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Self-induced velocity correction for improved drag estimation in Euler-Lagrange point-particle simulations. (English) Zbl 1416.76241

J. Comput. Phys. 376, 160-185 (2019); corrigendum ibid. 401, Article ID 108813, 2 p. (2020).
Summary: In Euler-Lagrange (EL) simulations the force on each particle is obtained from a point-particle model, which is then coupled back to the fluid momentum. The feedback force modifies the flow at the particle location and it is important to evaluate the resulting self-induced velocity disturbance, since the point-particle models are based on the undisturbed flow. An exact solution of the Oseen’s equation for flow generated by a steady Gaussian feedback force was obtained, which along with the corresponding finite Reynolds number numerical simulations, provided a steady model for the self-induced velocity disturbance. The unsteady problem of a time dependent Gaussian feedback force was then theoretically investigated in the zero Reynolds number limit. The corresponding finite Reynolds number unsteady results were obtained using companion numerical simulations. Based on these results an unsteady model for predicting the self-induced velocity disturbance was developed. The two main non-dimensional quantities affecting the self-induced velocity disturbance are the Reynolds number based on Gaussian width \(\operatorname{Re}_\sigma\) and the non-dimensional feedback force \(\widetilde{F}\). The resulting self-induced velocity correction model is general and can be applied in a variety of EL point-particle simulations, with the time history of \(\operatorname{Re}_\sigma\) and \(\widetilde{F}\) as input. The quasi-steady and unsteady versions of the model were tested in the context of a freely settling particle. The unsteady model was shown to predict the self-induced velocity disturbance to reasonable accuracy for a wide range of Reynolds and Stokes numbers. Issues pertaining to practical implementation and limitations are discussed.

MSC:

76M28 Particle methods and lattice-gas methods
76D07 Stokes and related (Oseen, etc.) flows

Software:

Nek5000
Full Text: DOI

References:

