Assessment of the TFM in predicting the onset of turbulent fluidization
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摘要
Accurate prediction of the onset of turbulent fluidization still remains elusive owing to the dependence of the transition velocity on several factors including measurement methods and interpretation of results. In this work, numerical simulations using the two fluid model(TFM) are performed in an attempt to predict the regime change reported by Gopalan et al.(2016) in a small scale pseudo-2 D gas–solid fluidized bed containing Geldart D particles. Various time and frequency domain analyses were applied on predicted absolute and differential pressure time series data to reveal the bed dynamics. Numerical predictions of the transition velocity, Ucare in reasonably good agreement with experimental results from the small scale challenge problem. The literature correlations completely fail to predict the transition velocity for the system considered in this work. This work thus provides a different approach for validating the CFD model against experimental measurements.
Accurate prediction of the onset of turbulent fluidization still remains elusive owing to the dependence of the transition velocity on several factors including measurement methods and interpretation of results. In this work, numerical simulations using the two fluid model(TFM) are performed in an attempt to predict the regime change reported by Gopalan et al.(2016) in a small scale pseudo-2 D gas–solid fluidized bed containing Geldart D particles. Various time and frequency domain analyses were applied on predicted absolute and differential pressure time series data to reveal the bed dynamics. Numerical predictions of the transition velocity, Ucare in reasonably good agreement with experimental results from the small scale challenge problem. The literature correlations completely fail to predict the transition velocity for the system considered in this work. This work thus provides a different approach for validating the CFD model against experimental measurements.
Accurate prediction of the onset of turbulent fluidization still remains elusive owing to the dependence of the transition velocity on several factors including measurement methods and interpretation of results. In this work, numerical simulations using the two fluid model(TFM) are performed in an attempt to predict the regime change reported by Gopalan et al.(2016) in a small scale pseudo-2 D gas–solid fluidized bed containing Geldart D particles. Various time and frequency domain analyses were applied on predicted absolute and differential pressure time series data to reveal the bed dynamics. Numerical predictions of the transition velocity, Ucare in reasonably good agreement with experimental results from the small scale challenge problem. The literature correlations completely fail to predict the transition velocity for the system considered in this work. This work thus provides a different approach for validating the CFD model against experimental measurements.
引文
[1]D.Kunii,O.Levenspiel,Fluidization Engineering,Second ed.ButterworthHeinemann,Boston,1991.
[2]J.R.Grace,Contacting modes and behaviour classification of gas-solid and other two-phase suspensions,Can.J.Chem.Eng.64(1986)353-363.
[3]H.T.Bi,J.R.Grace,Effect of measurement method on the velocities used to demarcate the onset of turbulent fluidization,Chem.Eng.J.Biochem.Eng.J.57(1995)261-271.
[4]J.Drahos,Quo vadis,the analysis of time series in reactor engineering?Chem.Eng.Res.Des.81(2003)411-412.
[5]J.R.Grace,Reflections on turbulent fluidization and dense suspension upflow,Powder Technol.113(2000)242-248.
[6]S.Nedeltchev,New methods for flow regime identification in bubble columns and fluidized beds,Chem.Eng.Sci.137(2015)436-446.
[7]J.Yerushalmi,N.T.Cankurt,Further studies of the regimes of fluidization,Powder Technol.24(1979)187-205.
[8]H.T.Bi,J.R.Grace,Flow regime diagrams for gas-solid fluidization and upward transport,Int.J.Multiphase Flow 21(1995)1229-1236.
[9]F.Johnsson,R.C.Zijerveld,J.C.Schouten,C.M.Van Den Bleek,B.Leckner,Characterization of fuidization regimes by time-series analysis of pressure fluctuations,Int.J.Multiphase Flow 26(2000)663-715.
[10]J.R.Van Ommen,S.Sasic,J.Van der Schaaf,S.Gheorghiu,F.Johnsson,M.O.Coppens,Time-series analysis of pressure fluctuations in gas-solid fluidized beds-A review,Int.J.Multiphase Flow 37(2011)403-428.
[11]S.Sasic,B.Leckner,F.Johnsson,Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations,Prog.Energy Combust.Sci.33(2007)453-496.
[12]R.A.Cocco,S.B.R.Karri,T.M.Knowlton,J.Findlay,T.Gauthier,J.W.Chew,C.M.Hrenya,Intrusive probes in riser applications,AIChE J.63(2017)5361-5374.
