Response behavior of nonspherical particles in homogeneous isotropic turbulent flows

In this study, the responsiveness of nonspherical particles, specifically ellipsoids and cylinders, in homogeneous and isotropic turbulence is investigated through kinematic simulations of the fluid velocity field. Particle tracking in such flow field includes not only the translational and rotation...

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Autores:
Laín Beatove, Santiago
Tipo de recurso:
Part of book
Fecha de publicación:
2019
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/13443
Acceso en línea:
https://hdl.handle.net/10614/13443
Palabra clave:
Cinemática
Kinematics
Kinematic simulations
Lagrangian tracking
Nonspherical particles
Response behavior
Preferential orientation
Rights
openAccess
License
https://creativecommons.org/licenses/by-nc-nd/4.0/
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oai_identifier_str oai:red.uao.edu.co:10614/13443
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
title Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
spellingShingle Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
Cinemática
Kinematics
Kinematic simulations
Lagrangian tracking
Nonspherical particles
Response behavior
Preferential orientation
title_short Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
title_full Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
title_fullStr Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
title_full_unstemmed Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
title_sort Response behavior of nonspherical particles in homogeneous isotropic turbulent flows
dc.creator.fl_str_mv Laín Beatove, Santiago
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
dc.subject.armarc.spa.fl_str_mv Cinemática
topic Cinemática
Kinematics
Kinematic simulations
Lagrangian tracking
Nonspherical particles
Response behavior
Preferential orientation
dc.subject.armarc.eng.fl_str_mv Kinematics
dc.subject.proposal.eng.fl_str_mv Kinematic simulations
Lagrangian tracking
Nonspherical particles
Response behavior
Preferential orientation
description In this study, the responsiveness of nonspherical particles, specifically ellipsoids and cylinders, in homogeneous and isotropic turbulence is investigated through kinematic simulations of the fluid velocity field. Particle tracking in such flow field includes not only the translational and rotational components but also the orientation through the Euler angles and parameters. Correlations for the flow coefficients, forces and torques, of the nonspherical particles in the range of intermediate Reynolds number are obtained from the literature. The Lagrangian time autocorrelation function, the translational and rotational particle response, and preferential orientation of the nonspherical particles in the turbulent flow are studied as function of their shape and inertia. As a result, particle autocorrelation functions, translational and rotational, decrease with aspect ratio, and particle linear root mean square velocity increases with aspect ratio, while rotational root mean square velocity first increases, reaches a maximum around aspect ratio 2, and then decreases again. Finally, cylinders do not present any preferential orientation in homogeneous isotropic turbulence, but ellipsoids do, resulting in preferred orientations that maximize the cross section exposed to the flow
publishDate 2019
dc.date.issued.none.fl_str_mv 2019
dc.date.accessioned.none.fl_str_mv 2021-11-16T20:30:06Z
dc.date.available.none.fl_str_mv 2021-11-16T20:30:06Z
dc.type.spa.fl_str_mv Capítulo - Parte de Libro
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dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/bookPart
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dc.identifier.isbn.none.fl_str_mv 9789535170501
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/13443
identifier_str_mv 9789535170501
url https://hdl.handle.net/10614/13443
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationedition.spa.fl_str_mv 1
dc.relation.citationendpage.spa.fl_str_mv 37
dc.relation.citationstartpage.spa.fl_str_mv 19
dc.relation.cites.eng.fl_str_mv Laín, S. (2018). Response Behavior of Nonspherical Particles in Homogeneous Isotropic Turbulent Flows. Advanced computational fluid dynamics for emerging engineering processes-Eulerian vs. Lagrangian. IntechOpen. (Capítulo 2), 19-37.
