Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T14:04:35.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag model from interface-resolved simulations of particle sedimentation in a periodic domain and vertical turbulent channel flows

Published online by Cambridge University Press:  29 June 2022

Yan Xia ,
Zhaosheng Yu Open the ORCID record for Zhaosheng Yu [Opens in a new window] ,
Dingyi Pan Open the ORCID record for Dingyi Pan [Opens in a new window] ,
Zhaowu Lin  and
Yu Guo Open the ORCID record for Yu Guo [Opens in a new window]
Yan Xia
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Zhaosheng Yu*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Dingyi Pan
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Zhaowu Lin
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Yu Guo
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A drag correlation is established for laminar particle-laden flows, based on data from the interfaced-resolved direct numerical simulations (IR-DNS) of particle sedimentation in a periodic domain at density ratio ranging from 2 to 1000, particle concentration ranging from 0.59 % to 14.16 %, and particle Reynolds number below 132. Our drag decreases slightly with increasing density ratio when the other parameters are fixed. The drag correlation is then corrected to account for the turbulence effect by introducing the relative turbulent kinetic energy, from the IR-DNS data of the upward turbulent channel flows laden with the particles larger than the Kolmogorov length scale at relatively low particle volume fractions. A drift velocity model is developed to obtain the effective slip velocity from the interphase mean velocity difference for the vertical turbulent channel flow by considering the effects of particle inertia, particle concentration distribution and large-scale streamwise vortices.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A25
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akiki, G., Jackson, T.L. & Balachandar, S. 2016 Force variation within arrays of monodisperse spherical particles. Phys. Rev. Fluids 1 (4), 044202.CrossRefGoogle Scholar
Alghalibi, D., Fornari, W., Rosti, M.E. & Brandt, L. 2020 Sedimentation of finite-size particles in quiescent wall-bounded shear-thinning and Newtonian fluids. Intl J. Multiphase Flow 129, 103291.CrossRefGoogle Scholar
Anderson, T.B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527–539.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15 (11), 3496–3513.CrossRefGoogle Scholar
Baker, M.C., Fox, R.O., Kong, B., Capecelatro, J. & Desjardins, O. 2020 Reynolds-stress modeling of cluster-induced turbulence in particle-laden vertical channel flow. Phys. Rev. Fluids 5 (7), 074304.CrossRefGoogle Scholar
Balachandar, S. 2020 Lagrangian and Eulerian drag models that are consistent between Euler–Lagrange and Euler–Euler (two-fluid) approaches for homogeneous systems. Phys. Rev. Fluids 5 (8), 084302.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bec, J., Homann, H. & Ray, S.S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112 (18), 184501.CrossRefGoogle ScholarPubMed
Beetstra, R., van der Hoef, M.A. & Kuipers, J.A.M. 2007 Drag force of intermediate Reynolds number flow past mono-and bidisperse arrays of spheres. AIChE J. 53 (2), 489–501.CrossRefGoogle Scholar
Bogner, S., Mohanty, S. & Rüde, U. 2015 Drag correlation for dilute and moderately dense fluid–particle systems using the lattice Boltzmann method. Intl J. Multiphase Flow 68, 71–79.CrossRefGoogle Scholar
