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Mean shear versus orientation isotropy: effects on inertialess spheroids’ rotation mode in wall turbulence

Published online by Cambridge University Press:  12 April 2018

Kun Yang ,
Lihao Zhao Open the ORCID record for Lihao Zhao [Opens in a new window]  and
Helge I. Andersson
Kun Yang
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Lihao Zhao*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway AML, Department of Engineering Mechanics, Tsinghua University, 10084 Beijing, China
Helge I. Andersson
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
*
†Email address for correspondence: [email protected]
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Abstract

The orientation of spheroidal particles dispersed in a fluid flow is known to influence the particles’ rotation mode. Rod-like and disk-like particles orient themselves differently and accordingly also rotate differently. In order to explore the role of the deterministic factors, i.e. mean shear and vorticity anisotropy, on the orientational behaviour of inertialess tracer spheroids, we adopted a purpose-made Couette–Poiseuille flow simulated numerically by Yang et al. (Intl J. Heat Fluid Flow, vol. 63, 2017, pp. 14–27). Typical wall turbulence with streamwise-oriented streaky structures caused by the locally high mean shear rate was observed only at one of the walls. The absence of mean shear at the other wall gave rise to an atypical turbulence field. Over a relatively wide and quasi-homogeneous core region, a modest mean shear rate made the vorticity field anisotropic. In spite of the mean shear, rod-like tracers were spinning and disk-like spheroids were tumbling, just as in homogeneous isotropic turbulence. We explained this phenomenon by the isotropic particle orientation and concluded that zero mean shear is not necessary for rod spinning and disk tumbling. The orientation and rotation of the Lagrangian tracer spheroids near the high shear wall were almost indistinguishable from the well-known behaviour in turbulent channel flows. Near the opposite wall, where the mean shear was negligibly small, disk-like particles aligned preferentially in the wall-normal direction and rotated similarly as in the presence of high shear. Rod-like particles, on the contrary, aligned more randomly and accordingly rotated similarly as in the core region. These observations revealed that the degree of particle orientation anisotropy has a major impact on the particle rotation mode, whereas mean shear, irrespective of the actual shear rate, only plays a secondary role in particle rotation. Deduction of the eigenvectors of the left Cauchy–Green tensor showed that the preferential orientation of the tracer spheroids was caused by the alignment of rods and disks with the strongest Lagrangian stretching and compression directions, respectively. Lagrangian stretching/compression determines the particle orientations and the particle orientation affects the particle rotation mode.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 796 - 816
Copyright
© 2018 Cambridge University Press 

