Startseite On the drag force closures for multiphase flow modeling
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On the drag force closures for multiphase flow modeling

  • Hamid Reza Norouzi EMAIL logo , Shahab Golshan und Reza Zarghami ORCID logo
Veröffentlicht/Copyright: 14. Mai 2021
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Chemical Product and Process Modeling
Aus der Zeitschrift Chemical Product and Process Modeling Band 17 Heft 5

Abstract

Drag force models are one of the most important factors that can affect TFM and CFD-DEM simulation results of two-phase systems. This article investigates the accuracies, implementation issues and limitations of the majority of the drag models for spherical, non-spherical and systems with size distribution and evaluates their performance in various simulations. Around 1888 data points were collected from 19 different sources to evaluate the drag force closures on mono-dispersed spherical particles. The Reynolds number and fluid volume fraction ranges were between 0.01 and 10,000 and between 0.33 and 1, respectively. In addition, 776 data points were collected from seven different sources to evaluate the drag force closures on poly-dispersed spherical particles. The Reynolds numbers were between 0.01 and 500, fluid volume fractions between 0.33 and 0.9, and diameter ratios up to 10. A comprehensive discussion on the accuracy and application of these models is given in the article.

Keywords: CFD-DEM; drag force; non-spherical; size distribution; TFM
Corresponding author: Hamid Reza Norouzi, Department of Chemical Engineering, Center of Engineering and Multiscale Modeling of Fluid Flow (CEMF), Amirkabir University of Technology, PO Box: 15875-4413, Hafez 424, Tehran, Iran, E-mail:

Funding source: Iran National Science Foundation (INSF)

Award Identifier / Grant number: 96015422

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors would like to express their gratitude to Iran National Science Foundation (INSF) for supporting this research under grant number 96015422.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

1. Hoomans, BPB, Kuipers, JAM, Briels, WJ, Swaaij, WPMV. Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach. Chem Eng Sci 1996;51:99–118. https://doi.org/10.1016/0009-2509(95)00271-5.Suche in Google Scholar

2. Norouzi, HR, Zarghami, R, Sotudeh-Gharebagh, R, Mostoufi, N. Coupled CFD-DEM modeling: formulation, implementation and application to multiphase flows. Hoboken, NJ: John Wiley & Sons; 2016.10.1002/9781119005315Suche in Google Scholar

3. Tsuji, Y, Kawaguchi, T, Tanaka, T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technol 1993;77:79–87. https://doi.org/10.1016/0032-5910(93)85010-7.Suche in Google Scholar

4. Gidaspow, D. Multiphase flow and fluidization: continuum and kinetic theory description. San Diego: Academic Press; 1994.Suche in Google Scholar

5. Golshan, S. Review and implementation of CFD-DEM applied to chemical process systems. Chem Eng Sci 2020;221:115646. https://doi.org/10.1016/j.ces.2020.115646.Suche in Google Scholar

6. Anderson, TB, Jackson, R. Fluid mechanical description of fluidized beds. Equations of motion. Ind Eng Chem Fundam 1967;6:527–39. https://doi.org/10.1021/i160024a007.Suche in Google Scholar

7. Almohammed, N, Alobaid, F, Breuer, M, Epple, B. A comparative study on the influence of the gas flow rate on the hydrodynamics of a gas–solid spouted fluidized bed using Euler–Euler and Euler–Lagrange/DEM models. Powder Technol 2014;264:343–64. https://doi.org/10.1016/j.powtec.2014.05.024.Suche in Google Scholar

8. Golshan, S, Esgandari, B, Zarghami, R. CFD-DEM and TFM simulations of spouted bed. Chem Eng Trans 2017;57:1249–54.Suche in Google Scholar

9. Norouzi, H, Mostoufi, N, Mansourpour, Z, Sotudeh-Gharebagh, R, Chaouki, J. Characterization of solids mixing patterns in bubbling fluidized beds. Chem Eng Res Des 2011;89:817–26. https://doi.org/10.1016/j.cherd.2010.10.014.Suche in Google Scholar

10. Peng, Z, Doroodchi, E, Luo, C, Moghtaderi, B. Influence of void fraction calculation on fidelity of CFD-DEM simulation of gas-solid bubbling fluidized beds. AIChE J 2014;60:2000–18. https://doi.org/10.1002/aic.14421.Suche in Google Scholar

11. Koralkar, NV, Bose, M. Performance of drag models for simulation of fluidized beds with Geldart D particles. Adv Powder Technol 2016;27:2377–98. https://doi.org/10.1016/j.apt.2016.11.008.Suche in Google Scholar

12. Stanly, R, Shoev, G. Detailed analysis of recent drag models using multiple cases of mono-disperse fluidized beds with Geldart-B and Geldart-D particles. Chem Eng Sci 2018;188:132–49. https://doi.org/10.1016/j.ces.2018.05.030.Suche in Google Scholar

13. Tian, T, Jia, Z, Geng, S, Liu, X. Two-fluid modeling of geldart A particles in gas-solid bubbling fluidized bed: assessment of drag models and solid viscosity correlations. Int J Chem React Eng 2018;16. https://doi.org/10.1515/ijcre-2017-0016.Suche in Google Scholar

14. Zhang, Y, Zhao, Y, Lu, L, Ge, W, Wang, J, Duan, C. Assessment of polydisperse drag models for the size segregation in a bubbling fluidized bed using discrete particle method. Chem Eng Sci 2017;160:106–12. https://doi.org/10.1016/j.ces.2016.11.028.Suche in Google Scholar

15. Du, W, Quan, N, Lu, P, Xu, J, Wei, W, Zhang, L. Experimental and statistical analysis of the void size distribution and pressure drop validations in packed beds. Chem Eng Res Des 2016;106:115–25. https://doi.org/10.1016/j.cherd.2015.11.023.Suche in Google Scholar

16. Ergun, S. Fluid flow through packed columns. Chem Eng Prog 1952;48:89–94.Suche in Google Scholar

17. Hicks, RE. Pressure drop in packed beds of spheres. Ind Eng Chem Fundam 1970;9:500–2. https://doi.org/10.1021/i160035a032.Suche in Google Scholar

