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Volumn 3, Issue , 2018, Pages 300-331

Nonlinear dynamic characteristics of bubbling fluidization

Author keywords

Chaotic attractor; Correlation dimension; Entropy; Hurst exponent; Nonlinear; Pressure fluctuation

Indexed keywords


EID: 85054020232     PISSN: None     EISSN: 18794467     Source Type: Book Series    
DOI: 10.2174/978160805228811203010300     Document Type: Chapter
Times cited : (6)

References (98)
  • 1
    • 34250811519 scopus 로고    scopus 로고
    • Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations
    • S. Sasic, B. Leckner, and F. Johnsson, “Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations”, Progr. Energy Combustion Sci., vol. 33, pp. 453-496, 2007.
    • (2007) Progr. Energy Combustion Sci , vol.33 , pp. 453-496
    • Sasic, S.1    Leckner, B.2    Johnsson, F.3
  • 2
    • 0032030575 scopus 로고    scopus 로고
    • Origin, propagation and attenuation of pressure waves in gas-solid fluidized beds
    • J. van der Schaaf, J. C. Schouten, and C. M. van den Bleek, “Origin, propagation and attenuation of pressure waves in gas-solid fluidized beds,” Powder Tech., vol. 95, pp. 220-233, 1998,
    • (1998) Powder Tech , vol.95 , pp. 220-233
    • van der Schaaf, J.1    Schouten, J.C.2    van den Bleek, C.M.3
  • 3
    • 0019566051 scopus 로고
    • Pressure fluctuations in a fluidized bed
    • L.T. Fan, T. C. Ho, S. Hiraoka, and W. P. Walawender, “Pressure fluctuations in a fluidized bed,” AIChE J., vol. 27, pp. 388-396, 1981.
    • (1981) Aiche J , vol.27 , pp. 388-396
    • Fan, L.T.1    Ho, T.C.2    Hiraoka, S.3    Walawender, W.P.4
  • 4
    • 0033037210 scopus 로고    scopus 로고
    • Measurement techniques in fluidized beds
    • J. Werther, “Measurement techniques in fluidized beds,” Powder Tech., vol. 102, pp. 15-36, 1999.
    • (1999) Powder Tech , vol.102 , pp. 15-36
    • Werther, J.1
  • 5
    • 0024088646 scopus 로고
    • Pressure fluctuations in turbulent fluidized beds
    • G. S. Lee and S. D. Kim, “Pressure fluctuations in turbulent fluidized beds,” J. Chem. Eng. Japan, vol. 21, pp. 515-521, 1988.
    • (1988) J. Chem. Eng. Japan , vol.21 , pp. 515-521
    • Lee, G.S.1    Kim, S.D.2
  • 7
    • 0029163793 scopus 로고
    • Transition from bubbling to turbulent fluidization
    • H. T. Bi, J. R. Grace, and K. S. Lim, “Transition from bubbling to turbulent fluidization”, Ind. Chem. Res. Dev., vol. 34, pp. 4003-4008, 1995.
    • (1995) Ind. Chem. Res. Dev , vol.34 , pp. 4003-4008
    • Bi, H.T.1    Grace, J.R.2    Lim, K.S.3
  • 8
    • 0030615443 scopus 로고    scopus 로고
    • Fractal Characteristics of gas-solids flow in a circulating fluidized bed
    • D. Bai, E. Shibuya, N. Nakagawa, and K. Kato, “Fractal Characteristics of gas-solids flow in a circulating fluidized bed,” Powder Tech., vol. 90, pp. 205-212, 1997.
    • (1997) Powder Tech , vol.90 , pp. 205-212
    • Bai, D.1    Shibuya, E.2    Nakagawa, N.3    Kato, K.4
  • 10
    • 0000759022 scopus 로고
    • Long-term storage capacity of reservoirs
    • H. E. Hurst, “Long-term storage capacity of reservoirs,” Trans. Am. Soc. Civ. Eng., vol. 116, pp. 770-799, 1951.
    • (1951) Trans. Am. Soc. Civ. Eng , vol.116 , pp. 770-799
    • Hurst, H.E.1
  • 11
    • 0037395853 scopus 로고    scopus 로고
    • Multiscale resolution of fluidized-bed pressure fluctuations
    • G. B. Zhao and Y. R. Yang, “Multiscale resolution of fluidized-bed pressure fluctuations,” AIChE J., vol. 49, pp. 869-882, 2003.
    • (2003) Aiche J , vol.49 , pp. 869-882
    • Zhao, G.B.1    Yang, Y.R.2
  • 12
    • 0042122527 scopus 로고    scopus 로고
    • Pressure fluctuations and transition from bubbling to turbulent fluidization
    • A. Chen, and H. T. Bi, “Pressure fluctuations and transition from bubbling to turbulent fluidization”, Powder Tech., vol. 133, pp. 237-246, 2003.
