Prediction of horizontal gas–solid flows under different gravitational fields

In this paper the performance of horizontal pneumatic conveying under different gravity environments is evaluated. An Euler–Lagrange approach validated versus ground experiments is employed to predict the relevant particle variables such as particle mass flux, mean conveying and fluctuating velociti...

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Autores:
Laín Beatove, Santiago
Sommerfeld, Martin
Tipo de recurso:
Article of investigation
Fecha de publicación:
2014
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/14045
Acceso en línea:
https://hdl.handle.net/10614/14045
https://red.uao.edu.co/
Palabra clave:
Transporte neumático
Pneumatic-tube transportation
Pneumatic conveying
Channel
Euler–lagrange approach
Wall roughness
Inter-particle collisions
Different gravity environments
Rights
openAccess
License
Derechos reservados - Elsevier, 2014
id REPOUAO2_0577bba9cb6f150db742775b1235f5a3
oai_identifier_str oai:red.uao.edu.co:10614/14045
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Prediction of horizontal gas–solid flows under different gravitational fields
title Prediction of horizontal gas–solid flows under different gravitational fields
spellingShingle Prediction of horizontal gas–solid flows under different gravitational fields
Transporte neumático
Pneumatic-tube transportation
Pneumatic conveying
Channel
Euler–lagrange approach
Wall roughness
Inter-particle collisions
Different gravity environments
title_short Prediction of horizontal gas–solid flows under different gravitational fields
title_full Prediction of horizontal gas–solid flows under different gravitational fields
title_fullStr Prediction of horizontal gas–solid flows under different gravitational fields
title_full_unstemmed Prediction of horizontal gas–solid flows under different gravitational fields
title_sort Prediction of horizontal gas–solid flows under different gravitational fields
dc.creator.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martin
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martin
dc.subject.armarc.spa.fl_str_mv Transporte neumático
topic Transporte neumático
Pneumatic-tube transportation
Pneumatic conveying
Channel
Euler–lagrange approach
Wall roughness
Inter-particle collisions
Different gravity environments
dc.subject.armarc.eng.fl_str_mv Pneumatic-tube transportation
dc.subject.proposal.eng.fl_str_mv Pneumatic conveying
Channel
Euler–lagrange approach
Wall roughness
Inter-particle collisions
Different gravity environments
description In this paper the performance of horizontal pneumatic conveying under different gravity environments is evaluated. An Euler–Lagrange approach validated versus ground experiments is employed to predict the relevant particle variables such as particle mass flux, mean conveying and fluctuating velocities in terrestrial, lunar and micro-gravity conditions. Gravity reduced computations predict a reduction in the global particle–wall collision frequency. Also, in the case of low wall roughness and small particle mass loading, reduction of gravity acceleration implies an increase of particle–wall collision frequency with the upper wall of the channel affecting greatly the particle mass flux profile. In the case of high wall roughness and/or high particle-to-fluid mass loading (i.e., around 1.0) particle conveying characteristics are similar in the three gravity conditions evaluated. This is due to the fact that both, wall roughness and inter-particle collisions reduce gravitational settling. However, the influence of gravity on the additional pressure loss along the channel due to the conveying of the particles is much reduced.
publishDate 2014
dc.date.issued.none.fl_str_mv 2014-11-01
dc.date.accessioned.none.fl_str_mv 2022-07-15T16:04:37Z
dc.date.available.none.fl_str_mv 2022-07-15T16:04:37Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv 2731177
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/14045
dc.identifier.reponame.spa.fl_str_mv Repositorio Educativo Digital
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identifier_str_mv 2731177
Repositorio Educativo Digital
url https://hdl.handle.net/10614/14045
https://red.uao.edu.co/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 1962
dc.relation.citationissue.spa.fl_str_mv 9
dc.relation.citationstartpage.spa.fl_str_mv 1949
dc.relation.citationvolume.spa.fl_str_mv 54
dc.relation.cites.eng.fl_str_mv Laín, S., Sommerfeld, M. (2014). Prediction of horizontal gas–solid flows under different gravitational fields. Advances in Space Research.54(9),1949-1962. https://hdl.handle.net/10614/14045
dc.relation.ispartofjournal.eng.fl_str_mv Advances in Space Research
dc.relation.references.none.fl_str_mv Adam, O. Untersuchungen über die Vorgänge in festoffbeladenen Gasströmungen. Forschungsberichte des Landes Nordrhein-Westfalen. Westdeutscher Verlag, Köln, 1960.