18. Koekemoer, A, Luckos, A. Effect of material type and particle size distribution on pressure drop in packed beds of large particles: extending the Ergun equation. Fuel 2015;158:232–8. https://doi.org/10.1016/j.fuel.2015.05.036.Suche in Google Scholar

19. Tallmadge, JA. Packed bed pressure drop—an extension to higher Reynolds numbers. AIChE J 1970;16:1092–3. https://doi.org/10.1002/aic.690160639.Suche in Google Scholar

20. Di Felice, R. The particle-in-a-tube analogy for a multiparticle suspension. Int J Multiphas Flow 1996;22:515–25. https://doi.org/10.1016/0301-9322(96)00005-5.Suche in Google Scholar

21. Khan, AR, Richardson, JF. Pressure gradient and friction factor for sedimentation and fluidisation of uniform spheres in liquids. Chem Eng Sci 1990;45:255–65. https://doi.org/10.1016/0009-2509(90)87097-c.Suche in Google Scholar

22. Richardson, JF, Zaki, WN. Sedimentation and fluidization: Part I. Trans Inst Chem Eng 1954;32:35–53.Suche in Google Scholar

23. Wen, CY, Yu, YH. Mechanics of fluidization. Chem Eng Prog Symp Ser 1966;62:100–11.Suche in Google Scholar

24. He, L, Tafti, DK. A supervised machine learning approach for predicting variable drag forces on spherical particles in suspension. Powder Technol 2019;345:379–89. https://doi.org/10.1016/j.powtec.2019.01.013.Suche in Google Scholar

25. Muralidhar, N, Bu, J, Cao, Z, He, L, Ramakrishnan, N, Tafti, D, et al.. Physics-guided deep learning for drag force prediction in dense fluid-particulate systems. Big Data 2020;8:431–49. https://doi.org/10.1089/big.2020.0071.Suche in Google Scholar PubMed

26. Allen, KG, von Backström, TW, Kröger, DG. Packed bed pressure drop dependence on particle shape, size distribution, packing arrangement and roughness. Powder Technol 2013;246:590–600. https://doi.org/10.1016/j.powtec.2013.06.022.Suche in Google Scholar

27. Clift, R, Grace, JR, Weber, ME. Bubbles, drops, and particles. London: Academic Press; 1978.Suche in Google Scholar

28. Geldart, D. Types of gas fluidization. Powder Technol 1973;7:285–92. https://doi.org/10.1016/0032-5910(73)80037-3.Suche in Google Scholar

29. Gibilaro, LG, Hossain, I, Foscolo, PU. Aggregate behaviour of liquid fluidised beds. Can J Chem Eng 1986;64:931–8. https://doi.org/10.1002/cjce.5450640607.Suche in Google Scholar

30. Shamlou, PA. Processing of solid–liquid suspensions. Amsterdam: Elsevier; 2016.Suche in Google Scholar

31. Grace, JR. Contacting modes and behaviour classification of gas—solid and other two-phase suspensions. Can J Chem Eng 1986;64:353–63. https://doi.org/10.1002/cjce.5450640301.Suche in Google Scholar

32. Çarpinlioğlu, MÖ, Özahi, E. A simplified correlation for fixed bed pressure drop. Powder Technol 2008;187:94–101.10.1016/j.powtec.2008.01.027Suche in Google Scholar

33. Das, S, Deen, NG, Kuipers, JAM. A DNS study of flow and heat transfer through slender fixed-bed reactors randomly packed with spherical particles. Chem Eng Sci 2017;160:1–19. https://doi.org/10.1016/j.ces.2016.11.008.Suche in Google Scholar

34. Happel, J, Epstein, N. Cubical assemblages of uniform spheres. Ind Eng Chem 1954;46:1187–94. https://doi.org/10.1021/ie50534a033.Suche in Google Scholar

35. Reddy, RK, Joshi, JB. CFD modeling of pressure drop and drag coefficient in fixed and expanded beds. Chem Eng Res Des 2008;86:444–53. https://doi.org/10.1016/j.cherd.2007.12.007.Suche in Google Scholar

36. Rong, LW, Dong, KJ, Yu, AB. Lattice-Boltzmann simulation of fluid flow through packed beds of uniform spheres: effect of porosity. Chem Eng Sci 2013;99:44–58. https://doi.org/10.1016/j.ces.2013.05.036.Suche in Google Scholar

37. Rumpf, H, Gupte, AP. The effects of porosity and parttclf size distribution on the flow through porous mia. Selected Translated Papers 1972;1. https://doi.org/10.4271/720772.Suche in Google Scholar

38. van der Hoef, MA, Beetstra, R, Kuipers, JAM. Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J Fluid Mech 2005;528:233–54. https://doi.org/10.1017/s0022112004003295.Suche in Google Scholar

39. White, FM. Fluid mechanics. New York: McGraw-Hill; 1991.Suche in Google Scholar

40. Mostoufi, N, Chaouki, J. Prediction of effective drag coeficient in fluidized beds. Chem Eng Sci 1999;54:851–8. https://doi.org/10.1016/s0009-2509(98)00290-5.Suche in Google Scholar

41. Beetstra, R. Drag force in random arrays of mono-and bidisperse spheres. Enschede, The Netherlands: University of Twente; 2005.Suche in Google Scholar

42. Ozahi, E, Gundogdu, MY, Carpinlioglu, MÖ. A modification on ergun’s correlation for use in cylindrical packed beds with non-spherical particles. Adv Powder Technol 2008;19:369–81. https://doi.org/10.1163/156855208x314985.Suche in Google Scholar

43. Haddadi, B, Jordan, C, Norouzi, HR, Harasek, M. Investigation of the pressure drop of random packed bed adsorbers. Chem Eng 2016;52.Suche in Google Scholar

44. Hill, RJ, Koch, DL, Ladd, AJC. Moderate-Reynolds-number flows in ordered and random arrays of spheres. J Fluid Mech 2001;448. https://doi.org/10.1017/s0022112001005936.Suche in Google Scholar

45. Hill, RJ, Koch, DL, Ladd, AJC. The first effects of fluid inertia on flows in ordered and random arrays of spheres. J Fluid Mech 2001;448:213–41. https://doi.org/10.1017/s0022112001005948.Suche in Google Scholar

