Numerical prediction of particle erosion of pipe bends

In the present study the Euler/Lagrange approach in combination with a proper turbulence model and full two-way coupling is applied for erosion estimation due to particle conveying along a horizontal to vertical pipe bend. Particle tracking considers both particle translational and rotational motion...

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Autores:
Laín Beatove, Santiago
Sommerfeld, Martín
Tipo de recurso:
Article of journal
Fecha de publicación:
2019
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
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oai:red.uao.edu.co:10614/11517
Acceso en línea:
http://hdl.handle.net/10614/11517
Palabra clave:
Electrostática
Electrostatics
Pneumatic conveying
Erosion
Four-way coupling
Wall roughness
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openAccess
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repository_id_str
dc.title.eng.fl_str_mv Numerical prediction of particle erosion of pipe bends
title Numerical prediction of particle erosion of pipe bends
spellingShingle Numerical prediction of particle erosion of pipe bends
Electrostática
Electrostatics
Pneumatic conveying
Erosion
Four-way coupling
Wall roughness
title_short Numerical prediction of particle erosion of pipe bends
title_full Numerical prediction of particle erosion of pipe bends
title_fullStr Numerical prediction of particle erosion of pipe bends
title_full_unstemmed Numerical prediction of particle erosion of pipe bends
title_sort Numerical prediction of particle erosion of pipe bends
dc.creator.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martín
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
Sommerfeld, Martín
dc.subject.armarc.spa.fl_str_mv Electrostática
topic Electrostática
Electrostatics
Pneumatic conveying
Erosion
Four-way coupling
Wall roughness
dc.subject.armarc.eng.fl_str_mv Electrostatics
dc.subject.proposal.eng.fl_str_mv Pneumatic conveying
Erosion
Four-way coupling
Wall roughness
description In the present study the Euler/Lagrange approach in combination with a proper turbulence model and full two-way coupling is applied for erosion estimation due to particle conveying along a horizontal to vertical pipe bend. Particle tracking considers both particle translational and rotational motion and all relevant forces such as drag, gravity/buoyancy and transverse lift due to shear and particle rotation were accounted for Laín and Sommerfeld (2012). Moreover, models for turbulent transport of the particles, collisions with rough walls and inter-particle collisions using a stochastic approach are considered Sommerfeld and Laín (2009). In this work, the different transport effects on spherical solid particle erosion in a pipe bend of a pneumatic conveying system are analysed. For describing the combined effect of cutting and deformation erosion the model of Oka et al. (2005) is used. Erosion depth was calculated for two- and four-way coupling and for mono-sized spherical glass beads as well as a size distribution of particles with the same number mean diameter (i.e. 40 μm). Additionally, particle mass loading was varied in the range from 0.3 to 1.0. The erosion model was validated on the basis of experiments by Mazumder et al. (2008) for a narrow vertical to horizontal pipe system with high conveying velocity. Then a 150 mm pipe system with 5 m horizontal pipe, pipe bend and 5 m vertical pipe with a bulk velocity of 27 m/s was considered for further analysis. As a result inter-particle collisions reduce erosion although the wall collision frequency is enhanced Sommerfeld and Laín (2015); additionally, considering a particle size distribution with the same number mean diameter as mono-sized particles yields much higher erosion depth. Finally, when particle mass loading is increased, bend erosion is reduced due to modifications of particle impact velocity and angle, although wall collision frequency grows
publishDate 2019
dc.date.accessioned.none.fl_str_mv 2019-11-15T19:16:08Z
dc.date.available.none.fl_str_mv 2019-11-15T19:16:08Z
dc.date.issued.none.fl_str_mv 2019-02
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.eng.fl_str_mv Text
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dc.identifier.issn.spa.fl_str_mv 9218831
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10614/11517
dc.identifier.doi.spa.fl_str_mv 10.1016/j.apt.2018.11.014
identifier_str_mv 9218831
10.1016/j.apt.2018.11.014
url http://hdl.handle.net/10614/11517
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.none.fl_str_mv 383
dc.relation.citationissue.none.fl_str_mv 2
dc.relation.citationstartpage.none.fl_str_mv 366
dc.relation.citationvolume.none.fl_str_mv 30
dc.relation.cites.none.fl_str_mv Lain, S., & Sommerfeld, M. (2019). Numerical prediction of particle erosion of pipe bends. Advanced Powder Technology, 30(2), 366-383. https://doi.org/10.1016/j.apt.2018.11.014
dc.relation.ispartofjournal.eng.fl_str_mv Advanced Powder Technology
dc.relation.references.none.fl_str_mv [1] S. Laín, M. Sommerfeld, Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behaviour, Int. J. Multiphase Flow 39 (2012) 105–120.
