A neutrally buoyant finite-size spherical particle in three-dimensional lid-driven cavity flow

LI Yang; XIA Zhenhua

doi:10.7638/kqdlxxb-2020.0435

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A neutrally buoyant finite-size spherical particle in three-dimensional lid-driven cavity flow

更新时间：2026-05-28

- A neutrally buoyant finite-size spherical particle in three-dimensional lid-driven cavity flow
- Vol. 40, Issue 3, Pages: 109-119(2022)
- 作者机构：
  
  浙江大学航空航天学院流体工程研究所,杭州,310027
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2020.0435
  CLC： O359
- Published：2022
- 稿件说明：
移动端阅览
李洋, 夏振华. 单个中性球形颗粒在三维方腔中的运动[J]. 空气动力学学报, 2022, 40(3): 109−119.

LI Yang, XIA Zhenhua. A neutrally buoyant finite-size spherical particle in three-dimensional lid-driven cavity flow[J]. 2022, 40(3): 109-119.
李洋, 夏振华. 单个中性球形颗粒在三维方腔中的运动[J]. 空气动力学学报, 2022, 40(3): 109−119. DOI： 10.7638/kqdlxxb-2020.0435

LI Yang, XIA Zhenhua. A neutrally buoyant finite-size spherical particle in three-dimensional lid-driven cavity flow[J]. 2022, 40(3): 109-119. DOI： 10.7638/kqdlxxb-2020.0435.

摘要

采用多松弛格子Boltzmann方法模拟了单个中性球形颗粒在三维顶盖驱动方腔流中的运动。考虑了展向弱受限的对称边界和强受限的固壁边界两种情况下初始位置、颗粒大小以及雷诺数的影响。对于展向弱受限的情形，发现颗粒的初始位置显著影响着最终的运动轨迹。根据相图被划分为三个区域：外层稳定区、内层稳定区以及涡中心区域。通过对颗粒受力的分解解释了其在极限环上运动的机理。此外，还详细介绍了球形颗粒在极限环上的顺时针旋转运动。随着雷诺数的增加，颗粒逐渐向外围靠近，不断旋转达到相应的极限环轨迹。对于选定的初始位置，观察到在高雷诺数时大颗粒向外迁移，而在低雷诺数时大颗粒的极限环靠近涡中心。对于展向强受限的情形，极限环与颗粒的初始位置无关。随着雷诺数的增加，除方腔左上角外，极限环轨迹有向外迁移的趋势。最后，随着颗粒尺寸的增大，极限环向方腔内部收缩。

Abstract

In this paper

the dynamics of a single neutrally buoyant spherical particle in three-dimensional lid-driven cavity flow is simulated by the multiple-relaxation time lattice Boltzmann method. The effects of initial position

particle size and Reynolds number are considered. For the cases with symmetric boundary conditions in the spanwise direction

it is found that the initial position of the particle critically affects its final trajectory. According to the phase diagram

it's roughly divided into three regions

the outer stable region

the inner stable region and the vortex center region. The mechanisms for the dynamics of particle on the stable limit cycle trajectory are explained by the force decomposition. In addition

a clockwise rotating motion of particle on the limit cycle trajectory is described in detail. With the increase of Reynolds number

the particle gradually approaches to the periphery

continuously rotates to reach the corresponding limit cycle trajectory. For the selected initial position

we observe that large particle migrates outward at higher Reynolds number

while the limit cycle of large particle at lower Reynolds number is close to vortex core. As for the cases of confined solid walls with no-slip boundaries

the limit cycle is independent of the initial positions of the particle. The limit cycle orbit tends to migrate outward with the increases of Reynolds number

except the top left corner of the cavity

and it will shrink if the particle’s size increases.

关键词

Keywords

references

KOSINSKI P, KOSINSKA A, HOFFMANN A C. Simulation of solid particles behaviour in a driven cavity flow[J]. Powder Technology, 2009, 191(3): 327-339. DOI:10.1016/j.powtec.2008.10.025

CHE SIDIK N A, NIAKI ATTARZADEH M R. The use of cubic interpolation method for transient hydrodynamics of solid particles[J]. International Journal of Engineering Science, 2012, 51: 90-103. DOI:10.1016/j.ijengsci.2011.08.014

XU A G, CHEN J, SONG J H, et al. Progress of discrete Boltzmann study on multiphase complex flows[J]. Acta Aerodynamica Sinica, 2021, 39(3): 138-169. (in Chinese)

XIA Z H, CONNINGTON K W, RAPAKA S, et al. Flow patterns in the sedimentation of an elliptical particle[J]. Journal of Fluid Mechanics, 2009, 625: 249-272. DOI:10.1017/s0022112008005521