46. Atmakidis, T, Kenig, EY. CFD-based analysis of the wall effect on the pressure drop in packed beds with moderate tube/particle diameter ratios in the laminar flow regime. Chem Eng J 2009;155:404–10. https://doi.org/10.1016/j.cej.2009.07.057.Suche in Google Scholar

47. Tenneti, S, Garg, R, Subramaniam, S. Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Int J Multiphas Flow 2011;37:1072–92. https://doi.org/10.1016/j.ijmultiphaseflow.2011.05.010.Suche in Google Scholar

48. Zaidi, AA, Tsuji, T, Tanaka, T. A new relation of drag force for high Stokes number monodisperse spheres by direct numerical simulation. Adv Powder Technol 2014;25:1860–71. https://doi.org/10.1016/j.apt.2014.07.019.Suche in Google Scholar

49. Baz-Rodríguez, SA, Aguilar-Madera, CG, Ruelas-Leyva, JP. Fluid–solid interfacial drag force on monodisperse assemblies of spherical particles. Powder Technol 2015;271:204–9. https://doi.org/10.1016/j.powtec.2014.11.020.Suche in Google Scholar

50. Tang, Y, Peters, EAJF, Kuipers, JAM, Kriebitzsch, SHL, van der Hoef, MA. A new drag correlation from fully resolved simulations of flow past monodisperse static arrays of spheres. AIChE J 2015;61:688–98.10.1002/aic.14645Suche in Google Scholar

51. Tang, Y, Peters, EAJF, Kuipers, JAM. Direct numerical simulations of dynamic gas-solid suspensions. AIChE J 2016;62:1958–69. https://doi.org/10.1002/aic.15197.Suche in Google Scholar

52. Zaidi, AA. Particle resolved direct numerical simulation of free settling particles for the study of effects of momentum response time on drag force. Powder Technol 2018a;335:222–34. https://doi.org/10.1016/j.powtec.2018.04.058.Suche in Google Scholar

53. Zaidi, AA. Study of particle inertia effects on drag force of finite sized particles in settling process. Chem Eng Res Des 2018b;132:714–28. https://doi.org/10.1016/j.cherd.2018.02.013.Suche in Google Scholar

54. Sarkar, S, van der Hoef, MA, Kuipers, JAM. Fluid–particle interaction from lattice Boltzmann simulations for flow through polydisperse random arrays of spheres. Chem Eng Sci 2009;64:2683–91. https://doi.org/10.1016/j.ces.2009.02.045.Suche in Google Scholar

55. Sarkar, S, Kriebitzsch, SHL, van der Hoef, MA, Kuipers, JAM. Gas–solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios. Particuology 2009;7:233–7. https://doi.org/10.1016/j.partic.2009.02.002.Suche in Google Scholar

56. Yin, X, Sundaresan, S. Fluid-particle drag in low-Reynolds-number polydisperse gas-solid suspensions. AIChE J 2009;55:1352–68. https://doi.org/10.1002/aic.11800.Suche in Google Scholar

57. Rong, LW, Dong, KJ, Yu, AB. Lattice-Boltzmann simulation of fluid flow through packed beds of spheres: effect of particle size distribution. Chem Eng Sci 2014;116:508–23. https://doi.org/10.1016/j.ces.2014.05.025.Suche in Google Scholar

58. Formisani, B, De Cristofaro, G, Girimonte, R. A fundamental approach to the phenomenology of #uidization of size segregating binary mixtures of solids. Chem Eng Sci 2001;56:109–19. https://doi.org/10.1016/s0009-2509(00)00426-7.Suche in Google Scholar

59. Blake, FC. The resistance of packing to fluid flow. Trans Am Inst Chem Eng 1922;1922:415–22.Suche in Google Scholar

60. Carman, PC. Fluid flow through granular beds. Trans Inst Chem Eng 1937;15:150–66.10.1016/S0263-8762(97)80003-2Suche in Google Scholar

61. Cheng, N-S. Comparison of formulas for drag coefficient and settling velocity of spherical particles. Powder Technol 2009;189:395–8. https://doi.org/10.1016/j.powtec.2008.07.006.Suche in Google Scholar

62. Dallavalle, JM. Micromeritics: the technology of fine particles. London: Pitman Publishing Corporation; 1948.Suche in Google Scholar

63. Schiller, L, Naumann, A. A drag coefficient correlation. Zeitschrift des Vereins Dtsch Ingenieure 1935;77:318–20.Suche in Google Scholar

64. Turton, R, Levenspiel, O. A short note on the drag correlation for spheres. Powder Technol 1986;37:83–6. https://doi.org/10.1016/0032-5910(86)80012-2.Suche in Google Scholar

65. Gibilaro, LG, Di Felice, R, Waldram, SP, Foscolo, PU. Generalized friction factor and drag coefficient correlations for fluid-particle interactions. Chem Eng Sci 1985;40:1817–23. https://doi.org/10.1016/0009-2509(85)80116-0.Suche in Google Scholar

66. Syamlal, M, Rogers, W, O’Brien, TJ. MFiX documentation theory guide. Technical Note. Golden, CO: U.S. Department of Energy, National Energy Technology Laboratory; 1993.10.2172/10145548Suche in Google Scholar

67. Garside, J, Al-Dibouni, MR. Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. Ind Eng Chem Process Des Dev 1977;16:206–14. https://doi.org/10.1021/i260062a008.Suche in Google Scholar

68. Di Felice, R. The voidage function for fluid–particle interaction systems. Int J Multiphas Flow 1994;20:153–9. https://doi.org/10.1016/0301-9322(94)90011-6.Suche in Google Scholar

69. Cello, F, Di Renzo, A, Di Maio, FP. A semi-empirical model for the drag force and fluid–particle interaction in polydisperse suspensions. Chem Eng Sci 2010;65:3128–39. https://doi.org/10.1016/j.ces.2010.02.006.Suche in Google Scholar

70. Mazzei, L, Lettieri, P. A drag force closure for uniformly dispersed fluidized suspensions. Chem Eng Sci 2007;62:6129–42. https://doi.org/10.1016/j.ces.2007.06.028.Suche in Google Scholar

