Characterisation of pneumatic conveying systems using the Euler/Lagrange approach

This paper deals with the transport of solid particles in pneumatic conveying systems, namely a 5 m horizontal pipe, a 90° bend and 5 m a vertical pipe. The pipe diameter is 150 mm in all cases and the average conveying velocity is 27 m/s. Three-dimensional stationary numerical computations were per...

Full description

Autores:
Laín Beatove, Santiago
Sommerfeld, Martin
Tipo de recurso:
Article of journal
Fecha de publicación:
2013
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/11991
Acceso en línea:
http://red.uao.edu.co//handle/10614/11991
Palabra clave:
Euler–Lagrange approach
Pneumatic conveying
Wall roughness
Inter-particle collisions
Segregation phenomena
Rights
openAccess
License
Derechos Reservados - Universidad Autónoma de Occidente
id REPOUAO2_56b0848ad3ee784fb265cab56f268103
oai_identifier_str oai:red.uao.edu.co:10614/11991
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
title Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
spellingShingle Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
Euler–Lagrange approach
Pneumatic conveying
Wall roughness
Inter-particle collisions
Segregation phenomena
title_short Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
title_full Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
title_fullStr Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
title_full_unstemmed Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
title_sort Characterisation of pneumatic conveying systems using the Euler/Lagrange approach
dc.creator.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martin
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martin
dc.subject.proposal.eng.fl_str_mv Euler–Lagrange approach
Pneumatic conveying
Wall roughness
Inter-particle collisions
Segregation phenomena
topic Euler–Lagrange approach
Pneumatic conveying
Wall roughness
Inter-particle collisions
Segregation phenomena
description This paper deals with the transport of solid particles in pneumatic conveying systems, namely a 5 m horizontal pipe, a 90° bend and 5 m a vertical pipe. The pipe diameter is 150 mm in all cases and the average conveying velocity is 27 m/s. Three-dimensional stationary numerical computations were performed by the Euler/Lagrange approach in connection with the k–ε turbulence model accounting for full two-way coupling. Particle transport is calculated by considering all the relevant forces (including drag, gravity and transverse lift forces) and dispersion due to turbulence. Particle–wall collisions and wall roughness are modelled according to Sommerfeld and Huber [1] and inter-particle collisions are described by the stochastic modelling approach of Sommerfeld [2]. The objective of the present contribution is to demonstrate the capability of this computational approach for accurately predicting more complex pneumatic conveying systems where the transported powder has a rather wide size distribution. In particular the effect of inter-particle collisions will be demonstrated
publishDate 2013
dc.date.issued.none.fl_str_mv 2013-02
dc.date.accessioned.none.fl_str_mv 2020-02-26T20:39:53Z
dc.date.available.none.fl_str_mv 2020-02-26T20:39:53Z
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/ARTREF
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.uri.none.fl_str_mv http://red.uao.edu.co//handle/10614/11991
url http://red.uao.edu.co//handle/10614/11991
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.eng.fl_str_mv Powder Technology. Volumen 235, (febrero 2013); páginas 764-782
dc.relation.cites.spa.fl_str_mv Laín Beatove, S., Sommerfeld, M (2013). Characterisation of pneumatic conveying systems using the Euler/Lagrange approach. Powder Technology. 235, 1-49. http://red.uao.edu.co//handle/10614/11991
dc.relation.ispartofjournal.none.fl_str_mv Powder Technology
dc.relation.references.none.fl_str_mv M. Sommerfeld, N. Huber. Experimental analysis and modelling of particle–wall collisions International Journal of Multiphase Flow, 25 (1999), pp. 1457-1489
M. Sommerfeld. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence International Journal of Multiphase Flow, 27 (2001), pp. 1828-1858
W. Siegel. Pneumatische Förderung: Grundlagen, Auslegung, Anlagenbau, Betrieb Vogel Verlag, Würzburg (1991)
J. Eustice. Flow of water in curved pipes Proceedings of the Royal Society of London Series A, 84 (1910), pp. 107-118
W.R. Dean. The stream-line motion of fluid in a curved pipe Philosophical Magazine, 30 (1928), pp. 673-693
J.A.C. Humphrey, J.H. Whitelaw, G. Yee. Turbulent flow in a square duct with strong curvature Journal of Fluid Mechanics, 103 (1981), pp. 363-443
