Zur Maßstabsübertragung beim Suspendieren im Rührgefäß

Scale-up of agitated vessels in the case of suspensions . In the scale-up of agitated vessels a decrease of specific power input ε is recommended in the case of suspensions. Up to now it has been assumed that turbulence is the reason for this decrease. This paper shows that there may also be a contribution due to decreasing wall areas causing less wall shear stresses and moreover a reduction of circulation due to lower cross-sectional areas per unit volume of the threads of flow. In the case of so-called ?complete suspension”? according to the ?1-s criterion”?, two mechanisms can be distinguished: On the one hand we have a lifting of solid particles without, and on the other hand such a lifting with formation of bulk accumulations of solids on the bottom of the vessel. In the first case, scale-up can be done as for a homogeneous distribution of the solid material. The specific power input ε is ～ μ⁰ up to ε ～ μ^?1 with the scale-up factor μ. In the second case (formation of dense solids clouds) a relationship ε ～ μ^m with m > 0 was found.     

Scaling-up rules for solids suspension in stirred vessels

Although extensively investigated, the scaling-up of stirred vessels with respect to solids suspension is still a difficult matter. In view of this we carried out a series of model suspension experiments in a large stirred vessel (4.3 m in diameter). Complete and homogeneous suspensions were studied and the tests were repeated carefully at the laboratory in a small-scale vessel under identical conditions. From a comparison of the results it became clear that the scaling criterion for complete suspension is a constant specific power input. Homogeneity of the suspension is better on the large scale than on the laboratory scale. However, absolute homogeneity is unattainable in practice. Therefore the position of the outlet in a continuously stirred tank reactor can have an important effect on the solids hold-up in reactors.The thickness of the stirrer blades has an important influence on the mixing performance, hence the blade thickness of a stirrer in model experiments must be taken into account. Incorrect scaling of the blade thickness can easily cause too optimistic figures for the power consumption on a commercial scale. The wide variety in scaling rules for suspension in the literature can be attributed to incorrect scaling of the stirrer blade thickness. Moreover, this effect can be used advantageously for the design of impeller blades. In our 80 1 vessel, a series of measurements was carried out using stirrer blades with a modified profile. Simple skewing off appeared to be an effective method of improving the performance of the stirrer or of maintaining a certain suspension quality at a lower power consumption. Savings of 17% in power consumption can easily be achieved in this way.     

Investigations of fluid dynamics in mechanically stirred aerated slurry reactors

The fluid dynamics of stirred aerated slurry reactors with A-310® propeller, 4-blade 45° pitch turbine and 6-blade Rushton disc turbine were studied over a wide range of gas flow rates. With respect to power consumption, gas hold-up, and fluid dynamically limiting cases, viz., suspension and flooding, the Rushton disc turbine was found to be the best in stirred aerated slurry reactors. The influence of particle density, shape and mass fraction and of liquid properties on gassed critical stirrer speed, N_jsg, and of gassed power input per unit volume, P_jsg, on particle suspension and gas dispersion, were investigated. Empircal correlations in combination with that of Zwietering were established for scale-up design in three-phase slurry reactors.     

Fluiddynamik des Suspendierens

Fluid dynamics of suspension. Data of primary interest associated with the use of suspension stirrers are the operating conditions required to suspend the particles of solids and to distribute them in the desired manner throughout the liquid. The tendency to undergo phase separation plays a decisive role in this connection. It has proved convenient in describing the material properties of the suspension to consider the sedimentation properties of the particles in the unperturbed liquid. The question of a scale-up rule for transferring the suspension state examined in an experimental stirrer to a large scale set-up has come in for much discussion. The data reported in the literature for the performance per unit volume lie in the range P/V ～ d^0.5, corresponding to the scale-up rule Fr* = const., and P/V ～ d^?1, corresponding to a constant circumferential velocity w_u = const. On the basis of results reported in this paper the recommended scale-up rule is P/V ～ d^?0.33.     