Akilli, H., Levy, E.K. Sahin, B. Gas-solid flow behaviour in a horizontal pipe after a 90° vertical-to-horizontal elbow. Powder Technology 116, 43-52, 2001.
Dennis, S.C.R., Singh, S.N., Ingham, D.B. The steady flow due to a rotating sphere at low and moderate Reynolds numbers. J. Fluid Mech. 101, 257–279, 1980.
Eskin, D. Modeling dilute gas-particle flows in horizontal channels with different wall roughness. Chem. Eng. Sci. 60, 655–663, 2005.
Fokeer, S., Kingman, S. Lowndes, I., Reynolds, A. Characterisation of the cross sectional particle concentration distribution in horizontal dilute flow conveying – a review. Chemical Engineering and Processing 43, 677–691, 2004.
Gibson, M.M., Launder, B.E. Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 86, 491–511, 1978.
Göz, M. F., Laín, S., Sommerfeld, M. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering 28, 2727–2733, 2004.
Göz, M.F., Sommerfeld, M., Laín, S. Instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Aiche J. 52, 469-477, 2006.
Kohnen, G., Sommerfeld, M. The effect of turbulence modelling on turbulence modification in two-phase flows using the Euler–Lagrange approach, Proc. 11th Symp. on Turbulent Shear Flows, Grenoble (France) 2, P3, pp. 23–28, 1997.
Kohnen, G., Rüger, M., Sommerfeld, M. Convergence behaviour for numerical calculations by the Euler/Lagrange method for strongly coupled phases. Num. Meth. for Multiphase Flows, FED vol. 185. Eds: Crowe et al., pp. 191-202, 1994.
Konan, A., Laín, S., Simonin, O., Sommerfeld, M. Comparison between Euler–Euler and Euler–Lagrange computations of gas–solid turbulent flow in a horizontal channel with different wall roughness. Proc. FEDSM06, 2006 ASME Joint U.S.—European Fluid Engineering Summer Meeting, July 17-20. Miami, FL, 2006.
Kussin, J., Sommerfeld, M. Experimental studies on particle behavior and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33, 143-159, 2002.
Laín, S., Aliod, R. Study of the Eulerian dispersed phase equations in non-uniform turbulent two-phase flows: Discussion and comparison with experiments, Int. J. Heat Fluid Flow 21, 374–380, 2000.
Laín, S., Sommerfeld, M., Kussin, J. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. Int. J. Heat and Fluid Flow 23, 647- 656, 2002.
Laín, S., Sommerfeld, M. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness. Powder Technology 184, 76-88, 2008.
Laín, S., Sommerfeld, M., Quintero, B. Numerical simulation of secondary flow in pneumatic conveying of solid particles in a horizontal circular pipe. Brazilian J. Chem. Eng. 26, 583-594, 2009.
Laín, S. On modelling and numerical computation of industrial disperse two-phase flow with the Euler-Lagrange approach. Shaker Verlag, Aachen, 2010.
Laín, S., Sommerfeld, M. Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behavior. Int. J. Multiphase Flow 39, 105-120, 2012.
Lun, C.K.K. Liu, H.S. Numerical simulation of dilute turbulent gas-solid flows. Int. J. Multiphase Flow 23, 575-605, 1997.
Lyubimov, D.V., Bratsun, D.A., Lyubimova, T.P., Roux, B. Influence of gravitational precipitations of solid particles on thermal buoyancy convection. Advances in Space Research 22, 1267-1270, 1998.
Mei, R. An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int. J. Multiphase Flow 18, 145–147, 1992.
Mueller, R.P., Townsend, I.I., Mantovani, J.G. Pneumatic regolith transfer systems for In- Situ Resource Utilization. NASA Technical Report 20110008766, 2011.
Oesterlé, B., Bui Dinh, T. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Exp. Fluids 25, 16–22, 1998.
Pan, X., Liu, X., Li, G., Li, T. Numerical investigation on gas-particle flows in horizontal channel under the reduced gravity environments. Acta Astronautica 68, 133-140, 2011.
