3 Ergun S. Fluid flow through packed columns. Chemical Engineering Progress, 1952, 48(1): 89-94
[4]
4 Gidaspow D. Hydrodynamics of fluidization and heat transfer: supercomputer modeling. Appl Mech Rev, 1986, 1(39):1-22
[5]
5 Di Felice R. The voidage function for fluid particle interaction systems. International Journal of Multiphase Flow,1994, 20(1): 153-159
[6]
6 Syamlal M, Obrien TJ. Simulation of granular layer inversion in liquid fluidized beds. International Journal of Multiphase Flow, 1988, 14(5): 473-481
[7]
7 Li JH, Mooson K. Particle-Fluid Two-Phase Flow, the Energy Minimization Multi-Scale Method. Beijing: Metallurgical Industry Press, 1994
[8]
8 Sundaresan S. Modeling the hydrodynamics of multiphase flow reactors: current status and challenges. AIChE Journal, 2000, 46(6): 1102-1105
[9]
9 Wang W, Li TC. Simulation of the clustering phenomenon in a fast fluidized bed: the importance of drag correlation. Chinese Journal of Chemical Engineering, 2004, 12(3):335-341
[10]
10 Benyahia S. On the effect of sub-grid drag closures. Industrial & Engineering Chemistry Research, 2010, 49(11):5122-5131
[11]
11 Benyahia S, Sundaresan S. Do we need sub-grid scale corrections for both continuum and discrete gas-particle flow models. Powder Technology, 2012, 220: 2-6
[12]
12 Andrews MJ, O'Rourke PJ. The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. International Journal of Multiphase Flow, 1996, 22(2): 379-402
[13]
13 Snider DM. An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. Journal of Computational Physics, 2001, 170 (2): 523-549
[14]
14 Snider DM. Three fundamental granular flow experiments and CPFD predictions. Powder Technology, 2007 176: 36-46
[15]
15 Chen C, Werther J, Heinrich S, et al. CPFD simulation of circulating fluidized bed risers. Powder Technology, 2013,235: 238-247
[16]
16 Li F, Song F, Benyahia S, et al. MP-PIC simulation of CFB riser with EMMS-based drag model. Chemical Engineering Science, 2012, 82(12): 104-113
[17]
17 Zhang DZ, Vanderheyden WB. The effects of mesoscopic structures on the macroscopic momentum equations for two-phase flows. International Journal of Multiphase Flow, 2002, 28(5): 805-822
[18]
18 Ye M,Wang J, van der Hoef MA, et al. Two-fluid modeling of Geldart A particles in gas-fluidized beds. Particuology,2008, 6(6): 540-548
[19]
27 Gao J, Chang J, Xu C, et al. CFD simulation of gas solid flow in FCC strippers. Chemical Engineering Science, 2008, 63(7): 1827-1841
[20]
28 Manyele SV, Parssinen, JH, Zhu JX. Characterizing particle aggregates in a high-density and high-flux CFB riser. Chemical Engineering Journal, 2002, 88(1): 151-161
[21]
29 Zhang Y, Lu C. Numerical study of the pressure fluctuation in a bubbling fluidized bed of FCC catalyst. The 3rd Asian Particle Technology Symposium, Beijing, 2007
[22]
30 Harris AT, Davidson JF, Thorpe RB. The prediction of particle cluster properties in the near wall region of a vertical riser. Powder Technology, 2002, 127(2): 128-143
[23]
31 Zou B, Li H, Xia Y, et al. Cluster structure in a circulating fluidized bed. Powder Technology, 1994, 78(2): 173-178
33 Guenther C, Breault R. Wavelet analysis to characterize cluster dynamics in a circulating fluidized bed. Powder Technology, 2007, 173(3): 163-173
[26]
34 Yang TY, Leu LP. Multiresolution analysis on identification and dynamics of clusters in a circulating fluidized bed. AIChE Journal, 2009, 55(3): 612-629
[27]
35 Wang J, Ge W, Li JH. Eulerian simulation of heterogeneous gas-solid flows in CFB risers: EMMS-based sub-grid scale model with a revised cluster description. Chemical Engineering Science, 2008, 63(6): 1553-1571
[28]
36 Ge W, Wang W, Dong W, et al. Meso-scale structure: a challenge of computational fluid dynamics for circulating fluidized bed risers. The 9th International Conference on Circulating Fluidized Beds: TuTech Innovation GmbH, Hamburg, 2008
[29]
37 Ye M, van der Hoef MA, Kuipers JAM. The effects of particle and gas properties on the fluidization of Geldart A particles. Chemical Engineering Science, 2005, 60(16):4567-4580
[30]
38 Di Renzo A, Di Maio FP. Homogeneous and bubbling fluidization regimes in DEM CFD simulations: hydrodynamic stability of gas and liquid fluidized beds. Chemical Engineering Science, 2007, 62(1): 116-130
[31]
39 Agrawal K, Loezos PN, Syamlal M, et al. The role of mesoscale structures in rapid gas-solid flows. J Fluid Mech,2001, 445(1): 151-185
[32]
40 Yesim Igci, Arthur T, Andrews IV, et al. Filtered twofluid models for fluidized gas-particle suspensions. AIChE Journal, 2008, 54(6): 1431-1448
[33]
41 Yesim Igci, Sundaresan S. Constitutive models for filtered two-fluid models of fluidized gas-particle flows. Industrial & Engineering Chemistry Research, 2011, 50(23): 13190-13201
[34]
42 Arthur T, Andrews IV, Loezos PN, et al. Coarse-grid simulation of gas-particle flows in vertical risers. Ind Eng Chem Res, 2005, 44(16): 6022-6037
[35]
