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Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

Published online by Cambridge University Press:  30 March 2022

Linfeng Jiang
Affiliation:
Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Cheng Wang
Affiliation:
Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Shuang Liu
Affiliation:
Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Chao Sun*
Affiliation:
Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
Enrico Calzavarini*
Affiliation:
Univ. Lille, Unité de Mécanique de Lille – J. Boussinesq – ULR 7512, F-59000 Lille, France
*
Email addresses for correspondence: chaosun@tsinghua.edu.cn, enrico.calzavarini@polytech-lille.fr
Email addresses for correspondence: chaosun@tsinghua.edu.cn, enrico.calzavarini@polytech-lille.fr

Abstract

We study the translational and rotational dynamics of neutrally buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which are reflected in distinct axial and lateral fluctuations for accelerations and rotation rates. The randomization of orientations does not occur even for particles with volume-equivalent diameter size in the inertial range, here up to $60$ dissipative units ($\eta$) at Taylor-scale Reynolds number ${Re_{\lambda }=120}$. Additionally, we demonstrate that the role of fluid boundary layers around the particles cannot be neglected in reaching a quantitative understanding of particle statistical dynamics, as they affect the intensities of the angular velocities and the relative importance of tumbling with respect to spinning rotations. This study brings to the fore the importance of inertial-scale flow structures in homogeneous and isotropic turbulence and their impacts on the transport of neutrally buoyant bodies with sizes in the inertial range.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ardekani, M.N., Costa, P., Breugem, W.P. & Brandt, L. 2016 Numerical study of the sedimentation of spheroidal particles. Intl J. Multiphase Flow 87, 1634.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98 (8), 084502.CrossRefGoogle ScholarPubMed
Bentkamp, L., Lalescu, C.C. & Wilczek, M. 2019 Persistent accelerations disentangle Lagrangian turbulence. Nat. Commun. 10 (1), 18.CrossRefGoogle ScholarPubMed
Benzi, R., Biferale, L., Calzavarini, E., Lohse, D. & Toschi, F. 2009 Velocity-gradient statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame. Phys. Rev. E 80, 066318.CrossRefGoogle ScholarPubMed
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. & Toschi, F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17 (2), 021701.CrossRefGoogle Scholar
Bordoloi, A.D. & Variano, E. 2017 Rotational kinematics of large cylindrical particles in turbulence. J. Fluid Mech. 815, 199222.CrossRefGoogle Scholar
Bounoua, S., Bouchet, G. & Verhille, G. 2018 Tumbling of inertial fibers in turbulence. Phys. Rev. Lett. 121, 124502.CrossRefGoogle ScholarPubMed
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242251.CrossRefGoogle Scholar
Brown, R.D., Warhaft, Z. & Voth, G.A. 2009 Acceleration statistics of neutrally buoyant spherical particles in intense turbulence. Phys. Rev. Lett. 103, 194501.CrossRefGoogle ScholarPubMed
Brändle de Motta, J.C., Estivalezes, J.L., Climent, E. & Vincent, S. 2016 Local dissipation properties and collision dynamics in a sustained homogeneous turbulent suspension composed of finite size particles. Intl J. Multiphase Flow 85, 369379.CrossRefGoogle Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G.A., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27 (3), 035101.CrossRefGoogle Scholar
Calzavarini, E. 2019 Eulerian–Lagrangian fluid dynamics platform: the ch4-project. Softw. Impacts 1, 100002.CrossRefGoogle Scholar
Calzavarini, E., Jiang, L. & Sun, C. 2020 Anisotropic particles in two-dimensional convective turbulence. Phys. Fluids 32 (2), 023305.CrossRefGoogle Scholar
Calzavarini, E., Kerscher, M., Lohse, D. & Toschi, F. 2008 Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 1324.CrossRefGoogle Scholar
Calzavarini, E., Volk, R., Bourgoin, M., Leveque, E., Pinton, J.F. & Toschi, F. 2009 Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces. J. Fluid Mech. 630, 179189.CrossRefGoogle Scholar
Calzavarini, E., Volk, R., Leveque, E., Pinton, J.F. & Toschi, F. 2012 Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence. Physica D 241D (3), 237244.CrossRefGoogle Scholar
Chong, M.S., Perry, A.E. & Cantwell, B.J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids 2 (5), 765777.CrossRefGoogle Scholar
Cisse, M., Homann, H. & Bec, J. 2013 Slipping motion of large neutrally buoyant particles in turbulence. J. Fluid Mech. 735, R1.CrossRefGoogle Scholar
Cooley, M.D.A. & O'Neill, M.E. 1969 On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere. Mathematika 16 (1), 3749.CrossRefGoogle Scholar
Costa, P., Boersma, B.J., Westerweel, J. & Breugem, W.P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92, 053012.CrossRefGoogle ScholarPubMed
