D.V. Vuković

Variational model for prediction of the fluid-particle interphase drag coefficient and particulate expansion of fluidized and sedimenting beds

Abstract An equation for prediction of the fluid-particle interphase drag coefficient in particulately fluidized and sedimenting beds is derived and experimentally verified. This equation is obtained by modeling the dimensionless drag coefficient-voidage relationship in a bed in which the superficial fluid velocity varies from minimum fluidization to terminal as a single constraint isoperimetric problem of the calculus of variations. The solution contains a single dimensionless parameter, U mF 2 / U 2 t ϵ mF 3 , and no adjustable constants. An equation for the superficial velocity-voidage relationship in the bed is also derived and experimentally verified. Fluidization and sedimentation experiments were conducted using water and spherical glass particles 1.20, 1.94 and 2.98 mm in diameter in columns 36, 40 and 50 mm in diameter to verify the model. Both the drag coefficient and velocity for voidages varying from minimum fluidization to 0.96 are predicted extremely well. Several empirical equations are shown to give limited descriptions of the data when considered over the whole range of voidages from minimum fluidization to terminal.

The effective buoyancy and drag on spheres in a water-fluidized bed

We are concerned with measurements of the effective buoyancy and fluid-dynamic drag on large particles of varying density settling or rising in a water-fluidized bed of monodisperse spheres of smaller size

Effect of particle diameter, particle density and loading ratio on the effective drag coefficient in steady turbulent gas-solids transport

Abstract Extending earlier work [1], effective drag coefficients for particles in steady turbulent gas-solids transport in a 28.45 mm vertical transport pipe 5.49 m long have been determined for 1 and 2 mm glass spheres and 1.99 mm rapeseed. The data are well represented by the equation C dn = 4 3 ∈Ar Re p 2 so that in the range studied, Cdn increases proportionally with dp and (ϱ p −ϱ f ) ϱ f and is essentially independent of loading ratio. Slip Reynolds numbers ranged from 469 to 1847 and pipe Reynolds numbers from 21400 to 33600. Loading ratios were varied from 7.03 to 45.4. The data reported here for Cdn fall below the standard drag curve as the slip velocity is increased due to the effects of freestream turbulence. The effect of neglecting particle-wall friction in our two-fluid model on the calculation of the solids fraction, slip velocity and drag coefficient is discussed.

Mass transfer between fluid and immersed surfaces in liquid fluidized beds of coarse spherical inert particles

Mass transfer coefficients between fluid and immersed surfaces in liquid fluidized beds of spherical inert particles have been studied experimentally using fluidization columns 40 mm and 70 mm in diameter. Mass transfer data were obtained in three experimental systems: i) transfer of methylene blue dye from very dilute aqueous methylene blue solution as the fluidizing fluid to plane solid surfaces using the adsorption method [Koncar-Djurdjevic, Nature, 172 (1953) 858]; ii) transfer of benzoic acid from a large spherical particle to flowing water using the dissolution method, and iii) transfer of benzoic acid from a plane solid surface to flowing water also using the dissolution method. In all runs mass transfer rates were determined in the presence of inert fluidized particles 1.20, 1.94 and 2.98 mm in diameter. Measurements covered a particle range having Reynolds number from 15 to 400, and two Schmidt numbers (20 °C), 1361 and 1932. Experimental data are correlated by the widely used formula jD=0.261 Ga0.324Rep−0.97 (jD = mass transfer number; Ga = Galileo number; Rep = Reynolds number). The data show that an analogy exists between the mass transfer factor and fluid–particle interphase drag coefficient, since both quantities vary with voidage in a similar way. The normalized mass transfer factor in liquid–phase fluidized beds of active or inert particles and the dimensionless drag coefficient are shown to be the same. Experimental data agree reasonably well with the proposed model.

An axisymmetric model for fluid flow in the annulus of a spout-fluid bed

Abstract The axisymmetric model previously developed for spouted beds is adapted to describe fluid flow in the annulus of a spout-fluid bed at the minimum spout-fluid flow rate. Experimental axial pressure profiles provide the boundary condition at the spout-annulus interface. The fluid streamlines, residence time distribution, average residence time, average axial fluid velocity in the annulus and the fluid flow rate entering the annulus from the spout are all calculated. The fluid streamlines in spout-fluid beds are shown to be very different from those of spouted beds in the lower part of the annulus. Although the residence time distribution of the fluid percolating through the annulus of a spout-fluid bed is more uniform than that of a spouted bed, the average residence time does not vary significantly with the inlet fluid flow to the annulus.

Mass transfer in liquid spout—fluid beds of ion exchange resin☆

Abstract Experiments were carried out to determine the liquid side mass transfer coefficient in spout-fluid beds of ion exchange resin. The ratio (Sh S—F ) overall /Sh fluidized is correlated with the ratio of the flow rate through the nozzle to the total flow rate for different experimental conditions. A method for the calculation of the initial conversion in a spout—fluid bed is given and a model of a spout—fluid bed ion exchanger involving liquid flow pattern is proposed. Particle motion in the annulus was measured. The model is based on the assumption of film diffusion control. Experimental results obtained in the study of the conversion of ion exchange resin “Amberlite IR-120” in Na + form and diluted hydrochloric acid in a spout—fluid bed are in agreement with theoretical predictions.