43 Yesim Igci, Sundaresan S. Verification of filtered two-fluid models for gas-particle flows in risers. AIChE Journal,2011, 57(10): 2691-2707
[36]
44 Yesim Igci, Sreekanth P, Sofiane B, et al. Validation studies on filtered model equations for gas-particle flows in Risers. Industrial & Engineering Chemistry Research, 2012, 51(4):2094-2103
[37]
45 Wang W, Lu B, Zhang N, et al. A review of multiscale CFD for gas-solid CFB modeling. International Journal of Multiphase Flow, 2010, 36(2): 109-118
[38]
46 Lu B, Wang W, Li JH. Searching for a mesh-independent sub-grid model for CFD simulation of gas solid riser flows. Chemical Engineering Science, 2009, 64(15): 3437-3447
[39]
47 Wang X, Liu K, You CF. Drag force model corrections based on non-uniform particle distributions in multiparticle systems. Powder Technology, 2011, 209: 112-118
[40]
48 Li JH, Zhang J, Ge W, et al. Multi-scale methodology for complex systems. Chemical Engineering Science, 2004,59(8): 1687-1700
[41]
49 Zhang Y, Ge W, Li JH. Simulation of heterogeneous structures and analysis of energy consumption in particle-fluid systems with pseudo-particle modeling. Chemical Engineering Science, 2005, 60(11): 3091-3099
[42]
50 Zhang Y, Ge W, Wang XW, et al. Validation of EMMSbased drag model using lattice Boltzmann simulations on GPUs. Particuology, 2011, 9(4): 365-373
[43]
51 Li JH, Kwauk M. Exploring complex systems in chemical engineeringthe multi-scale methodology. Chemical Engineering Science, 2003, 58(3-6): 521-535
[44]
52 Li JH, Ge W, Zhang J, et al. Multi-scale compromise and multi-level correlation in complex systems. Chemical Engineering Research & Design, 2005, 83(A6): 574-582
[45]
53 Ge W, Chen FG, Gao J, et al. Analytical multiscale method for multi-phase complex systems in process engineering-bridging reductionism and holism. Chemical Engineering Science, 2007, 62(13): 3346-3377
[46]
54 Li JH, Ge W, Wang W, et al. Focusing on the meso-scales of multi-scale phenomena-in search for a new paradigm in chemical engineering. Particuology, 2010, 8(6): 634-639
[47]
55 Lu B,Wang W, Li JH, et al. Multi-scale CFD simulation of gas-solid flow in MIP reactors with a structure-dependent drag model. Chemical Engineering Science, 2007, 62(18):5487-5494
[48]
56 Hartge EU, Ratschow L, Wischnewski R, et al. CFDsimulation of a circulating fluidized bed riser. Particuology,2009, 7(4): 283-296
[49]
57 Armstrong LM, Luo KH, Gu S. Two-dimensional and three-dimensional computational studies of hydrodynamics in the transition from bubbling to circulating fluidised bed. Chemical Engineering Journal, 2010, 160(1): 239-248
59 Ge W, Wang W, Yang N. Meso-scale oriented simulation towards virtual process engineering (VPE)-The EMMS paradigm. Chemical Engineering Science, 2011, 66(19):4426-4458
61 Yang N, Wang W, Ge W, et al. CFD simulation of concurrent-up gas-solid flow in circulating fluidized beds with structure-dependent drag coeffcient. Chemical Engineering Journal, 2003, 9(1-3): 71-80
[54]
62 Wang W, Li JH. Simulation of gas-solid two-phase flow by a multi-scale CFD approach-extension of the EMMS model to the sub-grid level. Chemical Engineering Science, 2007,62(1-2): 208-231
[55]
63 Wang W, Lu B, Li JH. Choking and flow regime transitions: simulation by a multi-scale CFD approach. Chemical Engineering Science, 2007, 62 (3): 814-819
66 Chen C, Li F, Qi HY. Modeling of the flue gas desulfurization in a CFB riser using the Eulerian approach with heterogeneous drag coeffcient. Chemical Engineering Science, 2012, 69(1): 659-668
[58]
67 Naren PR, Lali AM, Ranade VV. Evaluating EMMS model for simulating high solid flux risers. Chemical Engineering Research & Design, 2007, 85(A8): 1188-1202
[59]
19 Das Sharma S, Pugsley T, Delatour R. Three-dimensional CFD model of the deaeration rate of FCC particles. AIChE Journal, 2006, 52(7): 2391-2400
[60]
20 Mckeen T, Pugsley T. Simulation and experimental validation of a freely bubbling bed of FCC catalyst. Powder Technology, 2003, 129(1): 39-152
[61]
21 O'Brien TJ, Syamlal M. Particle cluster effects in the numerical simulation of a circulating fluidized bed. In: Avidan AA. Circulating. Fluidized Beds IV. New York: AIChE, 1993. 430-435
[62]
22 Cruz E, Steward FR, Pugsley T. New closure models for CFD modeling of high-density circulating fluidized beds. Powder Technology, 2006, 169(3): 115-122
[63]
23 Qi Haiying. Euler/Euler Simulation der Fluiddynamik Zirkulierender Wirbelschichten, Dissertation of RWTH Aachen. Germany: Press Mainz, 1997
[64]
24 Arastoopour H, Gidaspow D. Analysis of IGT pneumatic conveying data and fast fluidization using a thermohydrodynamic model. Powder Technology, 1979, 22: 77-87
[65]
25 Gu WK. Diameters of catalyst clusters in FCC. AIChE Symp, 1999, 95 (321): 42-47
[66]
26 Gu WK, Chen JC. A model for solid concentration in circulating fluidized beds. In: Fan LX, Knowlton T. Fluidization IX. New York: Engineering Foundation, 1998. 501-508