ENG  Vol.10 No.10 , October 2018
Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals
Abstract: The study of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using trajectory distances of the reconstructed attractors from solid concentration signals collected from a 76 mm internal diameters and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m2s solids flux. Spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3 together with 70% to 80% humid air was used. Solid concentration data were analyzed using codes prepared in FORTRAN 2008 to get trajectories of the reconstructed attractors and their distances apart. Trajectory distances were found to increase from the centre towards the wall indicating the expansion of the attractor. The probability density function (PDF) of the trajectory distances changes from single peak at the centre to multiple peaked profiles in the wall region. Multiple peaked profiles indicate multifractal flow behaviours. Cumulative distribution functions (CDF) of the trajectory distances changes from single S-shaped at the centre to multiple S-shaped profiles in some locations of the wall region indicating multifractal flow behaviours. The PDF distribution of these distances at the entrance section and in the wall region forms different types of statistical distributions showing differences in gas-solid flow structures in various spatial locations of the wall region and the entrance sections. Most of the distributions at the centre fall under the Gumbel max distribution for all flow development sections of the riser, especially at air velocities of 5.5 m/s and 8 m/s showing uniform flow structures. Further, it was found that increase of the number of the phase space reconstruction embedding dimension increases the trajectory distances between the state vectors leading to the expansion of the attractor.
Cite this paper: Jeremiah, J. , Manyele, S. , Temu, A. and Zhu, J. (2018) Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals. Engineering, 10, 688-703. doi: 10.4236/eng.2018.1010050.

[1]   Ahuja, P., Agrawal, H., Sethi, A.K. and Raj, U. (2005) Chaotic Analysis of Pressure Fluctuations in a Gas-Solid Fluidized Bed. Indian Journal of Chemical Technology, 12, 212-219.

[2]   Reguly Jr., H., Zinani, F., Indrusiak, M.L.S. and da Fonseca, C.E. (2015) Spectral Analysis of Pressure Fluctuations in Fluidized Beds under Different Regimes—A Numerical Study. IV Journeys in Multiphase Flows (JEM 2015), Campinas, SP, Brazil, 23-27 March 2015, 1-11.

[3]   Manyele, S.V., Zhu, J.-X., Khayat, R.E. and Pärssinen, J.H. (2006) Analysis of the Chaotic Dynamics of a High-Flux CFB Riser Using Solids Concentration Measurements. China Particuology, 4, 136-146.

[4]   de Castilho, G.J. and Cremasco, M.A. (2012) Comparison of Downer and Riser Flows in a Circulating Bed by Means of Optical Fiber Probe Signals Measurement. Procedia Engineering, 42, 295-302.

[5]   Cocco, R., Karri, S.B.R. and Knowlton, T. (2014) Introduction to Fluidisation Technology. American Institute of Chemical Engineers, New York.

[6]   Nichols, J.M. and Nichols, J.D. (2001) Attractor Reconstruction for Non-Linear Systems: A Methodological Note. Mathematical Biosciences, 171, 21-32.

[7]   Manyele, S.V., Khayat, R.E. and Zhu, J.-X. (2002) Investigation of the Dynamics of a High-Flux CFB Riser Using Chaos Analysis of Pressure. Chemical Engineering Technology, 25, 801-810.<801::AID-CEAT801>3.0.CO;2-F

[8]   Singh, P.P. and Handa, H. (2012) Various Synchronization Schemes for Chaotic Dynamical Systems (A Classical Survey). International Journal of Scientific Engineering and Technology, 3, 29-33.

[9]   Kantz, H. and Shreiber, T. (2004) Nonlinear Time Series Analysis. 2nd Edition, Cambridge University Press, Cambridge, UK.

[10]   Sevil, H.E. (2006) On the Predictability of Time Series by Metric Entropy. MSc Thesis, Izmir Institute of Technology, Izmir.

[11]   Manyele, S.V., Zhu J.-X. and Zhang, H. (2003) Analysis of the Microscopic Flow Structure of A CFB Downer Reactor Using Solids Concentration Signals. International Journal of Chemical Reactor Engineering, 1, 1-17.

[12]   Takens, F. (1981) Detecting Strange Attractors in Turbulence. In: Rand, D. and Young, L.S., Eds., Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics, Vol. 898, Springer, Berlin, Heidelberg.

[13]   Haro, A., Limaico, C. and Llosas, Y. (2015) Characterization of the Atmospheric Dynamics in Riobamba City Using the Chaos Theory. Atmospheric and Climate Sciences, 5, 441-449.

[14]   Packard, N., Crutchfield, J., Farmer, D. and Shaw, R. (1980) Geometry from a Time Series. Physical Review Letters, 45, 712.

[15]   Johnsson, J., Zijerveld, R.C., Schouten, J.C., van den Bleek, C.M. and Leckner, B. (2000) Characterization of Fluidization Regimes by Time-Series Analysis of Pressure Fluctuations. International Journal of Multiphase Flow, 26, 663-715.

[16]   Zeng, X. (1992) Chaos Theory and Its Application in the Atmosphere. Atmospheric Science Paper No. 504.

[17]   Strozzi, F., Tenrreiro, E.G., Noè, C., Rossi, T., Serati, M. and Comenges, J.Z. (2007) Application of Non-Linear Time Series Analysis Techniques to the Nordic Spot Electricity Market Data. Serie Tecnologia, 11, 1-51.

[18]   Shang, P., Li, X. and Kamae, S. (2005) Chaotic Analysis of Traffic Time Series. Chaos, Solitons and Fractals, 25, 121-128.

[19]   Grassberger, P. and Procaccia, I. (1983) Measurement of Strangeness of the Strange Attractors. Physica, 9D, 189-208.