    • (2003) Powder Tech , vol.133 , pp. 237-246
    • Chen, A.1    Bi, H.T.2
  • 13
    • 3042590653 scopus 로고    scopus 로고
    • Time series analysis of pressure fluctuation in gas-solid fluidized beds
    • S. Alberto, C. Felipe, and S. C. S. Rocha, “Time series analysis of pressure fluctuation in gas-solid fluidized beds,” Braz. J. Chem. Eng., vol. 21, pp. 497-507, 2004.
    • (2004) Braz. J. Chem. Eng. , vol.21 , pp. 497-507
    • Alberto, S.1    Felipe, C.2    Rocha, S.C.S.3
  • 14
    • 0034327275 scopus 로고    scopus 로고
    • A state-of-the-art review of gas-solids turbulent fluidization
    • H. T. Bi, I. A. Abba, N. Ellis, and J. R. Grace, “A state-of-the-art review of gas-solids turbulent fluidization,” Chem. Eng. Sci., vol. 55, pp. 4789-4825, 2000
    • (2000) Chem. Eng. Sci , vol.55 , pp. 4789-4825
    • Bi, H.T.1    Abba, I.A.2    Ellis, N.3    Grace, J.R.4
  • 15
    • 0023534717 scopus 로고
    • Control of quality of fluidization in a tall bed using the variance of pressure fluctuations
    • Y. O. Chong, D. P. O’Dea, E. T. White, P. L. Lee, and L. S. Leung, “Control of quality of fluidization in a tall bed using the variance of pressure fluctuations,” Powder Tech., vol. 53, pp. 237-246, 1987.
    • (1987) Powder Tech. , vol.53 , pp. 237-246
    • Chong, Y.O.1    O’Dea, D.2    Dea, E.T.3    White, P.L.L.4    Leung, L.S.5
  • 16
    • 4143100889 scopus 로고    scopus 로고
    • An early-warning-method for detecting bed agglomeration in fluidized bed combustors
    • FBC99-0150, R. B. Reuther, ed., ASME, New York
    • J. R. van Ommen, J. C. Schouten, and C. M. van den Bleek, “An early-warning-method for detecting bed agglomeration in fluidized bed combustors,” Paper No. FBC99-0150, Proc. 15th Int. Conf. Fluidized Bed Combustion, R. B. Reuther, ed., ASME, New York, 1999
    • (1999) Proc. 15Th Int. Conf. Fluidized Bed Combustion
    • van Ommen, J.R.1    Schouten, J.C.2    van den Bleek, C.M.3
  • 17
    • 0029158399 scopus 로고
    • Effect of measurement method on the velocities used to demarcate the onset of turbulent fluidization
    • H. T. Bi and J. R. Grace, “Effect of measurement method on the velocities used to demarcate the onset of turbulent fluidization,” Chem. Eng. J., vol. 57, pp. 261-271, 1995.
    • (1995) Chem. Eng. J , vol.57 , pp. 261-271
    • Bi, H.T.1    Grace, J.R.2
  • 18
    • 34548696055 scopus 로고
    • Independent coordinates for strange attractors from mutual information
    • A. Fraser and H. Swinney, “Independent coordinates for strange attractors from mutual information,” Phys. Rev. A, vol. 33, pp. 1134-1140, 1986.
    • (1986) Phys. Rev. A , vol.33 , pp. 1134-1140
    • Fraser, A.1    Swinney, H.2
  • 21
    • 0025500917 scopus 로고
    • Stochastic analysis of a three-phase fluidized bed: Fractal Approach
    • L. T. Fan, D. Neogi, M. Yashima, and R. Nassar, “Stochastic analysis of a three-phase fluidized bed: Fractal Approach,” AIChE J., vol. 36, pp. 1529-1535, 1990.
    • (1990) Aiche J , vol.36 , pp. 1529-1535
    • Fan, L.T.1    Neogi, D.2    Yashima, M.3    Nassar, R.4
  • 22
    • 0026189377 scopus 로고
    • The use of fractal techniques for flow regime identification
    • F. Franca, M. Acikgoz, R. T. Lahey, and A. Clausse, “The use of fractal techniques for flow regime identification,” Int. J. Multiphase Flow, vol. 17, pp. 545-552, 1991.
    • (1991) Int. J. Multiphase Flow , vol.17 , pp. 545-552
    • Franca, F.1    Acikgoz, M.2    Lahey, R.T.3    Clausse, A.4
  • 23
    • 0026933866 scopus 로고
    • Fractal behaviour of pressure fluctuations in a bubble column
    • J. Drahos, F. Bradka, M. Puncochar, “Fractal behaviour of pressure fluctuations in a bubble column,” Chem. Eng. Sci., vol. 47, pp. 4069-4075, 1992.
    • (1992) Chem. Eng. Sci , vol.47 , pp. 4069-4075
    • Drahos, J.1    Bradka, F.2    Puncochar, M.3
  • 24
    • 0029109896 scopus 로고
    • Characterization of dilute flows using the rescaled range analysis
    • F. J. Cabrejos and G. E. Klinzing, “Characterization of dilute flows using the rescaled range analysis,” Powder Tech., vol. 84, pp. 139-156, 1995.
