OPEN ACCESS
In dense gas–solid fluidized beds the heat transfer to immersed objects is strongly coupled to the hydrodynamic behavior. The objective of this study is to experimentally and numerically assess the heat transfer coefficient around a horizontal tube in a Geldart B bubbling fluidized bed and derive a numerical-correlative approach for predicting the angular dependent heat transfer coefficient. The considered system consists of corundum as the solid bed material and air as the fluidization gas, entering the cylindrical geometry through a Tuyere nozzle distributor. Experimental data are obtained from a pilot scale test-rig with different tubular heat transfer probes and evaluated in a comprehensive uncertainty analysis. The resulting magnitude and angle dependent variations of the heat transfer coefficient at different superficial gas velocities are compared to three dimensional numerical simulations. The applied CFD model of the fluidized bed treats both gas and powder as Eulerian phases. The size distribution of the particles is described by two granular phases with corresponding mean diameters and a sphericity factor to account for their non-spherical shape. The fluid–solid interactions in this Multi Fluid Model are considered by incorporating the Kinetic Theory of Granular Flow and a sphericity-adapted drag model. The hydrodynamics at the tube surface, e.g. solid volume fraction, gas and particle velocities, are used for a novel numerical-correlative calculation of the angle dependent heat transfer coefficient between the bed material and the immersed tube. Special focus is set on depicting the particle contact time at the tube surface appropriately. The numerical results show the correct tendency of an increasing heat transfer coefficient with rising gas velocity and are partially in good agreement with the experimental observations.
Eulerian approach, experimental investigation, fluidized bed, heat transfer coefficient, hydrodynamics, numerical simulation
[1] Kunii, D. & Levenspiel, O., Fluidization engineering, 2nd edn., Butterworth-Heinemann: Boston, 1991.
[2] Wen-Ching Yang, Handbook of fluidization and fluid-particle systems. Marcel Dekker: New York, 2003.
[3] Baskakov, A.P., Berg, B.V., Vitt, O.K., Filippovsky, N.F., Kirakosyan, V.A., Goldobin,
J.M. & Maskaev, V.K., Heat transfer to objects immersed in fluidized beds. Powder Technology, 8(5), pp. 273–282, 1973. https://doi.org/10.1016/0032-5910(73)80092-0
[4] Di Natale, F., Bareschino, P. & Nigro, R., Heat transfer and void fraction profiles around a horizontal cylinder immersed in a bubbling fluidised bed. International Journal of Heat and Mass Transfer, 53(17–18), pp. 3525–3532, 2010. https://doi.org/10.1016/j.ijheatmasstransfer.2010.04.013
[5] George, A.H. & Smalley, J.L., An instrumented cylinder for the measurement of instantaneous local heat flux in high temperature fluidized beds. International Journal of Heat and Mass Transfer, 34(12), pp. 3025–3036, 1991. https://doi.org/10.1016/0017-9310(91)90072-M
[6] George, A.H., Instantaneous local heat transfer coefficients and related frequency spectra for a horizontal cylinder in a high temperature fluidized bed. International Journal of Heat and Mass Transfer, 36(2), pp. 337–345, 1993. https://doi.org/10.1016/0017-9310(93)80009-J
[7] Khan, T. & Turton, R., The measurement of instantaneous heat transfer coefficients around the circumference of a tube immersed in a high temperature fluidized bed. International Journal of Heat and Mass Transfer, 35(12), pp. 3397–3406, 1992. https://doi.org/10.1016/0017-9310(92)90226-I
[8] Kim, S.W., Ahn, J.Y., Kim, S.D. & Hyun Lee, D., Heat transfer and bubble characteristics in a fluidized bed with immersed horizontal tube bundle. International Journal of Heat and Mass Transfer, 46(3), pp. 399–409, 2003. https://doi.org/10.1016/S0017-9310(02)00296-X
[9] Olsson, S.E. & Almstedt, A.E., Local instantaneous and time-averaged heat transfer in a pressurized fluidized bed with horizontal tubes: Influence of pressure, fluidization velocity and tube-bank geometry. Chemical Engineering Science, 50(20), pp. 3231– 3245, 1995. https://doi.org/10.1016/0009-2509(95)00150-4
[10] Pence, D.V., Beasley, D.E. & Figliola, R.S., Heat transfer and surface renewal dynamics in gas-fluidized beds. Journal of Heat Transfer, 116(4), p. 929, 1994. https://doi.org/10.1115/1.2911468
