Abstract
Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Re p = 50 and the ratio of the particle diameter d p to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (d p > η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.
Similar content being viewed by others
References
Ahmadi, G., Ma, D.: A thermodynamical formulation for dispersed multiphase turbulent flows: I. Basic theory. Int. J. Multiph. Flow 16(2), 323–340 (1990)
Ahmadi, G., Ma, D.: A thermodynamical formulation for dispersed multiphase turbulent flows: II. Simple shear flows for dense mixtures. Int. J. Multiph. Flow 16(2), 341–351 (1990)
Apte, S.V., Martin, M., Patankar, N.A.: A numerical method for fully resolved simulation (FRS) of rigid particle flow interactions in complex flows. J. Comput. Phys. 228, 2712–2738 (2009)
Bagchi, P., Balachandar, S.: Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15(11), 3496–3513 (2003)
Bagchi, P., Balachandar, S.: Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123 (2004)
Balzer, G., Boelle, A., Simonin, O.: Eulerian gas–solid flow modelling of dense fluidized bed. In: Fluidization VIII. International Symposium of Engineering Foundation, pp. 1125–1134 (1998)
Bhusarapu, S., Al Dahhan, M.H., Duduković, M.P.: Solids flow mapping in a gas–solid riser: mean holdup and velocity fields. Powder Technol. 163(1–2), 98–123 (2006)
Bolio, E., Yasuna, J., Sinclair, J.: Dilute turbulent gas-solid flow in risers with particle-particle interactions. AIChE J. 41(5), 1375–1388 (1995)
Bolio, E.J., Sinclair, J.L.: Gas turbulence modulation in the pneumatic conveying of massive particles in vertical tubes. Int. J. Multiph. Flow 21(6), 985–1001 (1995)
Brereton, C.M.H., Grace, J.R.: Microstructural aspects of the behavior of circulating fluidized-beds. Chem. Eng. Sci. 48(14), 2565–2572 (1993)
Burton, T.M., Eaton, J.K.: Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111 (2005)
Cocco, R., Shaffer, F., Hays, R., Reddy Karri, S.B., Knowlton, T.: Particle clusters in and above fluidized beds. Powder Technol. 203(1), 3–11 (2010)
Drew, D.A., Passman, S.L.: Theory of multicomponent fluids. Applied mathematical sciences, vol. 135. Springer (1999)
Fan, M., Marshall, W., Daugaard, D., Brown, R.C.: Steam activation of chars produced from oat hulls and corn stover. Bioresour. Technol. 93(1), 103–107 (2004)
Garg, R., Tenneti, S., Mohd.-Yusof, J., Subramaniam, S.: Direct numerical simulation of gas-solid flow based on the immersed boundary method. Engineering Science Reference, Ch. Computational Gas-Solids Flows and Reacting Systems: Theory, Methods and Practice (2009)
Glowinski, R., Pan, T., Helsa, T., Joseph, D.: A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiph. Flow 25(5), 755–794 (1999)
Glowinski, R., Pan, T.W., Helsa, T.I., Joseph, D.D., Periaux, J.: A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169(2), 363–426 (2001)
Goldstein, D., Handler, R., Sirovich, L.: Modeling a no–slip flow boundary with an external force field. J. Comput. Phys. 105(2), 354–366 (1993)
Gore, R.A., Crowe, C.T.: Effect of particle size on modulating turbulent intensity. Int. J. Multiph. Flow 15(2), 279–285 (1989)
Grace, J., Tuot, J.: Theory for cluster formation in vertically conveyed suspensions of intermediate density. T. I. Chem. Eng.–Lond. 57(1), 49–54 (1979)
Halvorsen, B., Guenther, C., O’Brien, T.J.: CFD calculations for scaling of a bubbling fluidized bed. In: Proceedings of the AIChE Annual Meeting, pp. 16–21. AIChE, San Francisco (2003)
Heynderickx, G.J., Das, A., De Wilde, J., Marin, G.: Effect of clustering on gas-solid drag in dilute two-phase flow. Ind. Eng. Chem. Res. 43(16), 4635–4646 (2004)
Hill, R., Koch, D.L., Ladd, A.J.C.: The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213–241 (2001)
Hill, R., Koch, D.L., Ladd, A.J.C.: Moderate-Reynolds-numbers flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243–278 (2001)
Hu, H.H., Patankar, N.A., Zhu, M.Y.: Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. J. Comput. Phys. 169(2), 427–462 (2001)
Jackson, R.: The dynamics of fluidized particles. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge (2000)
Kim, D., Choi, H.: Immersed boundary method for flow around an arbitrarily moving body. J. Comput. Phys. 212, 662–680 (2006)
Kim, J., Moin, P.: Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323 (1985)
Knowlton, T., Karri, S., Issangya, A.: Scale-up of fluidized-bed hydrodynamics. Powder Technol. 150, 72–77 (2005)
Krol, S.A.P., De Lasa, H.: Particle clustering in down flow reactors. Powder Technol. 108(1), 6–20 (2000)
Ladd, A.J.C.: Simulations of particle-fluid suspensions with the Lattice–Boltzmann equation. In: Plenary Lecture at the Third M.I.T. Conference on Computational Fluid and Solid Mechanics. Cambridge, Massachusetts (2005)
Ladd, A.J.C., Verberg, R.: Lattice–Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104, 119–1251 (2001)
Langford, J.A.: Toward Ideal Large-Eddy Simulation. Ph.D. thesis, University of Illinois at Urbana-Champaign, IL (2000)
Li, F.X., Fan, L.-S.: Clean coal conversion processes progress and challenges. Energy Environ. Sci. 1, 248–267 (2008)
Lucci, F., Ferrante, A., Elghobashi, S.: Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5 (2010)