    • (1995) Powder Tech , vol.84 , pp. 139-156
    • Cabrejos, F.J.1    Klinzing, G.E.2
  • 25
    • 0031193482 scopus 로고    scopus 로고
    • Hurst’s analysis to detect minimum fluidization and gas maldistribution in fluidized beds
    • C. L. Briens, L. A. Briens, J. Hay, C. Hudson, and A. Margaritis, “Hurst’s analysis to detect minimum fluidization and gas maldistribution in fluidized beds,” AIChE J., vol. 43, pp. 1904-1908, 1997.
    • (1997) Aiche J , vol.43 , pp. 1904-1908
    • Briens, C.L.1    Briens, L.A.2    Hay, J.3    Hudson, C.4    Margaritis, A.5
  • 26
    • 0030615439 scopus 로고    scopus 로고
    • A fractal approach for interpretation of local instantaneous temperature signals around a horizontal heat transfer tube in a bubbling fluidized bed
    • A. I. Karamavruc and N. N. Clark, “A fractal approach for interpretation of local instantaneous temperature signals around a horizontal heat transfer tube in a bubbling fluidized bed,” Powder Tech., vol. 90, pp. 235-244, 1997.
    • (1997) Powder Tech , vol.90 , pp. 235-244
    • Karamavruc, A.I.1    Clark, N.N.2
  • 27
    • 35949006375 scopus 로고
    • Estimation of the dimension of a noisy attractor
    • J. C. Schouten, F. Takens, and C. M. van den Bleek, “Estimation of the dimension of a noisy attractor,” Phys. Rev. E, vol. 50, pp. 1851-1861, 1994.
    • (1994) Phys. Rev. E , vol.50 , pp. 1851-1861
    • Schouten, J.C.1    Takens, F.2    van den Bleek, C.M.3
  • 28
    • 0002890249 scopus 로고
    • Application of deterministic chaos theory in understanding the fluid dynamic behavior of gas-solids fluidization
    • M. L. M. van der Stappen, J. C. Schouten, and C. M. van den Bleek, “Application of deterministic chaos theory in understanding the fluid dynamic behavior of gas-solids fluidization,” AIChE Symp. Ser., vol. 89, pp. 91-102, 1993.
    • (1993) Aiche Symp. Ser , vol.89 , pp. 91-102
    • van der Stappen, M.L.M.1    Schouten, J.C.2    van den Bleek, C.M.3
  • 30
    • 0016047283 scopus 로고
    • Periodic pressure fluctuations in fluidized beds
    • J. Verloop, P. M. Heertjes, “Periodic pressure fluctuations in fluidized beds,” Chem. Eng. Sci., vol. 29, pp. 1035-1042, 1974.
    • (1974) Chem. Eng. Sci , vol.29 , pp. 1035-1042
    • Verloop, J.1    Heertjes, P.M.2
  • 31
    • 0016902699 scopus 로고
    • Measurement and spectral analysis of pressure fluctuations in slugging beds
    • Keairns, D.L. (Ed.), Engineering Foundation, New York
    • T. E. Broadhurst and H. A. Becker, “Measurement and spectral analysis of pressure fluctuations in slugging beds,” In: Keairns, D.L. (Ed.), Fluidization Tech., Vol. 1, Engineering Foundation, New York, pp. 63-85, 1976.
    • (1976) Fluidization Tech , vol.1 , pp. 63-85
    • Broadhurst, T.E.1    Becker, H.A.2
  • 32
    • 0022129695 scopus 로고
    • Characteristics of slugging regime and transition to turbulent regime for fluidized beds of large coarse particles
    • S. Satija and L. S. Fan, “Characteristics of slugging regime and transition to turbulent regime for fluidized beds of large coarse particles”, AIChE J., vol. 31, pp. 1554-1562, 1985.
    • (1985) Aiche J , vol.31 , pp. 1554-1562
    • Satija, S.1    Fan, L.S.2
  • 34
    • 0030088208 scopus 로고    scopus 로고
    • Fluidization regimes in non-slugging fluidized beds: The influence of pressure drop across the air distributor
    • A. Svensson, F. Johnsson, and B. Leckner, “Fluidization regimes in non-slugging fluidized beds: the influence of pressure drop across the air distributor,” Powder Tech., vol. 86, pp. 299-312, 1996.
    • (1996) Powder Tech , vol.86 , pp. 299-312
    • Svensson, A.1    Johnsson, F.2    Leckner, B.3
  • 35
    • 0002673383 scopus 로고
    • Test of the scaling relationships for fluid-bed dynamics
    • K. Ostergaard and A. Sorensen, A. (Eds.), Engineering Foundation, New York
    • R. A. Newby and D. L. Keairns, “Test of the scaling relationships for fluid-bed dynamics,” In: K. Ostergaard and A. Sorensen, A. (Eds.), Fluidization V. Engineering Foundation, New York, pp. 31-38, 1986.