71. Kafui, KD, Thornton, C, Adams, MJ. Discrete particle-continuum fluid modelling of gas–solid fluidised beds. Chem Eng Sci 2002;57:2395–410. https://doi.org/10.1016/s0009-2509(02)00140-9.Suche in Google Scholar

72. Benyahia, S, Syamlal, M, O’Brien, TJ. Extension of Hill–Koch–Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technol 2006;162:166–74. https://doi.org/10.1016/j.powtec.2005.12.014.Suche in Google Scholar

73. Beetstra, R, van der Hoef, MA, Kuipers, JAM. Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. AIChE J 2007;53:489–501. https://doi.org/10.1002/aic.11065.Suche in Google Scholar

74. Kravets, B, Rosemann, T, Reinecke, SR, Kruggel-Emden, H. A new drag force and heat transfer correlation derived from direct numerical LBM-simulations of flown through particle packings. Powder Technol 2019;345:438–56. https://doi.org/10.1016/j.powtec.2019.01.028.Suche in Google Scholar

75. Ayeni, O, Wu, C, Nandakumar, K, Joshi, J. Development and validation of a new drag law using mechanical energy balance approach for DEM–CFD simulation of gas–solid fluidized bed. Chem Eng J 2016;302:395–405. https://doi.org/10.1016/j.cej.2016.05.056.Suche in Google Scholar

76. Bogner, S, Mohanty, S, Rüde, U. Drag correlation for dilute and moderately dense fluid-particle systems using the lattice Boltzmann method. Int J Multiphas Flow 2015;68:71–9. https://doi.org/10.1016/j.ijmultiphaseflow.2014.10.001.Suche in Google Scholar

77. Tenneti, S, Garg, R, Hrenya, CM, Fox, RO, Subramaniam, S. Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol 2010;203:57–69. https://doi.org/10.1016/j.powtec.2010.03.042.Suche in Google Scholar

78. Gilbertson, MA, Eames, I. Segregation patterns in gas-fluidized systems. J Fluid Mech 2001;433:347–56. https://doi.org/10.1017/s0022112001003950.Suche in Google Scholar

79. Norouzi, HR, Mostoufi, N, Sotudeh-Gharebagh, R. Segregation behaviour of particles in gas solid fluidized beds at elevated pressure. J Chem Petrol Eng 2012;46:111–21.Suche in Google Scholar

80. Olaofe, OO, Buist, KA, Deen, NG, van der Hoef, MA, Kuipers, JAM. Segregation dynamics in dense polydisperse gas-fluidized beds. Powder Technol 2013;246:695–706. https://doi.org/10.1016/j.powtec.2013.05.047.Suche in Google Scholar

81. Prasad Babu, M, Krishnaiah, K. Dynamics of jetsam layer in continuous segregation of binary heterogeneous particles in gas–solid fluidized bed. Powder Technol 2005;160:114–20. https://doi.org/10.1016/j.powtec.2005.08.017.Suche in Google Scholar

82. Prasad Babu, M, P.S.T, S, Krishnaiah, K. Continuous segregation of binary heterogeneous solids in a fast-fluidized bed. Particuology 2017;35:101–7. https://doi.org/10.1016/j.partic.2017.04.006.Suche in Google Scholar

83. Feng, YQ, Xu, BH, Zhang, SJ, Yu, AB, Zulli, P. Discrete particle simulation of gas fluidization of particle mixtures. AIChE J 2004;50:1713–28. https://doi.org/10.1002/aic.10169.Suche in Google Scholar

84. Norouzi, HR, Mostoufi, N, Sotudeh-Gharebagh, R. Effect of fines on segregation of binary mixtures in gas–solid fluidized beds. Powder Technol 2012;225:7–20. https://doi.org/10.1016/j.powtec.2012.03.025.Suche in Google Scholar

85. Bokkers, GA, van Sint Annaland, M, Kuipers, JAM. Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study. Powder Technol 2004;140:176–86. https://doi.org/10.1016/j.powtec.2004.01.018.Suche in Google Scholar

86. Fan, R, Fox, RO. Segregation in polydisperse fluidized beds: validation of a multi-fluid model. Chem Eng Sci 2008;63:272–85. https://doi.org/10.1016/j.ces.2007.09.038.Suche in Google Scholar

87. Sundaresan, S, Ozel, A, Kolehmainen, J. Toward constitutive models for momentum, species, and energy transport in gas–particle flows. Annu Rev Chem Biomol Eng 2018;9:61–81. https://doi.org/10.1146/annurev-chembioeng-060817-084025.Suche in Google Scholar PubMed

88. Ye, M, Wang, J, Van der Hoef, M, Kuipers, J. Two-fluid modeling of Geldart A particles in gas-fluidized beds. Particuology 2008;6:540–8. https://doi.org/10.1016/j.partic.2008.07.005.Suche in Google Scholar

89. Wang, J, Liu, Y. EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles. Powder Technol 2010;197:241–6. https://doi.org/10.1016/j.powtec.2009.09.022.Suche in Google Scholar

90. Askaripour, H, Dehkordi, AM. Simulation of 3D freely bubbling gas–solid fluidized beds using various drag models: TFM approach. Chem Eng Res Des 2015;100:377–90. https://doi.org/10.1016/j.cherd.2015.05.041.Suche in Google Scholar

91. Goldschmidt, M, Beetstra, R, Kuipers, J. Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of 3D discrete particle and continuum models. Powder Technol 2004;142:23–47. https://doi.org/10.1016/j.powtec.2004.02.020.Suche in Google Scholar

92. Müller, CR, Holland, DJ, Sederman, AJ, Scott, SA, Dennis, JS, Gladden, LF. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technol 2008;184:241–53. https://doi.org/10.1016/j.powtec.2007.11.046.Suche in Google Scholar

93. Kuipers, JAM. A two-fluid micro balance model of fluidized beds. Enschede, The Netherlands: Universiteit Twente; 1990.Suche in Google Scholar

94. Ku, X, Li, T, Løvås, T. Influence of drag force correlations on periodic fluidization behavior in Eulerian–Lagrangian simulation of a bubbling fluidized bed. Chem Eng Sci 2013;95:94–106. https://doi.org/10.1016/j.ces.2013.03.038.Suche in Google Scholar