dc.relation.ispartofbook.eng.fl_str_mv Advanced computational fluid dynamics for emerging engineering processes-Eulerian vs. Lagrangian
dc.relation.references.none.fl_str_mv [1] Simonin O. Statistical and continuum modelling of turbulent reactive particulate flows, Part II: Application of a two-phase second-moment transport model for prediction of turbulent gasparticle flows. In: Von Karman Institute for Fluid Mechanics Lecture Series, 2000-6. 2000
[2] Sommerfeld M, Lain S. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiphase Science and Technology. 2009;21:123-140
[3] Sommerfeld M, Lain S. Stochastic modelling for capturing the behaviour of irregular-shaped non-spherical particles in confined turbulent flows. Powder Technology. 2018;332:253-264
[4] Jeffery G. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society. 1922; 102A:161-179
[5] Happel J, Brenner H. Low Reynolds Number Hydrodynamics. 2nd ed. The Hague: Martinus Nijhoff; 1983. 553 p
[6] Blaser S. Forces on the surface of small ellipsoidal particles immersed in a linear flow field. Chemical Engineering Science. 2002;57:515-526
[7] Squires L, Squires WJr. The sedimentation of thin discs. Transaction of the American Institute of Chemical Engineers. 1937;33:1-12
[8] Pettyjohn ES, Christiansen EB. Effect of particle shape on free-settling rates of isometric particles. Chemical Engineering Progress. 1948;44:157-172
[9] Heiss JF, Coull J. The effect of orientation and shape on the settling velocity of non-isometric particles in a viscous medium. Chemical Engineering Progress. 1952;48:133-140
[10] Willmarth WW, Hawk NE, Harvey RL. Steady and unsteady motions and wakes of freely falling disks. Physics of Fluids. 1964;7:197-208
[11] McKay G, Murphy WR, Hills M. Settling characteristics of discs and cylinders. Chemical Engineering Research and Design. 1988;66:107-112
[12] Haider A, Levenspiel O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technology. 1989;58:63-70
[13] Thompson TL, Clark NN. A holistic approach to particle drag prediction. Powder Technology. 1991;67:57-66
[14] Swamee PK, Ojha CAP. Drag coefficient and fall velocity of nonspherical particles. Journal of Hydraulic Engineering. 1991;117: 660-667
[15] Ganser GH. A rational approach to drag prediction of spherical and nonspherical particles. Powder Technology. 1993;77:143-152
[16] Tran-Cong S, Gay M, Michaelides EE. Drag coefficients of irregularly shaped particles. Powder Technology. 2004;139:21-32
[17] Hölzer A, Sommerfeld M. New and simple correlation formula for the drag coefficient of non-spherical particles. Powder Technology. 2008;184:371-365
[18] Hölzer A, Sommerfeld M. Lattice Boltzmann simulations to determine drag, lift and torque acting on nonspherical particles. Computers and Fluids. 2009;38:572-589
[19] Vakil A, Green SI. Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers. Computers and Fluids. 2009; 38:1771-1781
[20] Zastawny M, Mallouppas G, Zhao F, van Wachem B. Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. International Journal of Multiphase Flow. 2012;39:227-239
[21] Ouchene R, Khalij M, Arcen B, Tanière A. A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds numbers. Powder Technology. 2016;303:33-43
[22] Fan FG, Ahmadi G. Dispersion of ellipsoidal particles in an isotropic pseudo-turbulent flow field. Transactions of the ASME, Journal of Fluids Engineering. 1995;117:154-161
[23] Olson JA. The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence. International Journal of Multiphase Flow. 2001;27:2083-2103
[24] Lin J, Shi X, Yu Z. The motion of fibers in an evolving mixing layer. International Journal of Multiphase Flow. 2003;29:1355-1372
[25] Zhang H, Ahmadi G, Fan FG, McLaughlin JB. Ellipsoidal particles transport and deposition in turbulent channel flows. International Journal of Multiphase Flow. 2001;27:971-1009
[26] Mortensen PH, Andersson HI, Gillissen JJJ, Boersma BJ. Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Physics of Fluids. 2008;20:093302
[27] Marchioli C, Fantoni M, Soldati A. Orientation, distribution and deposition of elongated, inertial fibers in turbulent channel flow. Physics of Fluids. 2010;22: 033301
[28] van Wachem B, Zastawny M, Zhao F, Malloupas G. Modelling of gas–solid turbulent channel flow with nonspherical particles with large stokes numbers. International Journal of Multiphase Flow. 2015;68:80-92
