Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle...

Full description

Autores:
Ernst, Martin
Sommerfeld, Martin
Laín Beatove, Santiago
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/13287
Acceso en línea:
https://hdl.handle.net/10614/13287
Palabra clave:
Análisis numérico
Turbulencia
Colisiones (Física)
Numerical analysis
Turbulence
Collisions (Physics)
Homogeneous isotropic turbulence
Lagrangian tracking
Deterministic collision model
Colliding particle-pair velocity correlation function
Rights
openAccess
License
Derechos reservados - MDPI, 2020
id REPOUAO2_178127e388ac7962d5bb752c440e27d7
oai_identifier_str oai:red.uao.edu.co:10614/13287
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
title Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
spellingShingle Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
Análisis numérico
Turbulencia
Colisiones (Física)
Numerical analysis
Turbulence
Collisions (Physics)
Homogeneous isotropic turbulence
Lagrangian tracking
Deterministic collision model
Colliding particle-pair velocity correlation function
title_short Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
title_full Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
title_fullStr Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
title_full_unstemmed Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
title_sort Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence
dc.creator.fl_str_mv Ernst, Martin
Sommerfeld, Martin
Laín Beatove, Santiago
dc.contributor.author.spa.fl_str_mv Ernst, Martin
Sommerfeld, Martin
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
dc.subject.armarc.spa.fl_str_mv Análisis numérico
Turbulencia
Colisiones (Física)
topic Análisis numérico
Turbulencia
Colisiones (Física)
Numerical analysis
Turbulence
Collisions (Physics)
Homogeneous isotropic turbulence
Lagrangian tracking
Deterministic collision model
Colliding particle-pair velocity correlation function
dc.subject.armarc.eng.fl_str_mv Numerical analysis
Turbulence
Collisions (Physics)
dc.subject.proposal.eng.fl_str_mv Homogeneous isotropic turbulence
Lagrangian tracking
Deterministic collision model
Colliding particle-pair velocity correlation function
description This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK ∼ 1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles
publishDate 2020
dc.date.issued.none.fl_str_mv 2020-12-19
dc.date.accessioned.none.fl_str_mv 2021-09-29T18:02:15Z
dc.date.available.none.fl_str_mv 2021-09-29T18:02:15Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.eng.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.eng.fl_str_mv Text
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.eng.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.eng.fl_str_mv info:eu-repo/semantics/publishedVersion
format http://purl.org/coar/resource_type/c_6501
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 14545101
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/13287
identifier_str_mv 14545101
url https://hdl.handle.net/10614/13287
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationedition.spa.fl_str_mv Volumen 10, número 24 (2020)
dc.relation.citationendpage.spa.fl_str_mv 22
dc.relation.citationissue.spa.fl_str_mv Número 24
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv Volumen 10
dc.relation.cites.eng.fl_str_mv Lain S., Ernst M., Sommerfeld M. (2020). Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence. Applied Sciences. Vol. 10 (24), pp.1-22. https://doi.org/10.3390/app10249095
dc.relation.ispartofjournal.eng.fl_str_mv Applied Sciences
dc.relation.references.eng.fl_str_mv Safronov, V.S. Evolution of the protoplanetary cloud and formation of the Earth and the planets. Nauka NASA Tech. Transl. 1969, 677, 1–206.
Zsom, A.; Ormel, C.W.; Guettler, C.; Blum, J.; Dullemond, C.P. The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier. Astron. Astrophys. 2010, 513, A57.
Falkovich, G.; Fouxon, A.; Stepanov, M.G. Acceleration of rain initiation by cloud turbulence. Nature 2002, 419, 151–154.
Shaw, R.A. Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 2003, 35, 183–227.
Motter, A.E.; Lai, Y.C.; Grebogi, C. Reactive dynamics of inertial particles in nonhyperbolic chaotic flows. Phys. Rev. E 2003, 68, 056307.