[13]L.T.Fan,T.C.Ho,S.Hiraoka,W.P.Walawender,Pressure fluctuations in a fluidized bed,AIChE J.27(1981)388-396.
[14]X.Lu,H.Li,Wavelet analysis of pressure fluctuation signals in a bubbling fluidized bed,Chem.Eng.J.75(1999)113-119.
[15]D.Bai,E.Shibuya,N.Nakagawa,K.Kato,Characterization of gas fluidization regimes using pressure fluctuations,Powder Technol.87(1996)105-111.
[16]S.H.Lee,S.D.Kim,S.H.Park,Statistical and deterministic chaos analysis of pressure fluctuations in a fluidized bed of polymer powders,Korean J.Chem.Eng.19(2002)1020-1025.
[17]J.van der Schaaf,J.R.van Ommen,F.Takens,J.C.Schouten,C.M.van den Bleek,Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds,Chem.Eng.Sci.59(2004)1829-1840.
[18]O.A.Jaiboon,B.Chalermsinsuwan,L.Mekasut,P.Piumsomboon,Effect of flow pattern on power spectral density of pressure fluctuation in various fluidization regimes,Powder Technol.233(2013)215-226.
[19]J.Xiang,Q.Li,Z.Tan,Y.Zhang,Characterization of the flow in a gas-solid bubbling fluidized bed by pressure fluctuation,Chem.Eng.Sci.174(2017)93-103.
[20]J.Zhu,M.Qi,S.Barghi,Identification of the flow structures and regime transition in gas-solid fluidized beds through moment analysis,AIChE J.59(2013)1479-1490.
[21]Y.T.Makkawi,P.C.Wright,Fluidization regimes in a conventional fluidized bed characterized by means of electrical capacitance tomography,Chem.Eng.Sci.57(2002)2411-2437.
[22]L.de Martín,J.V.Briongos,N.García-Hernando,J.M.Aragón,Detecting regime transitions in gas-solid fluidized beds from low frequency accelerometry signals,Powder Technol.207(2011)104-112.
[23]H.Azizpour,R.Sotudeh-Gharebagh,R.Zarghami,M.Abbasi,N.Mostoufi,M.J.Mahjoob,Characterization of gas-solid fluidized bed hydrodynamics by vibration signature analysis,Int.J.Multiphase Flow 37(2011)788-793.
[24]J.Wang,C.Ren,Y.Yang,L.Hou,Characterization of particle fluidization pattern in a gas solid fluidized bed based on Acoustic Emission(AE)measurement,Ind.Eng.Chem.Res.48(2009)8508-8514.
[25]Y.Zhou,L.Yang,Y.Lu,X.Hu,X.Luo,H.Chen,Flow regime identification in gas-solid two-phase fluidization via acoustic emission technique,Chem.Eng.J.334(2018)1484-1492.
[26]J.R.Grace,T.Li,Complementarity of CFD,experimentation and reactor models for solving challenging fluidization problems,Particuology 8(2010)498-500.
[27]B.Chalermsinsuwan,T.Thummakul,D.Gidaspow,P.Piumsomboon,Characterization of fluidization regime in circulating fluidized bed reactor with high solid particle concentration using computational fluid dynamics,Korean J.Chem.Eng.31(2014)350-363.
[28]G.Qiu,J.Ye,H.Wang,W.Yang,Investigation of flow hydrodynamics and regime transition in a gas-solids fluidized bed with different riser diameters,Chem.Eng.Sci.116(2014)195-207.
[29]V.Salikov,S.Antonyuk,S.Heinrich,V.S.Sutkar,N.G.Deen,J.A.M.Kuipers,Characterization and CFD-DEM modelling of a prismatic spouted bed,Powder Technol.270(2015)622-636.
[30]E.Ramirez,C.E.A.Finney,S.Pannala,C.S.Daw,J.Halow,Q.Xiong,Computational study of the bubbling-to-slugging transition in a laboratory-scale fluidized bed,Chem.Eng.J.308(2017)544-556.
[31]R.W.Breault,R.Panday,L.J.Shadle,R.Cocco,A.Issangya,S.B.Reddy Karri,T.M.Knowlton,C.Guenther,Preface,Powder Technol.203(2010)1-2.
[32]B.Sun,D.Gidaspow,Computation of circulating fluidized-bed riser flow for the fluidization VIII benchmark test,Ind.Eng.Chem.Res.38(1999)787-792.
