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Genetic Programming based Drag Model with Improved Prediction Accuracy for Fluidization Systems

  • R. R. Sonolikar , M. P. Patil , R. B. Mankar , S. S. Tambe und B. D. Kulkarni EMAIL logo
Veröffentlicht/Copyright: 11. Januar 2017
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International Journal of Chemical Reactor Engineering
Aus der Zeitschrift International Journal of Chemical Reactor Engineering Band 15 Heft 2

Abstract

The drag coefficient plays a vital role in the modeling of gas-solid flows. Its knowledge is essential for understanding the momentum exchange between the gas and solid phases of a fluidization system, and correctly predicting the related hydrodynamics. There exists a number of models for predicting the magnitude of the drag coefficient. However, their major limitation is that they predict widely differing drag coefficient values over same parameter ranges. The parameter ranges over which models possess a good drag prediction accuracy are also not specified explicitly. Accordingly, the present investigation employs Geldart’s group B particles fluidization data from various studies covering wide ranges of Re and εs to propose a new unified drag coefficient model. A novel artificial intelligence based formalism namely genetic programming (GP) has been used to obtain this model. It is developed using the pressure drop approach, and its performance has been assessed rigorously for predicting the bed height, pressure drop, and solid volume fraction at different magnitudes of Reynolds number, by simulating a 3D bubbling fluidized bed. The new drag model has been found to possess better prediction accuracy and applicability over a much wider range of Re and εs than a number of existing models. Owing to the superior performance of the new drag model, it has a potential to gainfully replace the existing drag models in predicting the hydrodynamic behavior of fluidized beds.

Keywords: Fluidization; drag force; modeling; genetic programming; computational fluid dynamics

Notation

Cd

drag coefficient

dp

particle mean diameter (m)

g0

radial distribution coefficient

I

unity matrix

I2D

2nd invariant of the deviatoric stress tensor (s−2)

∇P

gas phase pressure drop (N/m2)

∇ps

pressure drop due to solids (N/m2)

Re

Reynolds number

Sk

strain rate tensor (N/m2)

Uk

velocity of phase k (m/s)

v′

fluctuating velocity (m/s)

Greek notation

β

gas/solid momentum exchange (kg/m3s)

εg

gas volume fraction

εs

solid volume fraction

η

coefficient used in eq. (6) of Table S.1.

θs

granular temperature (m2/s2)

μs

solid viscosity

μscoll

collisional viscosity (Pa s)

μskin

kinetic viscosity (Pa s)

μg

gas viscocity (Pa s)

μk

viscosity of phase k (Pa s)

ξk

bulk viscosity (Pa s)

ρg

gas density (kg/m3)

τg

gas stress strain tensor (Pa)

τs

solid stress strain tensor (Pa)

τk

viscous stress tensor (N/m2)

ϕs

transfer rate of kinetic energy (kg/s3 m)

Acknowledgments

SST thankfully acknowledges partial support for this study by Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi, under TAPCOAL Network Project.

References

1. 1. Altantzis, C., Bates, R.B., Ghoniem, A.F., 2015. 3D Eulerian Modeling of Thin Rectangular Gas–Solid Fluidized Beds: Estimation of the Specularity Coefficient and Its Effects on Bubbling Dynamics and Circulation Times. Powder Technology 270, 256–270.10.1016/j.powtec.2014.10.029Suche in Google Scholar

2. 2. Anderson, T.B., Jackson, R., 1967. Fluid Mechanical Description of Fluidized Beds Equation of Motion. Ind. Eng. Chem. Fundam., 6, 527–39.10.1021/i160024a007Suche in Google Scholar

3. 3. Arastoopour, H., Pakdel, P., Adewumi, M., 1990. Hydrodynamic Analysis of Dilute Gas-Solids Flow in a Vertical Pipe. Pow. Tech. 62, 2, 163–170.10.1016/0032-5910(90)80080-ISuche in Google Scholar

4. 4. Beetstra, R., A Lattice Boltzmann Simulation Study of the Drag Coefficient of Clusters of Spheres. Comput. Fliuds, 2006, 35, 966–970.10.1016/j.compfluid.2005.03.009Suche in Google Scholar

