Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows

Patel, Ravi G.; Desjardins, Olivier; Kong, Bo; Capecelatro, Jesse; Fox, Rodney O.

doi:10.1002/aic.15949

Title: Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows

Abstract

Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posing fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent Eulerian statistics remains a challenge for all methods.

Authors:

Patel, Ravi G. ^[1]; Desjardins, Olivier ^[1];

^[2]; Capecelatro, Jesse ^[3]; Fox, Rodney O. ^[4]

Cornell Univ., Ithaca, NY (United States)
Ames Lab., Ames, IA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)
Ames Lab. and Iowa State Univ., Ames, IA (United States)

Publication Date:: 2017-09-01

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1409363

Alternate Identifier(s):: OSTI ID: 1392168

Report Number(s):: IS-J-9490
Journal ID: ISSN 0001-1541

Grant/Contract Number:: AC02-07CH11358

Resource Type:: Accepted Manuscript

Journal Name:: AIChE Journal

Additional Journal Information:: Journal Volume: 63; Journal Issue: 12; Journal ID: ISSN 0001-1541

Publisher:: American Institute of Chemical Engineers

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; computational fluid dynamics (CFD); fluid-particle flow; kinetic theory of granular flow; Euler-Lagrange method; quadrature-based moment methods

Citation Formats


                    Patel, Ravi G., Desjardins, Olivier, Kong, Bo, Capecelatro, Jesse, and Fox, Rodney O. Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows.  United States: N. p., 2017. 
Web.  doi:10.1002/aic.15949.

Copy to clipboard


                    Patel, Ravi G., Desjardins, Olivier, Kong, Bo, Capecelatro, Jesse, & Fox, Rodney O. Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows.  United States.  https://doi.org/10.1002/aic.15949

Copy to clipboard


                    Patel, Ravi G., Desjardins, Olivier, Kong, Bo, Capecelatro, Jesse, and Fox, Rodney O. Fri .  
"Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows".  United States.  https://doi.org/10.1002/aic.15949.  https://www.osti.gov/servlets/purl/1409363.

Copy to clipboard


                    
@article{osti_1409363,

  title        = {Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows},

  author       = {Patel, Ravi G. and Desjardins, Olivier and Kong, Bo and Capecelatro, Jesse and Fox, Rodney O.},

  abstractNote = {Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posing fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent Eulerian statistics remains a challenge for all methods.},

  doi          = {10.1002/aic.15949},

  journal      = {AIChE Journal},

  number       = 12,

  volume       = 63,

  place        = {United States},

  year         = {2017},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1002/aic.15949

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows
journal, November 2014

Vié, Aymeric; Doisneau, François; Massot, Marc
Communications in Computational Physics, Vol. 17, Issue 1
DOI: 10.4208/cicp.021213.140514a

On the apparent viscosity of a fluidized bed
journal, January 2007

Gibilaro, L. G.; Gallucci, K.; Di Felice, R.
Chemical Engineering Science, Vol. 62, Issue 1-2
DOI: 10.1016/j.ces.2006.08.030

Conditional quadrature method of moments for kinetic equations
journal, September 2011

Yuan, C.; Fox, R. O.
Journal of Computational Physics, Vol. 230, Issue 22
DOI: 10.1016/j.jcp.2011.07.020

Statistical modeling of sprays using the droplet distribution function
journal, March 2001

Subramaniam, S.
Physics of Fluids, Vol. 13, Issue 3
DOI: 10.1063/1.1344893

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence
journal, March 2017

Kong, Bo; Fox, Rodney O.; Feng, Heng
AIChE Journal, Vol. 63, Issue 7
DOI: 10.1002/aic.15686

Filtered two-fluid models for fluidized gas-particle suspensions
journal, January 2008

Igci, Yesim; Andrews, Arthur T.; Sundaresan, Sankaran
AIChE Journal, Vol. 54, Issue 6
DOI: 10.1002/aic.11481

Equation of State for Nonattracting Rigid Spheres
journal, July 1969

Carnahan, Norman F.; Starling, Kenneth E.
The Journal of Chemical Physics, Vol. 51, Issue 2
DOI: 10.1063/1.1672048