    • (1986) Fluidization V , pp. 31-38
    • Newby, R.A.1    Keairns, D.L.2
  • 36
    • 0027692914 scopus 로고
    • Simplified scaling relationships for fluidized beds
    • L. R. Glicksman, M. Hyre, and K. Woloshun, “Simplified scaling relationships for fluidized beds,” Powder Tech., vol. 77, pp. 177-199, 1993.
    • (1993) Powder Tech , vol.77 , pp. 177-199
    • Glicksman, L.R.1    Hyre, M.2    Woloshun, K.3
  • 37
    • 0029170144 scopus 로고
    • Analysis of flow in gas-liquid bubble columns using multi-resolution methods
    • B. R. Bakshi, H. Zhong, P. Jiang, and L. S. Fan, “Analysis of flow in gas-liquid bubble columns using multi-resolution methods,” Trans. Inst. Chem. Eng., vol. 73, Part A, pp. 608-614, 1995.
    • (1995) Trans. Inst. Chem. Eng , vol.73 , pp. 608-614
    • Bakshi, B.R.1    Zhong, H.2    Jiang, P.3    Fan, L.S.4
  • 38
    • 0031193959 scopus 로고    scopus 로고
    • Modeling pressure fluctuations via correlation structure in a gas-solids fluidized bed
    • Z. He, W. Zhang, K. He, and B. Chen, “Modeling pressure fluctuations via correlation structure in a gas-solids fluidized bed,” AIChE J., vol. 43, pp. 1914-1920, 1997.
    • (1997) Aiche J , vol.43 , pp. 1914-1920
    • He, Z.1    Zhang, W.2    He, K.3    Chen, B.4
  • 39
    • 0032697608 scopus 로고    scopus 로고
    • Wavelet analysis of pressure fluctuation signals in a bubbling fluidized bed
    • X. Lu and H. Li, “Wavelet analysis of pressure fluctuation signals in a bubbling fluidized bed,” Chem. Eng. J., vol. 75, pp. 113-119, 1999.
    • (1999) Chem. Eng. J , vol.75 , pp. 113-119
    • Lu, X.1    Li, H.2
  • 40
    • 0034699235 scopus 로고    scopus 로고
    • Compromise and resolution-exploring the multi-scale nature of gas-solid fluidization
    • J. Li, “Compromise and resolution-exploring the multi-scale nature of gas-solid fluidization,” Powder Tech., vol. 111, pp. 50-59, 2000.
    • (2000) Powder Tech , vol.111 , pp. 50-59
    • Li, J.1
  • 41
    • 0035247503 scopus 로고    scopus 로고
    • Wavelet Analysis of Dynamic Behavior in Fluidized Beds
    • J. Ren, Q. Mao, J. Li, and W. Lin, “Wavelet Analysis of Dynamic Behavior in Fluidized Beds,” Chem. Eng. Sci., vol. 56, pp. 981-988, 2001.
    • (2001) Chem. Eng. Sci , vol.56 , pp. 981-988
    • Ren, J.1    Mao, Q.2    Li, J.3    Lin, W.4
  • 42
    • 0037055068 scopus 로고    scopus 로고
    • Dynamics of pressure fluctuation in a bubbling fluidized bed at high temperature
    • Q. Guo, G. Yue, and J. Werther, “Dynamics of pressure fluctuation in a bubbling fluidized bed at high temperature,” Ind. Eng. Chem. Res., vol. 41, pp. 3482-3488, 2002.
    • (2002) Ind. Eng. Chem. Res. , vol.41 , pp. 3482-3488
    • Guo, Q.1    Yue, G.2    Werther, J.3
  • 43
    • 0037071214 scopus 로고    scopus 로고
    • Application of wavelet multi-resolution analysis to pressure fluctuations of gas-solid two-phase flow in a horizontal pipe
    • H. Li, “Application of wavelet multi-resolution analysis to pressure fluctuations of gas-solid two-phase flow in a horizontal pipe,” Powder Tech., vol. 125, pp. 61-73, 2002.
    • (2002) Powder Tech , vol.125 , pp. 61-73
    • Li, H.1
  • 44
    • 40849130773 scopus 로고    scopus 로고
    • Study of transition velocities from bubbling to turbulent fluidization by statistic and wavelet multi-resolution analysis on absolute pressure fluctuations
    • T. Y. Yang and L. Leu, “Study of transition velocities from bubbling to turbulent fluidization by statistic and wavelet multi-resolution analysis on absolute pressure fluctuations,” Chem. Eng. Sci., vol. 63, pp. 1950-1970, 2008.
    • (2008) Chem. Eng. Sci , vol.63 , pp. 1950-1970
    • Yang, T.Y.1    Leu, L.2
  • 45
    • 35949014155 scopus 로고
    • Chaotic characteristics of a complex gas-solid flow
    • C. S. Daw, W. F. Lawkins, D. J. Downing, and N. E. Clapp, Jr., “Chaotic characteristics of a complex gas-solid flow,” Phys. Re. A, vol. 41, pp. 1179-1181, 1990.