5. 5. Beetstra, R., van der Hoef, M.A., Kuipers, J.A.M., 2007. Drag Force of Intermediate Reynolds Number Flow Past Mono and Bidisperse Arrays of Spheres. AIChE J., 53, 2, 489–501.10.1002/aic.11065Suche in Google Scholar

6. 6. Behjat, Y., Shahhosseini, S., Hashemabadi, S.H., 2008. CFD Modeling of Hydrodynamic and Heat Transfer in Fluidized Bed Reactor. Int. Commun. Heat Mass. 35, 357–368.10.1016/j.icheatmasstransfer.2007.09.011Suche in Google Scholar

7. 7. Benyahia, S., Syamlal, M., O’Brien, T.J., 2006. Extension of Hill-Koch-Ladd Drag Correlation Over All Ranges of Reynolds Number of Solids Volume Fraction. Pow. Tech. 162, 166–174.10.1016/j.powtec.2005.12.014Suche in Google Scholar

8. 8. Benzarti, S., Mhiri, H., Bournot, H., 2012. Drag Models for Simulation Gas-Solid Flow in the Bubbling Fluidized Bed of FCC Particles. World Academy of Science, Eng. Tech., 61, 1138–1143.Suche in Google Scholar

9. 9. Dallavalle, J.M., 1948. Micrometrics Pitman, London.Suche in Google Scholar

10. 10. Davidson, J.F., Harrison, D., 1963. Fluidized Particles, Cambridge University Press, New York.Suche in Google Scholar

11. 11. Davidson, J.F., Harrison, D., 1971. Fluidization, 1st edn. Academic press, New York.Suche in Google Scholar

12. 12. De Felice, R., 1994. The Voidage Functions for Fluid-Particle Interaction Systems. Int. J. Multiph. Flow. 20, 1, 153–159.10.1016/0301-9322(94)90011-6Suche in Google Scholar

13. 13. Du Plessis, J.P., 1994. Analytical Quantification of Coefficient in the Ergun Equation for Fluid Friction in a Packed Bed. Trans. porous media 16, 189–207.10.1007/BF00617551Suche in Google Scholar

14. 14. Du, W., Bao, X., Xu, J., Wei, W., 2006. Computational Fluid Dynamics (CFD) Modeling of Spouted Bed: Assessment of Drag Coefficient Correlations. Chem. Eng. Sci., 61, 1401–1420.10.1016/j.ces.2005.08.013Suche in Google Scholar

15. 15. Enwald, H., Peirano, E., Almstedt, A.E., 1996. Eulerian Two Phase Flow Theory Applied to fluidization. Int. J. of Multiph. Flow, 22, 21–66.10.1016/S0301-9322(96)90004-XSuche in Google Scholar

16. 16. Ergun, S., 1952. Fluid Flow Through Packed Column. Chem. Eng. Prog. 48, 89.Suche in Google Scholar

17. 17. Esmaili, E., Mahinpey, N. 2011. Adjustment of Drag Coefficient Correlations in Three Dimensional CFD Simulation of gas-solid bubbling fluidized bed. Adv. Eng. Software, 42, 375–386.10.1016/j.advengsoft.2011.03.005Suche in Google Scholar

18. 18. Fattah, K.A., 2012. A New Approach Calculate Oil-Gas Ratio for Gas Condensate and Volatile Oil Reservoirs Using Genetic Programming. Oil and Gas Business. 1, 311–323.Suche in Google Scholar

19. 19. Garside, J., Al-Dibouni, M.R., 1977. Velocity voidage relationship for fluidization and sedimentation. Ind. Eng. Chem. Proc. Des. Dev. 16, 206–214.10.1021/i260062a008Suche in Google Scholar

20. 20. Gelderbloom, S.J., Gidaspow, D., Lyczkowski, R.W. 2003. CFD Simulations of Bubbling/Collapsing Fluidized Beds for Three Geldart Groups. AIChE J. 49, 844–858.10.1002/aic.690490405Suche in Google Scholar

21. 21. Ghugare, S.B., Tiwary, S., Elangovan, V., Tambe, S.S., 2014. Prediction of Higher Heating Value of Solid Biomass Fuels using Artificial Intelligence Formalisms. Bioenergy Research 7:681–692, doi:10.1007/s12155-013-9393–5.Suche in Google Scholar