Varas, A.E.C.; Peters, E.A.J.F.; Kuipers, J.A.M. CFD-DEM simulations and experimental validation of clustering phenomena and riser hydrodynamics. Chem. Eng. Sci. 2017, 169, 246–258.
Cahyadi, A.; Anantharaman, A.; Yang, S.; Reddy Karri, S.B.; Findlay, J.G.; Cocco, R.A.; Chew, J.W. Review of cluster characteristics in circulating fluidized bed (CFB) risers. Chem. Eng. Sci. 2017, 158, 70–95.
Laín, S.; Sommerfeld, M. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with di erent wall roughness. Powder Technol. 2008, 184, 76–88.
Laín, S.; Sommerfeld, M. Numerical calculation of pneumatic conveying in horizontal channels and pipes: Detailed analysis of conveying behavior. Int. J. Multiph. Flow 2012, 39, 105–120.
Laín, S.; Sommerfeld, M. Characterization of pneumatic conveying systems using the Euler/Lagrange approach. Powder Technol. 2013, 235, 764–782.
Laín, S.; Sommerfeld, M. Numerical prediction of particle erosion of pipe bends. Adv. Powder Technol. 2019, 30, 366–383.
Laín, S.; García, M.; Quintero, B.; Orrego, S. CFD Numerical simulations of Francis turbines. Rev. Fac. Ing. Univ. Antioq. 2010, 51, 24–33.
Westphal, D.L.; Toon, O.B.; Carlson, T.N. A two-dimensional numerical investigation of the dynamics and microphysics of Saharan dust storms. J. Geophys. Res. 1987, 92, 3027–3049.
Kroy, K.; Sauermann, G.; Herrmann, H.J. Minimal model for aeolian sand dunes. Phys. Rev. E 2002, 66, 031302.
Sundaram, S.; Collins, L.R. Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 1997, 335, 75–109.
Wang, L.P.; Wexler, A.S.; Zhou, Y. Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 2000, 415, 117–153.
Reade,W.C.; Collins, L.R. E ect of preferential concentration on turbulent collision rates. Phys. Fluids 2000, 12, 2530–2540.
Zaichik, L.I.; Alipchenkov, V.M.; Avetissian, A.R. Modelling turbulent collisions rates of inertial particles. Int. J. Heat Fluid Flow 2006, 27, 937–944.
Février, P.; Simonin, O.; Squires, K.D. Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: Theoretical formalism and numerical study. J. Fluid Mech. 2005, 533, 1–46.
Reeks, M.W. On the dispersion of small particles suspended in an isotropic turbulent field. J. Fluid Mech. 1977, 83, 529–546.
Bewley, G.P.; Saw, E.W.; Bodenschatz, E. Observation of the sling e ect. New J. Phys. 2013, 15, 083051.
Choi, J.; Park, Y.; Kwon, O.; Lee, C. Interparticle collision mechanism in turbulence. Phys. Rev. E 2016, 93, 013112.
Williams, J.J.E.; Crane, R.I. Particle collision rate in turbulent flow. Int. J. Multiph. Flow 1983, 9, 421–435.
Kruis, F.E.; Kusters, K.A. The collision rate of particles in turbulent media. J. Aerosol Sci. 1996, 27, 263–264.
Ireland, P.J.; Bragg, A.D.; Collins, L.R. The e ect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational e ects. J. Fluid Mech. 2016, 796, 617–658.
Bec, J.; Celani, A.; Cencini, M.; Musacchio, S. Clustering and collisions of heavy particle in random smooth flows. Phys. Fluids 2005, 17, 073301.
Wilkinson, M.; Mehlig, B. Caustics in turbulent aerosols. Europhys. Lett. 2005, 71, 186–192.
Vosskuhle, M.; Pumir, A.; Lévêque, E.;Wilkinson, M. Prevalence of the sling e ect for enhancing collision rates in turbulent suspensions. J. Fluid Mech. 2014, 749, 841–852.
