Zeljko Grbavcic

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.

Modeling and measurement of the effective drag coefficient in decelerating and non-accelerating turbulent gas—solids dilute phase flow of large parti

Abstract The one-dimensional modeling of decelerating and non-accelerating turbulent dilute phase flow has been studied by transporting 1 mm glass spheres with

Determination of non-spherical particle terminal velocity using particulate expansion data

Abstract A new method is proposed for the determination of the terminal velocity of non-spherical particles and compared with experimental data. The method is based on particulate expansion data of fluidized bed and variational model for calculating fluid–particle interphase drag coefficient. Other methods require knowledge of the particle shape, a parameter that is not easy to obtain for real materials. We use pressure drops data in packed bed for indirect determination of particle shape factor which depends on the reliability of coefficients in the Ergun equation. Our data, however, show that these coefficients are system-specific. The proposed method for the determination of non-spherical particle settling velocity in liquid as well as extrapolation to system gas-particles gives results which are in good agreement with experimental data. The method is restricted to particles which can be fluidized particulately by liquid.

Drying of Slurries in Fluidized Bed of Inert Particles

Abstract A fluid bed dryer with inert particles was used for drying of slurries. Experiments were performed in a cylindrical column 215 mm in diameter and 1200 mm in height with glass spheres as inert particles. Slurries of Zineb fungicide, copper hydroxide, calcium carbonate, and pure water were used as the feed material. The effects of operating conditions on dryer throughput and product quality were investigated. Main performance criteria, i.e., specific water evaporation rate, specific heat consumption, and specific air consumption, were quantified. Temperature profile along the bed was mapped, and nearly isothermal conditions were found due to thorough mixing of the particles. The material hold-up and residence time were determined. Simple heat and mass balances predict the dryer performance quite well.

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.

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.

Ethylene oxide removal in combined sorbent/catalyst system

The investigation of ethylene oxide (EtO) catalytic incineration over Pt/Al 2 O 3 catalyst conducted in fixed bed reactor (diameter of 315 mm) showed that significant degree of EtO adsorption occurred when the inlet gas temperature was lower than ignition temperature (180°C). This observation was a basis for the development of a hybrid reactor for EtO removal using modified spouted bed with draft tube loaded with Pt/Al 2 O 3 catalyst. The annular region of the bed was divided in two sections, the hot (reaction) section contained about 7% of catalyst and it behaved as a catalytic incinerator, while the cold (sorption) section, with the rest of the catalyst, behaved as an sorber. The catalyst particles recirculated between two sections by using a draft tube riser. To formulate the process parameters dynamics of EtO sorption on Pt/Al 2 O 3 catalyst and Al 2 O 3 support were studied. The proposed system for EtO removal gives the same efficiency as the fixed bed catalytic converter. The experimental data show that process is attractive for low EtO concentrations, because it enables significant energy savings. At steady state conditions temperature in the sorption section of 80-100°C was maintained. In the reaction section initial heating to the temperature of 200°C is sufficient to start up selfsustained deep EtO oxidation.

Experimental investigation of heat transfer in three phase fluidized bed cooling column

In this study, a three-phase (gas-liquid-solid) fluidized bed was used to study the heat transfer characteristics of the system. The system consisted of low density (290 kg/m3) spherical particles of the diameter of 2 cm in 0.25 m cylindrical column with the countercurrent flow of water and air. The experimental investigation and mathematical modeling of heat transfer between the hot air and the cooling water was carried out. The experiments were conducted for the variety of different fluid flow rates and inlet air temperatures, while the air flow rate was kept constant. Based on the obtained experimental results a new correlation for heat transfer in three-phase fluidized system was proposed. The mean percentage error between the experimental and the correlated values of the jHp obtained was 1.69%. The hydrodynamic parameters of the system were also calculated according to the available literature correlations. [Projekat Ministarstva nauke Republike Srbije, br. ON172022]

Prevention and control of dimethylamine vapors emission: Herbicide production plant

The widely used herbicide, dimethylamine salt of 2,4-dichlorophenoxy acetic acid (2,4-D-DMA), is usually prepared by mixing a dimethylamine (DMA) aqueous solution with a solid 2,4-dichlorophenoxy acetic acid (2,4-D). The vapors of the both, reactants and products, are potentially hazardous for the environment. The contribution of DMA vapors in overall pollution from this process is most significant, concerning vapor pressures data of these pollutants. Therefore, the control of the air pollution in the manufacture and handling of methylamines is very important. Within this paper, the optimal air pollution control system in preparation of 2,4-D-DMA was developed for the pesticides manufacturing industry. This study employed the simple pollution prevention concept to reduce the emission of DMA vapors at the source. The investigations were performed on the pilot plant scale. To reduce the emission of DMA vapors, the effluent gases from the herbicide preparation zone were passed through the packed bed scrubber (water scrubbing medium), and the catalytic reactor in sequence. The end result is a substantially improved air quality in the working area, as well as in the urbanized areas located near the chemical plant.