd, A.J.C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271 (1), 285–309.Google Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Monchaux, R. & Dejoan, A. 2017 Settling velocity and preferential concentration of heavy particles under two-way coupling effects in homogeneous turbulence. Phys. Rev. Fluids 2 (10), 104302.Google Scholar
Murray, S.P. 1970 Settling velocities and vertical diffusion of particles in turbulent water. J. Geophys. Res. 75 (9), 1647–1654.10.1029/JC075i009p01647CrossRefGoogle Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sediment. Res. 63 (5), 835–838.Google Scholar
O’Neill, P.L., et al. 2004 Autocorrelation functions and the determination of integral length with reference to experimental and numerical data. In Proceedings of the 15th Australasian Fluid Mechanics Conference, vol. 1, pp. 1–4. University of Sydney.Google Scholar
Peng, C., Ayala, O.M. & Wang, L.-P. 2019 A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part I, laminar flows. Comput. Fluids 192, 104233.CrossRefGoogle Scholar
Peng, C., Sun, Q. & Wang, L.-P. 2023 Parameterization of turbulence modulation by finite-size solid particles in forced homogeneous isotropic turbulence. J. Fluid Mech. 963, A6.10.1017/jfm.2023.317CrossRefGoogle Scholar
Peng, C. & Wang, L.-P. 2023 Mechanisms and models of particle drag enhancements in turbulent environments. J. Fluid Mech. 959, A30.CrossRefGoogle Scholar
Peng, C., Wang, L.-P. & Chen, S. 2024 Preferential accumulation of finite-size particles in near-wall streaks. J. Fluid Mech. 980, A38.Google Scholar
Petersen, A.J., Baker, L. & Coletti, F. 2019 Experimental study of inertial particles clustering and settling in homogeneous turbulence. J. Fluid Mech. 864, 925–970.Google Scholar
Qureshi, N.M., Bourgoin, M., Baudet, C., Cartellier, A. & Gagne, Y. 2007 Turbulent transport of material particles: an experimental study of finite size effects. Phys. Rev. Lett. 99 (18), 184502.CrossRefGoogle ScholarPubMed
Richardson, J.F. & Zaki, W.N. 1954 The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Engng Sci. 3 (2), 65–73.CrossRefGoogle Scholar
Rosa, B., Parishani, H., Ayala, O. & Wang, L.-P. 2016 Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS. Intl J. Multiphase Flow 83, 217–231.CrossRefGoogle Scholar
Schiller, L. & Naumann, A.Z. 1933 Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Ver. Deut. Ing. 77, 318–320.Google Scholar
Teixeira, M.A.C. & Mériaux, C.A. 2022 Estimating the filtering of turbulence properties by finite-sized particles using analytical energy spectra. Phys. Fluids 34 (4), 045117.10.1063/5.0084622CrossRefGoogle Scholar
Tom, J. & Bragg, A.D. 2019 Multiscale preferential sweeping of particles settling in turbulence. J. Fluid Mech. 871, 244–270.Google Scholar
Tom, J., Carbone, M. & Bragg, A.D. 2022 How does two-way coupling modify particle settling and the role of multiscale preferential sweeping? J. Fluid Mech. 947, A7.Google Scholar
Wang, L.-P., Ayala, O., Gao, H., Andersen, C. & Mathews, K.L. 2014 Study of forced turbulence and its modulation by finite-size solid particles using the lattice Boltzmann approach. Comput. Maths Appl. 67 (2), 363–380.CrossRefGoogle Scholar
Wang, L.-P., Ayala, O. & Grabowski, W.W. 2007 Effects of aerodynamic interactions on the motion of heavy particles in a bidisperse suspension. J. Turbul. 8, N25.Google Scholar
Wang, L.-P. & Maxey, M.R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.10.1017/S0022112093002708CrossRefGoogle Scholar
Wang, S., Wu, X., Peng, C., Chen, S. & Liu, H. 2025 Analysis on the force evaluation by the momentum exchange method and a localized refilling scheme for the lattice boltzmann method. Comput. Maths Appl. 183, 180–199.CrossRefGoogle Scholar
Wen, B., Zhang, C., Tu, Y., Wang, C. & Fang, H. 2014 Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations. J. Comput. Phys. 266, 161–170.10.1016/j.jcp.2014.02.018CrossRefGoogle Scholar
Yang, C.Y. & Lei, U. 1998 The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 371, 179–205.Google Scholar
Yang, T.S. & Shy, S.S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.CrossRefGoogle Scholar
Yin, X. & Koch, D.L. 2007 Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers. Phys. Fluids 19 (9), 093302.10.1063/1.2764109CrossRefGoogle Scholar