Franco Grisafi

Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modelling approaches

Abstract Numerical simulations of the flow field in baffled mixing tanks, based on three alternative methods, are presented and discussed. In the first method, the impeller is not explicitly simulated, and its effects are modelled by imposing suitable, empirically derived, boundary conditions to the external flow. In the second method, the whole vessel volume is divided into two concentric, partially overlapping, regions. In the inner region, containing the impeller, the flow field is simulated in the rotating reference frame of the latter, while in the outer region simulations are conducted in the reference frame of the laboratory. Information is iteratively exchanged between the two regions after azimuthally averaging and transforming for the relative motion. In the third method, the tank volume is divided into two concentric blocks, the inner one rotating with the impeller and the outer one stationary. The two blocks do not overlap and are coupled by a sliding-mesh technique. Predictions are presented here for baffled tanks stirred either by single and dual Rushton turbines (radial impellers) or by a constant-pitch helical impeller (axial impeller), and are compared with experimental data from the literature. Satisfactory results can be obtained by the first method only if reliable empirical data are available for the flow near the impeller, while large errors may arise if this is not known with reasonable accuracy. The other two methods both yield satisfactory results while requiring no empirical information, and thus allow a much greater generality.

Particle drag coefficients in turbulent fluids

Abstract An accurate estimation of particle settling velocities, and/or of particle drag coefficients, is required for modelling purposes in many industrially important multiphase processes involving the suspension of millimetre and sub-millimetre size particles in a liquid phase. It is known that the settling velocity of particles in a turbulent fluid may be significantly different from that in the still fluid, depending on turbulence and particle characteristics. Despite the wide range of processes that would benefit from a thorough understanding of this phenomenon, experimental data and reliable correlations are still lacking in the scientific literature, especially for the case of the above-mentioned intermediate size particles. This is probably due to the difficulties involved in the relevant experimentation. In this work, a new experimental technique for measuring average particle drag coefficients in turbulent media is presented. It is based on a direct measurement, by means of a suitable residence time technique, of the settling velocity exhibited by a cloud of particles. The experimental data obtained in a Couette–Taylor flow field are presented and discussed. These data confirm that free stream turbulence may significantly increase particle drag coefficients. At the highest turbulence intensities, drag coefficients more than 40 times greater than corresponding ones in the still fluid, were observed. A new correlation for the prediction of the influence of free stream turbulence on the drag coefficients of intermediate size particles is also proposed.

Turbulent flow in closed and free-surface unbaffled tanks stirred by radial impellers

The three-dimensional turbulent flow field in unbaffled tanks stirred by radial impellers was numerically simulated by a finite-volume method on body-fitted, co-located grids. Simulations were run, with no recourse to empirical input, in the rotating reference frame of the impeller. Free-surface problems were also simulated, in which the profile of the central vortex was computed as part of the solution by means of an iterative technique. Predicted velocity and turbulence fields in the whole vessel and power consumptions were assessed against available literature data; free-surface profiles were also compared with original experimental data obtained in a model tank. Both the eddy-viscosity k−e turbulence model and a second-order differential stress (DS) model were used and compared: satisfactory results were obtained only by using the latter model. The need for including source terms arising from fluctuating Coriolis forces in the Reynolds stress transport equations is highlighted.

CFD Simulation of Particle Distribution in Stirred Vessels

In this work the particle concentration distribution in two-phase stirred tanks is simulated on the basis of information on the three-dimensional flow field, as obtained by numerical solution of the flow equations (CFD) using the well known k –ɛ « turbulence model. Two modelling approaches are attempted. In the simpler method the flow field is first simulated neglecting the influence of the solid phase; on the basis of the resulting flow field a very simple sedimentation model is employed for solving the solids mass balance equations in order to compute the particle concentration field. In this case no inertial effects on the solid particles are considered, so that the convective and diffusional exchanges for the solid phase are assumed to coincide with those for the liquid phase. In the more advanced approach the momentum balance equations for both the solid and liquid phases are simultaneously solved. Experimental data on the axial profiles of particle concentration have been obtained in a laboratory scale agitated tank. The experimental technique utilized is non intrusive being based on light attenuation measurements and is also able to provide information at high particle concentrations. The comparison of experimental data with simulation results is satisfactory with both simulation approaches. Differences between the two approaches concerning their accuracy and computational effort are discussed. The need to make a suitable estimate of the particle drag coefficients in turbulent fluid media is emphasized.

