Hydrodynamic equivalent diameter for clusters in heterogeneous gas–solid flow

Abstract

This paper is devoted to establishing a simple correlation calculating the equivalent diameter of clusters in gas–solid flow. Three different kinds of cluster sizes were distinguished in accordance with the measuring techniques: (1) vertical length measured with optical fiber or capacitance probes; (2) cross-sectional size determined with image analysis of graphs taken by video camera or other suitable detection systems; and (3) hydrodynamic equivalent diameter of clusters derived from differential pressure drop (solid concentration) via appropriate fluid dynamic models. The hydrodynamic equivalent cluster diameter correlated in hydrodynamic modeling was generalized as the diameter of spheres (uniform in size) having the same total volume as actual clusters (not a single cluster), which is subject to hydrodynamic equations, such as force balance, for clusters. It was demonstrated that hydrodynamic equivalent cluster diameter is close to cross-sectional size, but much less than vertical length of clusters experimentally measured. The correlation reported in Xu and Li (1998) (Chem. Engng Sci., vol. 63, p. 1349) was found to be capable of predicting hydrodynamic equivalent cluster diameters of heterogeneous gas–solid systems for both Geldart A and Geldart B particles, which was then further simplified for facilitating its practical use.