    • (1990) Phys. Re. A , vol.41 , pp. 1179-1181
    • Daw, C.S.1    Lawkins, W.F.2    Downing, D.J.3    Clapp, N.E.4
  • 46
    • 0025795733 scopus 로고
    • Characterization of voidage and pressure signals from fluidized beds using deterministic chaos theory
    • E. J. Anthony, (Ed.), ASME, New York
    • C. S. Daw and J. S. Halow, “Characterization of voidage and pressure signals from fluidized beds using deterministic chaos theory,” In: E. J. Anthony, (Ed.), Proc. Eleventh Int. Conf. Fluidized Bed Combustion, ASME, New York, vol. 1, pp. 777-786, 1991.
    • (1991) Proc. Eleventh Int. Conf. Fluidized Bed Combustion , vol.1 , pp. 777-786
    • Daw, C.S.1    Halow, J.S.2
  • 47
    • 0000396583 scopus 로고
    • Self-Organization and chaos in a fluidized bed
    • C. S. Daw and E. J. Kostelich, “Self-Organization and chaos in a fluidized bed,” Phys. Rev. Lett., vol. 75, pp. 2308-2311, 1995.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 2308-2311
    • Daw, C.S.1    Kostelich, E.J.2
  • 48
    • 0027554936 scopus 로고
    • Fractal analysis of fluidized particle behavior in liquid-solid fluidized beds
    • L. T. Fan, Y. Kang, D. Neogi, and M. Yashima, “Fractal analysis of fluidized particle behavior in liquid-solid fluidized beds,” AIChE J., vol. 39, pp. 513-517, 1993.
    • (1993) Aiche J , vol.39 , pp. 513-517
    • Fan, L.T.1    Kang, Y.2    Neogi, D.3    Yashima, M.4
  • 49
    • 0027628316 scopus 로고
    • Can deterministic chaos create order in fluidized bed scale-up?
    • C. M. van den Bleek and J. C. Schouten, “Can deterministic chaos create order in fluidized bed scale-up?”, Chem. Eng. Sci., vol. 48, pp. 2367-2373, 1993.
    • (1993) Chem. Eng. Sci , vol.48 , pp. 2367-2373
    • van den Bleek, C.M.1    Schouten, J.C.2
  • 50
    • 0027690781 scopus 로고
    • Deterministic chaos: A new tool in fluidized bed design and operation
    • C. M. van den Bleek and J. C. Schouten, “Deterministic chaos: a new tool in fluidized bed design and operation,” Chem. Eng. J., vol. 53, pp. 75-87, 1993.
    • (1993) Chem. Eng. J , vol.53 , pp. 75-87
    • van den Bleek, C.M.1    Schouten, J.C.2
  • 51
    • 0011164785 scopus 로고
    • Characterization of the fluidization behavior of different solid types based on chaotic time-series analysis of pressure signals
    • L. Rubow and G. Commonwealth (Eds.), ASME Book No. I0344B, New York
    • D. P. Skrzycke, K. Nguyen, and C. S. Daw, “Characterization of the fluidization behavior of different solid types based on chaotic time-series analysis of pressure signals,” In: L. Rubow and G. Commonwealth (Eds.), Proc. Twelfth Int. Conf. Fluidized Bed Combustion, ASME Book No. I0344B, New York, pp. 155, 1993.
    • (1993) Proc. Twelfth Int. Conf. Fluidized Bed Combustion , pp. 155
    • Skrzycke, D.P.1    Nguyen, K.2    Daw, C.S.3
  • 52
    • 0029255809 scopus 로고
    • The calculation of the characteristics of a chaotic attractor in a gas-solid fluidized bed
    • J. M. Hay, B. H. Nelson, C. L. Briens, and M. A. Bergougnou, “The calculation of the characteristics of a chaotic attractor in a gas-solid fluidized bed,” Chem. Eng. Sci., vol. 50, pp. 373-380, 1995.
    • (1995) Chem. Eng. Sci , vol.50 , pp. 373-380
    • Hay, J.M.1    Nelson, B.H.2    Briens, C.L.3    Bergougnou, M.A.4
  • 54
    • 0030615443 scopus 로고    scopus 로고
    • Fractal Characteristics of gas-solids flow in a circulating fluidized bed
    • D. Bai, E. Shibuya, N. Nakagawa, and Kato, K., “Fractal Characteristics of gas-solids flow in a circulating fluidized bed,” Powder Tech., vol. 90, pp. 205, 1997.
    • (1997) Powder Tech , vol.90 , pp. 205
    • Bai, D.1    Shibuya, E.2    Nakagawa, N.3    Kato, K.4
  • 55
    • 0031147958 scopus 로고    scopus 로고
    • Chaotic behavior of fluidized beds based on pressure and voidage fluctuations
    • D. Bai, H. T. Bi, and J. R. Grace, “Chaotic behavior of fluidized beds based on pressure and voidage fluctuations,” AIChE J., vol. 43, pp. 1357-1361, 1997.