HUANG H B, YANG X, LU X Y. Sedimentation of an ellipsoidal particle in narrow tubes[J]. Physics of Fluids, 2014, 26(5): 053302. DOI:10.1063/1.4874606

QI D W, LUO L S. Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows[J]. Journal of Fluid Mechanics, 2003, 477: 201-213. DOI:10.1017/s0022112002003191

YU Z S, PHAN-THIEN N, TANNER R I. Rotation of a spheroid in a Couette flow at moderate Reynolds numbers[J]. Physical Review E, 2007, 76(2): 026310. DOI:10.1103/physreve.76.026310

HUANG H B, YANG X, KRAFCZYK M, et al. Rotation of spheroidal particles in Couette flows[J]. Journal of Fluid Mechanics, 2012, 692: 369-394. DOI:10.1017/jfm.2011.519

SEGRÉ G, SILBERBERG A. Radial particle displacements in Poiseuille flow of suspensions[J]. Nature, 1961, 189(4760): 209-210. DOI:10.1038/189209a0

CHUN B, LADD A J C. Inertial migration of neutrally buoyant particles in a square duct: An investigation of multiple equilibrium positions[J]. Physics of Fluids, 2006, 18(3): 031704. DOI:10.1063/1.2176587

NAKAGAWA N, YABU T, OTOMO R, et al. Inertial migration of a spherical particle in laminar square channel flows from low to high Reynolds numbers[J]. Journal of Fluid Mechanics, 2015, 779: 776-793. DOI:10.1017/jfm.2015.456

LASHGARI I, ARDEKANI M N, BANERJEE I, et al. Inertial migration of spherical and oblate particles in straight ducts[J]. Journal of Fluid Mechanics, 2017, 819: 540-561. DOI:10.1017/jfm.2017.189

SUN J S, LI M M, LIU C, et al. Double spiral microchannel for label-free tumor cell separation and enrichment[J]. Lab on a Chip, 2012, 12(20): 3952-3960. DOI:10.1039/c2lc40679a

LIU C, HU G Q, JIANG X Y, et al. Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers[J]. Lab on a Chip, 2015, 15(4): 1168-1177. DOI:10.1039/c4lc01216j

KHOJAH R, STOUTAMORE R, DI CARLO D. Size-tunable microvortex capture of rare cells[J]. Lab on a Chip, 2017, 17(15): 2542-2549. DOI:10.1039/c7lc00355b

HADDADI H, NAGHSH-NILCHI H, DI CARLO D. Separation of cancer cells using vortical microfluidic flows[J]. Biomicrofluidics, 2018, 12(1): 014112. DOI:10.1063/1.5009037

JIANG M Q, QIAN S Z, LIU Z H. Fully resolved simulation of single-particle dynamics in a microcavity[J]. Microfluidics and Nanofluidics, 2018, 22(12): 1-13. DOI:10.1007/s10404-018-2166-x

PAN F, ACRIVOS A. Steady flows in rectangular cavities[J]. Journal of Fluid Mechanics, 1967, 28(4): 643-655. DOI:10.1017/s002211206700237x

KOSEFF J R, STREET R L. Visualization studies of a shear driven three-dimensional recirculating flow[J]. Journal of Fluids Engineering, 1984, 106(1): 21-27. DOI:10.1115/1.3242393

AIDUN C K, TRIANTAFILLOPOULOS N G, BENSON J D. Global stability of a lid-driven cavity with throughflow: Flow visualization studies[J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(9): 2081-2091. DOI:10.1063/1.857891

KREIZER M, RATNER D, LIBERZON A. Real-time image processing for particle tracking velocimetry[J]. Experiments in Fluids, 2010, 48(1): 105-110. DOI:10.1007/s00348-009-0715-5

GHIA U, GHIA K N, SHIN C T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. Journal of Computational Physics, 1982, 48(3): 387-411. DOI:10.1016/0021-9991(82)90058-4

SCHREIBER R, KELLER H B. Driven cavity flows by efficient numerical techniques[J]. Journal of Computational Physics, 1983, 49(2): 310-333. DOI:10.1016/0021-9991(83)90129-8

SHU C, WANG L, CHEW Y T. Numerical computation of three-dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method[J]. International Journal for Numerical Methods in Fluids, 2003, 43(4): 345-368. DOI:10.1002/fld.566

ALBENSOEDER S, KUHLMANN H C. Accurate three-dimensional lid-driven cavity flow[J]. Journal of Computational Physics, 2005, 206(2): 536-558. DOI:10.1016/j.jcp.2004.12.024

MENDU S S, DAS P K. Fluid flow in a cavity driven by an oscillating lid—A simulation by lattice Boltzmann method[J]. European Journal of Mechanics - B/Fluids, 2013, 39: 59-70. DOI:10.1016/j.euromechflu.2012.12.002