[2] M. Sommerfeld, S. Laín, From elementary processes to the numerical prediction of industrial particle-laden flows, Multiphase Sci. Technol. 21 (2009) 123–140.
[3] Y. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact: part 1: effects of impact parameters on a predictive equation, Wear 259 (2005) 95–101.
[4] Q.H. Mazumder, S.A. Shirazi, B. McLaury, Experimental investigation of the location of maximum erosive wear damage in elbows, J. Pressure Vessel Technol. 130 (2008) 1–7.
[5] M. Sommerfeld, S. Laín, Parameters influencing dilute-phase pneumatic conveying through pipe systems: a computational study by the Euler/Lagrange approach, Can. J. Chem. Eng. 93 (2015) 1–17.
[6] M.S. El Togby, E. Ng, M.A. Elbestawi, Finite element modeling of erosive wear, Int. J. Mach. Tools Manuf. 45 (2005) 1337–1346.
[7] J. Bitter, A study of erosion phenomena, part I, Wear 6 (1963) 5–21.
[8] I.M. Hutchings, R.E. Winter, Particle erosion of ductile metals: a mechanism of material removal, Wear 27 (1974) 121–128.
[9] G.C. Pereira, F.J. de Souza, D.A. Martins, Numerical prediction of the erosion rate due to particles in elbows, Powder Technol. 261 (2014) 105–117.
[10] Y. Zhang, E.P. Reuterfors, B.S. McLaury, S.A. Shirazi, E.R. Rybicki, Comparison of computed and measured particle velocities and erosion in water and air flows, Wear 263 (2007) 330–338.
[11] X. Chen, B.S. McLaury, S. Shirazi, Application and experimental validation of a computational fluid dynamics (CFD) — based erosion prediction model in elbows and Plugged Tees, Comput. Fluids 33 (2004) 1251–1272.
[12] I. Finnie, The Mechanism of Erosion of Ductile Metals, 3rd U.S. Nat. Congress of Applied Mechanics, ASME, New York, 1958, pp. 527–532.
[13] A. Levy, Solid Particle Erosion and Erosion-Corrosion of Materials, ASM International, 1995.
[14] I. Kleis, P. Kulu, Solid Particle Erosion Occurrence, Prediction and Control, Springer-Verlag, Heidelberg, 2008.
[15] M. Parsi, K. Najmi, F. Najafifard, S. Hassani, B.S. McLaury, S.A. Shirazi, A comprehensive review of solid particle erosion modeling for oil and gas Wells and pipelines applications, J. Nat. Gas Sci. Eng. 21 (2014) 850–873.
[16] A. Levy, P. Chik, The effect of erodent composition and shape on the erosion of steel, Wear 89 (1983) 151–162.
[17] A. Levy, G. Hickey, Surface degradation of metals in simulated synthetic fuels plant environments, in: NACE Corrosion/82, International Corrosion Forum, 1982, p. 154.
[18] Y. Oka, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact: part 2: mechanical properties of materials directly associated with erosion damage, Wear 259 (2005) 102–109.
[19] H.H. Uuemis, I.R. Kleis, A critical analysis of erosion problems which have been little studied, Wear 31 (1975) 359–371.