A.M.P.K. Taylor, J.H. Whitelaw, M. Yianneskis. Curved ducts with strong secondary motion: velocity measurements of developing laminar and turbulent flow. Transactions of the ASME Journal of Fluids Engineering, 104 (1982), pp. 350-359
M.M. Enayet, M.M. Gibson, A.M.P.K. Taylor, M. Yianneskis Laser-Doppler measurements of laminar and turbulent flow in a pipe bend. International Journal of Heat and Fluid Flow, 3 (1982), pp. 213-219
K. Sudo, M. Sumida, H. Hibara. Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend. Experiments in Fluids, 25 (1998), pp. 42-49
A. Yilmaz, E.K. Levy. Roping phenomena in pulverized coal conveying lines. Powder Technology, 95 (1998), pp. 38-43
H. Akilli, E.K. Levy, B. Sahin. Gas–solid flow behaviour in a horizontal pipe after vertical-to-horizontal elbow. Powder Technology, 116 (2001), pp. 43-52
Th. Frank, F.P. Schade, D. Petrak. Numerical simulation and experimental investigation of a gas–solid two-phase flow in a horizontal channel. International Journal of Multiphase Flow, 19 (1993), pp. 187-198
M. Sommerfeld, J. Kussin. Wall roughness effects on pneumatic conveying of spherical particles in a narrow horizontal channel. Powder Technology, 142 (2004), pp. 180-192
H. Akilli, E.K. Levy, B. Sahin. Investigation of gas–solid flow structure after a 90° vertical-to-horizontal elbow for low conveying gas velocities. Advanced Powder Technology, 16 (2005), pp. 261-264
B. Kuan, W. Yang, M.P. Schwarz. Dilute gas–solid two-phase flows in a curved 90° duct bend: CFD simulation with experimental validation. Chemical Engineering Science, 62 (2007), pp. 2068-2088
Z.F. Tian, K. Intahvong, J.Y. Tu, G.H. Yeoh. Numerical investigation into the effects of wall roughness on a gas-particle flow in a 90° bend. International Journal of Heat and Mass Transfer, 51 (2008), pp. 1238-1250
S. Laín, M. Sommerfeld. Experimental and numerical study of the motion of non-spherical particles in wall bounded turbulent flows. Universidad Autónoma de Occidente, Cali (2008)
S. Laín, M. Sommerfeld. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness. Powder Technology, 184 (2008), pp. 76-88
M. Sommerfeld, S. Laín. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiphase Science and Technology, 21 (2009), pp. 123-140
S. Laín. On Modeling and Numerical Computation of Industrial Disperse Two-Phase Flow With the Euler–Lagrange Approach. Shaker Verlag, Aachen, Germany (2010)
S. Laín, M. Sommerfeld, J. Kussin. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. International Journal of Heat and Fluid Flow, 23 (2002), pp. 647-656
R. Mei. An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. International Journal of Multiphase Flow, 18 (1992), pp. 145-147
B. Oesterlé, T. Bui Dinh. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Experiments in Fluids, 25 (1998), pp. 16-22
M.F. Göz, S. Laín, M. Sommerfeld. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering, 28 (2004), pp. 2727-2733
C.T. Crowe, M.P. Sharma, D.E. Stock. The particle-source-in-cell (PSI-cell) model for gas-droplet flows. Journal of Fluids Engineering, 99 (1977), pp. 325-332
S. Lain, M. Sommerfeld. Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behaviour. International Journal of Multiphase Flow, 39 (2012), pp. 105-120
S. Laín, M. Sommerfeld, B. Quintero. Numerical simulation of secondary flow in pneumatic conveying of solid particles in a horizontal circular pipe. Brazilian Journal of Chemical Engineering, 26 (2009), pp. 583-594
Y.T. Ng, S.C. Luo, T.T. Lim, Q.W. Ho. On the relation between centrifugal force and radial pressure gradient in flow inside curved and S-shaped ducts. Physics of Fluids, 20 (2008), p. 055109
S. Laín, M. Sommerfeld. Structure and pressure drop in particle-laden gas flow through a pipe bend: a numerical analysis by the Euler–Lagrange approach Proc. ASME 2009 Fluids Engineering Division Summer Meeting FEDSM2009, paper FEDSM2009-78090 (2009)
M. Sommerfeld. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. International Journal of Multiphase Flow, 29 (2003), pp. 675-699
M. Sommerfeld, J. Kussin. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part II. Integral properties and validation. International Journal of Multiphase Flow, 29 (2003), pp. 701-718
dc.rights.spa.fl_str_mv Derechos Reservados - Universidad Autónoma de Occidente
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.eng.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 - Universidad Autónoma de Occidente
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.eng.fl_str_mv application/pdf
dc.format.extent.spa.fl_str_mv 49 páginas
