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A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow. (English) Zbl 1419.76372

Summary: Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76T20 Suspensions

Software:

Proteus
Full Text: DOI

References:

[1] Balachandar, S.; Eaton, J. K., Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech., 42, 111-133, (2010) · Zbl 1345.76106
[2] Botto, L.; Prosperetti, A., A fully resolved numerical simulation of turbulent flow past one or several spherical particles, Phys. Fluids, 24, 1, (2012)
[3] Bouzidi, M.; Firdaouss, M.; Lallemand, P., Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids, 13, 11, 3452-3459, (2001) · Zbl 1184.76068
[4] Brady, J. F.; Bossis, G., Stokesian dynamics, Annu. Rev. Fluid Mech., 20, 1, 111-157, (1988)
[5] Brändle De Motta, J. C.; Breugem, W.-P.; Gazanion, B.; Estivalezes, J.-L.; Vincent, S.; Climent, E., Numerical modelling of finite-size particle collisions in a viscous fluid, Phys. Fluids, 25, 8, (2013)
[6] Brändle De Motta, J. C.; Costa, P.; Derksen, J. J.; Peng, C.; Wang, L.-P.; Breugem, W.-P.; Estivalezes, J. L.; Vincent, S.; Climent, E.; Fede, P., Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows, Comput. Fluids, 179, 1-14, (2019) · Zbl 1411.76041
[7] Brändle De Motta, J. C.; Estivalezes, J.-L.; Climent, E.; Vincent, S., Local dissipation properties and collision dynamics in a sustained homogeneous turbulent suspension composed of finite size particles, Intl J. Multiphase Flow, 85, 369-379, (2016)
[8] Breugem, W.-P.2010A combined soft-sphere collision/immersed boundary method for resolved simulations of particulate flows. In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, pp. 2381-2392. American Society of Mechanical Engineers.
[9] Burton, T. M.; Eaton, J. K., Fully resolved simulations of particle-turbulence interaction, J. Fluid Mech., 545, 67-111, (2005) · Zbl 1085.76565
[10] Caiazzo, A., Analysis of lattice Boltzmann nodes initialisation in moving boundary problems, Intl J. Comput. Fluid Dyn., 8, 1-4, 3-10, (2008) · Zbl 1187.76723
[11] Du Cluzeau, A.; Bois, G.; Toutant, A., Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations, J. Fluid Mech., 866, 132-168, (2019) · Zbl 1415.76630
[12] Costa, P.; Picano, F.; Brandt, L.; Breugem, W.-P., Universal scaling laws for dense particle suspensions in turbulent wall-bounded flows, Phys. Rev. Lett., 117, 13, (2016)
[13] Crowe, C. T.; Schwarzkopf, J. D.; Sommerfeld, M.; Tsuji, Y., Multiphase Flows With Droplets and Particles, (2011), CRC Press
[14] Eaton, J. K., Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking, Intl J. Multiphase Flow, 35, 9, 792-800, (2009)
[15] Elghobashi, S.; Truesdell, G. C., On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification, Phys. Fluids, 5, 7, 1790-1801, (1993) · Zbl 0782.76087
[16] Eshghinejadfard, A.; Abdelsamie, A.; Hosseini, S. A.; Thévenin, D., Immersed boundary lattice Boltzmann simulation of turbulent channel flows in the presence of spherical particles, Intl J. Multiphase Flow, 96, 161-172, (2017)
[17] Feng, Z.-G.; Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202, 1, 20-51, (2005) · Zbl 1076.76568
[18] Feng, Z.-G.; Michaelides, E. E., Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows, Comput. Fluids, 38, 2, 370-381, (2009) · Zbl 1237.76137
[19] Ferrante, A.; Elghobashi, S., On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence, Phys. Fluids, 15, 2, 315-329, (2003) · Zbl 1185.76126
[20] Gao, H.; Li, H.; Wang, L.-P., Lattice Boltzmann simulation of turbulent flow laden with finite-size particles, Comput. Maths. Applics., 65, 2, 194-210, (2013) · Zbl 1268.76045
[21] Glowinski, R.; Pan, T.-W.; Hesla, T. I.; Joseph, D. D., A distributed lagrange multiplier/fictitious domain method for particulate flows, Intl J. Multiphase Flow, 25, 5, 755-794, (1999) · Zbl 1137.76592
[22] Gore, R. A.; Crowe, C. T., Effect of particle size on modulating turbulent intensity, Intl J. Multiphase Flow, 15, 2, 279-285, (1989)