[20] D. Mills, Erosive Wear Problems in Industry with Particular Reference to Process Plant, Power Station and Bulk Solids Handling Systems, SOLIDDEX’86 Conference/Exhibition, Harrogate, June, 1986.
[21] X. Chen, Application of Computational Fluid Dynamic (CFD) to Single Phase and Multiphase Flow Simulation and Erosion Prediction (Ph.D. dissertation), Department of Mechanical Engineering, University of Tulsa, 2004.
[22] T. Deng, A.R. Chaudhry, M. Patel, I. Hutchings, M.S.A. Bradley, Effect of particle concentration on erosion rate of mild steel bends in a pneumatic conveyor, Wear 258 (2005) 480–487.
[23] C.A.R. Duarte, F.J. de Souza, V.F. dos Santos, Numerical investigation of mass loading effects on elbow erosion, Powder Technol. 283 (2015) 593–606.
[24] M. Sommerfeld, S. Lain, Euler/Lagrange methods, in: E.E. Michalelides, C.T. Crowe, J.D. Schwarzkopf (Eds.), Multiphase Flow Handbook, second ed., CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 202–242.
[25] C.A.R. Duarte, F.J. de Souza, R.V. Salvo, V.F. dos Santos, The role of inter-particle collisions on elbow erosion, Int. J. Multiphase Flow 89 (2017) 1–22.
[26] S.M. El-Behery, M.H. Hamed, M.A.E. -Kadi, K.A. Ibrahim, Numerical simulation and CFD-based correlation of erosion threshold gas velocity in pipe bends, CFD Lett. 2 (2010) 39–53.
[27] X. Chen, B.S. McLaury, S. Shirazi, Numerical and experimental investigation of the relative erosion severity between plugged tees and elbows in dilute gas/solid two-phase flow, Wear 261 (2006) 715–729.
[28] H. Hadzˇiahmetovic´ , N. Hodzˇic´ , D. Kahrimanovic´, E. Dzˇaferovic´ , Computational fluid dynamics (CFD) based erosion prediction model in elbows, Tehnicˇki Vjesnik 21 (2014) 275–282.
[29] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332–333 (2015) 1090–1097.
[30] M. Sommerfeld, B. van Wachem, R. Oliemans, Best Practice Guidelines for Computational Fluid Dynamics of Dispersed Multiphase Flows, ERCOFTAC, Brussels, Belgium, 2008.
[31] M. Sommerfeld, Numerical methods for dispersed multiphase flows, in: T. Bodnár, G.P. Galdi, Š. Neccˇasová (Eds.), Particles in Flows, Series Advances in Mathematical Fluid Mechanics, Springer International Publishing, Heidelberg, 2017, pp. 327–396.
[32] M. Sommerfeld, Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport, Int. J. Multiphase Flow 29 (2003) 675–699.
[33] M. Sommerfeld, Modellierung und numerische Berechnung von partikelbeladenen turbulenten Strömungen mit Hilfe des Euler/Lagrange Verfahrens. Habilitation Thesis, University Erlangen-Nürnberg, Shaker Verlag, Aachen, 1996.
[34] S. Lain, M. Sommerfeld, Characterization of pneumatic conveying system using the Euler/Lagrange approach, Powder Technol. 235 (2013) 764–782.
[35] D.O. Njobuenwu, M. Fairweather, Modelling of pipe bend erosion by dilute particle suspensions, Comput. Chem. Eng. 42 (2012) 235–247.
[36] N. Huber, M. Sommerfeld, Modelling and numerical calculation of dilute-phase pneumatic conveying in pipe systems, Powder Technol. 99 (1998) 90–101.
[37] S. Laín, M. Sommerfeld, Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness, Powder Technol. 184 (2008) 76–88.
[38] M.F. Göz, S. Laín, M. Sommerfeld, Study of the numerical instabilities in lagrangian tracking of bubbles and particles in two-phase flow, Comput. Chem. Eng. 28 (2004) 2727–2733.
