Abstract
The rotational dynamics of finite-sized ellipsoidal particles with different aspect ratios around their fixed mass centers in shear flows have been investigated by direct numerical simulations. Particles are fully resolved by a revised immersed boundary projection method, and their rotational motion is governed by Euler’s equation which is calculated in the particle-fixed frame. The particle Reynolds number varies from 10 to 300 based on the longest axis of the particle. The steady states of the prolate and oblate spheroids in uniform flow, linear shear flow with the moving top wall and fixed bottom wall, and wall-bounded turbulence are analyzed. It is observed that the longest particle axes are perpendicular to or have a large angle with the local flow direction in the flow-gradient plane, which leads to a large drag force. A linear stability analysis on the rotational motion of a finite-sized particle in uniform flow is also carried out for supporting this finding. In the linear shear flow, the influence of fluid inertia and fluid shear on the inclined angle is examined in detail. In wall-bounded turbulence, it is found that the particles in the buffer region and the outside of the boundary layer behave similarly in the mean sense as in the linear shear flow and uniform flow, respectively. The present results with intermediate to large particle Reynolds numbers can be regarded as a starting point to understand the dynamics of heavy finite-sized particles in viscous flows.
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Ardekani, M.N., Costa, P., Breugem, W.P., Brandt, L.: Numerical study of the sedimentation of spheroidal particles. Int. J. Multiph. Flow 87, 16–34 (2016)
Ardekani, M.N., Costa, P., Breugem, W.P., Picano, F., Brandt, L.: Drag reduction in turbulent channel flow laden with finite-size oblate spheroids. J. Fluid Mech. 816, 43–70 (2016)
Brenner, H.: The Stokes resistance of an arbitrary particle—IV arbitrary fields of flow. Chem. Eng. Sci. 19(10), 703–727 (1964)
Challabotla, N.R., Nilsen, C., Andersson, H.I.: On rotational dynamics of inertial disks in creeping shear flow. Phys. Lett. A 379(3), 157–162 (2015)
Challabotla, N.R., Zhao, L., Andersson, H.I.: Shape effects on dynamics of inertia-free spheroids in wall turbulence. Phys. Fluids 27(6), 143 (2015)
Challabotla, N.R., Zhao, L.: Andersson H I. Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2 (2015). https://doi.org/10.1017/jfm.2015.38
Challabotla, N.R.: Nonspherical particle suspensions in wall turbulence. Ph.D. thesis. Norwegian University of Science and Technology, Norway (2016)
Clift, R., Grace, J.R., Weber, M.E.: Bubbles, Drops, and Particles. Academic Press, Cambridge (1978)
Ding, E.J., Aidun, C.K.: The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423(423), 317–344 (2000)
Eshghinejadfard, A., Abdelsamie, A., Hosseini, S.A., Thévenin, D.: Immersed boundary lattice Boltzmann simulation of turbulent channel flows in the presence of spherical particles. Int. J. Multiph. Flow 96, 161–172 (2017)
Eshghinejadfard, A., Hosseini, S.A., Thévenin, D.: Fully-resolved prolate spheroids in turbulent channel flows: a lattice Boltzmann study. AIP Adv. 7(9), 095007 (2017)
Huang, W.X., Chang, C.B., Sung, H.J.: Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method. J. Comput. Phys. 231(8), 3340–3364 (2012)
Huang, H., Yang, X., Krafczyk, M., Lu, X.Y.: Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692(692), 369–394 (2012)
Jeffery, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. 102(715), 161–179 (1922)
Kempe, T., Schwarz, S., Fröhlich, J.: Modelling of spheroidal particles in viscous flows. In: Proceedings of the Academy Colloquium Immersed Boundary Methods: Current Status and Future Research Directions (KNAW, Amsterdam, The Netherlands), 15–17 (2009)