An Euler–Lagrange strategy for simulating particle-laden flows
journal, April 2013

Capecelatro, Jesse; Desjardins, Olivier
Journal of Computational Physics, Vol. 238
DOI: 10.1016/j.jcp.2012.12.015

The role of meso-scale structures in rapid gas–solid flows
journal, October 2001

Agrawal, Kapil; Loezos, Peter N.; Syamlal, Madhava
Journal of Fluid Mechanics, Vol. 445
DOI: 10.1017/S0022112001005663

Lagrangian–Eulerian methods for multiphase flows
journal, April 2013

Subramaniam, Shankar
Progress in Energy and Combustion Science, Vol. 39, Issue 2-3
DOI: 10.1016/j.pecs.2012.10.003

A tensorial approach to computational continuum mechanics using object-oriented techniques
journal, January 1998

Weller, H. G.; Tabor, G.; Jasak, H.
Computers in Physics, Vol. 12, Issue 6
DOI: 10.1063/1.168744

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows
journal, December 2007

Garg, R.; Narayanan, C.; Lakehal, D.
International Journal of Multiphase Flow, Vol. 33, Issue 12
DOI: 10.1016/j.ijmultiphaseflow.2007.06.002

Turbulent Dispersed Multiphase Flow
journal, January 2010

Balachandar, S.; Eaton, John K.
Annual Review of Fluid Mechanics, Vol. 42, Issue 1
DOI: 10.1146/annurev.fluid.010908.165243

Exact regularized point particle method for multiphase flows in the two-way coupling regime
journal, May 2015

Gualtieri, P.; Picano, F.; Sardina, G.
Journal of Fluid Mechanics, Vol. 773
DOI: 10.1017/jfm.2015.258

Fluid Mechanical Description of Fluidized Beds. Equations of Motion
journal, November 1967

Anderson, T. B.; Jackson, Roy
Industrial & Engineering Chemistry Fundamentals, Vol. 6, Issue 4
DOI: 10.1021/i160024a007

Preferential concentration of heavy particles: A Voronoï analysis
journal, October 2010

Monchaux, R.; Bourgoin, M.; Cartellier, A.
Physics of Fluids, Vol. 22, Issue 10
DOI: 10.1063/1.3489987

On fluid–particle dynamics in fully developed cluster-induced turbulence
journal, September 2015

Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.
Journal of Fluid Mechanics, Vol. 780
DOI: 10.1017/jfm.2015.459

A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles
journal, May 1983

Jenkins, J. T.; Savage, S. B.
Journal of Fluid Mechanics, Vol. 130, Issue -1
DOI: 10.1017/S0022112083001044

Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion
journal, July 2014

Uhlmann, Markus; Doychev, Todor
Journal of Fluid Mechanics, Vol. 752
DOI: 10.1017/jfm.2014.330

High order conservative finite difference scheme for variable density low Mach number turbulent flows
journal, July 2008

Desjardins, Olivier; Blanquart, Guillaume; Balarac, Guillaume
Journal of Computational Physics, Vol. 227, Issue 15
DOI: 10.1016/j.jcp.2008.03.027

A solution algorithm for fluid–particle flows across all flow regimes
journal, September 2017

Kong, Bo; Fox, Rodney O.
Journal of Computational Physics, Vol. 344
DOI: 10.1016/j.jcp.2017.05.013

Preferential concentration of particles in isotropic turbulence: a comparison of the Lagrangian and the equilibrium Eulerian approaches
journal, March 2004

Rani, Sarma L.; Balachandar, S.
Powder Technology, Vol. 141, Issue 1-2
DOI: 10.1016/j.powtec.2004.02.016

Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development
journal, January 2014

Tenneti, Sudheer; Subramaniam, Shankar
Annual Review of Fluid Mechanics, Vol. 46, Issue 1
DOI: 10.1146/annurev-fluid-010313-141344

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows
journal, July 2011

Passalacqua, Alberto; Galvin, Janine E.; Vedula, Prakash
Communications in Computational Physics, Vol. 10, Issue 1
DOI: 10.4208/cicp.020210.160910a