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References

Andersson, H. I., Lygren, M. & Kristoffersen, R. 1998 Roll cells in turbulent plane Couette flow: reality or artifact? In Sixteenth International Conference on Numerical Methods in Fluid Dynamics (ed. Bruneau, C. H.), Lecture Notes in Physics, vol. 515, pp. 117–122. Springer.10.1007/BFb0106570Google Scholar
Andersson, H. I., Zhao, L. & Variano, E. A. 2015 On the anisotropic vorticity in turbulent channel flows. Trans. ASME J. Fluids Engng 137 (8), 084503.10.1115/1.4030003Google Scholar
Arcen, B., Ouchene, R., Khalij, M. & Taniére, A. 2017 Prolate spheroidal particles behavior in a vertical wall-bounded turbulent flow. Phys. Fluids 29 (3), 093301.10.1063/1.4994664Google Scholar
Ardekani, M. N., Costa, P., Breugem, W. P., Picano, F. & Brandt, L. 2017 Drag reduction in turbulent channel flow laden with finite-size oblate spheroids. J. Fluid Mech. 816, 43–70.10.1017/jfm.2017.68Google Scholar
Ardeshiri, H., Benkeddad, I., Schmitt, F. G., Souissi, S., Toschi, F. & Calzavarini, E. 2016 Lagrangian model of copepod dynamics: clustering by escape jumps in turbulence. Phys. Rev. E 93, 043117.Google Scholar
Ardeshiri, H., Schmitt, F. G., Souissi, S., Toschi, F. & Calzavarini, E. 2017 Copepods encounter rates from a model of escape jump behaviour in turbulence. J. Plankton Res. 39, 878–890.10.1093/plankt/fbx051Google Scholar
Balachandar, S. 2009 A scaling analysis for point-particle approaches to turbulent multiphase flows. Intl J. Multiphase Flow 35, 801–810.10.1016/j.ijmultiphaseflow.2009.02.013Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 43, 111–133.10.1146/annurev.fluid.010908.165243Google Scholar
Barboza, L. G. A. & Gimenez, B. C. G. 2015 Microplastics in the marine environment: current trends and future perspectives. Marine Poll. Bull. 97 (1), 5–12.10.1016/j.marpolbul.2015.06.008Google Scholar
Barry, M. T., Rusconi, R., Guasto, J. S. & Stocker, R. 2015 Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton. J. R. Soc. Interface 12 (112), 20150791.10.1098/rsif.2015.0791Google Scholar
Bech, K. H., Tillmark, N., Alfredsson, P. H. & Andersson, H. I. 1995 An investigation of turbulent plane Couette flow at low Reynolds number. J. Fluid Mech. 286, 291–325.10.1017/S0022112095000747Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2013 The effect of large-scale turbulent structures on particle dispersion in wall-bounded flows. Intl J. Multiphase Flow 51, 55–64.10.1016/j.ijmultiphaseflow.2012.11.007Google Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G. A., Mehlig, B. & Variano, E. A. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27 (3), 035101.10.1063/1.4913501Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015a Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2.10.1017/jfm.2015.38Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015b Shape effects on dynamics of inertia-free spheroids in wall turbulence. Phys. Fluids 27 (6), 061703.10.1063/1.4922864Google Scholar
Coleman, G. N., Pirozzoli, S., Quadrio, M. & Spalart, P. R. 2017 Direct numerical simulation and theory of a wall-bounded flow with zero skin friction. Flow Turbul. Combust. 99, 553–564.10.1007/s10494-017-9834-xGoogle Scholar
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.Google Scholar
Durham, W. M., Climent, E., Barry, M., De Lillo, F., Boffetta, G., Cencini, M. & Stocker, R. 2013 Turbulence drives microscale patches of motile phytoplankton. Nature Comm. 4, 2148.10.1038/ncomms3148Google Scholar
Eaton, J. K. 2009 Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking. Intl J. Multiphase Flow 35, 792–800.10.1016/j.ijmultiphaseflow.2009.02.009Google Scholar
Eshghinejadfard, A., Hosseini, S. A. & Thevenin, D. 2017 Fully-resolved prolate spheroids in turbulent channel flows: a lattice Boltzmann study. AIP Adv. 7, 095007.10.1063/1.5002528Google Scholar
Gerz, T., Schumann, U. & Elghobashi, S. E. 1989 Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563–594.10.1017/S0022112089000765Google Scholar
Gourlay, T. 2006 Flow beneath a ship at small underkeel clearance. J. Ship Res. 50, 250–258.Google Scholar
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.10.1146/annurev-fluid-120710-101156Google Scholar
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014 Tumbling of small axisymmetric particles in random and turbulent flows. Phys. Rev. Lett. 112 (1), 014501.10.1103/PhysRevLett.112.014501Google Scholar
Handler, R. A., Swean, T. F., Leighton, R. I. & Swearingen, J. D. 1993 Length scales and the energy balance for turbulence near a free surface. AIAA J. 31, 1998–2007.10.2514/3.11883Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.10.1017/S0022112096003965Google Scholar
Jiménez, J. 1997 Oceanic turbulence at millimeter scales. Sci. Mar. 61, 47–56.Google Scholar
Katz, J. 2006 Aerodynamics of race cars. Annu. Rev. Fluid Mech. 38, 27–63.10.1146/annurev.fluid.38.050304.092016Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.10.1017/S0022112087000892Google Scholar
Kuroda, A., Kasagi, N. & Hirata, M. 1995 Direct numerical simulation of turbulent Couette-Poiseuille flows: effect of mean shear rate on the near wall turbulence structures. In Turbulent Shear Flows (ed. Durst, F., Kasagi, N., Launder, B. E., Schmidt, F. W., Suzuki, K. & Whitelaw, J. H.), vol. 9, pp. 241–257. Springer.10.1007/978-3-642-78823-9_16Google Scholar
