As particle-resolved simulations (PRSs) of turbulent flows laden with finite-size solid particles become feasible, methods are needed to analyze the simulated flows in order to convert the simulation data to a form useful for model development. In this paper, the focus is on turbulence statistics at the moving fluid–solid interfaces. An averaged governing equation is developed to quantify the radial transport of turbulent kinetic energy when viewed in a frame moving with a solid particle. Using an interface-resolved flow field solved by the lattice Boltzmann method (LBM), we computed each term in the transport equation for a forced, particle-laden, homogeneous isotropic turbulence. The results illustrate the distributions and relative importance of volumetric source and sink terms, as well as pressure work, viscous stress work, and turbulence transport. In a decaying particle-laden flow, the dissipation rate and kinetic energy profiles are found to be self-similar.
Issue Section:
Multiphase Flows
References
1.
Balachandar
, S.
, and Eaton
, J. K.
, 2010
, “Turbulent Dispersed Multiphase Flow
,” Annu. Rev. Fluid Mech.
42
(1
), pp. 111
–133
.2.
Corsini
, A.
, Rispoli
, F.
, Sheard
, A. G.
, and Venturini
, P.
, 2013
, “Numerical Simulation of Coal Fly-Ash Erosion in an Induced Draft Fan
,” ASME J. Fluids Eng.
, 135
(1
), p. 081303
.3.
Patro
, P.
, and Dash
, S. K.
, 2014
, “Computations of Particle-Laden Turbulent Jet Flows Based on Eulerian Model
,” ASME J. Fluids Eng.
, 136
(1
), p. 011301
.4.
Maxey
, M. R.
, and Riley
, J. J.
, 1983
, “Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow
,” Phys. Fluids
, 26
(4
), pp. 883
–889
.5.
Wang
, L.-P.
, Rosa
, B.
, Gao
, H.
, He
, G. W.
, and Jin
, G. D.
, 2009
, “Turbulent Collision of Inertial Particles: Point-Particle Based, Hybrid Simulations and Beyond
,” Int. J. Multiphase Flow
, 35
(9
), pp. 854
–867
.6.
Squires
, K. D.
, and Eaton
, J. K.
, 1991
, “Preferential Concentration of Particles by Turbulence
,” Phys. Fluids A
, 3
(5
), pp. 1169
–1179
.7.
Wang
, L.-P.
, and Maxey
, M. R.
, 1993
, “Settling Velocity and Concentration Distribution of Heavy Particles in Homogeneous Isotropic Turbulence
,” J. Fluid Mech.
, 256
, pp. 27
–68
.8.
Squires
, K. D.
, and Eaton
, J. D.
, 1990
, “Particle Response and Turbulence Modification in Isotropic Turbulence
,” Phys. Fluids A
, 2
(7
), pp. 1191
–1203
.9.
Elghobashi
, S.
, and Truesdell
, G.
, 1993
, “On the 2-Way Interaction Between Homogeneous Turbulence and Dispersed Solid Particles. I: Turbulence Modification
,” Phys. Fluids A
, 5
(7
), pp. 1790
–1801
.10.
Sundaram
, S.
, and Collins
, L. R.
, 1997
, “Collision Statistics in an Isotropic Particle-Laden Turbulent Suspension. Part 1. Direct Numerical Simulations
,” J. Fluid Mech.
, 335
, pp. 75
–109
.11.
Zhou
, Y.
, Wexler
, A. S.
, and Wang
, L.-P.
, 2001
, “Modeling Turbulent Collision of Bidisperse Inertial Particles
,” J. Fluid Mech.
, 433
, pp. 77
–104
.12.
Ayala
, O.
, Grabowski
, W. W.
, and Wang
, L.-P.
, 2007
, “A Hybrid Approach for Simulating Turbulent Collisions of Hydrodynamically-Interacting Particles
,” J. Comput. Phys.
, 225
(1
), pp. 51
–73
.13.
Jin
, G. D.
, He
, G. W.
, and Wang
, L.-P.
, 2010
, “Large Eddy Simulation of Collisional Statistics of Inertial Particles in Isotropic Turbulence
,” Phys. Fluids.
, 22
(5
), p. 055106
.14.
Burton
, T. M.
, and Eaton
, J. K.