Kempe, T., Vowinckel, B., Fröhlich, J.: On the relevance of collision modeling for interface-resolving simulations of sediment transport in open channel flow. Int. J. Multiph. Flow 58(1), 214–235 (2014)
Kim, K., Baek, S.J., Sung, H.J.: An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Int. J. Numer. Methods Fluids 38, 125–138 (2002)
Ku, X.K., Lin, J.Z.: Inertial effects on the rotational motion of a fibre in simple shear flow between two bounding walls. Physica Scripta 27(80), 025801 (2009)
Larson, R.G., Ottinger, H.C.: Effect of molecular elasticity on out of-plane orientations in shearing flows of liquid-crystalline polymers. Macromolecules 24(23), 6270–6282 (1991)
Li, R.Y., Xie, C.M., Huang, W.X., Xu, C.X.: An efficient immersed boundary projection method for flow over complex/moving boundaries. Comput. Fluids 140, 122–135 (2016)
Lund, T.S., Wu, X., Squires, K.D.: Generation of turbulent inflow data for spatially–developing boundary layer simulations. J. Comput. Phys. 140(2), 233–258 (1998)
Lundell, F., Carlsson, A.: Heavy ellipsoids in creeping shear flow: transitions of the particle rotation rate and orbit shape. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 81(2), 016323 (2010)
Mao, W., Alexander, A.: Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166 (2014)
Marchioli, C., Fantoni, M., Soldati, A.: Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22(3), 245 (2010)
Mortensen, P.H., Andersson, H.I., Gillissen, J.J.J., Boersma, B.J.: Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Phys. Fluids 20(9), 1211 (2008)
Mortensen, P.H., Andersson, H.I., Gillissen, J.J.J., Boersma, B.J.: On the orientation of ellipsoidal particles in a turbulent shear flow. Int. J. Multiph. Flow 34(7), 678–683 (2008)
Peskin, C.S.: The immersed boundary method. Acta Numerica 11, 479–517 (2002)
Qi, D., Luo, L.S.: Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows. J. Fluid Mech. 477(477), 201–213 (2003)
Redheffer, R.M., Port, D.: Differential Equations: Theory and Applications. Jones and Bartless, Burlington (1991)
Rosen, T., Do-Quang, M., Aidun, C.K., Lundell, F.: Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow. Phys. Rev. E 91, 053017 (2015)
Subramanian, G., Koch, D.L.: Inertial effects on fibre motion in simple shear flow. J. Fluid Mech. 535(535), 383–414 (2005)
Subramanian, G., Koch, D.L.: Inertial effects on the orientation of nearly spherical particles in simple shear flow. J. Fluid Mech. 557(557), 257–296 (2006)
Uhlmann, M.: An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209(2), 448–476 (2005)
Voth, G.A., Soldati, A.: Anisotropic particles in turbulence. Ann. Rev. Fluid Mech. 49(1), 249–276 (2017)
Xia, Q.J., Huang, W.X., Xu, C.X., Cui, G.X.: Direct numerical simulation of spatially developing turbulent boundary layers with opposition control. Fluid Dyn. Res. 47, 025503 (2015)
Yu, Z.S., Phan-Thien, N., Tanner, R.I.: Rotation of a spheroid in a Couette flow at moderate Reynolds numbers. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 76(2), 026310 (2007)
Zastawny, M., Mallouppas, G., Zhao, F., Wachem, B.V.: Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Int. J. Multiph. Flow 39, 227–239 (2012)
Zettner, C.M., Yoda, M.: The circular cylinder in simple shear at moderate Reynolds numbers: an experimental study. Exp. Fluids 30(3), 346–353 (2001)
Acknowledgements
The work was supported by National Natural Science Foundation of China under Grant Nos. 11490551, 11772172 and 11702158. The authors would like to thank Tsinghua National Laboratory for Information Science and Technology for support in parallel computation.
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Li, RY., Cui, ZW., Huang, WX. et al. On rotational dynamics of a finite-sized ellipsoidal particle in shear flows. Acta Mech 230, 449–467 (2019). https://doi.org/10.1007/s00707-018-2295-z
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DOI: https://doi.org/10.1007/s00707-018-2295-z