Van Wachem, B.; Curran, T.; Evrard, F. Fully Correlated Stochastic Inter-Particle Collision Model for Euler–Lagrange Gas–Solid Flows. Flow Turb. Comb. 2020.
Sommerfeld, M.; Laín, S. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiph. Sci. Technol. 2009, 21, 123–140.
Sommerfeld, M. Validation of a stochastic Lagrangian modeling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiph. Flow 2001, 27, 1829–1858.
Berlemont, A.; Achim, P.; Chang, Z. Lagrangian approaches for particle collisions: The colliding particle velocity correlation in the multiple particles tracking method and in the stochastic approach. Phys. Fluids 2001, 13, 2946–2956.
Sommerfeld, M.; Lipowsky, J.; Laín, S. (Keynote lecture). Transient Euler/Lagrange modelling for predicting unsteady rope behaviour in gas-particle flows. In Proceedings of the FEDSM2010 ASME Joint U.S.–European Fluids Engineering Summer Meeting, Montreal, QB, Canada, 1–5 August 2010. Paper No. FEDSM-ICNMM2010-31335.
Laviéville, J.; Deutsch, E.; Simonin, O. Large eddy simulation of interactions between colliding particles and a homogeneous isotropic turbulence field. Gas-Solid-Flows 1995, 228, 347–357.
Lipowsky, J.; Sommerfeld, M. Time dependent simulation of a swirling two-phase flow using an anisotropic turbulent dispersion model. In Proceedings of the ASME Fluids Engineering Summer Conference, Houston, TX, USA, 19–23 June 2005. Paper No. FEDSM2005-77210.
Laín, S.; Ernst, M.; Sommerfeld, M. Colliding particle-pair velocity correlation function in turbulent flows. In Proceedings of the 7th International Conference on Multiphase Flow, ICMF 2010, Tampa, FL, USA, 30 May–4 June 2010.
Zaichik, L.I.; Alipchenkov, V.M. Pair dispersion and preferential concentration of particles in isotropic turbulence. Phys. Fluids 2003, 15, 1776–1787.
Ernst, M.; Sommerfeld, M. On the volume fraction e ects of inertial colliding particles in homogeneous isotropic turbulence. ASME J. Fluids Eng. 2012, 134, 031302.
Ernst, M.; Sommerfeld, M.; Laín, S. Quantification of preferential concentration of colliding particles in a homogeneous isotropic turbulent flow. Int. J. Multiph. Flow 2019, 117, 163–181.
Schiller, L.; Naumann, A. Über die grundlegenden Berechnungen bei der Schwerkraftaufbe-reitung. Z. Ver. Deut. Ing. 1933, 77, 318–320.
Comte-Bellot, G.; Corrsin, S. Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 1971, 48, 273–337.
Crowe, C.T. On the relative importance of particle-particle collisions in gas-particle flows. In Proceedings of the Conference on Gas Borne Particles, Oxford, UK, June 1981; pp. 135–137. Available online: https: //pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL82X0129704 (accessed on 5 October 2020).
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. 2004, 519, 233–271.
Saffman, P.G.; Turner, J.S. On the collisions of drops in turbulent clouds. J. FluidMech. 1956, 1, 16–30.
Abrahamson, J. Collision rates of small particles in a vigorously turbulent fluid. Chem. Eng. Sci. 1975, 30, 1371–1379.
Vosskuhle, M. Particle Collisions in Turbulent Flows. Ph.D. Thesis, University of Lyon, Lyon, France, 2013.
Sundaram, S.; Collins, L.R. Numerical Considerations in Simulating a Turbulent Suspension of Finite-Volume Particles. J. Comp. Phys. 1996, 124, 337–350.