[39] M.F. Göz, M. Sommerfeld, S. Laín, Instabilities in Lagrangian tracking of bubbles and particles in two-phase flow, AIChE J. 52 (2006) 469–477.
[40] M. Sommerfeld, G. Kohnen, M. Rüger, Some open questions and inconsistencies of Lagrangian dispersion models, in: Proc. 9th Symp. On Turbulent Shear Flows, Kyoto, Japan, 1993, paper 15-1.
[41] M. Sommerfeld, N. Huber, Experimental analysis and modelling of particlewall collisions, Int. J. Multiphase Flow 25 (1999) 1457–1489.
[42] S. Laín, M. Sommerfeld, J. Kussin, Experimental studies and modelling of fourway coupling in particle-laden horizontal channel flow, Int. J. Heat Fluid Flow 23 (2002) 647–656.
[43] M. Sommerfeld, Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence, Int. J. Multiphase Flow 27 (2001) 1828–1858.
[44] G. Kohnen, M. Rüger, M. Sommerfeld, Convergence behaviour for numerical calculations by the Euler/Lagrange method for strongly coupled phases, in: Crowe et al., (Ed.), Num. Meth. for Multiphase Flows, FED vol. 185, 1994, pp. 191–202.
[45] I. Finnie, Erosion of surfaces by solid particles, Wear 3 (1960) 87–103.
[46] H.C. Meng, Wear Modeling: Evaluation and Categorization of Wear Models, University of Michigan, Ann Arbor, MI, USA, 1994.
[47] H.C. Meng, K.C. Ludema, Wear models and predictive equations—their form and content, Wear 181 (1995) 443–457.
[48] C.B. Solnordal, C.Y. Wong, A. Zamberi, M. Jadid, Z. Johar, Determination of erosion rate characteristics for particles with size distributions in the low Stokes range, Wear 305 (2013) 205–215.
[49] V.B. Nguyen, Q.B. Nguyen, Z.G. Liu, S. Wan, C.Y.H. Lim, Y. Zhang, A combined numerical-experimental study on the effect on the water-sand multiphase flow characteristics and the material erosion behaviour, Wear 319 (2014) 96–109.
[50] G. Grant, W. Tabakoff, Erosion prediction in turbomachinery resulting from environmental solid particles, J. Aircraft 12 (1975) 471–478.
[51] C.B. Solnordal, C.Y. Wong, J. Boulanger, An experimental and numerical analysis of erosion caused by sand pneumatically conveyed through a standard pipe elbow, Wear 336–337 (2015) 43–57.
[52] S. Laín, M. Sommerfeld, Influence of inter-particle collisions on erosion of pipe bends, ERCOFTAC Bull. 112 (2017) 10–16.
[53] F.A. Bikbaev, V.I. Krasnov, V.L. Berezin, I.B. Zhilinski, N.T. Otroshko, Main factors affecting gas abrasive wear of elbows in pneumatic conveying pipes, Chem. Pet. Eng. 9 (1973) 73–75.
[54] S. Laín, M. García, B. Quintero, S. Orrego, CFD numerical simulations of Francis turbines, Rev. Facultad de Ingeniería Universidad de Antioquia 51 (2010) 24–33.
[55] A.D. Caballero, S. Laín, Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta, Comput. Methods Biomech. Biomed. Eng. 18 (2015) 1200–1216.
