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On the rotation of a circular porous particle in 2D simple shear flow with fluid inertia

Published online by Cambridge University Press:  02 November 2016

Chenggong Li ,
Mao Ye  and
Zhongmin Liu
Chenggong Li
Affiliation:
Dalian National Laboratory for Clean Energy, National Engineering Laboratory for MTO, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Dalian Institute of Chemical Physics, Dalian, 116023, China
Mao Ye*
Affiliation:
Dalian National Laboratory for Clean Energy, National Engineering Laboratory for MTO, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Dalian Institute of Chemical Physics, Dalian, 116023, China
Zhongmin Liu
Affiliation:
Dalian National Laboratory for Clean Energy, National Engineering Laboratory for MTO, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Dalian Institute of Chemical Physics, Dalian, 116023, China
*
†Email address for correspondence: maoye@dicp.ac.cn
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Abstract

We investigate numerically the rotational behaviour of a circular porous particle suspended in a two-dimensional (2D) simple shear flow with fluid inertia at particle shear Reynolds number up to 108. We use the volume-averaged macroscopic momentum equation to formulate the flow field inside and outside the moving porous particle, which is solved by a modified single relaxation time lattice Boltzmann method. The effects of fluid inertia, confinement of the bounding walls, and permeability of the particle are studied. Our two-dimensional simulation results confirm that the permeability has little effect on the rotation of a porous particle in unbounded shear flow without fluid inertia (Masoud, Stone & Shelley, J. Fluid Mech., vol. 733, 2013, R6), but also suggest that the role of permeability cannot be neglected when the confinement effect is significant, or the fluid inertia is not negligible. The fluid inertia and the confined walls have similar effects on the rotation of a porous particle as that on a solid impermeable particle. The angular velocity decays with an increase in fluid inertia, and the confinement effect suppresses the angular velocity to a shear rate ratio below 0.5. A simple scaling argument based on the balance of torque exerted by fluid flows adjacent to the two bounding walls and that due to the flow recirculation can explain our results.

JFM classification

Low-Reynolds-number flows: Porous media Complex Fluids: Suspensions Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , R3
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Copyright
© 2016 Cambridge University Press 

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References

Bhattacharyya, B., Dhinakaran, S. & Khalili, A. 2006 Fluid motion around and through a porous cylinder. Chem. Engng Sci. 61, 4451–4461.Google Scholar
Bluemink, J. J., Lohse, D., Prosperetti, A. & van Wijngaarden, L. 2008 A sphere in a uniformly rotating or shearing flow. J. Fluid Mech. 600, 201–233.Google Scholar
Brinkman, H. C. 1949 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. 1, 27–34.Google Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27, 035101.Google Scholar
Chen, C. B. & Cai, A. 1999 Hydrodynamic interactions and mean settling velocity of porous particles in a dilute suspension. J. Colloid Interface Sci. 217, 328–340.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.Google Scholar
Dalwadi, M. P., Chapman, S. J., Waters, S. L. & Oliver, J. M. 2016 On the boundary layer structure near a highly permeable porous interface. J. Fluid Mech. 798, 88–139.CrossRefGoogle Scholar
Debye, P. & Bueche, M. 1948 Intrinsic viscosity, diffusion, and sedimentation rate of polymers in solution. J. Chem. Phys. 16, 573–579.Google Scholar
Ding, E. J. & Aidun, C. K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317–344.CrossRefGoogle Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48, 89–94.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Klein, S., Gibert, M., Bérut, A. & Bodenschatz, E. 2013 Simultaneous 3d measurement of the translation and rotation of finite-size particles and the flow field in a fully developed turbulent water flow. Meas. Sci. Technol. 24, 1–10.Google Scholar
Kossack, C. A. & Acrivos, A. 1974 Steady simple shear flow past a circular cylinder at moderate Reynolds numbers: a numerical solution. J. Fluid Mech. 66, 353–376.Google Scholar
Ku, X. K. & Lin, J. Z. 2009 Inertial effects on the rotational motion of a fibre in simple shear flow between two bounding walls. Phys. Scr. 80, 025801.Google Scholar
Ladd, A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part 2. numerical results. J. Fluid Mech. 271, 311–339.Google Scholar
Li, H., Lu, X., Fang, H. & Qian, Y. 2004 Force evaluations in lattice Boltzmann simulations with moving boundaries in two dimensions. Phys. Rev. E 70, 026701.Google Scholar
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech. 44, 1–17.Google Scholar
Mao, W. B. & Alexeev, A. 2014 Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166.Google Scholar
Masoud, H., Stone, H. A. & Shelley, M. J. 2013 On the rotation of porous ellipsoids in simple shear flows. J. Fluid Mech. 733, R6.Google Scholar
Mathai, V., Neut, M. W. M., van der Poel, E. P. & Sun, C. 2016 Translational and rotational dynamics of a large buoyant sphere in turbulence. Exp. Fluids 57, 51.Google Scholar
Mei, R., Yu, D. & Shyy, W. 2002 Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65, 041203.Google Scholar
Michalopoulou, A. C., Burganos, V. N. & Payatakes, A. C. 1993 Hydrodynamic interactions of two permeable particles moving slowly along their centerline. Chem. Engng Sci. 48, 2889–2900.Google Scholar
Neale, G. & Epstein, N. 1973 Creeping flow relative to permeable spheres. Chem. Engng Sci. 28, 1865–1874.Google Scholar
Ollila, S. T. T., Ala-Nissila, T. & Denniston, C. 2012 Hydrodynamic forces on steady and oscillating porous particles. J. Fluid Mech. 709, 123–148.Google Scholar
Poe, G. G. & Acrivos, A. 1975 Closed-streamline flows past rotating single cylinders and spheres: inertia effects. J. Fluid Mech. 72, 605–623.Google Scholar
Robertson, C. R. & Acrivos, A. 1970 Low Reynolds number shear flow past a rotating circular cylinder. part 1. momentum transfer. J. Fluid Mech. 40, 685–703.Google Scholar
Roy, B. C. & Damiano, R. 2008 On the motion of a porous sphere in a Stokes flow parallel to a planar confining boundary. J. Fluid Mech. 606, 75–104.CrossRefGoogle Scholar
Shahsavari, S., Wardle, B. & McKinley, G. H. 2014 Interception efficiency in two-dimensional flow past confined porous cylinders. Chem. Engng Sci. 116, 752–762.Google Scholar
Wang, L., Wang, L. P., Guo, Z. & Mi, J. 2015 Volume-averaged macroscopic equation for fluid flow in moving porous media. Intl J. Heat Mass Transfer 82, 357–368.Google Scholar
Wood, B. D. 2007 Inertial effects in dispersion in porous media. Water Resour. Res. 43, W12S16.Google Scholar
Wu, Y., Wu, X., Yao, L., Brunel, M., Coetmellec, S., Lebrun, D., Grehan, G. & Cen, K. 2015 Simultaneous measurement of 3d velocity and 2d rotation of irregular particle with digital holographic particle tracking velocimetry. Powder Tech. 284, 371–378.Google Scholar
Zettner, C. M. & Yoda, M. 2001 The circular cylinder in simple shear at moderate Reynolds numbers: An experimental study. Exp. Fluids 30, 346–353.Google Scholar
Zimmermann, R., Gasteuil, Y., Bourgoin, M., Volk, R., Pumir, A. & Pinton, J. 2011 Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow. Phys. Rev. Lett. 106, 154501.Google Scholar
Zou, Q. & He, X. 1997 On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9, 1591–1598.Google Scholar