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence
journal, January 2012

Tagawa, Yoshiyuki; Mercado, Julián Martínez; Prakash, Vivek N.
Journal of Fluid Mechanics, Vol. 693
DOI: 10.1017/jfm.2011.510

A numerically convergent Lagrangian–Eulerian simulation method for dispersed two-phase flows
journal, April 2009

Garg, R.; Narayanan, C.; Subramaniam, S.
International Journal of Multiphase Flow, Vol. 35, Issue 4
DOI: 10.1016/j.ijmultiphaseflow.2008.12.004

Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling
journal, June 2017

Ireland, Peter J.; Desjardins, Olivier
Journal of Computational Physics, Vol. 338
DOI: 10.1016/j.jcp.2017.02.070

A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
journal, May 1954

Bhatnagar, P. L.; Gross, E. P.; Krook, M.
Physical Review, Vol. 94, Issue 3
DOI: 10.1103/PhysRev.94.511

Influence of grid resolution, parcel size and drag models on bubbling fluidized bed simulation
journal, October 2017

Lu, Liqiang; Konan, Arthur; Benyahia, Sofiane
Chemical Engineering Journal, Vol. 326
DOI: 10.1016/j.cej.2017.06.002

A scaling analysis for point–particle approaches to turbulent multiphase flows
journal, September 2009

Balachandar, S.
International Journal of Multiphase Flow, Vol. 35, Issue 9
DOI: 10.1016/j.ijmultiphaseflow.2009.02.013

Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence
journal, December 2015

Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.
Journal of Fluids Engineering, Vol. 138, Issue 4
DOI: 10.1115/1.4031703

On multiphase turbulence models for collisional fluid–particle flows
journal, February 2014

Fox, Rodney O.
Journal of Fluid Mechanics, Vol. 742
DOI: 10.1017/jfm.2014.21

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields
journal, January 1987

Maxey, M. R.
Journal of Fluid Mechanics, Vol. 174
DOI: 10.1017/S0022112087000193

Enskog kinetic theory for monodisperse gas–solid flows
journal, September 2012

Garzó, V.; Tenneti, S.; Subramaniam, S.
Journal of Fluid Mechanics, Vol. 712
DOI: 10.1017/jfm.2012.404

Lagrangian Properties of Particles in Turbulence
journal, January 2009

Toschi, Federico; Bodenschatz, Eberhard
Annual Review of Fluid Mechanics, Vol. 41, Issue 1
DOI: 10.1146/annurev.fluid.010908.165210

Works referencing / citing this record:

Validation study on spatially averaged two-fluid model for gas-solid flows: II. Application to risers and fluidized beds
journal, March 2018

Schneiderbauer, Simon
AIChE Journal, Vol. 64, Issue 5
DOI: 10.1002/aic.16141

Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence
journal, December 2019

Kasbaoui, M. Houssem
Physical Review Fluids, Vol. 4, Issue 12
DOI: 10.1103/physrevfluids.4.124308

A kinetic-based hyperbolic two-fluid model for binary hard-sphere mixtures
journal, August 2019

Fox, Rodney O.
Journal of Fluid Mechanics, Vol. 877
DOI: 10.1017/jfm.2019.608

Similar Records in DOE PAGES and OSTI.GOV collections:

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

Journal Article Kong, Bo ; Fox, Rodney O. ; Feng, Heng ; ... - AIChE Journal

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore »« less
Cited by 24
https://doi.org/10.1002/aic.15686

Full Text Available
Lagrangian and Eulerian drag models that are consistent between Euler-Lagrange and Euler-Euler (two-fluid) approaches for homogeneous systems