[11] Sunderesan, S.R. & Clark, N.N., Local heat transfer coefficients on the circumference of a tube in a gas fluidized bed. International Journal of Multiphase Flow, 21(6), pp. 1003–1024, 1995. https://doi.org/10.1016/0301-9322(95)00020-X
[12] Kurosaki, Y., Ishiguro, H. & Takahashi, K., Fluidization and heat-transfer characteristics around a horizontal heated circular cylinder immersed in a gas fluidized bed. International Journal of Heat and Mass Transfer, 31(2), pp. 349–358, 1988. https://doi.org/10.1016/0017-9310(88)90017-8
[13] Abid, B.A., Ali, J.M. & Alzubaidi, A.A., Heat transfer in gas–solid fluidized bed with various heater inclinations. International Journal of Heat and Mass Transfer, 54(9–10), pp. 2228–2233, 2011. https://doi.org/10.1016/j.ijheatmasstransfer.2010.12.028
[14] Friedman, J., Koundakjian, P., Naylor, D. & Rosero, D., Heat transfer to small horizontal cylinders immersed in a fluidized bed. Journal of Heat Transfer, 128(10), p. 984, 2006. https://doi.org/10.1115/1.2345425
[15] Grewal, N.S. & Saxena, S.C., Heat transfer between a horizontal tube and a gas-solid fluidized bed. International Journal of Heat and Mass Transfer, 23(11), pp. 1505–1519, 1980. https://doi.org/10.1016/0017-9310(80)90154-4
[16] Masoumifard, N., Mostoufi, N., Hamidi, A.-A. & Sotudeh-Gharebagh, R., Investigation of heat transfer between a horizontal tube and gas–solid fluidized bed. International Journal of Heat and Fluid Flow, 29(5), pp. 1504–1511, 2008. https://doi.org/10.1016/j.ijheatfluidflow.2008.06.004
[17] Vreedenberg, H.A., Heat transfer between a fluidized bed and a horizontal tube. Chemical Engineering Science, 9(1), pp. 52–60, 1958. https://doi.org/10.1016/0009-2509(58)87007-4
[18] Grewal, N.S. & Saxena, S.C., Maximum heat transfer coefficient between a horizontal tube and a gas-solid fluidized bed. Industrial & Engineering Chemistry Process Design and Development, 20(1), pp. 108–116, 1981. https://doi.org/10.1021/i200012a017
[19] Pisters, K. & Prakash, A., Investigations of axial and radial variations of heat transfer coefficient in bubbling fluidized bed with fast response probe. Powder Technology, 207(1–3), pp. 224–231, 2011. https://doi.org/10.1016/j.powtec.2010.11.003
[20] Stefanova, A., Bi, H.T., Lim, J.C. & Grace, J.R., Local hydrodynamics and heat transfer in fluidized beds of different diameter. Powder Technology, 212(1), pp. 57–63, 2011. https://doi.org/10.1016/j.powtec.2011.04.026
[21] Di Natale, F., Lancia, A. & Nigro, R., Surface-to-bed heat transfer in fluidised beds: effect of surface shape. Powder Technology, 174(3), pp. 75–81, 2007. https://doi.org/10.1016/j.powtec.2007.01.010
[22] George, S.E. & Grace, J.R., Heat transfer to horizontal tubes in a pilot-scale fluidized bed. International Journal of Heat and Mass Transfer, 25(4), pp. 592–594, 1982. https://doi.org/10.1016/0017-9310(82)90063-1
[23] Hull, A.S., Chen, Z., Fritz, J.W. & Agarwal, P.K., Influence of horizontal tube banks on the behavior of bubbling fluidized beds: 1. Bubble hydrodynamics. Powder Technology, 103(3), pp. 230–242, 1999. https://doi.org/10.1016/S0032-5910(99)00021-2
[24] Hull, A.S., Chen, Z. & Agarwal, P.K., Influence of horizontal tube banks on the behavior of bubbling fluidized beds: 2. Mixing of solids. Powder Technology, 111(3), pp. 192–199, 2000. https://doi.org/10.1016/S0032-5910(99)00284-3
[25] Grewal, N.S. & Saxena, S.C., Experimental studies of heat transfer between a bundle of horizontal tubes and a gas-solid fluidized bed of small particles. Industrial & Engineering Chemistry Process Design and Development, 22(3), pp. 367–376, 1983. https://doi.org/10.1021/i200022a005
[26] Xavier A.M. & Davidson J.F., Heat transfer in fluidized beds: Convective heat transfer in fluidized beds. In Davidson J.F., Clift R., Harrison D., Fluidization. 2nd edn., Academic Press: London, 1985.
[27] Masoumifard, N., Mostoufi, N. & Sotudeh-Gharebagh, R., Prediction of the maximum heat transfer coefficient between a horizontal tube and gas–solid fluidized beds. Heat Transfer Engineering, 31(10), pp. 870–879, 2010. https://doi.org/10.1080/01457630903550275
[28] Martin, H., Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements, part I. Chemical Engineering and Processing: Process Intensification, 18(3), pp. 157–169, 1984.