[29] Arcen B, Ouchene R, Kahlij M, Tanière A. Prolate spheroidal particles’ behavior in a vertical wall-bounded turbulent flow. Physics of Fluids. 2017; 29:093301
[30] Rosendahl L. Using a multiparameter particle shape description to predict the motion of non-spherical particle shapes in swirling flow. Applied Mathematical Modelling. 2000;24:11-25
[31] Yin C, Rosendahl L, Kaer SK, Sorensen H. Modelling the motion of cylindrical particles in a nonuniform flow. Chemical Engineering Science. 2003;58:3489-3498
[32] Yin C, Rosendahl L, Kaer SK, Condra TJ. Use of numerical modelling in design for co-firing biomass in wallfired burners. Chemical Engineering Science. 2004;59:3281-3292
[33] Goldstein H. Classical Mechanics. 2nd ed. Vol. 793. New York: Addison- Wesley; 1980
[34] Gallily I, Cohen AH. On the orderly nature of the motion of nonspherical aerosol particles II. Inertial collision between a spherical large droplet and an axially symmetrical elongated particle. Journal of Colloid and Interface Science. 2979;68:338-356
[35] Göz MF, Lain S, Sommerfeld M. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering. 2004;28: 2727-2733
[36] Göz MF, Sommerfeld M, Lain S. Instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. AICHE Journal. 2006;52:469-477
[37] Thijssen MJ. Computational Physics. 2nd ed. Cambridge: Cambridge University Press; 2007. 620 p
[38] Malik NA, Vassilicos JC. A Lagrangian model for turbulent dispersion with turbulent-like flow structure: Comparison with DNS for two-particle statistics. Physics of Fluids. 1999;11:1572-1580
[39] El-Maihy A. Study of diffusion and dispersion of particles using kinematic simulation [thesis]. Sheffield: University of Sheffield; 2003
[40] Davila J, Vassilicos JC. Richardson pair diffusion and the stagnation point structure of turbulence. Physical Review Letters. 2003;91:144501
[41] Hyland KE, McKee S, Reeks MW. Exact analytic solutions to turbulent particle flow equations. Physics of Fluids. 1999;11:1249-1261
[42] Hölzer A, Sommerfeld M. Analysis of the behaviour of cylinders in homogeneous isotropic turbulence by lattice Boltzmann method. ERCOFTAC Bulletin. 2010;82:11-16
[43] Khayat RE, Cox RG. Inertial effects on the motion of long slender bodies. Journal of Fluid Mechanics. 1989;209: 435-462
[44] Newsom RK, Bruce CW. Orientational properties of fibrous aerosols in atmospheric turbulence. Journal of Aerosol Science. 1998;29: 773-797
[45] Mandø M, Rosendahl L. On the motion of non-spherical particles at high Reynolds number. Powder Technology. 2010;202:1-13
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spelling Laín Beatove, Santiagovirtual::2526-12021-11-16T20:30:06Z2021-11-16T20:30:06Z20199789535170501https://hdl.handle.net/10614/13443In this study, the responsiveness of nonspherical particles, specifically ellipsoids and cylinders, in homogeneous and isotropic turbulence is investigated through kinematic simulations of the fluid velocity field. Particle tracking in such flow field includes not only the translational and rotational components but also the orientation through the Euler angles and parameters. Correlations for the flow coefficients, forces and torques, of the nonspherical particles in the range of intermediate Reynolds number are obtained from the literature. The Lagrangian time autocorrelation function, the translational and rotational particle response, and preferential orientation of the nonspherical particles in the turbulent flow are studied as function of their shape and inertia. As a result, particle autocorrelation functions, translational and rotational, decrease with aspect ratio, and particle linear root mean square velocity increases with aspect ratio, while rotational root mean square velocity first increases, reaches a maximum around aspect ratio 2, and then decreases again. Finally, cylinders do not present any preferential orientation in homogeneous isotropic turbulence, but ellipsoids do, resulting in preferred orientations that maximize the cross section exposed to the flowPrimera edición19 páginasapplication/pdfengIntechOpenhttps://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_abf2Response behavior of nonspherical particles in homogeneous isotropic turbulent flowsCapítulo - Parte de Librohttp://purl.org/coar/resource_type/c_3248Textinfo:eu-repo/semantics/bookParthttps://purl.org/redcol/resource_type/CAP_LIBinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85CinemáticaKinematicsKinematic