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spelling Laín Beatove, Santiagovirtual::2573-1Sommerfeld, Martín584f85f313767d3025329c2e43274122Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-15T19:16:08Z2019-11-15T19:16:08Z2019-029218831http://hdl.handle.net/10614/1151710.1016/j.apt.2018.11.014In the present study the Euler/Lagrange approach in combination with a proper turbulence model and full two-way coupling is applied for erosion estimation due to particle conveying along a horizontal to vertical pipe bend. Particle tracking considers both particle translational and rotational motion and all relevant forces such as drag, gravity/buoyancy and transverse lift due to shear and particle rotation were accounted for Laín and Sommerfeld (2012). Moreover, models for turbulent transport of the particles, collisions with rough walls and inter-particle collisions using a stochastic approach are considered Sommerfeld and Laín (2009). In this work, the different transport effects on spherical solid particle erosion in a pipe bend of a pneumatic conveying system are analysed. For describing the combined effect of cutting and deformation erosion the model of Oka et al. (2005) is used. Erosion depth was calculated for two- and four-way coupling and for mono-sized spherical glass beads as well as a size distribution of particles with the same number mean diameter (i.e. 40 μm). Additionally, particle mass loading was varied in the range from 0.3 to 1.0. The erosion model was validated on the basis of experiments by Mazumder et al. (2008) for a narrow vertical to horizontal pipe system with high conveying velocity. Then a 150 mm pipe system with 5 m horizontal pipe, pipe bend and 5 m vertical pipe with a bulk velocity of 27 m/s was considered for further analysis. As a result inter-particle collisions reduce erosion although the wall collision frequency is enhanced Sommerfeld and Laín (2015); additionally, considering a particle size distribution with the same number mean diameter as mono-sized particles yields much higher erosion depth. Finally, when particle mass loading is increased, bend erosion is reduced due to modifications of particle impact velocity and angle, although wall collision frequency growsapplication/pdf18 páginasengElsevier B.V.Derechos 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_abf2Numerical prediction of particle erosion of pipe bendsArtículo 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_970fb48d4fbd8a85ElectrostáticaElectrostaticsPneumatic conveyingErosionFour-way couplingWall roughness383236630Lain, S., & Sommerfeld, M. (2019). Numerical prediction of particle erosion of pipe bends. Advanced Powder Technology, 30(2), 366-383. https://doi.org/10.1016/j.apt.2018.11.014Advanced Powder Technology[1] S. Laín, M. Sommerfeld, Numerical calculation of pneumatic conveying in horizontal channels and pipes: detailed analysis of conveying behaviour, Int. J. Multiphase Flow 39 (2012) 105–120.[2] M. Sommerfeld, S. Laín, From elementary processes to the numerical prediction of industrial particle-laden flows, Multiphase Sci. Technol. 21 (2009) 123–140.[3] Y. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact: part 1: effects of impact parameters on a predictive equation, Wear 259 (2005) 95–101.[4] Q.H. Mazumder, S.A. Shirazi, B. McLaury, Experimental investigation of the location of maximum erosive wear damage in elbows, J. Pressure Vessel Technol. 130 (2008) 1–7.[5] M. Sommerfeld, S. Laín, Parameters influencing dilute-phase pneumatic conveying through pipe systems: a computational study by the Euler/Lagrange approach, Can. J. Chem. Eng. 93 (2015) 1–17.[6] M.S. El Togby, E. Ng, M.A. Elbestawi, Finite element modeling of erosive wear, Int. J. Mach. Tools Manuf. 45 (2005) 1337–1346.[7] J. Bitter, A study of erosion phenomena, part I, Wear 6 (1963) 5–21.[8] I.M. Hutchings, R.E. Winter, Particle erosion of ductile metals: a mechanism of material removal, Wear 27 (1974) 121–128.[9] G.C. Pereira, F.J. de Souza, D.A. Martins, Numerical prediction of the erosion rate due to particles in elbows, Powder Technol. 