Rubinow, S.I., Keller, J.B. The transverse force on a spinning sphere moving in a viscous liquid. J. Fluid Mech. 11, 447–459, 1961.
Saffman, P.G. The lift on a small sphere in a shear flow. J. Fluid Mech. 22, 385–400, 1965.
Sommerfeld, M., Huber, N. Experimental analysis and modelling of particle-wall collisions. Int. J. Mutiphase Flow 25, 1457-1489, 1999.
Sommerfeld, M. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiphase Flow 27, 1828-1858, 2001.
Sommerfeld, M. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. Int. J. Multiphase Flow 29, 675 – 699, 2003.
Sommerfeld, M., Ho, C.A. Numerical calculation of particle transport in turbulent wall bounded flows. Powder Technology 131, 1-6, 2003.
Sommerfeld, M., Kussin, J. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part II. Integral properties and validation. Int. J. Multiphase Flow 29, 701–718, 2003.
Sommerfeld, M., Kussin, J. Wall roughness effects on pneumatic conveying of spherical particles in a narrow horizontal channel. Powder Technology 142, 180-192, 2004.
Sommerfeld, M., van Wachem, B., Oliemans, R. Best Practice Guidelines for Computational Fluid Dynamics of Dispersed Multiphase Flows. ERCOFTAC (European Research Community on Flow, Turbulence and Combustion), ISBN 978-91- 633-3564-8, 2008.
Sornchamni, T., Jovanovic, G.N., Reed, B.P., Atwater, J.E., Akse, J.R., Wheeler, R.R. Operation of magnetically assisted fluidized beds in microgravity and variable gravity: experiment and theory. Advances in Space Research 34, 1494-1498, 2004.
Stubbs, T.J., Vondrak, R.R., Farrell, W.M. A dynamic fountain model for lunar dust. Advances in Space Research 37, 59-66, 2006.
Sullivan, T.A., Koenig, E., Knudsen, C.W., Gibson, M.A. Pneumatic conveying of materials at partial gravity. J. Aerosp. Eng. 7, 199-208, 1994.
Tsuji, Y., Morikawa, Y., Tanaka, T., Nakatsukasa, N., Nadatani, M. Numerical simulation of gas-solid two-phase flow in a two-dimensional horizontal channel. Int. J. Multiphase Flow 13, 671 – 684, 1987.
Yilmaz, A., Levy, E.K. Formation and dispersion of ropes in pneumatic conveying. Powder Technology 114, 168 – 185, 2001.
Zhang, X. and Zhou, L. A second-order moment particle-wall collision model accounting for the wall roughness. Powder Technology 159, 111–120, 2005.
dc.rights.spa.fl_str_mv Derechos reservados - Elsevier, 2014
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spelling Laín Beatove, Santiagovirtual::2530-1Sommerfeld, Martin4225b01693727b10986bcc383715fa702022-07-15T16:04:37Z2022-07-15T16:04:37Z2014-11-012731177https://hdl.handle.net/10614/14045Repositorio Educativo Digitalhttps://red.uao.edu.co/In this paper the performance of horizontal pneumatic conveying under different gravity environments is evaluated. An Euler–Lagrange approach validated versus ground experiments is employed to predict the relevant particle variables such as particle mass flux, mean conveying and fluctuating velocities in terrestrial, lunar and micro-gravity conditions. Gravity reduced computations predict a reduction in the global particle–wall collision frequency. Also, in the case of low wall roughness and small particle mass loading, reduction of gravity acceleration implies an increase of particle–wall collision frequency with the upper wall of the channel affecting greatly the particle mass flux profile. In the case of high wall roughness and/or high particle-to-fluid mass loading (i.e., around 1.0) particle conveying characteristics are similar in the three gravity conditions evaluated. This is due to the fact that both, wall roughness and inter-particle collisions reduce gravitational settling. However, the influence of gravity on the additional pressure loss along the channel due to the conveying of the particles is much reduced.28 páginasapplication/pdfengElsevierDerechos reservados - Elsevier, 2014https://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_abf2Prediction of horizontal gas–solid flows under different gravitational fieldsArtículo de