The generalized fluidization diagram was drawn by Kwauk [Scientia Sinica, 1963, 12 (4), 587–612] and Kwauk [Science Press, Beijing: 1992] for fluidization under steady-state motion. In this article, we try to extend the work of Kwauk and redraw the diagram by taking into account the effects of mesoscale structures on drag force closure. The generalized choking is then defined on the new diagram, which is characterized by the bistable, coexisting states in both concurrent and countercurrent flows. The theoretical predictions are tested against experimental data, showing fair agreement especially for countercurrent gas-up flows and concurrent-down flows.

A virtual experimentation combining computational fluid dynamics (CFD) and computed tomography (CT) simulations was presented to evaluate the beam hardening effect in the CT application to multiphase flow measurement. A semi-industrial scale circulating fluidized bed (CFB) reactor was simulated with a multiscale CFD approach, and its computed flow fields was taken as the dynamic phantom for CT. By this means, a 3rd generation X-ray CT with different filter parameters was simulated. Since the computed flow fields can be manipulated in detail and reproduced at will, this virtual approach enables quantitative evaluation of the beam hardening effect and helps establish the optimal filter parameters for CT measurement of multiphase flow.Graphical abstractA virtual experimentation combining computational fluid dynamics (CFD) and computed tomography (CT) simulations was presented to evaluate the beam hardening effect in the CT application to multiphase flow measurement. A semi-industrial scale circulating fluidized bed (CFB) reactor was simulated with a multiscale CFD approach, and its computed flow fields was taken as the dynamic phantom for CT scanning.

Meso-scale structure is of critical importance to circulating fluidized bed (CFB) applications. Computational fluid dynamics (CFD) with consideration of meso-scale structures can help understand the structure-oriented coupling between flow, heat/mass transfer and reactions. This article is to review our recent progress on the so-called multiscale CFD (MSCFD), which characterizes the sub-grid meso-scale structure with stability criteria in addition to conservation equations. It is found that the mesh-independent solution of fine-grid two-fluid model (TFM) without sub-grid structures is inexact, in the sense that it overestimates the drag coefficient and fails to capture the characteristic S-shaped axial profile of voidage in a CFB riser. By comparison, MSCFD approach in terms of EMMS/matrix seems to reach a mesh-independent solution of the sub-grid structure, and succeeds in predicting the axial profile and flow regime transitions. Further application of MSCFD finds that neglect of geometric factors is one of the major reasons that cause disputes in understanding the flow regime transitions in a CFB. The operating diagram should, accordingly, include geometric factors besides commonly believed operating parameters for the intrinsic flow regime diagram. Recent extension of MSCFD to mass transfer finds that Reynolds number is insufficient for correlating the overall Sherwood number in a CFB. This is believed the main reason why the conventional correlations of Sherwood number scatter by several orders of magnitude. Certain jump change of state of motion around Reynolds number of 50–100 can be expected to clarify the abrupt decay of Sherwood number in both classical- and circulating-fluidized beds. Finally, we expect that the real-size, 3-D, full-loop, time-dependent multiscale simulation of CFB is an emerging paradigm that will realize virtual experiment of CFBs.

An EMMS/bubbling model for gas–solid bubbling fluidized bed was proposed based on the energy-minimization multi-scale (EMMS) method (Li and Kwauk, 1994). In this new model, the meso-scale structure was characterized with bubbles in place of clusters of the original EMMS method. Accordingly, the bubbling fluidized bed was resolved into the suspending and the energy-dissipation sub-systems over three sub-phases, i.e., the emulsion phase, the bubble phase and their inter-phase in-between. A stability condition of minimization of the energy consumption for suspending particles (Ns→min) was proposed, to close the hydrodynamic equations on these sub-phases. This bubble-based EMMS model has been validated and found in agreement with experimental data available in literature. Further, the unsteady-state version of the model was used to calculate the drag coefficient for two-fluid model (TFM). It was found that TFM simulation with EMMS/bubbling drag coefficient allows using coarser grid than that with homogeneous drag coefficient, resulting in both good predictability and scalability.Highlights► The cluster-based EMMS model was extended to a bubble-based version. ► The new model can be applied to bubbling and turbulent fluidization regime. ► The model allows using much coarser grid than the conventional two-fluid model.