    • (1997) Aiche J , vol.43 , pp. 1357-1361
    • Bai, D.1    Bi, H.T.2    Grace, J.R.3
  • 56
    • 0013078521 scopus 로고    scopus 로고
    • Predictive model and deterministic mechanism in a bubbling fluidized bed
    • G. B. Zhao, J. Z. Chen, and Y. R. Yang, “Predictive model and deterministic mechanism in a bubbling fluidized bed,” AIChE J., vol. 47, pp. 1524-1532, 2001.
    • (2001) Aiche J , vol.47 , pp. 1524-1532
    • Zhao, G.B.1    Chen, J.Z.2    Yang, Y.R.3
  • 57
    • 0000779360 scopus 로고
    • Detecting strange attractors in turbulence
    • D. A. Rand and L. S. Young, (Eds.), Springer Verlag, Berlin, Germany
    • F. Takens, “Detecting strange attractors in turbulence,” Lecture Notes in Mathematics, Dynamical Systems and Turbulence, D. A. Rand and L. S. Young, (Eds.), Springer Verlag, Berlin, Germany, vol. 898, pp. 366-381, 1981.
    • (1981) Lecture Notes in Mathematics, Dynamical Systems and Turbulence , vol.898 , pp. 366-381
    • Takens, F.1
  • 58
    • 0342978428 scopus 로고
    • Is there a strange attractor in a fluidized bed?
    • N. B. Abraham, A. M. Albano, A. Passamante, P. E. Rapp, (Eds.), New York
    • S. W. Tam and M. K. Devine, “Is there a strange attractor in a fluidized bed?” In: N. B. Abraham, A. M. Albano, A. Passamante, P. E. Rapp, (Eds.). Measures of Complexity and Chaos, Plenum, New York, pp. 193-197, 1989.
    • (1989) Measures of Complexity and Chaos, Plenum , pp. 193-197
    • Tam, S.W.1    Devine, M.K.2
  • 59
    • 0007846880 scopus 로고
    • Noise/chaos distinction applied to the study of a fluidized bed
    • N. Letaief, C. Roze, and G. Gouesbet, “Noise/chaos distinction applied to the study of a fluidized bed,” J. Physique II France, vol. 5, pp. 1883-1899, 1995.
    • (1995) J. Physique II France , vol.5 , pp. 1883-1899
    • Letaief, N.1    Roze, C.2    Gouesbet, G.3
  • 60
    • 57949096251 scopus 로고    scopus 로고
    • Nonlinear characterization of pressure fluctuations in fluidized beds
    • R. Zarghami, N. Mostoufi, and R. Sotudeh-Gharebagh, “Nonlinear characterization of pressure fluctuations in fluidized beds”, Ind. Eng. Chem. Res., vol. 47, pp. 9497-9507, 2008.
    • (2008) Ind. Eng. Chem. Res. , vol.47 , pp. 9497-9507
    • Zarghami, R.1    Mostoufi, N.2    Sotudeh-Gharebagh, R.3
  • 61
    • 48549112428 scopus 로고
    • Dimensions and entropies of strange attractors from a fluctuating dynamics approach
    • P. Grassberger and I. Procaccia, “Dimensions and entropies of strange attractors from a fluctuating dynamics approach,” Physica D: Nonlinear Phenomena, vol. 13, pp. 34-54, 1984.
    • (1984) Physica D: Nonlinear Phenomena , vol.13 , pp. 34-54
    • Grassberger, P.1    Procaccia, I.2
  • 63
    • 35949012282 scopus 로고
    • Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra
    • H. D. I. Abarbanel, R. Brown, J. B. Kadtke, “Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra,” Phys. Rev. A, vol. 41, pp. 1742-1807, 1990.
    • (1990) Phys. Rev. A , vol.41 , pp. 1742-1807
    • Abarbanel, H.D.I.1    Brown, R.2    Kadtke, J.B.3
  • 64
    • 0032701078 scopus 로고    scopus 로고
    • Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: How to prevent pitfalls in dynamic pressure measurements
    • J. R. van Ommen, J. C. Schouten, M. L. M. van der Stappen, and C. M. van den Bleek, “Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: how to prevent pitfalls in dynamic pressure measurements”, Powder Tech., vol. 106, pp. 199-218, 1999.
    • (1999) Powder Tech , vol.106 , pp. 199-218
    • van Ommen, J.R.1    Schouten, J.C.2    van der Stappen, M.L.M.3    van den Bleek, C.M.4
  • 66
    • 0001613549 scopus 로고
    • Symposium on Fluidization Discussion
    • J. F. Davidson, Symposium on Fluidization Discussion, Trans. Instn. Chem. Engrs., vol. 39, pp. 230-232, 1961.
    • (1961) Trans. Instn. Chem. Engrs. , vol.39 , pp. 230-232
    • Davidson, J.F.1
  • 67
    • 0001424560 scopus 로고
    • An extension of Davidson's theory of bubbles in fluidized beds
    • Collins, R., “An extension of Davidson's theory of bubbles in fluidized beds,” Chem. Eng. Sci., vol. 20, pp. 747-755, 1965.