revistahttp://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_970fb48d4fbd8a85Transporte neumáticoPneumatic-tube transportationPneumatic conveyingChannelEuler–lagrange approachWall roughnessInter-particle collisionsDifferent gravity environments19629194954Laín, S., Sommerfeld, M. (2014). Prediction of horizontal gas–solid flows under different gravitational fields. Advances in Space Research.54(9),1949-1962. https://hdl.handle.net/10614/14045Advances in Space ResearchAdam, O. Untersuchungen über die Vorgänge in festoffbeladenen Gasströmungen. Forschungsberichte des Landes Nordrhein-Westfalen. Westdeutscher Verlag, Köln, 1960.Akilli, H., Levy, E.K. Sahin, B. Gas-solid flow behaviour in a horizontal pipe after a 90° vertical-to-horizontal elbow. Powder Technology 116, 43-52, 2001.Dennis, S.C.R., Singh, S.N., Ingham, D.B. The steady flow due to a rotating sphere at low and moderate Reynolds numbers. J. Fluid Mech. 101, 257–279, 1980.Eskin, D. Modeling dilute gas-particle flows in horizontal channels with different wall roughness. Chem. Eng. Sci. 60, 655–663, 2005.Fokeer, S., Kingman, S. Lowndes, I., Reynolds, A. Characterisation of the cross sectional particle concentration distribution in horizontal dilute flow conveying – a review. Chemical Engineering and Processing 43, 677–691, 2004.Gibson, M.M., Launder, B.E. Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 86, 491–511, 1978.Göz, M. F., Laín, S., Sommerfeld, M. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering 28, 2727–2733, 2004.Göz, M.F., Sommerfeld, M., Laín, S. Instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Aiche J. 52, 469-477, 2006.Kohnen, G., Sommerfeld, M. The effect of turbulence modelling on turbulence modification in two-phase flows using the Euler–Lagrange approach, Proc. 11th Symp. on Turbulent Shear Flows, Grenoble (France) 2, P3, pp. 23–28, 1997.Kohnen, G., Rüger, M., Sommerfeld, M. Convergence behaviour for numerical calculations by the Euler/Lagrange method for strongly coupled phases. Num. Meth. for Multiphase Flows, FED vol. 185. Eds: Crowe et al., pp. 191-202, 1994.Konan, A., Laín, S., Simonin, O., Sommerfeld, M. Comparison between Euler–Euler and Euler–Lagrange computations of gas–solid turbulent flow in a horizontal channel with different wall roughness. Proc. FEDSM06, 2006 ASME Joint U.S.—European Fluid Engineering Summer Meeting, July 17-20. Miami, FL, 2006.Kussin, J., Sommerfeld, M. Experimental studies on particle behavior and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33, 143-159, 2002.Laín, S., Aliod, R. Study of the Eulerian dispersed phase equations in non-uniform turbulent two-phase flows: Discussion and comparison with experiments, Int. J. Heat Fluid Flow 21, 374–380, 2000.Laín, S., Sommerfeld, M., Kussin, J. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. Int. J. Heat and Fluid Flow 23, 647- 656, 2002.Laín, S., Sommerfeld, M. Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness. Powder Technology 184, 76-88, 2008.Laín, S., Sommerfeld, M., Quintero, B. Numerical simulation of secondary flow in pneumatic conveying of solid particles in a horizontal circular pipe. Brazilian J. Chem. Eng. 26, 583-594, 2009.Laín, S. On modelling and numerical computation of industrial disperse two-phase flow with the Euler-Lagrange approach. Shaker Verlag, Aachen, 2010.Laín, S., Sommerfeld, M. Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behavior. Int. J. Multiphase Flow 39, 105-120, 2012.Lun, C.K.K. Liu, H.S. Numerical simulation of dilute turbulent gas-solid flows. Int. J. Multiphase Flow 23, 575-605, 1997.Lyubimov, D.V., Bratsun, D.A., Lyubimova, T.P., Roux, B. Influence of gravitational precipitations of solid particles on thermal buoyancy convection. Advances in Space Research 22, 1267-1270, 1998.Mei, R. An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int. J. Multiphase Flow 18, 145–147, 1992.Mueller, R.P., Townsend, I.I., Mantovani, J.G. Pneumatic regolith transfer systems for In- Situ Resource Utilization. NASA Technical Report 20110008766, 2011.Oesterlé, B., Bui Dinh, T. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Exp. Fluids 25, 16–22, 1998.Pan, X., Liu, X., Li, G., Li, T. Numerical investigation on gas-particle flows in horizontal channel under the reduced gravity environments. Acta Astronautica 68, 133-140, 2011.Rubinow, S.I., Keller, J.B. The transverse force on a spinning sphere moving in a viscous liquid. J. Fluid Mech. 11, 447–459, 1961.Saffman, P.G. The lift on a small sphere in a shear flow. J. Fluid Mech. 22, 385–400, 1965.Sommerfeld, M., Huber, N. Experimental analysis and modelling of particle-wall collisions. Int. J. Mutiphase Flow 25, 1457-1489, 1999.Sommerfeld, M. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiphase Flow 27, 1828-1858, 2001.Sommerfeld, M. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. Int. J. Multiphase Flow 29, 675 – 699, 2003.Sommerfeld, M., Ho, C.A. Numerical calculation of particle transport in turbulent wall bounded flows. Powder Technology 131, 1-6, 2003.Sommerfeld, M., Kussin, J. Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part II. Integral properties and validation. Int. J. Multiphase Flow 29, 701–718, 2003.Sommerfeld, M., Kussin, J. Wall roughness effects on pneumatic conveying of spherical particles in a narrow horizontal channel. Powder Technology 142, 180-192, 2004.Sommerfeld, M., van Wachem, B., Oliemans, R. Best Practice Guidelines for Computational Fluid Dynamics of Dispersed Multiphase Flows. ERCOFTAC (European Research Community on Flow, Turbulence and Combustion), ISBN 978-91- 633-3564-8, 2008.Sornchamni, T., Jovanovic, G.N., Reed, B.P., Atwater, J.E., Akse, J.R., Wheeler, R.R. Operation of magnetically assisted fluidized beds in microgravity and variable gravity: experiment and theory. Advances in Space Research 34, 1494-1498, 2004.Stubbs, T.J., Vondrak, R.R., Farrell, W.M. A dynamic fountain model for lunar dust. Advances in Space Research 37, 59-66, 2006.Sullivan, T.A., Koenig, E., Knudsen, C.W., Gibson, M.A. Pneumatic conveying of materials at partial gravity. J. Aerosp. Eng. 7, 199-208, 1994.Tsuji, Y., Morikawa, Y., Tanaka, T., Nakatsukasa, N., Nadatani, M. Numerical simulation of gas-solid two-phase flow in a two-dimensional horizontal channel. Int. J. Multiphase Flow 13, 671 – 684, 1987.Yilmaz, A., Levy, E.K. Formation and dispersion of ropes in pneumatic conveying. Powder Technology 114, 168 – 185, 2001.Zhang, X. and Zhou, L. A second-order moment particle-wall collision model accounting for the wall roughness. Powder Technology 159, 111–120, 2005.Comunidad generalPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2530-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2530-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2530-10000-0002-0269-2608virtual::2530-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2530-1LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/0c8d485e-c41e-4f64-8e9f-49648b5939fb/download20b5ba22b1117f71589c7318baa2c560MD52ORIGINALPrediction of horizontal 14_Manuscript.pdfPrediction of horizontal 14_Manuscript.pdfapplication/pdf522941https://red.uao.edu.co/bitstreams/dcb5ab61-708b-4a3e-ae34-4326ef2261ab/download28de9fff9d0ffc63dd1752908e932c92MD53TEXTPrediction of horizontal 14_Manuscript.pdf.txtPrediction of horizontal 14_Manuscript.pdf.txtExtracted texttext/plain62823https://red.uao.edu.co/bitstreams/c279b4b8-9774-4cd1-896a-a38eb10086fe/downloadb9e2fb982e17dafa3309b677ae092b9dMD54THUMBNAILPrediction of horizontal 14_Manuscript.pdf.jpgPrediction of horizontal 14_Manuscript.pdf.jpgGenerated Thumbnailimage/jpeg6523https://red.uao.edu.co/bitstreams/66cbce54-d268-4288-a207-5f45d10c6ea9/downloadba8e5b8460a98c9e919d61a94325c159MD5510614/14045oai:red.uao.edu.co:10614/140452024-03-06 16:02:18.146https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - Elsevier, 2014open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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