Flow characteristics of hyperboloid stirrers

The flows in a fully-baffled vessel with a diameter T = 144 mm driven by hyperboloid stirrers of diameters D = 773 and 27/3 have been visualised and characterised by local measurements of velocity and turbulence and by power number. The results were obtained for a range of rotational speeds from 6 to 40 rev/s. The visualisation showed that the larger stirrer gave rise to a radial jet and that the smaller stirrer formed a jet inclined towards the base of the vessel so that there was a tendency for the system of two vortices, one above and one below the jet, to give way to a single vortex as the clearance between the stirrer and the base of the vessel was reduced. The velocity measurements revealed bulk-flow values an order of magnitude less than that of the maximum radial velocity in the jet, that the maximum radial velocity was 24% of the circumferential velocity of the tip of the stirrer, and that the radial velocities were proportional to the rotational speed. The flows generated by the hyperboloid stirrer were less vigorous than those of Rushton impellers of similar radius and were associated with power numbers 28 times less. The power number did not vary with rotational speed or with clearance within the measured range. The contrast with propeller and disc stirrers is less pronounced, but the hyperbolic profile is likely to find application and the present results provide a basis for choice.     

Quantitative Measurements of the Critical Impeller Speed for Solid‐Liquid Suspensions

A quantitative methodology for particle suspension assessment is presented. A new parameter, f_mov/tot, the ratio of the mean number of moving particles to the total number of particles, is introduced to evaluate the minimum speed required to just suspend solids. This approach is tested to investigate the impact of impeller clearance on the minimum impeller speed, N_js, in a vessel when using a radial flow Rushton turbine. Flow patterns and power numbers obtained experimentally and computationally support the suspension findings. Image analysis is an appropriate method for determining N_js. Lowering the impeller clearance reduces the speed required for particle suspension with a change of flow pattern from a radial discharge with two loops to a single loop scouring the vessel base. The power number also falls markedly at the two‐to‐one loop transition as does the strain rate near the base.     

Scale-up in laminar and transient regimes of a multi-stage stirrer, a CFD approach

A multi-stage industrial agitator system adapted to the mixing of a mixture whose viscosity varies during the process has been characterized by using CFD. In the entire study the mixture is supposed to have a Newtonian behavior even though it is rarely the case. It is shown that the well-adapted propeller is able to efficiently blend high viscous media provided the Reynolds number is not too low. A scale-up study of the agitated system has also been carried out by respecting the classical scale-up rules such as the geometrical similarity and the conservation of the power per volume in the particular case of viscous media.Using an Eulerian approach, the hydrodynamics of three different scales with geometrical similarity have been numerically characterized by the energy curve (power number versus Reynolds number) and by the Metzner and Otto constant in which both are required for scale-up procedure. Experimental power measurements have been carried out at the smaller scale so that simulations have been partially validated. New hydrodynamic criteria have also been introduced in order to quantify the flows in the case of a multi-stage stirrer running at low Reynolds number. It has been shown how this hydrodynamic differs dramatically from one scale to another when scale-up at constant energy per volume is applied. From the CFD results, recommendations about the widely used scale-up rules have been suggested and modifications of stirring geometry have been proposed in order to reduce the flow pattern variations during scale-up.     

搅拌槽中固液悬浮及其放大的研究

研究了具有盘管、碟形底和斜叶涡轮固液悬浮搅拌槽的放大规律。试验用槽径（外径）分别为０．２ｍ、０．５ｍ和１．０ｍ的三个有机玻璃搅拌槽。用激光法测定悬浮液浓度。得出离底悬浮及均匀悬浮时搅拌转速和比功率的经验关联式，与测定槽内轴向速度分布所导出的均匀悬浮方程相吻合，并表明槽径的放大指数主要由循环流数所决定。     

The effect of flow reversal on solids suspension in agitated vessels

Flow patterns in agitated vessels are influenced by geometry, particularly impeller diameter and impeller off-bottom clearance. Large impellers and/or high off-bottom clearances lead to reversed flow in which the flow at the base of the vessel is radially-inward as opposed to radially-outward as expected with axial-flow impellers. Reversed flow is detrimental in solids suspension agitation because inordinately high torque and power are required to achieve suspension. This work experimentally characterizes the effect of flow reversal on solids suspension performance, including guidelines for avoiding flow reversal with straight-blade turbines, pitched-blade turbines, and high-efficiency impellers.     

