(85a) Discrete Approximation of a Continuous Size Distribution for Use In Kinetic-Theory Predictions of Solids Flows

J. Aaron Murray, Chemical and Biological Engineering, University of

Colorado at Boulder, Boulder, CO

Christine M. Hrenya, Chemical and Biological Engineering, University of

Colorado at Boulder, Boulder, CO

It is common in nature and industry for the distribution of particle sizes within a granular mixture to be essentially continuous. The focus of this work pertains to kinetic-theory-based models for rapid flows of continuous particle size distributions (PSDs). Such models are restricted to a finite number (s) of particle species. Accordingly, a continuous PSD must be approximated as a discretization of s particle diameters and associated volume (or number) fractions. The kinetic-theory-based model used as a basis in this study was proposed by Garzó, Hrenya, and Dufty (2007; hereafter referred to as GHD). The overall aim of the current work is to determine the suitability of the GHD theory to predict the flow behavior of a continuous size distribution of solids. In particular, the objective of this effort is twofold: (i) to determine the number of discrete species required to accurately approximate a continuous PSD, and (ii) to validate these results via a comparison with molecular dynamics (MD) simulations for continuous PSDs. In both cases, the discrete approximation is determined by matching an increasing number of moments of the distributions as the value of s increases. Regarding (i), the number of discrete species needed for a desired level of accuracy is found via an evaluation of all scalar transport coefficients for increasing values of s. This process was carried out for a variety of Gaussian and lognormal PSDs, as well as an experimental bimodal PSD supplied by Department of Energy (DOE NETL). With regards to (ii), a comparison between MD simulations (Dahl, Clelland and Hrenya, 2003) and GHD predictions of granular pressure and shear viscosity for a simple shear flow is conducted. The results indicate that wider continuous PSDs require a larger number of particle species for a given level of accuracy, whereas the effect of overall solids fraction and restitution coefficient is less pronounced. Also, the GHD predictions match the MD data quite well (on par with monodisperse predictions) for the values of s determined above.

References:

Dahl, S., R. Clelland and C. Hrenya (2003). "Three-dimensional, rapid shear flow of particles with continuous size distributions." Powder Technology 138(1): 7-12.

Garzó, V., J. W. Dufty and C. M. Hrenya (2007). "Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport." Physical Review E 76(3): 031303.

Garzó, V., C. M. Hrenya and J. W. Dufty (2007). "Enskog theory for polydisperse granular mixtures. II. Sonine polynomial approximation." Physical Review E 76(3): 031304.