Do-Quang, M., Amberg, G., Brethouwer, G. & Johansson, A.V. 2014 Simulation of finite-size fibers in turbulent channel flows. Phys. Rev. E 89, 013006.CrossRefGoogle ScholarPubMed
Dolata, B.E. & Zia, R.N. 2021 Faxén formulas for particles of arbitrary shape and material composition. J. Fluid Mech. 910, A22.CrossRefGoogle Scholar
Fiabane, L., Zimmermann, R., Volk, R., Pinton, J.F. & Bourgoin, M. 2012 Clustering of finite-size particles in turbulence. Phys. Rev. E 86, 035301.CrossRefGoogle ScholarPubMed
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014 Tumbling of small axisymmetric particles in random and turbulent flows. Phys. Rev. Lett. 112, 014501.CrossRefGoogle ScholarPubMed
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651, 8191.CrossRefGoogle Scholar
Jeffery, G.B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161179.Google Scholar
Jiang, L., Calzavarini, E. & Sun, C. 2020 Rotation of anisotropic particles in Rayleigh–Bénard turbulence. J. Fluid Mech. 901, A8.CrossRefGoogle Scholar
Jiang, L., Wang, C., Liu, S., Sun, C. & Calzavarini, E. 2021 Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations. Theor. Appl. Mech. Lett. 11, 100227.CrossRefGoogle Scholar
Kuperman, S., Sabban, L. & van Hout, R. 2019 Inertial effects on the dynamics of rigid heavy fibers in isotropic turbulence. Phys. Rev. Fluids 4, 064301.CrossRefGoogle Scholar
La Porta, A., Voth, G.A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 22.CrossRefGoogle ScholarPubMed
Liberzon, A., Luthi, B., Holzner, M., Ott, S., Berg, J. & Jakob, M. 2012 On the structure of acceleration in turbulence. Physica D 241 (3), 208215.CrossRefGoogle Scholar
Luo, K., Wang, Z., Fan, J. & Cen, K. 2007 Full-scale solutions to particle-laden flows: multidirect forcing and immersed boundary method. Phys. Rev. E 76, 066709.CrossRefGoogle ScholarPubMed
Mathai, V., Calzavarini, E., Brons, J., Sun, C. & Lohse, D. 2016 Microbubbles and microparticles are not faithful tracers of turbulent acceleration. Phys. Rev. Lett. 117 (2), 024501.CrossRefGoogle Scholar
Mathai, V., Huisman, S.G., Sun, C., Lohse, D. & Bourgoin, M. 2018 Dispersion of air bubbles in isotropic turbulence. Phys. Rev. Lett. 121 (5), 054501.CrossRefGoogle ScholarPubMed
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.CrossRefGoogle Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239261.CrossRefGoogle Scholar
Ni, R., Ouellette, N.T. & Voth, G.A. 2014 Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence. J. Fluid Mech. 743, R3.CrossRefGoogle Scholar
Oehmke, T.B., Bordoloi, A.D., Variano, E. & Verhille, G. 2021 Spinning and tumbling of long fibers in isotropic turbulence. Phys. Rev. Fluids 6, 044610.CrossRefGoogle Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G.A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109 (13), 134501.CrossRefGoogle ScholarPubMed
Parsa, S. & Voth, G.A. 2014 Inertial range scaling in rotations of long rods in turbulence. Phys. Rev. Lett. 112, 024501.CrossRefGoogle ScholarPubMed
Peskin, C.S. 2002 The immersed boundary method. Acta Numerica 11, 479517.CrossRefGoogle Scholar
Pujara, N., Oehmke, T.B., Bordoloi, A.D. & Variano, E.A. 2018 Rotations of large inertial cubes, cuboids, cones, and cylinders in turbulence. Phys. Rev. Fluids 3, 054605.CrossRefGoogle Scholar
Pujara, N., Voth, G.A. & Variano, E.A. 2019 Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence. J. Fluid Mech. 860, 465486.CrossRefGoogle Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13 (9), 093030.CrossRefGoogle 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
Shen, J., Lu, Z., Wang, L. & Peng, C. 2021 Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows. Phys. Rev. E 104, 025109.CrossRefGoogle ScholarPubMed
Squires, K.D. & Eaton, J.K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids 3, 1169.CrossRefGoogle Scholar
Suzuki, K. & Inamuro, T. 2011 Effect of internal mass in the simulation of a moving body by the immersed boundary method. Comput. Fluids 49 (1), 173187.CrossRefGoogle Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448476.CrossRefGoogle Scholar
Volk, R., Calzavarini, E., Leveque, E. & Pinton, J.F. 2011 Dynamics of inertial particles in a turbulent von Kármán flow. J. Fluid Mech. 668, 223235.CrossRefGoogle Scholar
Voth, G.A., Porta, L.A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121160.CrossRefGoogle Scholar
Voth, G.A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249276.CrossRefGoogle Scholar
Wang, C., Jiang, L., Jiang, H., Sun, C. & Liu, S. 2021 a Heat transfer and flow structure of two-dimensional thermal convection overratchet surfaces. J. Hydrodyn. 33, 970978.CrossRefGoogle Scholar
Xu, H. & Bodenschatz, E. 2008 Motion of inertial particles with size larger than Kolmogorov scale in turbulent flows. Physica D 237 (14–17), 20952100.CrossRefGoogle Scholar
Xu, H., Ouellette, N.T., Vincenzi, D. & Bodenschatz, E. 2007 Acceleration correlations and pressure structure functions in high-Reynolds number turbulence. Phys. Rev. Lett. 99, 204501.CrossRefGoogle ScholarPubMed