Suspension of solid particles in agitated vessels—II. Archimedes numbers > 40, reliable prediction of minimum stirrer angular velocities

A criterion for the prediction of minimum stirrer rotation speeds is derived for the suspension of coarse-grained particles (Archimedes numbers ≳ 40). Minimum stirrer rotation speeds can be predicted by the evaluation of two diagrams for the drag of fluidized particles as a function of the concentration and for the pressure-head volumetric flow rate characteristics of an agitated vessel. The reliable prediction of required minimum stirrer angular velocities is discussed in the light of the results derived in this paper and in Part I of this series.     

Rühreinrichtungen in Schneckendosiergeräten — Wirkung und Auslegungsstrategie

Stirring Devices in Screw Metering Equipment – Action and Design Strategy. The accurarcy of metering by screw dosage equipment with or without gravimetric control depends primarily on the flow of material to the discharging screw. In the case of cohesive solids, stirring devices are generally required to prevent bridging. Experimental observations show that flow conditions correlate directly with the intensity of stirring. Mass flow in the metering container and hence optimum constancy of metering are attainable only from certain stirring efficiencies upwards. Cases of interference to metering due to poor flow of solids can be explained and overcome by modified dimensioning. The effects of the principal parameters – geometry and speed of rotation of the stirrer – are studied with the aid of two stirrer configurations – viz. overhead and concentric. Straightforward model calculations provide a mathematical method of estimation for optimum and reliable stirrer dimensioning also applicable to strongly cohesive solids.     

Complete Suspension of Microcapsules in Baffled and Unbaffled Stirred Tanks

The study of rotational speed for complete suspension have been carried out by varying different parameters: density ratio, stirrer diameter, clearance of stirrer, solid particle diameter, and particle concentration. The equations of correlation available in the literature were tested in order to obtain the one giving the best prediction of experimental values. The proposed correlation enables the determination of the minimal rotational speed for complete suspension of microcapsules in a pilot reactor with a good accuracy. The results will be used for the scale up of a microencapsulation process from laboratory to the pilot stirred vessel, for which it is considered that the extrapolation factor is the minimal rotational speed for complete suspension.     

Pressure buildup in gas‐liquid flow through packed beds due to deposition of fine particles

In order to understand the increase in pressure drop in hydrotreating reactors due to deposition of fine solids, experiments were conducted with a model suspension of kaolin clay in kerosene. The suspension was circulated through packed beds of catalyst pellets in the trickle‐flow and pulse‐flow regimes, and the increase in pressure drop measured as a function of particle concentration in the bed. The increase in pressure drop was linear with particle concentrations over the range 0–60 kg.m^?3. A consistent approach to modeling the pressure drop behavior was to determine an effective porosity of the packed bed as a function of the concentration of fine particles, then use this porosity in the Ergun equation as a basis for calculating the two‐phase pressure drop.     

Liquid Homogenization in Aerated Multi‐Impeller Stirred Vessel

The macroflow of fluid in a tall cylindrical vessel stirred with multiple stirrers was studied in the case of aeration of a liquid charge. The time of homogenization of the charge (mixing time) was calculated from the time dependency of the tracer concentration measured at various locations. Two types of stirrer were used in the experiments: six‐bladed Rushton turbines and/or pitched‐blade turbines with inclined blades pumping the liquid down or up. Four stirrers of the same type were located on the shaft. Other variables during the experiments were the stirrer frequency and the gas flow rate. It was found that the liquid macroflow in the vessel could be interpreted by the cell model or by the axial dispersion model for unaerated as well as for aerated systems. The influence of the aeration on the macroflow and mixing time was explained by the interaction of buoyancy and radial forces, and equations for the model parameters were proposed containing gas flow numbers and Froude numbers.     