95. Syamlal, M. The derivation of a drag coefficient formula from velocity-voidage correlations. Technical note. Morgantown, WV: US Department of energy, Office of Fossil Energy, NETL; 1987.Suche in Google Scholar

96. Agrawal, V, Shinde, Y, Shah, MT, Utikar, RP, Pareek, VK, Joshi, JB. Effect of drag models on CFD–DEM predictions of bubbling fluidized beds with Geldart D particles. Adv Powder Technol 2018;29:2658–69. https://doi.org/10.1016/j.apt.2018.07.014.Suche in Google Scholar

97. Zhou, L, Zhang, L, Bai, L, Shi, W, Li, W, Wang, C, et al.. Experimental study and transient CFD/DEM simulation in a fluidized bed based on different drag models. RSC Adv 2017;7:12764–74. https://doi.org/10.1039/c6ra28615a.Suche in Google Scholar

98. Liu, D, van Wachem, B. Comprehensive assessment of the accuracy of CFD-DEM simulations of bubbling fluidized beds. Powder Technol 2019;343:145–58. https://doi.org/10.1016/j.powtec.2018.11.025.Suche in Google Scholar

99. Goldschmidt, M, Link, J, Mellema, S, Kuipers, J. Digital image analysis measurements of bed expansion and segregation dynamics in dense gas-fluidised beds. Powder Technol 2003;138:135–59. https://doi.org/10.1016/j.powtec.2003.09.003.Suche in Google Scholar

100. Kloss, C, Goniva, C, Hager, A, Amberger, S, Pirker, S. Models, algorithms and validation for opensource DEM and CFD–DEM. Prog Comput Fluid Dynam Int J 2012;12:140–52. https://doi.org/10.1504/pcfd.2012.047457.Suche in Google Scholar

101. Norouzi, H, Zarghami, R, Mostoufi, N. New hybrid CPU-GPU solver for CFD-DEM simulation of fluidized beds. Powder Technol 2017;316:233–44. https://doi.org/10.1016/j.powtec.2016.11.061.Suche in Google Scholar

102. Cody, GD, Goldfarb, DJ, Storch, GV, Norris, AN. Particle granular temperature in gas fluidized beds. Powder Technol 1996;87:211–32. https://doi.org/10.1016/0032-5910(96)03087-2.Suche in Google Scholar

103. Ding, J, Gidaspow, D. A bubbling fluidization model using kinetic theory of granular flow. AIChE J 1990;36:523–38. https://doi.org/10.1002/aic.690360404.Suche in Google Scholar

104. Huilin, L, Gidaspow, D. Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures. Chem Eng Sci 2003;58:3777–92. https://doi.org/10.1016/s0009-2509(03)00238-0.Suche in Google Scholar

105. Kriebitzsch, SHL, van der Hoef, MA, Kuipers, JAM. Drag force in discrete particle models—continuum scale or single particle scale? AIChE J 2013;59:316–24. https://doi.org/10.1002/aic.13804.Suche in Google Scholar

106. Zhou, G, Xiong, Q, Wang, L, Wang, X, Ren, X, Ge, W. Structure-dependent drag in gas–solid flows studied with direct numerical simulation. Chem Eng Sci 2014;116:9–22. https://doi.org/10.1016/j.ces.2014.04.025.Suche in Google Scholar

107. Mostoufi, N, Chaouki, J. Flow structure of the solids in gas–solid fluidized beds. Chem Eng Sci 2004;59:4217–27. https://doi.org/10.1016/j.ces.2004.06.006.Suche in Google Scholar

108. Sharma, AK, Tuzla, K, Matsen, J, Chen, JC. Parametric effects of particle size and gas velocity on cluster characteristics in fast fluidized beds. Powder Technol 2000;111:114–22. https://doi.org/10.1016/s0032-5910(00)00247-3.Suche in Google Scholar

109. Yerushalmi, J, Gluckman, MJ, Graff, RA, Dobner, S, Squires, AM. Production of gaseous fuels from coal in the fast fluidized bed, fluidization technology. Washington, DC: Hemisphere; 1976. p. 437.Suche in Google Scholar

110. Wylie, JJ, Koch, DL, Ladd, AJC. Rheology of suspensions with high particle inertia and moderate fluid inertia. J Fluid Mech 2003;480:95–118. https://doi.org/10.1017/s0022112002003531.Suche in Google Scholar

111. Yin, X, Sundaresan, S. Drag law for bidisperse gas-solid suspensions containing equally sized spheres. Ind Eng Chem Res 2009;48:227–41. https://doi.org/10.1021/ie800171p.Suche in Google Scholar

112. Kriebitzsch, SHL, van der Hoef, MA, Kuipers, JAM. Fully resolved simulation of a gas-fluidized bed: a critical test of DEM models. Chem Eng Sci 2013;91:1–4. https://doi.org/10.1016/j.ces.2012.12.038.Suche in Google Scholar

113. Luo, K, Tan, J, Wang, Z, Fan, J. Particle-resolved direct numerical simulation of gas-solid dynamics in experimental fluidized beds. AIChE J 2016;62:1917–32. https://doi.org/10.1002/aic.15186.Suche in Google Scholar

114. Rubinstein, GJ, Derksen, JJ, Sundaresan, S. Lattice Boltzmann simulations of low-Reynolds-number flow past fluidized spheres: effect of Stokes number on drag force. J Fluid Mech 2016;788:576–601. https://doi.org/10.1017/jfm.2015.679.Suche in Google Scholar

115. Rubinstein, GJ, Ozel, A, Yin, X, Derksen, JJ, Sundaresan, S. Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force. J Fluid Mech 2017;833:599–630. https://doi.org/10.1017/jfm.2017.705.Suche in Google Scholar

116. Lane, G, Schwarz, M, Evans, GM. Numerical modelling of gas–liquid flow in stirred tanks. Chem Eng Sci 2005;60:2203–14. https://doi.org/10.1016/j.ces.2004.11.046.Suche in Google Scholar

117. Doroodchi, E, Evans, G, Schwarz, M, Lane, G, Shah, N, Nguyen, A. Influence of turbulence intensity on particle drag coefficients. Chem Eng J 2008;135:129–34. https://doi.org/10.1016/j.cej.2007.03.026.Suche in Google Scholar