[1] Marchioli, C.; Soldati, A.; Kuerten, J.; Arcen, B.; Taniere, A.; Goldensoph, G.; Squires, K.; Cargnelutti, M.; Portela, L., Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: results of an international collaborative benchmark test, Int. J. Multiph. Flow, 34, 879-893 (2008)
[2] Eaton, J. K., Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking, Int. J. Multiph. Flow, 35, 792-800 (2009)
[3] Balachandar, S., A scaling analysis for point-particle approaches to turbulent multiphase flows, Int. J. Multiph. Flow, 35, 801-810 (2009)
[4] Balachandar, S.; Eaton, J. K., Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech., 42, 111-133 (2010) · Zbl 1345.76106
[5] Subramaniam, S., Lagrangian-Eulerian methods for multiphase flows, Prog. Energy Combust. Sci., 39, 215-245 (2013)
[6] Maxey, M. R.; Riley, J. J., Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids, 26, 883-889 (1983) · Zbl 0538.76031
[7] Gatignol, R., The faxén formulas for a rigid particle in an unsteady non-uniform Stokes-flow, J. Méc. Théor. Appl., 2, 143-160 (1983) · Zbl 0544.76032
[8] Magnaudet, J.; Eames, I., The motion of high-Reynolds-number bubbles in inhomogeneous flows, Annu. Rev. Fluid Mech., 32, 659-708 (2000) · Zbl 0989.76082
[9] Schwarzkopf, J. D.; Sommerfeld, M.; Crowe, C. T.; Tsuji, Y., Multiphase Flows with Droplets and Particles (2011), CRC Press
[10] Tenneti, S.; Garg, R.; Subramaniam, S., Drag law for monodisperse gas-solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres, Int. J. Multiph. Flow, 37, 1072-1092 (2011)
[11] Zaidi, A. A.; Tsuji, T.; Tanaka, T., A new relation of drag force for high Stokes number monodisperse spheres by direct numerical simulation, Adv. Powder Technol., 25, 1860-1871 (2014)
[12] Tang, Y. (Yali); Peters, E. (Frank); Kuipers, J. (Hans); Kriebitzsch, S. (Sebastian); van der Hoef, M. (Martin), A new drag correlation from fully resolved simulations of flow past monodisperse static arrays of spheres, AIChE J., 61, 688-698 (2015)
[13] Akiki, G.; Jackson, T.; Balachandar, S., Force variation within arrays of monodisperse spherical particles, Phys. Rev. Fluids, 1, Article 044202 pp. (2016)
[14] Akiki, G.; Jackson, T.; Balachandar, S., Pairwise interaction extended point-particle model for a random array of monodisperse spheres, J. Fluid Mech., 813, 882-928 (2017) · Zbl 1383.76484
[15] Garg, R.; Narayanan, C.; Lakehal, D.; Subramaniam, S., Accurate numerical estimation of interphase momentum transfer in Lagrangian-Eulerian simulations of dispersed two-phase flows, Int. J. Multiph. Flow, 33, 1337-1364 (2007)
[16] Garg, R.; Narayanan, C.; Subramaniam, S., A numerically convergent Lagrangian-Eulerian simulation method for dispersed two-phase flows, Int. J. Multiph. Flow, 35, 376-388 (2009)
[17] Diggs, A.; Balachandar, S., Evaluation of methods for calculating volume fraction in Eulerian-Lagrangian multiphase flow simulations, J. Comput. Phys., 313, 775-798 (2016) · Zbl 1349.76871
[18] Parmar, M.; Haselbacher, A.; Balachandar, S., Equation of motion for a sphere in non-uniform compressible flows, J. Fluid Mech., 699, 352-375 (2012) · Zbl 1248.76124
[19] Annamalai, S.; Balachandar, S., Faxén form of time-domain force on a sphere in unsteady spatially varying viscous compressible flows, J. Fluid Mech., 816, 381-411 (2017) · Zbl 1383.76415
[20] Ireland, P. J.; Desjardins, O., Improving particle drag predictions in Euler-Lagrange simulations with two-way coupling, J. Comput. Phys., 338, 405-430 (2017) · Zbl 1415.76498
[21] Elghobashi, S.; Truesdell, G., On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification, Phys. Fluids A, Fluid Dyn., 5, 1790-1801 (1993) · Zbl 0782.76087
[22] Saffman, P., On the settling speed of free and fixed suspensions, Stud. Appl. Math., 52, 115-127 (1973) · Zbl 0264.76077
[23] Sundaram, S.; Collins, L. R., Numerical considerations in simulating a turbulent suspension of finite-volume particles, J. Comput. Phys., 124, 337-350 (1996) · Zbl 0849.76054
[24] Mehrabadi, M.; Horwitz, J.; Subramaniam, S.; Mani, A., A direct comparison of particle-resolved and point-particle methods in decaying turbulence, J. Fluid Mech., 850, 336-369 (2018) · Zbl 1415.76260
[25] Capecelatro, J.; Desjardins, O., An Euler-Lagrange strategy for simulating particle-laden flows, J. Comput. Phys., 238, 1-31 (2013) · Zbl 1286.76142
[26] Capecelatro, J.; Desjardins, O.; Fox, R. O., Numerical study of collisional particle dynamics in cluster-induced turbulence, J. Fluid Mech., 747 (2014)
[27] Finn, J. R.; Li, M.; Apte, S. V., Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer, J. Fluid Mech., 796, 340-385 (2016) · Zbl 1462.76195
[28] Gualtieri, P.; Picano, F.; Sardina, G.; Casciola, C. M., Exact regularized point particle method for multiphase flows in the two-way coupling regime, J. Fluid Mech., 773, 520-561 (2015) · Zbl 1331.76123
[29] Horwitz, J.; Mani, A., Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows, J. Comput. Phys., 318, 85-109 (2016) · Zbl 1349.76477
[30] Horwitz, J.; Mani, A., Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction, Int. J. Multiph. Flow, 101, 74-84 (2018)
[31] Fukada, T.; Takeuchi, S.; Kajishima, T., Interaction force and residual stress models for volume-averaged momentum equation for flow laden with particles of comparable diameter to computational grid width, Int. J. Multiph. Flow, 85, 298-313 (2016)
[32] Fukada, T.; Fornari, W.; Brandt, L.; Takeuchi, S.; Kajishima, T., A numerical approach for particle-vortex interactions based on volume-averaged equations, Int. J. Multiph. Flow, 104, 188-205 (2018)
[33] Anderson, T. B.; Jackson, R., Fluid mechanical description of fluidized beds. Equations of motion, Ind. Eng. Chem. Fundam., 6, 527-539 (1967)
[34] Drew, D. A., Mathematical modeling of two-phase flow, Annu. Rev. Fluid Mech., 15, 261-291 (1983) · Zbl 0569.76104
[35] P.F. Fischer, J.W. Lottes, S.G. Kerkemeier, et al., nek5000 web page, 2008, URL http (2008).; P.F. Fischer, J.W. Lottes, S.G. Kerkemeier, et al., nek5000 web page, 2008, URL http (2008).
[36] Batchelor, G. K., An Introduction to Fluid Dynamics (2000), Cambridge University Press · Zbl 0958.76001
[37] Esmaily, M.; Horwitz, J., A correction scheme for two-way coupled point-particle simulations on anisotropic grids (2017), arXiv preprint · Zbl 1416.76210
[38] Mei, R.; Adrian, R. J., Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number, J. Fluid Mech., 237, 323-341 (1992) · Zbl 0747.76038
[39] Coimbra, C.; Rangel, R., General solution of the particle momentum equation in unsteady Stokes flows, J. Fluid Mech., 370, 53-72 (1998) · Zbl 0935.76018
[40] Ling, Y.; Haselbacher, A.; Balachandar, S., Importance of unsteady contributions to force and heating for particles in compressible flows: Part 1: modeling and analysis for shock-particle interaction, Int. J. Multiph. Flow, 37, 1026-1044 (2011)
[41] Ling, Y.; Haselbacher, A.; Balachandar, S., Importance of unsteady contributions to force and heating for particles in compressible flows. Part 2: application to particle dispersal by blast waves, Int. J. Multiph. Flow, 37, 1013-1025 (2011)
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