Tanaka, T.; Tsuji, Y. Numerical simulation of gas-solid two-phase flow in a vertical pipe: On the e ect of inter-particle collisions. ASME Gas-Solid-Flows 1991, 121, 123–128.
dc.rights.spa.fl_str_mv Derechos reservados - MDPI, 2020
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.none.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.eng.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.creativecommons.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
rights_invalid_str_mv Derechos reservados - MDPI, 2020
https://creativecommons.org/licenses/by-nc-nd/4.0/
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv 22 páginas
dc.format.mimetype.eng.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv MDPI
institution Universidad Autónoma de Occidente
bitstream.url.fl_str_mv https://red.uao.edu.co/bitstreams/71efe8e0-a997-47cf-8b03-247a4008ffd8/download
https://red.uao.edu.co/bitstreams/9e8ad063-db2e-4058-81c4-69812fcb595a/download
https://red.uao.edu.co/bitstreams/50480834-5cc0-47d2-8138-389a264f8b41/download
https://red.uao.edu.co/bitstreams/4f8ca82a-1850-4f18-9ff5-30cafa80fbb4/download
bitstream.checksum.fl_str_mv 20b5ba22b1117f71589c7318baa2c560
9d7e6343117a65353bf46ef608baea55
eacba581654985137bff4780bc8e6d02
8fc33feadf4a5fcc3ebed037796b2b37
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Digital Universidad Autonoma de Occidente
repository.mail.fl_str_mv repositorio@uao.edu.co
_version_ 1814259820961726464
spelling Ernst, Martin1728e3bd5d87985c07257ed65e4a1abdSommerfeld, Martin4225b01693727b10986bcc383715fa70Laín Beatove, Santiagovirtual::2563-12021-09-29T18:02:15Z2021-09-29T18:02:15Z2020-12-1914545101https://hdl.handle.net/10614/13287This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK ∼ 1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles22 páginasapplication/pdfengMDPIDerechos reservados - MDPI, 2020https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulenceArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Análisis numéricoTurbulenciaColisiones (Física)Numerical analysisTurbulenceCollisions (Physics)Homogeneous isotropic turbulenceLagrangian trackingDeterministic collision modelColliding particle-pair velocity correlation functionVolumen 10, número 24 (2020)22Número 241Volumen 10Lain S., Ernst M., Sommerfeld M. (2020). Study of colliding particle-pair velocity correlation in homogeneous isotropic turbulence. Applied Sciences. Vol. 10 (24), pp.1-22. https://doi.org/10.3390/app10249095Applied SciencesSafronov, V.S. Evolution of the protoplanetary cloud and formation of the Earth and the planets. Nauka NASA Tech. Transl. 1969, 677, 1–206.Zsom, A.; Ormel, C.W.; Guettler, C.; Blum, J.; Dullemond, C.P. The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier. Astron. Astrophys. 2010, 513, A57.Falkovich, G.; Fouxon, A.; Stepanov, M.G. Acceleration of rain initiation by cloud turbulence. Nature 2002, 419, 151–154.Shaw, R.A. Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 2003, 35, 183–227.Motter, A.E.; Lai, Y.C.; Grebogi, C. Reactive dynamics of inertial particles in nonhyperbolic chaotic flows. Phys. Rev. E 2003, 68, 056307.Varas, A.E.C.; Peters, E.A.J.F.; Kuipers, J.A.M. CFD-DEM simulations and experimental validation of clustering phenomena and riser hydrodynamics. Chem. Eng. Sci. 2017, 169, 246–258.Cahyadi, A.; Anantharaman, A.; Yang, S.; Reddy Karri, S.B.; Findlay, J.G.; Cocco, R.A.; Chew, J.W. Review of cluster characteristics in circulating fluidized bed (CFB) risers. Chem. Eng. Sci. 2017, 158, 70–95.Laín, S.; Sommerfeld, M. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with di erent wall roughness. Powder Technol. 