Journal Article Balachandar, S. - Physical Review Fluids

The undisturbed flow of a particle is of fundamental importance since it controls both the undisturbed flow force and the perturbation force (which includes quasisteady, added-mass, and history forces). Here we use the pairwise interaction extended point particle framework to evaluate the undisturbed flow of each particle through superposition of the perturbation flow induced by all its neighbors. This approach allows calculation of various statistics related to undisturbed fluid velocity under conditions of both stationary and nonstationary particles. In a random distribution of stationary particles, while the macroscale undisturbed flow is slowly varying, the microscale undisturbed flow that arises due to the perturbation flow of neighbors varies substantially from one particle to another and this in turn leads to large variation in the hydrodynamic force exerted on the particles. The effect of particle motion is generally to increase the particle-to-particle variation in the undisturbed fluid velocity of the particles. We observe that this increase is greater for the transverse component than for the streamwise component. As a result, with increasing random particle motion, the distribution of undisturbed fluid-velocity fluctuation becomes isotropic. Three different normalized forces are defined:more »« less
https://doi.org/10.1103/physrevfluids.5.084302

Full Text Available
Coupling a Lagrangian–Eulerian Spark-Ignition (LESI) model with LES combustion models for engine simulations

Journal Article Kazmouz, Samuel J. ; Scarcelli, Riccardo ; Cheng, Zhen ; ... - Science and Technology for Energy Transition

In the United States transportation sector, Light-Duty Vehicles (LDVs) are the largest energy consumers and CO₂ emitters. Electrification of LDVs is posed as a potential solution, but SI engines can still contribute to decarbonization. Car manufacturers have turned to unconventional engine operation to increase the efficiency of Spark-Ignition (SI) engines and reduce the carbon emissions of their fleets. Dilute, lean, and stratified-charge engine operation has the potential for engine efficiency improvements at the expense of increased cyclic variability and combustion instability. At such demanding engine conditions, the spark ignition event is key for flame initiation and propagation and for enhancedmore »« less
https://doi.org/10.2516/stet/2022009

Full Text Available
Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics

Journal Article Horwitz, J. A. K. ; Mani, A. - Physical Review Fluids

Euler-Lagrange point-particle simulation has emerged as a premier methodology for studying dispersed particle-laden flows. This method's popularity stems from its ability to resolve fine-scale fluid structures while also tracking individual particles at reduced cost using an appropriate particle acceleration model. However, the point-particle model has known convergence issues in that refinement of the fluid grid can lead to changes in the predicted statistics. The reasons for non-convergence are twofold: the point-particle two-way coupling force in the Navier-Stokes equations requires a numerical regularization and, without careful implementation, yields a singular force on the fluid with grid refinement. The second factor thatmore »« less
https://doi.org/10.1103/physrevfluids.5.104302

Full Text Available
Unit physics testing of a mix model in an eulerian fluid computation

Conference Vold, Erik ; Douglass, Rod

A K-L turbulence mix model driven with a drag-buoyancy source term is tested in an Eulerian code in a series of basic unit-physics tests, as part of a mix validation milestone. The model and the closure coefficient values are derived in the work of Dimonte-Tipton [D-T] in Phys.Flu.18, 085101 (2006), and many of the test problems were reported there, where the mix model operated in Lagrange computations. The drag-buoyancy K-L mix model was implemented within the Eulerian code framework by A.J. Scannapieco. Mix model performance is evaluated in terms of mix width growth rates compared to experiments in select regimes.more »« less
Full Text Available

Similar Records

Title: Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for turbulent fluid-particle flows

Abstract

Citation Formats

On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows journal, November 2014

On the apparent viscosity of a fluidized bed journal, January 2007

Conditional quadrature method of moments for kinetic equations journal, September 2011

Statistical modeling of sprays using the droplet distribution function journal, March 2001

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence journal, March 2017

Filtered two-fluid models for fluidized gas-particle suspensions journal, January 2008

Equation of State for Nonattracting Rigid Spheres journal, July 1969

An Euler–Lagrange strategy for simulating particle-laden flows journal, April 2013

The role of meso-scale structures in rapid gas–solid flows journal, October 2001

Lagrangian–Eulerian methods for multiphase flows journal, April 2013

A tensorial approach to computational continuum mechanics using object-oriented techniques journal, January 1998

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows journal, December 2007

Turbulent Dispersed Multiphase Flow journal, January 2010

Exact regularized point particle method for multiphase flows in the two-way coupling regime journal, May 2015