On the simulation of stirred tank reactors via computational fluid dynamics

Abstract Predictions of flow fields in a stirred tank reactor, obtained by computational fluid dynamics, were used for the simulation of a mixing sensitive process consisting of two parallel reactions competing for a common reagent: A + B → Prod .1 A + C → Prod .2. Experimental data were obtained for A = OH − , B = 1 2 Cu ++ and C=ethyl-chloroacetate. For this reaction scheme the final selectivity of the process, easily measured by a simple colorimetric analysis of the residual Cu++, was found to depend on agitation speed and therefore on the mixing history during the batch process. The flow field-based three-dimensional simulations performed here led to predictions that compared very well with the experimental data, though no adjustable parameters were used. Interestingly, these encouraging results were obtained by modelling only the “macromixing” phenomenon, while “micromixing” phenomena were neglected, i.e. the system was always considered as being locally perfectly micro-mixed. The good agreement found between simulation predictions and experimental data retrospectively confirms the negligibility of micromixing phenomena in the system investigated.

Assessment of Particle Suspension Conditions in Stirred Vessels by Means of Pressure Gauge Technique

In this work the quantitative assessment of the mass of suspended solid particles in stirred vessels is performed using the Pressure Gauge Technique. This is based on the measurements of the pressure increase on the tank bottom due to the presence of suspended solid particles at any agitation speed. The method has the advantages of not utilising visual observations and of easy and inexpensive application to both laboratory and industrial equipment. Very few data are available in literature and the experimental results collected using the present PGT technique and the correlations here proposed are of considerable academic and industrial interest.

Modeling and simulation of dense cloud dispersion in urban areas by means of computational fluid dynamics

The formation of toxic heavy clouds as a result of sudden accidental releases from mobile containers, such as road tankers or railway tank cars, may occur inside urban areas so the problem arises of their consequences evaluation. Due to the semi-confined nature of the dispersion site simplified models may often be inappropriate. As an alternative, computational fluid dynamics (CFD) has the potential to provide realistic simulations even for geometrically complex scenarios since the heavy gas dispersion process is described by basic conservation equations with a reduced number of approximations. In the present work a commercial general purpose CFD code (CFX 4.4 by Ansys(®)) is employed for the simulation of dense cloud dispersion in urban areas. The simulation strategy proposed involves a stationary pre-release flow field simulation followed by a dynamic after-release flow and concentration field simulations. In order to try a generalization of results, the computational domain is modeled as a simple network of straight roads with regularly distributed blocks mimicking the buildings. Results show that the presence of buildings lower concentration maxima and enlarge the side spread of the cloud. Dispersion dynamics is also found to be strongly affected by the quantity of heavy-gas released.

Gas-liquid-solid Operation of a High Aspect Ratio Self-ingesting Reactor

Gas-liquid stirred vessels are widely employed to carry out chemical reactions involving a gas reagent and a liquid phase. The usual way for introducing the gas stream into the liquid phase is through suitable distributors placed below the impeller. An interesting alternative is that of using “self ingesting” vessels where the headspace gas phase is injected and dispersed into the vessel through suitable surface vortices. In this work the performance of a Long Draft Tube Self-ingesting Reactor (LDTSR) dealing with three-phase (gas-liquid-solid) systems, is investigated. Preliminary experimental results on the effectiveness of this contactor for particle suspension and gas-liquid mass transfer performance in the three-phase system, are presented. Mass-transfer parameter kLa was measured by the recently introduced Simplified Dynamic Pressure Method (SDPM). It is found that the presence of low particle fractions causes a significant increase of the minimum speed required for vortex ingestion of the gas. Impeller pumping capacity and gas-liquid mass transfer coefficient are found to be affected by the presence of solid particles.

Solids Suspension in Three-Phase Stirred Tanks

The ‘pressure gauge technique’ recently developed for the quantitative assessment of the mass of solid particles suspended at any agitation speed is extended to the case of three-phase stirred tanks. As a result, curves of the fraction of suspended solids at various gas flow rates, versus agitator speed, are presented. The difficulties involved in the extension of the technique to three phase systems are addressed and discussed. The experimental results show that the presence of the gas phase causes a significant increase of the agitation speed required to attain complete suspension of solids and lowers the degree of suspension at all agitation speeds below it. The experimental data obtained are shown to be well fitted by the Weibull functions previously adopted for two-phase systems. Correlations for the estimation of the influence of particle size, particle concentration and gas flow rate on the suspension degree are presented and discussed. Finally, the fractional suspension dependence on particle size is found to be very different when very large particles are dealt with.

Characterization of pressure retarded osmosis lab-scale systems

AbstractPower generation from salinity gradient is a viable alternative to produce energy from renewable sources. Pressure Retarded Osmosis (PRO) is one of the technologies proposed so far for the exploitation of such energy source. In the present preliminary work, two different geometry modules were tested under atmospheric pressure (i.e. forward osmosis or depressurized-PRO conditions). The first one is a conventional planar geometry cell. The second is a customized cylindrical membrane module, able to mechanically support the osmotic membrane along with the spacers. The latter, thanks to its design, allows membranes and spacers to be easily changed for testing purposes. A novel simplified procedure is proposed and employed in the planar geometry module to characterize an asymmetric membrane commercially available (i.e. assessing the water and salt permeability coefficients and the porous structure parameter). The parameters found were employed to mathematically estimate the permeate fluxes experimental...