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Statistics of velocity fluctuations of Geldart A particles in a circulating fluidized bed riser

Avinash Vaidheeswaran*, Franklin Shaffer, and Balaji Gopalan†

  • National Energy Technology Laboratory, 3610 Collins Ferry Road, Morgantown, West Virginia 26505, USA

  • *Also at Oak Ridge Institute for Science and Education, Oak Ridge, TN 37831-0117; avinash. vaidheeswaran@netl.doe.gov
  • †Also at West Virginia University Research Corporation, Morgantown, WV 26505.
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Phys. Rev. Fluids 2, 112301(R) – Published 21 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.112301

Abstract

The statistics of fluctuating velocity components are studied in the riser of a closed-loop circulating fluidized bed with fluid catalytic cracking catalyst particles. Our analysis shows distinct similarities as well as deviations compared to existing theories and bench-scale experiments. The study confirms anisotropic and non-Maxwellian distribution of fluctuating velocity components. The velocity distribution functions (VDFs) corresponding to transverse fluctuations exhibit symmetry, and follow a stretched-exponential behavior up to three standard deviations. The form of the transverse VDF is largely determined by interparticle interactions. The tails become more overpopulated with an increase in particle loading. The observed deviations from the Gaussian distribution are represented using the leading order term in the Sonine expansion, which is commonly used to approximate the VDFs in kinetic theory for granular flows. The vertical fluctuating VDFs are asymmetric and the skewness shifts as the wall is approached. In comparison to transverse fluctuations, the vertical VDF is determined by the local hydrodynamics. This is an observation of particle velocity fluctuations in a large-scale system and their quantitative comparison with the Maxwell-Boltzmann statistics.

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References (24)

  1. T. P. C. van Noije and M. H. Ernst, Velocity distributions in homogeneous granular fluids: The free and the heated case, Granular Matter 1, 57 (1998).
  2. M. H. Ernst and R. Brito, Driven inelastic Maxwell models with high energy tails, Phys. Rev. E 65, 040301 (2002).
  3. A. Barrat, T. Biben, Z. Rácz, E. Trizac, and F. van Wijland, On the velocity distributions of the one-dimensional inelastic gas, J. Phys. A: Math. Gen. 35, 463 (2002).
  4. J. S. Olafsen and J. S. Urbach, Clustering, Order, and Collapse in a Driven Granular Monolayer, Phys. Rev. Lett. 81, 4369 (1998).
  5. J. S. Olafsen and J. S. Urbach, Velocity distributions and density fluctuations in a granular gas, Phys. Rev. E 60, R2468 (1999).
  6. F. Rouyer and N. Menon, Velocity Fluctuations in a Homogeneous 2D Granular Gas in Steady State, Phys. Rev. Lett. 85, 3676 (2000).
  7. P. Melby, F. Vega Reyes, A. Prevost, R. Robertson, P. Kumar, D. A. Egolf, and J. S. Urbach, The dynamics of thin vibrated granular layers, J. Phys.: Condens. Matter 17, S2689 (2005).
  8. P. M. Reis, R. A. Ingale, and M. D. Shattuck, Forcing independent velocity distributions in an experimental granular fluid, Phys. Rev. E 75, 051311 (2007).
  9. I. S. Aranson and J. S. Olafsen, Velocity fluctuations in electrostatically driven granular media, Phys. Rev. E 66, 061302 (2002).
  10. K. Kohlstedt, A. Snezhko, M. V. Sapozhnikov, I. S. Aranson, J. S. Olafsen, and E. Ben-Naim, Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions, Phys. Rev. Lett. 95, 068001 (2005).
  11. E. Ben-Naim and P. L. Krapivsky, Scaling, multiscaling, and nontrivial exponents in inelastic collision processes, Phys. Rev. E 66, 011309 (2002).
  12. E. Ben-Naim and J. Machta, Stationary States and Energy Cascades in Inelastic Gases, Phys. Rev. Lett. 94, 138001 (2005).
  13. S. Moka and P. R. Nott, Statistics of Particle Velocities in Dense Granular Flows, Phys. Rev. Lett. 95, 068003 (2005).
  14. V. Garzó and J. W. Dufty, Dense fluid transport for inelastic hard spheres, Phys. Rev. E 59, 5895 (1999).
  15. V. Garzó, S. Tenneti, S. Subramaniam, and C. M. Hrenya, Enskog kinetic theory for monodisperse gas-solid flows, J. Fluid Mech. 712, 129 (2012).
  16. H. Nakanishi, Velocity distribution of inelastic granular gas in a homogeneous cooling state, Phys. Rev. E 67, 010301 (2003).
  17. N. V. Brilliantov and T. Pöschel, Breakdown of the Sonine expansion for the velocity distribution of granular gases, Europhys. Lett. 74, 424 (2006).
  18. X. Liu, L. Wang, and W. Ge, Meso-scale statistical properties of gas-solid flow-a direct numerical simulation (DNS) study, AIChE J. 63, 3 (2017).
  19. B. Gopalan and F. Shaffer, A new method for decomposition of high speed particle image velocimetry data, Powder Technol. 220, 164 (2012).
  20. D. Geldart, Types of gas fluidization, Powder Technol. 7, 285 (1973).
  21. R. Cocco, F. Shaffer, R. Hays, S. B. Reddy Karri, and T. Knowlton, Particle clusters in and above fluidized beds, Powder Technol. 203, 3 (2010).
  22. B. Gopalan and F. Shaffer, Higher order statistical analysis of Eulerian particle velocity data in CFB risers as measured with high speed particle imaging, Powder Technol. 242, 13 (2013).
  23. F. Rouyer, J. Martin, and D. Salin, Non-Gaussian Dynamics in Quasi-2D Noncolloidal Suspensions, Phys. Rev. Lett. 83, 1058 (1999).
  24. F. Shaffer, B. Gopalan, R. W. Breault, R. Cocco, S. B. Reddy Karri, R. Hays, and T. Knowlton, High speed imaging of particle flow fields in CFB risers, Powder Technol. 242, 86 (2013).

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Phys. Rev. Fluids 2, 112301(R)– Published 21 November, 2017
  • Received 6 July 2017

©2017 American Physical Society

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