, 2005
, “Fully Resolved Simulations of Particle-Turbulence Interaction
,” J. Fluid Mech.
, 545
, pp. 67
–111
.15.
Gore
, R. A.
, and Crowe
, C. T.
, 1989
, “Effect of Particle Size on Modulating Turbulent Intensity
,” Int. J. Multiphase Flow
, 15
(2
), pp. 279
–285
.16.
Crowe
, C. T.
, 2000
, “On Models for Turbulence Modulation in Fluid-Particle Flows
,” Int. J. Multiphase Flow
, 26
(5
), pp. 719
–727
.17.
Uhlmann
, M.
, 2005
, “An Immersed Boundary Method With Direct Forcing for the Simulation of Particulate Flows
,” J. Comput. Phys.
209
(2
), pp. 448
–476
.18.
Uhlmann
, M.
, 2008
, “Interface-Resolved Direct Numerical Simulation of Vertical Particulate Channel Flow in the Turbulent Regime
,” Phys. Fluids
, 20
(5
), p. 053305
.19.
Shao
, X.
, Wu
, T.
, and 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
, pp. 319
–344
.20.
Yang
, J. M.
, and Stern
, F.
, 2014
, “A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows
,” ASME J. Fluids Eng.
, 136
(4
), p. 040904
.21.
Zhang
, Z.
, and Prosperetti
, A.
, 2005
, “A Second-Order Method for Three-Dimensional Particle Simulation
,” J. Comput. Phys.
, 210
(1
), pp. 292
–324
.22.
Yeo
, K.
, Dong
, S.
, Climent
, E.
, and Maxey
, M. R.
, 2010
, “Modulation of Homogeneous Turbulence Seeded With Finite Size Bubbles or Particles
,” Int. J. Multiphase Flow
, 36
(3
), pp. 221
–233
.23.
Homann
, H.
, and Bec
, J.
, 2010
, “Finite-Size Effects in the Dynamics of Neutrally Buoyant Particles in Turbulent Flow
,” J. Fluid Mech.
, 651
, pp. 81
–91
.24.
Gao
, H.
, Li
, H.
, and Wang
, L.-P.
, 2013
, “Lattice Boltzmann Simulation of Turbulent Flow Laden With Finite-Size Particles
,” Comput. Math. Appl.
, 65
(2
), pp. 194
–210
.25.
Wang
, L.-P.
, Ayala
, O.
, Gao
, H.
, Andersen
, C.
, and Mathews
, K.
, 2014
, “Study of Forced Turbulence and Its Modulation by Finite-Size Solid Particles Using the Lattice Boltzmann Approach
,” Comput. Math. Appl.
, 67
(2
), pp. 363
–380
.26.
Gillissen
, J.
, 2013
, “Turbulent Drag Reduction Using Fluid Spheres
,” J. Fluid Mech.
, 716
, pp. 83
–95
.27.
Ten Cate
, A.
, Derksen
, J. J.
, Portela
, L. M.
, and van den Akker
, H. E. A.
, 2004
, “Fully Resolved Simulations of Colliding Monodisperse Spheres in Forced Isotropic Turbulence
,” J. Fluid Mech.
, 519
, pp. 233
–271
.28.
Wang
, L.-P.
, Peng
, C.
, Guo
, Z.
, and Yu
, Z.
, 2015
, “Flow Modulation by Finite-Size Neutrally Buoyant Particles in a Turbulent Channel Flow
,” ASME J. Fluids Eng.
(in press).29.
Peng
, C.
, Teng
, Y.
, Hwang
, B.
, Guo
, Z.
, and Wang
, L.-P.
, 2015
, “Implementation Issues and Benchmarking of Lattice Boltzmann Method for Moving Particle Simulations in a Viscous Flow
,” Comput. Math. Appl.
(in press).30.
Lucci
, F.
, Ferrante
, A.
, and Elghobashi
, S.
, 2010
, “Modulation of Isotropic Turbulence by Particles of Taylor Length-Scale Size
,” J. Fluid Mech.
, 650
, pp. 5
–55
.31.
Chen
, S.
, and Doolen
, G.
, 1998
, “Lattice Boltzmann Method for Fluid Flows
,” Annu. Rev. Fluid Mech.
