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Inertial torque on a small spheroid in a stationary uniform flow

F. Jiang1, L. Zhao2, H. I. Andersson3, K. Gustavsson4, A. Pumir5, and B. Mehlig4

  • 1SINTEF Ocean, NO-7052 Trondheim, Norway
  • 2AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, China
  • 3Department of Energy and Process Engineering, NTNU, NO-7491 Trondheim, Norway
  • 4Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
  • 5Université Lyon, ENS de Lyon, Université Claude Bernard, Centre National de la Recherche Scientifique, Laboratoire de Physique, F-69342 Lyon, France

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Phys. Rev. Fluids 6, 024302 – Published 2 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024302

Abstract

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio λ=1/6) to prolate (λ=6), and we consider low and moderate particle Reynolds numbers (Re≤50). We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers, remains qualitatively correct for Reynolds numbers up to Re∼10. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as Re increases. For Re larger than 10, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in a turbulent flow.

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References (41)

  1. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Martinus Nijhof, Hague, The Netherlands, 1983).
  2. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, 1991).
  3. R. E. Khayat and R. G. Cox, Inertia effects on the motion of long slender bodies, J. Fluid Mech. 209, 435 (1989).
  4. F. Candelier and B. Mehlig, Settling of an asymmetric dumbbell in a quiescent fluid, J. Fluid Mech. 802, 174 (2016).
  5. A. Roy, R. J. Hamati, L. Tierney, D. L. Koch, and G. A. Voth, Inertial torques and a symmetry breaking orientational transition in the sedimentation of slender fibres, J. Fluid Mech. 875, 576 (2019).
  6. R. G. Cox, The steady motion of a particle of arbitrary shape at small Reynolds numbers, J. Fluid Mech. 23, 625 (1965).
  7. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
  8. V. Dabade, N. K. Marath, and G. Subramanian, Effects of inertia and viscoelasticity on sedimenting anisotropic particles, J. Fluid Mech. 778, 133 (2015).
  9. A. Hölzer and M. Sommerfeld, Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles, Comput. Fluids 38, 572 (2009).
  10. R. Ouchene, M. Khalij, A. Tanière, and B. Arcen, Drag, lift and torque coefficients for ellipsoidal particles: From low to moderate particle Reynolds numbers, Comput. Fluids 113, 53 (2015).
  11. R. Ouchene, M. Khalij, B. Arcen, and A. Tanière, A new set of correlations of drag, lift and torque coefficients for non-spherical particles at large Reynolds numbers, Powder Technol. 303, 33 (2016).
  12. R. Ouchene, Numerical simulation and modeling of the hydrodynamic forces and torque acting on individual oblate spheroids, Phys. Fluids 32, 073303 (2020).
  13. M. Zastawny, G. Mallouppas, F. Zhao, and B. van Wachem, Derivation of drag and lift forces and torque coefficients for non-spherical particles in flow, Int. J. Multiphase Flow 39, 227 (2012).
  14. S. K. P. Sanjeevi, J. A. M. Kuipers, and J. T. Padding, Drag, lift and torque correlations for non-spherical particles from Stokes limit to high Reynolds numbers, Int. J. Multiphase Flow 106, 325 (2018).
  15. M. Shin and D. L. Koch, Rotational and translational dispersion of fibres in isotropic turbulent flows, J. Fluid Mech. 540, 143 (2005).
  16. K. Fröhlich, M. Meinke, and W. Schröder, Correlations for inclide prolates based on highly resolved simulations, J. Fluid Mech. 901, A5 (2020).
  17. J. Fries, J. Einarsson, and B. Mehlig, Angular dynamics of small crystals in viscous flow, Phys. Fluids 2, 014302 (2017).