22. 22. Gibilaro, G., 2001. Fluidization Dynamics, Butterworth Heinemann.10.1016/B978-075065003-8/50013-6Suche in Google Scholar

23. 23. Gidaspow, D., Ettihadieh, B. 1983. Fluidization in Two Dimensional Beds with a Jet and Hydrodynamic Modeling. Ind. Eng. Chem., 22, 193–201.10.1021/i100010a008Suche in Google Scholar

24. 24. Hill, R.J., Koch, D.L., Ladd, A.J.C., 2001. Moderate Reynolds Numbers Flows in Ordered and Random Arrays of Spheres. J. Fluid Mech., 448, 243–278.10.1017/S0022112001005936Suche in Google Scholar

25. 25. Holland, J.H., Adaptation in Natural and Artificial Systems. 1975. University of Michigan Press, Ann Arbor.Suche in Google Scholar

26. 26. Hosseini, S.H., Rahimi, R., Zivdar, M., Samini, A., 2009. CFD Simulation of Gas-Solid Fluidized Bed Containing FCC Particles. Korean J. of Chem. Engg. 26, 5, 1405–1413.10.1007/s11814-009-0220-9Suche in Google Scholar

27. 27. Iaccarino, G., 2001. Predictions of a Turbulent Separated Flow Using Commercial CFD Codes. J. Fluids Eng. 123, 819–828.10.1115/1.1400749Suche in Google Scholar

28. 28. Jackson, R., 2000. The Dynamics of Fluidized Particles, Cambridge University Press.Suche in Google Scholar

29. 29. Jenkins, J.T., Savage, S.B., 1983. A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical Particles. J Fluid Mech., 130, 187–202.10.1017/S0022112083001044Suche in Google Scholar

30. 30. Khandai, D., Derksen, J.J., Van den Akker, H.E.A., 2003. Interphase Drag Coefficients in Gas-Solid Flows. AIChE J. 49, 4, 1060–1065.10.1002/aic.690490423Suche in Google Scholar

31. 31. Kotanchek, M., 2004. Symbolic Regression via Genetic Programming, in: Wolfram Technology conference http://library.wolfram.com/infocenter/Conferences/5392/(accessed 03.02.2015).Suche in Google Scholar

32. 32. Koza, J.R., 1990. Genetically Breeding Populations of Computer Programs to Solve Problems in Artificial Intelligence. In: Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence, 6–9 November, 819–827, http://dx.doi.org/10.1109/TAI.1990.130444.10.1109/TAI.1990.130444Suche in Google Scholar

33. 33. Kunni, D., Levenspiel, O., 1991. Fluidization Engineering, 2nd Edition Butterworth Heinemann, Boston.Suche in Google Scholar

34. 34. Li, T., Benyahia, S. 2012. Revisiting Johnson and Jackson Boundary Conditions for Granular Flows. AlChE J58, 7, 2058–2068.10.1002/aic.12728Suche in Google Scholar

35. 35. Li, T., Pougatch, K., Salcudean, M., Grecov, D., 2008. Numerical Simulation of Horizontal Jet Penetration in a Three Dimensional Fluidized Bed. Pow. Technol., 184, 89–99.10.1016/j.powtec.2007.08.007Suche in Google Scholar

36. 36. Loha, C., Chattopadhyay, H., Chatterjee, P., 2012. Assesment of Drag Models in Simulating Bubbling Fluidized Bed Hydrodynamics. Chem Eng. Sci. 75, 400–407.10.1016/j.ces.2012.03.044Suche in Google Scholar

37. 37. Lun, C.K.K., Savage, S.B., Jefferey, D.J., Chepurniy, N., 1984. Kinetic theory of granular flow; in elastic particles in a general flow fields. J. Fluid Mech. 140, 223–256.10.1017/S0022112084000586Suche in Google Scholar

38. 38. Lundberg, J., Halvorsen, B.M. 2008. A Review of Some Existing Drag Models Describing the Interaction between Phases in a Bubbling Fluidized Bed. Proc. 49th Scand. Conf. Simulation and Modeling, Oslo University College, Oslo, Norway.Suche in Google Scholar

39. 39. Mckeen, T., Pugsley, T., 2003. Simulation and Experimental Validation of a Freely Bubbling bed Of FCC Catalyst. Pow. Tech., 129, 1-3, 139–152.10.1016/S0032-5910(02)00294-2Suche in Google Scholar