KU H C, HIRSH R S, TAYLOR T D. A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations[J]. Journal of Computational Physics, 1987, 70(2): 439-462. DOI:10.1016/0021-9991(87)90190-2

SHANKAR P N, DESHPANDE M D. Fluid mechanics in the driven cavity[J]. Annual Review of Fluid Mechanics, 2000, 32(1): 93-136. DOI:10.1146/annurev.fluid.32.1.93

TSORNG S J, CAPART H, LAI J S, et al. Three-dimensional tracking of the long time trajectories of suspended particles in a lid-driven cavity flow[J]. Experiments in Fluids, 2006, 40(2): 314-328. DOI:10.1007/s00348-005-0070-0

TSORNG S J, CAPART H, LO D C, et al. Behaviour of macroscopic rigid spheres in lid-driven cavity flow[J]. International Journal of Multiphase Flow, 2008, 34(1): 76-101. DOI:10.1016/j.ijmultiphaseflow.2007.06.007

SAFDARI A, KIM K C. Lattice Boltzmann simulation of solid particles behavior in a three-dimensional lid-driven cavity flow[J]. Computers Mathematics with Applications, 2014, 68(5): 606-621. DOI:10.1016/j.camwa.2014.07.004

SAFDARI A, KIM K C. Lattice Boltzmann simulation of the three-dimensional motions of particles with various density ratios in lid-driven cavity flow[J]. Applied Mathematics and Computation, 2015, 265: 826-843. DOI:10.1016/j.amc.2015.05.106

HU J J. Motion of a neutrally buoyant elliptical particle in a lid-driven square cavity[J]. European Journal of Mechanics-B/Fluids, 2021, 85: 124-133. DOI:10.1016/j.euromechflu.2020.09.008

CHEN H D, CHEN S Y, MATTHAEUS W H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method[J]. Physical Review A, 1992, 45(8): R5339. DOI:10.1103/physreva.45.r5339

QIAN Y H, D'HUMIÈRES D, LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters (EPL), 1992, 17(6): 479-484. DOI:10.1209/0295-5075/17/6/001

CHEN S Y, DOOLEN G D. Lattice Boltzmann method for fluid flows[J]. Annual Review of Fluid Mechanics, 1998, 30(1): 329-364. DOI:10.1146/annurev.fluid.30.1.329

GUO Z L, ZHENG C G, SHI B C. Discrete lattice effects on the forcing term in the lattice Boltzmann method[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2002, 65(4): 046308. DOI:10.1103/PhysRevE.65.046308

D'HUMIÈRES D, GINZBURG I, KRAFCZYK M, et al. Multiple–relaxation–time lattice Boltzmann models in three dimensions[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002, 360(1792): 437-451. DOI:10.1098/rsta.2001.0955

SUGA K, KUWATA Y, TAKASHIMA K, et al. A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows[J]. Computers Mathematics with Applications, 2015, 69(6): 518-529. DOI:10.1016/j.camwa.2015.01.010

PENG C, GENEVA N, GUO Z L, et al. Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method[J]. Journal of Computational Physics, 2018, 357: 16-42. DOI:10.1016/j.jcp.2017.11.040

LI L R, SHI Y P, ZHANG S Q, et al. On the comparison between lattice Boltzmann methods and spectral methods for DNS of incompressible turbulent channel flows on small domain size[J]. Advances in Applied Mathematics and Mechanics, 2019, 11(3): 598-607. DOI:10.4208/aamm.2018.s04

BOUZIDI M, FIRDAOUSS M, LALLEMAND P. Momentum transfer of a Boltzmann-lattice fluid with boundaries[J]. Physics of Fluids, 2001, 13(11): 3452-3459. DOI:10.1063/1.1399290

LADD A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation[J]. Journal of Fluid Mechanics, 1994, 271: 285-309. DOI:10.1017/s0022112094001771

AIDUN C K, LU Y N, DING E J. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation[J]. Journal of Fluid Mechanics, 1998, 373: 287-311. DOI:10.1017/s0022112098002493

CHEN Y, CAI Q D, XIA Z H, et al. Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions[J]. Physical Review E, 2013, 88: 013303. DOI:10.1103/PhysRevE.88.013303

WEN B H, ZHANG C Y, TU Y S, et al. Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations[J]. Journal of Computational Physics, 2014, 266: 161-170. DOI:10.1016/j.jcp.2014.02.018

FENG Z G, MICHAELIDES E E. The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems[J]. Journal of Computational Physics, 2004, 195(2): 602-628. DOI:10.1016/j.jcp.2003.10.013

HU J J. Motion of a neutrally buoyant circular particle in a clockwise double-lid-driven square cavity[J]. Physics of Fluids, 2020, 32(11): 113304. DOI:10.1063/5.0023789

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