Capecelatro, J., Desjardins, O. & Fox, R.O. 2016 Strongly coupled fluid–particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics. Phys. Fluids 28 (3), 033306.CrossRefGoogle Scholar
Chouippe, A. & Uhlmann, M. 2015 Forcing homogeneous turbulence in direct numerical simulation of particulate flow with interface resolution and gravity. Phys. Fluids 27 (12), 123301.CrossRefGoogle Scholar
Cisse, M., Homann, H. & Bec, J. 2013 Slipping motion of large neutrally buoyant particles in turbulence. J. Fluid Mech. 735, R1.CrossRefGoogle Scholar
Crowe, C.T., Schwarzkopf, J.D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with Droplets and Particles. CRC.CrossRefGoogle Scholar
Deen, N.G., Van Sint Annaland, M., Van der Hoef, M.A. & Kuipers, J.A.M. 2007 Review of discrete particle modeling of fluidized beds. Chem. Engng Sci. 62 (1–2), 28–44.CrossRefGoogle Scholar
Di Felice, R. 1994 The voidage function for fluid–particle interaction systems. Intl J. Multiphase Flow 20 (1), 153–159.CrossRefGoogle Scholar
Ding, J. & Gidaspow, D. 1990 A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523–538.CrossRefGoogle Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48, 89–94.Google Scholar
Fornari, W., Picano, F. & Brandt, L. 2016 a Sedimentation of finite-size spheres in quiescent and turbulent environments. J. Fluid Mech. 788, 640–669.CrossRefGoogle Scholar
Fornari, W., Picano, F., Sardina, G. & Brandt, L. 2016 b Reduced particle settling speed in turbulence. J. Fluid Mech. 808, 153–167.CrossRefGoogle Scholar
Fornari, W., Zade, S., Brandt, L. & Picano, F. 2019 Settling of finite-size particles in turbulence at different volume fractions. Acta Mechanica 230 (2), 413–430.CrossRefGoogle Scholar
Gidaspow, D. 1994 Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic.Google Scholar
Glowinski, R., Pan, T.-W., Hesla, T.I. & Joseph, D.D. 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25 (5), 755–794.CrossRefGoogle Scholar
Good, G.H., Ireland, P.J., Bewley, G.P., Bodenschatz, E., Collins, L.R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.CrossRefGoogle Scholar
Goossens, W.R.A. 2019 Review of the empirical correlations for the drag coefficient of rigid spheres. Powder Technol. 352, 350–359.CrossRefGoogle Scholar
Guazzelli, E. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43, 97–116.CrossRefGoogle Scholar
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014 Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112 (21), 214501.CrossRefGoogle Scholar
Hill, R.J., Koch, D.L. & Ladd, A.J.C. 2001 Moderate-Reynolds-number flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243–278.CrossRefGoogle Scholar
van der Hoef, M.A., Beetstra, R. & Kuipers, J.A.M. 2005 Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233–254.CrossRefGoogle Scholar
van der Hoef, M.A., van Sint Annaland, M., Deen, N.G. & Kuipers, J.A.M. 2008 Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Annu. Rev. Fluid Mech. 40, 47–70.CrossRefGoogle Scholar
Holloway, W., Yin, X. & Sundaresan, S. 2010 Fluid–particle drag in inertial polydisperse gas–solid suspensions. AIChE J. 56 (8), 1995–2004.Google Scholar
Homann, H., Bec, J. & Grauer, R. 2013 Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer. J. Fluid Mech. 721, 155–179.CrossRefGoogle Scholar
Huang, Z., Wang, H., Zhou, Q. & Li, T. 2017 Effects of granular temperature on inter-phase drag in gas–solid flows. Powder Technol. 321, 435–443.CrossRefGoogle Scholar