simulationsLagrangian trackingNonspherical particlesResponse behaviorPreferential orientation13719Laín, S. (2018). Response Behavior of Nonspherical Particles in Homogeneous Isotropic Turbulent Flows. Advanced computational fluid dynamics for emerging engineering processes-Eulerian vs. Lagrangian. IntechOpen. (Capítulo 2), 19-37.Advanced computational fluid dynamics for emerging engineering processes-Eulerian vs. Lagrangian[1] Simonin O. Statistical and continuum modelling of turbulent reactive particulate flows, Part II: Application of a two-phase second-moment transport model for prediction of turbulent gasparticle flows. In: Von Karman Institute for Fluid Mechanics Lecture Series, 2000-6. 2000[2] Sommerfeld M, Lain S. From elementary processes to the numerical prediction of industrial particle-laden flows. Multiphase Science and Technology. 2009;21:123-140[3] Sommerfeld M, Lain S. Stochastic modelling for capturing the behaviour of irregular-shaped non-spherical particles in confined turbulent flows. Powder Technology. 2018;332:253-264[4] Jeffery G. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society. 1922; 102A:161-179[5] Happel J, Brenner H. Low Reynolds Number Hydrodynamics. 2nd ed. The Hague: Martinus Nijhoff; 1983. 553 p[6] Blaser S. Forces on the surface of small ellipsoidal particles immersed in a linear flow field. Chemical Engineering Science. 2002;57:515-526[7] Squires L, Squires WJr. The sedimentation of thin discs. Transaction of the American Institute of Chemical Engineers. 1937;33:1-12[8] Pettyjohn ES, Christiansen EB. Effect of particle shape on free-settling rates of isometric particles. Chemical Engineering Progress. 1948;44:157-172[9] Heiss JF, Coull J. The effect of orientation and shape on the settling velocity of non-isometric particles in a viscous medium. Chemical Engineering Progress. 1952;48:133-140[10] Willmarth WW, Hawk NE, Harvey RL. Steady and unsteady motions and wakes of freely falling disks. Physics of Fluids. 1964;7:197-208[11] McKay G, Murphy WR, Hills M. Settling characteristics of discs and cylinders. Chemical Engineering Research and Design. 1988;66:107-112[12] Haider A, Levenspiel O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technology. 1989;58:63-70[13] Thompson TL, Clark NN. A holistic approach to particle drag prediction. Powder Technology. 1991;67:57-66[14] Swamee PK, Ojha CAP. Drag coefficient and fall velocity of nonspherical particles. Journal of Hydraulic Engineering. 1991;117: 660-667[15] Ganser GH. A rational approach to drag prediction of spherical and nonspherical particles. Powder Technology. 1993;77:143-152[16] Tran-Cong S, Gay M, Michaelides EE. Drag coefficients of irregularly shaped particles. Powder Technology. 2004;139:21-32[17] Hölzer A, Sommerfeld M. New and simple correlation formula for the drag coefficient of non-spherical particles. Powder Technology. 2008;184:371-365[18] Hölzer A, Sommerfeld M. Lattice Boltzmann simulations to determine drag, lift and torque acting on nonspherical particles. Computers and Fluids. 2009;38:572-589[19] Vakil A, Green SI. Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers. Computers and Fluids. 2009; 38:1771-1781[20] Zastawny M, Mallouppas G, Zhao F, van Wachem B. Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. International Journal of Multiphase Flow. 2012;39:227-239[21] Ouchene R, Khalij M, Arcen B, Tanière A. A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds numbers. Powder Technology. 2016;303:33-43[22] Fan FG, Ahmadi G. Dispersion of ellipsoidal particles in an isotropic pseudo-turbulent flow field. Transactions of the ASME, Journal of Fluids Engineering. 1995;117:154-161[23] Olson JA. The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence. International Journal of Multiphase Flow. 2001;27:2083-2103[24] Lin J, Shi X, Yu Z. The motion of fibers in an evolving mixing layer. International Journal of Multiphase Flow. 2003;29:1355-1372[25] Zhang H, Ahmadi G, Fan FG, McLaughlin JB. Ellipsoidal particles transport and deposition in turbulent channel flows. International Journal of Multiphase Flow. 2001;27:971-1009[26] Mortensen PH, Andersson HI, Gillissen JJJ, Boersma BJ. Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Physics of Fluids. 