40. 40. Patil-Shinde, V., Kulkarni, T., Kulkarni, R., Chavan, P.D., Sharma, T., Sharma, B.K., Tambe, S. S., Kulkarni, B. D., 2014. Artificial Intelligence based Modelling of High Ash Coal Gasification in a Pilot-plant Scale Fluidized Bed Gasifier. Ind. Eng. Chem. Res., 53, 49, 18678–18689.10.1021/ie500593jSuche in Google Scholar

41. 41. Poli, R., Langdon, W, Mcphee, N. 2008. A Field Guide to Genetic Programming. Published via http://lulu.com and freely available at http://www.gp-field-guide.org.uk.Suche in Google Scholar

42. 42. Richardson, J.F., Zaki, W.N., 1954. Sedimentation and Fluidization, Part I. Trans. Inst. Chem. Engg. 32, 82–100.Suche in Google Scholar

43. 43. Rowe, P.N., McGillivray, H.J., Cheesman, D.J., 1979. Gas Discharge from an Orifice into a Gas Fluidized Bed. Trans. Inst. Chem. Engg. 57, 194.Suche in Google Scholar

44. 44. Schaeffer, D.G., 1987. Instability in the Evolution Equations Describing Incompressible Granular Flow. J. Diff. Equation. 66, 19–50.10.1016/0022-0396(87)90038-6Suche in Google Scholar

45. 45. Schmidt, M., Lipson, H. 2009. Distilling Free-Form Natural Laws from Experimental Data. Science 324, 81–85.10.1126/science.1165893Suche in Google Scholar

46. 46. Sharma, S., Tambe, S.S., 2014. Soft-Sensor Development for Biochemical Systems Using Genetic Programming. Biochem. Eng. J. 85, 89–100.10.1016/j.bej.2014.02.007Suche in Google Scholar

47. 47. Shrinivas, K., Kulkarni, R., Shaikh, S., Ghorpade, R., Vyas, R., Tambe, S.S., Ponrathnam, S., Kulkarni, B.D., 2016. Prediction of Reactivity Ratios in Free Radical Copolymerization from Monomer Resonance-Polarity (Q-e) Parameters: Genetic Programming-Based Models, Int. J. Chem. React. Eng. 14(1), 361–372.10.1515/ijcre-2014-0039Suche in Google Scholar

48. 48. Syamlal, M., O’Brien, T.J., 1987. Derivation of Drag Coefficient from Velocity-Voidage Correlation. U.S. Dept. of energy office of fossil energy national energy tech. lab., Morgantown W.V.Suche in Google Scholar

49. 49. Syamlal, M., O’Brien, T.J., 1988. Simulation of Granular Later Inversion in Liquid Fluidized Beds. Int. J. Multiphase Flow, 14, 4, 473–481.10.1016/0301-9322(88)90023-7Suche in Google Scholar

50. 50. Syamlal, M., Rogers, W., O‘Brien, T.J. MFIX Documentation, Theory Guide, Technical Note. U.S. Dept. of Energy, Office of Fossil Energy, National Energy Tech. Lab., Morgantown WV, 1993. DOE/METC-94/1004. https://mfix.netl.doe.gov/download/mfix/mfix_legacy_manual/Theory.pdf10.2172/10145548Suche in Google Scholar

51. 51. van der Hoef, M.A., van sint Annaland, M., Kuipers, J.A.M., 2005. Computational Fluid Dynamics for Dense Gas-Solid Fluidized Beds: A Multiscale Strategy. Chem. Eng. Sci. 59, 51–57.10.1016/j.ces.2004.07.013Suche in Google Scholar

52. 52. Vejahati, F., Mahinpey, N., Ellis, N., Nikoo, M.B., 2009. CFD Simulation of Gas-Solid Bubbling Fluidized Bed; A New Method for Adjusting Drag Law. Canadian J. Chem. Engg. 48, 19–30.10.1002/cjce.20139Suche in Google Scholar

53. 53. Wang, J., 2008. High-Resolution Eulerian Simulation of RMS of Solid Volume Fraction Fluctuation and Particle Clustering Characteristics in a CFB Riser. Chem. Eng. Sci., 63, 3341–3347.10.1016/j.ces.2008.03.041Suche in Google Scholar