Huck, P.D., Bateson, C., Volk, R., Cartellier, A., Bourgoin, M. & Aliseda, A. 2018 The role of collective effects on settling velocity enhancement for inertial particles in turbulence. J. Fluid Mech. 846, 1059–1075.CrossRefGoogle Scholar
Igci, Y., Andrews, A.T. IV, Sundaresan, S., Pannala, S. & O'Brien, T. 2008 Filtered two-fluid models for fluidized gas–particle suspensions. AIChE J. 54 (6), 1431–1448.CrossRefGoogle Scholar
Jeffrey, D.J. 1982 Low-Reynolds-number flow between converging spheres. Mathematika 29 (1), 58–66.CrossRefGoogle Scholar
Kandhai, D., Derksen, J.J. & Van den Akker, H.E.A. 2003 Interphase drag coefficients in gas–solid flows. AIChE J. 49 (4), 1060–1065.CrossRefGoogle Scholar
Kidanemariam, A.G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.CrossRefGoogle Scholar
Kravets, B., Rosemann, T., Reinecke, S.R. & Kruggel-Emden, H. 2019 A new drag force and heat transfer correlation derived from direct numerical LBM-simulations of flown through particle packings. Powder Technol. 345, 438–456.CrossRefGoogle Scholar
Kulkarni, P.M. & Morris, J.F. 2008 Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20 (4), 040602.CrossRefGoogle Scholar
Ladd, A.J.C. 1997 Sedimentation of homogeneous suspensions of non-Brownian spheres. Phys. Fluids 9 (3), 491–499.CrossRefGoogle Scholar
Lattanzi, A.M., Yin, X. & Hrenya, C.M. 2020 Heat and momentum transfer to a particle in a laminar boundary layer. J. Fluid Mech. 889, A6.CrossRefGoogle Scholar
Li, J. 1994 Particle-Fluid Two-Phase Flow: the Energy-Minimization Multi-Scale Method. Metallurgical Industry Press.Google Scholar
Li, J. & Huang, W. 2018 From multiscale to mesoscience: addressing mesoscales in mesoregimes of different levels. Annu. Rev. Chem. Biomol. Engng 9, 41–60.CrossRefGoogle ScholarPubMed
Li, T., Wang, L., Rogers, W., Zhou, G. & Ge, W. 2017 An approach for drag correction based on the local heterogeneity for gas–solid flows. AIChE J. 63 (4), 1203–1212.CrossRefGoogle Scholar
Liu, X., Ge, W. & Wang, L. 2020 Scale and structure dependent drag in gas–solid flows. AIChE J. 66 (4), e16883.CrossRefGoogle Scholar
Lomholt, S., Stenum, B. & Maxey, M.R. 2002 Experimental verification of the force coupling method for particulate flows. Intl J. Multiphase Flow 28 (2), 225–246.CrossRefGoogle Scholar
Luo, K., Tan, J., Wang, Z. & Fan, J. 2016 Particle-resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds. AIChE J. 62 (6), 1917–1932.CrossRefGoogle Scholar
Ma, T., Yu, Y., Chen, X. & Zhou, Q. 2020 Effect of anisotropic microstructures on fluid–particle drag in low-Reynolds-number monodisperse gas–solid suspensions. AIChE J. 66 (4), e16910.CrossRefGoogle Scholar
Maxey, M. 2017 Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49, 171–193.CrossRefGoogle Scholar
Mazzei, L. & Lettieri, P. 2007 A drag force closure for uniformly dispersed fluidized suspensions. Chem. Engng Sci. 62 (22), 6129–6142.CrossRefGoogle Scholar
Mehrabadi, M., Tenneti, S., Garg, R. & Subramaniam, S. 2015 Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions. J. Fluid Mech. 770, 210–246.CrossRefGoogle Scholar
Nguyen, N.-Q. & Ladd, A.J.C. 2005 Sedimentation of hard-sphere suspensions at low Reynolds number. J. Fluid Mech. 525, 73.CrossRefGoogle Scholar
Rosa, B., Parishani, H., Ayala, O. & Wang, L.-P. 2016 Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS. Intl J. Multiphase Flow 83, 217–231.CrossRefGoogle Scholar
