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On the orientational dependence of drag experienced by spheroids

Published online by Cambridge University Press:  02 May 2017

Sathish K. P. Sanjeevi  and
Johan T. Padding Open the ORCID record for Johan T. Padding [Opens in a new window]
Sathish K. P. Sanjeevi
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
Johan T. Padding*
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: J.T.Padding@tudelft.nl
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Abstract

The flow around different prolate (needle-like) and oblate (disc-like) spheroids is studied using a multi-relaxation-time lattice Boltzmann method. We compute the mean drag coefficient $C_{D,\unicode[STIX]{x1D719}}$ at different incident angles $\unicode[STIX]{x1D719}$ for a wide range of Reynolds numbers ($\mathit{Re}$). We show that the sine-squared drag law $C_{D,\unicode[STIX]{x1D719}}=C_{D,\unicode[STIX]{x1D719}=0^{\circ }}+(C_{D,\unicode[STIX]{x1D719}=90^{\circ }}-C_{D,\unicode[STIX]{x1D719}=0^{\circ }})\sin ^{2}\unicode[STIX]{x1D719}$ holds up to large Reynolds numbers, $\mathit{Re}=2000$. Further, we explore the physical origin behind the sine-squared law, and reveal that, surprisingly, this does not occur due to linearity of flow fields. Instead, it occurs due to an interesting pattern of pressure distribution contributing to the drag at higher $\mathit{Re}$ for different incident angles. The present results demonstrate that it is possible to perform just two simulations at $\unicode[STIX]{x1D719}=0^{\circ }$ and $\unicode[STIX]{x1D719}=90^{\circ }$ for a given $\mathit{Re}$ and obtain particle-shape-specific $C_{D}$ at arbitrary incident angles. However, the model has limited applicability to flatter oblate spheroids, which do not exhibit the sine-squared interpolation, even for $\mathit{Re}=100$, due to stronger wake-induced drag. Regarding lift coefficients, we find that the equivalent theoretical equation can provide a reasonable approximation, even at high $\mathit{Re}$, for prolate spheroids.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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References

Aidun, C. K., Lu, Y. & Ding, E.-J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.Google Scholar
Bouzidi, M., Firdaouss, M. & Lallemand, P. 2001 Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 13, 3452–3459.Google Scholar
El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2010 Crossflow past a prolate spheroid at Reynolds number of 10 000. J. Fluid Mech. 659, 365–374.Google Scholar
El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2012 Wakes behind a prolate spheroid in crossflow. J. Fluid Mech. 701, 98–136.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. vol. 1. Springer.Google Scholar
Hecht, M. & Harting, J. 2010 Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann simulations. J. Stat. Mech. Theory Exp. 2010, P01018.Google Scholar
Hölzer, A. & Sommerfeld, M. 2009 Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles. Comput. Fluids 38, 572–589.Google Scholar
Huang, H., Yang, X., Krafczyk, M. & Lu, X.-Y. 2012 Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692, 369–394.Google Scholar
d’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Luo, L.-S. 2002 Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437–451.CrossRefGoogle ScholarPubMed
Jiang, F., Gallardo, J. P., Andersson, H. I. & Zhang, Z. 2015 The transitional wake behind an inclined prolate spheroid. Phys. Fluids 27, 093602.Google Scholar
Kruggel-Emden, H., Kravets, B., Suryanarayana, M. K. & Jasevicius, R. 2016 Direct numerical simulation of coupled fluid flow and heat transfer for single particles and particle packings by a LBM-approach. Powder Technol. 294, 236–251.Google Scholar
Lallemand, P. & Luo, L.-S. 2003 Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184, 406–421.Google Scholar
Ouchene, R., Khalij, M., Arcen, B. & Tanière, A. 2016 A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds numbers. Powder Technol. 303, 33–43.Google Scholar
Pan, C., Luo, L.-S. & Miller, C. T. 2006 An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 35, 898–909.Google Scholar
Ploumhans, P., Winckelmans, G. S., Salmon, J. K., Leonard, A. & Warren, M. S. 2002 Vortex methods for direct numerical simulation of three-dimensional bluff body flows: application to the sphere at Re = 300, 500, and 1000. J. Comput. Phys. 178, 427–463.Google Scholar
Vakarelski, I. U., Berry, J. D., Chan, D. Y. C. & Thoroddsen, S. T. 2016 Leidenfrost vapor layers reduce drag without the crisis in high viscosity liquids. Phys. Rev. Lett. 117, 114503.Google Scholar
Zastawny, M., Mallouppas, G., Zhao, F. & Van Wachem, B. 2012 Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Intl J. Multiphase Flow 39, 227–239.Google Scholar