[23] Gupta, A.; Clercx, H. J. H.; Toschi, F., Computational study of radial particle migration and stresslet distributions in particle-laden turbulent pipe flow, Eur. Phys. J. E, 41, 3, 34, (2018)
[24] Hall, D., Measurements of the mean force on a particle near a boundary in turbulent flow, J. Fluid Mech., 187, 451-466, (1988)
[25] Joseph, G.2003 Collisional dynamics of macroscopic particles in a viscous fluid. PhD thesis, California Institute of Technology, Pasadena, CA.
[26] Kajishima, T.; Takiguchi, S.; Hamasaki, H.; Miyake, Y., Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding, JSME Intl J., 44, 4, 526-535, (2001)
[27] Kataoka, I.; Serizawa, A., Basic equations of turbulence in gas – liquid two-phase flow, Intl J. Multiphase Flow, 15, 5, 843-855, (1989) · Zbl 0684.76054
[28] Kim, J.; Moin, P.; Moser, R. D., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177, 133-166, (1987) · Zbl 0616.76071
[29] Kulick, J. D.; Fessler, J. R.; Eaton, J. K., Particle response and turbulence modification in fully developed channel flow, J. Fluid Mech., 277, 109-134, (1994)
[30] Kurose, R.; Komori, S., Drag and lift forces on a rotating sphere in a linear shear flow, J. Fluid Mech., 384, 183-206, (1999) · Zbl 0939.76099
[31] Kussin, J.; Sommerfeld, M., Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. Fluids, 33, 1, 143-159, (2002)
[32] Lammers, P.; Beronov, K. N.; Volkert, R.; Brenner, G.; Durst, F., Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow, Comput. Fluids, 35, 1137-1153, (2006) · Zbl 1177.76160
[33] Legendre, D.; Zenit, R.; Daniel, C.; Guiraud, P., A note on the modelling of the bouncing of spherical drops or solid spheres on a wall in viscous fluid, Chem. Engng Sci., 61, 11, 3543-3549, (2006)
[34] Li, Y.; Mclaughlin, J. B.; Kontomaris, K.; Portela, L., Numerical simulation of particle-laden turbulent channel flow, Phys. Fluids, 13, 10, 2957-2967, (2001) · Zbl 1184.76325
[35] Lucci, F.; Ferrante, A.; Elghobashi, S., Modulation of isotropic turbulence by particles of Taylor length-scale size, J. Fluid Mech., 650, 5-55, (2010) · Zbl 1189.76251
[36] Maxey, M. R., Simulation methods for particulate flows and concentrated suspensions, Annu. Rev. Fluid Mech., 49, 171-193, (2017) · Zbl 1359.76232
[37] Maxey, M. R.; Riley, J. J., Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids, 26, 4, 883-889, (1983) · Zbl 0538.76031
[38] Mei, R., An approximate expression for the shear lift force on a spherical particle at finite Reynolds number, Intl J. Multiphase Flow, 18, 1, 145-147, (1992) · Zbl 1144.76419
[39] Mollinger, A. M.; Nieuwstadt, F. T. M., Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer, J. Fluid Mech., 316, 285-306, (1996)
[40] Pan, Y.; Banerjee, S., Numerical investigation of the effects of large particles on wall-turbulence, Phys. Fluids, 9, 12, 3786-3807, (1997)
[41] Paris, A. D.2001 Turbulence attenuation in a particle-laden channel flow. PhD thesis, Stanford University, CA.
[42] Peng, C.; Geneva, N.; Guo, Z.; Wang, L.-P., Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method, J. Comput. Phys., 357, 16-42, (2018) · Zbl 1381.76131
[43] Peng, C.; Teng, Y.; Hwang, B.; Guo, Z.; Wang, L.-P., Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow, Comput. Maths Applics., 72, 2, 349-374, (2016) · Zbl 1358.76061
[44] Peng, C.; Wang, L.-P., Direct numerical simulations of turbulent pipe flow laden with finite-size neutrally buoyant particles at low flow Reynolds number, Acta Mechanica, 230, 517-539, (2018) · Zbl 1412.76049
[45] Picano, F.; Breugem, W.-P.; Brandt, L., Turbulent channel flow of dense suspensions of neutrally buoyant spheres, J. Fluid Mech., 764, 463-487, (2015)
[46] Prosperetti, A.; Tryggvason, G., Computational Methods for Multiphase Flow, (2009), Cambridge University Press
[47] Reeks, M. W., The transport of discrete particles in inhomogeneous turbulence, J. Aero. Sci., 14, 6, 729-739, (1983)
[48] Saffman, P. G. T., The lift on a small sphere in a slow shear flow, J. Fluid Mech., 22, 2, 385-400, (1965) · Zbl 0218.76043