    • (1965) Chem. Eng. Sci , vol.20 , pp. 747-755
    • Collins, R.1
  • 68
    • 0002101338 scopus 로고
    • Isolated bubbles in fluidized beds-theory and experiment
    • P. S. B. Stewart, “Isolated bubbles in fluidized beds-theory and experiment,” Trans. Inst. Chem. Eng., vol. 46, pp. T60, 1968.
    • (1968) Trans. Inst. Chem. Eng. , vol.46 , pp. T60
    • Stewart, P.S.B.1
  • 69
    • 0026108838 scopus 로고
    • Frequency analysis of pressure fluctuation in fluidized bed plenum
    • H. Kage, N. Iwasaki, H. Yamaguchi, and Y. Matsuna, “Frequency analysis of pressure fluctuation in fluidized bed plenum,” J. Chem. Eng. Japan, vol. 24, pp. 76-81, 1991.
    • (1991) J. Chem. Eng. Japan , vol.24 , pp. 76-81
    • Kage, H.1    Iwasaki, N.2    Yamaguchi, H.3    Matsuna, Y.4
  • 70
    • 0022441010 scopus 로고
    • A study of pressure fluctuations in a bubbling fluidized bed
    • A. P. Baskakov, V. G. Tuponogov, and N. F. Filippovsky, “A study of pressure fluctuations in a bubbling fluidized bed,” Powder Tech., vol. 45, pp. 113-117, 1986.
    • (1986) Powder Tech , vol.45 , pp. 113-117
    • Baskakov, A.P.1    Tuponogov, V.G.2    Filippovsky, N.F.3
  • 71
    • 0029135623 scopus 로고
    • Propagation of pressure waves and forced oscillations in gas-solid fluidized beds and their influence on diagnostics of local hydrodynamics
    • H. T. Bi, J. R. Grace, and J. Zhu, “Propagation of pressure waves and forced oscillations in gas-solid fluidized beds and their influence on diagnostics of local hydrodynamics,” Powder Tech., vol. 82, pp. 239-253, 1995.
    • (1995) Powder Tech , vol.82 , pp. 239-253
    • Bi, H.T.1    Grace, J.R.2    Zhu, J.3
  • 75
    • 0025158947 scopus 로고
    • Measurements of pressure fluctuations in two-dimensional gas solid fluidized beds at elevated temperatures
    • L. P. Leu and C. W. Lan, “Measurements of pressure fluctuations in two-dimensional gas solid fluidized beds at elevated temperatures,” J. Chem. Eng. Jpn., vol. 23, pp. 555-562, 1990.
    • (1990) J. Chem. Eng. Jpn , vol.23 , pp. 555-562
    • Leu, L.P.1    Lan, C.W.2
  • 76
    • 0026383075 scopus 로고
    • The two-phase theory of fluidization: Successes and opportunities
    • J. F. Davidson, “The two-phase theory of fluidization: successes and opportunities,” AIChE Symp. Ser., vol. 87, No. 281, pp. 1-12, 1991.
    • (1991) Aiche Symp. Ser , vol.87 , Issue.281 , pp. 1-12
    • Davidson, J.F.1
  • 77
    • 20444416147 scopus 로고
    • On the mechanism of pressure pulsation in a bubbling fluidized bed
    • A. P. Baskakov, A. V. Mudrichenko, N. F. Filipovskii, “On the mechanism of pressure pulsation in a bubbling fluidized bed,” J. Eng. Phys. Thermophys., vol. 66 (1), pp. 30-33, 1994.
    • (1994) J. Eng. Phys. Thermophys , vol.66 , Issue.1 , pp. 30-33
    • Baskakov, A.P.1    Mudrichenko, A.V.2    Filipovskii, N.F.3
  • 78
    • 0003287402 scopus 로고
    • The Fractal Geometry of Nature
    • San Francisco
    • B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982.
    • (1982) Freeman
    • Mandelbrot, B.1
  • 79
    • 44049112233 scopus 로고
    • Distinguishing between low dimensional dynamics and randomness in measured time series
    • A. Provenzale, L. A. Smith, R. Vio, and G. Murante, “Distinguishing between low dimensional dynamics and randomness in measured time series,” Physica D: Nonlinear Phenomena, vol. 58, 31-49, 1992.
    • (1992) Physica D: Nonlinear Phenomena , vol.58 , pp. 31-49
    • Provenzale, A.1    Smith, L.A.2    Vio, R.3    Murante, G.4
  • 81
    • 44049113708 scopus 로고
    • Comparison of algorithms calculating optimal parameters for delay time coordinate
    • Th. Buzug, G. Pfister, “Comparison of algorithms calculating optimal parameters for delay time coordinate,” Physica D: Nonlinear Phenomena, vol. 58, pp. 127-137, 1992.
    • (1992) Physica D: Nonlinear Phenomena , vol.58 , pp. 127-137
    • Buzug, T.1    Pfister, G.2
  • 82
    • 0001295575 scopus 로고
    • Differentiable manifolds
    • H. Whitney, “Differentiable manifolds,” Ann. Math., vol. 37, pp. 645-680, 1936.