https://doi.org/10.1016/0255-2701(84)80005-7
[29] Martin, H., Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements, Part II. Chemical Engineering and Processing: Process Intensification, 18(4), pp. 199–223, 1984. https://doi.org/10.1016/0255-2701(84)87003-8
[30] Di Natale, F., Lancia, A. & Nigro, R., A single particle model for surface-to-bed heat transfer in fluidized beds. Powder Technology, 187(1), pp. 68–78, 2008. https://doi.org/10.1016/j.powtec.2008.01.014
[31] Molerus, O., Burschka, A. & Dietz, S., Particle migration at solid surfaces and heat transfer in bubbling fluidized beds—I. Particle migration measurement systems. Chemical Engineering Science, 50(5), pp. 871–877, 1995. https://doi.org/10.1016/0009-2509(94)00445-W
[32] Molerus, O., Burschka, A. & Dietz, S., Particle migration at solid surfaces and heat transfer in bubbling fluidized beds—II. Prediction of heat transfer in bubbling fluidized beds. Chemical Engineering Science, 50(5), pp. 879–885, 1995. https://doi.org/10.1016/0009-2509(94)00446-X
[33] Di Natale, F. & Nigro, R., A critical comparison between local heat and mass transfer coefficients of horizontal cylinders immersed in bubbling fluidised beds. International Journal of Heat and Mass Transfer, 55(25–26), pp. 8178–8183, 2012. https://doi.org/10.1016/j.ijheatmasstransfer.2012.08.002
[34] Kuipers, J.A.M., Prins, W. & Van Swaaij,W. P. M., Numerical calculation of wall-to-bed heat-transfer coefficients in gas-fluidized beds. AIChE Journal, 38(7), pp. 1079–1091, 1992. https://doi.org/10.1002/aic.690380711
[35] Schmidt, A. & Renz, U., Eulerian computation of heat transfer in fluidized beds. Chemical Engineering Science, 54(22), pp. 5515–5522, 1999. https://doi.org/10.1016/S0009-2509(99)00298-5
[36] Schmidt, A. & Renz, U., Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle. Heat and Mass Transfer, 41(3), pp. 257–270, 2005. https://doi.org/10.1007/s00231-004-0510-z
[37] Patil, D.J., Smit, J., van Sint Annaland, M. & Kuipers, J.A.M., Wall-to-bed heat transfer in gas-solid bubbling fluidized beds. AIChE J., 52(1), pp. 58–74, 2006. https://doi.org/10.1002/aic.10590
[38] Armstrong, L.M., Gu, S. & Luo, K.H., Study of wall-to-bed heat transfer in a bubbling fluidised bed using the kinetic theory of granular flow. International Journal of Heat and Mass Transfer, 53(21–22), pp. 4949–4959, 2010. https://doi.org/10.1016/j.ijheatmasstransfer.2010.05.047
[39] Armstrong, L.M., Gu, S. & Luo, K.H., The influence of multiple tubes on the tube-to-bed heat transfer in a fluidised bed. International Journal of Multiphase Flow, 36(11–12), pp. 916–929, 2010. https://doi.org/10.1016/j.ijmultiphaseflow.2010.07.004
[40] Yusuf, R., Halvorsen, B. & Melaaen, M.C., Eulerian–Eulerian simulation of heat transfer between a gas–solid fluidized bed and an immersed tube-bank with horizontal tubes. Chemical Engineering Science, 66(8), pp. 1550–1564, 2011. https://doi.org/10.1016/j.ces.2010.12.015
[41] Yusuf, R., Halvorsen, B. & Melaaen, M.C., An experimental and computational study of wall to bed heat transfer in a bubbling gas–solid fluidized bed. International Journal of Multiphase Flow, 42, pp. 9–23, 2012. https://doi.org/10.1016/j.ijmultiphaseflow.2012.01.003
[42] Zehner, P. & Schlünder, E.U., Wärmeleitfähigkeit von Schüttungen bei mäßigen Temperaturen. Chemie Ingenieur Technik, 42(14), pp. 933–941, 1970 (in German). https://doi.org/10.1002/cite.330421408
[43] Legawiec, B. & Ziólkowski, D., Structure, voidage and effective thermal conductivity of solids within near-wall region of beds packed with spherical pellets in tubes. Chemical Engineering Science, 49(15), pp. 2513–2520, 1994. https://doi.org/10.1016/0009-2509(94)E0070-7
[44] Enwald, H., Peirano, E. & Almstedt, A.-E., Eulerian two-phase flow theory applied to fluidization. International Journal of Multiphase Flow, 22, pp. 21–66, 1996. https://doi.org/10.1016/S0301-9322(96)90004-X
[45] Ostermeier, P., Vandersickel, A., Gleis, S. & Spliethoff, H., Three dimensional multi fluid modeling of Geldart B bubbling fluidized bed with complex inlet geometries. Powder Technology, 312, pp. 89–102, 2017. https://doi.org/10.1016/j.powtec.2017.02.015
[46] Fedors, R.F. & Landel, R.F., An Empirical method of estimating the void fraction in mixtures of uniform particles of different size. Powder Technology, 23(2), pp. 225–231, 1979. https://doi.org/10.1016/0032-5910(79)87011-4
[47] Wen, C.Y. & Yu, Y.H., A generalized method for predicting the minimum fluidization velocity. AIChE Journal, 12(3), pp. 610–612, 1966. https://doi.org/10.1002/aic.690120343
[48] Huilin, L. & Gidaspow, D., Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures. Chemical Engineering Science, 58(16), pp. 3777–3792, 2003. https://doi.org/10.1016/S0009-2509(03)00238-0
[49] Syamlal, M., The particle-particle drag term in a multiparticle model of fluidization. National Technical Information Service: Springfield, 1987.