[49] Santarelli, C.; Roussel, J.; Fröhlich, J., Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel, Chem. Engng Sci., 141, 46-62, (2016)
[50] Shao, X.; Wu, T.; Yu, Z., Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number, J. Fluid Mech., 693, 319-344, (2012) · Zbl 1250.76176
[51] Squires, K. D.; Eaton, J. K., Particle response and turbulence modification in isotropic turbulence, Phys. Fluids, 2, 7, 1191-1203, (1990)
[52] Tanaka, T.; Eaton, J. K., Classification of turbulence modification by dispersed spheres using a novel dimensionless number, Phys. Rev. Lett., 101, 11, (2008)
[53] Tanaka, T.; Eaton, J. K., Sub-Kolmogorov resolution partical image velocimetry measurements of particle-laden forced turbulence, J. Fluid Mech., 643, 177-206, (2010) · Zbl 1189.76046
[54] Tao, S.; Hu, J.; Guo, Z., An investigation on momentum exchange methods and refilling algorithms for lattice Boltzmann simulation of particulate flows, Comput. Fluids, 133, 1-14, (2016) · Zbl 1390.76771
[55] Ten Cate, A.; Derksen, J. J.; Portela, L. M.; Van Den Akker, H. E. A., Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence, J. Fluid Mech., 519, 233-271, (2004) · Zbl 1065.76194
[56] Ten Cate, A.; Nieuwstad, C. H.; Derksen, J. J.; Van Den Akker, H. E. A., Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. Fluids, 14, 11, 4012-4025, (2002) · Zbl 1185.76073
[57] Tenneti, S.; Subramaniam, S., Particle-resolved direct numerical simulation for gas-solid flow model development, Annu. Rev. Fluid Mech., 46, 199-230, (2014) · Zbl 1297.76179
[58] Uhlmann, M., Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime, Phys. Fluids, 20, 5, (2008) · Zbl 1182.76785
[59] Uhlmann, M.; Chouippe, A., Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence, J. Fluid Mech., 812, 991-1023, (2017) · Zbl 1383.76295
[60] Vreman, A. W., Turbulence attenuation in particle-laden flow in smooth and rough channels, J. Fluid Mech., 773, 103-136, (2015)
[61] Vreman, A. W., Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres, J. Fluid Mech., 796, 40-85, (2016) · Zbl 1462.76081
[62] Vreman, A. W.; Kuerten, J. G. M., Turbulent channel flow past a moving array of spheres, J. Fluid Mech., 856, 580-632, (2018) · Zbl 1415.76701
[63] Wang, L.-P.; Ardila, O. G. C.; Ayala, O.; Gao, H.; Peng, C., Study of local turbulence profiles relative to the particle surface in particle-laden turbulent flows, J. Fluids Engng, 138, 4, (2016)
[64] Wang, L.-P.; Peng, C.; Guo, Z.; Yu, Z., Flow modulation by finite-size neutrally buoyant particles in a turbulent channel flow, J. Fluids Engng, 138, 4, (2016)
[65] Wang, L.-P.; Peng, C.; Guo, Z.; Yu, Z., Lattice Boltzmann simulation of particle-laden turbulent channel flow, Comput. Fluids, 124, 226-236, (2016) · Zbl 1390.76774
[66] Wen, B.; Zhang, C.; Tu, Y.; Wang, C.; Fang, H., Galilean invariant fluid – solid interfacial dynamics in lattice Boltzmann simulations, J. Comput. Phys., 266, 161-170, (2014) · Zbl 1362.76044
[67] Wu, T.; Shao, X.; Yu, Z., Fully resolved numerical simulation of turbulent pipe flows laden with large neutrally-buoyant particles, J. Hydrodyn., 23, 1, 21-25, (2011)
[68] Xu, Y.; Subramaniam, S., Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study, Flow, Turbul. Combust., 85, 3, 735-761, (2010) · Zbl 1410.76127
[69] Yang, F.-L.; Hunt, M. L., Dynamics of particle – particle collisions in a viscous liquid, Phys. Fluids, 18, 12, (2006) · Zbl 1146.76569
[70] Yu, Z.; Lin, Z.; Shao, X.; Wang, L.-P., Effects of particle-fluid density ratio on the interactions between the turbulent channel flow and finite-size particles, Phys. Rev. E, 96, (2017)
[71] Zeng, L.; Balachandar, S.; Fischer, P.; Najjar, F., Interactions of a stationary finite-sized particle with wall turbulence, J. Fluid Mech., 594, 271-305, (2008) · Zbl 1159.76337
[72] Zhao, W.; Yong, W.-A., Single-node second-order boundary schemes for the lattice Boltzmann method, J. Comput. Phys., 329, 6, 1-15, (2017) · Zbl 1406.76075
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