dc.coverage.spatial.none.fl_str_mv Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí
dc.publisher.eng.fl_str_mv Elsevier
institution Universidad Autónoma de Occidente
bitstream.url.fl_str_mv https://red.uao.edu.co/bitstreams/0ada0485-f7ac-4a3e-95a0-f14aa3c79af0/download
https://red.uao.edu.co/bitstreams/77400758-c7c7-4c77-b234-26456c6c518d/download
https://red.uao.edu.co/bitstreams/92c6c5d0-5c40-4f63-bd32-7aa8c62e8bc1/download
https://red.uao.edu.co/bitstreams/1ac36dc7-98e7-425e-909d-0d1b4ee95b58/download
https://red.uao.edu.co/bitstreams/324e6faa-cf17-4f45-b659-06728a3c869a/download
bitstream.checksum.fl_str_mv 4460e5956bc1d1639be9ae6146a50347
20b5ba22b1117f71589c7318baa2c560
03d59633da35a0ba82a6adebe286a3ca
48f3649c8779c9b7ec44fe8932142e76
12a82d736ffae0de024137344b25e9d6
bitstream.checksumAlgorithm.fl_str_mv MD5
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_ 1814259997059579904
spelling Laín Beatove, Santiagovirtual::2566-1Sommerfeld, Martin4225b01693727b10986bcc383715fa70Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2020-02-26T20:39:53Z2020-02-26T20:39:53Z2013-02http://red.uao.edu.co//handle/10614/11991This paper deals with the transport of solid particles in pneumatic conveying systems, namely a 5 m horizontal pipe, a 90° bend and 5 m a vertical pipe. The pipe diameter is 150 mm in all cases and the average conveying velocity is 27 m/s. Three-dimensional stationary numerical computations were performed by the Euler/Lagrange approach in connection with the k–ε turbulence model accounting for full two-way coupling. Particle transport is calculated by considering all the relevant forces (including drag, gravity and transverse lift forces) and dispersion due to turbulence. Particle–wall collisions and wall roughness are modelled according to Sommerfeld and Huber [1] and inter-particle collisions are described by the stochastic modelling approach of Sommerfeld [2]. The objective of the present contribution is to demonstrate the capability of this computational approach for accurately predicting more complex pneumatic conveying systems where the transported powder has a rather wide size distribution. In particular the effect of inter-particle collisions will be demonstratedapplication/pdf49 páginasengElsevierPowder Technology. Volumen 235, (febrero 2013); páginas 764-782Laín Beatove, S., Sommerfeld, M (2013). Characterisation of pneumatic conveying systems using the Euler/Lagrange approach. Powder Technology. 235, 1-49. http://red.uao.edu.co//handle/10614/11991Powder TechnologyM. Sommerfeld, N. Huber. Experimental analysis and modelling of particle–wall collisions International Journal of Multiphase Flow, 25 (1999), pp. 1457-1489M. Sommerfeld. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence International Journal of Multiphase Flow, 27 (2001), pp. 1828-1858W. Siegel. Pneumatische Förderung: Grundlagen, Auslegung, Anlagenbau, Betrieb Vogel Verlag, Würzburg (1991)J. Eustice. Flow of water in curved pipes Proceedings of the Royal Society of London Series A, 84 (1910), pp. 107-118W.R. Dean. The stream-line motion of fluid in a curved pipe Philosophical Magazine, 30 (1928), pp. 673-693J.A.C. Humphrey, J.H. Whitelaw, G. Yee. Turbulent flow in a square duct with strong curvature Journal of Fluid Mechanics, 103 (1981), pp. 363-443A.M.P.K. Taylor, J.H. Whitelaw, M. Yianneskis. Curved ducts with strong secondary motion: velocity measurements of developing laminar and turbulent flow. Transactions of the ASME Journal of Fluids Engineering, 104 (1982), pp. 350-359M.M. Enayet, M.M. Gibson, A.M.P.K. Taylor, M. Yianneskis Laser-Doppler measurements of laminar and turbulent flow in a pipe bend. International Journal of Heat and Fluid Flow, 3 (1982), pp. 213-219K. Sudo, M. Sumida, H. Hibara. Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend. Experiments in Fluids, 25 (1998), pp. 42-49A. Yilmaz, E.K. Levy. Roping phenomena in pulverized coal conveying lines. Powder Technology, 95 (1998), pp. 38-43H. Akilli, E.K. Levy, B. Sahin. Gas–solid flow behaviour in a horizontal pipe after vertical-to-horizontal elbow. Powder Technology, 116 (2001), pp. 43-52Th. Frank, F.P. Schade, D. Petrak. Numerical simulation and experimental investigation of a gas–solid two-phase flow in a horizontal channel. International Journal of Multiphase Flow, 19 (1993), pp. 187-198M. Sommerfeld, J. Kussin. Wall roughness effects on pneumatic conveying of spherical particles in a narrow horizontal channel. Powder Technology, 142 (2004), pp. 180-192H. Akilli, E.K. Levy, B. Sahin. Investigation of gas–solid flow structure after a 90° vertical-to-horizontal elbow for low conveying gas velocities. Advanced Powder Technology, 16 (2005), pp. 261-264B. Kuan, W. Yang, M.P. Schwarz. Dilute gas–solid two-phase flows in a curved 90° duct bend: CFD simulation with experimental validation. Chemical Engineering Science, 62 (2007), pp. 2068-2088Z.F. Tian, K. Intahvong, J.Y. Tu, G.H. Yeoh. Numerical investigation into the effects of wall roughness on a gas-particle flow in a 90° bend. International Journal of Heat and Mass Transfer, 51 (2008), pp. 1238-1250S. Laín, M. Sommerfeld. Experimental and numerical study of the motion of non-spherical particles in wall bounded turbulent flows. Universidad Autónoma de Occidente, Cali (2008)S. Laín, M. Sommerfeld. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness. Powder Technology, 184 (2008), pp. 76-88M. Sommerfeld, S. Laín. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiphase Science and Technology, 21 (2009), pp. 123-140S. Laín. On Modeling and Numerical Computation of Industrial Disperse Two-Phase Flow With the Euler–Lagrange Approach. Shaker Verlag, Aachen, Germany (2010)S. Laín, M. Sommerfeld, J. Kussin. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. International Journal of Heat and Fluid Flow, 23 (2002), pp. 647-656R. Mei. An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. International Journal of Multiphase Flow, 18 (1992), pp. 145-147B. Oesterlé, T. Bui Dinh. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Experiments in Fluids, 25 (1998), pp. 16-22M.F. Göz, S. Laín, M. Sommerfeld. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering, 28 (2004), pp. 2727-2733C.T. Crowe, M.P. Sharma, D.E. Stock. The particle-source-in-cell (PSI-cell) model for gas-droplet flows. Journal of Fluids Engineering, 99 (1977), pp. 325-332S. Lain, M. Sommerfeld. Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behaviour. International Journal of Multiphase Flow, 39 (2012), pp. 105-120S. Laín, M. Sommerfeld, B. Quintero. Numerical simulation of secondary flow in pneumatic conveying of solid particles in a horizontal circular pipe. Brazilian Journal of Chemical Engineering, 26 (2009), pp. 583-594Y.T. Ng, S.C. Luo, T.T. Lim, Q.W. Ho. On the relation between centrifugal force and radial pressure gradient in flow inside curved and S-shaped ducts. Physics of Fluids, 20 (2008), p. 055109S. Laín, M. Sommerfeld. Structure and pressure drop in particle-laden gas flow through a pipe bend: a numerical analysis by the Euler–Lagrange approach Proc. ASME 2009 Fluids Engineering Division Summer Meeting FEDSM2009, paper FEDSM2009-78090 (2009)M. Sommerfeld. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. International Journal of Multiphase Flow, 29 (2003), pp. 675-699M. Sommerfeld, J. Kussin. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part II. Integral properties and validation. International Journal of Multiphase Flow, 29 (2003), pp. 701-718Derechos Reservados - Universidad Autónoma de Occidentehttps://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_abf2Characterisation of pneumatic conveying systems using the Euler/Lagrange approachArtículo 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/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Euler–Lagrange approachPneumatic conveyingWall roughnessInter-particle collisionsSegregation phenomenaPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2566-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2566-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2566-10000-0002-0269-2608virtual::2566-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2566-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/0ada0485-f7ac-4a3e-95a0-f14aa3c79af0/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/77400758-c7c7-4c77-b234-26456c6c518d/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALJournalPaper2_LS2_v4.pdfJournalPaper2_LS2_v4.pdfapplication/pdf1118970https://red.uao.edu.co/bitstreams/92c6c5d0-5c40-4f63-bd32-7aa8c62e8bc1/download03d59633da35a0ba82a6adebe286a3caMD54TEXTJournalPaper2_LS2_v4.pdf.txtJournalPaper2_LS2_v4.pdf.txtExtracted texttext/plain98926https://red.uao.edu.co/bitstreams/1ac36dc7-98e7-425e-909d-0d1b4ee95b58/download48f3649c8779c9b7ec44fe8932142e76MD55THUMBNAILJournalPaper2_LS2_v4.pdf.jpgJournalPaper2_LS2_v4.pdf.jpgGenerated Thumbnailimage/jpeg6619https://red.uao.edu.co/bitstreams/324e6faa-cf17-4f45-b659-06728a3c869a/download12a82d736ffae0de024137344b25e9d6MD5610614/11991oai:red.uao.edu.co:10614/119912024-03-06 16:45:42.688https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidenteopen.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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

Publicaciones similares