261 (2014) 105–117.[10] Y. Zhang, E.P. Reuterfors, B.S. McLaury, S.A. Shirazi, E.R. Rybicki, Comparison of computed and measured particle velocities and erosion in water and air flows, Wear 263 (2007) 330–338.[11] X. Chen, B.S. McLaury, S. Shirazi, Application and experimental validation of a computational fluid dynamics (CFD) — based erosion prediction model in elbows and Plugged Tees, Comput. Fluids 33 (2004) 1251–1272.[12] I. Finnie, The Mechanism of Erosion of Ductile Metals, 3rd U.S. Nat. Congress of Applied Mechanics, ASME, New York, 1958, pp. 527–532.[13] A. Levy, Solid Particle Erosion and Erosion-Corrosion of Materials, ASM International, 1995.[14] I. Kleis, P. Kulu, Solid Particle Erosion Occurrence, Prediction and Control, Springer-Verlag, Heidelberg, 2008.[15] M. Parsi, K. Najmi, F. Najafifard, S. Hassani, B.S. McLaury, S.A. Shirazi, A comprehensive review of solid particle erosion modeling for oil and gas Wells and pipelines applications, J. Nat. Gas Sci. Eng. 21 (2014) 850–873.[16] A. Levy, P. Chik, The effect of erodent composition and shape on the erosion of steel, Wear 89 (1983) 151–162.[17] A. Levy, G. Hickey, Surface degradation of metals in simulated synthetic fuels plant environments, in: NACE Corrosion/82, International Corrosion Forum, 1982, p. 154.[18] Y. Oka, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact: part 2: mechanical properties of materials directly associated with erosion damage, Wear 259 (2005) 102–109.[19] H.H. Uuemis, I.R. Kleis, A critical analysis of erosion problems which have been little studied, Wear 31 (1975) 359–371.[20] D. Mills, Erosive Wear Problems in Industry with Particular Reference to Process Plant, Power Station and Bulk Solids Handling Systems, SOLIDDEX’86 Conference/Exhibition, Harrogate, June, 1986.[21] X. Chen, Application of Computational Fluid Dynamic (CFD) to Single Phase and Multiphase Flow Simulation and Erosion Prediction (Ph.D. dissertation), Department of Mechanical Engineering, University of Tulsa, 2004.[22] T. Deng, A.R. Chaudhry, M. Patel, I. Hutchings, M.S.A. Bradley, Effect of particle concentration on erosion rate of mild steel bends in a pneumatic conveyor, Wear 258 (2005) 480–487.[23] C.A.R. Duarte, F.J. de Souza, V.F. dos Santos, Numerical investigation of mass loading effects on elbow erosion, Powder Technol. 283 (2015) 593–606.[24] M. Sommerfeld, S. Lain, Euler/Lagrange methods, in: E.E. Michalelides, C.T. Crowe, J.D. Schwarzkopf (Eds.), Multiphase Flow Handbook, second ed., CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 202–242.[25] C.A.R. Duarte, F.J. de Souza, R.V. Salvo, V.F. dos Santos, The role of inter-particle collisions on elbow erosion, Int. J. Multiphase Flow 89 (2017) 1–22.[26] S.M. El-Behery, M.H. Hamed, M.A.E. -Kadi, K.A. Ibrahim, Numerical simulation and CFD-based correlation of erosion threshold gas velocity in pipe bends, CFD Lett. 2 (2010) 39–53.[27] X. Chen, B.S. McLaury, S. Shirazi, Numerical and experimental investigation of the relative erosion severity between plugged tees and elbows in dilute gas/solid two-phase flow, Wear 261 (2006) 715–729.[28] H. Hadzˇiahmetovic´ , N. Hodzˇic´ , D. Kahrimanovic´, E. Dzˇaferovic´ , Computational fluid dynamics (CFD) based erosion prediction model in elbows, Tehnicˇki Vjesnik 21 (2014) 275–282.[29] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332–333 (2015) 1090–1097.[30] M. Sommerfeld, B. van Wachem, R. Oliemans, Best Practice Guidelines for Computational Fluid Dynamics of Dispersed Multiphase Flows, ERCOFTAC, Brussels, Belgium, 2008.[31] M. Sommerfeld, Numerical methods for dispersed multiphase flows, in: T. Bodnár, G.P. Galdi, Š. Neccˇasová (Eds.), Particles in Flows, Series Advances in Mathematical Fluid Mechanics, Springer International Publishing, Heidelberg, 2017, pp. 327–396.[32] M. Sommerfeld, Analysis of collision effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport, Int. J. Multiphase Flow 29 (2003) 675–699.[33] M. 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