Rubinstein, G.J., Derksen, J.J. & Sundaresan, S. 2016 Lattice Boltzmann simulations of low-Reynolds-number flow past fluidized spheres: effect of Stokes number on drag force. J. Fluid Mech. 788, 576–601.CrossRefGoogle Scholar
Rubinstein, G.J., Ozel, A., Yin, X., Derksen, J.J. & Sundaresan, S. 2017 Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force. J. Fluid Mech. 833, 599–630.CrossRefGoogle Scholar
Schiller, L. & Naumann, A. 1933 Über die grundlegenden berechnungen bei der schwerkraftaufbereitung. Z. Verein. Deutsch. Ing. 77, 318–321.Google Scholar
Seyed-Ahmadi, A. & Wachs, A. 2020 Microstructure-informed probability-driven point-particle model for hydrodynamic forces and torques in particle-laden flows. J. Fluid Mech. 900, A21.CrossRefGoogle Scholar
Shao, X., Wu, T. & Yu, Z. 2012 Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number. J. Fluid Mech. 693, 319–344.CrossRefGoogle Scholar
Tang, Y., Peters, E.A.J.F. & Kuipers, J.A.M. 2016 Direct numerical simulations of dynamic gas–solid suspensions. AIChE J. 62 (6), 1958–1969.CrossRefGoogle Scholar
Tang, Y., Peters, E.A.J.F., Kuipers, J.A.M., Kriebitzsch, S.H.L. & van der Hoef, M.A. 2015 A new drag correlation from fully resolved simulations of flow past monodisperse static arrays of spheres. AIChE Journal 61 (2), 688–698.CrossRefGoogle Scholar
Tavanashad, V., Passalacqua, A., Fox, R.O. & Subramaniam, S. 2019 Effect of density ratio on velocity fluctuations in dispersed multiphase flow from simulations of finite-size particles. Acta Mechanica 230 (2), 469–484.CrossRefGoogle Scholar
Tavanashad, V., Passalacqua, A. & Subramaniam, S. 2021 Particle-resolved simulation of freely evolving particle suspensions: flow physics and modeling. Intl J. Multiphase Flow 135, 103533.CrossRefGoogle Scholar
Tenneti, S., Garg, R. & Subramaniam, S. 2011 Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Intl J. Multiphase Flow 37 (9), 1072–1092.CrossRefGoogle Scholar
Tenneti, S., Mehrabadi, M. & Subramaniam, S. 2016 Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions. J. Fluid Mech. 788, 695–729.CrossRefGoogle Scholar
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas–solid flow model development. Annu. Rev. Fluid Mech. 46, 199–230.CrossRefGoogle Scholar
Tsuji, Y., Kawaguchi, T. & Tanaka, T. 1993 Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 77 (1), 79–87.CrossRefGoogle Scholar
Tsuji, Y., Tanaka, T. & Ishida, T. 1992 Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71 (3), 239–250.CrossRefGoogle Scholar
Uhlmann, M. & Doychev, T. 2014 Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310–348.CrossRefGoogle Scholar
Wang, J. 2020 Continuum theory for dense gas–solid flow: a state-of-the-art review. Chem. Engng Sci. 215, 115428.CrossRefGoogle Scholar
Wang, L.-P. & Maxey, M.R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Wang, L.-P., Peng, C., Guo, Z. & Yu, Z. 2016 Flow modulation by finite-size neutrally buoyant particles in a turbulent channel flow. Trans. ASME J. Fluids Engng 138 (4), 041306.CrossRefGoogle Scholar
Wang, X., Liu, K. & You, C. 2011 Drag force model corrections based on nonuniform particle distributions in multi-particle systems. Powder Technol. 209 (1–3), 112–118.CrossRefGoogle Scholar
Wen, C.Y. & Yu, Y.H. 1966 Mechanics of fluidization. In Chemical Engineering Progress Symposium Series, vol. 62, pp. 100–111.Google Scholar
Xia, Y., Lin, Z., Pan, D. & Yu, Z. 2021 Turbulence modulation by finite-size heavy particles in a downward turbulent channel flow. Phys. Fluids 33 (6), 063321.CrossRefGoogle Scholar