[33]T.Li,J.F.Dietiker,M.Shahnam,MFIX simulation of NETL/PSRI challenge problem of circulating fluidized bed,Chem.Eng.Sci.84(2012)746-760.
[34]R.Panday,L.J.Shadle,M.Shahnam,R.Cocco,A.Issangya,J.S.Spenik,J.C.Ludlow,B.Gopalan,F.Shaffer,M.Syamlal,C.Guenther,S.B.R.Karri,T.Knowlton,Challenge problem:1.Model validation of circulating fluidized beds,Powder Technol.258(2014)370-391.
[35]B.Gopalan,M.Shahnam,R.Panday,J.Tucker,F.Shaffer,L.Shadle,J.Mei,W.Rogers,C.Guenther,M.Syamlal,Measurements of pressure drop and particle velocity in a pseudo 2-D rectangular bed with Geldart Group D particles,Powder Technol.291(2016)299-310.
[36]J.R.Grace,F.Taghipour,Verification and validation of CFD models and dynamic similarity for fluidized beds,Powder Technol.139(2004)99-110.
[37]A.R.Khan,J.F.Richardson,The resistance to motion of a solid sphere in a fluid,Chem.Eng.Commun.62(1987)135-150.
[38]B.Gopalan,F.Shaffer,A new method for decompositing of high speed particle image velocimetry data,Powder Technol.220(2011)164-171.
[39]M.Lungu,H.Wang,J.Wang,Y.Yang,F.Chen,Two-fluid model simulations of the national energy technology laboratory bubbling fluidized bed challenge problem,Ind.Eng.Chem.Res.55(2016)5063-5077.
[40]A.T.Andrews IV,P.N.Loezos,S.Sundaresan,Coarse-grid simulation of gas-particle flows in vertical risers,Ind.Eng.Chem.Res.44(2005)6022-6037.
[41]M.Syamlal,T.J.O'Brien,Fluid dynamic simulation of O-3 decomposition in a bubbling fluidized bed,AIChE J.49(2003)2793-2801.
[42]P.C.Johnson,P.Nott,R.Jackson,Frictional-collisional equations of motion for particulate flows and their application to chutes,J.Fluid Mech.210(1990)501-535.
[43]R.Kikuchi,T.Yano,A.Tsutsumi,K.Yoshida,M.Punchochar,J.Drahos,Diagnosis of Chaotic Dynamics of Bubble Motion in a Bubble Column,Nos.21,1997 3741-3745.
[44]M.Askarishahi,M.Salehi,H.R.Godini,G.Wozny,CFD study on solids flow pattern and solids mixing characteristics in bubbling fluidized bed:Effect of fluidization velocity and bed aspect ratio,Powder Technol.274(2015)379-392.
[45]M.Lungu,H.Wang,G.Mwandila,J.Wang,Y.Yang,F.Chen,J.Siame,Effect of bed thickness on a pseudo 2D gas-solid fluidized bed turbulent flow structures and dynamics,Powder Technol.336(2018)594-608.
[46]N.N.Clark,E.A.McKenzie Jr.,M.Gautam,Differential pressure measurements in a slugging fluidized bed,Powder Technol.67(1991)187-199.
[47]M.J.V.Goldschmidt,J.a M.Kuipers,W.P.M.Van Swaaij,Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow:Effect of coefficient of restitution on bed dynamics,Chem.Eng.Sci.56(2001)571-578.
[48]L.Godfroy,F.Larachi,J.Chaouki,Position and Velocity of a Large Particle in a Gas/Solid Riser Using the Radioactive Particle Tracking Technique,Can.J.Chem.Eng.77(2)(1999)253-261.
[49]L.T.Fan,T.-C.Ho,W.P.Walawender,Measurements of the rise velocities of bubbles,slugs and pressure waves in a gas-solid fluidized bed using pressure fluctuation signals,AIChE J.29(1983)33-39.
[50]J.Van Der Schaaf,J.C.Schouten,F.Johnsson,C.M.Van Den Bleek,Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series,Int.J.Multiphase Flow 28(2002)865-880.
[51]N.Ellis,Hydrodynamics of Gas-Solid Turbulent Fluidized Beds,Ph D Thesis,The University of British Columbia,2003.