2008;20:093302[27] Marchioli C, Fantoni M, Soldati A. Orientation, distribution and deposition of elongated, inertial fibers in turbulent channel flow. Physics of Fluids. 2010;22: 033301[28] van Wachem B, Zastawny M, Zhao F, Malloupas G. Modelling of gas–solid turbulent channel flow with nonspherical particles with large stokes numbers. International Journal of Multiphase Flow. 2015;68:80-92[29] Arcen B, Ouchene R, Kahlij M, Tanière A. Prolate spheroidal particles’ behavior in a vertical wall-bounded turbulent flow. Physics of Fluids. 2017; 29:093301[30] Rosendahl L. Using a multiparameter particle shape description to predict the motion of non-spherical particle shapes in swirling flow. Applied Mathematical Modelling. 2000;24:11-25[31] Yin C, Rosendahl L, Kaer SK, Sorensen H. Modelling the motion of cylindrical particles in a nonuniform flow. Chemical Engineering Science. 2003;58:3489-3498[32] Yin C, Rosendahl L, Kaer SK, Condra TJ. Use of numerical modelling in design for co-firing biomass in wallfired burners. Chemical Engineering Science. 2004;59:3281-3292[33] Goldstein H. Classical Mechanics. 2nd ed. Vol. 793. New York: Addison- Wesley; 1980[34] Gallily I, Cohen AH. On the orderly nature of the motion of nonspherical aerosol particles II. Inertial collision between a spherical large droplet and an axially symmetrical elongated particle. Journal of Colloid and Interface Science. 2979;68:338-356[35] Göz MF, Lain S, Sommerfeld M. Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering. 2004;28: 2727-2733[36] Göz MF, Sommerfeld M, Lain S. Instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. AICHE Journal. 2006;52:469-477[37] Thijssen MJ. Computational Physics. 2nd ed. Cambridge: Cambridge University Press; 2007. 620 p[38] Malik NA, Vassilicos JC. A Lagrangian model for turbulent dispersion with turbulent-like flow structure: Comparison with DNS for two-particle statistics. Physics of Fluids. 1999;11:1572-1580[39] El-Maihy A. Study of diffusion and dispersion of particles using kinematic simulation [thesis]. Sheffield: University of Sheffield; 2003[40] Davila J, Vassilicos JC. Richardson pair diffusion and the stagnation point structure of turbulence. Physical Review Letters. 2003;91:144501[41] Hyland KE, McKee S, Reeks MW. Exact analytic solutions to turbulent particle flow equations. Physics of Fluids. 1999;11:1249-1261[42] Hölzer A, Sommerfeld M. Analysis of the behaviour of cylinders in homogeneous isotropic turbulence by lattice Boltzmann method. ERCOFTAC Bulletin. 2010;82:11-16[43] Khayat RE, Cox RG. Inertial effects on the motion of long slender bodies. Journal of Fluid Mechanics. 1989;209: 435-462[44] Newsom RK, Bruce CW. Orientational properties of fibrous aerosols in atmospheric turbulence. Journal of Aerosol Science. 1998;29: 773-797[45] Mandø M, Rosendahl L. On the motion of non-spherical particles at high Reynolds number. Powder Technology. 2010;202:1-13GeneralPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2526-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2526-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2526-10000-0002-0269-2608virtual::2526-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2526-1LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/ae519e0e-f836-4c2d-b9a9-2fe016a8b1f2/download20b5ba22b1117f71589c7318baa2c560MD52ORIGINALResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdfResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdfTexto archivo completo del capítulo del libro, PDFapplication/pdf405498https://red.uao.edu.co/bitstreams/d3474a07-f00d-4bbd-9fe1-1e3de8cf7b25/download7a3fa67cea38eba9f15d63dad6198623MD53TEXTResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdf.txtResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdf.txtExtracted texttext/plain105902https://red.uao.edu.co/bitstreams/13a8da77-6b07-4d0f-b182-cd3dbfe40885/download8f8a07760ecc1aed9b57a816c74c5d2fMD54THUMBNAILResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdf.jpgResponse behavior of nonspherical particles in homogeneous isotropic turbulent flows.pdf.jpgGenerated Thumbnailimage/jpeg12772https://red.uao.edu.co/bitstreams/01137158-c01a-468c-974d-ad3cafb98a08/downloadb96eb7d7d833d1c462fce0c98991c449MD5510614/13443oai:red.uao.edu.co:10614/134432024-03-06 15:55:40.449https://creativecommons.org/licenses/by-nc-nd/4.0/open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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