, 30
(1
), pp. 329
–364
.32.
Qian
, Y. H.
, d'Humières
, D.
, and Lallemand
, P.
, 1992
, “Lattice BGK Models for Navier–Stokes Equation
,” Europhys. Lett.
, 17
(6BIS
), pp. 479
–484
.33.
d'Humières
, D.
, Ginzburg
, I.
, Krafczyk
, M.
, Lallemand
, P.
, and Luo
, L.-S.
, 2002
, “Multiple-Relaxation-Time Lattice Boltzmann Models in Three-Dimensions
,” Phil. Trans. R. Soc. London A
, 360
(1792
), pp. 437
–451
.34.
Wang
, L.-P.
, Peng
, C.
, Guo
, Z.
, and Yu
, Z.
, 2015
, “Lattice Boltzmann Simulation of Particle-Laden Turbulent Channel Flow
,” Comput. Fluids
(in press).35.
Guo
, Z.
, Zheng
, C.
, and Shi
, B.
, 2002
, “Discrete Lattice Effects on the Forcing Term in the Lattice Boltzmann Method
,” Phys. Rev. E.
, 65
(4
), p. 046308
.36.
Lu
, J.
, Han
, H.
, Shi
, B.
, and Guo
, Z.
, 2012
, “Immersed Boundary Lattice Boltzmann Model Based on Multiple Relaxation Times
,” Phys. Rev. E
, 85
(1
), p. 016711
.37.
Lallemand
, P.
, and Luo
, L.-S.
, 2003
, “Lattice Boltzmann Method for Moving Boundaries
,” J. Comp. Phys.
, 184
(2
), pp. 406
–421
.38.
Chen
, L.
, Yu
, Y.
, Lu
, J.
, and Hou
, G.
, 2014
, “A Comparative Study of Lattice Boltzmann Methods Using Bounce-Back Schemes and Immersed Boundary Ones for Flow Acoustic Problems
,” Int. J. Numer. Meth. Fluids
, 74
(6
), pp. 439
–467
.39.
Wen
, B.
, Zhang
, C.
, Tu
, Y.
, Wang
, C.
, and Fang
, H.
, 2014
, “Galilean Invariant Fluid-Solid Interfacial Dynamics in Lattice Boltzmann Simulations
,” J. Comput. Phys.
, 266
, pp. 161
–170
.40.
Nguyen
, N. Q.
, and Ladd
, A. J. C.
, 2002
, “Lubrication Corrections for Lattice-Boltzmann Simulations of Particle Suspensions
,” Phys. Rev. E
, 66
(4
), p. 046708
.41.
Dance
, S. L.
, and Maxey
, M. R.
, 2003
, “Incorporation of Lubrication Effects Into the Force-Coupling Method for Particulate Two-Phase Flow
,” J. Comput. Phys.
, 189
(1
), pp. 212
–238
.42.
Peng
, Y.
, Liao
, W.
, Luo
, L.-S.
, and Wang
, L.-P.
, 2010
, “Comparison of the Lattice Boltzmann and Pseudo-Spectral Methods for Decaying Turbulence: Low-Order Statistics
,” Comput. Fluids
, 39
(4
), pp. 568
–591
.43.
Crowe
, C. T.
, Schwarzkopf
, J. D.
, Sommerfeld
, M.
, and Tsuji
, Y.
, 2012
, Multiphase Flows With Droplets and Particles
, 2nd ed., CRC Press
, Boca Raton
.44.
Fox
, R. O.
, 2012
, “Large-Eddy-Simulation Tools for Multiphase Flows
,” Annu. Rev. Fluid Mech.
, 44
(1
), pp. 47
–76
.45.
Mei
, R.
, Luo
, L.-S.
, Lallemand
, P.
, and d'Humières
, D.
, 2006
, “Consistent Initial Conditions for Lattice Boltzmann Simulations
,” Comput. Fluids
, 35
(8–9
), pp. 855
–862
.46.
Yu
, H.
, Luo
, L.-S.
, and Girimaji
, S. S.
, 2006
, “LES of Turbulent Square Jet Flow Using an MRT Lattice Boltzmann Model
,” Comput. Fluids
, 35
(8–9
), pp. 957
–965
.Copyright © 2016 by ASME
You do not currently have access to this content.
