434900 Effect of Particle-to-Fluid Density Ratio on Stable-Unstable Transition in a Small-Scale Sedimentating Fluid-Solid System to Test the Limit of a Kinetic-Theory-Based Model

Tuesday, November 10, 2015: 5:15 PM
150A/B (Salt Palace Convention Center)
William Fullmer, Chemical and Biological Engineering, University of Colorado, Boulder, CO, Guodong Liu, School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, China, Xiaoqi Li, Petroleum Engineering Department, Colorado School of Mines, Golden, CO, Xiaolong Yin, Petroleum Engineering, Colorado School of Mines, Golden, CO and Christine M. Hrenya, Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO

Kinetic-theory-based continuum models for gas-solid two-phase flow have been known to qualitatively predict the clustering instability for over a decade. More recently, quantitative analyses have been conducted to assess the accuracy of such predictions by studying the critical length scale necessary for the onset of clustering in a granular (no fluid) system (Mitrano et al. 2014). A similar approach is taken here for fluid-solid systems to study the effect of the particle-to-fluid density ratio in an unbounded, small-scale sedimentation (or fluidization) system. The Archimedes number is held at 71 and the solid volume fraction is varied between 0.1 and 0.4. As we increase the density ratio from 5 to 1000, the system makes a gradual transition from liquid-solid to gas-solid, and a variety of behaviors are observed: near-homogeneous at low density ratios, highly dynamic/chaotic at intermediate density ratios, and limit cycles in the form of a traveling wave at high density ratios. In each case, the type of flow behavior has a significant impact on the mean properties of the system. The sedimenting Reynolds number, which uses the vertical component of the solid-phase velocity as the velocity scale, is compared to LBM-DNS data of the same system. The results are good to favorable over a majority of the parameter space. However, at low density ratios the comparisons are not as good. It is suggested that this failure stems from the collision-dominated assumption inherent in the kinetic-theory approach, i.e., lubrication forces have been neglected in the continuum model. This hypothesis is tested using a Stokes-number criterion based on the fluctuating velocity (granular temperature), which shows that the largest errors do indeed occur where the underlying assumptions of the kinetic-theory-based model break down.

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