Xia, Y., Xiong, H., Yu, Z. & Zhu, C. 2020 a Effects of the collision model in interface-resolved simulations of particle-laden turbulent channel flows. Phys. Fluids 32 (10), 103303.CrossRefGoogle Scholar
Xia, Y., Yu, Z. & Guo, Y. 2020 b Interface-resolved numerical simulations of particle-laden turbulent channel flows with spanwise rotation. Phys. Fluids 32 (1), 013303.CrossRefGoogle Scholar
Yang, C.Y. & Lei, U. 1998 The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 371, 179–205.CrossRefGoogle Scholar
Yin, X. & Koch, D.L. 2007 Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers. Phys. Fluids 19 (9), 093302.CrossRefGoogle Scholar
Yin, X. & Koch, D.L. 2008 Lattice-Boltzmann simulation of finite Reynolds number buoyancy-driven bubbly flows in periodic and wall-bounded domains. Phys. Fluids 20 (10), 103304.CrossRefGoogle Scholar
Yu, Z., Lin, Z., Shao, X. & Wang, L. 2017 Effects of particle–fluid density ratio on the interactions between the turbulent channel flow and finite-size particles. Phys. Rev. E 96 (3), 033102.CrossRefGoogle ScholarPubMed
Yu, Z., Lin, Z., Shao, X. & Wang, L.P. 2016 A parallel fictitious domain method for the interface-resolved simulation of particle-laden flows and its application to the turbulent channel flow. Engng Appl. Comput. Fluid Mech. 10 (1), 160–170.Google Scholar
Yu, Z. & Shao, X. 2007 A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227 (1), 292–314.CrossRefGoogle Scholar
Yu, Z., Xia, Y., Guo, Y. & Lin, J. 2021 Modulation of turbulence intensity by heavy finite-size particles in upward channel flow. J. Fluid Mech. 913, A3.CrossRefGoogle Scholar
Yu, Z., Zhu, C., Wang, Y. & Shao, X. 2019 Effects of finite-size neutrally buoyant particles on the turbulent channel flow at a Reynolds number of 395. Appl. Math. Mech. 40 (2), 293–304.CrossRefGoogle Scholar
Zaidi, A.A. 2018 Study of particle inertia effects on drag force of finite sized particles in settling process. Chem. Engng Res. Des. 132, 714–728.CrossRefGoogle Scholar
Zaidi, A.A., Tsuji, T. & Tanaka, T. 2014 A new relation of drag force for high Stokes number monodisperse spheres by direct numerical simulation. Adv. Powder Technol. 25 (6), 1860–1871.CrossRefGoogle Scholar
Zhang, Y.H. & Reese, J.M. 2003 The drag force in two-fluid models of gas–solid flows. Chem. Engng Sci. 58 (8), 1641–1644.CrossRefGoogle Scholar
Zhou, G., Xiong, Q., Wang, L., Wang, X., Ren, X. & Ge, W. 2014 Structure-dependent drag in gas–solid flows studied with direct numerical simulation. Chem. Engng Sci. 116, 9–22.CrossRefGoogle Scholar
Zhou, Q. & Fan, L.-S. 2015 a Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres. J. Fluid Mech. 765, 396.CrossRefGoogle Scholar
Zhou, Q. & Fan, L.-S. 2015 b Direct numerical simulation of moderate-Reynolds-number flow past arrays of rotating spheres. Phys. Fluids 27 (7), 073306.CrossRefGoogle Scholar
Zhu, C., Yu, Z., Pan, D. & Shao, X. 2020 a Interface-resolved direct numerical simulations of the interactions between spheroidal particles and upward vertical turbulent channel flows. J. Fluid Mech. 891, A6.CrossRefGoogle Scholar
Zhu, C., Yu, Z., Shao, X. & Deng, J. 2020 b Interface-resolved numerical simulations of particle-laden turbulent flows in a vertical channel filled with Bingham fluids. J. Fluid Mech. 883, A43.CrossRefGoogle Scholar
Zhu, H.P., Zhou, Z.Y., Yang, R.Y. & Yu, A.B. 2007 Discrete particle simulation of particulate systems: theoretical developments. Chem. Engng Sci. 62 (13), 3378–3396.CrossRefGoogle Scholar