F. Magelli

Experiments and CFD Predictions of Solid Particle Distribution in a Vessel Agitated with Four Pitched Blade Turbines

The distribution of solid particles in a high aspect-ratio baffled tank agitated with four 45° pitched blade turbines (PBT) was investigated using both experimental measurements and CFD simulations. Dilute suspensions of glass beads in water and moderately viscous liquids were considered. The measurement of axial particle concentration profiles was conducted by means of a light attenuation technique. Fully predictive simulations of solid-liquid suspensions were performed using a Sliding-Grid approach coupled with the Eulerian-Eulerian Two Fluid Model and the ‘homogeneous’ two-phase k-ɛ turbulence model. The simulated particle axial concentration profiles were compared with the experimental data and good agreement was found.

Solid distribution in vessels stirred with multiple impellers

Abstract Solid distribution for solid—liquid suspensions was investigated under batch and semibatch conditions in completely closed tanks. The tanks had an aspect ratio equal to four and were stirred with multiple Rushton turbines. Spherical particles of different materials and sizes were used as the solid phase in various liquids. Average solid concentrations along the vertical axis of the tank were measured by means of an optical technique. The solid profiles can be fairly well modelled with the one-dimensional sedimentation-dispersion model. A correlation of the solid Peclet number with dimensionless groups that include physical and operating parameters was obtained for batch conditions. A procedure to apply the model also in the case of semibatch conditions was checked. The results also give additional evidence of the reduction of the settling velocities of solid particles in a stirred medium with respect to that in a quiescent liquid—at least for some operating conditions. The interaction between the particles and the turbulence field is proposed as a means to explain this behaviour.

CFD prediction of fluid flow and mixing in stirred tanks: Numerical issues about the RANS simulations

Abstract This work is aimed at verifying the effect of numerical issues on the RANS-based predictions of single phase stirred tanks. In particular, the effect of grid size and discretization schemes on global parameters, mean velocity, turbulent dissipation rate and homogenization is considered. Although contradictory results have been reported so far on the capability of RANS methods in fluid mixing, the most widely accepted conclusion is that adequate values are generally to be expected for the predicted mean flow quantities, while much less confidence must be put on the calculated turbulent quantities and related phenomena. The results obtained in this work partially revise this last statement and demonstrate that firm conclusions on the limits of RANS simulations can be drawn only after careful verification of numerical uncertainties. The simulation results are discussed and compared to the literature experimental data and to original passive tracer homogenization curves determined with planar laser induced fluorescence.

Modelling of solids distribution in stirred tanks: analysis of simulation strategies and comparison with experimental data

The predictive capabilities of CFD techniques as applied to solid–liquid stirred vessels are investigated. The distribution of solid particles was simulated in three baffled stirred tanks agitated with single and multiple impellers. Suspensions of glass beads of different diameters and average concentration up to 6 vol. % in water were studied. The simulations of solid–liquid suspensions in the stirred vessels were performed by using fully predictive approaches. Eulerian multiphase models were adopted for modelling the solid–liquid flow, coupled with three different extensions of the standard k-ϵ model to the case of multiphase flows. The simulated particle axial concentration profiles are compared with experimental data and critically discussed. The most successful simulation strategy and one possible implementation are described.

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

Abstract The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.

A fluid-dynamic study of a gas—liquid, non-standard vessel stirred by multiple impellers

Abstract The fluid-dynamic behaviour of a non-standard vessel working with air—water dispersions and stirred by means of multiple impellers was investigated. The study concerned the overall behaviour of the system as well as holdup and power consumption measurements. The overall behaviour can be modelled as a cascade of ideal stages with back-mixing; in the experimental range investigated the back-flow rate can be considered as independent of the presence of the dispersed gas phase. Holdup values are substantially the same as for the single impeller configuration; the applicability of published correlations for holdup prediction is discussed. The interpretation of power measurements confirms previous findings that power is unevenly consumed by the different turbines.

