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The role of particle collisions in pneumatic transport

Published online by Cambridge University Press:  26 April 2006

M. Y. Louge ,
E. Mastorakos  and
J. T. Jenkins
M. Y. Louge
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
E. Mastorakos
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
J. T. Jenkins
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
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Abstract

We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 345 - 359
Copyright
© 1991 Cambridge University Press

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References

Bellman, R. E. & Kalaba, R. E. 1965 Quasilinearization and Nonlinear Boundary-Value Problems. Elsevier.
Berker, A. & Tulig, T. J. 1986 Hydrodynamics of gas-solid (low in a catalytic cracker riser: Implications for reactor selectivity performance. Chem. Engng Sci. 41, 821–827.Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.
Chen, C. P. & Wood, P. E. 1985 A turbulence closure model for dilute gas-particle flows. Can. J. Chem. Engng 63n, 349–360.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles, p. 111. Academic.
Elghobashi, S. E. & Aboc-Auab, T. W. 1983 A two-equation turbulence model for two-phase flows. Phys. Fluids 26, 931–938.Google Scholar
Govan, A. H., Hewitt, G. F. & Ngan, C. F. 1989 Particle motion in turbulent pipe flow. Intl J. Multiphase Flow 15, 471–481.Google Scholar
Hinze, J. O. 1972 Turbulent fluid and particle interaction. Prog. Heat Mass Transfer 6, 433–452.Google Scholar
Hinze, J. O, 1975 Turbulence, 2nd edn, p. 474, McGraw-Hill.
Jenkins, J. T. 1991 Boundary conditions for rapid granular flows: flat frictional walls. Trans. ASME E: J. Appl. Mech., in press.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Koch, D. L. 1990 Kinetic theory for a monodisperse gas-solid suspension. Phys. Fluids A 2, 1711–1723.Google Scholar
Lee, S. L. & Durst, F. 1982 On the motion of particles in turbulent duct flows. Intl J. Multiphase Flow 8, 125–146.Google Scholar
Lourenco, L., Riethmuller, M. L. & Essers, J.-A. 1983 The kinetic model for gas-particle flow and its numerical implementation. In Proc. Intl Conf. on the Physical Modelling of Multiphase Flow, pp. 501–525. BHRA Fluid Engineering, Cranfield, UK.
Min, K. 1967 Intensity of particle motion in solid-gas suspension flow. J. Appl. Phys. 38. 564–507.Google Scholar
Modaress, D., Tan, H. & Elghobashi, S. 1984 Two-component LDA measurements in a two-phase turbulent jet. AIAA J. 22, 624–630.Google Scholar
Pourahmadi, F. & Humphrey, J. A. C. 1983 Modeling solid-fluid turbulent flows with application. to predicting erosive wear. Physico-Chem. Hydrodyn. 4, 191–219.Google Scholar
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Sinclair, J. L. & Jackson, R, 1989 Gas-particle flow in a vertical pipe with particle-particle interactions. AIChE J. 35, 1473–1486.Google Scholar
Soo, S. L., Ihrig, H. K. & El Kouh, A. F. 1960 Experimental determination of statistical properties of two-phase turbulent motion. Trans. ASME D. J. Basic Engng 82D, 609–621.Google Scholar
Tsuji, Y., Morikawa, Y. & Shiomi, H. 1984 LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1977 Introduction to Physical Gas Dynamics, p. 424. Krieger.