118. Hjelmfelt, A, Mockros, L. Motion of discrete particles in a turbulent fluid. Appl Sci Res 1966;16:149–61. https://doi.org/10.1007/bf00384062.Suche in Google Scholar

119. Torobin, L, Gauvin, W. The drag coefficients of single spheres moving in steady and accelerated motion in a turbulent fluid. AIChE J 1961;7:615–19. https://doi.org/10.1002/aic.690070417.Suche in Google Scholar

120. Nouri, J, Whitelaw, J. Particle velocity characteristics of dilute to moderately dense suspension flows in stirred reactors. Int J Multiphas Flow 1992;18:21–33. https://doi.org/10.1016/0301-9322(92)90003-y.Suche in Google Scholar

121. Schwartzberg, H, Treybal, R. Fluid and particle motion in turbulent stirred tanks. Fluid motion. Ind Eng Chem Fundam 1968;7:1–6. https://doi.org/10.1021/i160025a001.Suche in Google Scholar

122. Brucato, A, Grisafi, F, Montante, G. Particle drag coefficients in turbulent fluids. Chem Eng Sci 1998;53:3295–314. https://doi.org/10.1016/s0009-2509(98)00114-6.Suche in Google Scholar

123. Bagchi, P, Balachandar, S. Effect of turbulence on the drag and lift of a particle. Phys Fluids 2003;15:3496–513. https://doi.org/10.1063/1.1616031.Suche in Google Scholar

124. Yang, T, Shy, S. The settling velocity of heavy particles in an aqueous near-isotropic turbulence. Phys Fluids 2003;15:868–80. https://doi.org/10.1063/1.1557526.Suche in Google Scholar

125. Yang, T, Shy, S. Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J Fluid Mech 2005;526:171–216. https://doi.org/10.1017/s0022112004002861.Suche in Google Scholar

126. Ghatage, SV, Sathe, MJ, Doroodchi, E, Joshi, JB, Evans, GM. Effect of turbulence on particle and bubble slip velocity. Chem Eng Sci 2013;100:120–36. https://doi.org/10.1016/j.ces.2013.03.031.Suche in Google Scholar

127. Crowe, CT. On models for turbulence modulation in fluid–particle flows. Int J Multiphas Flow 2000;26:719–27. https://doi.org/10.1016/s0301-9322(99)00050-6.Suche in Google Scholar

128. Ghadirian, E, Arastoopour, H. CFD simulation of a fluidized bed using the EMMS approach for the gas-solid drag force. Powder Technol 2016;288:35–44. https://doi.org/10.1016/j.powtec.2015.10.034.Suche in Google Scholar

129. Li, T, Wang, L, Rogers, W, Zhou, G, Ge, W. An approach for drag correction based on the local heterogeneity for gas-solid flows. AIChE J 2017;63:1203–12. https://doi.org/10.1002/aic.15507.Suche in Google Scholar

130. Luo, H, Lu, B, Zhang, J, Wu, H, Wang, W. A grid-independent EMMS/bubbling drag model for bubbling and turbulent fluidization. Chem Eng J 2017;326:47–57. https://doi.org/10.1016/j.cej.2017.04.145.Suche in Google Scholar

131. Arastoopour, H, Gidaspow, D. Vertical pneumatic conveying using four hydrodynamic models. Ind Eng Chem Fundam 1979;18:123–30. https://doi.org/10.1021/i160070a006.Suche in Google Scholar

132. Gao, X, Li, T, Sarkar, A, Lu, L, Rogers, WA. Development and validation of an enhanced filtered drag model for simulating gas-solid fluidization of Geldart A particles in all flow regimes. Chem Eng Sci 2018;184:33–51. https://doi.org/10.1016/j.ces.2018.03.038.Suche in Google Scholar

133. Igci, Y, Andrews IV, AT, Sundaresan, S, Pannala, S, O’Brien, T. Filtered two‐fluid models for fluidized gas‐particle suspensions. AIChE J 2008;54:1431–48. https://doi.org/10.1002/aic.11481.Suche in Google Scholar

134. Parmentier, JF, Simonin, O, Delsart, O. A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed. AIChE J 2012;58:1084–98. https://doi.org/10.1002/aic.12647.Suche in Google Scholar

135. Sarkar, A, Milioli, FE, Ozarkar, S, Li, T, Sun, X, Sundaresan, S. Filtered sub-grid constitutive models for fluidized gas-particle flows constructed from 3-D simulations. Chem Eng Sci 2016;152:443–56. https://doi.org/10.1016/j.ces.2016.06.023.Suche in Google Scholar

136. Ozel, A, Kolehmainen, J, Radl, S, Sundaresan, S. Fluid and particle coarsening of drag force for discrete-parcel approach. Chem Eng Sci 2016;155:258–67. https://doi.org/10.1016/j.ces.2016.08.014.Suche in Google Scholar

137. Radl, S, Sundaresan, S. A drag model for filtered Euler–Lagrange simulations of clustered gas–particle suspensions. Chem Eng Sci 2014;117:416–25. https://doi.org/10.1016/j.ces.2014.07.011.Suche in Google Scholar

138. Mehrabadi, M, Murphy, E, Subramaniam, S. Development of a gas–solid drag law for clustered particles using particle-resolved direct numerical simulation. Chem Eng Sci 2016;152:199–212. https://doi.org/10.1016/j.ces.2016.06.006.Suche in Google Scholar

139. Li, J. Particle-fluid two-phase flow: the energy-minimization multi-scale method. Beijing: Metallurgical Industry Press; 1994.Suche in Google Scholar

140. Li, J, Ge, W, Wang, W, Yang, N, Liu, X, Wang, L, et al.. From multiscale modeling to meso-science. Berlin‐Heidelberg, Germany: Hong Kong University of Science and Technology, Springer; 2013.10.1007/978-3-642-35189-1Suche in Google Scholar

141. Wang, W, Li, J. Simulation of gas–solid two-phase flow by a multi-scale CFD approach—of the EMMS model to the sub-grid level. Chem Eng Sci 2007;62:208–31. https://doi.org/10.1016/j.ces.2006.08.017.Suche in Google Scholar