[52]P.Cai,Y.Jin,Z.-Q.Yu,Z.-W.Wang,Mechanism of flow regime transition from bubbling to turbulent fluidization,AIChE J.36(1990)955-956.
[53]J.Shabanian,J.Chaouki,Hydrodynamics of a gas-solid fluidized bed with thermally induced interparticle forces,Chem.Eng.J.259(2015)135-152.
[54]Y.Zhang,H.T.Bi,J.R.Grace,C.Lu,Comparison of decoupling methods for analyzing pressure fluctuations in gas-fluidized beds,AIChE J.56(2010)869-877.
[55]V.P.Chilekar,M.J.F.Warnier,J.van der Schaaf,B.F.M.Kuster,J.C.Schouten,J.R.van Ommen,Bubble size estimation in slurry bubble columns from pressure fluctuations,AIChE J.51(2005)1924-1937.
[56]K.C.Ruthiya,V.P.Chilekar,M.J.F.Warnier,J.van der Schaaf,B.F.M.Kuster,J.C.Schouten,J.R.van Ommen,Detecting regime transitions in slurry bubble columns using pressure time series,AIChE J.51(2005)1951-1965.
[57]Y.Zhang,H.T.Bi,J.Grace,C.Lu,Comparison of Decoupling Methods for Analyzing Pressure Fluctuations in Gas-Fluidized Beds,AIChE J.56(2009)869-877.
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[60]J.W.Chew,R.Hays,J.G.Findlay,T.M.Knowlton,S.B.Reddy Karri,R.A.Cocco,C.M.Hrenya,Cluster characteristics of Geldart Group B particles in a pilot-scale CFBriser.I.Monodisperse systems,Chem.Eng.Sci.68(2012)72-81.
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[67]N.Ellis,H.T.Bi,C.J.Lim,J.R.Grace,Hydrodynamics of turbulent fluidized beds of different diameters,Powder Technol.141(2004)124-136.
[2]J.R.Grace,Contacting modes and behaviour classification of gas-solid and other two-phase suspensions,Can.J.Chem.Eng.64(1986)353-363.
[3]H.T.Bi,J.R.Grace,Effect of measurement method on the velocities used to demarcate the onset of turbulent fluidization,Chem.Eng.J.Biochem.Eng.J.57(1995)261-271.
[4]J.Drahos,Quo vadis,the analysis of time series in reactor engineering?Chem.Eng.Res.Des.81(2003)411-412.
[5]J.R.Grace,Reflections on turbulent fluidization and dense suspension upflow,Powder Technol.113(2000)242-248.
[6]S.Nedeltchev,New methods for flow regime identification in bubble columns and fluidized beds,Chem.Eng.Sci.137(2015)436-446.
[7]J.Yerushalmi,N.T.Cankurt,Further studies of the regimes of fluidization,Powder Technol.24(1979)187-205.
[8]H.T.Bi,J.R.Grace,Flow regime diagrams for gas-solid fluidization and upward transport,Int.J.Multiphase Flow 21(1995)1229-1236.
[9]F.Johnsson,R.C.Zijerveld,J.C.Schouten,C.M.Van Den Bleek,B.Leckner,Characterization of fuidization regimes by time-series analysis of pressure fluctuations,Int.J.Multiphase Flow 26(2000)663-715.
[10]J.R.Van Ommen,S.Sasic,J.Van der Schaaf,S.Gheorghiu,F.Johnsson,M.O.Coppens,Time-series analysis of pressure fluctuations in gas-solid fluidized beds-A review,Int.J.Multiphase Flow 37(2011)403-428.
[11]S.Sasic,B.Leckner,F.Johnsson,Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations,Prog.Energy Combust.Sci.33(2007)453-496.
[12]R.A.Cocco,S.B.R.Karri,T.M.Knowlton,J.Findlay,T.Gauthier,J.W.Chew,C.M.Hrenya,Intrusive probes in riser applications,AIChE J.63(2017)5361-5374.
[13]L.T.Fan,T.C.Ho,S.Hiraoka,W.P.Walawender,Pressure fluctuations in a fluidized bed,AIChE J.27(1981)388-396.
[14]X.Lu,H.Li,Wavelet analysis of pressure fluctuation signals in a bubbling fluidized bed,Chem.Eng.J.75(1999)113-119.
[15]D.Bai,E.Shibuya,N.Nakagawa,K.Kato,Characterization of gas fluidization regimes using pressure fluctuations,Powder Technol.87(1996)105-111.