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583.10.1017/S0022112090000532Google Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55.10.1017/S0022112009994022Google Scholar
Marcus, G. G., Parsa, S., Kramel, S., Ni, R. & Voth, G. A. 2014 Measurements of the solid-body rotation of anisotropic particles in 3D turbulence. New J. Phys. 16 (10), 102001.10.1088/1367-2630/16/10/102001Google Scholar
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008 Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Phys. Fluids 20 (9), 093302.10.1063/1.2975209Google Scholar
Nagaosa, R. & Handler, R. A. 2003 Statistical analysis of coherent vortices near a free surface in a fully developed turbulence. Phys. Fluids 15, 375–394.10.1063/1.1533071Google Scholar
Ni, R., Kramel, S., Ouellette, N. T. & Voth, G. A. 2015 Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence. J. Fluid Mech. 766, 202–225.10.1017/jfm.2015.16Google 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, R3.10.1017/jfm.2014.32Google Scholar
Ouchene, R., Khalij, M., Arcen, B. & Taniére, A. 2016 A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds number. Powder Tech. 303, 33–43.10.1016/j.powtec.2016.07.067Google Scholar
Pan, Y. & Banerjee, S. 1995 A numerical study of free-surface turbulence in channel flow. Phys. Fluids 7, 1649–1663.10.1063/1.868483Google Scholar
Papavassiliou, D. V. & Hanratty, T. J. 1997 Interpretation of large-scale structures observed in a turbulent plane Couette flow. Intl J. Heat Fluid Flow 18, 55–69.10.1016/S0142-727X(96)00138-5Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.10.1103/PhysRevLett.109.134501Google Scholar
Parsa, S., Guasto, J. S., Kishore, M., Ouellette, N. T., Gollub, J. P. & Voth, G. A. 2011 Rotation and alignment of rods in two-dimensional chaotic flow. Phys. Fluids 23, 043302.10.1063/1.3570526Google Scholar
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313–358.10.1146/annurev.fl.24.010192.001525Google Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.10.1088/1367-2630/13/9/093030Google Scholar
Reidenbach, M. A., Koseff, J. R. & Koehl, M. 2009 Hydrodynamic forces on larvae affect their settlement on coral reefs in turbulent, wave-driven flow. Limnol. Oceanogr. 54, 318–330.10.4319/lo.2009.54.1.0318Google Scholar
Richter, D. H. & Sullivan, P. P. 2013 Momentum transfer in a turbulent, particle-laden Couette flow. Phys. Fluids 25, 053304.10.1063/1.4804391Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.10.1146/annurev.fl.23.010191.003125Google Scholar
Rogers, M. M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.10.1017/S0022112087000569Google Scholar
Rosén, T., Lundell, F. & Aidun, C. K. 2014 Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow. J. Fluid Mech. 738, 563–590.10.1017/jfm.2013.599Google Scholar
Ruiz, J., Macías, D. & Peters, F. 2004 Turbulence increases the average settling velocity of phytoplankton cells. Proc. Natl Acad. Sci. USA 101, 17720–17724.10.1073/pnas.0401539101Google Scholar
Schumacher, J. & Eckhardt, B. 2000 On statistically stationary homogeneous shear turbulence. Europhys. Lett. 52, 627–632.10.1209/epl/i2000-00484-4Google Scholar
Sekimoto, A., Dong, S. & Jiménez, J. 2016 Direct numerical simulation of statistically stationary and homogenous shear turbulence and its relation to other shear flows. Phys. Fluids 28, 035105.10.1063/1.4942496Google Scholar
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014 Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56.10.1016/j.atmosres.2013.08.011Google Scholar
Spencer, N. B., Lee, L. L., Parthasarathy, R. N. & Papavassiliou, D. V. 2009 Turbulence structure for plane Poiseuille–Couette flow and implications for drag reduction over surfaces with slip. Can. J. Chem. Engng 87, 38–46.10.1002/cjce.20136Google Scholar
Thurlow, E. M. & Klewicki, J. C. 2000 Experimental study of turbulent Poiseuille–Couette flow. Phys. Fluids 12, 865–875.10.1063/1.870341Google Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.10.1146/annurev-fluid-010816-060135Google Scholar
Yang, K., Zhao, L. & Andersson, H. I. 2017a Preferential particle concentration in wall-bounded turbulence with zero skin friction. Phys. Fluids 29, 113302.10.1063/1.4998547Google Scholar
Yang, K., Zhao, L. & Andersson, H. I. 2017b Turbulent Couette–Poiseuille flow with zero wall shear. Intl J. Heat Fluid Flow 63, 14–27.10.1016/j.ijheatfluidflow.2016.11.011Google Scholar
Yang, K., Zhao, L. & Andersson, H. I. 2018 Particle segregation in turbulent Couette–Poiseuille flow with vanishing wall shear. Intl J. Multiphase Flow 98, 45–55.10.1016/j.ijmultiphaseflow.2017.09.001Google Scholar
Zhang, H., Ahmadi, G., Fan, F. G. & McLaughlin, J. B. 2001 Ellipsoidal particles transport and deposition in turbulent channel flows. Intl J. Multiphase Flow 27, 971–1009.10.1016/S0301-9322(00)00064-1Google Scholar
Zhao, L. & Andersson, H. I. 2016 Why spheroids orient preferentially in near-wall turbulence. J. Fluid Mech. 807, 221–234.10.1017/jfm.2016.619Google Scholar
Zhao, L., Challabotla, N. R., Andersson, H. I. & Variano, E. A. 2015 Rotation of nonspherical particles in turbulent channel flow. Phys. Rev. Lett. 115, 244501.10.1103/PhysRevLett.115.244501Google Scholar