142. Milioli, CC, Milioli, FE, Holloway, W, Agrawal, K, Sundaresan, S. Filtered two‐fluid models of fluidized gas‐particle flows: new constitutive relations. AIChE J 2013;59:3265–75. https://doi.org/10.1002/aic.14130.Suche in Google Scholar

143. Igci, Y, Pannala, S, Benyahia, S, Sundaresan, S. Validation studies on filtered model equations for gas-particle flows in risers. Ind Eng Chem Res 2011;51:2094–103. https://doi.org/10.1021/ie2007278.Suche in Google Scholar

144. Cao, Z, Tafti, DK, Shahnam, M. Development of drag correlation for suspensions of ellipsoidal particles. Powder Technol 2020;369:298–310. https://doi.org/10.1016/j.powtec.2020.05.049.Suche in Google Scholar

145. Cao, Z, Tafti, DK, Shahnam, M. Modeling drag force in ellipsoidal particle suspensions with preferential orientation. Powder Technol 2021;378:274–87. https://doi.org/10.1016/j.powtec.2020.09.067.Suche in Google Scholar

146. Mandø, M, Rosendahl, L. On the motion of non-spherical particles at high Reynolds number. Powder Technol 2010;202:1–13.10.1016/j.powtec.2010.05.001Suche in Google Scholar

147. Hilton, JE, Cleary, PW. The influence of particle shape on flow modes in pneumatic conveying. Chem Eng Sci 2011;66:231–40. https://doi.org/10.1016/j.ces.2010.09.034.Suche in Google Scholar

148. Hilton, JE, Mason, LR, Cleary, PW. Dynamics of gas–solid fluidised beds with non-spherical particle geometry. Chem Eng Sci 2010;65:1584–96. https://doi.org/10.1016/j.ces.2009.10.028.Suche in Google Scholar

149. van Wachem, B, Zastawny, M, Zhao, F, Mallouppas, G. Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers. Int J Multiphas Flow 2015;68:80–92. https://doi.org/10.1016/j.ijmultiphaseflow.2014.10.006.Suche in Google Scholar

150. Yin, CG, Rosendahl, L, Kaer, SK, Sørensen, H. Modelling the motion of cylindrical particles in a nonuniform flow. Chem Eng Sci 2003;58:3489–98. https://doi.org/10.1016/s0009-2509(03)00214-8.Suche in Google Scholar

151. Haidar, A, Levenspiel, O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 1989;58:63–70.10.1016/0032-5910(89)80008-7Suche in Google Scholar

152. Swamee, PK, Ojha, CSP. Drag coefficient and fall velocity of nonspherical particles. J Hydraul Eng 1991;117:660–7. https://doi.org/10.1061/(asce)0733-9429(1991)117:5(660).10.1061/(ASCE)0733-9429(1991)117:5(660)Suche in Google Scholar

153. Ganser, GH. A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol 1993;77:143–52. https://doi.org/10.1016/0032-5910(93)80051-b.Suche in Google Scholar

154. Leith, D. Drag on nonspherical objects. Aerosol Sci Technol 1987;6:153–61. https://doi.org/10.1080/02786828708959128.Suche in Google Scholar

155. Loth, E. Drag of non-spherical solid particles of regular and irregular shape. Powder Technol 2008;182:342–53. https://doi.org/10.1016/j.powtec.2007.06.001.Suche in Google Scholar

156. Tran-Cong, S, Gay, M, Michaelides, EE. Drag coefficients of irregularly shaped particles. Powder Technol 2004;139:21–32. https://doi.org/10.1016/j.powtec.2003.10.002.Suche in Google Scholar

157. Hölzer, A, Sommerfeld, M. New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technol 2008;184:361–5. https://doi.org/10.1016/j.powtec.2007.08.021.Suche in Google Scholar

158. Hölzer, A, Sommerfeld, M. Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles. Comput Fluids 2009;38:572–89. https://doi.org/10.1016/j.compfluid.2008.06.001.Suche in Google Scholar

159. Guo, X, Lin, J, Nie, D. New formula for drag coefficient of cylindrical particles. Particuology 2011;9:114–20. https://doi.org/10.1016/j.partic.2010.07.027.Suche in Google Scholar

160. Richter, A, Nikrityuk, PA. Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers. Int J Heat Mass Tran 2012;55:1343–54. https://doi.org/10.1016/j.ijheatmasstransfer.2011.09.005.Suche in Google Scholar

161. Richter, A, Nikrityuk, PA. New correlations for heat and fluid flow past ellipsoidal and cubic particles at different angles of attack. Powder Technol 2013;249:463–74. https://doi.org/10.1016/j.powtec.2013.08.044.Suche in Google Scholar

162. Rosendahl, L. Using a multi-parameter particle shape description to predict the motion of non-spherical particle shapes in swirling flow. Appl Math Model 2000;24:11–25. https://doi.org/10.1016/s0307-904x(99)00023-2.Suche in Google Scholar

163. Yow, HN, Pitt, MJ, Salman, AD. Drag correlations for particles of regular shape. Adv Powder Technol 2005;16:363–71. https://doi.org/10.1163/1568552054194221.Suche in Google Scholar

164. Zastawny, M, Mallouppas, G, Zhao, F, van Wachem, B. Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Int J Multiphas Flow 2012;39:227–39. https://doi.org/10.1016/j.ijmultiphaseflow.2011.09.004.Suche in Google Scholar

165. Sanjeevi, SKP, Kuipers, JAM, Padding, JT. Drag, lift and torque correlations for non-spherical particles from Stokes limit to high Reynolds numbers. Int J Multiphas Flow 2018;106:325–37. https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.011.Suche in Google Scholar

166. Asif, M. Flow dynamic characterization of cylindrical particles. Part Part Syst Char 2009;26:210–19. https://doi.org/10.1002/ppsc.200700025.Suche in Google Scholar

167. Bolejs, V, Machac, I. Pressure drop during the flow of a Newtonian fluid through a fixed bed of particles. Chem Eng Process 1995;34:1–8.10.1016/0255-2701(94)00566-4Suche in Google Scholar

