Evaluation of Eulerian Two-Fluid Numerical Method for the Simulation of Heat Transfer in Fluidized Beds
Authors
Abstract
Accurate modeling of fluidization and heat transfer phenomena in gas-solid fluidized beds is not solely dependent on the particular selected numerical model and involved algorithms. In fact, choosing the right model for each specific operating condition, the correct implementation of each model, and the right choice of parameters and boundary conditions, determine the accuracy of the results in the evaluation of the performance of fluidized beds. In this research, in order to accurately simulate heat transfer in fluidized beds, important and effective parameters on two-fluid Eulerian model that incorporate the kinetic theory of granular flow were investigated. For this purpose, effects of particle-particle and particle-wall restitution coefficient, specularity coefficient, granular temperature and effective thermal conductivity coefficients determination methods on the numerical solution were evaluated. These investigations were first carried out on heat transfer from hot air to solid particles in an adiabatic fluidized bed, and then on a fluidized bed with constant temperature walls for bubbling and turbulent regimes. Results showed that specularity coefficient and effective thermal conductivity are important parameters in heat transfer process from wall to bed. In this case, the zero value of the specularity coefficient causes the air temperature to increase by about 7 degrees in the bubbling regime and about 5 degrees in the turbulent regime, and its unit value gives the same results with the no-slip condition. In addition, considering the solid and gas material thermal conductivities causes the outlet air temperature to be about 26 degrees higher than the temperature that is obtained by considering the effective thermal conductivity coefficients with standard approach. The partial differential and algebraic form of the conservation equation for the particles kinetic energy show identical results in dense fluidized beds, although considering a constant granular temperature can cause computational errors.
Keywords
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34. Zhou, Z. Y., Yu, A. B., and Zulli, P., “Particle Scale Study of Heat Transfer in Packed and Bubbling Fluidized Beds”, American Institute of Chemical Engineers Journal, Vol. 55, No. 4, pp. 868-884, 2009.
35. Johnson, P. C., and Jackson, R., “Frictional-Collisional Constitutive Relations for Granular Materials, with Application to Plane Shearing”, Journal of Fluid Mechanics, Vol. 176, pp. 67-93, 1987.
2. Martin, H., “Heat Transfer Between Gas Fluidized Beds of Solid Particles and Surfaces of Immersed Heat Exchanger Elements, Part I”, Chemical Engineering and Processing, Vol. 18, pp. 157-169, 1984.
3. Kunii, D., and Levenspiel, O., Fluidization Engineering, Second edition ed. Boston, Butterworth-Heinemann, 1991.
4. Ranade, V. V., “Computational Flow Modeling for Chemical Reactor Engineering”, Fluidized bed reactors, India: Industrial Flow Modeling Group Chemical Engineering Division National Chemical Laboratory Pune, pp. 367-402, 2002.
5. Abdelmotalib, H. M., Youssef, M. A. M., Hassan, A. A. , Youn, S. B., and Im, I. T., “Heat Transfer Process in Gas-Solid Fluidized Bed Combustors: a Review”, International Journal of Heat and Mass Transfer, Vol. 89, pp. 567-575, 2015.
6. Ravelli, S., Perdichizzi, A., and Barigozzi, G., “Description, Applications and Numerical Modeling of Bubbling Fluidized Bed Combustion in Waste-to-Energy Plants”, Progress in Energy and Combustion Science, Vol. 34, pp. 224-253, 2008.
7. Singh, R. I., Brink, A., and Hupa, M., “CFD Modeling to Study Fluidized Bed Combustion and Gasification”, Applied Thermal Engineering, Vol. 52, pp. 585-614, 2013.
8. Torfeh, S., and Kouhikamali, R., “Numerical Study of Different Gas–Solid Flow Regimes Effects on Hydrodynamics and Heat Transfer Performance of a Fluidized Bed Reactor” Heat Transfer-Asian Research, Vol. 49, No. 1, pp. 213-235, 2020.
9. Wachem, B. G. M., Schaaf, J. V. d., Schouten, J. C., Krishna, R., and Bleek, C. M. V. d., “Experimental Validation of Lagrangian-Eulerian Simulations of Fluidized Beds”, Powder Technology, Vol. 116, pp. 155-165, 2001.
10. Taghipour, F., Ellis, N., and Wong, C., “Experimental and Computational Study of Gas-Solid Fluidized Bed Hydrodynamics”, Chemical Engineering Science, Vol. 60, pp. 6857-6867, 2005.
11. Mostafazadeh, M., Rahimzadeh, H., and Hamzei, M., “Numerical Analysis of the Mixing Process in a Gas-Solid Fluidized Bed Reactor”, Powder Technology, Vol. 239, pp. 422-433, 2013.
12. Mehdizad, M., and Kouhikamali, R., “Numerical Investigation of the Minimum Fluidization Velocity in a Gas–Solid Fluidized Bed Using Discrete Phase Model”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, pp. 272-288, 2018.
13. Bakshi, A., Altantzis, C., Bates, R. B., and Ghoniem, A. F., “ Eulerian-Eulerian Simulation of Dense Solid-Gas Cylindrical Fluidized Beds: Impact of Wall Boundary Condition and Drag Model on Fluidization”, Powder Technology, Vol. 277, pp. 47-62, 2015.
14. Agrawal, V., Shinde, Y., Shah, M. T., Utikar, R. P., and Pareek, V. K., “Effect of Drag Models on CFD–DEM Predictions of Bubbling fluidized Beds With Geldart D Particles”, Advanced Powder Technology, Vol. 29, No. 11, pp. 2658-2669, 2018.