[16]S.H.Lee,S.D.Kim,S.H.Park,Statistical and deterministic chaos analysis of pressure fluctuations in a fluidized bed of polymer powders,Korean J.Chem.Eng.19(2002)1020-1025.
[17]J.van der Schaaf,J.R.van Ommen,F.Takens,J.C.Schouten,C.M.van den Bleek,Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds,Chem.Eng.Sci.59(2004)1829-1840.
[18]O.A.Jaiboon,B.Chalermsinsuwan,L.Mekasut,P.Piumsomboon,Effect of flow pattern on power spectral density of pressure fluctuation in various fluidization regimes,Powder Technol.233(2013)215-226.
[19]J.Xiang,Q.Li,Z.Tan,Y.Zhang,Characterization of the flow in a gas-solid bubbling fluidized bed by pressure fluctuation,Chem.Eng.Sci.174(2017)93-103.
[20]J.Zhu,M.Qi,S.Barghi,Identification of the flow structures and regime transition in gas-solid fluidized beds through moment analysis,AIChE J.59(2013)1479-1490.
[21]Y.T.Makkawi,P.C.Wright,Fluidization regimes in a conventional fluidized bed characterized by means of electrical capacitance tomography,Chem.Eng.Sci.57(2002)2411-2437.
[22]L.de Martín,J.V.Briongos,N.García-Hernando,J.M.Aragón,Detecting regime transitions in gas-solid fluidized beds from low frequency accelerometry signals,Powder Technol.207(2011)104-112.
[23]H.Azizpour,R.Sotudeh-Gharebagh,R.Zarghami,M.Abbasi,N.Mostoufi,M.J.Mahjoob,Characterization of gas-solid fluidized bed hydrodynamics by vibration signature analysis,Int.J.Multiphase Flow 37(2011)788-793.
[24]J.Wang,C.Ren,Y.Yang,L.Hou,Characterization of particle fluidization pattern in a gas solid fluidized bed based on Acoustic Emission(AE)measurement,Ind.Eng.Chem.Res.48(2009)8508-8514.
[25]Y.Zhou,L.Yang,Y.Lu,X.Hu,X.Luo,H.Chen,Flow regime identification in gas-solid two-phase fluidization via acoustic emission technique,Chem.Eng.J.334(2018)1484-1492.
[26]J.R.Grace,T.Li,Complementarity of CFD,experimentation and reactor models for solving challenging fluidization problems,Particuology 8(2010)498-500.
[27]B.Chalermsinsuwan,T.Thummakul,D.Gidaspow,P.Piumsomboon,Characterization of fluidization regime in circulating fluidized bed reactor with high solid particle concentration using computational fluid dynamics,Korean J.Chem.Eng.31(2014)350-363.
[28]G.Qiu,J.Ye,H.Wang,W.Yang,Investigation of flow hydrodynamics and regime transition in a gas-solids fluidized bed with different riser diameters,Chem.Eng.Sci.116(2014)195-207.
[29]V.Salikov,S.Antonyuk,S.Heinrich,V.S.Sutkar,N.G.Deen,J.A.M.Kuipers,Characterization and CFD-DEM modelling of a prismatic spouted bed,Powder Technol.270(2015)622-636.
[30]E.Ramirez,C.E.A.Finney,S.Pannala,C.S.Daw,J.Halow,Q.Xiong,Computational study of the bubbling-to-slugging transition in a laboratory-scale fluidized bed,Chem.Eng.J.308(2017)544-556.
[31]R.W.Breault,R.Panday,L.J.Shadle,R.Cocco,A.Issangya,S.B.Reddy Karri,T.M.Knowlton,C.Guenther,Preface,Powder Technol.203(2010)1-2.
[32]B.Sun,D.Gidaspow,Computation of circulating fluidized-bed riser flow for the fluidization VIII benchmark test,Ind.Eng.Chem.Res.38(1999)787-792.
[33]T.Li,J.F.Dietiker,M.Shahnam,MFIX simulation of NETL/PSRI challenge problem of circulating fluidized bed,Chem.Eng.Sci.84(2012)746-760.
[34]R.Panday,L.J.Shadle,M.Shahnam,R.Cocco,A.Issangya,J.S.Spenik,J.C.Ludlow,B.Gopalan,F.Shaffer,M.Syamlal,C.Guenther,S.B.R.Karri,T.Knowlton,Challenge problem:1.Model validation of circulating fluidized beds,Powder Technol.258(2014)370-391.