Production of l(+) and d(−) lactic acid isomers by Lactobacillus casei subsp. casei DSM 20011 and Lactobacillus coryniformis subsp. torquens DSM 20004 in continuous fermentation

Abstract With the aim of producing l (+) and d (−) lactic acid to be employed in poly-lactic acid polymer production, for biomedical applications, the strains Lactobacillus casei subsp. casei DSM 20011 and Lactobacillus coryniformis subsp. torquens DSM 20004 were studied in a conventional chemostat mode using various dilution rates. The results obtained showed that the dilution rate influences the fermentation pattern, modifying various fermentation parameters. Nevertheless, the product and biomass yields remained constant and the ratio of the l (+) and d (−) isomers of lactic acid was not affected by the dilution rate. The optimal glucose concentration on inlet feed medium was also determined for the L. coryniformis fermentation.

MODELLING OF NON-STANDARD MIXERS STIRRED WITH MULTIPLE IMPELLERS†

Little attention has so far been devoted to characterizing fluid-dynamic behaviour of multiple-impeller mixers which are often implicitly modelled as perfectly stirred tanks. In the present paper a study is made of this type of equipment—stirred with four turbines; either six- or four-flat-blade disc turbines were used. Mean local concentration inside the mixers was measured and experimental pulse-response curves were compared with the theoretical curves corresponding to two one-parameter models (i.e., a cascade of ideal stages with backmixing and one-dimensional diffusion model) and to perfect mixing. The results of both analyses show that both the one-parameter models considered represent the actual fluid-dynamic behaviour quite satisfactorily and the model of perfect mixing can be considered only as a first approach for macromixing modelling purposes. Extensive investigation was then carried out in order to determine the dependence of the characteristic parameter of the stagewise model on operating con...

Some features of a novel gas dispersion impeller in a dual-impeller configuration

The performance of the concave blade BT-6 impeller was evaluated in a dual-impeller agitated tank (T= 0.48m, H/T=2). Power draw was measured and almost constant Pg/Pu ratio with aeration was found in agreement with what had been reported previously. Gas hold-up exhibited the same dependence on power per unit volume and superficial velocity as shown by other types of impellers. The same holds true for the volumetric mass transfer coefficients. Mixing time was measured at several vertical positions in the tank, after a pulse of an electrolytic tracer or a dye was introduced. No significant compartmentalization was apparent. Mixing time at a given specific power input under ungassed and gassed conditions is in between that of standard radial turbines and hydrofoil axial impellers, very close to the latter. Mixing time dependence on power consumption per unit volume exhibits –1/3 law, i.e. the same as reported in the literature for other impeller types. The experimental curves from which mixing time was determined were also analysed in terms of the axial dispersion model, that proved satisfactory to interpret the behaviour of dual BT-6 impellers under both ungassed and gassed conditions.

Solids concentration distribution in slurry reactors stirred with multiple axial impellers

Abstract The solids concentration distribution in solid—liquid suspensions in batch, mechanically stirred, vessels was investigated. The vessels were characterized by a high aspect ratio and were stirred with various combinations of multiple axial impellers. The suspensions were made of glass beads of various sizes in water and aqueous solutions of polyvinylpyrrolidone (PVP). The solids concentration was measured along the vertical axis of the vessel by means of an optical technique. The suspension efficiency of the impellers was compared on the basis of the departure of the solids concentration from suspension homogeneity (given as the variance of the solids concentration along the axis with respect to the mean) versus power consumption per unit mass. The solids concentration profiles were also modelled with the one-dimensional sedimentation—dispersion model having the Peclet number as a single adjustable parameter. For each geometrical configuration the Peclet number was correlated with the ratio of the tip speed to particle settling velocity and a Reynolds number based on the Kolmogorov theory. Once the difference in aspect ratio is taken into account, a single correlation for all the geometrical configurations could be obtained.