(215c) Cluster Instabilities in Gas-Solid Flows Using Direct Numerical Simulation and Two-Fluid Model: Quantifying the Mean Sedimentation Velocity and Particle Velocity Fluctuations
Sedimentation velocities from DNS are compared with existing drag correlations [1-3]. DNS sedimentation velocities are significantly influenced by the clustering instability, and appear to decrease with increasing density ratio as a result of clustering. The influences of the parameters on the instability and the sedimentation velocity are reported. Velocity fluctuations in horizontal and vertical directions are largely driven by the motion of the clusters and depend significantly on the particle-fluid density ratio and the mean flow Stokes number. Vertical fluctuations coming from particle clusters characterized by non-dimensional variance are low when Stokes numbers are medium and high. Under most situations, whether the collisions are elastic or inelastic (normal restitution coefficient = 0.9) did not generate significant difference in the mean sedimentation velocity and variance.
Sedimentation velocities and particle velocity fluctuations are also compared to results from continuum simulations using a recently developed kinetic-theory-based TFM . In general, the KT-TFM results agree both qualitatively and quantitatively with the DNS data. Two significant deviations are observed, however. At intermediate mean flow Stokes numbers, the KT-TFM has a tendency to over-predict the degree of fluctuations which, in turn, leads to over-prediction of the mean sedimenting velocity. It is believed that this behavior stems from an over-prediction in the degree of segregation and studies are currently underway to either verify or refute this hypothesis. At the lowest mean flow Stokes numbers the KT-TFM becomes essentially uniform, i.e., clustering vanishes. Consequently, the KT-TFM fails to capture the departure from homogeneous velocities (mean and fluctuating) observed in the DNS data. This breakdown has been determined to stem from a violation of one of the underlying assumptions of the KT derivation. In other words, it is not necessarily a failure of the model, but a failure to apply it within its range of validity. One of the most promising results of the comparison is the match in the anisotropy of the fluctuating particle velocity. The fluctuations in the streamwise (y-) dimension are always strongest, followed by the wide transverse (x-) dimension and finally the narrow transverse (z-) dimension, which is near the homogenous value. The KT-TFM is able to accurately capture these trends qualitatively and quantitatively where the theory is valid.
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