Fluid Mechanical Description of Fluidized Beds. Equations of Motion journal, November 1967

Preferential concentration of heavy particles: A Voronoï analysis journal, October 2010

On fluid–particle dynamics in fully developed cluster-induced turbulence journal, September 2015

A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles journal, May 1983

Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion journal, July 2014

High order conservative finite difference scheme for variable density low Mach number turbulent flows journal, July 2008

A solution algorithm for fluid–particle flows across all flow regimes journal, September 2017

Preferential concentration of particles in isotropic turbulence: a comparison of the Lagrangian and the equilibrium Eulerian approaches journal, March 2004

Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development journal, January 2014

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows journal, July 2011

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence journal, January 2012

A numerically convergent Lagrangian–Eulerian simulation method for dispersed two-phase flows journal, April 2009

Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling journal, June 2017

A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems journal, May 1954

Influence of grid resolution, parcel size and drag models on bubbling fluidized bed simulation journal, October 2017

A scaling analysis for point–particle approaches to turbulent multiphase flows journal, September 2009

Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence journal, December 2015

On multiphase turbulence models for collisional fluid–particle flows journal, February 2014

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields journal, January 1987

Enskog kinetic theory for monodisperse gas–solid flows journal, September 2012

Lagrangian Properties of Particles in Turbulence journal, January 2009

Validation study on spatially averaged two-fluid model for gas-solid flows: II. Application to risers and fluidized beds journal, March 2018

Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence journal, December 2019

A kinetic-based hyperbolic two-fluid model for binary hard-sphere mixtures journal, August 2019

On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows
journal, November 2014

On the apparent viscosity of a fluidized bed
journal, January 2007

Conditional quadrature method of moments for kinetic equations
journal, September 2011

Statistical modeling of sprays using the droplet distribution function
journal, March 2001

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence
journal, March 2017

Filtered two-fluid models for fluidized gas-particle suspensions
journal, January 2008

Equation of State for Nonattracting Rigid Spheres
journal, July 1969

An Euler–Lagrange strategy for simulating particle-laden flows
journal, April 2013

The role of meso-scale structures in rapid gas–solid flows
journal, October 2001

Lagrangian–Eulerian methods for multiphase flows
journal, April 2013

A tensorial approach to computational continuum mechanics using object-oriented techniques
journal, January 1998

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows
journal, December 2007

Turbulent Dispersed Multiphase Flow
journal, January 2010

Exact regularized point particle method for multiphase flows in the two-way coupling regime
journal, May 2015

Fluid Mechanical Description of Fluidized Beds. Equations of Motion
journal, November 1967

Preferential concentration of heavy particles: A Voronoï analysis
journal, October 2010

On fluid–particle dynamics in fully developed cluster-induced turbulence
journal, September 2015

A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles
journal, May 1983

Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion
journal, July 2014

High order conservative finite difference scheme for variable density low Mach number turbulent flows
journal, July 2008

A solution algorithm for fluid–particle flows across all flow regimes
journal, September 2017

Preferential concentration of particles in isotropic turbulence: a comparison of the Lagrangian and the equilibrium Eulerian approaches
journal, March 2004

Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development
journal, January 2014

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows
journal, July 2011

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence
journal, January 2012

A numerically convergent Lagrangian–Eulerian simulation method for dispersed two-phase flows
journal, April 2009

Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling
journal, June 2017

A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
journal, May 1954

Influence of grid resolution, parcel size and drag models on bubbling fluidized bed simulation
journal, October 2017

A scaling analysis for point–particle approaches to turbulent multiphase flows
journal, September 2009

Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence
journal, December 2015

On multiphase turbulence models for collisional fluid–particle flows
journal, February 2014

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields
journal, January 1987

Enskog kinetic theory for monodisperse gas–solid flows
journal, September 2012

Lagrangian Properties of Particles in Turbulence
journal, January 2009

Validation study on spatially averaged two-fluid model for gas-solid flows: II. Application to risers and fluidized beds
journal, March 2018

Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence
journal, December 2019

A kinetic-based hyperbolic two-fluid model for binary hard-sphere mixtures
journal, August 2019