    • (1936) Ann. Math , vol.37 , pp. 645-680
    • Whitney, H.1
  • 84
    • 35949006791 scopus 로고
    • Determining embedding dimension for phase-space reconstruction using a geometrical construction
    • M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A, vol. 45, pp. 3403-3411, 1992.
    • (1992) Phys. Rev. A , vol.45 , pp. 3403-3411
    • Kennel, M.B.1    Brown, R.2    Abarbanel, H.D.I.3
  • 85
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett., vol. 50, pp. 346-349, 1983
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Procaccia, I.2
  • 86
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D: Nonlinear Phenomena, vol. 9, pp. 189-208, 1983.
    • (1983) Physica D: Nonlinear Phenomena , vol.9 , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 87
    • 0001413326 scopus 로고
    • Spurious dimension from correlation algorithms applied to limited time series data
    • J. Theiler, “Spurious dimension from correlation algorithms applied to limited time series data,” Phys. Rev. A, vol. 34, pp. 2427-2432, 1986.
    • (1986) Phys. Rev. A , vol.34 , pp. 2427-2432
    • Theiler, J.1
  • 88
    • 0001874436 scopus 로고    scopus 로고
    • Practical method for determining the minimum embedding dimension of a scalar time series
    • L. Cao, “Practical method for determining the minimum embedding dimension of a scalar time series,” Physica D: Nonlinear Phenomena, vol. 110, pp. 43-50, 1997.
    • (1997) Physica D: Nonlinear Phenomena , vol.110 , pp. 43-50
    • Cao, L.1
  • 90
    • 34249988665 scopus 로고
    • Extracting qualitative dynamics from experimental data
    • D. S. Broomhead and G. P. King, “Extracting qualitative dynamics from experimental data,” Physica D, vol. 20, pp. 217-236, 1986.
    • (1986) Physica D , vol.20 , pp. 217-236
    • Broomhead, D.S.1    King, G.P.2
  • 91
    • 0034326251 scopus 로고    scopus 로고
    • Early warning of agglomeration in fluidized beds by Attractor Comparison
    • J. R. van Ommen, M. O. Coppens, C. M. van den Bleek, and J. C. Schouten, “Early warning of agglomeration in fluidized beds by Attractor Comparison,” AIChE J., vol. 46, pp. 2183-2197, 2000.
    • (2000) Aiche J , vol.46 , pp. 2183-2197
    • van Ommen, J.R.1    Coppens, M.O.2    van den Bleek, C.M.3    Schouten, J.C.4
  • 92
    • 0002405786 scopus 로고
    • On the numerical determination of the dimension of an attractor
    • B. L. J. Braaksma, H. W. Broer, F. Takens, (Eds.), Springer Verlag, Berlin
    • F. Takens, “On the numerical determination of the dimension of an attractor,” In: B. L. J. Braaksma, H. W. Broer, F. Takens, (Eds.), Proc. Dynamical Systems and Bifurcations, Lecture Notes in Mathematics, Springer Verlag, Berlin, vol. 1125, pp. 99-106, 1985.
    • (1985) Proc. Dynamical Systems and Bifurcations, Lecture Notes in Mathematics , vol.1125 , pp. 99-106
    • Takens, F.1
  • 93
    • 18444400763 scopus 로고
    • Maximum likelihood estimation of the entropy of an attractor
    • J. C. Schouten, F. Takens, and C. M. van den Bleek, “Maximum likelihood estimation of the entropy of an attractor,” Phys. Rev. E, vol. 49, pp. 126-129, 1994
    • (1994) Phys. Rev. E , vol.49 , pp. 126-129
    • Schouten, J.C.1    Takens, F.2    van den Bleek, C.M.3
  • 95
    • 0001282028 scopus 로고
    • Method to distinguish possible chaos from colored noise and to determine embedding parameters
    • M. B. Kennel and S. Isabelle, “Method to distinguish possible chaos from colored noise and to determine embedding parameters,” Phys. Rev. A, vol. 46, pp. 3111-3118, 1992.
    • (1992) Phys. Rev. A , vol.46 , pp. 3111-3118
    • Kennel, M.B.1    Isabelle, S.2
  • 96
    • 21344492190 scopus 로고
    • Detecting nonlinearities in stationary time series
    • F. Takens, “Detecting nonlinearities in stationary time series,” Int. J. Bifurcation Chaos, vol. 3, pp. 241-256, 1993
    • (1993) Int. J. Bifurcation Chaos , vol.3 , pp. 241-256
    • Takens, F.1
  • 98
    • 0031864910 scopus 로고    scopus 로고
    • Monitoring the quality of fluidization using the short-term predictability of pressure fluctuations
    • J. C. Schouten and C. M. van den Bleek, “Monitoring the quality of fluidization using the short-term predictability of pressure fluctuations,” AIChE J., vol. 44, pp. 48-60, 1998.
    • (1998) Aiche J , vol.44 , pp. 48-60
    • Schouten, J.C.1    van den Bleek, C.M.2


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