# Spherical Particle Migration Evaluation in Low Reynolds Number Couette Flow Using Smooth Profile Method

Spherical Particle Migration Evaluation in Low Reynolds Number Couette Flow Using Smooth Profile Method

Mahyar Pourghasemi Nima Fathi Peter Vorobieff Goodarz Ahmadi Seyed Sobhan Aleyasin Luís Eça

Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, USA

Mechanical and Aeronautical Engineering Department, Clarkson University, Potsdam, NY, USA

Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada

Mechanical Engineering Department, Instituto Superior Técnico, Lisbon, Portugal

Page:
261-275
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DOI:
https://doi.org/10.2495/CMEM-V9-N3-261-275
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Revised:
N/A
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Accepted:
N/A
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Available online:
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| Citation

OPEN ACCESS

Abstract:

An Eulerian–Lagrangian model is developed to investigate the solid particle migration in low Reynolds number shear flows between two parallel plates. A continuous kernel function with a predefined thickness is applied in the implemented numerical model to smooth the discontinuity at the interface between primary and secondary phases. At each time step, the solid particle’s rotation and displacement are calculated to directly capture the interaction between the solid particle and primary liquid phase without simplification. Solution verification is performed using the global deviation grid convergence index approach. The observed order of accuracy for the primary phase solver approaches 2, consistent with the formal order of accuracy of the applied discretization scheme. The obtained velocity pro- files from the implemented numerical approach show a good agreement with the analytical solution, confirming the single-phase flow solver’s reliability. The obtained numerical results from the applied Eulerian–Lagrangian multiphase model are also compared with experimental data from a linear shear flow apparatus with suspended buoyant particles, and good agreement was found.

Keywords:

CFD, multiphase flow, particle migration, shear flow, solid–fluid interaction, verification and validation

References

[1] Evans, M.W. & Harlow F.H., 1957, The Particle-in-Cell Method for Hydrodynamic Calculations. Los Alamos National Laboratory Report LA-2139.

[2] Harlow, F., Hydrodynamic problems involving large fluid distortion. Journal of ACM, 4, p. 137, 1957. https://doi.org/10.1145/320868.320871

[3] Harlow, F. & Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Physics of Fluids, 8, pp. 2182–2189, 1965. https://doi.org/10.1063/1.1761178

[4] Yoo, J.Y., & Na, Y., A numerical study of the planar contraction flow of a viscoelas-  tic fluid using the simpler algorithm. Journal of Non-Newtonian Fluid Mechanics, 30, pp. 89–106, 1991. https://doi.org/10.1016/0377-0257(91)80005-5

[5] MCkee, S., Tome, M.F., Feireira, V.G., Cuminato, J.A., Castelo, A. & Sousa, F.S. & Mangiavacchi, N., The MAC method. Computers & Fluids, 37, pp. 907–930, 2008. https://doi.org/10.1016/j.compfluid.2007.10.006

[6] Lemos, C., Higher-order schemes for free surface flows with arbitrary configurations. International Journal of Numerical Methods in Fluids, 23, pp. 545–566, 1996. https:// doi.org/10.1002/(sici)1097-0363(19960930)23:6<545::aid-fld440>3.0.co;2-r

[7] Sussman, M., Smereka, P. & Osher, S.J., A level set approach for computing solu- tions to incompressible two-phase flow. Journal of Computational Physics, 114(1),  pp. 146–159, 1994. https://doi.org/10.1006/jcph.1994.1155

[8] Unverdi, S.H. & Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics, 100(1), pp. 25–37, 1992. https:// doi.org/10.1016/0021-9991(92)90307-k

[9] Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber W., Han, J., Nas, S. & Jan, Y.J., A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 169, pp. 708–759, 2001. https://doi.org/10.1006/ jcph.2001.6726

[10] Razi, M. & Pourghasemi, M., Direct numerical simulation of deformable droplets motion with uncertainphysical properties in macro and micro channels. Computer & Fluids, 154(1), pp. 200–210, 2017. https://doi.org/10.1016/j.compfluid.2017.06.005

[11] Ingber, M.S., Combined static and hydrodynamic interactions of two rough spheres in nonlinear shear flow. Journal of Rheology, 54(4), 707–718, 2010. https://doi. org/10.1122/1.3429067

[12] Ingber, M.S. & Zinchenko, A., Semi-analytic solution of the motion of two spheres in arbitrary shear flow. International Journal of Multiphase Flow, 42, pp. 152–163, 2012. https://doi.org/10.1016/j.ijmultiphaseflow.2012.01.005

[13] Fathi, N., Ingber, M., & Vorobieff, P. Particle interaction in oscillatory Couette and Poiseuille flows. Bulletin of the American Physical Society, 58, 2013.

[14] Fathi, N., Ingber, M., & Vorobieff, P., Particle behavior in linear shear flow: An experi- mental and numerical study. Bulletin of the American Physical Society, 57, 2012.

[15] Fathi, N. & Vorobieff, P., Spherical Particles in a Low Reynolds Number Flow: A V&V Exercise. ASME Verification and Validation Symposium, 2013.

[16] Pourghasemi, M., Fathi, N., Vorobieff, P., Ahmadi, G. & Kevin, R., Anderson. Multiphase flow development on single particle migration in low Reynolds number fluid domains. In Fluids Engineering Division Summer Meeting, vol. 83723, p. V002T04A038. Ameri- can Society of Mechanical Engineers, 2020.

[17] Vorobieff, P., Fathi, N., Aleyasin, S. S. & Ahmadi, G., Transport of a single spherical particle in low Reynolds numbers’ linear shear flows: Experiment and modeling. WIT Transactions on Engineering Sciences, 128, pp. 69–76, 2020.

[18] Nakayama, Y., Kim, K. & Yamamoto, R., Simulating (electro) hydrodynamic effects in colloidal dispersions: Smoothed profile method. The European Physical Journal E, 26(4), pp. 364–368, 2008. https://doi.org/10.1140/epje/i2007-10332-y

[19] Nakayama, Y. & Yamamoto, R., Simulation method to resolve hydrodynamic interac- tions in colloidal dispersion. Physical Review E, 71, 2006. 036707-1-036707-7

[20] Chorin, A.R., Numerical solution of the Navier–Stokes equations. Mathematics of Computation, 22, p. 745, 1968. https://doi.org/10.1090/s0025-5718-1968-0242392-2

[21] Saffman, P.G.T., The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics, 22(2), pp. 385–400, 1965. https://doi.org/10.1017/s0022112065000824