[35]B.Gopalan,M.Shahnam,R.Panday,J.Tucker,F.Shaffer,L.Shadle,J.Mei,W.Rogers,C.Guenther,M.Syamlal,Measurements of pressure drop and particle velocity in a pseudo 2-D rectangular bed with Geldart Group D particles,Powder Technol.291(2016)299-310.
[36]J.R.Grace,F.Taghipour,Verification and validation of CFD models and dynamic similarity for fluidized beds,Powder Technol.139(2004)99-110.
[37]A.R.Khan,J.F.Richardson,The resistance to motion of a solid sphere in a fluid,Chem.Eng.Commun.62(1987)135-150.
[38]B.Gopalan,F.Shaffer,A new method for decompositing of high speed particle image velocimetry data,Powder Technol.220(2011)164-171.
[39]M.Lungu,H.Wang,J.Wang,Y.Yang,F.Chen,Two-fluid model simulations of the national energy technology laboratory bubbling fluidized bed challenge problem,Ind.Eng.Chem.Res.55(2016)5063-5077.
[40]A.T.Andrews IV,P.N.Loezos,S.Sundaresan,Coarse-grid simulation of gas-particle flows in vertical risers,Ind.Eng.Chem.Res.44(2005)6022-6037.
[41]M.Syamlal,T.J.O'Brien,Fluid dynamic simulation of O-3 decomposition in a bubbling fluidized bed,AIChE J.49(2003)2793-2801.
[42]P.C.Johnson,P.Nott,R.Jackson,Frictional-collisional equations of motion for particulate flows and their application to chutes,J.Fluid Mech.210(1990)501-535.
[43]R.Kikuchi,T.Yano,A.Tsutsumi,K.Yoshida,M.Punchochar,J.Drahos,Diagnosis of Chaotic Dynamics of Bubble Motion in a Bubble Column,Nos.21,1997 3741-3745.
[44]M.Askarishahi,M.Salehi,H.R.Godini,G.Wozny,CFD study on solids flow pattern and solids mixing characteristics in bubbling fluidized bed:Effect of fluidization velocity and bed aspect ratio,Powder Technol.274(2015)379-392.
[45]M.Lungu,H.Wang,G.Mwandila,J.Wang,Y.Yang,F.Chen,J.Siame,Effect of bed thickness on a pseudo 2D gas-solid fluidized bed turbulent flow structures and dynamics,Powder Technol.336(2018)594-608.
[46]N.N.Clark,E.A.McKenzie Jr.,M.Gautam,Differential pressure measurements in a slugging fluidized bed,Powder Technol.67(1991)187-199.
[47]M.J.V.Goldschmidt,J.a M.Kuipers,W.P.M.Van Swaaij,Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow:Effect of coefficient of restitution on bed dynamics,Chem.Eng.Sci.56(2001)571-578.
[48]L.Godfroy,F.Larachi,J.Chaouki,Position and Velocity of a Large Particle in a Gas/Solid Riser Using the Radioactive Particle Tracking Technique,Can.J.Chem.Eng.77(2)(1999)253-261.
[49]L.T.Fan,T.-C.Ho,W.P.Walawender,Measurements of the rise velocities of bubbles,slugs and pressure waves in a gas-solid fluidized bed using pressure fluctuation signals,AIChE J.29(1983)33-39.
[50]J.Van Der Schaaf,J.C.Schouten,F.Johnsson,C.M.Van Den Bleek,Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series,Int.J.Multiphase Flow 28(2002)865-880.
[51]N.Ellis,Hydrodynamics of Gas-Solid Turbulent Fluidized Beds,Ph D Thesis,The University of British Columbia,2003.
[52]P.Cai,Y.Jin,Z.-Q.Yu,Z.-W.Wang,Mechanism of flow regime transition from bubbling to turbulent fluidization,AIChE J.36(1990)955-956.
[53]J.Shabanian,J.Chaouki,Hydrodynamics of a gas-solid fluidized bed with thermally induced interparticle forces,Chem.Eng.J.259(2015)135-152.
[54]Y.Zhang,H.T.Bi,J.R.Grace,C.Lu,Comparison of decoupling methods for analyzing pressure fluctuations in gas-fluidized beds,AIChE J.56(2010)869-877.
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