Notes on the Onset of Clustering in Gas-Solid HCS.

This study contributes to the body of work on instabilities in the homogeneous cooling system focusing on clustering in the multiphase gas-particle system. The critical system size for the onset of instability, $L^*_c$, is studied via three different numerical methods: i) particle resolved direct numerical simulation; ii) computational fluid dynamics-discrete element method; and iii) a two-fluid model derived from kinetic theory. In general, the $L^*_c$ results at several concentrations, inelasticities and initial thermal Reynolds numbers are in good qualitative agreement with one another. Additionally, most of the expected trends (i.e., general $L^*_c (\phi)$ behavior) are observed. However, there is a larger level of quantitative discrepancy between the continuum and discrete particle methods than observed previous (simpler) granular results. While the level of agreement may be expected to decrease with the increased physical complexity of the gas-solid system, a significant time-dependence is revealed and shown to be responsible for some of the oddities in the numerical data.