2008, 184, 76–88.Laín, S.; Sommerfeld, M. Numerical calculation of pneumatic conveying in horizontal channels and pipes: Detailed analysis of conveying behavior. Int. J. Multiph. Flow 2012, 39, 105–120.Laín, S.; Sommerfeld, M. Characterization of pneumatic conveying systems using the Euler/Lagrange approach. Powder Technol. 2013, 235, 764–782.Laín, S.; Sommerfeld, M. Numerical prediction of particle erosion of pipe bends. Adv. Powder Technol. 2019, 30, 366–383.Laín, S.; García, M.; Quintero, B.; Orrego, S. CFD Numerical simulations of Francis turbines. Rev. Fac. Ing. Univ. Antioq. 2010, 51, 24–33.Westphal, D.L.; Toon, O.B.; Carlson, T.N. A two-dimensional numerical investigation of the dynamics and microphysics of Saharan dust storms. J. Geophys. Res. 1987, 92, 3027–3049.Kroy, K.; Sauermann, G.; Herrmann, H.J. Minimal model for aeolian sand dunes. Phys. Rev. E 2002, 66, 031302.Sundaram, S.; Collins, L.R. Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 1997, 335, 75–109.Wang, L.P.; Wexler, A.S.; Zhou, Y. Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 2000, 415, 117–153.Reade,W.C.; Collins, L.R. E ect of preferential concentration on turbulent collision rates. Phys. Fluids 2000, 12, 2530–2540.Zaichik, L.I.; Alipchenkov, V.M.; Avetissian, A.R. Modelling turbulent collisions rates of inertial particles. Int. J. Heat Fluid Flow 2006, 27, 937–944.Février, P.; Simonin, O.; Squires, K.D. Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: Theoretical formalism and numerical study. J. Fluid Mech. 2005, 533, 1–46.Reeks, M.W. On the dispersion of small particles suspended in an isotropic turbulent field. J. Fluid Mech. 1977, 83, 529–546.Bewley, G.P.; Saw, E.W.; Bodenschatz, E. Observation of the sling e ect. New J. Phys. 2013, 15, 083051.Choi, J.; Park, Y.; Kwon, O.; Lee, C. Interparticle collision mechanism in turbulence. Phys. Rev. E 2016, 93, 013112.Williams, J.J.E.; Crane, R.I. Particle collision rate in turbulent flow. Int. J. Multiph. Flow 1983, 9, 421–435.Kruis, F.E.; Kusters, K.A. The collision rate of particles in turbulent media. J. Aerosol Sci. 1996, 27, 263–264.Ireland, P.J.; Bragg, A.D.; Collins, L.R. The e ect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational e ects. J. Fluid Mech. 2016, 796, 617–658.Bec, J.; Celani, A.; Cencini, M.; Musacchio, S. Clustering and collisions of heavy particle in random smooth flows. Phys. Fluids 2005, 17, 073301.Wilkinson, M.; Mehlig, B. Caustics in turbulent aerosols. Europhys. Lett. 2005, 71, 186–192.Vosskuhle, M.; Pumir, A.; Lévêque, E.;Wilkinson, M. Prevalence of the sling e ect for enhancing collision rates in turbulent suspensions. J. Fluid Mech. 2014, 749, 841–852.Van Wachem, B.; Curran, T.; Evrard, F. Fully Correlated Stochastic Inter-Particle Collision Model for Euler–Lagrange Gas–Solid Flows. Flow Turb. Comb. 2020.Sommerfeld, M.; Laín, S. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiph. Sci. Technol. 2009, 21, 123–140.Sommerfeld, M. Validation of a stochastic Lagrangian modeling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiph. Flow 2001, 27, 1829–1858.Berlemont, A.; Achim, P.; Chang, Z. Lagrangian approaches for particle collisions: The colliding particle velocity correlation in the multiple particles tracking method and in the stochastic approach. Phys. Fluids 2001, 13, 2946–2956.Sommerfeld, M.; Lipowsky, J.; Laín, S. (Keynote lecture). Transient Euler/Lagrange modelling for predicting unsteady rope behaviour in gas-particle flows. In Proceedings of the FEDSM2010 ASME Joint U.S.