15. Bian, W., Chen, X., and Wang, J., “A Critical Comparison of Two-fluid Model, Discrete Particle Method and Direct Numerical Simulation for Modeling Dense Gas-Solid flow of Rough Spheres”, Chemical Engineering Science, Vol. 210, 2019.
16. Mostafaei, F., Golshan, S., Zarghami, R., Gharebagh, R. S., and Mostoufi, N., “Investigating the Bubble Dynamics In Fluidized Bed by CFD-DEM”, Powder Technology, Vol. 366, No. 15, pp. 938-948, 2020.
17. Hou, Q. F., Zhou, Z. Y., and Yu, A. B., “Gas-solid Flow and Heat Transfer in Fluidized Beds with Tubes: Effects of Material Properties and Tube Array Settings”, Powder Technology, Vol. 296, pp. 59-71, 2016.
18. Ngoh, J., and Lim, E. W. C., “Effects of Particle Size and Bubbling Behavior on Heat Transfer in Gas fluidized Beds”, Applied Thermal Engineering, Vol. 105, pp. 225-242, 2016.
19. Ostermeier, P., Dawo, F., Vandersickel, A., Gleis, S., and Spliethoff, H., “Numerical Calculation of Wall-to-Bed Heat Transfer Coefficients in Geldart B Bubbling Fluidized Beds with Immersed Horizontal Tubes”, Powder Technology, Vol. 333, pp. 193-208, 2018.
20. Li, B., Ma, M., Yu, Y., Chen, C., and Zhou, C., “Particle Scale Study on Heat Transfer of Gas-Solid Spout Fluidized Bed with Hot Gas Injection”, Particulate Science and Technology, Vol. 36, pp. 1-10, 2018.
21. Wang, L., Yuan, W., Duan, S., Sun, J., and Xu, L., “Experimental and Numerical Investigation of Heat Transfer Characteristics in an Internally Circulating Fluidized Bed”, Heat and Mass Transfer, Vol. 55, No. 4, pp. 1195-1205, 2019.
22. Patro, B., Kumar, K. K., and Krishna, D. J., “Prediction of Local Heat Transfer Characteristics of Dilute Gas-Solid Flows Through an Adiabatic, Horizontal Pipe”, Heat Transfer-Asian Research, pp. 1-20, 2019.
23. Xue, J., Xie, L., Shao, Y., and Zhong, W., “CFD-DEM Study of the Effects of Solid Properties and Aeration Conditions on Heat Transfer in Fluidized Bed”, Advanced Powder Technology, Vol. 31, No. 9, pp. 3974-3992, 2020.
24. Chang, J., Wang, G., Gao, J., Zhang, K., Chen, H., and Yang, Y., “CFD Modeling of Particle-Particle Heat Transfer in Dense Gas-Solid Fluidized Beds of Binary Mixture”, Powder Technology, Vol. 217, pp. 50-60, 2012.
25. Gidaspow, D., “Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions”, Boston, USA, Academic Press, 1994.
26. Hamzehei, M., and Rahimzadeh, H., “Experimental and Numerical Study of Hydrodynamics with Heat Transfer in a Gas-Solid Fluidized-Bed Reactor at Different Particle Sizes”, Industrial & Engineering Chemistry Research, Vol. 48, pp. 3177-3186, 2009.
27. Gidaspow, D., Bezburuah, R., and Ding, J., “Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory Approach, In Fluidization VII”, Proceedings of the 7th Engineering Foundation Conference on Fluidization, 1992.
28. Abdelmotalib, H. M., Ko, D. G., and Im, I. T., “A Study on Wall-to-Bed Heat Transfer in a Conical Fluidized Bed Combustor”, Applied Thermal Engineering, Vol. 25, pp. 928-937, 2016.
29. Kuipers, J. A. M., Prins, W., and Swaaij, W. P. M. V., “Numerical Calculation of Wall-to-Bed Heat-Transfer Coefficients in Gas-fluidized Beds”, American Institute of Chemical Engineers Journal, Vol. 38, pp. 1079-1091, 1992.
30. Abdelmotalib, H. M., Youssef, M. A. M., Hassan, A. A., Youn, S. B., and Im, I. T., “Numerical Study on the Wall to Bed Heat Transfer in a Conical Fluidized Bed Combustor”, International Journal of Precision Engineering and Manufacturing, Vol. 16, No. 7, pp. 1551-1559. 2015;
31. Zehner, P., Schlünder, E. U., “Wärmeleitfähigkeit Von Schüttungen Bei Mäßigen Temperaturen”, Chemie Ingenieur Technik, Vol. 42, pp. 933-941, 1970.
32. Gidaspow, D., and Syamlal, M., “Hydrodynamics of fluidization: Prediction of Wall to Bed Heat Transfer Coefficients”, American Institute of Chemical Engineers Journal, Vol. 31, No. 1, pp. 127-135, 1985.
33. Hunt, M. L., “Discrete Element Simulations for Granular Material flows: Effective Thermal Conductivity and Self Diffusivity”, International Journal of Heat and Mass Transfer, Vol. 40, No. 13, 3059–3068, 1997.
34. Zhou, Z. Y., Yu, A. B., and Zulli, P., “Particle Scale Study of Heat Transfer in Packed and Bubbling Fluidized Beds”, American Institute of Chemical Engineers Journal, Vol. 55, No. 4, pp. 868-884, 2009.
35. Johnson, P. C., and Jackson, R., “Frictional-Collisional Constitutive Relations for Granular Materials, with Application to Plane Shearing”, Journal of Fluid Mechanics, Vol. 176, pp. 67-93, 1987.
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