(149b) Enhancing the Physical Picture of Particle Clustering Due to Mean-Flow Effects

Particle laden, gas-solid flows are prone to instabilities that manifest as either bubbles in dense regions, such as a fluidized bed, or as clusters in more dilute regions, such as a riser. One such source causing the clustering instability can be traced to the dissipation of granular temperature, as originally described by Goldhirsch and Zanetti (1993). Thanks in large part to the seminal work of Anderson and Jackson (1968), another source is known to exist â?? independent of the first â?? due to (non-zero) mean relative motion between the gas and solid phases; this source that has been reaffirmed countless times by subsequent linear stability analyses and direct simulations of the continuum governing equations. Despite this large body of work, a clear, physical picture of the underlying mechanism causing the instability remains somewhat lacking. In this work, we take a complete two-fluid model, closed by kinetic theory, and begin by simplifying it drastically. By retaining only the essential components, we are able to show that clustering results from the interplay between a Kelvin-Helmholtz instability and a kinematic instability. For most practical cases, the Kelvin-Helmholtz mechanism is insufficient to produce instability alone, although it is responsible for decreasing the magnitude of the dynamic wave speed, making it easier to be exceeded by the kinematic wave speed â?? the root cause of the kinematic instability. This finding is reminiscent of previous work by Wallis (1969), who first suggested from simple physical arguments that gas-solid particulate instabilities were a type of kinematic instability, a position which was subsequently confirmed by Batchelor (1988) thorough linear stability analysis. Our focus here is adding to the physical interpretation for the causes of the clustering instability. In addition to mathematical interpretation, some numerical simulations will also be provided to aid the discussion.

References:

Anderson TB, Jackson R. (1968) Fluid Mechanical Description of Fluidized Beds - Stability of State of Uniform Fluidization. Industrial & Engineering Chemistry Fundamentals 7: 12-21.

Batchelor GK. (1988) A New Theory of the Instability of a Uniform Fluidized-Bed. Journal of Fluid Mechanics 193: 75-110

Goldhirsch I, Zanetti G. (1993) Clustering Instability in Dissipative Gases. Physical Review Letters 70: 1619-22.

Wallis GB. (1969) One-dimensional two-phase flow. New York, McGraw-Hill.