168. Dolejs̆, V, Machac̆, I. Pressure drop during the flow of a Newtonian fluid through a fixed bed of particles. Chem Eng Process: Process Intensification 1995;34:1–8.10.1016/0255-2701(94)00566-4Suche in Google Scholar

169. Nemec, D, Levec, J. Flow through packed bed reactors: 1. Single-phase flow. Chem Eng Sci 2005;60:6947–57. https://doi.org/10.1016/j.ces.2005.05.068.Suche in Google Scholar

170. Tian, F-Y, Huang, L-F, Fan, L-W, Qian, H-L, Yu, Z-T. Wall effects on the pressure drop in packed beds of irregularly shaped sintered ore particles. Powder Technol 2016;301:1284–93. https://doi.org/10.1016/j.powtec.2016.07.073.Suche in Google Scholar

171. Dorai, F, Moura Teixeira, C, Rolland, M, Climent, E, Marcoux, M, Wachs, A. Fully resolved simulations of the flow through a packed bed of cylinders: effect of size distribution. Chem Eng Sci 2015;129:180–92. https://doi.org/10.1016/j.ces.2015.01.070.Suche in Google Scholar

172. Kriebitzsch, SHL, van der Hoef, MA, Kuipers, JAM. Fully resolved simulaiton of flows with non-spherical particles using an immersed boundary method. In: Ninth 1International Conference on CFD in Minerals and Process Industries. Melbourne Australia: CSIRO; 2012.10.1016/j.ces.2012.12.038Suche in Google Scholar

173. Matsumura, Y, Jackson, TL. Numerical simulation of fluid flow through random packs of polydisperse cylinders. Phys Fluids 2014;26:123302. https://doi.org/10.1063/1.4903954.Suche in Google Scholar

174. Vollmari, K, Oschmann, T, Wirtz, S, Kruggel-Emden, H. Pressure drop investigations in packings of arbitrary shaped particles. Powder Technol 2015;271:109–24. https://doi.org/10.1016/j.powtec.2014.11.001.Suche in Google Scholar

175. Chhabra, RP, Agarwal, L, Sinha, NK. Drag on non-spherical particles: an evaluation of available methods. Powder Technol 1999;101:288–95. https://doi.org/10.1016/s0032-5910(98)00178-8.Suche in Google Scholar

176. Eisfeld, B, Schnitzlein, K. The influence of confining walls on the pressure drop in packed beds. Chem Eng Sci 2001;56:4321–9. https://doi.org/10.1016/s0009-2509(00)00533-9.Suche in Google Scholar

177. Rong, LW, Zhou, ZY, Yu, AB. Lattice–Boltzmann simulation of fluid flow through packed beds of uniform ellipsoids. Powder Technol 2015;285:146–56. https://doi.org/10.1016/j.powtec.2015.06.047.Suche in Google Scholar

178. Ren, B, Zhong, W, Jiang, X, Jin, B, Yuan, Z. Numerical simulation of spouting of cylindroid particles in a spouted bed. Can J Chem Eng 2014;92:928–34. https://doi.org/10.1002/cjce.21900.Suche in Google Scholar

179. Ren, B, Zhong, W, Jin, B, Lu, Y, Chen, X, Xiao, R. Study on the drag of a cylinder-shaped particle in steady upward gas flow. Ind Eng Chem Res 2011;50:7593–600. https://doi.org/10.1021/ie102263u.Suche in Google Scholar

180. Zhong, WQ, Zhang, Y, Jin, BS, Zhang, MY. Discrete element method simulation of cylinder‐shaped particle flow in a gas‐solid fluidized bed. Chem Eng Technol: Ind Chem-Plant Equip-Process Eng-Biotechnol 2009;32:386–91. https://doi.org/10.1002/ceat.200800516.Suche in Google Scholar

181. Oschmann, T, Hold, J, Kruggel-Emden, H. Numerical investigation of mixing and orientation of non-spherical particles in a model type fluidized bed. Powder Technol 2014;258:304–23. https://doi.org/10.1016/j.powtec.2014.03.046.Suche in Google Scholar

182. Nan, W, Wang, Y, Wang, J. Numerical analysis on the fluidization dynamics of rodlike particles. Adv Powder Technol 2016;27:2265–76. https://doi.org/10.1016/j.apt.2016.08.015.Suche in Google Scholar

183. Mahajan, VV, Nijssen, TM, Kuipers, J, Padding, JT. Non-spherical particles in a pseudo-2D fluidised bed: modelling study. Chem Eng Sci 2018;192:1105–23. https://doi.org/10.1016/j.ces.2018.08.041.Suche in Google Scholar
Received: 2020-10-28
Accepted: 2021-04-11
Published Online: 2021-05-14

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Three-phase modeling and optimization of benzene alkylation in commercial catalytic reactors
  4. Control of negative gain nonlinear processes using sliding mode controllers with modified Nelder-Mead tuning equations
  5. Novel control strategy for non-minimum-phase unstable second order systems: generalised predictor based approach
  6. Modelling adiabatic flame temperature for methane with an overview for advanced combustion process: flameless combustion
  7. Evaluation the effect of the ambient temperature on the liquid petroleum gas transportation pipeline
  8. Performance of molecular dynamics simulation for predicting of solvation free energy of neutral solutes in methanol
  9. Reviews
  10. Phase equilibria modeling of biorefinery-related systems: a systematic review
  11. On the drag force closures for multiphase flow modeling
https://doi.org/10.1515/cppm-2020-0103
Schlagwörter für diesen Artikel
CFD-DEM; drag force; non-spherical; size distribution; TFM

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Three-phase modeling and optimization of benzene alkylation in commercial catalytic reactors
  4. Control of negative gain nonlinear processes using sliding mode controllers with modified Nelder-Mead tuning equations
  5. Novel control strategy for non-minimum-phase unstable second order systems: generalised predictor based approach
  6. Modelling adiabatic flame temperature for methane with an overview for advanced combustion process: flameless combustion
  7. Evaluation the effect of the ambient temperature on the liquid petroleum gas transportation pipeline
  8. Performance of molecular dynamics simulation for predicting of solvation free energy of neutral solutes in methanol
  9. Reviews
  10. Phase equilibria modeling of biorefinery-related systems: a systematic review
  11. On the drag force closures for multiphase flow modeling
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