A drag force closure for uniformly dispersed fluidized suspensions

The present study is concerned with the problem of closure for the drag force with regard to fluidized suspensions of uniformly dispersed spherical particles. A new closure relationship, based on the empirical correlation by Richardson and Zaki [1954. Sedimentation and fluidization: Part I. Transactions of the Institution of Chemical Engineers 32, 35] is derived. The main distinctive feature of the equation advanced by the authors is its being consistent with the Richardson and Zaki correlation over the whole range of fluid dynamic regimes and for any value of the fluid volume fraction. This property, usually not met by the equations of closure currently used in multiphase fluid dynamics, is nonetheless essential when simulating the motion of fluidized suspensions as it ensures a more accurate prediction of the expansion profiles of homogeneous systems, a feature that indirectly reflects a better assessment of the drag force magnitude. The article contains a brief critical overview on some closure relationships commonly employed in most computational fluid dynamics commercial codes, more specifically those based on the work by Ergun [1952. Fluid flow through packed columns. Chemical Engineering Progress 48, 89], Di Felice [1994. The voidage function for fluid–particle interaction systems. Internation Journal of Multiphase Flow 20, 153], Kmiec [1982. Equilibrium of forces in a fluidized bed—experimental verification. Journal of Chemical Engineering 23, 133], Lewis et al. [1949. Characteristics of fluidized particles. Industrial and Engineering Chemistry 41, 1104] and Wen and Yu [1966. Mechanics of fluidization. Chemical Engineering Progress Symposium Series 62, 100]. Furthermore, to test the validity of the equation herein proposed, its predictions are compared with experimental data obtained for homogeneous assemblies of spherical particles reported in literature and based on the work by Happel and Epstein [1954. Viscous flow in multiparticle systems: cubical assemblages of uniform spheres. Industrial and Engineering Chemistry 46, 1187], Richardson and Zaki [1954. Sedimentation and fluidization: Part I. Transactions of the Institution of Chemical Engineers 32, 35], Rumpf and Gupte [1971. Einflüsse der porosität und korngrößenverteilung im widerstandsgesetz der porenströmung. Chemie Ingenieur Technik 43, 367] and Wilhelm and Kwauk [1948. Fluidization of solid particles. Chemical Engineering Progress 44, 201]. A good agreement is found between theoretical results and experimental values.