Mohd. Yusof, J.: Interaction of Massive Particles with Turbulence. Ph.D. thesis, Cornell University (1996)
Moran, J.C., Glicksman, L.R.: Experimental and numerical studies on the gas flow srrounding a single cluster applied to a circulating fluidized bed. Chem. Eng. Sci. 58(9), 1879–1886 (2003)
Moran, J.C., Glicksman, L.R.: Mean and fluctuating gas phase velocities inside a circulating fluidized bed. Chem. Eng. Sci. 58, 1867–1878 (2003)
Morinishi, Y., Lund, T.S., Vasilyev, O.V., Moin, P.: Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 142, 1 (1998)
Nomura, T., Hughes, T.J.R.: An arbitrary Lagrangian–Eulerian finite element method for interaction of fluid and a rigid body. Comput. Methods Appl. Mech. Eng. 95, 115 (1992)
O’Brien, T., Syamlal, M.: Particle cluster effects in the numerical simulation of a circulating fluidized bed. In: Fourth International Conference on Circulating Fluidized Beds. Somerset, PA (1993)
Pai, M.G., Subramaniam, S.: Second-order transport due to fluctuations in clustering particle systems. In: Proceedings of the 60th Annual Meeting of the Division of Fluid Dynamics. The American Physical Society. Salt Lake City, UT (2007)
Pai, M.G., Subramaniam, S.: A comprehensive probability density function formalism for multiphase flows. J. Fluid Mech. 628, 181–228 (2009)
Patankar, N., Singh, P., Joseph, D., Glowinski, R., Pan, T.: A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiph. Flow 26(9), 1509–1524 (2000)
Peskin, C.S.: Flow patterns around heart valves: a numerical method. J. Comput. Phys. 25, 220 (1977)
Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479–517 (2002)
Pita, J., Sundaresan, S.: Gas-solid flow in vertical tubes. AIChE J. 37(7), 1009–1018 (1991)
Pita, J., Sundaresan, S.: Developing flow of a gas-particle mixture in a vertical riser. AIChE J. 39(4), 541–552 (1993)
Pope, S.: Turbulent Flows. Cambridge University Press (2000)
Prosperetti, A., Oguz, H.: PHYSALIS: a new o(N) method for the numerical simulation of disperse systems. Part I: potential flow of spheres. J. Comput. Phys 167, 196–216 (2001)
Rogallo, R.S.: Numerical Experiments in Homogeneous Turbulence. Technical Report TM81315, NASA (1981)
Saw, E.W., Shaw, R.A., Ayyalasomayajula, S., Chuang, P.Y., Gylfason, A.: Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100(21), 214501 (2008)
Sharma, N., Patankar, N.: A fast computation technique for the direct numerical simulation of rigid particulate flows. J. Comput. Phys. 205(2), 439–457 (2005)
Sinclair, J., Jackson, R.: Gas-particle flow in a vertical pipe with particle-particle interactions. AIChE J. 35, 1473–1486 (1989)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications. Wiley, NY (1995)
Takagi, S., Oguz, H., Zhang, Z., Prosperetti, A.: PHYSALIS: a new method for particle simulation. Part II: two-dimensional Navier-stokes flow around cylinders. J. Comput. Phys. 187, 371–390 (2003)
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)
Tenneti, S., Garg, R., Hrenya, C.M., Fox, R.O., Subramaniam, S.: Direct numerical simulation of gas-solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol. 203(1), 57–69 (2010)
Tsuji, Y., Morikawa, Y., Shiomi, H.: LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434 (1984)
Uhlmann, M.: An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209(2), 448–476 (2005)
Uhlmann, M.: Investigating turbulent particulate channel flow with interface-resolved DNS. In: 6th International Conference on Multiphase Flow ICMF 2007. Leipzig, Germany, 9–13 July 2007
van der Hoef, M.A., Beetstra, R., Kuipers, J.: 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 (2005)
Vasilyev, O.V.: High order finite difference schemes on non-uniform meshes with good conservation properties. J. Comput. Phys. 157, 746–761 (1999)
Wylie, J., Koch, D.L., Ladd, A.: Rheology of suspensions with high particle inertia and moderate fluid inertia. J. Fluid Mech. 480, 95 (2003)
Xu, Y.: Modeling and direct numerical simulation of particle–laden turbulent flows. Ph.D. thesis, Iowa State Univ., Ames, IA (2008)
Xu, Y., Subramaniam, S.: Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows. Phys. Fluids doi:10.1063/1.2756579 (2007)
Yang, N., Wang, W., Ge, W., Li, J.H.: CFD simulation of concurrent-up gas-solid flow in circulating fluidized beds with structure-dependent drag coefficient. Chem. Eng. J. 96(1–3), 71–80 (2003)
Yin, X., Sundaresan, S.: Drag law for bidisperse gas-solid suspensions containing equally sized spheres. Ind. Eng. Chem. Res. 48(1), 227–241 (2008)
Zhang, Z., Prosperetti, A.: A method for particle simulations. J. Appl. Mech. 70, 64–74 (2003)
Zhang, Z., Prosperetti, A.: A second-order method for three-dimensional particle flow simulations. J. Comput. Phys 210, 292–324 (2005)
Zhang, M., Qian, Z., Yu, H., Wei, F.: The solid flow structure in a circulating fluidized bed riser/downer of 0.42-m diameter. Powder Technol. 129(1–3), 46–52 (2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted for the Special Issue dedicated to S. B. Pope.
Rights and permissions
About this article
Cite this article
Xu, Y., Subramaniam, S. Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study. Flow Turbulence Combust 85, 735–761 (2010). https://doi.org/10.1007/s10494-010-9298-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-010-9298-8