  18. M. Manhart, F. Tremblay, and R. Friedrich, MGLET: A parallel code for efficient DNS and LES of complex geometries, in Parallel Computational Fluid Dynamics–Trends and Applications, edited by C. B. Jenssen, T. Kvamsdal, H. I. Andersson, B. Pettersen, A. Ecer, J. Periaux, N. Satofuka, and P. Fox (Elsevier, 2001), pp. 449–456.
  19. H. I. Andersson and F. Jiang, Forces and torques on a prolate spheroid: Low-Reynolds number and attack angle effects, Acta Mech. 230, 431 (2019).
  20. G. Subramanian and D. L. Koch, Inertial effects on fibre motion in simple shear flow, J. Fluid Mech. 535, 383 (2005).
  21. F. Jiang, J. P. Gallardo, and H. I. Andersson, The laminar wake behind a 6:1 prolate spheroid at 45∘ incidence angle, Phys. Fluids 26, 113602 (2014).
  22. W. W. Willmarth, N. E. Hawk, and R. L. Harvey, Steady and unsteady motions and wakes of freely falling disks, Phys. Fluids 7, 197 (1964).
  23. S. B. Field, M. Klaus, M. G. Moore, and F. Nori, Chaotic dynamics of falling disks, Nature (London) 388, 252 (1997).
  24. F. Jiang, J. P. Gallardo, H. I. Andersson, and Z. Zhang, The transitional wake behind an inclined prolate spheroid, Phys. Fluids 27, 093602 (2015).
  25. J. D. Klett, Orientation model for particles in turbulence, J. Atmospheric Sci. 52, 2276 (1995).
  26. F.-M. Bréon and B. Dubrulle, Horizontally oriented plates in clouds, J. Atmos. Sci. 61, 2888 (2004).
  27. S. Kramel, Non-spherical particle dynamics in turbulence, Ph.D. thesis, Wesleyan University, 2017.
  28. U. Menon, A. Roy, S. Kramel, G. Voth, and D. Koch, Theoretical predictions of the orientation distribution of high-aspect-ratio, inertial particles settling in isotropic turbulence, Abstract No. Q36.00011, Proceedings of the 70th Annual Meeting of the APS Division of Fluid Dynamics, 2017 (unpublished).
  29. D. Lopez and E. Guazzelli, Inertial effects on fibers settling in a vortical flow, Phys. Rev. Fluids 2, 024306 (2017).
  30. K. Gustavsson, M. Z. Sheikh, D. Lopez, A. Naso, A. Pumir, and B. Mehlig, Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence, New J. Phys. 21, 083008 (2019).
  31. M. Z. Sheikh, K. Gustavsson, D. Lopez, E. Leveque, B. Mehlig, A. Pumir, and A. Naso, Importance of fluid inertia for the orientation of spheroids settling in turbulent flow, J. Fluid Mech. 886, A9 (2020).
  32. K. Gustavsson, M. Z. Sheikh, A. Naso, A. Pumir, and B. Mehlig, Effect of particle inertia on the alignment of small ice crystals in turbulent clouds, arXiv:2007.11530.
  33. H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation, 2nd ed. (Kluwer, Dordrecht, The Netherlands, 1997).
  34. J.-P. Chen and D. Lamb, The theoretical basis for the parameterization of ice crystal habits: Growth by vapor deposition, J. Atmos. Sci. 51, 1206 (1994).
  35. J. Einarsson, F. Candelier, F. Lundell, J. R. Angilella, and B. Mehlig, Rotation of a spheroid in a simple shear at small Reynolds number, Phys. Fluids 27, 063301 (2015).
  36. U. Frisch, Turbulence (Cambridge University, Cambridge, England, 1997).
  37. F. Candelier, J. Einarsson, and B. Mehlig, Rotation of a Small Particle in Turbulence, Phys. Rev. Lett. 117, 204501 (2016).
  38. F. Candelier, B. Mehlig, and J. Magnaudet, Time-dependent lift and drag on a rigid body in a viscous steady linear flow, J. Fluid Mech. 864, 554 (2019).
  39. L. B. Esteban, J. S. Shrimpton, and B. Ganapathisubramani, Disks settling in turbulence, J. Fluid Mech. 883, A58 (2020).
  40. J. H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35, 48 (1980).
  41. H. L. Stone, Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5, 530 (1968).

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Phys. Rev. Fluids 6, 024302– Published 2 February, 2021
  • Received 12 May 2020
  • Accepted 30 November 2020
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