ENG  Vol.10 No.10 , October 2018
Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series
Abstract: Analysis of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using embedded solid concentration time series collected from a 76 mm internal diameter and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s air velocity and 50 to 550 kg/m2s solids flux of spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3. Data were analyzed using prepared FORTRAN 2008 code to get correlation integral followed by determination of correlation dimensions with respect to the hyperspherical radius and their profiles, plots of which were studied. It was found that correlation dimension profiles at the centre have single peak with higher values than the wall region profiles. Towards the wall, these profiles have double or multiple peaks showing bifractal or multifractal flow behaviors. As the velocity increases the wall region profiles become random and irregular. Further it was found that, as the height increases the correlation dimension profiles shift towards higher hyperspherical radius at the centre and towards lower hyperspherical radius in the wall region at r/R = 0.81. The established method of mapping correlation dimension profiles in this study forms a suitable tool for analysis of high-flux riser dynamics compared to other analyses approaches. However, further analysis is recommended to other gas-solid CFB riser of different dimensions operated at high-flux conditions using the established method.
Cite this paper: Jeremiah, J. , Manyele, S. , Temu, A. and Zhu, J. (2018) Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series. Engineering, 10, 655-679. doi: 10.4236/eng.2018.1010048.

[1]   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.

[2]   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.

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

[6]   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.

[7]   Qiu, G., Ye, J. and Wang, H. (2015) Investigation of Gas-Solid Flow Characteristics in a Circulating Fluidized Bed with Annular Combustion Chamber by Pressure Measurements and CPFD Simulation. Chemical Engineering Science, 134, 433-447.

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

[9]   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.

[10]   Reagan, A. (2014) Predicting Flow Reversal in a Computational Fluid Dynamics Simulated Thermosyphon Using Data Simulation. Master Thesis, University of Vermont, Burlington.

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

[12]   Ding, M., Grebogi, C., Ott, E., Sauer, T. and Yorke, J.A. (1993) Estimating Correlation Dimension from a Chaotic Time Series: When Does Plateau Onset Occur? Physica D, 69, 404-424.

[13]   Lai, Y. and Lerner, D. (1998) Effective Scaling Regime for Computing the Correlation Dimension from Chaotic Time Series. Physica D, 115, 1-18.

[14]   Ji, C.C., Zhu, H. and Jiang, W. (2011) A Novel Method to Identify the Scaling Region for Chaotic Time Series Correlation Dimension Calculation. Chinese Science Bulletin, 56, 925-932.

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

[16]   Hanias, M.P., Nistazakis, H.E. and Tombras, G.S. (2011) Optoelectronic Chaotic Circuits. In: Sergiyenko, O., Ed., Optoelectronic Devices and Properties, Intech, Shanghai, 631-650.

[17]   Galka, A., Maaß, T. and Pfister, G. (1998) Estimating the Dimension of High-Dimensional Attractors: A Comparison between Two Algorithms. Physica D, 121, 237-251.

[18]   Park, J.C. (2000) Chaos and Predictability of Internet Transmission Times. Complex Systems, 12, 297-316.

[19]   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. Liuc Papers n. 200, Serie Tecnologia, 11, 1-51.

[20]   Li, Q. and Li, K. (2007) Low-Dimensional Chaos of High-Latitude Solar Activity. Astronomical Society of Japan, 59, 983-987.

[21]   Kugiumtzis, D. (1996) State Space Reconstruction Parameters in the Analysis of Chaotic Time Series—The Role of the Time Window Length. Physica D: Nonlinear Phenomena, 95, 13-28.

[22]   Martins, O.Y., Sadeeq, M.A. and Ahaneku, I.E. (2011) Nonlinear Deterministic Chaos in Benue River Flow Daily Time Sequence. Journal of Water Resource and Protection, 3, 747-757.

[23]   Liang, W.-G. and Zhu, J.-X. (1997) A Core-Annulus Model for the Radial Flow Structure in a Liquid-Solid Circulating Fluidized Bed (LSCFB). Chemical Engineering Journal, 68, 51-62.