–European Fluids Engineering Summer Meeting, Montreal, QB, Canada, 1–5 August 2010. Paper No. FEDSM-ICNMM2010-31335.Laviéville, J.; Deutsch, E.; Simonin, O. Large eddy simulation of interactions between colliding particles and a homogeneous isotropic turbulence field. Gas-Solid-Flows 1995, 228, 347–357.Lipowsky, J.; Sommerfeld, M. Time dependent simulation of a swirling two-phase flow using an anisotropic turbulent dispersion model. In Proceedings of the ASME Fluids Engineering Summer Conference, Houston, TX, USA, 19–23 June 2005. Paper No. FEDSM2005-77210.Laín, S.; Ernst, M.; Sommerfeld, M. Colliding particle-pair velocity correlation function in turbulent flows. In Proceedings of the 7th International Conference on Multiphase Flow, ICMF 2010, Tampa, FL, USA, 30 May–4 June 2010.Zaichik, L.I.; Alipchenkov, V.M. Pair dispersion and preferential concentration of particles in isotropic turbulence. Phys. Fluids 2003, 15, 1776–1787.Ernst, M.; Sommerfeld, M. On the volume fraction e ects of inertial colliding particles in homogeneous isotropic turbulence. ASME J. Fluids Eng. 2012, 134, 031302.Ernst, M.; Sommerfeld, M.; Laín, S. Quantification of preferential concentration of colliding particles in a homogeneous isotropic turbulent flow. Int. J. Multiph. Flow 2019, 117, 163–181.Schiller, L.; Naumann, A. Über die grundlegenden Berechnungen bei der Schwerkraftaufbe-reitung. Z. Ver. Deut. Ing. 1933, 77, 318–320.Comte-Bellot, G.; Corrsin, S. Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 1971, 48, 273–337.Crowe, C.T. On the relative importance of particle-particle collisions in gas-particle flows. In Proceedings of the Conference on Gas Borne Particles, Oxford, UK, June 1981; pp. 135–137. Available online: https: //pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL82X0129704 (accessed on 5 October 2020).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. 2004, 519, 233–271.Saffman, P.G.; Turner, J.S. On the collisions of drops in turbulent clouds. J. FluidMech. 1956, 1, 16–30.Abrahamson, J. Collision rates of small particles in a vigorously turbulent fluid. Chem. Eng. Sci. 1975, 30, 1371–1379.Vosskuhle, M. Particle Collisions in Turbulent Flows. Ph.D. Thesis, University of Lyon, Lyon, France, 2013.Sundaram, S.; Collins, L.R. Numerical Considerations in Simulating a Turbulent Suspension of Finite-Volume Particles. J. Comp. Phys. 1996, 124, 337–350.Tanaka, T.; Tsuji, Y. Numerical simulation of gas-solid two-phase flow in a vertical pipe: On the e ect of inter-particle collisions. ASME Gas-Solid-Flows 1991, 121, 123–128.GeneralPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2563-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2563-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2563-10000-0002-0269-2608virtual::2563-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2563-1LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/71efe8e0-a997-47cf-8b03-247a4008ffd8/download20b5ba22b1117f71589c7318baa2c560MD52ORIGINALStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdfStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf3822228https://red.uao.edu.co/bitstreams/9e8ad063-db2e-4058-81c4-69812fcb595a/download9d7e6343117a65353bf46ef608baea55MD53TEXTStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdf.txtStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdf.txtExtracted texttext/plain113869https://red.uao.edu.co/bitstreams/50480834-5cc0-47d2-8138-389a264f8b41/downloadeacba581654985137bff4780bc8e6d02MD54THUMBNAILStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdf.jpgStudy of colliding particle-pair velocity correlation in homogeneous isotropic turbulence.pdf.jpgGenerated Thumbnailimage/jpeg14826https://red.uao.edu.co/bitstreams/4f8ca82a-1850-4f18-9ff5-30cafa80fbb4/download8fc33feadf4a5fcc3ebed037796b2b37MD5510614/13287oai:red.uao.edu.co:10614/132872024-03-06 16:43:15.177https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - MDPI, 2020open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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

Publicaciones similares