(70d) Structured Flow in Gas-Solid Fluidized Beds: Particle Clustering and Bubble Self-Organisation

Fluidized beds are widely used to put in contact solid and gas phases in a variety of industrial processes. The interaction force between the gas and the suspended solids and the energy dissipated in particle collisions originate complex flow features that are dependent on the solids properties e.g. spouting, channelling, jetting or bubbling. Despite the advance in design and control, multi-phase flow models still struggle to describe many of these structures and scale up requires from a significant amount of historical practice and experimentation. The performance of a bubbling fluidized bed for instance is heavily reliant on a good level of mixing, associated to the observed solid circulation and the bubble characteristics e.g. size, velocity. From a fundamental perspective, the formation of bubbles can be explained by the instability of the coupled momentum equations or any similar phenomenological model used to study the bed response and the pressure fluctuations associated to nucleation, coalescence and rupture. While this type of analysis allows the formulation of a theoretical framework [1], important effects such as particle polydispersity, segregation, particle inertia and shape remain poorly understood. Furthermore, hydrodynamic models leave open questions regarding the behaviour of dense granular systems where multiple particle contacts and local anisotropy become important in the transport of momentum [2]. This constitutes the general pitfall of numerical frameworks based in the kinetic theory of granular flow. While they remain the only alternative to support the design of full scale units, most kinetic models rely on a microscale description of particle interactions that is inconsistent with the complex granular rheology of granular media in the dense and quasi-static regimes [3].

Allowing for more degrees of freedom at the design stage is a promising way to introduce a higher level of control in the operation of bubbling fluidized beds. In recent years, several alternatives have been put forward to manipulate the time and spatial scales of particle and particle-fluid interactions at a micro- and mesoscale in order to render a more reproducible flow structure in the macroscopic system. In addition to other methods based in modifying the spatial distribution of forces in the bed e.g. particle-particle applying electric fields or particle-fluid using fractal injectors [4], the pulsation of the inlet gas has been identified as a promising candidate to structure the flow in bubbling beds. Pulsating the gas flow introduces a temporal dynamic in the drag force that can supress the natural instability of the gas-solid flow system. Ripples in sandy beaches or dunes in deserts are good examples of dynamic granular structures that emerge as a response to a periodic perturbation in the flow around them, e.g., tides and waves, wind gusts and eddies. Transferring the same principle into the operation of quasi-2D fluidised bed, we have demonstrated that under certain conditions it is possible for gas bubbles to reorganise into a regular pattern that propagates throughout the bed into an stable large scale flow structure [5]. Under these operating conditions one has a much tighter control over the resulting bubble size, velocity and separation, thus opening the way for an entirely new concept in unit control and design.

This contribution investigates how dynamic bubble flows emerge in the fluidization of Geldart B particles under a pulsed airflow. At certain conditions, bubbles rearrange into a triangular tessellation with a narrow bubble size and wavelength distribution, independent of the bed width. We discuss the role that the dissipation of energy through friction plays in the bubble nucleation mechanism and how the local changes in rheology can stabilise the bubble pattern. We report a series of experimental data in quasi-2D pulsating beds along numerical studies under different airflow conditions, inter-particle friction factors and bed dimensions. The transition from the formation of a surface waves in a shallow layer to the nucleation of bubbles in thicker beds is related to the analysis of large clustered regions appearing in the wake and around pairs of rising bubbles. A comparison between continuous and discrete numerical formulations given by Eulerian-Eulerian (TFM) and Eulerian-Lagrangian (CFD-DEM) frames is used to showcase the limitations of classical kinetic and rheology models in predicting the behaviour of the granular flow in a dense and plastic regime. The inherent difficulty of a kinetic model to deal with correlated particle velocities and the resulting anisotropic distribution of contacts can explain why the common closures for the solid stress fail to capture how bubble self-organise under dense conditions[5]. The explicit solution of the rheology through an Eulerian-Lagrangian frame however succeeds in tracking the local changes in granular rheology and is shown to reproduce the observed bubble dynamics [6].

References

[1] Batchelor G.K. (1993). Secondary instability of a gas-fluidized bed, J. Fluid Mech. 251, 359-311.

[2] Chialvo S., Sun J., Sundaresan S. (2012). Bridging the rheology of granular flows in three regimes Physical Review E 85, 021305 1-8.

[3] Chialvo S., Sundaresan S. (2013) A modified kinetic theory for frictional granular flows in dense and dilute regimes. Physics of Fluids 25, 070603.

[4] Coppens M-O, Ommen J.R, (2003). Structuring chaotic fluidized beds, Chem. Eng. J. 96 117-124.

[5] Wu K, De Martin L., Mazzei L., Coppens M-O. (2016). Pattern formation in fluidized beds as a tool for model validation: A two-fluid model based study. Powder Tech., 295, 35-42

[6] Wu K, De Martin L., Coppens M-O. Pattern formation in pulsed gas-solid fluidized beds – The role of granular solid mechanics. Chemical Engineering Journal (2017). In Press. https://doi.org/10.1016/j.cej.2017.05.152