DETERMINATION OF THE MIXING RATE OF A HIGH VELOCITY FEED STREAM IN AGITATED VESSELS

In semi-batch or continuously stirred reactors, often a feed containing one or more reactants has to be mixed with the contents of the vessel. For fast competitive or consecutive reactions the mixing rate of the feed stream with the vessel contents has a large influence on the product quality. The mixing rate is often controlled by the turbulent dispersion process. Therefore, it has been suggested in the literature to keep the turbulent dispersion time constant upon scale-up to obtain a constant product quality. In this study, based on a combination of a theoretical model, Planar Laser Induced Fluorescence experiments and Laser Doppler Velocimetry experiments, the turbulent dispersion coefficient is determined. This has been done for the case that a feed stream is mixed in a stirred vessel by a combination of feed stream and stirrer generated turbulence. The turbulent dispersion coefficient is used to derive an equation for the turbulent dispersion time as function of several design and process variables.     

DETERMINATION OF THE MIXING RATE OF A HIGH VELOCITY FEED STREAM IN AGITATED VESSELS

In semi-batch or continuously stirred reactors, often a feed containing one or more reactants has to be mixed with the contents of the vessel. For fast competitive or consecutive reactions the mixing rate of the feed stream with the vessel contents has a large influence on the product quality. The mixing rate is often controlled by the turbulent dispersion process. Therefore, it has been suggested in the literature to keep the turbulent dispersion time constant upon scale-up to obtain a constant product quality. In this study, based on a combination of a theoretical model, Planar Laser Induced Fluorescence experiments and Laser Doppler Velocimetry experiments, the turbulent dispersion coefficient is determined. This has been done for the case that a feed stream is mixed in a stirred vessel by a combination of feed stream and stirrer generated turbulence. The turbulent dispersion coefficient is used to derive an equation for the turbulent dispersion time as function of several design and process variables.     

Empirical and scale-up modeling in stirred ball mills

Stirred ball mills are frequently used for ultrafine- and nanogrinding in food, pharmaceutical and chemical industry, but only few investigations have been published on empirical or scale-up modeling of stirred ball mills. Experiments have been carried out with a laboratory scale stirred ball mill. During the experiments the main technical parameters such as stirrer speed, grinding media, filling ratio, grinding time and the solid mass concentration have been systematically adjusted. The particle size distribution of mill products can be well estimated by empirical functions, so an empirical model has been prepared for the laboratory mill. The relation between the grinding fineness, grinding time and specific grinding work was represented for several materials such as pumice, andesite, limestone and tailings of ore mining industry. The power consumption of the stirred ball mill for scale-up was determined by a method based on the dimensional analysis. A new scale-up model has been presented as well by with industrial size stirred ball mills can be designed on the basis of the laboratory measurements.     

Suspension of solid particles in agitated vessels—I. Archimedes numbers ≲ 40

Complete suspension of fine-grained particles is achieved at mean circulation velocities of the fluid exceeding the settling velocities of the particles by several orders of magnitude. It is therefore argued that boundary layer effects are significant. In this paper, through an analysis of the boundary layer flow in an agitated vessel two theoretical criteria for the required minimum stirrer angular velocities are derived. The evaluation of own experiments proves the significance of one of them for Archimedes numbers Ar ≲ 40, i.e. for particles completely immersed in the viscous sublayer. For higher Archimedes numbers, i.e. for particles protruding into the buffer layer and into the turbulent near wall layer, criteria based on the boundary layer flow turn out not to be suitable.     

Solids suspension behaviour in profiled bottom and flat bottom mixing tanks

Solids suspension in the classical flat bottom mixing tank was analysed phenomenologically in detail. Abrupt re-direction of the flow in the centre and the periphery of the flat bottom tank gives rise to induced recirculation loops which account for the formation of central and peripheral fillets of unsuspended solids. The extent of these recirculation loops has a controlling influence on the attainment of complete off-bottom suspension in this tank geometry. Therefore the use of the complete off-bottom suspension condition in the flat bottom tank as the sole criterion for scale-up is likely to lead to scale-up parameters which do not represent the behaviour of the bulk of the tank.A fully profiled tank bottom and its approximation, a “cone and fillet” bottom design were used as alternative geometries to mitigate recirculation loops. Streamlining of the mixing tank substantially improved solid and suspension efficiency and also produced a more homogeneous hydrodynamic regime in the bottom zone of the tank. This latter effect potentially simplifies theoretical modelling of solids suspension and further justifies the preference for profiled bottom mixing tanks rather than the flat bottom tank.