54. 54. Wang, X., Li, Y., Hu, Y., Wang, Y., 2008. Synthesis of Heat-Integrated Complex Distillation Systems via Genetic Programming. Comput. Chem. Eng. 32, 1908–1917.10.1016/j.compchemeng.2007.10.009Suche in Google Scholar

55. 55. Wen, C.Y., Yu, Y.H., Mechanics of Fluidization, Chem. Ngg. Prog. Symp. 1966. Ser 62, 100–111.Suche in Google Scholar

56. 56. Yang, Y., Soh, C.K., 2002. Automated Optimum Design of Structures Using Genetic Programming. Comp. and Struc. 80, 1537–1546.10.1016/S0045-7949(02)00108-6Suche in Google Scholar

57. 57. Yang, N., Wang, W., Ge, W., Li, J., 2003. CFD Simulation of Concurrent-Up Gas-Solid Flow in Circulating Fluidized Beds with Structure-Dependent Drag Coefficient. Chem. Eng J., 96, 71–80.10.1016/j.cej.2003.08.006Suche in Google Scholar

58. 58. Yi, L., Wanli, K., 2011. A New Genetic Programming Algorithm for Building Decision Tree. Procedia Eng. 15, 3658–3662.10.1016/j.proeng.2011.08.685Suche in Google Scholar

59. 59. Zhang, Y., Reese, J.M., 2003. The Drag Force in Two Fluid Models of Gas-Solid Flows. Chem. Eng. Sci. 58, 8, 1641–1644.10.1016/S0009-2509(02)00659-0Suche in Google Scholar

60. 60. Zimmermann, S., Taghipour, F., 2005. CFD Modeling of the Hydrodynamics and Reaction Kinetics of FCC Fluidized Bed Reactors. Ind. Eng. Chem. Res., 44, 9818–9827.10.1021/ie050490+Suche in Google Scholar

61. 61. Zinani, F., Philippsen, C.G., Indrusiak, M.L. 2013. Numerical study of gas-solid drag models in bubbling fluidized bed. 22nd International Congress of Mechanical Engineering, November 3-7, Ribeirão Preto, SP, Brazil.Suche in Google Scholar

Supplemental Material

The online version of this article (DOI: 10.1515/ijcre-2016-0210) offers supplementary material, available to authorized users.

Published Online: 2017-01-11
Published in Print: 2017-04-01

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijcre-2016-0210
Schlagwörter für diesen Artikel
Fluidization; drag force; modeling; genetic programming; computational fluid dynamics

Artikel in diesem Heft

  1. Articles
  2. Genetic Programming based Drag Model with Improved Prediction Accuracy for Fluidization Systems
  3. Catalytic Photodegradation of Rhodamine B in the Presence of Natural Iron Oxide and Oxalic Acid under Artificial and Sunlight Radiation
  4. Esterification of Lauric Acid with Glycerol in the Presence of STA/MCM-41 Catalysts
  5. Existence of Synergistic Effects During Co-pyrolysis of Petroleum Coke and Wood Pellet
  6. Photocatalytic Treatment of Binary Mixture of Dyes using UV/TiO2 Process: Calibration, Modeling, Optimization and Mineralization Study
  7. Aqueous Phase Biosorption of Pb(II), Cu(II), and Cd(II) onto Cabbage Leaves Powder
  8. Design and Simulation of a Chaotic Micromixer with Diamond-Like Micropillar Based on Artificial Neural Network
  9. Experimentally Validated CFD Model for Gas-Liquid Flow in a Round-Bottom Stirred Tank Equipped with Rushton Turbine
  10. Pyrolysis Products Characterization and Dynamic Behaviors of Hydrothermally Treated Lignite
  11. Pd/ZrO2: An Efficient Catalyst for Liquid Phase Oxidation of Toluene in Solvent Free Conditions
  12. Micro-reactor for Non-catalyzed Esterification Reaction: Performance and Modeling
  13. Mathematical Modeling of Carbon Nanotubes Formation in Fluidized Bed Chemical Vapor Deposition
  14. Electrogeneration of Active Chlorine in a Filter-Press-Type Reactor Using a New Sb2O5 Doped Ti/RuO2-ZrO2 Electrode: Indirect Indigoid Dye Oxidation
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